WST

PUBUCATIONS

BUILDING SCIENCE SERIES 39

Use of Computers

for Environmental

Epgineering Related

to Buildings

DATE DUE

AUG 7 1975

DEC % 1

CAVLORO PRINTED IN U.S.A.
ATIONAL BUREAU OF STANOAI^S

FEB 1 6 1972

1B3J.48

, u

C. So
UNITED STATES DEPARTMENT OF COMMERCE . Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Use of Computers for Environmental

Engineering Related To Buildings

Proceedings of a Symposium Sponsored by the National Bureau

of Standards, the American Society of Heating, Refrigerating

and Air-Conditioning Engineers, Inc., and the Automated

Procedures for Engineering Consultants, Inc.

Held at the National Bureau of Standards

Gaithersburg, Maryland

November 30 - December 2. 1970

Edited by

T. Kusuda

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Building Science Series 39

Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 39, 826 pages (Sept. 1971)

CODEN: BSSNB

Issued October 1971

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C 13.29/2:39). Price $7. 75

Stock Number 0303 - 0926
Abstract

These proceedings of the First Symposium on the Use of Computers for Environmental Engineering

Related to Buildings contain all of the technical papers and invited addresses presented at the

symposium, which was held November 30 - December 2, 1970, at the National Bureau of Standards.

The fifty-nine papers deal with the application of the computer to such environmental engineering problems as building heat transfer calculations, heating and cooling load calculations, system

simulations, energy usage analyses, computer graphics, air and smoke movement inside buildings, and

weather data analyses for load and energy usage calculations.

Key Words: Building heat transfer analysis, energy usage, environmental engineering,

heating and air conditioning, use of computers

Library of Congress Catalog Card Number: 70 - 177420

II
Foreword

For a number of years the National Bureau of Standards has been a leader in the development and

use of computers in scientific and engineering fields. We strongly believe that the effective application of computers to the problems of the building industry will be of significant benefit to that industry. In what we hope to be a helpful step in this direction, we were pleased to be able to join

with the American Society of Heating, Refrigerating, and Air Conditioning Engineers and the Automated

Procedures for Engineering Consultants, Incorporated, in sponsoring this First Symposium on the Use

of Computers for Environmental Engineering Related to Buildings.

In recent years the use of computers has had a rapidly increasing impact on the design, performance

analysis, and control of environmental systems related to buildings. The purpose of the Symposium was

to provide a forum for exchange of the latest information and ideas among engineers, architects, and

planners who use computers. The Symposium attracted leading authorities in the field of environmental

engineering not only from all parts of the United States but also from many parts of the world. Over

400 architects and engineers representing the building industry, governments, universities, and utilities participated. Applications of computer programs and calculation methods covering several topics

in environmental engineering are presented in these proceedings in a form useful to consulting firms,

government agencies, research organizations, and industrial firms.

Lewis M. Branscomb, Director

National Bureau of Standards

III
Preface

The use of computers is now widespread among environmental engineers working with buildings. Subjects ranging from routine heating and cooling load calculations to sophisticated computer graphic display systems are being handled. Although the environmental engineers have been slow in adapting the

computer to their needs, at least until the middle of the 1960's, their use of the computer is now increasing rapidly. This development is In fact taking place so fast that no major coordinated activities

for exchanging ideas and disseminating information have been undertaken except those of the APEC (Automated Procedures for Engineering Consultants). While the APEC is active mainly In the area of programs

for practicing engineers, needs are also recognized for advanced techniques or new procedures--such as

the calculation of accurate room temperature change under realistic climatic conditions, simulation of

air conditioning system d5mamics, optimization of the system and component selection based upcn relatively advanced mathematical concepts, and effective use of graphic displays or data structuring. The

First Symposium on the Use of Computers for Environmental Engineering Related to Buildings was to serve

this need by providing opportunities for creative environmental engineers to meet each other and exchange

new ideas. Because this was the first symposixjm of its kind and because heating and cooling load calculations are currently the most popular subject among the environmental engineers, the largest percentage of the papers presented dealt with the temperature and the thermal load calculations for

buildings. The papers presented illustrated that there exists much duplication of effort in many parts

of the world as well as In the United States. Although the program committee's selection of papers led

to some redundancy, the purpose of their inclusion was to encourage the participation of as many of the

first line investigators in the field who have been active in the use of computers for environmental

calculations. The symposium gathered 59 papers from 12 countries and was attended by approximately

400 engineers, scientists, and architects--firmly justifying this type of conference. The papers presented Include those which are highly theoretical as well as those which describe popular programs.

Nine sessions were required during three days to present all of these papers. In addition, a technical

forum was held one evening to exchange Informal opinions on computerized controls. This was well attended. It is hoped that this symposium made a major contribution to environmental engineering design

and these proceedings will be useful to all using computers in this field. The program committee will

welcome reactions and suggestions as an aid to planning future conferences of this kind.

T. KUSUDA, Chairman

Program Committee

IV
General Committee

P. R. Achenbach, Chairman

F. J. Powell, Vice-chairman

A. T. Boggs, Vice-Chairman

J. R. Ahart, APEC (U.S.A.)

J. M. Anders, ASHRAE (U.S.A.)

R. Cadiergues, (France)

W . Caemmerer , (Germany

)

B. Givoni, (Israel)

J. L. Haecker, NBS (U.S.A.)'

I. Hoglund, (Sweden)

G. Wil,

K. Kimura, (Japan)

V, Korsgaard, (Denmark)

T. Kusuda, NBS (U.S.A.)

A. G. Loudon, (England)

H. F. T. Meffert, (Netherlands)

R. W. Muncey, (Australia)

C. W. Phillips, NBS (U.S.A.)

K. R. Rao, (India)

R. H. Tull, ASHRAE (U.S.A.)

J. F. Van Straaten, (South Africa)

, (Canada)

V
Program Committee

Dr . T . Kusuda , Chairman Room A307, Building 226 National Bureau of Standards

Washington, D. C. 20234

Professor Eugene Stamper, Vice Chairman

Department of Mechanical Engineering

Newark College of Engineering

Newark, New Jersey 07102

Dr. D. G. Stephenson

National Research Council

Division of Building Research

Ottawa, Ontario, Canada

Mr. Metin Lokmanhekim

GARD/GATX

7449 N. Natchez Avenue

Niles, Illinois 60643

Mr. D. L. Richardson

Arthur D. Little, Inc. Acorn Park

Cambridge, Massachusetts 02138

Mr. H. C. S. Thorn ESSA Room 716, Gramax Building

8060 13th Street Silver Spring, Maryland 20910

Mr. E. M. Barber Room B309, Building 226 National Bureau of Standards

Washington, D. C. 2 0234

Dr. F. G. Shuman

Director

National Meteorological Center Room 1302, FOB-4

Suit land, Maryland 2 0023

Mr. Z. 0. Cumali

Consultants Computation Bureau

594 Howard Street

San Francisco, California 94105

Professor J. B. Chaddock

Mechanical Engineering Department

Duke University

Durham, North Carolina 27706

Professor L. 0. Degelman

The Pennsylvania State University

Department of Architectural Engineering

University Park, Pennsylvania 16802

Mr. B. E. Birdsall

Ziel-Blossom and Associates, Inc. 700 Walnut

Cincinnati, Ohio 452 02

Mr. W. A. Schmidt

Office of Construction

(08H) Veterans Administration

Central Office

810 Vermont Avenue, N. W. Washington, D. C. 2 042 0

Mr. J. Marx Ayres

Ayres, Cohen & Hayakawa

1180 South Beverly Drive

Los Angeles, California 90036

Arrangements Committee

C. W. Phillips, Chairman B. Steele

J. Szabo, Vice-Chairman S. Torrence

W. Carroll

VI
Contents

Abstract

Foreword

Preface

Members of General Conrmittee

Members of Program Committee

Members of Arrangements Committee

PLENARY SESSION

Chairman: P. R. Achenbach

National Bureau of Standards

1. Welcome Address

Dr. F. K. Willenbrock

Director, Institute for Applied Technology

National Bureau of Standards

2. Keynote Address: Some Objectives for the Technological Man

Bruce J. Graham

Skidmore, Owings and Merrill

COMPUTER GRAPHICS

Co-chairmen: J. B. Chaddock

E. M. Barber

3. An Insight Into Three Dimensional Graphics

A. R. Paradis

Dynamic Graphics, Inc. San Francisco, California 94105

4. The Use of Graphics in the Development of Computer-Aided

Environmental Design for Two-Storey Houses

A. Bijl, T. Renshaw and D. F. Barnard

University of Edinburgh

Edinburgh, Scotland

5. Anticipatory Techniques for Enhancing Remote Computer Graphic

T. N. Pyke

National Bureau of Standards

Washington, D. C. 20234

6. Computer Graphic Data Structures for Building Design

M. Abrams

National Bureau of Standards

Washington, D. C. 2 0234

VII
MODELING, DESIGN, SURVEY AND LINEAR PROGRAMMING

Co-chairmen: Z. 0. Cumali

J. Marx Ayres

« 7. A Systems Model for Environmental Design of Buildings 61

C. L. Gupta

CSIRO

Highett, Victoria, Australia

8. Design Considerations for a Practical Heat Gain Computer Code 71

S. F. Nermann and N. E. Mutka

DERAC Consultants, Inc. Mercer Island, Washington 98OA-0 ^ 9. Solving the Communication Problem in a Computer-Controlled 87 Environmental System

T. Prickett, J. L. Seymour, D. L. Willson and R. W. Haines

Collins Radio Company

Dallas, Texas 752 07

10. A Linear Programming Model for Analyzing Preliminary Design Criteria

for Multizone Air Distributions Systems 95

R. A. Gordon

Cornell, Howland, Hayes and Merryfield

Corvallis, Oregon 97330

11. A Conceptual Survey of Computer-oriented Thermal Calculation Methods ^03

C. L, Gupta, J. Spencer and R. Muncey

CSIRO

Highett, Victoria, Australia

12. Method for Thermal Calculations Using Total Building Response Factors

R. Muncey, J. Spencer and C. Gupta

CSIRO

Highett, Victoria, Australia

13. Calculation of Building Thermal Response Factors (BTLRF)

as Wiener Filter Coefficients

T. Kusuda

National Bureau of Standards

Washington, D. C. 2 0234

ANALOG COMPUTATION & TIME SHARING Co-chairmen: L. 0. Degelman

E. M. Barber

14. Thermal Studies by Electrical Simulation. Application example to the study of the heating equipment of an apartment building heated by

electricity 127

J. Anquez and L. Bertolo

CSTB Champs-sur-Marne 77, France

VIII
15. Analog Computer Simulation of an Air Conditioning System in a Com- mercial Building Incorporating Yearly Weather Data 147

J. Magnus sen Honeywell, Inc. Minneapolis, Minnesota 55408

16. Experience with a Thermal Network Analysis Programme Applied to Heat Flow in Buildings 159

N. Sheridan

University of Queensland

Brisbane, Australia

17. A Method of Computer Simulation Through Modified Signal Flow Graphs

and Operator Concepts and Its Application to Syntheses of Heating

Equipment Capacities 171

S. Matsuura

Hokkaido University

Sapporo , Japan

18. Shared Time System Computer Programs for Heating and Cooling Energy

Analysis of Building Air Conditioning Systems 181

C. J. R. McClure and J. C. Vorbeck

Mechanical Engineering Data Services, Inc.

St. Louis, Missouri 63141

ENERGY LOAD CALCULATIONS

Co-chairmen: E. Stamper

W. A. Schmidt

19. The Program of the ASHRAE Task Group on the Determination of Energy Requirements for Heating and Cooling Buildings 199

R. H. Tull ASHRAE Task Group on Energy Requirements

for Heating and Cooling Buildings

Lebanon, New Jersey 08833

20. Successful Applications of Energy Analysis Programs 205

K. M. Graham

Southern Counties Gas Company

El Monte, California 91734

21. Comparison of a Short Form Load and Energy Program with the Detailed Westinghouse Load and Energy Programs 213

B. G. Liebtag and J. R. Sarver Duquesne Light Company

Pittsburgh, Pennsylvania 15219

22. Energy Estimating - How Accurate? 217

R. Romanchek

Pennsylvania Power and Light Company

Allentown, Pennsylvania 18101

IX
23. Instantaneous Cooling Loads by Computer Based on ASHEAE's Time

Averaging Method 225

R. V. Thomas

Naval Facilities Engineering Command

Washington, D. C. 20390

24. Computer Method for Estimating Net Energy Requirement for Heating

Buildings 229

N. E. Hager

Armstrong Cork Company

Lancaster, Pennsylvania 17604

25. The Practical Application of Small Computers for Heating and Air

Conditioning Load Evaluation 241

T , Romine

Romine and Slaughter, Inc. Fort Worth, Texas 76107

26. Accuracy Requirements for Computer Analysis of Environmental

Systems 263

R. Cook and J. A. Serfass

Westinghouse Electric Corporation

East Pittsburgh, Pennsylvania 15112

27. Calculation of Energy Requirements with the Proposed ASHRAE

Algorithms for U.S. Postal Buildings 279

M. Lokmanhekim

GARD/GATX

Niles, Illinois 60648

289

28. An Accurate Computing Method for the Analysis of the NonSteady Thermal Behavior of Office Buildings

S. Oegema and P. Euser

Institute of Applied Physics, TNO-TN

Delft, Postbus, The Netherlands

29. A Successive Integration Method for the Analysis of the Thermal Environment of Building

N, Aratani, N. Sasaki and M. Enai

Hokkaido University

Sapporo , Japan

30. Digital Simulation of Building Thermal Behavior ^'•^

M. J. Wooldridge

CSIRO

Highett, Victoria, Australia

31. A Computer Programme for the Calculation of Individual Room

Air Temperature of Multi-Roomed Buildings ^27

K. Rao and P. Chandra

Central Building Research Institute

Roorkee, India

32. A Practical Method for Calculating Room Temperature Heating

Load and Cooling Load of a Multiroom

K. Ochifuji

Hokkaido University

Sapporo , Japan

X
33. Simulation by Digital Computer Program of the Temperature

Variation in a Room

G . Brown

The Royal Institute of Technology

Stockholm, Sweden

ENERGY CALCULATIONS, AIR DUCT SYSTEMS Co-chairmen: D. L. Richardson

B. E. Birdsall

34. Optimization of an Air-Supply Duct System

W. F. Stoecker, R. C. Winn and C. 0. Pedersen

University of Illinois

Urbana, Illinois 60603

35. Computerized Calculation of Duct Friction

H. F. Behls Sargent and Lundy, Engineers

Chicago, Illinois 60603

36. Pressure Loss Coefficients for the 45-Degree Return Air Tee

H. F. Behls and W. K. Brown

Sargent and Lundy, Engineers

Chicago, Illinois 606 03

37. Automatic Design of Optimal Duct Systems

M. Kovarik

CSIRO Cheltenham, Australia

38. A System of Computer Programs Widely Used in Europe for Designing, Selecting and Analyzing Different Air Conditioning

Systems

A. Boeke and S. Larm Technische Hogeschool, Leerstoel

Delft, Holland

39. Standardized Method for Optimizing Building Construction and

Heating and Ventilating Installations for Various Indoor

Climate Criteria

A. Boysen and S. Mandorff

National Swedish Institute for Building Research

Stockholm, Sweden

40. Designing Installations by Computer in Sweden

L, Sundberg

Wahling's Installation and Development Company

Danderyd , Sweden

41. A Cost Analysis Service Helps Optimize Building Costs and

Environmental Benefits

J. T. Malarky

PPG Industries

Pittsburgh, Pennsylvania 15222

393

405

415

423

XI
42. Comparative Computer Analysis of the Thermal Cost Performance

of Building Enclosures 437

W. A. Oberdick

University of Michigan Ann Arbor, Michigan 48105

SOLAR EFFECTS Co-chairmen: AND CONVECTION

F. G. Shuman

H. C. S. Thorn

43. A Numerical Method for Computing the Non-Linear, Time Dependent,

Buoyant Circulation of Air in Rooms 451

J. E. Fromm

IBM Corporation

San Jose, California 95114

* 44. Fortran IV Program to Calculate Absorption and Transmission of Thermal Radiation by Single and Double-glazed Windows 465

G. P. Mitalas and J. G. Arseneault

National Research Council

Ottawa, Canada

ts 45 . A Computer Analysis of Window Shading Coefficients by Calculating

Optical and Thermal Transmission 477

I. Isfalt The Royal Institute of Technology

Stockholm, Sweden

46. Optimum Shape of External Shade for the Window to Minimize

Annual Solar Heat Gain and to Maximize View Factor 487

K. Kimura

Waseda University

Tokyo, Japan

47. Calculation of Smoke Movement in Buildings 501

T. Wakamatsu

Building Research Institute

Tokyo , Japan

*» 48. Use of Actual Observed Solar Radiation Values in the Determination

of Building Energy Requirements 519

J. Thies

Southern Services, Inc. Birmingham, Alabama 352 02

XII
AIR CONDITIONING CALCULATIONS AND WEATHER DATA

Co-chairmen: M, Lokmanhekim

D. L. Richardson

49. Design of Direct -Expansion Evaporator Coils by Digital Computer 525

D. G. Rich J. B. Chaddock

Carrier Corporation Duke University

Syracuse, New York 13201 Durham, North Carolina 27706

50. Simulation of a Multicylinder Reciprocating Refrigeration System

with Chilled Water Coil and Evaporative Condenser 545

E. Stamper and M. Greenberger

Newark College of Engineering

Newark, New Jersey 07102

51. Use of Digital Computers for the Heat and Mass Transfer Analyses

of Controlled Environment Greenhouses 557

M. K. Selcuk

Orta Dogu Teknik Universitesi

Turkey

52. Automated Design Program for Air-Handling Apparatus 579

M. Nagatomo, S. Tanaka and N. Tohda

Kajima Institute of Construction Technology

Tokyo , Japan

53. Computer-aided System for Preliminary Air Conditioning Design 589

E. Maki and Y. Okuda

Nikken Sekkei Komu Company, Ltd. Osaka , Japan

54. Computer Selection and Evaluation of Design Weather Data 603

E. N. Van Deventer National Building Research Institute, CSIR

Pretoria, South Africa

* 55. Quality Rules for Thermal Performance of Low Cost Dwellings

(Building Climatology for Argentine) 613

R. Alvarez Forn and I. Lotersztain

INTI Buenos Aires, Argentina

WALL CONDUCTION AND THERMAL LOAD SIMULATION

Co-Chairmen: D. G. Stephenson

T. Kusuda

56. Fortran IV Program to Calculate z-Transfer Function for the Calculation of Transient Heat Transfer Through Walls and Roofs 633

C. P. Mitalas and J. G. Arseneault

National Research Council of Canada

Ottawa, Canada

XIII
57. Application of Multilayer Periodic Heat Flow Theory to the Design

and Optimization of Roofing Systems 669

C, Smolensk!, E. Halteman and E. M. Krokosky

Pittsburgh Corning Corporation

Pittsburgh, Pennsylvania 15239

58. Pulse Transfer Function and Its Application Related to Buildings 687

H, Yamazaki

Kyushu Institute of Design

Kyushu , Japan

59. A Calculating Method for Heating Loads of Buildings 693

Y. Nakazawa

Kyoto Technical University

Kyoto, Japan

60. An Example of Heating and Cooling Load Calculation Method for AirConditioning of Building by Digital Computer 715

S. Kuramochi

Taisei Construction Company, Ltd. Chou-ku, Tokyo, Japan

^ 61. Heating and Cooling Load Calculations by Means of Periodic Window

Function 745

K. Eguchi

Building Research Institute

Ministry of Construction

Tokyo , Japan

62. Banquet Address: Computers and the Building Industry 787

S . Daryanani

Syska and Hennessy, Inc. New York, New York 10016

XIV
Good morning.

Welcome to the National Bureau of Standards. I am substituting for the Director, Dr. Branscomb,

who unfortunately will be unable to greet you in person.

The Bureau has a deep interest in this First Sympositam on the Use of Computers for Environmental

Engineering Related to Buildings. We are pleased to be one of the three sponsors; we are happy to be

your host. While you are here we hope that you will find time to meet and talk with our staff, and

that you will take advantage of the tour of your facilities. I said your facilities to the American

taxpayers present because the Bureau is a tax-supported public institution with a goal to "strengthen

and advance the Nation's science and technology, and to facilitate their effective application for the

public benefit" .

The National Bureau of Standards from its inception in 1901 has been closely involved with building research and technology. In the early days buildings were not viewed from a systems standpoint

and the work was organized in response to specific, recognized needs for technical information on the

properties of building materials .

As early as 1905, the Bureau had a 100-thousand pound testing machine which was used to measure

the strength of structural materials, such as steel and concrete. Later, the Bureau joined with the

National Fire Protection Association and the Underwriters' Laboratory in a program from which flowed a

large amount of data on the fire resistance of materials. These data were subsequently incorporated

in fire and electrical codes throughout the country.

1
In 1921, these scattered activities were combined by the Secretary of Commerce, at that time

Herbert Hoover, into a Division of Building and Housing. The functions of the Division were to coordinate scientific, technical, and economic research on building; to aid in the revision of state and municipal codes, and to engage in the simplification and standardization of building materials. Despite

these broad goals, the primary effort remained in the materials evaluation area, and the application of

the findings to building codes and standards based on materials specifications. During this period,

however, there was a small but growing program concerned with the environmental conditions in housing.

The first attempts to study the habitability of housing could also be considered as the exploratory

examinations of buildings from a systems standpoint.

During the 1920's, the emphasis was on a "Better Homes Program". In the depression of the 1930's,

the Better Homes Program became low-cost housing; in World War II, the conservation of scarce building

materials was the major effort. After the war, for fifteen or so years, the building research programs

again stressed the properties of various kinds of building materials, with the exception of the environmental work which continued in the direction of a systems approach to building problems.

But the winds of change have influenced even the Bureau, and today in our building research and

technology program we talk primarily about building systems; we are challenged by the problems of

evaluating the function and performance of buildings as they satisfy the user. We are still concerned

with materials, but view them as components which are part of a system. Our efforts are toward the

development of performance requirements and performance evaluation techniques for building components

and systems. Such efforts are compatible with the national trend toward industrialized building construction.

The development of standards based on performance, and the consideration of buildings as systems

requires the evaluation of masses of data which are orders of magnitude larger than required for the

earlier materials evaluation or specifications studies. It is clear that the computer has influenced

our investigations in many fundamental ways and it is my prediction that it will have an increasing

impact on our thinking about building systems in the future.

A good Ph.D. subject for a student of the history of technology would be to determine how much

the change in our perceptions of buildings has been influenced by the availability of the computer as

a data and information-handling device.

Even today we are well past the relatively simple use of computers for the analysis of masses of

data. During this symposium we shall hear how computers are used in modeling or design studies related

to the environment of buildings; how they are used for evaluating the non-steady thermal behavior of

office buildings, how they are used for the design of heat /air-conditioning installations.

2
Our speakers in this symposium come from 11 foreign countries and from all across the United

States. They represent industry, the research community, the universities, and government. We shall

hear from architects, engineers, computer specialists, systems analysts, and from those in other disciplines. Indeed, this symposium program is Indicative of how computers are stimulating a "quiet revolution" in the building technology field. What is being done in this segment of the building process

points the way to what must inevitably be the norm for the entire building process.

So welcome once again to the Bureau, and to this First Symposium on the Use of Computers for Environmental Engineering Related to Buildings. It Is our hope this symposium will provide an effective

forvun for the exchange of Ideas in the field. It is our hope that these sessions will stimulate others

to explore how computers may be used throughout all parts of the building process.

3

A recent article in Time MaRazine pointed out that the Unisex Society developing in the United

States is a s3miptoin of the decay of our civilization. As ultimate proof, it indicated that out of two

thousand previous civilizations - fifty five which suffered of this same symptom - such as the Greek

and the Roman eventually disappeared. I would propose that the other nineteen hundred and forty five

also disappeared or at least there is no evidence of their existence today.

The rise and fall of civilization has very little to do with the morality of those civilizations.

It becomes important to define what we mean by civilization. In Webster's dictionary definitions read:

"the condition of being civilized; social organization of a high order, marked by advances in the arts,

sciences, etc.; the total culture of a people, nation, period, etc: as, the civilization of the Occident

differs from that of the Orient". And finally, "the countries and peoples considered to have reached a

high stage of social and cultural development.". I contend that the American people do not fall under

any of those definitions. We certainly do not have order nor have we reached a high stage of social

and cultural development. In fact, there may never be an American civilization. I believe that we are

engaged in the process of developing a single civilization throughout the world - one in which America

will play a very important and, I hope, responsible role. Other nations have contributed in great

measure and will continue to do so. We are in fact children of past civilizations from Greco-Roman,

from African, Mayan and Chinese ancestries. It is, therefore, nonsense to talk gloom and doom when we

are barely participating in the dawn of this emerging culture.

The technological equipment today is breath-taking in scope. We have been able in the last thirty

years to break through barriers of exploration which did not exist one hundred years ago. Yet, we have

failed miserably on this earth in the efforts that deal with the problems of an ever-expanding population. Recently man has created the first reproducing cell, but he has been unable to control the reproduction of man. We have created a completely antiseptic environment that can hurdle into space at

unbelievable speed - returning to earth with a relative safe and healthy human specimen, but we have

5
been unable to provide even the most basic of housing needs for the great majority of people of the

world.

It matters little what political system we support, what nations we swear allegiance to - singly

or jointly all nations have failed. The promise in America that capitalistic democracy would achieve

individual freedom is a myth. The much touted equality of communism is a fiasco and the self-serving

smugness of Scandinavian countries exists only at the expense of suffering millions around the world.

We are all aware of the usual capability of nations to wage war, regardless of financial stability.

Starving millions find no food, but plenty of guns with which to serve militarist demagogues.

Of paramount importance in our time is not the search for the secret new technology or the wonderful do-all material, but the philosophical leadership which will redirect the great energy being expended

for the benefit - rather than the detriment - of people. There is hardly a technical problem existing

that cannot be solved, but equally there is hardly a solution in sight for the sufferings in the world.

No leaders plead the case for civilization.

The City today is hell bent on disaster. This phenomenon exists, by no means, only in America.

It matters very little whether we speak about a socialistic or capitalistic nation. Technocratic

achievement and production have become the paramount value. Other values are secondary. The cries

and, in fact, the screams of a few have had very little effect on the relentless progress of production for the sake of production. It matters little what we produce, so long as we feed labor and raw

materials to the machine. As a result other values cannot be served. The typical urban center is

plagued with a series of fantastic problems - pollution, not only of the air and the water, but pollution of sound - of vision - of taste - and of mind. Transportation is a story book of failures.

Tokyo, like New York City and London are reaching the point of standstill. The customary jokes about

traffic jams in Rome and Paris are no laughing matter to the Romans and Parisians. Tempers have risen

on this subject alone to a point of no return. Transportation has created and fostered economic

segregation; the poor in the cancerous center, the middle class in the greenbelt.

The university - once a sacred place - is in complete disarray everywhere. It matters little

whether we speak of disillusionment of the student at the Sorbonne, Kent University or the University

of San Marcos in Lima. The academy is no longer believable. Academic isolation has led to irrelevance.

Yet we know, or have faith that solutions could be found and that these solutions will depend heavily on

our technological baggage. This premise has been held for some time, but our credibility has lapsed.

The philosophical evaluation of priorities has eluded our grasp.

6
Much has been said about the expanding population of the world, and this is a problem. Much has

been said about the depleting resources of the world, and this is a problem; but little recognition

exists that it is not expansion in numbers alone, but rather the accelerated increase in ambitions

which cause the confrontations we now experience. The wandering Arab is no longer happy to wander.

The potato-growing Quechua Indian is no longer happy with a diet of potatoes. The millions of India

are no longer happy with an 18-year life span. In fact, not even the people of Wales are satisfied

with 2nd-class citizenship.

We do not need any more automobiles from General Motors or from Volkswagon or from Toyota. The

people need a healthy environment first, and it is not up to the leadership to deny it. The advertising

campaigns which are used to sell unnecessaries should now be used to sell the necessaries.

Poll-taking as an excuse for leadership is the instrument of the present political scientist.

This method will lead to continued mediocrity and worse. Ask a drug addict what he wants, he will

say drugs. Ask a hunter, he will say guns, but we need neither drugs nor guns. It seems inconceivable

that in this day we can produce models of the human body in a computer and measure the good and bad

effect of environmental inputs. Yet we cannot decide once and for all what is a good diet - what kind

of air we should breathe - what kind of noise we can bear or what kind of environment we can survive

in. The priorities of the modem economist do not recognize the primacy of human life.

It may become important at last that we begin to make value commitments, for the survival of

existing governments, universities and intellectual leadership will depend upon their ability to commit

the energies of human kind immediately towards the needs for survival. The pressure towards such

commitment will not come from the fickle and easily converted popular movements. Those are easily

swayed by Madison Avenue advertising or Latin American demagogues. Each and every educated man must

mold his well trained efforts towards the simple realities that face the world. This individual effort

can have tremendous influence since it is the technocrat who controls the valves of cornucopia. It

wasn't Hitler or Churchill or Roosevelt or Stalin who invented the atom bomb, but it is their outmoded heritage that is rattling that frightening instrument.

Architects and planners of the last twenty years have been pre-occupied with their profession.

They are designers of objects. It appears today that they have proven without a doubt their own

irrelevancy. Walter Gropius many years ago decried the lack of involvement by architects epitomized

by the Ecole Beaux Arts in Paris - the Aesthetic of the Renaissance was but a symptom of the selfish

role the professional had carved unto himself. The Bauhaus movement of the 20 's in Germany was a

successful attempt to convert the industrial machinery into a viable architectonic language. Mies

van der Rohe epitomizes that success. In his hand the products of modem man became a poetry of space.

However, his lingo combined with the virile language of Corbusier - has been converted into a substitute for the cliques of the renaissance. We are now extremely capable modern temple builders, except

that we care little what gods dwell in our temples. Our works are terribly important and, since they

7
serve the Images of false gods, they curse the life of the urban dweller around them.

Architects and planners have to turn about and realize that we are but transitory instruments in

the evolution of cities. Instant civilization is not about to happen - we are just barely defining the

kind of civilization we expect to create. We know that in such a civilization national boundaries do

not exist. Isolation from the dynamic world forces is impossible and existing political systems are

obsolete. All people of the world must participate, for in exclusion we seed discontent, and in segregation moral decay.

The larger picture of the world affects the life of every individual and we must be prepared to

meet both ends of this candle. Some glimpses of such a society are possible. We know that the individual

citizen must participate in those decisions that affect his immediate life and that of his family. He

must, therefore, have something to say about where he lives - the school that his children attend - the

work he does, but on the other hand, he must enjoy the fruits of international medical research, the

writing of poets - the art of painters and scultors - the pleasures of travel - free air - all these

which cannot 'come about through micro systems, but that belong to larger structures.

Computer technology, if it has any promise, is this: it can make available to an individual the

knowledge of all; and the ability to make decisions at the most personal of levels under that larger

umbrella of knowledge. It is that promise which must direct the efforts of your conference.

I would propose to this conference that the papers presented here and at future conferences should

concentrate on the problems that face the urban centers of the world:

1. On Transportation - not how to move people, but how a city can exist, expand and grow

without the convulsion of movement we now enjoy. How can man live near his place of

work - near his children - breathe free air? Today that freedom of choice is denied.

2. What is a house - what kind of a house does a family need - what kind of environment

and air should children breathe - what kind of neighborhood does this house belong

to - how can a man move from one stage of life to a later one without the loss of

ties to his family and to his tribe?

3. What kind of diet does man need - how can this be distributed equitably from the

farmer to the dinner table?

4. Medicine - should not be the hunting ground for doctors. How do we provide medical

care for all, but more important, preventative medical care so that healthy lives

can be a backbone for fulfillment. As an example - humidified air is now the

privilege of machine environment, but shouldn't the delicate nasal passage of

children be protected?

5. In the integrated community how do we distribute the benefits of culture - music - dance -

theater - art - and all the other fulfilling human experiences, so that they become a

part of all peoples' lives - rather than the privilege of the few?
6. How do we maximize the fruits of this earth - preservation of forest - clean rivers

and lakes - in fact clean oceans? How should the resources be protected?

7. Education is an integral part of all the prior values, but how do we expand, elaborate

and create a meaningful civilization so that the recognized values of the intellectual

become the every day values of all citizens?

I propose that a conference such as yours should address itself to what end you work. It is not

important to develop a new program of heat transfer or of the design for sophisticated duct systems

unless that program is a meaningful part of the value set which makes up the fiber of our emerging

civilization.

The fracturized construction industry in America with its multiplicity of goals is only matched

in disarray by the even more fracturized Industry of construction in other parts of the world. Self

interest is the motivating force in construction. This force rules everyone connected with our labors

from bankers and land owners to government and labor unions. I was told five years ago by a high

government official that if architects do not respond to the crying needs of society, the government

would step in and solve it. At that time it seemed a ludicrous statement. Today, government's failure

to respond is even more obvious. The housing stock in America is depleting at a faster rate than anyone

will recognize. We have even gone so far as to substitute trailer and trailer parts for units of

housing. The trailer is not a viable housing - it Is sub-standard by anybody's definition.

For your work to become meaningful we must learn to make it part of a larger whole, we must

recognize that we are in the childhood of an emerging world civilization. For myself I find being

a part of this transition much more satisfying than believing we could be in the Golden Age.

9

An Insight into Three Dimensional Graphics

Arthur R. Paradis

Dynamic Graphics, Inc.

Computer graphics can be used to relieve much of the tedium

and time associated with the production of perspective drawings.

It frees the architects for more creative aspects of the design

process. It enables the architect to work closer with his client

through a constant flow of perspective drawings. There are problems associated with implementing such a graphics system. First,

the formatible image of the computer must be overcome. Then, a simple project description process must be implemented. It must

be simple enough to use and flexible enough to make the system

worth using. Ideally, there would be a common data structure for

the graphics programs and the various engineering packages. Finally, there must be an efficient hidden line removal technique to make the system feasible. Techniques are now developed which can make such a system possible. Preliminary work done for Skidmore,

Owings & Merrill indicates that such a system can be an economical

and time saving tool. This paper will present the technical aspects

of three dimensional computer graphics: the basic tools; the structure necessary; and a comparison of hidden line removal techniques.

Key Words: Architectural Graphics, computer graphics, data

structure, hidden line removal, perspective drawings, pro- jective geometry.

1. Introduction

Three dimensional computer graphics is becoming a cost-effective and time saving tool for architects and designers. Computer graphics allows architects and designers the freedom to study their layouts with perspective drawings from more vantage points and to try more design variations than would be otherwise possible with conventional means. This paper will introduce the basic tools of three dimensional computer graphics, both software and hardware; discuss the various components of the structure necessary for a three dimensional graphics system; and compare techniques for producing perspective

Figure la

Two views of San Francisco waterfront area produced for Skidmore, Owings £ Merrill

11
Figure lb

A computer generated perspective plot of the San Francisco waterfront area showing a proposed

waterfront project

2. Basic Tools of Three Dimensional Computer Graphics

2.1 Software Tools

There are three basic software tools which are combined to provide a flexible system for producing

perspective drawings: the projection of lines in space, the representation of surfaces (topography), and

the portrayal of complex solid objects. Each area will be presented as current capabilities and as advanced features which are being developed or are considered feasible.

a. Projection of Lines in Space

Lines in space may be represented by connecting a series of projected points with straight line segments. More advanced features allow the line to be represented by a smooth curve through the projected

points and permit the line to pierce surfaces or solid objects.

Figure 2

A projected line in space

12
b. Surfaces

Topography may be represented as a rectangular gridded mesh which may be displayed as a projected

mesh (fig. 3) or as a projected contour. It is not difficult to have either regular or irregularly

spaced grid lines. Thus, flat areas need not contain the same information density as rougher terrain.

It is more difficult to handle missing grid points. These may be computed by some interpolation process

or left as holes in the grid. Finally, there exists a whole series of functions which may operate on

either gridded data or randomly spaced data points.

Figure 3

A surface defined by a gridded mesh

c. Solids

Complex solid objects are generally represented by a series of bounded planar surfaces. The visible

portions of the planar boundaries are drawn with solid lines which the non-visible portions are generally

either blanked or drawn with dashed lines. For added flexibility, boundary lines can be specified as non-visible and additional lines or patterns can be drawn on the face of any surface. Within the framework of the basic system, curved surfaces must be approximated by a series of small planar surfaces.

More advanced features could include the ability to specify curved surfaces. Also, solid objects

could pierce each other. The amount of detail shown could be a function of the final viewing size such

that buildings or trees in the far distance would not be drawn to the same degree of detail as buildings very close to the observation point.

Figure 4

Representations of solid objects defined by planar surfaces

2.2 Graphics Hardware

There is a wide range of graphical display equipment available which can be used at computer ser- vice bureaus or purchased for in-house usage. The features, application areas, and price ranges for various types of graphics equipment will be given below.

a. Pen Plotters

Pen plotters are computer driven pen and ink plotting devices. They are the most inexpensive and most common graphics devices used. Pen plotters are available in a wide range of sizes from small drum

plotters to large flat bed plotters. Optional extra pens for different colors or line widths are also available. Perspectives, plan views, PERT charts, etc. can be produced using pen plotters when used

with the appropriate software.

Price Range: $8,000 to $100,000 (including input device)

13
b. CRT Displays

CRT (Cathode Ray Tube) displays are becoming more popular. There are two basic types — the raster scan CRT, which works much like a normal television set; and a vector CRT which draws lines in any

sequence. The vector CRT's are much easier to program for general graphics work as lines can be displayed as they are calculated. Some CRT's use a mini-computer for picture refreshing and local editing,

thus reducing the computer load and special software requirements of the main computer. Keyboards, light

pens, moveable cursors, and Rand Tablets are available as input devices for CRT displays. CRT displays

are valuable for providing quick results and effective data editing capabilities. They are capable of providing general graphics output for applications which do not require high resolution, large display

area or hard copy (hard copy devices may be connected to a CRT).

Price Range: $10,000 to $250,000.

c. Microfilm Plotters

A microfilm plotter is basically a CRT display with a camera attached for producing hard copy. They are ideal for creating computer generated movies. Hard copy can be directly produced or can be

made from the 16mm or 35mm film. The film is convenient for long term storage.

Price Range: $50,000 to $250,000.

d. Electrostatic Plotters

Electrostatic plotters produce a grid of dots. This type of plotter can produce either line plots

or render areas with a halftone effect. It has the potential for effectively displaying shadows.

Price Range: $12,000 to $50,000 (including input device)

e. Halftone Displays

The University of Utah has done a great deal of research into producing computer generated color

halftone pictures. These spectacular pictures are for the time being more of a laboratory tool and not economical for most applications.

3. Structure of Three Dimensional Graphics

The structure of three dimensional graphics may be divided into four areas — Application Language, Data Structure, Projective Geometry, and the Hidden Line Problem.

3.1 Application Language

The value of a graphics system, in this case an architectural system, lies with economic factors

and convenience. For an architectural graphics system to embody both flexibility and convenience, it must be carefully interfaced with the architect in mind. Skidmore, Owings and Merrill are currently

working on this problem with encouraging results. The following shortcuts have proved very helpful

in simplifying the data description.

a. Implicit Relatsionships

The planes which define a rectangular block can be defined in more than one way. The easiest and most cumbersome way is to define the coordinates (X,Y,Z) triplets for each of the six planes. This

would require the definition of twenty-four points (72 numbers) and would win few friends. By using

the implicit relationships of the orientation of the six planes of the rectangular box, it can be

defined by a height, width, length, location and orientation (the orientation can be implicitly defined

in many cases). This is defined by six numbers and is much more liveable.

b. Repetitive Definitions

A single window definition can be repeated to provide a whole face of windows or the windows for

the whole building. Similarly, the definition of a building can serve for similar buildings in the site.

' , c. Predefined Objects

Trees, vehicles, people, surface textures, building complexes, and even areas of large cities may

exist as predefined objects in the architect's library.

14
mxziziiizzi HJ II II -I

Figure 5

Windows are defined by patterns and the trees are predefined objects

3.2 Data Structure

The resulting data structure should contain more information than just the definition of lines and

planes. Information about the logical groupings and any hierarchial structure will allow more powerful

editing and manipulation capabilities. The data structure should be flexible enough to interface with

engineering programs such as duct layout, space allocation programs, or heating and cooling load calcu- lation programs with minimal additional information. Plan views and elevations can also use the same

data structure.

3.3 Projective Geometry

Both perspective projections and parallel projections are easily implemented. Perspective projections add realism to the drawings and the required mathematics is clearly presented by Kubert, Szabo and Giulieri [1].^

3.4 Hidden Line Removal

Determining by computer which lines are "hidden" when viewing from a specific point is a very challenging and frustrating problem. There exist various solutions, each tailored to a specific purpose,

such as surface algorithms, planar solid algorithms, etc., and these may be combined to efficiently

solve complex problems, but the resulting system is far from simple. Much work and possibly larger

computers are required before simple general algorithms can be developed which will process in a reasonable time and at a reasonable cost.

4. Comparison of Surface Algorithms

Three different algorithms for solving the hidden line problem for surfaces will be compared. The advantages and disadvantages of each will be explored and general statements describing the relative

efficiency of the algorithms will be presented.

Yd)

Y(2)

Y(3)

YCt)

zCi.i) Z(2,l) Z(3.1) Z{4J) Z(5J)

Zi\.l) 1(1.2) Zf3.2) 7(U ?) Z{5,2)

Z(l,3) Z(2,3) Z(3,3) Z(it,3) Z(5,3)

2(1.4) Z(2,4) Z(3,'*) Z(4,4) Z(5,4)

Example of structure of gridded mesh used in sur- face definitions. In FORTRAN terms the structure

is comprised of an X array, a Y array and a doubly

dimensioned Z array; and the mathematical relationship between the X, Y, and Z arrays is Z(I,J) = f(X(I),Y(J))

where f is a single valued function.

X(l) X(2) X(3) X(4) X(5) Figure 5

Figures in brackets indicate the literature references at the end of this paper.

15
4.1 Aerospace Algorithm

TMs algorithm was developed by Ruber t, Szabo and Giulieri [1] at the Aerospace Corp.

a. Definitions

The point to be tested for visibility will be called the test point; the line between the observation point and the test point will be called the test line and the plane perpendicular to the X-Y plane

containing the test line will be called the test plane.

Figure 6

Test point, test line, and test plane

b. Basis of the Method

For a point to be non-visible, the test line has to pierce the surface. A brief step by step

method will be given below;

c. The Basic Algorithm

STEP 1: A series of test criteria points are calculated from the intersection of the test plane

and the gridded mesh. (Note: only the points between the test point and the observation

point are calculated.)

STEP 2; The test line divides the test plane into two sections. The test point is declared non- visible if there is at least one test criteria point in each of the two sections of the test plane; otherwise, the test point is visible.

STEP 3: When two adjacent grid mesh points are visible, the connecting line is drawn.

STEP 4: When a grid point is visible and the adjacent grid mesh point is non-visible, the visibility, non-visibility transition point is calculated by using a binary search and using the above steps to determine the visibility of the successive midpoints.

d. Advantages

This algorithm is easy to implement and requires a relatively small program.

e. Disadvantages

The execution time rises exponentially as the size of the defining grid mesh increases. There are more test points and each test point requires the calculation of more test criteria points for the visibility testing. (This exponential relationship became painfully clear when it was discovered that a surface defined by 150 by 150 mesh points costs over $400.00 to compute.) This method also requires the whole grid mesh to reside in memory at all times. Finally, the method does not always produce the exact solution to the hidden line problem as steps 3 and 4 do not catch all changes of visibility.

4.2 Warnock Algorithm

This algorithm was developed by Dr. John Warnock [2] at the University of Utah. The following des- cription does not do this algorithm justice as its real power lies in its ability to easily produce halftone pictures when coupled with the appropriate plotting equipment.

16
a. Definitions

Picture resolution will refer to the smallest distance between two adjacent points on the given

display device.

b. Basis of the Method

This algorithm uses an interesting method for solving the hidden line problem. An area of the pro- jection plane is examined. If the method determines that the area is "simple" then it contains no visible line so processing is finished on that area; otherwise the problem is simplified by subdividing the area into smaller sub-areas. The process is then applied to each of the sub-areas and reapplied until

the sub-area is either simple or the picture resolution is reached. If the picture resolution is reached the square contains a visible line and the resolution sized area can be displayed as a dot.

Figure 7

Subdivision Process

c. The Basic Algorithm

STEP 1: For a given sub-area of the projection plane, determine the proper classification (out of three) for each plane in the surface.

Case 1) The projected boundary of the plane surrounds the area of the projection plane

being considered.

Case 2) Part of the area of the projected surface overlaps with the area of the projection

plane being considered.

Case 3) The projected boundary of the plane lies totally outside of the area of the pro- jection plane such that the two areas do not overlap.

Projected

Boundary

of

Pol ygo!

Pol ygon

Case 1 Case 2 Figure 8

Po ] ygon

Sub-area

Case 3

Three possible relationships betweeen sub-area

and projected boundary of a polygon

STEP 2: For each case 1 or case 2 plane, determine the distance from the observation point to the plane at all four corners of the surface plane.

STEP 3: Determine whether the sub-area of the projection plane is simple. The sub-area is simple

if:

17
1) The sub-area contains no planes of case 1 or case 2. It is blank.

2) There exists a case 1 plane which is clearly closer to the observation point than all other case 1 or case 2 planes. A plane will be clearly the closest if the plane is closest to the observation point at all four corners

STEP 4: If the sub-area is not simple then subdivide it into four equal sub-areas and depending on

the size of the new sub-area either

If the sub-area is larger than a the picture resolution, start with step 1 and process the first new sub-area.

If the new sub-area is not larger than the picture resolution, then it contains a portion

of a visible line on the surface, so add the point to the display file.

If the sub-area is simple, it implies that no visible lines in the surface are contained

in that sub-area, so go on and process any of the other of the four sub-areas which remain

to be processed, or then process any of the sub-areas remaining in the next higher level

until the processing is finished.

d. Advantages

The algorithm works well with both surfaces and planar solids. Intersecting solids present no problem. Time for solving the hidden line problem is reasonable, although it could get excessive with a large quantity of data. This is a good method for producing half tone pictures.

e. Disadvantages

This method works well only with CRT type displays as pen and ink devices use an extreme amount of excess pen motion. Also, computer storage rises rapidly for large problems because each sub-area contains two list of planes associated with it.

4.3 Horizon Method

This method was developed by the author at the University of California at Berkeley [3].

a. Definitions

Horizons — An upper and lower horizon delineate a closed opaque region.

Grid Line — The line connecting any two adjacent grid mesh points.

Mesh Element — Any four grid lines which form a closed rectangular box.

1)

2)

Visible Region ypper

Hor i zon

Figure 9

Upper and lower horizons delineate

visible region from opaque region

Example of a grid line

and grid element

b. Basis of the Method

This algorithm uses the basic property that portions of a surface closer to the observation point cannot be covered by portions of the surface more distant.

18
c. The Basic Algorithm

Figure 11

Sample grid to be processed

The surface is processed from near to far. The method presented is for viewing the surface from a corner area. Other viewing areas require an additional step.

STEP 1: The edge row closest to the observation point will always be visible. It is plotted and

the projection of the edge row is used to define the opaque region.

Figure 12

Upper and lower horizons after first row has been processed (identical)

STEP 2: The grid lines not already processed in the first mesh element (the bottom grid line would

have already been processed) of the next row are now processed. The lines are compared

with the opaque region defined by the horizons. The portions of the projected grid lines

visible are plotted, and the closed visible portions expand the definition of the horizons.

Figure 13

Upper and lower horizons after first grid

element of second row has been processed

STEP 3: The mesh element adjacent to the element just processed by step 2 is processed by comparing

plotting, and expanding the opaque region as in step 2. This process is continued until

each mesh element in the row has been processed. Steps 2 and 3 are continued for the remaining rows

Figure 14 Grid Lines compared with horizons and produced one visible segment for this example

19
c . Advantages

Processing time is nearly a linear functions of the number of mesh points. The method also produces

the exact solution to the surface hidden line problem. Also, the whole surface need not reside in memory

at any one time.

d. Disadvantages

The algorithm is more difficult to implement and the actual program requires a larger computer.

4.4 General Observations for the Surface Algorithm Comparisons

a. To be economically feasible, solution times should not increase exponentially as the size of the problem increases. This implies that the time required to test the visibility of a point

is independent of the size of the problem.

b. By using projected points for the hidden line removal, the last two methods were significantly

faster.

c. Using any pre-knowledge is also helpful for a faster solution, i.e., the inherent ordering of a mesh surface can be used to advantage and further increase processing speeds.

5. Extensions into Solid Algorithms

Basically the same principles apply for the solid case that apply for the surface case. The three surface algorithms each have their counterparts in a solid algorithm. The solid case is generally harder

since the implicit ordering of the gridded mesh is missing.

a. Extension of the Aerospace Algorithm

The basic test of visibility is modified to test whether a test line pierces any of the other planes

of the solid object. This can produce a tremendous number of tests and is definitely not feasible for data representations produced from large quantities of data.

b. Extension of the Warnock Algorithm

The Harnock algorithm basically works equally well for both surfaces and solid representations. Any

solid program will process gridded surfaces with minor modifications as a surface can be represented by a series of planes. However, since they do not take advantage of implicit ordering they are not as fast as specialized surface programs.

c. Extension of the Horizon Algorithm

If the planes defining the solid object are ordered from near to far, then a series of small opaque

regions are defined as the planes are processed. Methods are being developed which minimize the effect

of having a large number of small opaque regions necessary for testing.

6. Conclusion

It is now possible to use computer graphics to produce perspective line drawings for a limited num- ber of design applications which are cost competitive and produce drawings in a fraction of the time of conventional methods. The sphere of feasible applications is growing rapidly and it will now be up to the architects and designers to learn how to use this powerful new tool and to guide future developments.

7. References

II] B. Kubert, J. Seabo, S. Giulieri, The Perspec- [3] A. Paradis, An Algorithm for the Efficient

tive Representation of Functions of Two Var- Removal of Hidden Lines from Projected Sur- Lables, JACM, Vol. 15, 1968, pp. 193-204. faces. Tech. Report 34, University of California, Berkeley, California, June 1969.

[2] J. Warnock, A Hidden Line Algorithm for Halftone Picture Presentation, Tech. Report 4-5,

University of Utah, Salt Lake City, Utah,

May 1969.

20
The Use of Graphics in the Development

of Computer Aided Environmental

Design for Two Storey Houses

Aart Bijl^

^ Tony Renshaw and David F. Barnard

Architecture Research Unit

University of Edinburgh, Scotland

The Architecture Research Unit (ARU) is working on a two year research

project to develop the use of computers in the field of housing design and production. This research is sponsored jointly by the Scottish Special Housing

Association and the Ministry of Public Building and Works. The ARU's task is to develop a convenient technique for generating a description of the fabric of a

building, within a computer. This must convey the geometric information which

is traditionally contained in architects' drawings, in such a way that it remains

intelligible to the user and is also suited to the further attachments of topological

relationships associated with a variety of design considerations. Current use of graphics by designers is being studied, to prepare for new and acceptable conventions which are suitable for computer graphics input and output. It is now

possible to use the computer to design a house plan on a cathode ray tube display,

and introduce modifications to shape, size and building elements. This information can be fed into a program to check for consequences on construction, thermal

environment, daylighting and other design properties which may be stored in the computer's data structure. This paper considers the relevance of graphics in an existing context of house design and production, and shows how this rele- vance is maintained through the application of a computer aided design system.

Computer equipment currently being used on this project include a DEC PDP7

and 340 display with light pen, linked to an Elliott 4130 with disc backing. Hard

copy output is obtained from a Calcomp 563 incremental plotter. Application

of this research will be directed at two storey house production by the Scottish

Special Housing Association; and benefits may be expected in subsequent

improved ability to meet evolving environmental design requirements, to make

greater use of scarce professional services, and to facilitate costing and construction of houses.

Key Words: Computer graphics, design practice, design process,

geometry, graphic conventions, housing, information structures, man

machine interaction, problem description, production information,

topology.

1. Introduction

Any benefit from the use of computers in assisting the solution of a problem is dependent on an

appropriate and clear description of that problem. The problem description needs to be un- ambiguous and intelligible to the machine, whilst also remaining recognisable to the person who is using the machine. In problems concerning environmental design relating to buildings, satisfactory

solutions are dependent on suitable means for describing buildings.

2 Research Architect

Architect/programmer and mathematician/programmer, respectively.

21
Prior to the availability of interactive computer graphics, building description for input to computers required a lengthy process of identifying co-ordinate reference points relating to a building's geometry. This information had to be compiled into long lists of numbers, unfamiliar to the designer. The task of translating the building description into a form suited to computer

input (1) ^ required the skills and dedication of a specialised designer /programmer . This difficulty

is a principal cause of the slow and reluctant acceptance of computers by designers, in the building

industry.

The present object is to discover v/hether the opportunities provided by computer graphics

facilities are suited to closing the comprehension gap between designers and the machine; to see whether designers may benefit from using computers as a general design aid, and so be encouraged to accept its use in practice.

2. Design Functions

The process of designing buildings is sometimes described as a linear sequence of activities,

from inception of a new design through to completion of building (table 1) (2) and could continue

throughout the useful life of a building to the time of its demolition.

Stage

Table 1. Stages in Design Process (based on the RIBA Outline Plan of Work)

Usual Terminology

A. Inception

B. Feasibility

\

Briefing

/

1 C. Outline Proposals i

1 D. Scheme Design i

Sketch

Plans

/ Detail Design

F. Production Information

G. Bills of Quantities H. Tender Action

1 Working

Drawings

I

I

J. Project Planning

K. Operations on Site

L. Completion

M. Feed-Back

Site Operations

\

The linear sequence of these activities is readily questioned when considering the evidence of practice, and observing the return loops and the lateral deviations which actually occur. But the linear description is useful as a scale by which to refer to the particular levels of operation in any

system, to produce relevant indications of the kind of information which will need to be processed,

and the appropriate manner of presenting and conveying this information.

Using the scale A to M of table 1, and by reference to the work of others in the field of computer aided design, it becomes possible to define the scope of the ARU's work. Some of the work

undertaken in Britain can be regarded as dealing primarily with production information after design

decisions have been taken (3), producing bills of quantities, ordering schedules and references to standard construction details; operating from E to H. The other end of the scale is represented

by work on analytical processes which lead to early design decisions, relating the results of computer

1 Figures in brackets refer to the bibliography at the end of this paper.

22
analysis to single line design representations on a c. r. t. (4); and operating from A to C.

The field of application offered by the Scottish Special Housing Association, with its commitment

to build, places a bias on the ARU's work towards achievement of benefit at the production information end of the design process. However, having the precedent of work produced by others in this field and seeing difficulties in bridging the gap in operation between the design and production ends of the scale, the ARU decided that it should attempt to operate within this gap and work outwards towards

both ends. Thus the ARU is currently operating from C to F, with the intention of allowing a designer to build up a problem description in various ways, to respond to property analysis by the computer relating to design decisions, and leading gradually towards specific and detailed production

information.

2. 1. Graphics related to Design Functions

Existing precedent in design practice indicates a relationship between the levels of specificacy

relating to stages in the design process and the form of graphics used to convey information (table 2). The relationship of graphics to stages in the design process will vary, in response to varying fields

of application. Where the building type leads to repetition of relatively stable information, as in housing, the link between a and c will occur early in the design process. Where complex and nonrepetitive building forms are involved, as in schools or hospitals, the progression from a to c is likely to be more gradual. This is illustrated in table 3, which relates the use of different forms of graphics to the applications fields of new housing, modification to standard housing and more complex

buildings

Table 2. Association of Graphics with stages in the Design Process

Form of Graphics RIBA Stages

A to B

Diagramatic

single line B to C

c. General Arrangement

double line (locational reference

for detail information)

d. Detail Representation

complex graphics

(assembly information)

e. Component Information

C to H

E to H

E to H
Table 3. Relationship of Graphics to stages in the Design Process effective in different Design Fields

Stage Design Fields : New House

Design

Std. House

Modification

Schools

etc.

Inception

FeasibilityOutline Proposals

Scheme Design

Working Drawings

Details

ab c c

c

c d

d e

c

cc

c

c d

d e

a

a b

b c

cc d

d e

The alpha characters refer to the forms

of graphics given in table 2.

The use of graphics represented by c under new and standard housing closely resembles

practice at the SSHA and is used to refer to the more variable information being accessed and

generated during design.

2.2. Communication of Information

In building design practice a number of particular circumstances exist which influence the way in which information can be conveniently handled. The functions of storage and recall of information are affected by the large variety of people with diverse motives and ability, who are

involved in building. The interdependence and interaction of a great variety of interests present

during design requires that any system cannot depend on a linear sequence of functions and must be

capable of entry at various points.

A designer's presentation of information normally consists of an assembly of previously

known bits of information, which make up a proposal, or instructions, for a new building. The newness and relevance of a particular presentation exists in the relationship of one bit of information to another; its presence, location and physical fit (5). In detail considerations this may

include shape; a new relationship of one surface to another which encloses a specified material.

This amounts to the geometric or topological information of or between objects or activities.

The different bits of known information contained in the assemblage are identified by the use

of conventions which are familiar to all the people involved. The convention enables each person

to recall the particular information which is being referred to.

The general predominance of geometric or topological information, as the meaningful content

in a designer's presentation of information, has formed the basis for extensive use of graphics.

This is true of the past, and if people are to continue being involved in building design and be in control of their environment, then this dependence on graphics is likely to continue into the future.

2. 3. Computer Graphics

In order to devise new and acceptable conventions which are suitable as computer input and

output, it is necessary to consider first the current use of graphics by designers and relate this to alternative vehicles for conveying information i.e. niimeric or verbal descriptions.

Verbal or numeric representations are built up by stringing together many characters or numerals, either singly or in groups; and the association between characters or numerals is governed by the operation of laws i. e. grammar or mathematics discipline. Each character alone

is meaningless, the combination of characters is made to be meaningful. This structure is absent

24
from most conventional graphic modes of presenting information; and it is this difference which has

led to the discrepancy between* the use of machine aids for alphanumeric information and the lack of use of machine aids for graphic information.

SYMBOL

NOTATION MECHANICAL ELECTRONIC

"WORDS

NUMBERS

fingers

GRAPmCS

ABC

alphabet

2 3 4

numerals

typewriter

^

print

tables sliderule calculator

J

K

I electronic _ computing

' memory system

hand

figure 1. The use of symbols or characters in combination to represent information, affecting

development of appropriate machine aids.

Computers must receive information in bits, each with prespecified relevance, which can be

compiled within a system to represent a whole assembly of meaningful data. In current design

practice information is presented by drawing lines by hand; each bit of line on its own conveying

little information to anybody other than the person doing the drawing. It is only as the drawing

develops that its information content becomes more meaningful. The hand drawn information does

not have to make sense until the drawing is complete. New graphic conventions need to be

developed which consist of separate elements, or bits, of prespecified significance, which can be

assembled to convey new and complex data. In this way a useful "grammar" for graphics should

begin to grow.

3. Field of Application

A two year research project has been undertaken by the Architecture Research Unit (ARU) of the University of Edinburgh, which is being sponsored jointly by the Ministry of Public Building and

Works and the Scottish Special Housing Association (SSHA). The initial two years of research is aimed at establishing the feasibility of applying computer graphics within an existing building design

organisation, to serve as a useful aid to the production of new buildings.

A narrow field of application has deliberately been chosen, to maximise the opportunity for establishing principles of computer operation. If a satisfactory form of problem description can be

achieved, which is applicable to a narrowly defined design environment, then the principles of operation which will have been developed should be capable of subsequent expansion to suit a wider

range of more complex applications.

The field of application is provided by the SSHA. This is an organisation which builds

approximately 5, 000 houses per year and is one of the largest house producers in Scotland. Most

of this housing consists of two- storey terraces, bviilt of "No-fines" concrete, though the total output

includes single and multi-storey houses and flats and includes brick construction.

The SSHA designs, manages and maintains the houses which it builds, usually on behalf of local borough or city authorities. It provides all the professional, constructional and managerial

services associated with the entire life of its houses, within the one organisation. As such it already has an exceptionally large store of information which should become readily available to designers through the application of computers, to lead to informed decisions relating to new designs.

25
The great majority of house forms consist of simple rectangles with rectilinear internal subdivision, on two floors of equal and constant storey height. The roofs are usually pitched, with tile cladding. The range of materials and details used for construction are limited and there is little variation in the required environment within houses. These small and simple building forms appear

to be ideally suited to standardization, both of design requirement and building product; but the amount of variation which actually occurs at a detail level of specificacy, relating to construction

information, is extensive. The permutation of these detail variations within a whole house or between one house and another gives rise to lengthy manual search procedures to check that all con- sequences are accommodated in new construction information

3. 1. Graphic Requirements

The function of graphics is to convey geometric or topological descriptions; to provide

locations for bits of information; to identify the spaces which may contain material specifications.

Where the function of graphics is to describe a building to a computer, such problem

description should not anticipate or predetermine a solution. The graphics alone should not auto- matically indicate a particular form of construction, but should allow free and gradual opportunity

for subsequent decisions leading to a specific design solution.

In providing geometric information graphics will tend to indicate relative size. This has to be

accommodated and controlled by the graphic conventions which are developed for the applications

context; the implied size accuracy should not be finer than person's ability to read off the viewed

image.

Given the context of SSHA houses, together with current national moves to co-ordinate all height dimensions occurring within housing, it is possible to interpolate much of the three-dimensional

information required for building design and production from plans. In this context the need for three-dimensional or animated computer graphic projections receives a low priority and it is possible

to concentrate effort on purely orthogonal projections.

A convenient form of building description input to computers could provide quick access to computer analysis routines, which check the design for compliance with design standards or

regulations. Design alterations could be fed into a program to check for consequences on construction, thermal standards, daylighting and other environmental properties.

Suitable computer input should enable cost information to be accessible at all stages during

design and this information could be continually updated by new information received from building

operations. Such use of computers should further provide output in the form of printed bills of quantities, ordering schedules and intelligible working drawings.

3. 2. Equipment

The project team at the ARU has access to computing facilities in other University departments.

This consists of a DEC PDP7 and 340 interactive graphics display terminal with light pen, and a Calcomp 563 incremental plotter.

The graphics terminal is connected by high speed link to an Elliott 4130 central processor,

with 64K word core and magnetic disc backing store.

In a design environment such as that of the SSHA, which does not yet practice the general

application of computers, fully interactive graphics may initially prove too expensive. The ARU is therefore considering alternative cheaper and less sophisticated graphics facilities; and a parallel

research programme has been started which aims to develop the application of an ARDS direct view

storage tube, linked by delay line to an ICL System 4/75. The possibility of using a d. v. s. t. has

been taken into account in writing the program for the fully interactive graphics facilities.

The ARU has its own on-line Teletype terminal linked by voice grade line to a remote time

sharing bureau service, which is being used as a convenient form of computer access for interactive

program development.

26
4. Development of a Computer Graphics Application

Research work by the ARU on the application of computer graphics techniques to the work of the SSHA is described in the following paragraphs and illustrations.

4. 2. Information Structures

The general data handling capability of computers is usually dependent on a precise and predetermined logic structure, so that it will make sense of any data it receives. In design practice a similar methodical approach to handling information is sometimes attempted; but rules are often broken. Where information passes between understanding people the method may appear to survive,

but where information passes to a computer any violated rules will cause a failure of the system. In applying computers to the work of the SSHA, it is necessary to reassess the use of familiar information structures, so that these may be modified to fit a computer's data structure; specifying those areas of design activity which can best be handled by user interaction with a computing system.

In order to prepare for the need to process SSHA information through a computing system, the ARU's approach to data structures has been to distinguish between different principal computer

functions. These differences are used to distinguish between the requirements of different data structures. Each separate structure is developed to interrelate with the others but each is suited to

its own particular function. So far work has been based on distinctions between a graphics data structure (GDS), an applications data structure (ADS), and a file handling system (LIBRARY).

The GDS notes the way in which points and lines come together on the screen, to represent

meaningful information to the user. It stores the relationships between the points and lines, and the walls, windows, doors, rooms and surfaces which these represent; to which the user may want to attach other non- graphic information.

4-

COMPONENT

/K7^

ext jnc

ext jnc

^ROOM

surface

COMPONENT

/K/N

U

tiu

1

J I L surface

COMP.

ext jnc

surfac e

figure 2. Example of an Applications Data Structure referring to a Room

27
The ADS holds the computer's pool of information which is received from the user and is interpreted by reference to a permanent file of information stored on magnetic tape or disc. This

pool of information, which grows as the user builds up a design, is structured in terms of accommodation zones (floors), spaces (rooms), components (walls, windows, doors), surfaces and

junctions (fig. 2). The ADS has to note the relationships which exist between these items and has to relate incoming information from the user to a corresponding stored item or group of items.

The computer has constantly to compare information received from the user with that already

stored in its LIBRARY, e. g. comparing component junctions with known working detail specifications.

It also sends information taken from the LIBRARY and qualified by the ADS to the user, e. g. ranges

of options for material specification displayed on the c. r. t. screen. A request by the user to give or receive information is usually initiated by the user indicating a point on the display. The computer uses the GDS to identify which item, or group of items, in the ADS is being referred to. The computer then uses its immediate experience (the ADS) and its LIBRARY to interpret the request, and supply or store the information relevant to the request.

4. 3. The Application

The representation of house plans on the c. r.t. is achieved by selecting graphic symbols which

can be used to build up graphic elements depicting walls, doors or windows. These elements then serve as locating devices within the computer, for insertion of components of information.

The symbols are the basic graphic bits, rather like individual characters in an alphanumeric

presentation, which are used to assemble the graphics. Individually each symbol carries very

little information, other than an approximate indication of relative size and direction. A limited

range of five symbols is found to be s\afficient for representing the building fabric of houses (fig. 3). A simple square is used to represent external or party walls and main internal loadbearing walls. The same square bisected represents windows through such walls. The single bisecting line without

the square represents doors in the same walls. A smaller square is used to represent partition

walls, and a short straight line represents partition doors.

The first three symbols are used to fill 300 mm. square zones on a house plan and the last two

symbols fill 100 mm. zones. This corresponds to the nationally adopted incremental system of 300 mm. and 100 mm. for house building, accompanying the change to metric measures and the introduction of dimensional co-ordination. These two dimensions are used in the computer application to provide the basic order by which more complex graphics may be assembled.

Graphic elements are built up from symbols on the c. r. t. Each element (fig. 5) carries

information on the location, form, length and approximate width of a building element, e. g. wall. The design environment may further allow interpolation of overall height, and the subdivision into parts, e. g. window cill and head height. A number of elements can be assembled, changing the symbol for windows, doors and partitions, until a complete house plan is produced.

A component of information refers to the data which the user wishes to associate with the graphic element, which the computer receives into its ADS, and which may be filed in the LIBRARY.

Such a component may refer to conceptual properties or performance characteristics of the design,

e. g. the intended heat transference through a wall, or the required structural stability to withstand

given loading. A component may refer directly to a material specification, or partial specification, for an element which constitutes a part of the building fabric. A graphic element does not necessarily

have to carry a component of information, it can be empty.

The figures 3 to 9 generally illustrate the procedure for assembling the graphic representation

of house plans on to the c. r. t. Plans may be modified, by deleting and rebxiilding one or more

elements (figs. 10 to 12); and plans can be stored by the computer on disc or paper tape for subsequent retrieval and further modification. Hard copy output is provided by the digital plotter.

The facility for materials specification is considered to be a necessary part of the procedures

available to the user for describing a problem to a computer. Materials specification, as with

graphics representation, is optional to the user, depending on the particular computer analysis which

is to be performed on the problem description (fig. 17).

28
The user can build up a materials specification for a symbol or an element by selecting options

which appear as computer controlled menus on the c. r.t. He is guided through the process of selection by messages which appear over the menus, which inform him of the stage of specification

which has been reached. In the case of walls the specification is made in three stages i. e. primary

material, external cladding and internal cladding (figs. 14 to 16). As each selection is made the computer ADS references the LIBRARY in order to generate an appropriate subsequent menu, for display

and further selection.

If a symbol is selected for materials specification, the computer will generate an appropriate menu of general primary options, followed by appropriate general internal and external claddings.

These tend to be short menus including only those materials which can be used whenever the symbol

is used to build up elements throughout a plan. When the user indicates a particular element for materials specification the computer will generate appropriate menus containing specific options; and

these menus tend to be longer, containing the wider range of materials suited to specific locations in a

plan.

The specification for any symbol or element does not need to be complete; the user may select

the SKIP option in any menu to call the next menur, or select EXIT if he wishes to terminate the specification (fig. 15). At any stage-of the development of the problem description the user may subsequently return materials specification to modify or add to previous information.

The materials specification built up through user selection from menus displayed on the c. r. t. assigns materials to a graphic representation of a house plan which is viewed at a scale of 1 : 50. As

soon as the specification refers to a number of adjacent elements the computer can assemble associated

data leading to' information on jimctions between components. The computer can then identify construction details and recognise fit or misfit conditions. In the ARU application this information is cross-referenced with manually prepared standard construction details which back up the computer's

store of information to allow the output of practical production information.

Operation of the system which allows the user to prepare and interact with the problem

description is illustrated in figure 17 and the various stages, or modes of operation, are explained

in the accompanying table 4. Lines linking the stages indicate a sample of possible routes through

the system; the continuous line showing an entry through the general specification of materials to symbols, leading on to graphics; the dotted line showing an entry through graphics, leading directly on to some analytical function or passing through specific materials specification; and the dashed

line showing an entry through modification of an existing problem description.

Figure 18 and the accompanying table 5 illustrate an example of one analysis function which can

be performed. This example is concerned with heating, and the analysis is structured to allow the user to select alternative start points, and by varying the input data, to arrive at computed information on either the temperature levels which will be maintained or the heat input which is required.

Where the desired result cannot be obtained by manipulating the variables ( D E G or J) in this function, the user can return to modify the main problem description.

The major part of the ARU's research effort has concentrated on the development of an

operating system (fig. 17) which allows the designer to describe a building to a computer, introduce

modifications and build up information at various levels of specificacy; to prepare for the operation

of a wide range of computer analysis functions. This technique for problem description needs to be

tested for a wider range of applications, involving different and more complex building forms and

including the arrangement of grouped buildings.

29
CMtM UimM WIMT

O — • mm mmt mat B - • ** tm mm

Mit ;RETllRM» mif 4NK «» mi RETURHv' ' ; kit RETURMr

figures 3 4 5, 6

Initially the display shows a planning grid representing 300 mm. squares, with five graphic symbols

and a number of light buttons displayed along the bottom. The user selects a symbol with a light pen

and tracking cross, and this is used to locate the extremities and corner positions of a graphic

element. If a graphic element representing a window is built up on the display, the user is given an

opportunity to specify particular height information.

figures 7 8 9

The user proceeds to construct elements to represent a house plan, completing the perimeter

boundary walls and proceeding with the internal subdivision. When the graphics is complete the user can call up the space function which causes a display of room labels and he can proceed to identify the spaces bounded by elements as rooms.

30
figures 10 11 12

The user can modify completed house plans, by deleting elements and selecting new symbols in order to build up new and different graphic elements.

tnmex muum immtt Mun •I tumm tuiKt onniM.' eutom

iigures 1-1 ID 10

Material specification is carried out by selecting MATERIAL from a list of functions displayed on

the screen. The user identifies a symbol, or an element, with the light pen, and a range of appropriate primary material options appear in the menu area, together with a message calling on

the user to make a selection. The menus are paged under computer control, for internal and external

claddings, until the specification is complete.

31
32
Table 4. MAN MACHINE INTERACTION - CAAD OPERATING SYSTEM

USER PARTICIPATION STAGE LABEL COMPUTER FUNCTION

User enters job reference

code

User indicates new pro- blem

User indicates old problem

User selects problem

description for display

User defines geometry and

topology of components of the problem description, by

assembling graphic elements

on the c . r . t.

User modifies existing

graphics on the c. r. t. by

deleting and adding new

graphic elements

User labels spaces which

are described by graphic

elements

User can assign material

specifications to each or any

of the symbols before ele- ments are assembled on the

c. r. t. ; the specification is made by user selection from

menus, which appear on the screen

A. Enter

B. New

C. Old

D. Display

E. Draw

F. Modify

G. Space

H., Material

general

Computer uses user identity as control on

further information which will become available,

identifies existing project files and is ready to create new ones, calls for description of problem: new or old?

Computer is ready to create new information

file; to receive new problem description for translation into computer model.

Computer retrieves existing model from store,

deposits this in core; ready for display, modification or analysis.

Problem description is displayed on c. r. t.

Computer begins to assemble associative

model by restructuring elements into components, surfaces and junctions

Computer modifies existing model and checks

consequences on affected data already contained

in the ADS.

Computer defines the space by forming a ring

of surfaces to the components which form the boundaries of the space.

As each symbol is indicated, the computer

searches the library file in order to build up

appropriate menus and store the selected

specification for subsequent entry into components as graphic elements are input on the

c. r. t. ; this information can serve as a control on later decisions by the user as the graphic

description proceeds.

User can assign material

specifications to displayed

graphic elements on the c. r. t.

User can indicate particular

analytical function which is to be performed by the computer on the problem

description

J. Material

specific

K. Functions

Computer enters data into the ADS and will over- write data which may previously have been used

to describe the affected components; this information can be made subject to controls, i. e. recognition of fit between components.

Computer calls the appropriate analytical

routines into core, to operate on the model contained in the ADS, and the first function is to check whether the model is complete for purposes of executing the required analysis; at

this point, or at any stage of analysis, the computer can indicate the need or opportvinity to return to any of the stages D to J.

33
figure 18 Function : HEATING

The arrows indicate a few of nnany possible routes through

the system.

Table 5. MAN MACfflNE INTERACTION - FUNCTION : HEATING

USER PARTICIPATION

User selects HEATING from

list of functions displayed on

the c. r . t.

A. function:

HEATING

Computer checks request against appropriate

completion of building model (problem description) already in the ADS, informs user if not complete and awaits input of required

further data.

User indicates heating

evaluation relating to all the space within external wall

boundary.

User indicates heating

evaluation relating to a specific space

User specifies amount of heat to be supplied to the space

B. Whole

Building

C. Part

building

D. Heat

input

Computer extracts information from ADS on

state of external walls.

Computer extracts information from ADS on

the state of the boundaries to the specific space.

34
User specifies temperaiture

range to be maintained in the space (against a given

external environment)

User calls for information on previous decisions relating to the problem

User can assign U values

to each or any of the symbols

User can assign material

specifications to each or any

of the symbols

User can assign U values to each or any of the elements

User can assign material

specifications to each or any

of the elements

User calls for information

on the heating levels which

will be maintained, in response to previously

entered data; the user may

return to modify data until satisfactory heating levels are achieved.

User calls for information

on the amount of heat input

which is required, in response to previously

entered data; the user may

return to modify data until a satisfactory figure for

the amount of heat input is obtained.

E. Temperature

required

F. State of model

G. U value

general

H. Material

general

J. U value

specific

K. Material

specific

L. Temperature

maintained

Computer tells user whether materials have

been specified for the boundary elements and

whether there are restraints on exercising

further options.

Computer enters data into the ADS at the appropriate locations indicated by the graphic

elements on the c. r. t.

Computer searches the library file for specifications which provide the required U value

appropriate to each symbol indicated by the user; in order to build up appropriate menus,

and relate the selected specification to the corresponding elements already existing in the problem description; newly selected material

specifications will replace previous specifications.

Computer enters data into the ADS; and overwrites previously specified corresponding

data for the same locations with this new data.

Computer searches the library file in order to btdld up menus which provide the required

U value (as for H above).

Computer checks whether input data is complete

and then proceeds to perform heating analysis

taking account of: a) exterior temperatures

b) surface area of space

c) U values of boundaries

d) amotint of heat input

to arrive at figures which describe the heating

levels which will be maintained.

M. Heat

required

Computer checks whether input data is complete and then proceeds to perform heating

analysis taking account of: a) exterior temperatures

b) surface area of space

c) U values of boundaries

d) range of temperature to be maintained

to arrive at figures which describe the amount of heat input which is required.

35
5. References

D.J.O. Ferry; Measurement of Structural

Concrete Work by Co-ordinate Reference,

University of Southampton U. K. , CE/ 2/68.

Computer Development in West Sussex 1 and

2, Architects' Journal 21 and 28 February

1968, pages 421 to 426 and 489 to 493

respectively.

R. J. Stibbs and J. P. Steadman; A Computer

Aided System for Architectural Design

Analysis, reprint from Cambridge Research

U.K., Michaelmas 1968.

(4) Handbook of Architectural Practice and

Management, Part 3. 220 Plan of Work,

Royal Institute of British Architects,

revised 1967.

(5) Aart Bijl; Computer Aided Architectural

Design, paper to Computer Graphics 70 at Brunei University U.K. , April 1970.

36
Anticipatory Techniques for Enhancing Remote Computer Graphics

Thomas N. Pyke, Jr. ^

Center for Computer Sciences and Technology

National Bureau of Standards

Washington, D. C. 20234

Techniques for enhancing the performance of graphical display

terminals located remotely from a central computer system and

connected by limited communication lines are discussed, with

emphasis on the system requirements of environmental engineering

applications. A set of mechanisms that anticipate a user's needs is presented, including related techniques that have been used to support

computer graphics terminals and new ideas for optimizing display

operation.

Factors considered in this study of anticipatory techniques

include the effect of communication line loading and central system

response to requests from a local display- driving computer. Also

of interest are various ways for deciding what to anticipate and for considering multiplexed communication lines. Extension into a computer networking environment is also discussed. A few potential

application areas for anticipation, including some in environmental

engineering, are described to illustrate the possible use of these

techniques

Key Words: Computer-aided design, computer graphics,

interactive graphics, remote graphics terminals.

1. An Engineering Problem

There has been much discussion the past few years concerning the use of graphical displays

attached to supporting computer systems. The load placed on such systems by highly interactive

display usage has demanded a large percentage of central system resources and has led to the use of local logic and in some cases small computers associated with displays to relieve this burden from the central system [1], [2], [3]. ^

It is desirable to have access to large computer systems which have large, high-speed main

memory, powerful instruction repertoires, and large backup file systems. The nature of the interactive activity associated with display usage is such that these powerful resources are required only

for short periods at relatively infrequent intervals. It is, therefore, economically advantageous to attach several display terminals to a large computer system and to control their operation with a timesharing executive.

Chief, Computer Systems Section.

Figures in brackets indicate the literature references at the end of this paper.

37
The problems involved in supporting a number of graphical displays are greater than for supporting slower teletypewriter devices, and early systems have served only a few displays, along

with a much larger number of teletypewriters [4], [5]. The use of intermediary computers to assist

each display terminal or a group of terminals promises to increase the number of displays that can

be serviced by one large computer.

Problems that arise v/hen using a local display computer to drive either one or many displays are accentuated when the local computer is located at a considerable distance from the central system.

When located near the central system it is assumed that a very high bandwidth communication line can

be established between the local computer and the central system. At longer distances this may not be

possible. Even when it is possible, the cost of doing so may be unbearably high.

It is desirable, then, to utilize a restricted bandwidth communication line to interconnect the local and central systems. For instance, it would be convenient if successful operation could be

obtained utilizing a single voice -grade line with a capacity of 2400 bits per second.

The limitations imposed on system operation with such a restricted line are immediately

obvious, since the nature of the data transmitted to and from the display is such that large amounts of data are involved in the transfer of a complete picture. A picture with 1000 elements, each requiring

20 to 50 bits per element, requires 20, 000 to 50, 000 bits. With a single phone line, 8 to 20 seconds

would be required for transmission of a complete picture. If pictures are frequently required, this time interval is too great for satisfactory man-machine interaction at the graphical terminal.

The question of what is done locally versus what is done at the central system acquires a new

meaning with a restricted communication line. The possibility of transmitting parts of pictures and

assembling them locally looks more appealing. Means for compressing data on the communication

line may also be useful, and any additional techniques that can be developed to enhance user response

time or system performance for graphical applications are of interest. The justification for a local display-driving computer, rather than a buffer plus some simple editing logic, is even greater than

for displays adjacent to the central system.

It appears desirable to maintain an image of the general data structure stored in the central

system with a smaller, simpler one in the local system. Changes initiated by the display user can

thus be used to update the local image and immediately change the displayed picture as well as to update the complete data structure in the central system at the same time. Minor changes made by

a display applications program in the central system to the complete data structure may be trans- mitted incrementally to change the appropriate portion of the simplified local display structure. The

changes are immediately incorporated in the displayed image. Only when major changes are made to the central data structure is it necessary to recreate from scratch the complete local structure. It is only at such times that long delays will be experienced when using a restricted communication line.

One simple means for imaging a complex data structure is useful when an over-all picture is composed of sub-pictures and perhaps mioltiple levels of sub-pictures. The basic sub-picture

elements can be stored locally and the composition of these sub-pictures into display images can be

directed from the central system. Sub-pictures, such as schematic representations of coils, fans,

and diffusers, may be identified by a short code and given a position for each "instance" in the displayed picture. It is unnecessary to transmit the detailed display generation information for each

sub-picture every time that sub-picture is used.

Despite use of such techniques, there will still be times when entirely new pictures are to be

transmitted or when such a sub-picture strategy is not useful. At times, a lengthy delay in responding

to a user's request may be inevitable. At other times, however, the technique described in this paper, anticipating a user's needs, may be employed to minimize this delay.

2. The Anticipation Concept

Although several systems utilize anticipatory methods in one way or another, to the author's

knowledge there has not been a general exposition of these methods as a whole. Various anticipatory

techniques can be unified and applied in general to remote computer graphics. In some cases, use of anticipation can lead to substantially improved terminal operation.

38
The concept is essentially the prediction of a remote terminal user's needs and the preloading

of programs and/or data that he may soon require. If, at any giv6n point in a user's interaction with

a system, the number of alternatives for major display changes are minimal and the probability of choosing one or a few of these alternatives is high, then it is possible to anticipate his needs. While

the user is performing local interaction, or when the terminal is idle while the user is thinking, the local computer can request one of the high probability pictures or programs. The request can be

transmitted and the requested pictures returned via the communication line, which is normally idle during this interval between direct central system requests on the part of the user.

One example of anticipation has already been given. The prestoring of sub-pictures locally

in preparation for their assembly into complete pictures is the anticipation of the use of these parts of larger pictures. Transmitting them to the local processor before they are needed makes the trans- mission of full pictures shorter, and can decrease the over-all system response time to a user's request which requires such transmission.

Another example of anticipation is the pre-loading of an entire set of programs and data for a

local computer from a central system in preparation for a particvilar application or class of applications. It has been suggested that for each application the larger computer could assemble a package of programs for the local computer that will enable it to operate as independently as possible

and to require minimal service from the central system.

In both of these examples the success of the anticipation is dependent on the high probability

of usage of the pre-loaded programs and data. It is assumed that if a user requests an air distribution

system design program, for instance, then he will make use of this program, and therefore use the prestored component sub-pictures, before calling another program having a different set of components.

It is likewise assumed that once a user has called for an application program, or has designated an

application class, that he will then be working in this application area for a reasonable period before

switching to another one. He may, however, have made a mistake; or he may change his mind. So

the proability of using the pre-loaded programs and data is not unity.

In general, anticipation is successful when the estimated probability of using data or a program

is sufficiently high. For any given collection of data and programs stored in the central computer

system, there is a probability of usage in the near future associated with each item in the collection.

There must be adequate local storage for that activity requiring immediate attention by the local computer. To take advantage of anticipation, there must be some additional storage for data and

programs of slightly lower usage probability. If this storage is large enough to hold the entire

collection, then the need for central system storage is eliminated. This extreme represents a substantial local investment and will not usually be practical. It is for a local storage size larger

than a few items, but less than adequate for the entire collection that it is useful to anticipate.

When the probability of need for an item is unity, it shall be considered essential for

immediate display terminal operation. If the item is not located locally, it must be requested from

the central computer system, and the user must wait for transmission of the request to the central

system and for receipt of the requested item. The usage probabilities of all presently loaded items,

data and programs, the probabilities of needing items still located in the central system, and the amount of unused local storage must all be considered in determining possible anticipatory requests

by the local computer to the central system.

A request should not be made unless there is an item not located locally that has a high nearfuture usage probability. The communication line must not be needed for direct activity in support

of immediate display operation. Storage must be available for the item locally. In some cases, items may reside in local storage that are not needed immediately and which have a near-future

usage probability lower than these that can be requested. This space may be considered reclaimable

for high probability items as they are received.

Depending on the response time of the central computer to anticipatory requests, it may be

desirable to have several requests pending simultaneously. If a probability indicator is attached to such requests, the central system might give them appropriate priority. Since assigned probabilities are relative, it is possible for the probability of a requested item to change after the request has been

sent to the central system because of continuing display-user interaction. Depending on the system,

it may be desirable, if a significant change occurs, to send an addendum request or even an entirely new request to change the priority given to the previous request. To do this, the local computer

39
should keep a list of pending requests. One important instance of such a change is if the probability

of an item changes from moderately high to unity, i. e. , it is immediately needed. If it has already

been requested, and if the central system does not vary service based on priority, then the local

computer just waits' for the reply. If priority is adjustable, then it might ask the central system to increase the priority of the prior request or might submit a new, high priority request.

The notion of priority in submitting and servicing anticipatory requests can be extended to take into account more than just the expected probability of usage in the near future. It can also

include some measure of estimated size of items being requested, thereby considering transmission

and service delay in obtaining the item and local storage that will be consumed by it after it is received. These delays may be a function of current central system and communication line loading,

which might be measured by the local computer dynamically by noting the response times from the central system. These times may vary according to type as well as length of requested items. All

of these considerations may be included in the priority- determining algorithms used for submitting

anticipatory requests as well as by the central system in servicing requests.

If the prime objective of system design is to optimize the display/user interface, taking into accoiint the limited communication line, but not caring about the burden placed on it or on the central

system, then the primary concern in anticipating is to make sure the various system resources are

available for the highest probability requests when they occur, even if this means abandoning lower

priority requests in progress. Under some conditions, the added burden on the central system of servicing anticipatory requests may be enough to limit the rate of input of such requests and may be

used to limit the generation of these requests by the local computer.

With respect to the communication line from the remote terminal to the central system, two

kinds of configurations may be considered: a dedicated line and a shared line.

3. Anticipation with a Dedicated Communication Line

If a single communication line connects the display terminal with the central system, then

conflicts of line usage may be resolved in favor of optimum user service. This selfish operation on

the part of the local computer may have to be tempered when central system loading requirements

are taken into account.

The nature of typical interaction between terminal and central system is such that the communication line is used normally only in bursts and is idle during relatively long intervals between bursts.

Here is a major system resource going unused- -a situation which can be used to advantage in some

cases by anticipatory techniques.

The resultant higher average usage of the communication line must not disturb the unity

probability item requests. Items needed before man/terminal interaction can continue must be given

highest priority. One way of accomplishing this is to give the local computer control over the communication line in such a way that it can interrupt transmission in either direction. This would ensure that high priority messages are transmitted immediately. Another mechanism is to assign priorities to requests and to ensure that all transmissions on the communication line are short. Short transmissions

can be achieved by selecting short message formats or by segmenting longer messages. In either case,

a highest priority message would be guaranteed of having the line within the maximum transmission

time of a short message or message segment. Highest priority transmissions in both directions need

not be as short as lower probability transmissions.

For the dedicated line the average usage should be higher than without anticipation, and there

will be some increased load on the central system to service the additional anticipatory requests.

4. Anticipation with a Shared Communication Line

Several graphical display users may share a communication line, either by mviltiplexing

through a corfimon local display-driving computer or through a communications concentrator, even

though each has his own local computer. With such shared activity on the line the average usage

will likely be higher even without anticipation, so there may be less unused capacity for anticipatory

use.

40
The same techniques for message priorities, inter ruptable low-priority messages or short

message segments, will allow highest priority requests to take over the line. With the shared line,

however, the effect of the low bandwidth line can be more evident if high priority requests are made

by two display terminals simultaneously. While in the worst case for one terminal a delay of 5 to 10 seconds might occur, this would double to 10 or 20 seconds with just two terminals. Of course, the probability of exactly simxiltaneous requests is low, and the probability of worst case occurrence is usually low with shared line usage.

Sharing of a communications line is a means for increasing the average utilization of an

expensive resource. Since effective anticipation thrives on unused resources, it does not do as well

as the load on the line becomes heavier. The same effect is evident as low priority anticipatory

requests compete for central system service. It is necessary to give higher priority requests from

all commiinication lines better service; otherwise, the system could be saturated servicing a large

number of requests that really should be given only unused central system resources.

5. Potential Applications

A few application areas appear very likely for the use of anticipation techniques. It is not expected that all work in these particular application areas can benefit from these techniques, but

anticipation is a tool to be used as appropriate.

Suppose a user is scanning a large drawing, the entire detail of which is stored in the central

system. He observes the drawing, and may modify it, by looking through a "window" at some part

of the complete picture. In general, the greater the magnification, the more detail shown in the window and the less area of the full picture that can be observed at one time.

Also assume that the local storage is adequate for what is currently being shown in the window

and for the necessary programs to manipulate it and to communicate with the central system. In addition, suppose that some additional local storage is available, but not enough to store the entire

picture with full detail.

The user is scanning the over-all picture. This process consists of a combination of scanning

horizontally and vertically at a given magnification as well as switching to other magnifications as needed. Suppose that a user has been observing a particular area for some time and that no prior

history is available to predict what he might do next. Equal probability may be given all sides of the window- -unless it is at or near an edge of the over-all picture. It is possible to assemble those

picture elements just outside the window in a band as shown in figure 1. The elements in this predictor band are at the same magnification as the current window. Thus, if the user starts moving

in one direction, say to the right, the anticipation program can immediately handle movement the width of the predictor band without communication with the central system.

Once such movement has been initiated, however, the local computer must request additional

picture elements to fill out a new band surrounding the current window. It may be desirable, depending

on user scan speed, available storage, and nearness to the over-all picture's edge, to bias the anticipation band in the direction of movement, as shown in figure 2. When scan movement slows or

halts, estimated probabilities for movement in each direction based on the last and possibly earlier

movements can be used to determine any desired predictor band bias.

The operation of combining part of the predictor band with the present window during the scanning process may be difficult. The effect of scissoring at the window edge, of viewing parts of individual display elements, must be maintained as the window moves over the picture. A similar

problem exists on the opposite window boundary, where display elements or parts of elements must

be removed from the window.

This anticipatory scan at one magnification level may improve system response to the user.

It will not be adequate, however, if frequent magnification changes are requested. If the probability

of changing magnification is high, and if particular zoom levels are more probable than others, all or

part of windows at these levels may be anticipated and stored locally. If both single and multi-level

magnification scanning is possible and likely, then the anticipation routines must take both into account--perhaps doing so dynamically depending on the user's operation. For the first few minutes

of a session the anticipatory routines can either use prior data for this user or use some universal

initial parameters. The anticipator can, thus, be made to adapt to particular conditions. It can

41
directly sense how well it is doing, since it can measure response times apparent to the user and can

adjust anticipation parameters to optimize some measure of response time.

Another potential application of anticipation is for scanning text. Such text might be

descriptive notes associated with working drawings within an interactive graphics application or it could stand alone as separate documentation. Scrolling up or down continuous text is an operation

similar to, but simpler, than the full graphics scanning described above. Figure 3 shows a predictor band above and below a window of viewed text. Each band might include several lines of text and variable predictor band bias can be applied as above once scrolling has begun.

The boundary problem is much simpler, since lines of text can appear and disappear as entities without disturbing the window presentation. Structural text, that is, text having a hierarchial

structure with respect to detail, can be anticipated in a manner similar to that used for multiple

magnification levels, as described above.

Figure 4 shows the possible use of multiple predictor bands for text in various stages of preparation for viewing. Those lines in band A might be ready for immediate viewing, while those in band B are being retrieved from the central system.

Other potential application areas for anticipation include information retrieval from a highly

structured data base and browsing through a collection of documents. If the retrieval process is gradual, such as working down a tree while narrowing in on an area of interest, then nodes may be

reached at which one or more branches have a very high probability of selection compared to the others at that node. Especially in the case when selection of a likely branch requires substantial

transmission to the display terminal, anticipation coiild lead to considerably improved average

response times.

These few potential applications of anticipatory techniques will hopefiilly suggest many others

for which anticipation can be a valuable tool for improving system response. While looking forward to the day in which high bandwidth communications lines will be widely available, this paper proposes some ideas as to how to live with reality for some time to come. Even as such communications

capability is realized, the cost of a high capacity line will still be higher than a low one, and system

design trade offs will take into account the difference at any point in time.

6. References

[1] W.S. Barlett, K.J. Busch, M. L. Flynn, and Machine Communication," I.E.E.E. TransR. L. Salmon, "SIGHT, a Satellite Interactive actions on Systems Science and Cybernetics,

Graphic Terminal," Proc. 1968 ACM June 1967, p. 47. National Conference, p. 499.

[4] F. J. Corbato, M. M. Daggett, and R. C. Daley,

[2] D.E. RippyandD. E. Humphries, "MAGIC-- "An Experimental Time -Sharing System, " A Machine for Automatic Graphics Interface F. J. C. C. , Vol. 21, p. 335(1962).

to a Computer, " Proc. F. J. C. C. , Vol. 27,

p. 819(1964). [5] Schwartz, J. I., Coffman, C. , and Weiss man,

C. , "A General- Purpose Time-Sharing

[3] J.E. Ward, "Systems Engineering Problems System," Proc. S. J. C. C. , Vol. 25, p. 397

in Computer-Driven CRT Displays for Man- (1964).

42
Window

Predictor Band

Figure 1. Uniform Predictor Band

Window

Direction of Movement

Predictor Band

Figure 2. Biased Predictor Band

43
Figure 3. Text Anticipation

44
Computer Graphic Data Structures for Building Design

Marshall D. Abrams

Center for Computer Sciences and TechnologyNational Bureau of Standards

Washington, D. C. 20234

The data structures employed in computer graphics are

studied with the objective of discovering the common aspects of structures now in use. A general graphic data structure is developed

for its educational value and employed to represent simple display

items. The use of list processing languages is discussed; an example

of a special-purpose structure is given

Key Words: Data structure, computer graphics, list processing, pointers, hash coding, subpicture,

associative memory, multi-level storage.

1. Introduction

"Computer graphics" is the general term applied to th-e use of a digital computer to form an

internal model representation of an externally perceived graphical entity. The objective of such

modeling is to extract information from the graphical entity so that it may be modified, manipulated,

or otherwise processed.

After graphical information has been digitized, an organization must be provided for the storage and retrieval of this data within the memory of the computer system. The linear array is the simplest scheme available, but it is not of interest within the scope of this report even though it enjoys wide use in certain classes of applications. Rather, this report will be directed to a discussion of those organizations which represent the relationships among the components of the graphical entity. The relationships which must be represented within this subset of computer

graphics include topology and dependency relationships. It is most convenient to represent such

information in a hierarchical data structure which, in some abstract way, models the external

graphical entity.

Historically, this subset has been restricted to the study of line drawings, but gray-scale and

color representations are currently under investigation. The purpose of the data structure is to facilitate the extraction of intelligence and manipulation of both the image and the information it represents.

A graphical image is a preferred medium of human communication because of the possibilities

inherent for maximum information transfer with minimum effort. Graphical communication is often highly stylized, requiring significant training for both the generation and interpretation of images.

Conventions are established and propagated through architectural education, which enable precise

communication with a minimum effort and non- graphical information.

Since graphical communication among humans is such an easy and effective technique, effort has been expended to extend this communication to digital systems. As with other languages which

are clase to human language and far from machine language, considerable resources must be allocated

to store and manipulate the graphical communication within the digital system.

45
2. Overview of Graphical Data Structures

Both medium and conventions present difficulties associated with the digital representation

of graphical information. The significant attribute of the medium problem is dimensionality.

Graphics deals with two dimensions, often representing three dimensions. High speed primary

memory is usually addressed in a piece-wise linear fashion, therefore a transformation is required

to map the graphical structure into a one -dimensional frame. The information describing a graphical

entity must be stored in such a way that it can be retrieved, manipulated, edited, and used to produce

the desired graphical image.

The pertinent information associated with a graphical entity frequently consists of the geometrical description of the graphical item: scaling, position, and orientation data; relationships and

connections to other items; name and identification of the item; graphical constraints on the item

itself and on its relationship to other items; and non-display (textual) data intimately connected with

the graphical entity.

One of the first decisions to be made in designing a graphical data structure is whether it should be completely general, or tailored to a specific application. The general fixed structure format is usually inefficient of storage since it must provide for unused options ^ [1]. Furthermore,

no matter how general the fixed structure was designed to be, there always exists the pathological case which exceeds the capability of the structure. In such a case, one has no choice but to redesign

the structure, hopefiilly maintaining upward compatibility.

The tailored structure meets all of these objections, but necessitate the effort of construction.

In fact, the existence of general-purpose structures is extremely helpful to the user interested in tailoring a structure to his application. The intellectual effort implicit in the general structure may

simply be transferred to the tailored structure, simiiltaneously modifying the structure to meet the current objectives. Since most graphical data structures are pointer-type structures, with such

pointers being explicit or associatively addressed, the presence of a language designed to work with

such pointers greatly facilitates the construction of a data structure.

While it is certainly possible to build the entire graphical data structure up from scratch, the use of a list processing or associative processing language greatly simplifies the work. In fact, most

of the literature ostensibly devoted to computer-aided design is in fact concerned with data structure. Particular attention is called to references [1], [2], [3], [9] and [11] where the salient features of new

and more established "service" languages are discussed.

The next problem to be considered involves the communication of data to and from the graphical data structure. This data will often be involved in the process of drawing a picture, in modifying an existing picture, or in re-drawing a picture from the data structure. The use of computer graphics in facilitating the convenient use of computers requires that this info rination transferal process not be a burden on the human user [25]. Delay that is annoying to the user should be

avoided; a measure of tolerable delay is the user's concept of the difficulty of the task. While the design of graphical processors is not within the scope of this survey, one cannot ignore the hardware

requirements forced by the desire for rapid response.

The mode of operation is for the user to communicate his desires to the digital system, often using graphical input devices such as light pen,joystick, and mouse; and for the system to respond by

displaying the desired picture on his CRT display. Simiiltaneously the data structure needs to be

updated to reflect the changes resultant from the CRT activity. Rapid response criteria require that

at least part of the data structure must be instantaneously accessible to the user at the terminal [5],

[6]. The size of the local processor and the capacity of the communication line with the main system

determine the extent of the local image of the complete data structure. A final problem is concerned with storage capacity in both the display driving computer and

in the central system. The portion of the data structure represented in the local memory is usually

less than that stored in the central system and may reasonably be restricted to that portion of the structure being displayed. If additional storage is available, this may be augmented by logically

adjacent substructures possibly selected by an anticipator mode algorithm.

Figures in brackets indicates the literature references at the end of this paper.

46
Storage restrictions in the central system require greater attention and careful study. At the time that a structure is created or modified, it is necessary that the storage used not be the limitation

upon the process. Thus, high speed core storage is required. Considering the possible extent of graphical data structures and the core use limitations imposed by the operating system environment,

it is quite reasonable to expect and provide for the possibility of insufficient core storage being available. The solution exists in the form of a paging scheme, but careful attention and re -examination

must be paid to the design and handling of the paging [1[, [2], [3], [IZ].

3. General Graphic Data Structure

The concepts and techniques of graphical data structures will be introduced here in the form

of an example structure. This structure will purposely be kept at a level comprehendable to human

users and modifiable by them. It is not intended that this presentation be exhaustive, but rather

typical and hopefully educational. The organization of the data structure presented here is an

explicit referencing structure, similar to that of Cotton and Greatorex [5], the GRAPHIC- Z system

[4], [7] and GRASP [8]. The structure is certainly not exclusive; additional examples are given the surveys by Gray [9] and Dodd [21]. The structure will be presented in the form of a directed graph;

the mechanism of representing such a structure in a computer memory will be discussed subsequently.

In an effort to minimize the amount of graphics terminal machine language programming

required, especially by users that are not interested in such a level of detail, the commonly used

picture -building elements are provided as building blocks called "basic subpictures" . A basic subpicture may be a single command to draw (display) a point, line, or conic section; it may also be a sequence of such commands to draw a commonly used geometric entity. Such basic subpictures are

often in the form of the "frame" or "skeleton" of an open subroutine, because the essential positioning

information must be supplied by each reference to (use of) the basic subpicture. The basic subpicture

data block must also contain the identification and relative location of the externally accessible

terminals of the subpicture, such terminals being the parts of points of connection to the subpicture

by the greater, outside world. If there are to be constraints on the use of the basic subpicture, these

constraints must also be contained within a block pointed to by the basic subpicture data block.

Within the context of basic subpictures lie all of the characters and geometric figures

directly presentable with a single machine level command, these constitute the "hardware character

set". Commonly used graphical entities may also be coded in graphical control language as a short

program, and provided as a time-saving service. Such basic subpictures provided might include

walls, pipes, conduits, doors, windows, etc. In addition it is desirable for a user to be able to define his own subpictures which are useful for his application. The definition of a subpicture is usually not within the scope of the graphical language -data structure being herein described, but is at the level of graphical control language.

Thus, a picture is the highest level, encompassing all lower constituent levels. These lower

levels being collectively referred to as subpictures. The lowest level is termed a basic subpicture

in that it is the only level which references the display.

Using graph terminology, each basic subpicture is a node in the directed graph which is the graphical data structure. Although it is quite possible for the node block to be of variable size,

herein pointers will be used to reference variable sized data segment blocks. Under these conventions,

a basic subpicture node can appear as in figure 1.

Since a basic subpicture does not possess any absolute frame of reference, it cannot in and by

itself cause any display. It must be referenced by a higher node to be used as a display item. These

higher nodes will in general reference multiple lower nodes, thus building a picture out of previously

created components. The terms "higher" and "lower" relate only to position in a directed graph

drawn to describe the structure and might instead be termed "subsequent" and "prior" respectively.

The construction of a picture is described by a directed graph wherein the top node is the picture, the intermediate nodes are subpictures, and the terminal nodes are the basic subpicture.

A sample graphical data structure is represented in figure Z.

47
While it is fairly obvious that when expressed in computer code the picture and subpicture

nodes need to be represented by data blocks, it may not be immediately clear that the same is true

for the branches connecting the nodes. There is of course a trade-off between the information

associated with the node block and that associated with the branch block. The following selections are somewhat arbitrary although typical [7]. The subpicture node block will essentially consist of pointers to other information containing blocks. Among these blocks is the branch block, wh'ich

deserves special mention.

The branch block contains the necessary transformation on the lower nodes to incorporate

them into the subpicture defined by the subpicture node. Certain blanks in the skeleton frame of the lower level picture must be completed, and other parameters may require systematic modification.

The transformation information consists essentially of displacement, scale, and rotation information.

Since all nodes except the highest "picture" node are intrinsicly referenced to zero, a new

reference displacement must be provided for each instance of use of subpicture and basic subpicture

node. This displacement may occur in a virtual display space having no size relationship to the display viewing area; therefore, an additional displacement calculation may be required in the process of display generation when the segment of the structure is selected for display.

Scale and rotation information must also be provided when constructing the present subpicture out of lower level items. In most applications it is unlikely that the rotation information will require changing after picture -gene ration time, but scale may be a continuously varying parameter.

The analogy of photographic enlargement is accomplished by a modification of the scale parameter.

In certain applications this operation could be the critical item in operation of the facility. This

technique was first introduced as "homogenious coordinates" in Sketchpad [26],

The connectivity of the subpicture constituting the present level subpicture must be separately

treated. It is not sufficient to build a picture by appropriately placing subpictures so that their

terminals coincide. Subsequent parameter change in the branch blocks, or minor malfunction in the hardware, could easily destroy such coincidence. Thus, there must be explicit provision for an ordered relationship among the terminals of subpictures associated within a higher level picture.

For this reason, another block is provided, this being the "connector" block. The connector block is a specific example of a constraint. It is presented as a separate block by virtue of its prevalence. The connector block must identify the lower level terminals to be connected, and it must point to the constraints on such connection. These constraints might include a requirement for coincidence. If the terminals being connected were not coincident, the connector block would be

required to provide a line to form the connection. This line in turn could have attributes such as

intensity and rate of blink. These blocks may be represented by figures 3, 4, 5 and 6.

The design of the pointer scheme is a critical part of any data structure. An excellent discussion is given by Dodd [21], to which the reader is referred. The most simple pointer structure

is the single linked list wherein each block contains a pointer to the succeeding block in the list. The

pointer field in the terminal block contains a special symbol known as the "null pointer" indicating

the termination of the list.

The major shortcoming of the single linked list is the inability to return to the head of the

list without having previously saved the location of this head in a well known location to which

reference might be made.

The single linked list is rarely employed simply because a ring structure may be obtained by

having the end of the list point back to the head. Of course, the head and tail must be suitably flagged

to avoid endless ring-chasing. Another way of returning to the head of the list is to use a doublylinked list possessing a backward as well as a forward pointer, but this involves twice as many

pointers. It is, on the average, twice as fast as the single linked list in returning to the head of the

list.

Since the purpose of rings or doubly-linked lists is to be able to return to the head of the list, or the list pointer, when a success or failure has occurred, the second pointer which the doublylinked list requires is often replaced by a back pointer to the head of the list. To conserve space,

the pointer to the head of the list may not occur in every block, but rather in strategically placed

blocks. Such a scheme is similar to, but simpler than, the CORAL structure [9], [13], [14], [21]. No common name exists for this pointer scheme. It is suggested that it be called a "pie" structure,

based on the diagram of figure 7. 48
A great deal of effort has gone into the development of pointer arrangements, this being the

critical decision in designing a data structure. The structures examined by Gray [9] appear more

different than similar, yet they are all concerned with related problems.

4. Constraints

One of the most important valuable aspects of the data structure for building design application

is the utilization of constraints. As has been mentioned, the terminal block is a form of constraint.

Additional constraints particular to this application are perpendicularity of planar surfaces and

inclusion of subpictures. The perpendicularity constraint assures that as subpictures are manipulated

that they retain the desired form. It is not sufficient to draw such perpendicularity without also constraining the data structure to preserve it under transformation.

Another valuable constraint is inclusion of one subpicture within another. By constraining

windows, doors, pipes and electrical services to remain within a wall it is possible to move the wall during the design process and assure that loose ends are not left dangling.

5. Associative Addressing

The pointers used in the sample structure above are "explicit" pointers in that they address

direct access media [21]. For large classes of problems wherein the data base is subject to random

access, and is possibly stored in multiple levels of secondary and primary memory, content addressability offers certain advantages. The essence of content-addressable, or associative,

memory is that it does not employ explicit addresses. A stored item is addressed by a partial

description of its contents. Current implementations [1], [2], [3], [15] are accomplished by soft- ware, there being serious problems with hardware associative memories [1].

Interactive processors in general, and interactive graphics in particular, can benefit from the use of associative languages. The programming techniques possibly may require a re-orientation on the part of the user, but the poptolarity of associative language is attested to by several sources

[1], [3]. In part, the decision to use an explicit pointer or associative pointer language depends on

the availability, support, ease of utilization, and prevailing attitude at the installation where the user

is to work. The only a priori advantage of associative processing seems to be in the area of utilization

of secondary storage, which is discussed below.

6. Calculated Addressing

Since hardware associative memories have not economically arrived, associative systems

are currently implemented using a calculated addressing mechanism [1], Calculated addresses are

not restricted to schemes which explicitly involve content addressability, but even when they do not, the underlying concept remains the same: namely, that the address of the memory location to be

accessed is determined by an algorithmic operation upon the contents of the pointer. In this usage,

the pointer is more aptly termed a "key" which may be part of information content of the data structure rather than a separate item devoted strictly to pointing. Calculated addressing works by

treating the symbolic information as a set of numeric items which are to be manipulated by a known

and well-defined algorithm to produce a memory location address [1], [21], [22]; such an operation is often called "hash coding".

One of the disadvantages of hash coding is that the calc\ilated address is not necessarily

unique. When two keys are calculated to point to the same memory location an ambiguity, or

collision, occurs. To provide for the advent of collisions, the pointer-chasing mechanism must

check that the contents of the calculated address matches the key used to calculate that address.

One strategy is to treat the contents of the calculated address as a pointer, usually a direct address

pointer, to a location within a block area where all the collision items may be found. It is perhaps

safest if a disjoint area is reserved for this purpose.

49
7. Multiple Levels of Data Structure Storage

The requirements *of fast response to operationally complex requirements and possible large

data structures necessitate that the structure be simultaneously maintained in more than one level of storage, at least in part. First, consider the question of storage in the display.

Early graphical displays required the exclusive service of a large computer system. Today

the trend is to provide a small computer as the local service to each display and to service this local

processor-graphical terminal from the central system only when necessary. There is a whole

spectrum of capabilities of local processor attached to graphical processors. We shall not go into the evolution of such dedicated processors here; the situation has been stated elsewhere [16]. Needless to say, however, the extent and kind of representation of the graphical data structure in the local

computer is highly dependent upon the kind(s) and amount of storage available, the instruction

repertoire, and the speed of the local processor.

The minimum information to be kept in the local processor is the display list which directly

controls the picture presented. The display list is extremely machine -dependent, containing the necessary machine instructions to generate the display. If the computing capability of the local processor is non-existent or extremely minimal it may be necessary to construct the display list in the main system for transmission to the graphical display. In such a case the local processor fulfills only the function of refreshing. In this situation it is impossible to reference the graphical data structure via the display image because the display list has been generated only for display purposes.

In systems with minimum local processing ability, or even in more substantial systems, it seems a waste of an expensive resource to store the display list in randomly addressable core

storage. It appears a better allocation of resources to use rotating storage for the display list. Not

only does this free core storage for programs, but it makes it possible to carry on display refresh as

a parallel process. Recent [17], [18], [19] and not so recent systems [20] have used this approach2.

The next step is to provide an association between the display list and the graphical data structure. Such an association requires a referencing technique from the display list back to the data structure. A pointer scheme can be implemented, but difficulty occurs as to the subpicture

level to be pointed to. Under various conditions the user at the graphical terminal might be

interested in pointing to a picture, a level of subpicture, or a basic subpicture. An automatic safe technique is to have the pointer go to the highest level of subpicture being referenced, with the user

being able to initiate pointer chasing under his control to reach the desired lower level.

If memory and speed allow, part or all of the graphic data structure may be contained in the local processor. If sufficiently large and fast, the local processor could contain the entire data

structure, generate its own display list, and reference the main system only for archival purpose or

for linking to other subsystems. In this form of operation the graphical subsystem can be considered

a "sketchpad" on which various trial drawings are made. When an acceptable one is produced it can

be preserved by referring it to the central computer.

In general, the data structure will be too vast to be contained completely in the graphical

terminal. A compromise is then effected wherein part of the data structure might be transported as needed between the central system and the graphical subsystem. The degree of compromise is a function of the processing capability of the graphical terminal, a subject well discussed by Myer and

Sutherland [16]. For convenient operation the transmission must occur within the user's wait

tolerance. When only part of the data structure is resident in the graphical subsystem, extreme

care must be taken with the pointer to the non-resident parts of the structure. There must be a mechanism for flagging references to non-resident items; there must be a mechanism for enlarging

or contracting the size of the portion of the data structure available. These problems are quite akin

to the multiple -level storage problem in the central system, which shall be discussed next.

But a cycling display carries with it three prices to pay: (1) it is usually slow to access,

(2) it is fixed in size (but the size can be very large), and (3) it can be quite difficult to respond to light pen interactions.

50
The adage of "a picture being worth a thousand words" is magnified in computer representation.

It can easily require many thousand words to store a moderately complex picture. Such storage

requirements can easily consume available high-speed primary memory.

It is certainly possible to design the driving and service program, the "resident system", into minimally- interacting modules. These modules can be brought into core as pages [1] or overlays [12], thus reducing the core storage which must be devoted to the system.

For user-created programs and data structures the situation is different. It is desirable that as few restrictions as necessary be placed on the programmer. Therefore, systems are written which

automatically assign program and data to storage pages [1], [3], [12]. However, there is not total rigidity in these page assignments; variable-sized pages [1] and partial user control [3] helps to adapt

the system to its current use. For the storage of the graphical data structures it is even more

important that the system be given as much information as is available. With complete information it is possible to implement valid anticipation of program needs [3].

8. Sample Use of General Graphic Data Structure

Representing a graphical data structure on paper is an awkward necessity; awkward because

the confines of standard paper size makes it an exercise in topological ingenuity on the part of the writer and parallax error elimination on the part of the reader; necessary because the expository

approach alone generally produces an incomplete information transferal.

The first illustration, in figure 8, is of the structure representing a triangle. This is a

trivially simple structure involving only one node and one basic subpicture. The one node, which is automatically the top (picture) node points to three rings: branch, terminal, and connector. Each

block in the branch ring contains a pointer to the basic subpicture used, namely "point", the X, Y

coordinates of the instance of that point, and a pointer to the next branch block and back to the node

block. Each terminal block contains the coordinates of the terminal relative to the origin of the subpicture (which in this case are selected to be all the verticies), and the forward ring pointer. Each

connector block contains a pair of pointers to the terminals being connected, and the forward ring

pointer. All of the remaining fields contain zeroes interpreted as null pointers. The organization

of the blocks is in conformance with figures 1, 3, 4, 5, and 6.

Let us now use this triangle as a subpicture in building a larger picture. As an example,

consider the hexagon shown in figure 9(a). The triangle used of the subpicture is assumed to have

been drawn in the position shown in figure 9(b). Note that external terminals are denoted by small

circles in these figures.

The data structure of the hexagon is drawn in figure 10. Included is the terminal block ring

of the triangle data structure which is necessarily referenced by the connector ring of the hexagon.

Note the dotted lines representing pointers from the connector ring of the hexagon to the terminal

ring of the triangle.

These dotted lines from connector blocks to terminal blocks associated with another node

block are representations of an amazingly complex pointer chasing mechanism required. The

connector block must point to the branch ring which it accesses by pointing to the branch pointer in the node block. From the appropriate branch block it obtains a pointer to the node block of the subpicture references. Also from the branch block it obtains the displacement, rotation, and scale

data which is necessary for the calculation of location of the desired terminal in the particiilar

instance of use. From the node block pointed to by the branch block it obtains the pointer to the terminal ring associated with that level of subpicture. Finally, that terminal ring is traversed until the particular terminal desired has been acquired.

Since such pointer chasing is not an abnormality in graphic data structures, there must be a mechanism easing such constructions. The pointer concatenation facility of [23], recently

implemented by R. A. Siegler in conversational form as CL6 [24], is one technique which facilitates such pointer chasing.

51
9. The Tailored Graphical Data Structure

As discussed in the overview, it is frequently convenient to construct a data structure which

is tailored to the graphical image to be modeled. The tailored structure can eliminate those features

of the general graphic data structure which do not apply to the problem at hand. The structure of the graphical entity may be taken into account in designing the tailored structure; conditions which were

provided for in the general case may not occur. Therefore, the space reserved for the eventualities

in the general structure could be released for other use in a tailored structure.

Also as discussed in the overview, the use of a list processing language greatly simplifies the work of creating a tailored data structure. Rather than continue with the abstract rendering of geometric figures, the illustrative example of a tailored data structure will be concerned with compute

program flowcharts with which the author has been working.

10. Sample Tailored Graphical Data Structure

Our illustrative example will be a data structure used for the (internal) representation of flowcharts. The data structure is created using the list processing language CL16 [24], a version of

Ij6 [23]. The defining portion of the program is exhibited as figure 11. Since the reader is most

probably not conversant in L^, the operations which are pertinent to the creation and use of the data structure will be discussed in detail.

One useful feature in is the ability to define the location of a "field" within a "block" of consecutive computer words. A field, once defined, may contain a pointer to another block, an

arithmetic value, or anything else the programmer desires. A field is designated by a single letter name. The complete specification of a field includes the word in the block in which the field is to exist, the name of the field, and the inclusive bit boundaries constituting the field within the computer

word.

The format of the field definition command is

( <word>, D, <field name>, <bit bound 1>, <bit bound 2>)

where <word> , <bit bound 1> , and <bit bound 2> are all integers indicating the relative work in the block, and the inclusive bit botindaries within that word. < field name > is the single letter name

by which the field is symbolically referenced.

Like most programming languages, provides the programmer with a means for inserting

comment lines for internal documentation. In such comment lines must contain an asterisk in column one and are ignored by the translator. In figure 11 the first six lines numbered 1 are comment lines which explain the usage of the fields defined in line 0.

In the program, line 0 defines three fields in word zero: field I, the block number, bits 31 through 36; field B, the first forward pointer or message pointer, bits 1 through 15; and field C, variously used as the back pointer, the input block pointer, or the count of the number of words in the message, bits 16 through 30. The meaning attributed to field contents is the programmer's

responsibility. Note also that field definitions are non-unique, for line 4 defines field J to be bits 1 through 36 of word 0.

The ability to define those fields appropriate to the specific application is only one advantage

of the tailored data structure. It is used in this example to define fields in words 0 through 2 of the block. Another advantage of this tailored data structure is the ability to define variable size blocks,

the size being determined during program execution. This feature permits optimum memory

utilization.

In L^, the procedure of defining a block is performed by the "get" operation having the format

( <block name > , GT, <block size> )

52
where <block name> is the single letter, called a "bug", which points to and thereby identifies the block, and <block size> is the number of words in the block which is being gotten.

In line 5 of the program, two fixed length blocks are obtained; block E being 3 words long and

block B being 65 words long. Skipping a few details, in line 12 a line of up to 65 characters is read

into B. This block is scanned for the end of line character, the carriage return, in lines 13 thtough 16, keeping count of the number of characters in the line. In line 17 a new block D is gotten having length

C, where C was determined by the counting of lines 13 through 16. In essence, block B was used as

a fixed size input buffer from which the contents are transferred to the custom sized block D. We could, if we chose, continue this detailed analysis of l6 as used for this application

program. The author does not believe that to do so would be of further educational benefit. Those

interested in following the workings of L;6 are referred to the defining paper by Knowlton [23].

In addition to the main pointer structure an auxiliary structure is provided. This auxiliary structure consists of one word blocks, the fields of which are perforce identical to those of the zeroth

word of the main structure as shown in figure 12. This second string forms a linear chain most

easily searched and is only used for retrieving blocks in the main structure. This second string is created on line 18 of figure 11. An example of the application of this structure is given in figure 13. The flowchart segment represented is drawn in figure 14.

11. Refe:

[1] Feldman, J. A. and Rovner, P. D. , An ALGOL

Based Associative Language, Comm. ACM 12, No. 8, 439-449 (Aug. 1969).

[2] Rovner, P. D. , and Feldman, J. A. , The

Leap Language and Data Structure, Proc. IFIP Congress 1968, C73-C77.

[3] Evans, D. and Van Dam, A., Data Structure Programming System, op. cit. , C67-C72.

[4] Ninke, W.H. , A Satellite Display Console

System for a Multi-Access Central Computer,

op. cit. , E65-E71.

[5] Cotton, I. W. and Greatorex, F. S. , Data

Structures and Techniques for Remote Computer Graphics, Fall Joint Computer

Conference, 1968, 533-544.

[6] Kulsrud, H. D. , A General Purpose Graphic

Language, Comm. ACM, _H, No. 4, 247-

254 (April 1968).

[7] Christensen, C. , and Pinson, E. N. , MultiFunction Graphics for a Large Computer

System, Fall Joint Computer Conference,

1967, 697-711.

[8] Thomas, E. M. , GRASP- -A Graphic Service

Program, Proc. ACM National Meeting,

1967, 395-402.

[9] Gray, J. C. , Compound Data Structure for Computer Aided Design: A Survey, op. cit.,

355-365.

[10] Wexeblat, R. L. , and Free dman, H. A. , The MULTILANG On-line Programming

System, Spring Joint Computer Conference, 1967, 559-569.

[11] Van Dam, A., and Evans, D. A Compact

Data Structure for Storing, Retrieving,

and Manipiolating Line Drawings, op. cit. , 601-610.

[12] Bobrow, D. G. , and Murphy, D. L. , Structure of a LISP System Using TwoLevel Storage, Comm. ACM, 10, No. 3, 155-159 (March 1967).

[13] Sutherland, W. R. , The On- Line Graphical

Specification of Computer Procedures,

Ph.D. Dissertation, M. I. T. (Jan. 1966).

[14] Kantrowitz, W. , CORAL Macros -

Reference Guide, Lincoln Labs . (1965).

[15] Feldman, J. A., Aspects of As sociative

Processing, CFSTI AD 614-634 (April

1965).

[16] Myer, T. H. , and Sutherland, I.E., On

the Design of Display Processors, Cormn.. ACM, U_, No. 6, 410-414.

[17] Rippy, D.E., MAGIC U - Graphical

Display Terminal Interfaced to a Digital

Computer, Computer/Display Interface

Study, Final Report, AD 699366 (April

1969).

53
[18] Gear, C. W. , An Interactive Graphic Modeling

System, Dept. of Computer Science, Univ. of ni. Report No. 318 (April 1969).

[19] Hostovsky, R. , Design of a Display Processing Unit in a Multi- Terminal Environment, op. cit. , Report No. 343 (July 1969).

[20] Rippy, D.E., and Humphries, D.E., MAGICA Machine for Automatic Graphics Interface

to a Computer, Fall Joint Computer Conference, 1965, 819.

[21] Dodd, G. G. , Elements of Data Management

Systems, Computing Surveys, J_ , No. 2, 117-133 (July 1969).

[22] Morris, R. , Scatter Storage Techniques,

Comm. ACM, 11, No. 1, 38-44 (Jan. 1968).

[23] Knowlton, K. C. , A Programmer's Description of l6. Comm. ACM, 9, No. 8 (Aug. 1966).

[24] Siegler, R. A, , The CL6 Conversational

List Processing System, Computer/Display

Interface Study, Final Report, AD 699366

(April 1969).

[25] Miller, R. B. , Response Time in Man

Computer Conversational Transactions,

Fall Joint Computer Conference, 1968,

267-277.

[26] Sutherland, I.E., SKETCHPAD: A ManMachine Graphical Communication System,

Spring Joint Computer Conference, 1963.

FIGURE 2. SAMPLE GRAPHICAL DATA STRUCTURE

54
Identification as Connector Block

Pointers to Terminals

Blink Rate, Constraints

Pointer to Next Connector Block

Figure 3. Connector Block

Identification as Branch Block

Name of Branch

Pointer to Lower Node

Displacement, Rotation and Scale of Lower Node

Pointer to Non-display Information

Pointer to Next Branch Block

Figure 4. Branch Block

Identification as Node Block

Name of Node

Pointer to Terminal Block

Pointer to Branch Block

Pointer to Connector Block

Pointer to Non-display Information

Figure 5. Node Block

Identification as Terminal Block

Relative Location of Terminal

Pointer to Next Terminal Block

Figure 6. Terminal Block
BRANCH ma

POINT I

X| |Y| I 0 I 0

BRANCH BLOCK POINT 2'

X2

I Y2I 0 I T

BRANCH BLOCK

POINT 3

X3 I Y3 I 0 I O"

' POINT" DISPLAY LIST

NODE Bli3CK

•TRIANGLE"

BASIC SUBPICTURE

•• POINT' TERMINAL BLOCK

0 0

TERMINAL BLOCK h

TERMINAL BLOCK

Y2

TERMINAL BU3CK

"3 ^3

CONNECTOR BLOCK

CONNECTOR BIflCK

0 0

CONNECTOR BLOCK

FIGURE 8. DATA STRUCTURE OF A TRIANGlf

(0.)

(b.l

FIGURE 9. HEXAGON, (o) COMPOSED FROM TRIANGLE, (b) TERMINALS DENOTED THUS: (^)

56
57
0 SETUPl :(0,D,C, 16,30)(0,D,B,1,15)(0,D,I,31,36)

1 * I z BLOCK NUMBER

I * B : FORWARD PR #1

1 * B = MESSAGE POINTER

1 * C = # WDS IN MESSAGE

1 * C : BACK PR

1 * C : INPUT BLOCK PR

1 : (

I ,D, A, 1 ,30) ( 1 ,D,D,31 ,36)

2 * A: BOX TYPE

2 * D : # FWRD PR

2 : (2,D,E, 1

, 15)(2,D,F,16,30)(2,D,G,31 ,36)

3 * E : FWRD PR # 2

3 * F : FWRD PR # 3

3 * G : # CHARS

3 : (3,0, H, 1,36)

A * H : ASCII WORD

A : (0,D, J, 1 ,36)

5 :(E,GT,3)(B,GT,65)(X,GT,4)

6 * X IS SUBR C<M BLOCK

6 * E : 3 CHAR COMMAND BUFFER

6 * B = INPUT STRING BUFFER

6 * N : MESSAGES

6 * M = POINTERS TO MESSAGES

10 F0UND3 : (Z,E,5)(D0,MSG)(65,RL,B) (EJ,CP,3,B)

11 : (F0UND3,D0,B0XTYP)

12 * C IS LOCAL POINTER

12 CONTNT : (Z, E, 7) (DO.MSG) (65, RL,B) (Y,P,B) (C,E,2)

13 LOOPl : (C, A, 1 )( Y, A, 1) 14 IF(YJ, EO, 432000000000) : FOUNDl

15 IF (C,G,67) : STOP

16 : LOOPl

17 FOUNDl : (C, A, 1) (D,GT,C) (DD,E, 1 ) (DO,FORPTR) (DA,E,XD)

18 : (DI,E,G)(HC,P,D)(HI,E,G)(H,GT, 1,HB)(HBB,P,H)(C,S,3)

19 :(DG,E,C)(C,E,0)(Z,P,D)(Y,P,B)

20 IF(DA,E,4): (DD,E,3)

21 * H IS BLOCK OF POINTER STRING

21 L00P2 :(ZH,E,Y.J)

22 : (Z, A, I ) (C, A, 1) (Y, A, 1

)

23 IF(C,G,DG) : (G, A, DNEXT?

24 : L00P2

25 FINDF :(I,P,JB)

26 * I IS TEMPORARY POINTER

26- L00P3 IF(II,E,F):(D,E,0)FORPTR

27 IF(II,E,0): (Z,E,3)(D0,MSG)FAIL

28 : (I,P, IB)L00P3

Figure 11. Portion of CLi6 Program

58
36 I 31 30 C

16 15 B

,

36 D 31 30 A 1

36 G 31 30 F

16 15 E ,

36 H 1

0

FIGURE 12. DEFINED FIELDS FOR FLDWCHART DATA STRUCTURE

5

DECISION

ARITHMETIC

0 0

ARITHMETIC

5

1 SUBROUTINE

0 0

INPUT

ARITHMETIC

0 0

FIGURE 13. FLOW CHART GRAPHICAL DATA STRUCTURE

59
FIGURE 14. FUDWCHART REPRESENTED BY DATA STRUCTURE

60
A Systems Model for Environmental Design of Buildings

C.L. Gupta

Division of Building Research

Commonwealth Scientific and Industrial Research Organization

Melbourne, Australia

This paper presents a computer-oriented design model for evolving

optimized building performance specifications to achieve satisfactory

indoor environment. The interactive aspects of environmental design

with respect to thermal and lighting sub-systems are considered in terms

of fifteen design variables specifying insulation, inertia, glazing,

shading, siting, and surface treatments. The criterion of optimality

is chosen to be minimum design cooling load.

The method consists in coupling an optimization program based on a simplex search type technique to an analysis program for buildings

subjected to variable climatic and use conditions. Provision has been

made for varying the environmental performance criteria and for imposing

constraints on the design variables.

An open plan office is chosen as an example for application of this model. Results obtained on a CDC 3600 computer are presented.

Key Words: Air-conditioning, building design, computer,

daylighting, environment, indoor climate, load calculation,

optimization, performance specifications, thermal behavior.

1. Introduction

In any building design it Is necessary to consider the interaction of environment and building,

for the primary role of the latter is to modify the environment. In the most general case, this would

require an understanding of how the outdoor environment affects and is affected by a building or a complex of buildings, and their interaction to produce the indoor environment. Not much is known about

how the buildings affect their external environment, and so it is usually considered to be specified for

a given design problem. However, the provision of feasible solutions to the creation of a desired

indoor environment generates many inter-related problems, which require careful handling of a number of inter-dependent systems such as thermal, visual, and aural and a complex array of interacting variables

defining building materials and components, shape and orientation, occupancy, fenestration, user requirements, and similar factors for their solution. The existing design practice cannot handle these interactions adequately because of lack of integration and generality in its structure. In addition,

there are too many empirical assumptions based on rationalization of past experience, which may no longer be valid for significant design problems faced in the context of radical and rapid changes in technology and society. On the other hand, availability of large computers and development of system

engineering techniques specially suited to deal with interactions, strongly suggest the formulation of a system model for the environmental design of buildings. Such a model can be further linked to other

aspects of building such as structural and economic, and is ideally suited for efficient evolution of an optimum environmental design with respect to some chosen criterion or a set of allied criteria.

A systems approach to optimum thermal design has been developed by Gupta {1}^. It has been

utilized by Gupta and Spencer {2} to optimize the thermal design of panelized constructions for residential use. As a further step towards the objective of optimum integrated environmental design,

interactive aspects of thermal and lighting sub-systems as they affect the design of building envelope

have been incorporated into the systems model outlined in the present paper. The objective of the formulation is to provide optimum performance specifications and the effect of perturbation in these on the chosen criterion of optimality at the sketch plan stage.

Figures in brackets indicate the literature references at the end of this paper.

61
2. Basic Design Philosophy

Indoor environment in a building is primarily influenced by four basic elements and their interactions : outside climate, the building structure, the indoor space and contents, and the occupancy.

For environmental evaluation of architectural design alternatives and optimization of design variables

with respect to performance, it is advisable to perform unsteady-state analyses for a cycle of repre- sentative design climatic data. Three-hourly values of air temperature, wind velocity, and solar radiation for a minimum period of three days, and sunlight and clear sky illumination values for a specified solar altitude are used for the outdoor climatic data relevant to the building location.

For the thermal sub-system, three-hourly values of indoor environmental temperatures {3} and cooling loads are computed by employing a distributed thermal network representation of the building and using the harmonic method of analysis {4,5}. For load estimation, allowance is made for considering

either constant indoor environmental temperatures or a known variation permitting temperature swings. The particular method of analysis chosen is more accurate and economic in use of computer time than the finite difference methods {6}, but it cannot consider temperature-dependent properties or variable network representations. The design variables are considered in section 3.2 and the calculation method is discussed in section 4.1.

For the lighting sub-system, calculations are made of the distance from windows at which a given

level of natural illumination will be available on different sides of the building for a reference solar altitude of 30 and a clear design sky proposed by Kittler {7}. These distances determine the floor area over which artificial lighting is required in the interior of the building. In this way, relative

contribution of natural and artificial lighting to cooling loads can be taken into account. Direct sky

component and sunlight, internal reflected components, ground-reflected sunlight and daylight are taken

into account, but obstructions due to other buildings are not considered in any of the sub-systems.

The computational scheme is oriented to office buildings with relatively large window areas, and as yet

does not include the computation of glare index. The design variables are considered in section 3.3 and the calculation method is discussed in section 4.2.

For the purposes of system optimization, some of the system parameters are kept fixed as specifications for a given problem and the rest are allowed as design variables within explicity stated upper and lower constraints. These constraints are usually governed by economic and aesthetic considerations

and by requirements imposed by bye-laws, materials, land availability, and such other factors not directly taken into account. The limits imposed by mutual interactions of these design variables, if any, are also taken into account in terms of implicit constraints. The design alternatives are generated within the computer program and the objective function based on performance criterion or criteria is evaluated. In this design model the objective function is chosen to be degree of discomfort {1,2} for unconditioned buildings and peak cooling load for the conditioned ones. A cost function

is currently under development. As compared to an intuitive process or exhaustive enumeration scheme

{8,9}, an optimization scheme generally makes it possible to evolve an optimal design solution in a much

smaller number of evaluations. The technique adopted for the present paper is discussed in section 5. A schematic diagram showing a building as an environmental system is shown in figure 1.

3. System Design Variables

3.1 General Considerations

The system provides for optimizing up to fourteen design variables, any one or more of which can be fixed if desired. For simplicity, a rectangular plan with specified floor area on an exposed site is considered. As such, the model is applicable to a residential building as a whole, a single storey of an open plan multi-storey office building, or any one air-conditioning zone of big buildings. In detailed estimation of design loads or lighting, the calculations can be done room by room, if desired.

3.2 Thermal Design Variables

a. Materials

The thermal penetration coefficient, P, which is defined as the product of thermal conductivity, k, density, p, and specific heat, c, is utilized as the basic thermophysical property defining the materials. Values for the insulating materials in the roof and walls and for the outer skin material

of the walls are considered as design variables. The remaining materials such as floor, roof type, and

inner lining of walls are initially specified for the type of building being optimized. The outer skin

of the wall is considered in particular since it provides the major variable component of thermal

inertia in constructions popular in Australia. The model is flexible and can consider materials other

than these.

62
b. Components

For the three materials specified in section 3.2(a), thicknesses are also the design variables.

To convert these thicknesses into thermal resistances, a predefined linear relationship between pene- tration coefficient and conductivity is used. The locations of these components in the buildisng ele- ments are fixed initially. The final specifications list thermal resistance as well as thicknesses,

so that departure of individual materials from the P-k relationship can be taken into account.

c. Spatial Envelope

The design variables fixing the configuration define the areas of various elements constituting the envelope and the volume enclosed therein. The variables are orientation, aspect ratio (defined as equal to length/width) , and ceiling height, and these determine availability and extent of natural

lighting and incidence of solar radiation. For a given floor area, the aspect ratio and ceiling height

determine the exposed envelope area, and the volume of air required for ventilation or air-conditioning.

The minimum number of air changes corresponding to lower ceiling heights is governed by health require- ments and also by the effect of ceiling height on the flow jets from inlet diffusers or grills {10}.

d. Glazing and Shading

The area of glazing per unit wall area and its shading coefficient are considered as design

variables. All four walls are considered to have the same percentage of window area unless specified

otherwise. The total glazed area as a percentage of floor area is checked so as to remain within the constraints imposed by bye-laws or the psychophysical requirements of view and vision {11}.

e. Surface Treatments

Two design variables specify the solar absorptivity of the outdoor surface of opaque elements such

as roof and walls. These determine the contribution of solar radiation to the design outdoor environ- ment denoted by sol-air temperatures.

Internal furnishing, furniture, and partition areas are not considered as design variables and

their resistance-capacitance values are prespecif led . However, their areas are fixed relative to the floor area and ceiling height, and although these ratios may be fixed the actual values would vary

within an optimization run. These masses are very important in relation to the internal lighting loads and direct sunshine through windows. Internal convective loads due to occupancy are specified per unit

floor area for any given problem.

3.3 Lighting Design Variables

The design variables common to thermal and lighting sub-systems are orientation, shape, celling

height, and window area. Internal luminous reflectance for ceiling, walls, and floor and for outside

ground can be fixed as problem specifications. The design daylight factor beyond which artificial

lighting would be required and the design solar altitude can also be specified. The only design

variable considered is luminous transmittance of windows. Since this is usually related to the shading

coefficient, check constraints are imposed so that the ratio of the two remains within the limits for available types of shading arrangements.

4. Methods of Analysis

A hierarchy for environmental performance of buildings comprising thermal performance, heating or cooling, and daylighting branches, is shown in figure 2. In the present system simulation program, the design variables are considered from the lowest level and the optimization is performed on the basis of

a definitive part of the building, as indicated in section 3.1. The following methods of calculation

for thermal and lighting sub-systems have been programmed and are used as components of the system

simulation on a digital computer.

4.1 Thermal Sub- system

The basic method of calculation used is due to Muncey {4}. For sinusoidal heat flow and temperatures, the indoor environmental temperature, t is represented by

n

lA t^ (1/P^p - W

^ ]A~(P^^7p7^rT7B~(Q^^7Q^

63
where exp (jwt) is air or sol-air temperature on a typical external heat flow path of area A and transmission matrix (P), W exp (jwt) is the heat flow to the inside air, B is the area of an internal

path having transmission matrix (Q) for half the thickness, and the summation is over the parallel heat

paths constituting the building. Transmission matrices (P) and (Q) are of the type

P =

P P

11 12

^11 ^22

(2)

These are obtained by matrix multiplication of the matrices for individual layers in the relevant heat

path, which are of the form

Cos Z - { (R sin Z)/Z}

{ (Z sin Z)/R} Cos Z

The complex argument Z is given by

Z = (jwCR)

, where R is the thermal resistance and C is the thermal capacity per unit area of the layer.

Internal radiant loads can be handled by using a heat flow multiplier developed by Muncey and Spencer {5}. The internal environmental temperature t , under practical situations, is obtained by

superposing eq. 1 for a reasonable number of frequencies to get

m=n

^ea "

^

^""P ^^""^^ m=o

(3)

where 2Trm/T, and T is the number of hours in the design

climatic cycle.

The degree of discomfort, D, can be computed by using the equation in {2}.

°4 J

<-

day

hours

AD night

hours

(t -t ) ea un

AN

(4)

where N

un

ADAN+

= number of ordinates in the design climatic cycle at which the temperatures t are known in a cycle.

= indoor environmental temperature at some hour

= daytime preferred temperature for comfort

= upper limit for night time comfort

= half the variation allowed in daytime

= variation allowed in the night time

(only positive values to be considered)

For load calculations to maintain an indoor environmental temperature t^^^, the component for the frequency w, (L)^, is obtained by the equation

= -[ {^At^ (~) -W} -t^ {^A(^ll/^12) + ^B('^21/^22)}] (5)

If the indoor temperature t has already been computed, eq (5) reduces to

(L). -(tg-tj^) {);a(^11/^12) + ^B('521/^22)> (6)

where

Ra I exp (jwt) m=o

The sign convention is such that negative values of load mean cooling loads and positive values mean heating loads.

4.2 Lighting Sub-system

As in the thermal sub-system, clear day conditions are assumed for design. The analysis tackles

the inverse problem of determining the distance, D, from the window at which a prespecified level of

64
natural illumination, E , is available in the work plane and beyond which artificial lighting would be required. A flux methSd similar to the lumen method {12} is used except that tabulated coefficients

of utilization cannot be used« in optimization studies. This problem is resolved by treating the internal reflected component and the direct illumination from the sun and the clear sky separately.

The intensity of sunlight normal to the beam, E , the design diffuse illumination on a horizontal

surface from the clear sky, E^, and visible reflectances are specified for the problem.

Instead of considering it as a time-varying problem like the thermal sub-system, a design solar altitude with respect to the horizon is fixed for lighting. This is a reasonable assumption, since it has been shown by Hopkinson, Petherbridge, and Longmore {13} that for lighting in clear sky areas, where

reflected sunlight is very significant, the daylight and reflected sunlight components so adjust during

the working day that the sum of their contributions to internal lighting is practically constant.

To calculate natural lighting, the first step is to determine the amounts of direct and reflected

sunlight and skylight on any wall surface. The following equations have been used for the purpose:

= E^[ A + {B + C cos (a - a^)}"*"] (7)

E = E cos 6 cos (a - a ) (8) oV n s

^SV = 0.5 R^.E Sin 9 (10)

(j n

^'^'1 = cos 1 {(sin 6 - sin L sin 0) / (cos L cos 9)} (12)

where E^ is the direct sky illumination, E^^ is the direct sunlight, is the ground-reflected

skylight, and is the ground-reflected sunlight, a is the bearing of the normal to the wall, is the solar azimuth, 9 is the specified solar altitude, 6 is solar declination, L is the latitude of the

place, is the uniformly reflecting ground reflectance, and + means only positive values to be taken. The reflections from neighboring facades have not been taken into account but direct sunlight has been

allowed for walls having (a-a ) less than 60 . For solar altitude of 30 , values of A,B,C are found

to be 0.40, 0.16 and 0.67 respectively for the clear sky {7}. These are based on computations by

Krochman {14}, and the values of E^ so computed are in good agreement with those recommended for summer in the lES Lighting Handbook {12}.

The internal reflected component (I.R.C.) of natural illumination is computed by using the splitflux principle {14} applied to clear sky conditions. The computation is oriented to an open plan

office so that the average internal reflectance is determined for the whole Internal surface area under consideration. The actual component is determined for windows on each wall separately, and with

no constraints imposed by partition walls and no contributions from windows on other walls.

With these assumptions,

I.R.C. = T. K A^ [(VEsv> + ^V\SV^ \^ / ^13)

where T is the diffuse luminous transmittance of the windows (a design variable), K is the maintenance

and frame reduction factor, usually taken as equal to half, A is the total window area in any wall, K is the floor reflectance, is the ceiling reflectance, A^ is the total internal surface area of the building envelope, ceiling, and floor, and R^ is the area weighted average internal reflectance.

The required depth, D, is now obtained by solving the following transcendental equation by Newton Raphson's method {15}

E = I.R.C. + T.KE ftan"! (^) - { (D) (H^+D^)"^} tan'^ { W(H^+D^

) "^} 1 (14)

o w >• w J where W is half the window width and H is the window height above the working plane.

From these values of D, one for each side, the area for artificial lighting is calculated. The uniform luminance assumptions {13} implied in taking the bracketed expression in eq (14) are fairly

justified when reflected sunlight makes a dominant contribution to indoor lighting. It has not been

considered worthwhile to do more sophisticated lighting calculations for these optimization studies at the present stage, but it may be done later at the detailed plan stage or when the groundwork and procedure for the systems model proposed in this paper have been established in practice.

65
5. System Design and Optimization

5.1 Design Problem Formulation

The environmental design of buildings has been formulated in terms of the independent systems design

variables P., as described in section 3. There are also dependent system variables, Q. such as the ratio of luminous transmittance to the shading coefficient of windows, and total wall thickness, which

have to be considered in evolving practicable design solutions. As stated in section 1, the dependence

of external microclimate on design has not been considered in this model and is prespecified as input;

The response variables, R , such as indoor environmental temperature and daylight illumination determine

the performance level. Constraints are usually placed on the variables P. to satisfy the requirements

of bye-laws and the client's brief, on Q . to ensure practicality and economy, and on R^^ to satisfy

predefined environmental performance criteria. The mathematical formulation of the problem is as follows

Let P, Qj R be the column vectors defined by equations:

P = {P.} ; 1

i = 1,2, m^ (15)

Q

= (Q.> ; j = 1,2, m^

R = k = 1,2, m^

where Q = Q (P)

R = R^ (P,Q,F)

- R (P)

for a given outdoor climate vector{F}and m^^, m^, m^ are the number of independent, dependent, and response variables. If the lower and upper bounds vectors L and U be such that

{l}< (P, Q, R) <{u} (16)

where P, Q, R is the complete set consisting of vectors P, Q, and R, the design problem is to find a vector P consistent with eq (16), which defines the feasible design space. Obviously, there are many

possible design solutions corresponding to the multitude of points enclosed in this space and in conventional practice; only a very few intuitively selected alternatives are evaluated and one of these is chosen.

5.2 System Optimization

The object of formulating a systems model and optimizing it is to select the best or near best of an infinite number of possible designs without having to evaluate too many of them. First of all, an objective function, S, has to be defined which is design dependent and is related to the merit of the system. For environmental design, this may be minimum overall cost or minimum design cooling load for satisfactory environmental performance when artificial control systems are available, or minimum degree

of discomfort for unconditioned buildings. The optimum design problem consists in selecting a vector,

P, so that S is optimized subject to eq (16).

The choice of optimization procedures is generally governed by the nature of the function S and the constraint vectors L and U. The environment design problem formulated in sections 2 to 5.1 is a constrained optimization problem with a non-linear objective function and linear inequality constraints.

Also, it is desirable not to have to calculate the derivatives of the objective function to suit the methods of analysis adopted. Further, the sensitivity of the optimum solution with respect to perturbations in the design variables is more significant design information at the sketch plan stage rather

than the attainment of a global optimum. On account of these considerations, a sequential simplex type

search technique {16} has been selected. The search proceeds from an initial point, which may represent the best judgment for the values of design variables in the absence of optimization, or may be generated pseudo-randomly in the feasible space. According to Mitchell and Kaplan {17}, a simplex of points is generated around this initial point and the values of objective function are determined for each of these points by a simulation program incorporating methods of analysis of section 4. The optimization procedure continues through successive changes of the simplex position so that the worst vertex is replaced by another one in a favorable direction {16} in any single move. The process is continued until three successive changes do not modify the value of the objective function at the simplex centroid by more than a desired amount governed by precision. The best point is obtained after

a specified number of such iterations, which use the best point from previous iteration as the initial

point for the next run. The result of optimization consists in the best value obtained for the objective function, the corresponding optimum design solution comprising a set of values for the design

variables and the values of the objective function at the vertices of the simplex around this point.

66
It is to be noted, however, that the search methods do not guarantee the evolution of a global optimum.

In physical terms, the optimum design values correspond to the desired performance specifications,

and variations in the objective functions at the vertices indicate the sensitivity of this performance

to the largest permissible perturbations in the specifications, varied singly around the best design

solution.

6. Demonstration Example

As an example of application of the systems model formulated in sections 2 to 5, the top floor of a multi-storeyed building located in Sydney (latitude 33.8 south, longitude 151.2 east) has been considered for optimization. The objective function has been chosen to be minimum peak cooling load (sensible part only) for a typical climatic design cycle during summer {2}. Criteria for satisfactory

indoor environment specified that the indoor environmental temperature be maintained at the preferred

temperature for Sydney, 73 F with a2permissible rise of 3 deg F in the afternoons and an artificial

lighting intensity of 75 lumens ft to be available^on the horizontal work plane in all areas where the design daylight intensity is less than 30 lumens ft

An open plan office is considered, with a central service core occupying 10 percent of the floor

area. The roof is designed to be a six layered structure with provisions for an acoustic ceiling, 1 ft thick air space, 6 in concrete deck, insulation to be designed, waterproofing layer, and 2 in of concrete

topping. The floor is a similar structure except that there is a carpet instead of the three top

layers of insulation, waterproofing, and topping. The walls are specified to be rendered inside and have three layers, two of which are design variables. The conditions of occupancy provide for 30 persons on each floor and a fresh air supply rate of three air changes per hour including infiltration.

Windows are considered to be provided on all four sides of the building, which is assumed to be located

on an exposed site. Nominal values of the other parameters which constitute the set of design

variables, and their upper and lower limits, are shown in Table 1.

Table 1. Input values for design variables of an open plan office building

Independent Design Variables (P.) Nominal Lower Upper

value limit limit

1 Wall, thickness of outer skin (in) 4.0 3.,0 7.5

2 Wall, penetration coefficient of outer skin (P*) 300.0 180,,0 330.0

3 Wall, thickness of insulation (in) 1.0 0,,01 2.0

4 Wall, penetration coefficient of insulation (P*) 0.15 0.,07 0.25

5 Roof, thickness of insulation (in) 3.0 2.,0 5.0

6 Roof, penetration coefficient of insulation (P*) 6.4 3.,0 24.0

7 Roof, absorptivity 0.7 0,,5 0.8

8 Wall, absorptivity 0.7 0,,6 0.8

9 Window shading coefficient 0.5 0,,4 0.6

10 Aspect ratio (north wall/east wall) 0.71 0,,5 2.0

11 Window, light transmittance 0.1 0,,1 0.8

12 Glazing ratio (glazed area/wall area) 0.5 0.,3 0.6

13 Orientation (t^ue bearing) 082 082 082

14 Floor area (ft ) 3264 3264 3264

15 Ceiling height (ft) 9 9 9

Dependent Variables (Q^)

1 Wall thickness (P^^ + P^) 5.0 2,,9 8.0

2 Window area/floor area 0.32 0.,1 0.5

3 Light/heat ratio (Pj^^/Pg) 0.2 0.,2 2.0

* p. Penetration_coef f icient = thermal conductivity x specification x density

(BTU in ft hr deg F)

The convergence criterion for the optimization program 'Design' is fixed so that if three conse- cutively occurring design alternatives indicate peak cooling loads within 0.02 tons, the iteration is terminated. Two such iterations have been provided for in the case of this example. The optimized

specifications and the sensitivity analysis are arrived at after about 150 design alternatives have

been examined by the computer. The CDC 3600 computer uses about 20 minutes of machine time for a com- plete run of this type. Table 2 contains a set of optimized specifications and values for peak

cooling load ratios when each of the variables is successively put equal to the lower and upper limits

(Table 1), the others being kept fixed at the optimum level. The peak cooling load for initial

nominal design is 6.6 tons and it is reduced by 37 percent for the optimum design. Peak cooling load

67
ratios are the actual peak cooling loads divided by the value for optimum design.

Table 2. Optimization results for an open plan office building

Sensitivity analysis

T, c -c- ^- ^ ^- (Peak cooling load ratio)

No. Performance specifications Optimum

value , , „ -, Value at lower Value at upper

limit limit

1 Wall, thermal resistance of outer skin (R*) 0.56 1,.02 0.98

2 Wall, penetration coefficient of outer skin (P) 2.81 1 .00 1.00

3 Wall, thermal resistance of insulation (R*) 0.89 1,.01 1.00

Wall, penetration coefficient of insulation (P) 0.15 1 .00 1.00

5 Roof, thermal resistance of insulation (R*) 4.6 1 .06 0.98

6 Roof, penetration coefficient of insulation (P) 6.25 0,.99 1.04

7 Roof, absorptivity 0.6 0 .99 1.03

8 Wall, absorptivity 0.68 0,.99 1.01

9 Window shading coefficient 0.53 0 .96 1.16

10 Aspect ratio (north wall/east wall) l.Al 0 .99 1.00

11 Window, light transmittance 0.42 1 .00 1.00

12 Glazing ratio (glazed area/wall area) 0.57 1 .01 1.00

13 Orientation (tjue bearing)

Floor area (ft ) fixed

14 fixed

15 Ceiling height (ft) fixed

* R = Thermal resistance = thickness/ thermal conductivity (ft hr degF Btu )

' 7. Acknowledgments

Thanks are extended to Mr. J.W. Spencer for help in the computer work and to Mr. E.R. Ballantyne

and Dr. R.W.R. Muncey for discussions. All computations were carried out on a CDC 3600 digital

computer which is part of CSIRO computer network.

8. References

{1} Gupta, C.L., A systematic approach to optimum

thermal design, ANZAAS Congress (Adelaide,

1969).

{2} Gupta, C.L. and Spencer, J.W., Building

design for optimum thermal performance, AIRAH

1970 Jubilee Conference (Melbourne, 1970).

{3} Loudon, A.G., Summertime temperatures in

buildings without airconditioning , Building

Research Station, Garston, CP 47/68 (1968).

{4} Muncey, R.W. , The calculation of temperatures

inside buildings having variable external

conditions, Aust. J. Appl. Sci. 4_, 189 (1953).

{5} Muncey, R.W. and Spencer, J.W. , Calculations

of temperatures in buildings by the matrix

method: some particular cases, Bldg Sci. 3^, 227 (1969).

(6) Buchberg, H. , Sensitivity of the thermal response of buildings to perturbations in the climate, Bldg Sci. 4-, 43 (1969).

{7} Kittler, R. , Standardisation of outdoor con- ditions for the calculation of daylight factor

with clear skies, in "Sunlight in Buildings".

CLE. 1965 Conference Proceedings, 273 (1967)

{8} Button, D.A. and Owens, P.G.T., Considerations

for the optimised fabric design, in "Engineering in the Home", 64 (Allen & Heath , 1969).

{9} Sheridan, N.R., Energy conservation applied to the rational design of a dwelling for the tropics. World Power Conference, Lausanne,

IV-B (1964).

{10} Vanning, J., Design of buildings to minimise

airconditioning loads, in "Airconditioning

System Design in Buildings", p. 72 (Elsevier, 1969).

{11} Hopkinson, R.G. and Longmore, J., Daylight,

artificial light and acoustics in relation to the thermal environment, J. Instn Heat Vent. Engrs 37_, 82 (1969).

{ 12} Illuminating Engineering Society, USA,

Lighting Handbook, p. 9-45 (1967).

{13} Hopkinson, R.G., Petherbridge, P. and Longmore, J., Daylighting, p. 509 (Heinemann,

1966).

68
{14} Krochmann, J., The calculation of daylight

factor for clear sky conditions, in "Sunlight

in Buildings", CLE. 1965 Conference

Proceedings, 287 (1967).

{15} Lance, G.N., Numerical methods for high speed

computers, p. 128 (Iliffe & Sons, 1960).

(16) Kowallk, J., and Osborne, M.R., Methods for unconstrained optimization problems, p. 24 (Elsevier, 1968).

{17} Mitchell, R.A. and Kaplan, J.L., Non-linear

constrained optimization by a non-random

complex method, J. Res. Natn Bur. Stand. C72 , 249 (1968).

Materials

and components

Design

variables

Simulation program

Indoor environment

Compute

objective

function

System

simulation

System

optimization

Optimum

design

variables

Op t imum

as initial point

Sensitivity

analysis

/ Optimized

j performance

specifications

End ^

Figure 1 - Building as an environmental system

69
Spatial envelope + internal components + external environment + heat sources

(Air temperature, degree of discomfort)/(plant capacity, loads)

Internal components

(Furniture and partitions; areas

and types)

Spatial envelope + external environment

(Net rate of heat gain + radiant solar heat gain)

Heat sources or sinks

(Mechanical services,

occupants, appliances)

E

^Air conditioning^

Spatial envelope + external

environment (Available

daylight - artificial lighting)

required

Spatial envelope

(Orientation, aspect ratio, ceiling height,

window area, surface absorptivities)

Elements of spatial envelope

e.g. wall (admittance, transfer ratio),

windows (shading coefficient)

Components of spatial envelope

e.g. wall outer skin

(Resistance and capacity)

Internal luminous

reflectances of elements

of spatial envelope

flight ing^

Materials of spatial envelope

(Penetration coefficient, P)

^Thermal^

Figure 2 - Hierarchy for environmental performance simulation program

70
Design Considerations for a Practical Heat Gain Computer Code

Soren F. Nermann and Norman E. Mutka

DERAC Consultants, Inc. Bothell, Washington

A digital computer program for heat gain computation is described. Einphasis

is placed on the development of engineering and programming design criteria to ensure practicality, flexibility and ease of usage. Fenestrated and opaque surfaces, internal loading, plenum usage, duct losses, ventilation, et cetera are considered. Computational questions are encountered which may form the basis

for future analysis and research. Results from the implemented code include the determination of such design conditions as apparatus dew point, mixing and entering air temperatures, leaving and supply air temperatures, design and return air

quantities, number of air changes smd tonnage.

Key Words: Heat gain computation, design condition computation,

cooling load, apparatus dew point, air quantities, system design,

zone design.

1. Introduction

This paper describes the steps involved in the development of a particular digital computer program to perform heat gain and resultant design condition computations. The program is structured to be of value to the practicing engineer but is not a substitute for engineering experience and knowledge.

Evolved as a part-time project over a period of some three years, the program utilizes much of the presently available knowledge, provides a framework wherein new developments may be quickly implemented

and has been thoroughly tested. There are, however, areas where it is felt additional research is needed or where additional capability should be included. These areas form the basis for the future

evolution of the code.

2, Design Objectives

Before initiating any development of the code, the following design objectives were stipulated:

1) Engineering computations should include methods for the determination of:

a) fenestration heat gain.

b) wall or opaque surface heat gain.

c) internal heat gain.

d) plenum heat gain.

e) duct heat gains and losses.

f) ventilation and exhaust requirements.

g) leakage.

The computations should be valid at any site in either the northern or southern hemisphere.

2) The methods employed should be "standard practice" except where formulas might be developed

which would represent tabular data to some degree of accuracy in the least squares sense. New developments should only be considered in unusual circumstances.

3) The code structure should be sufficiently flexible to permit the determination of the design

conditions within a zone or system given the applicability of any or all of the above heat

gain computations.

71
k) The input should be minimal consistent with the desires of the user for various capa- bilities and should be structured to reduce the chances of error.

5) The results obtained from the code should be sufficiently detailed to permit hand

computation for checking purposes and to augment engineering experience.

6) The code structure should be sufficiently flexible to permit rapid changes, additions,

or deletions with a minimum of impact on the code, thereby enabling the code to keep

pace with new developments and techniques.

In addition a guideline was established whereby the criteria for selection between various methods

was practicality, i.e., if a particular technique was simpler or easier to implement and did not possess

any distinct advantage with respect to the final result obtained, then this technique was to be preferred.

3. Engineering Methods

Because of the number of algorithms employed to perform the engineering computations, only the more significant techniques will be mentioned. A more detailed presentation will be found in

reference 8.

3.1 Preliminary Computation

The code employs the U.S. Standard Atmosphere, 1962 [?]''' to determine atmospheric pressure and

density at a given altitude. Solar data and sol-air temperatures are determined using the methods of

references 6 and 9.

Surface heat transfer film coefficients are determined from the following relations:

Internal film coefficient ['t]

= 0.0826 cos^ T + 0.295^ cos T + 1.078 , (1)

-1 -2 -1 where H. is the internal film coefficient (Btu hr ft °F ) , 1

T is the tilt angle of the surface (radians from vertical).

Elxternal opaque surface film coefficient [1,2]

H =2+4 W/15 (2) e

—1 -2 -1 where is the external opaque surface film coefficient (Btu hr ft "F ) , W is the wind velocity (miles hr

External fenestration film coefficient [6]

= - 0.00125 + 0.262 W + 1.45 , (3)

-1 -2 -1 where H is the external fenestration film coefficient (Btu hr ft "F )

,

W is the wind velocity (miles hr ).

It will be noted that the selection with respect to the external opaque surface film coefficient

does not include a factor for surface roughness. On investigation it was found that the best available data for this coefficient [l,6] involved a subjective judgement on the part of the user which

' Figures in brackets indicate the literature references at the end of this paper.

72
2 could cause wide variation in the determination of the coefficient . In addition the data did not cover

the full spectrum of today's surfaces. It is strongly recommended that future research be undertaken

which will more exactly quaintify this term.

3.2 Heat Gain Computation

3.2.1 Fenestrated Surfaces

Heat gain through a fenestrated surface is found from the relation

H = A |u(t -t.) + C[S^S^D,,(T^ + N A_ + N.A^ ) g g| oi ALND oD iD.

o a

+ D„(T, + N A, + N.A^ )] I , (h) Id o d la.

o 1

'

where H^ is the fenestration heat gain (Btu hr

A is the fenestration area (ft ), 2 -1 -2 -1 U is the fenestration heat transmission coefficient (Btu hr ft °F )

,

t^ is the outdoor dry full temperature (°F),

t^ is the indoor dry full temperature (°F),

C is a composite correction factor for haze, altitude, and internal shading [3]« is a sash or frame correction factor,

S is the sunlit fraction of the fenestration area,

-1 -2

Dj^, are the direct amd diffuse incident solar intensity respectively (Btu hr ft )

,

N , N. are the inward flowing fractions of the absorbed radiation through the outer

and inner panes respectively,

A A

D ' D. are the incident absorption coefficients for the outer and inner pames

respectively,

A A

d ' d. are the diffuse absorption coefficients for the outer and inner panes

0 1..,^ respectively,

Tjj, are the incident and diffuse transmission coefficients respectively.

The determination of the absorption and transmission coefficients is via a table look-up procedure

utilizing the data of reference 2.

The determination of the sunlit fraction of the fenestration area utilizes a generalization of the procedure of Tseng-Yao Sun [9] to permit the use of tilted window surfaces. Adopting the same notation

as Sun, the shadow area depth is computed from the relation

ip _ ptanB-cosY cot6 ^

< cosy+tanP cot 6

'

where T is the shadow area depth (in.), P is the projection outward normal to the window surface (in.).

^ However, preliminary analysis of the data showed that two of the coefficients were related by the relation

A = .004 C - .0078 , and that the coefficient B might be related to the emissivity E by the expression

B = .45787 e5-05567 .

Here A, B, and C are as defined in reference 6.

73
3 is the solar altitude (radians),

Y is the wall-solar azimuth (radians),

6 is the counter-clockwise angle between the horizontal and the outward normal to the surface (radians),

In addition provision has been incorporated in the code to eliminate the possibility of overlapped

shadow areas.

3.2.2 Opaque Surface Heat Gain

An extension of the method of H. A. Johnson [5] is utilized which enables application of the te nique to heterogeneous structures. To make the extension, the homogeneous conditions postulated by

Johnson were approximated by computing "equivalent parameters" for specific heat, wall thickness,

thermal conductivity and specific weight as follows:

Specific heat

-I -1

(6)

Wall thickness

(7)

Thermal conductivity

(8)

Specific weight

H W.X.

1 /

(9)

where X. is the thickness of material i (ft),

W. is the specific weight of material i (lbs ft ), -1 -1

C. is the specific heat of material i (Btu lb °F ),

•'- _]_ _]_ _]_ is the specific conductivity of material i (Btu ft hr °F ).

Hence the thermal diffusivity, A^, of the wall is given by

C W

e e

\ 1 ' 1 (10)

(x.A.

)

1 1

The heat gain is then given by

H,., = A I D(T„ -T.) + H. T_ B cos(uu t-3 -6 ) , (11)

ID Si 1 — b n n n n I

' m n n

where A is the wall surface area (ft^), D is the overall heat transfer coefficient (Btu ft hr °F "'"),

Tg is the mean sol-air temperature obtained from the Fourier analysis ("F), m

T. is the room temperature (°F),

74
• • -2-1-1 is the interior air surface film transfer coefficient (Btu ft hr °F )

,

T is the'n!!! Fourier coefficient (°F),

s

'

i*)^ is the n«! harmonic frequency from the Fourier analysis (cycles hr )

,

is the nU) harmonic phase angle from the Fourier analysis (radians),

n

t is the time measured from midnight (hr).

B and 6 are factors determined from the expressions

n n

B = d / Jf^ + i_ , (12)

n n / ' n n

6^ = tan"^(g /f ) , (13)

where

1 ^ e

f^ = a^ cosh T] cos ^ + ^ (sinh ^ cos r] + cosh r\ sin T])

+ a^ (sinh 11 cos r\ = cosh r] sin T)) , (15)

= cosh T\ cos 'H - ^

(sinh ti cos fl - cosh ri sin "P)

+ (sinh ri cos T) + cosh r\ sin t]) . (16)

Here

^n 4 J 2?r ' ^17)

o ^ e

o ^ e

n = x„ l-nn- . (19)

e e

3. 2. 3 Internal Heat Gain

The internal heat gain is computed from the input sensible and latent heat data according to the relation

h = Z d^.^M. • ^20)

1 11

where H^^ is the internal heat load (Btu hr ''),

dy is the diversity factor for load i,

i

Hj^ is the maximum internal heat for load i. i

75
3.2.4 Plenum Heat Gain

The code provides for the computation of heat gain from that portion of the internal load entering

the plenum directly and from the transfer of heat from either the space or through the exterior building structure. The impact of the air movement through the plenum is not accounted for at present.

3.2.5 Duct Heat Gain

Two methods are provided for the user. The first employs percentages of room sensible and room latent loads to estimate the duct heat gains or losses. The second involves actual physical data con- cerning the duct's construction and location as may be seen from the relation utilized to determine the heat gain or loss, namely

h - "P^^^^^ 28.f;Vp!pX . (21)

where H_ is the duct heat gain (Btu hr ''")

, -1 -1 -1 U is the heat transfer coefficient (Btu ft hr °F )

P is the duct perimeter (ft),

X is the duct length (ft).

At is the temperature difference between the surrounding environment and the air entering the duct (°r),

2 A is the cross sectional area of the duct (ft ) , V is the average duct air velocity (ft min *")

,

p is the density of the air (lbs ft .

3.2.6 Ventilation and Exhaust Requirements

Ventilation requirements are imposed via the relations

A is the amount of outside air required (cfm)

,

where 0

s is the

°L

is the

A is the

t0 is the

t.1 is the

w

o is the

w.1 is the

0 = 1.08 A(t - t. ) , (22)

s o 1

'

0, = 0.68 A(w - w. ) , (23) L o 1

'

Lr load (Btu hr "'')

,

, , -l^

door moisture content (grains lb-")

,

oor moisture content (grains lb-").

Utilizing this information as well as other information, an initial estimate is made of the return air

required. The air loads are then modified to reflect the percent (input) of the return air which is

to be exhausted.

3.2.7 Leakage

At the present time the amount of leaikage is specified as an infiltration quantity via input. An extension to accommodate a more exact evaluation of this quantity based on crack length, door usage, shaft and stack effects, et cetera, is under development.

76
3.3 Design Condition Computation

To determine the zone and system design conditions, the prograjm utilizes a mathematical formulation whose exact structure is proprietary. However, because any such formulation must have an analog

with the more traditional graphical technique, it is convenient to describe the process in these terras.

Briefly, referring to figure 1, the apparatus dew point, T^, is found at the intersection of the saturation curve with the effective sensible heat factor (ESHF) line, the mixture point is found at the intersection of the grand sensible heat factor (GSHF) line with the line joining the indoor and outdoor

design points, and the supply air point is found at the intersection of the GSHF line with the room sensible heat factor (RSHF) line. Note, however, that even under normal conditions the temperature of

the supply air, T^, will not be coincident with that of the leaving air, T^^, and hence a separate com- putation for this point is included.

The program treats several abnormal conditions which may be categorized as follows:

a) T. - T > AT - the amount of sensible reheat is determined such that T. - T s AT

1 s max 1 s max

b) The ESHF line fails to intersect the saturation curve - a value of T^ is selected such

that T. - T s AT and the amount of reheat required is computed.

1 s max ^

c) The RSHF line fails to intersect the saturation curve - the amount of dehumidification

required to make the ESHF line tangent to the saturation curve is determined and then if further refinement is required, the amount of reheat is computed so that

T. - T AT

1 s max

Obviously the above actions in response to the conditions mentioned will not satisfy all designers

but printout of the reheat sind dehumidification required will serve as an indication of the trouble

encountered. The designer can then take whatever action he considers best.

't. Program Structure

In order to meet the design objective of minimal input consistent with conditions and to provide

the maximum flexibility in use, modification, and extension, a modular approach was adopted not only

for the computational sequence but also for the input. To accomplish the latter a set of 25 key words

were defined which when coded on cards enable a structuring or blocking of the input stream. A particular block can then be included or omitted as conditions dictate. At the present time these words

are as follows:Basic Data

TITLE Titling information data block

ENVIRON Exterior environment data block

DESIGN Interior environment data block

ORIENT Building orientation data block

GLASS Fenestration data block

SASH Sash data block

PROJECT Window projection data block

MATERIAL Building material data block

CONSTRUCT Building construction data block

DUCT Duct construction data block

DIVERSITY Diversity schedule data block

77
Configuration Control

SYSTEM System definition block

ZONE Zone definition block

Space Data

AIR Outside air load data block

INTERN Space internal loads data block

WINDOW Window data block

BUILD Building surface data block

PLENUM Return plenum data block

RETURN Return duct data block

SUPPLY Supply duct data block

Execution Control

COMPUTE Initiate computation

UPDATE Data update or parametric analysis

NEXT Next building analysis

STOP Termination of computation

Referring now to figure 2 we see that after initialization the program scans for key words during

the input process, placing these key words and their associated data on auxiliary storage until a OM'UTE

card is encountered. This set of data forms the base line data case against which all subsequent up- dating or parametric studies may be conducted. Since updating is accomplished dynamically during execution, the base line data case is preserved iintil a NEXT or STOP card is encountered.

It will also be noted in figure 1 that the input data stream is segregated into basic data, space data and the two types of control functions permitting a preliminary scan of the data ordering to minimize chances of computational failure. It will be further noted that the actual data input is accomplished via selection of a subroutine and its execution. Each subroutine reads and prints the input

data, performs whatever preliminary computation may be required and places the resulting data on auxiliary storage.

Figure 5 shows the computational control sequence for the base line data case. The sequence is

designed to further ensure that the proper ordering of the input data has been accomplished. However,

it will be noted that it is possible to make a change in the basic data during execution of the case, providing, for example, the capability to alter the interior design conditions within a particular

system or within a particular zone. Note also that the supply or return ducts require special treatment, this treatment being necessitated by the fact that the data input for these data blocks may contain percentages of room heat to determine the various heat gain or loss quantities.

The subroutines selected perform fenestration heat gain, opaque surface heat gain, plenum heat gain,

internal heat gain, et cetera. Following the determination and printout of the relevant heat gain contributions, a table of the various sensible and latent heat factors is generated and printed for the user's information. A design point is selected which reflects the maximiim heat gain and the design

conditions determined using a proprietary psychrometric process. Printout of these conditions is

given for each individual zone, if a multiple zone system, and for the total system.

78
5. Application

The program has been applied to a variety of structures, the following being typical:

A three story department store is located at h7.5° N. latitude, 122.3° W. longitude and at an altitude of 300 feet above mean sea level. The building consists of a basement with an exposed loading

dock, a first floor sales area, and a second floor sales, stock, phone and office areas. The orientation of the structure is as shown in figure k. The construction is principally brick and concrete with

a single glass entrance shaded by an overhang.

The building was divided into four systems with the basement and first floor being treated as single zoned systems SI and S2, respectively, and the second floor being treated as two multi-zoned

systems, S3 and Sk. Input to the program specified not only the location and orientation but the weather conditions for the design day of August 21, the interior design condition of 7^°^ dry bulb and

62°F wet bulb, the detailed cross sections of the construction, the diversity schedules, and the internal peak load conditions. Duct factors, plenum conditions and required ventilation were also input as required by the designer.

lypical of the output is that shown in figures 5 and 6 for system S2. Note that the various sensible and latent loads are given on an hourly basis. The design point occurred at 5:00 P.M. when the maximum grand total heat was reached. Since the system was of the draw-through type, the mixture and

entering coil temperatures were the same. Note also that the difference between the supply air temperature and the space design temperature is less than the 23°F maximum difference which the designer

specified.

The results, in general, agreed with the hand computations, especially with respect to the compu- tations pertinent to the psychrometric process where it is felt that the code produced a more reliable

result than the traditional graphical technique.

6. References

[l] ASHRAE Guide and Data Book - Fundamentals

sind equipment for 1965 and 1966, George Bantu Co., Menasha, Wisconsin, 1965.

[2] ASHRAE Handbook of Fundamentals, 196?,

George Bantu Co. , Menasha, Wisconsin, 196?.

[3^ Carrier System Design Manual, Carrier Corp.,

Syracuse, New York, I96O.

[4] Hutchinson, F. W, , A rational re-evaluation

of surface conductances for still air, ASHRAE Transactions, 70 105 (196^).

[5] Johnson, Harold A., Periodic heat transfer

at the inner surface of a homogeneous wall, ASHVE Transactions, 5ft 1^3 (19^+8).

[6] Lokmanhekim, Metin (ed.). Proposed procedure

for determining heating and cooling loads

for energy calculations - algorithms for

building heat transfer subroutines, (Preliminary report by the task group on energy requirements for heating and cooling, ASHRAE,

1968),

[7] National Aeronautics and Space Administration,

U.S. Standard Atmosphere, U.S. Government Printing Office, Washington, D.C. , I962.

[8] Nermann, S. F. , COOL - A practical heat gain

computer code, DERAC Consultants document.

[9] Sun, Tseng-Yao, Shadow area equations for window overhangs and side fins and their

application in computer calculations, ASHRAE

Transactions, 7^, I968.

[10] Threlkeld, J. L. , Thermal environmental

engineering, Prentice Hall, I962.

79
Figure 1

Typical Psychroraetric Process

80
81
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82
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83
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84
Output for System S2 Volume = IOO8OOO.OOO

System Design Conditions

Time of Peak Load I7OO Hours

Outdoor Dry Bulb Temperature = 83.000

Grand Total Heat = 2593712.000

Design Air (Variable Volume System) = 927^7.563

Return Air (Variable Volume System) = 7^7^+7.563

Design Air (Constant Volume System) = 927^*7. 553

Return Air (Constant Volume System) = 7^7^+7.563

Apparatus Dew Point Temperature = 5I.781

Mixture Temperature = 76.285

Entering Coil Temperature = 76.285

Leaving Coil Temperature = ^k.231

Supply Air Temperature = 56.1^9

Number of Air Changes Per Hour = 5.521

Tonnage = 216.1^3

Figure 6

System S2 Design Conditions

85
j
Solving the Communication Problem in A Computer-Controlled Environmental System

T. Prickett, Jr., J. L. Seymour, Jr., D. L. Willson, and R. W. Haines

Collins Radio Company

Dallas, Texas 75207

The use of computers in the control and supervision of environmental and other

systems for large buildings and complexes is just getting under way.

A fundamental problem in this type of application is the transmission of data

to and from the computer. The traditional methods of hardwiring, frequency multiplexing and electro-mechanical multiplexing are not satisfactory in a computer

environment, or in any complex, large-scale dynamic environment.

Both digital and analog data are needed in the control system. Digital data

can be handled faster and more accurately than analog data in both the communication

system and the computer. Analog-digital and digital-analog converters are needed,

with all information being transmitted in digital form. Then each data item becomes

a series of bits in a stream of digital bits, and can be transmitted over any type

of digital communication system.

This paper describes a communication system utilizing "time-division" in which

each discrete sensor and control element is assigned a unique time address in a high-speed digital bit stream. By this means, the problem of addressing and communication is greatly simplified.

It is noted that this approach is made possible by the recent advances in microcircuit technology which makes it economically possible, for example, to use individual A/D converters for each analog sensor.

The concept of approaching the "control problem" as a "communication problem"

should make it easier to analyze and design large computer-operated systems.

Key Words: Control, digital communication system, environmental system,

multiplexing, supervisory control, time-division address.

1. Introduction

There is a growing consideration of the use of computers for control of large and/or complex

systems, such as environmental systems in buildings or complexes. A few such systems have been installed and others are being designed.

Central supervisory systems with or without computers become virtually essential for adequate

monitoring and control in large institutional or commercial complexes. They are justified economically

on the basis of improved visibility and control as well as reduction in personnel requirements and lower operating costs.

The use of computers with supervisory systems increases the speed of data acquisition and simplifies data reduction. If the computerized system is properly designed, much of the start-up,

shut-down and reset programming can be done automatically through computer-executed programs.

Since most large building complexes are dynamic and expandable the supervisory system must also be dynamic and expandable.

A careful analysis of such systems indicates that a basic difficulty is the need to deal quickly,

accurately and efficiently with large quantities of data. For example, in a typical industrial complex

with 2,000,000 square feet of air-conditioned floor space, proper monitoring and control requires

87
communication with about 3000 sensor and control devices. Some of these must be monitored regularly,

others only intermittently.

This paper considers various traditional methods of data communication, and concludes that a digital system using time-division addressing may be the best approach.

2. History of Supervisory Control Systems

Central supervisory controls for environmental systems are a comparatively recent development.

Design changes have been evolutionary, rather than revolutionary, dictated by the increasing size and complexity of the buildings.

The first such systems were simply extensions of the control wiring (or piping) from a few systems

to a central point (fig. 1). Since separate, permanent connections are required for each control function, this is usually termed a "hardwired" system. This approach is satisfactory so long as the subsystems to be coordinated are few in number and closely related geographically.

As the number of subsystems increases and they become more widely separated, the cost and com- plexity of the "hardwired" approach makes it necessary to look for alternatives. Multiplexing, in one form or another, is such an alternative. The basic idea of multiplexing is to use a common bus or a set of "common function" wires which serve all the subsystem control devices. Some means of "addressing" is necessary to select each station in turn for monitoring and control operations. The devices which perforin the addressing and selecting functions are called multiplexers (fig. 2). Multiplexers take various forms depending on the concept and the type of data being handled. The more

common forms are frequency multiplexing and electro-mechanical and solid state multiplexing.

The frequency multiplexer uses a set of discrete frequency carrier waves, one frequency for each station to be addressed, on which the signals to be sent and received are superimposed. This is, of course, subject to error due to variations in frequency or voltage at the power source, and extraneous

"noise" due to frequencies from other sources.

Another type of scheme uses a series of pulses as the carrier system. The number of pulses per unit time, or the elapsed time between pulses can be varied to correspond with the signal value. These

pulse groups can be combined to form a continuous stream, with divisions between individual signals

indicated by some sort of a coding system.

Electro-mechanical and solid state multiplexers use relays which will, in response to a proper

address signal, connect the common function wires to the subsystem desired. This operates reliably,

but is comparatively slow.

The first central supervisory systems to use computers simply patched an analog computer into the manual control board and used the computer for monitoring and data acquisition (fig. 3). It was obvious

from the beginning that the analog computer could also be used for control. However, the digital com- puter is preferable for control purposes, although there are many software problems, including those associated with multiplexing and demultiplexing.

3. The Nature of Control Data

Data in an environmental control system are both analog and digital in nature. Analog signals are associated with temperature, humidity, flow, pressure and modulating position, while digital signals

are associated with two-position, on-off, start-stop, go-no go, and similar functions. If these data

are handled on a manual basis, as they are in most presently installed supervisory systems, then speed

is not important and data can be transmitted in either form. If, however, we wish to use a computercontrolled communication system, then digital data should be used. Digital data can be transmitted at much higher speeds, and with greater accuracy, than analog data. It then becomes necessary to provide

analog to digital (A/D) or digital to analog (D/A) converters for the analog-type sensors and con- trollers; thus the communication system need handle only digital data.

Only a small amount of data is derived from any single function, and this can be handled at rates

as low as 120 bits per second (BPS) or less. The computer, however, operates at speeds up to several million BPS. It is therefore necessary to provide hardware to make these bit speeds operate together.

One such system which is used is called time-division multiplexing.

4. Time-Division Multiplexing

Time-division multiplexing is defined by its name. A high-speed, repeated, digital bit stream is generated by the computer and fed into the main communications bus (usually a coaxial cable). At each

device, or group of devices, a coupler is connected to the main bus in such a way that it interfaces

88
with a small portion of this bit stream (fig. 4). A typical "slice" is one word, and consists of the same word each time. That is, the coupler is identified by a particular time segment (or slot) in the repeated bit stream. Another word is identified with a second coupler and so on. In one system, the

bit rate of the coupler is 4800 bits per second. This is derived by repeating the 32-bit data word 150 times a second. The minimum bit rate required on the main bus is then 4800 BPS times the number of couplers on the bus. The actual bus bit rate is usually greater than this minimum to provide for buffering and synchronization.

In this system the coupler address is said to be "strapped," that is, a particular time slot is permanently assigned to that coupler and the computer identifies the data as coming from that coupler

by its location in the repeated bit stream. Strapping is essentially a hardware function and is used to reduce software. We noted earlier that most control devices require 120 BPS or less. Therefore, it is not necessary to use a separate 4800 BPS coupler for each device. But we can serve several control devices from this one coupler by using a secondary bus with low speed device connectors to reduce the

bit rate still farther (fig. 5). If these connectors are also strapped, no further addressing is necessary.

Many control devices require regular monitoring and a permanently strapped connection. But some devices may require only infrequent service and a permanent connection is not required. By assigning

a group of connectors to a larger group of devices and providing a "switching" program, these devices

can be connected (addressed) as required with a reduction in hardware, but with an increase in software

to take care of the switching. A certain amount of overhead is necessary to provide addressing, but it

is much less where part of the addressing capability is inherent in the hardware. Providing switching/

addressing routines in the operating programs increases the overhead and slows down the operation. A trade-off study must be made in each case to determine the most economical method.

In a similar manner, a single A/D or D/A converter can be made to serve several devices by multiplexing techniques. This is feasible because these converters now operate at high speeds. It is possible to provide a "free-running" A/D conversion system which continuously scans several analog

signals and stores the present values of those signals in a set of digital storage registers. The computer operating program then provides for reading the contents of the registers at timed intervals.

While time-division multiplexing may be programmed into almost any general -purpose computer, it would be very wasteful of software and storage capability. It is preferable and desirable to use a computer system which has the time-division addressing and data handling included as part of the basic

hardware-software package. The operating programs then become much simpler to write and debug.

The operating program must be written for each specific application. However, this too can be simplified by the use of a high-level language, such as ATLAS, which uses a fairly simple English

syntax and covers a broad spectrum of test and control functions. Of course, any high-level language

requires a compiler resident in the computer. This, in turn, implies a fairly large computer, but greatly reduces the cost of the software, both for the original program and for changes and additions.

The time-division multiplex system thus described is made possible by the recent advances in microcircuit technology, which allow the design of complex circuits in small packages and at low cost.

We expect to soon see most of the necessary hardware contained in small MOS/LSI chips at a cost of less than $100 each. By using this approach, the computer is relieved of complex addressing operations and

is free to concentrate on the business of control.

5. Conclusion

We believe that the effectiveness of a computer-controlled system depends largely on fast and efficient communication. A time-division multiplex system designed to be integral with the operating

computer system provides the best, simplest and most reliable communication available today. This

system also allows for connection by a simple coaxial cable, and is easy to expand, requiring only

additional interface hardware, extension of the coax bus, and small additions to the operating program

as more devices are added.

Appendix

Time-division addressing systems may be "bit-interlaced" or "word-interlaced." Figure 6 shows a typical main bus "frame" for a bit-interlaced system. This contains 16 channels (bits) per frame, with

the first bit being amplitude-coded for synchronization. A coupler may be strapped to read one specific

bit (time slot) from each frame as in figure 7. When 36 frames have passed the coupler, 36 bits have

been extracted to form a complete word. (This number 36 is arbitrary, and varies to suit the manufacturer. A 36-bit word, as shown, provides four supervisory bits and 32 bits of data. The supervisory

bits identify the type of data being transmitted.)

89
Figure 8 shows a word-interlaced system, in which the coupler is strapped to identify and read one specific word out of a frame which contains 256 words or channels. (Again, the number 256 is arbitrary.)

With either system, it can be seen that the time slot is identified with a specific coupler and that all channels in the frame are serviced essentially simultaneously. Thus the system is ideal for real-time, on-line control.

ROOM TEMPERATURE

AIR HANDLING UNIT

SUPPLY PRESSURE WATER

TEMP

BURN I NG MOTOR

PUMP MOTOR

RETURN WATER

TEMP

CENTRAL

CONTROL

PANEL

COMPRESSOR

MOTOR

SUPPLY WATER

TEMP ©

PUMP MOTOR

RETURN WATER

TEMP

RETURN WATER

TEMP ©

COOLING TOWER ©PUMP MOTOR

SUPPLY WATER

TEMP

Figure 1. Hardwired Central Control

90
CENTRAL

CONTROL

PANEL WITH MUX

COOL I NG TOWER

Figure 2. Central Control with Mux

91
COMPUTER

CENTRAL

CONTROL

PANEL WITH MUX

Figure 3. Central Control with Mux and Computer

92
PROCESSOR

PRIMARY COMMUNICATION BUS

COUPLER

2

SECONDARY BUS

COUPLER

N

TO DEVICES

TO DEVICESTO DEVICES

Figure 4. TDM Bus with Mux

DEVICE

COUPLER

PRIMARY BUS

SECONDARY BUS

ADAPTER

ADAPTER 2

ADAPTER 3

ADAPTER N

Figure 5. Mux with Secondary Bus and Device Adapter

93
LI FRAME

13 14 15 12 3 4 10 13

16 BITS

16 CHANNELS (TIME SLOTS)

Figure 5. LI Frame Format

LI FRAME 0 LI FRAME 1

14 15 1 2 f

14 15

( 0

LI FRAME 35

2 0

1

1

SO SI S2 S3 0 31

DATA WORD FROM CHANNEL I

Figure 7. Channel/Data Word Relationship

TDM FRAME

WORD 252 WORD 253 WORD 254 WORD 2 55

27 28 29 30 31

COMMAND

* BITS "i INFORMATION BITS

I WORD (TIME SLOT)

Figure 8. TDM Frame Format

94
A Linear Programming Model for Analyzing

Preliminary Design Criteria for Multizone

Air Distribution Systems

R. A. Gordon

Cornell, Howland, Hayes (t Merryfield

Engineers - Planners - Economists

Corvallis, Oregon 97330

A linear programming model has been developed to analyze design

criteria affecting multizone air distribution systems and to provide

information for making design decisions during the preliminary, or conceptual, phase of building design. The location of potential primary mechanical equipment spaces; physical constraints for the air

distribution systems; zone data, including preliminary air requirements and single-point zone distribution coordinates, and basic system

configurations are fed into an IBM 1130 computer to develop a mathematical model of the building multizone air distribution system. Linear

programming is then applied to determine the "least first cost" multizone

air distribution system. Postoptiraal reports are developed to show the effects of price changes in the air distribution systems or primary

equipment selections, the physical size of mechanical equipment spaces,

and changes in zone requirements (and the ranges for which the effects

would be valid) on the least first cost system selection. Parametric

reports are also developed to show the effects of utilizing alternate

primary mechanical equipment spaces as well as other system changes in which several variables are changed simultaneously. Examples of applications of linear programming in preliminary multizone system design situations are presented.

Key Words: Air conditioning systems, air distribution systems, equip- ment selection, linear programming, mathematical programming, multizone systems, optimization, postoptimal analysis.

1. Introduction

The conceptual development of design criteria affecting mechanical systems is a phase of building

design that must be reevaluated before optimal design of these systems can be accomplished. Computeraided design systems and new mathematical techniques offer designers new opportunities to optimize the conceptual and ultimate final design and to provide additional tools for maintaining cost controls

over the project. The need for additional tools for analysis of mechanical system design criteria is becoming of greater importance as the costs of building continue to rise and as the costs of the mechanical system continue to consume an ever-increasing portion of the project budget.

In this paper, we will discuss an application of linear programming as a component of a design

system to assist in evaluating design criteria effecting a multizone air distribution system. Some basic requirements for a system of this scope are: a data base permitting up-dating of the original

design criteria with a minimal amount of data m.anipulation by the designer, the ability to analyze

changes in design criteria in terms of effects on the total system and capability of providing the results in the form required for the decision-making activities of the designer, performance of design

calculations, optimizing the design and, to some extent, estimating costs, material quantities and equipment selection. All these must be accomplished with an economic advantage over the traditional

methods of the conceptual design.

95
2. Linear Programming

It is difficult to define the class of problems which linear programming can solve. In general,

these problems include a variety of different resources to be distributed in a variety of ways. A

number of constraints may be applied. Some or all of the items may be available in limited quantities,

or are tolerable only up to certain limits, or some may be parceled out only in integral units. Under

these constraints, an overall measure, such as cost or profit, is to be minimized or maximized.

* For a precise formulation of the general linear programming problem L2J, we assume aj^^ , b^, and Cj are sets of constants (i = 1, ...,m; j = 1, ...,n) and Xj (j = 1, . .

. ,n) is a set of decision variables,

We seek solutions X = (x^, X2 , . . . ,Xjj) which satisfy the inequalities

I a^jX. > bi

j=l

i = 1, ,m (1)

Xj >_ 0 1, (2)

and at the same time minimize the linear functional

X = I c .X

J J

j = 1

(3)

The linear programming problem is to obtain such a solution.

Equation (3) defines the objective function X and this function is linear in each set Xj . The value of X is a function of the vector X = (x^,

''n^

' ^^"^ hence we may express (3) as

X = f (x^, x^, ... ,x^) . (4)

The function is defined for all values of X with finite components; however, our consideration is limited to those values whose components satisfy restrictions (1) and (2)

We see that in eq (1), we require that the components satisfy m linear inequalities, and in eq (2), we require that all components be non-negative. We commonly refer to eq (2) as the non-negativity

restrictions, and to the inequalities (1) as the functional constraints. In matrix terminology, we may represent the functional constraints by the equation

A = X _> B (5)

in which A = (a^^j) aiid B = col (i) .

While the non-negativity restrictions merely limit the set of admissible vectors to vectors X with

positive or zero components, the functional constraints further limit this set to those vectors satisfying the matrix inequality (5). The restrictions and the functional X characterize that part of linear

programming in which we attempt to minimize an objective function.

The linear programming problem may be stated in an equivalent form in which a linear functional is to be maximized and the functional constraints are >_ relations rather than <^ relations. Since this problem is obtained from the one stated by multiplying eq (1) by -1 and minimizing -X, this case can be covered adequately by discussions of the minimizing problem.

Number in the bracket refers to the reference.

96
3. Development of Preliminary Design Criteria

3.1 Assumptions

In the development of conceptual design system involving the application of linear programming as

a design tool, some initial ground rules must be defined. The reason for selecting the multizone

system out of all mechanical systems available is simply because data regarding packaged units are readily available. Also, the distribution systems for each zone are much easier to identify and thus lend themselves more readily to this type of a system solution.

Those portions of multizone air distribution system representing the primary cost variables are used in this model. Supply registers and other hardware, will remain fairly constant in the basic

system configurations. However, the return and exhaust systems are actually separate systems somewhat

similar in scope to the supply distribution systems. As such, they could very easily be included as additional elements of this same model. Their presence would lengthen this presentation so they have

been omitted. Other discrepancies resulting from the assumptions made so far can be partially ex- plained since the design system being discussed is used to define conceptual design criteria. Hence,

only the variable cost factors that make it difficult to determine optimal system design are included.

3.2 Preliminary Design Criteria

Preliminary design computations are performed within the limitations of conceptual design criteria

through a series of subroutines described very briefly herein.

a. Air Volume Computation

In the early phases of design development, a method of estimating the cfm requirements for supply

zones, is required to establish realistic bounds for the mathematical model being developed.

The amount of ventilation air required is computed on the basis of any one of the following criteria :

1. Number of air changes per hour,

2. Volume of air required per occupant,

3. Volume required per square foot of floor space.

first method, C = n x V : for the second, C = A x N: and for the third, C = B x S.

* V r V v

= volume of ventilation air flowing, cubic feet per hour.

= number of air changes per hour.

V = volume of the room in cubic feet,

rA = cubic feet of air per hour per occupant.

N = the number of occupants.

B = air volume required per square foot of floor space.

S = the area of the floor in square feet.

The method selected and used depends upon the judgment of the designer.

b. Duct Sizing

After computation of the zone air volumes, we can determine the size of ducts that are required

to transport the air. The subroutine presently used for this purpose computes the equivalent duct diameter using a constant friction loss of 0.1 inches w.g. per 100 feet of equivalent duct length for air volumes less than 2130 cfm, and a constant velocity of 1200 feet per minute for air volumes in excess of 2130 cfm.

For the

CV

n

97
For the volume of air less than 2130 cfm, the equivalent duct diameter ClD is:

= (2.7(Q/250t)l-«2)l/l-^0

(6)

For Q greater than 2130 cfm,

D = (AQ/Vtt)-'-''^ (7)

In eqs (6) and (7) ,

= equivalent duct diameter, feet,

V = air velocity, feet per minute,

Q = air flow rate, cubic feet per minute.

The general form of the equation for conversion of the circular duct diameter to the equivalent

rectangular duct is

d = 1.30(ab)°-"/(a+b)0-"0 , (8)

c where

a = length of one side of rectangular duct, inches,

b = length of adjacent side of rectangular duct, inches,

and

d^ = circular equivalent of a rectangular duct for equal friction and capacity, inches.

In the conversion, it is necessary to consider both the aspect ratio and any space restrictions in which the ducts are to be routed.

The aspect ratio (AR) is the ratio of the long side to the short side. An increase in the AR in- creases both the installation cost and operating cost of the system. Therefore, it is desirable to maintain an AR as near unity as practical. This is accomplished using the following algorithm.

For the case in which the aspect ratio is 1, let a = b in eq (8) and compute d . If d , as pre- viously computed, is less than the limiting d , then set a = b and recompute 'a' us5ng the computed

value of d :

a = (1.46D ) c 1/2.375

(9)

If d^ is greater than the limiting value for d^, set be equal to the maximum depth and compute 'a'

Interpreting 'a' as the length of the longest dimension of the rectangular duct, the gage of galvanzied steel required is then selected from Table 1.

Table 1. Galvanized steel sheet metal gage for rectangular low pressure ducts ClU.

Dimension 'a' Inches

Through 12 13 - 30

31 - 54

55 - 84

85 and greater

Gage

2624

22

2018

Lb/ft

0.906

1.156

1.406

1.656

2.156

98
This information is contained within the duct sizing subroutine so that all information about t duct run required to make a cost analysis has been determined except for the length of duct run. The method of obtaining the length of duct run for each zone is briefly described in the next section.

c. Spacial Description

Determination of lengths of duct runs is assumed to be based upon a single point of delivery to each zone. In most projects during preliminary design, this assumption is presumed sufficient.

Similarly, assuming that the discharge plenum from the multizone units may also be adequately

described as a single point, it is easy to describe the multizone unit in the three dimensional space

Using the three dimensional coordinate system, the points of supply and distribution are then uniquely described by sets of coordinates. By comparing coordinates, it is then a simple task to com

pute the length of ductwork from each zone to each multizone unit. With this final data, the cost pe unit volume of air for the ductwork for all possible system configurations is easily obtainable.

d. Multizone Unit Costs

In Table 2, the incremental costs for multizone units are listed.

Table 2. Incremental costs for horizontal blow through, heating and cooling multizone units with insulated coil and fan section, drain pan, forward curved

wheels, DWDI, Class 1, motor with vari-drive and belt guard and heating and cooling zone system of 2

: dampers , with

inches C43.

a coding coil face velocity of 550 fpm,, and

ASU

No. min

cfm max

First Cost

$ +80%

Total

Cost

$ min

$/cfm

ave max

1 2,500 3,500 850 680 1,530 .612 .525 .437

2 3,500 4,500 1,000 800 1,800 .514 .457 .400

3 4,500 6,500 1,200 960 2,160 .480 .406 .332

4 6,500 8,800 1,420 1,136 2,556 .393 .342 .290

5 8,800 11,000 1,700 1,360 3,060 .347 .313 .278

6 11,000 14,000 2,080 1.664 3,744 .340 .303 .267

7 14,000 17,000 2,480 1,984 4,464 .318 .290 .262

8 17,000 21,000 3,000 2,400 5,400 .317 .287 .257

9 21,000 23,500 3,300 2,640 5,940 .282 .267 .252

10 23,500 30,000 3,970 3,176 7,146 .304 .271 .238

To determine the appropriate cost factors to use in the objective function of the LP model, the cost per cfm of air volume for the recommended mtiximum cfm and the minimum cfm, are averaged. As indicated in Table 2, these values include consideration for the installation costs.

e. Duct Costs

Table 3 represents the installed costs of galvanized sheet metal ductwork L4ll. The costs also

include the sheet metal contractor's profit.

To determine the total installed costs of low pressure, straight rectangular ducts on a lineal

foot basis , add the width in inches and the depth in inches and multiply by the appropriate multiplie

from Table 3.

99
Table 3. Cost factors for galvanized steel sheet metal for low pressure rectangular

ducts [Ia3.

Duct Gage Multiply by

26 0.140

24 0.162

22 0.195

20 0.217

18 0.234

To determine the cost per cfm for the duct from each multizone unit, the total cost is divided

by the volume of air being supplied. This figure is then used in the LP model in the objective

function.

4. Formulation of the Multizone LP Model

A linear programming model for multizone air distribution systems can now be developed from the previous discussions. Given 'n' competing activities consisting of the volume of air required for each zone, Zk, and the volume of air available from each source, ASUs , the decision variables

X. , X , . . . ,x , in (2), represent the levels of these activities. The general form of the model is illustrated in figure 1.

In our model, the volume of air required for the k^'^ zone is formulated as

rEZil.K = ZK k = 1, . . . ,p (10)

1 = 1

for a system with 'r' multizone units and 'p' zones.

Similarly, the volume of air supplied by the r'"'^ multizone unit is formulated as

r

TASUJl.s <_ TCAP s = 1, ...,t (11)

a = 1

where there are 't' possible selections for the r''^ multizone unit.

The summation of the individual zone air volume requirements supplied by a particular multizone

unit and the total capacity of the multizone units in the solution base must be zero, or

r p t E (IZl.k. - lASVl.s) = 0 . (12) 1=1 k=l s=l

Furthermore, the volume of air supplied to each zone from a particular multizone unit must not exceed the total volume of air required by the zone, or for the k zone,

ZH.k <_ Zk i = 1, ... ,v (13)

and each multizone unit cannot supply a volume of air in excess of ASUs, or for the s^^ multizone unit,

ASUil.s < ASUs 1 = 1 r . (14)

100
Finally, the objective function, COST, can now be written as

r p. t

Z (j:(CO)l,k) (Zi.k) + r(CAi^.s) (ASUi.s)) = min COST (15) 1=1 k«=l s=l

Since, by our previous discussions, each of the Zil.k and the ASU2..S are assumed linear over the range

for which they appear in the solution base, our model then performs according to the general linear

programming problem.

5. Results

The experimental values obtained during testing of the computer-aided design model thus far sub- stantiate the possible economical use of the model in analyzing conceptual design criteria for multizone air distribution systems.

A test building for which design data has been recorded, has been used to verify the results ob- tained from the model. Typically, input data for 30 zones has required about one hour for preparation. Using an IBM 1130 computing system, about 15 minutes are required for computation of the bounds

for the LP model and the cost coefficients for the objective function. The LP model, using the IBM LPMOSS C3ll program, requires about 30 minutes to obtain the first optional solution.

Output from the computer-aided design model includes the following:

1. The minimal possible first cost for the multizone air distribution system using

the given set of design criteria,

2. The determination of the multizone unit from which each zone must be supplied to obtain the minimal system first cost,

3. The multizone unit selection for each subsystem required to minimize the first

costs

,

4. Cost per unit of air volume for all duct runs and multizone units in the range for which the solution is applicable,

5. Cost reduction or increase possible per unit volume of air within the vicinity of the optimal solution achieved by changes on the constraints.

After the initial optimal solution has been determined, the output data is extremely useful in indicating the directions in which to proceed to improve upon the solution. This may be as simple as changing one or two bounds, or as complicated as changing the location of multizone units or a number

of zones. The constraints are automatically modified, as well as the coefficients in the objective

function. Since the initial optimal solution is maintained by the program and used as the new initial

solution, the analysis of the new design criteria is accomplished in a substantially reduced time and reduced design cost.

Additional modifications to the model will include printout of the optimal air distribution system

using a plotter, modeling of additional basic air distribution systems, the use of graphical display

devices, and the consideration of return and exhaust air systems.

101
6, References

ASHRAE Guide and Data Book, Systems and Equipment. 1967. ASHRAE, New York, N.Y.

936 p.

Hillier, Frederic S. and Gerald J. Lieberman.

1968. Introduction to operations research.

San Francisco, Holden-Day, Inc. 632 p.

[3] International Business Machines. 1968. 1130 Linear Programming - Mathematical Optimization Subroutine System (1130 LP-MOSS) , Pro- gram Reference Manual. White Plains, New

York; IBM.

C^D Richardson Engineering Services. 1969. Manual of Commercial and Industrial Construction

Estimating & Engineering Standards. Vol. I.

3 3

< <

3 3

C/3 CO < <

<O

O I-

< <

< <

102
A Conceptual Survey of Computer-oriented

Thermal Calculation Methods

C. L. Gupta , J. W. Spencer and R. W. R. Muncey

Commonwealth Scientific and Industrial Research Organization,

Melbourne, Australia

This paper surveys computer-oriented methods used for calculating cooling or heating loads and/or for determining indoor space temperatures in buildings. The

methods have been classified into groups depending upon the way they tackle the underlying heat conduction problem. Limitations and merits of each of these techniques are then discussed in terms of the ease of computation and degree of exactness with which they handle considerations such as heat conduction through

multilayer walls and roofs, heat capacity of the enclosing fabric and of the contents,

internal radiant loads and radiative-convective exchanges, ability to provide for an internal temperature swing and thermostatic operation, variable ventilation,

shading, surface coefficients of heat transfer, and heat flow through the ground.

Harmonic or matrix methods and response factor methods are discussed in greater

detail.

Key Words: Air conditioning, computer, indoor climate, load calculation,

survey, thermal performance.

1. Introduction

The importance of designing buildings as environment modifiers and the economic necessity

of accurately estimating the loads for correct

sizing of air conditioning devices has led to considerable development of dynamic thermal

calculation methods. The advent of high speed

electronic computers has shifted the emphasis

from development of simplified handbook methods,

necessarily based on very restrictive assumptions,

towards making more routine use of sophisticated

methods already available and to develop more

exact ones. An ideal method should permit the designer to know accurately how the thermal

performance or air conditioning loads on a building vary with time of day and time of year

and the influence of variations in the building

structure, the control conditions within the enclosed space, the capacity and operating

schedule of the plant, and the behaviour of the sensing and thermostatic control devices.

The thermal environment of any confined

space is the result of interaction between the outdoor climate, the enclosing structure and the energy sources or sinks within. The commonly

required data for thermal calculations are design

climatic conditions, thermophysical properties of the structure, heat inputs due to occupancy,

appliances, ventilation, and lighting, and the desired indoor conditions required for comfort.

To obtain design climatic conditions, a selection

criterion is used to pick out time sequences for external air temperatures, wind velocity and solar radiation from meteorological records. Alternatively, solar radiation can be computed

from an assumption of atmospheric conditions and

a knowledge of solar position. The selection

criterion is independent of thermal calculation

methods and has not been discussed in this paper.

It has to be noted, however, that simplified

handbook methods, which form the basis of the majority of current computer programs in routine

use, do not permit as wide a selection of design

solar radiation values as they do for air

temperatures. Similarly, the design values for internal heat input and thermal comfort conditions

are independent of the calculation method adopted, even though they may be handled differently by

different methods.

In regard to heat flow through building

elements, most computer-oriented methods assume it

to be unidirectional and thus neglect corners and heat bridges such as studs and rafters. The

thermal conductivity and heat capacity of homogeneous layers are considered to be constant even though their values may be taken with

reference to moisture conditions likely to occur

Division of Building Research

)'Division of Forest Products

103
in use. Thus the governing differential equation

for heat conduction through a building element is the one dimensional, linear heat conduction

equation. The corresponding simplification in boundary conditions, obtained by neglecting the non-linear character of surface coefficients of heat transfer or by treating them as constant, is no longer universally adopted. Air in the enclosed space is still considered to be at a uniform temperature and non-absorbing to radiation.

2. Types of Thermal Calculation Problems

In the field of thermal design of buildings

and load estimation, four main types of problems

are encountered:

(a) Calculation of indoor air temperature in

the absence of artificial cooling or heating.

(b) Calculation of indoor air temperature when

some heat is being removed or added but the indoor temperature is still variable.

(c) Calculation of heat gains or losses and cooling or heating loads when the indoor

air temperature is kept constant at a known value.

(d) Calculation of heat gains or losses and cooling or heating loads when the indoor

air temperature is variable and specified - the case of "temperature swing".

Further, the variable inputs may be of periodic type or of any general type. The former yield to exact steady periodic analyses and are usually sufficiently representative of design

conditions but the latter are necessary when

energy usage is being considered over a large

period of time or actual comparisons are being

made in the field between observed and computed

values.

Significant concepts to be discussed in

relation to the various thermal calculation

problems are:

(a) Heat conduction through multilayer elements.

(b) Converting the solar radiation transmitted

through windows and the internal radiant

loads to cooling loads or changes in indoor

air temperature.

(c) The ability to handle variable networks

representing either a variable amount of ventilation or variable coefficients of heat transfer at the surfaces of walls

and roof.

(d) Automatic controls such as thermostatic

control of temperature and operation of blinds.

(e) Interactions with daylighting, latent load calculations, shading due to other

buildings, more complicated considerations

of multidimensional heat flow through heat

bridges and ground, and coupled heat and mass transfer problems.

3. Established Design Methods

A limited comparison of the established

design load estimation methods, which form the basis of most computer programs in current use, has been carried out by Milbank and HarringtonLynn(l)^. A detailed discussion of the mechanism of heat transfer in buildings has been

reported by Gupta(2). To provide a proper perspective for the methods reported in later sections of this paper, major concepts in relation

to three methods, which are widely used and represent basically different approaches, are discussed in this section.

The ASHRAE method (3) is limited to load estimation for conditioned spaces held at constant

air temperature. Specified values of surface

coefficients of heat transfer are assumed in the exact analytical treatment for steady periodic

flow, which forms the basis of determining the equivalent temperature differences used in this method. Heat conduction through multilayer

elements is treated rather empirically. Sol-air

temperature allows for the effect of solar

radiation on opaque elements and solar heat gain

factors and shading coefficients allow for the amount of solar radiation entering through

windows of different types. Average clear days

are used for estimating solar radiation. The

instantaneous cooling load due to internal radiant

loads and transmitted solar radiation is obtained

by averaging these over a period of time governed

by the weight of the structure.

In the Carrier method(4), the equivalent

temperature differences for opaque elements are calculated for sunlit as well as shaded conditions

by using numerical methods. The internal radiant

loads and transmitted solar radiation are considered to be absorbed by the structure. Based

on field measurements, hourly storage factors are tabulated, which when multiplied by the peak solar

heat gain through ordinary glass give hourly

cooling loads corresponding to different weights

of structure, different shading conditions and different hours of plant operation. Allowance is made for reduction in peak values of load for different amounts of temperature swings permitted

in internal space temperatures. The incident

solar radiation values can be adjusted for a haze

factor.

The method due to Boeke(5) is widely used in Scandinavian countries and seems to be very

general in its approach. It calculates loads for

a specified indoor air temperature which may be constant or variable or else determines the indoor

'Figures in brackets indicate the literature references at the end of this paper.

104
air temperature for a given plant capacity and

also in the absence of artificial sources and

sinks. Computations on an hourly basis are done

for cycles of clear as well as cloudy days in every month of the year by using hourly heat

balance equations for similar modules in the building. The modules are supposed to have only

one wall exposed. Heat transmitted through

opaque portions, shaded as well as sunlit, are calculated by using Carrier's tables (4).^ Internal

radiant loads and transmitted solar radiation

through windows are considered to be absorbed by

a hypothetical element representing the ceiling,

partitions and floor in a two lump system

corresponding to the core and surface. The special features of the method are its capacity

to tackle variable shading due to other buildings,

variable ventilation, environmentally controlled

operation of blinds and lighting, thermostatic

control of indoor air temperatures and intermittent plant operation in a straight

forward operation. The inaccuracies involved in

the handling of conduction through multilayered

slabs are of the same order as in other design

methods. The main limitation seems to be the provision for only one exposed element.

There are many other proprietary programs

such as ARTHUR and BASIL in France, WESTINGHOUSE,

APEC and GATE in the USA. Also there are a large

number of easily programmable desk calculation

methods, using unsteady state heat flow

considerations, which are very widely used in the USSR and European countries. By and large, these

do not use any significantly different concepts

and differ only in detail. A discussion of these

is omitted for lack of space.

For purely numerical methods, which form the basis of digital computer programs of this type,

both space and time derivatives are converted into

finite differences. This results in a set of algebraic equations which can be easily handled by

matrix algebra. In physical terms, this

approximation amounts to representing a distributed

thermal system by a lumped thermal network

consisting of resistances between nodes and capacitances at the nodes and to calculating step

by step with respect to time. The larger the number of lumps and steps, the nearer to the actual system this representation would be but the computer time required would be increased.

A vast body of literature(lO) exists for numerical methods of solving the heat conduction

equation, but the following discussion should be

sufficient for outlining the concepts and defining

the terms.

The one dimensional heat conduction equation

for a homogeneous medium with constant thermal

properties is represented by

3^1 _ 1 8T

2 ~ a 3t (1) 3x

where T is the temperature, x is the space

dimension, t is the time and a is thermal

diffusivity. Considering h to be the incremental

step in x and e in time t and using the notation

T(m,n) to represent the temperature at position

mh at time ne, a general finite difference

representation of eq 1 would be

4. Numerical Methods

It is not always convenient to obtain exact analytical solutions of the one-dimensional heat

conduction equation under the varied boundary

conditions of interest in building heat transfer

problems. In fact, it is not possible to obtain

these by purely analytical means if the boundary

conditions are non linear or thermal properties

become temperature or time dependent. Also, for multilayered slabs, the exact number of layers

have to be specified in advance, thereby

restricting the generality of application. It is,

therefore, of interest to consider numerical

methods, which essentially involve the conversion

of derivatives into finite differences. If only

the space derivatives are converted, the equation

reduces to a set of simultaneous ordinary

differential equations at a grid of points or nodes. These have been solved by using R-C network analysers, analog computers and thermal

analysers, which require a specific type of equipment and involve experimental errors. Large

size analogs, which can handle thermal problems

of buildings as a whole, have been reported in recent literature by Korsgaard and Lund(6), Button and Owens (7) and Euser(8). The basic

principles of these have been reviewed by

Stephenson(9) and these will not be discussed

further in the present paper.

&{r(m+l,n+l) -2 r(m,n+l) + T(m-l,n+l))

+ (1-6) (Tfm+l^n) -2 Tfm^n) + T(m-l,n))

J

T(m,n+1) - Km,n) (2)

where M = aeh is the modulus and 6 is the interpolation parameter. The relative magnitudes

of £ and h are to be chosen such that the scheme

is computationally stable, i.e. the rounding off errors do not go on increasing and their actual

magnitudes govern the accuracy of finite

difference representation. The conditions of stability(lO) are that

M > 0, if 0.5 $ 6 ^ 1

0 < M $ 0.5 if 6 = 0 (3)

If 6 = 1, an implicit form is obtained, which is stable for all values of M. It involves solving

a set of simultaneous equations for every time

increment, which may, however, be large. If

6 = 0, an explicit form is obtained, which is stable only for M ^ 0.5. This means that even

though only one equation has to be solved for

105
each time increment at each node, the increment

has to be very small, being necessarily less than half the smallest time constant of all the nodes for stability.

Two well known cases are obtained as follows:

If 6 = 0, M = 0.5, eq (3) becomes

T(m,n+1) =0.5 {T(m+l,n) + T(m-l,n)} (4)

If B = 0.5, M > 0, eq (3) becomes

^{Ol(m+l,n+l) + Km+l,n)) - 2(J(m,n+l) + 1(m,n))

+ (.T(m-2,n+l) + T(m-l,n))} = Km,n+1) - T(m,n)

(5)

Equation (4) corresponds to Schmidt's method

and eq (5) corresponds to Crank-Nicholson's

method (quoted in 10). The former is simple but accurate only up to second order differences and

can give oscillating errors if the initial

estimates are not chosen properly. The latter is more accurate and is stable for all positive

values of M.

All numerical methods require initial values

to be specified and generate temperature data at all nodes even when only air temperature and surface temperatures are required. There are also lumping errors due to nodal approximation of

a distributed network by a discrete system, which

can be made quite small at the cost of considerable increase in computer time. Nevertheless, the arithmetic is very simple, and multilayered structures, non-linear boundary

conditions and variable networks can all be handled. Programs are general in nature and are not necessarily limited to buildings (11)

Climatic data inputs are completely open ended data sequences and any length of period can be

considered. Some of the well known methods of this class, which treat the whole building and use digital computers are discussed hereunder:

Kusuda and Achenbach(12) have used an explicit technique to solve three dimensional

heat and mass transfer problems associated with

underground shelters. Space increments of one

foot and time increments of the order of two hours have been taken for predicting the temperatures for a fourteen-day period. Buchberg

et al(13) and Sheridan(14) have developed

similar types of explicit techniques for predicting loads or temperatures in a room which

is characterised by the finite difference

representation of its elements combined in parallel in the form of a lumped network system.

The maximum value of time increment is fixed by

stability considerations to be less than the minimum value of the product

{C./Zd/R. .) }

which denotes the thermal time constant for the node i connected with nodes j . The temperature

and time dependent boundary conditions

incorporating the radiative and convective modes

of heat transfer are taken into account in the form of a delta network. Buchberg et al(13) have

also included heat exchange with the ground and

sky at the outdoor surfaces and solar radiation

penetration through windows is considered to impinge on the floor. For calculations over long

periods of time, say a year, Buchberg and Roulet

(15) have also developed a very fast implicit type

technique and applied it to compute loads fox a structure of homogeneous construction with no direct solar radiation transmission and for constant indoor air temperature. Wheway and Vahl

Davis (16) have specifically developed a method

for rooms in intermediate storeys of air

conditioned multistoreyed buildings having only

one side exposed to outside conditions and with

constant indoor air temperature. Variable shading

and reflected radiation due to adjacent buildings,

reflected radiation from ground and a variable

coefficient of heat transfer at the external

surface are taken into account. Radiation

transmission through the windows has been

considered to be a cooling load and a constant value of the combined coefficient of heat transfer

at the indoor surfaces taken. Beckman(ll) has developed a multimode, multinode model for systems

with combined conduction, radiation and convection

heat transfer, which can be applied to buildings.

It assumes a semi-gray enclosure and a speculardiffuse model(17) for internal radiation exchange

and uses fifth order Hamming's method(18) to solve

the set of first order non-linear ordinary

differential equations obtained for a lumped

system. It is specifically coded to provide data

for variations in temperatures caused by changes

in the physical parameters. Non-linear boundary

conditions, variable networks and switching inputs

can be easily handled. There is difficulty in obtaining surface temperatures as nodes with zero capacity cannot be handled. Two major advantages

are that the time increment can be large and the initial temperature estimates are not a critical

part of the solution.

5. Harmonic Methods

When the climatic data can be considered as periodic cycles, which is usually the case for design studies, the methods surveyed in this

section have a special merit on account of their

mathematical elegance and speed and ease of computation. The input data sequences are harmonically analysed into a steady state term and

a sufficient number of harmonics with frequencies

in integral multiples and then each one of the pure sine waves is considered as a separate input. The responses are then synthesised to give the desired loads or temperatures. The main

restrictions on the applicability are that the building system parameters have to be time

invariant, linearisation approximations have to be

used for the convective and radiative boundary

conditions and switching inputs are subject to Gibb's phenomena (quoted in 19) as they have to be

harmonically analysed.

106
One of the earliest analyses was done by

Mackey and Wright (20) for estimating heat gains

into buildings maintained at constant Indoor air

temperature. Exact heat conduction solutions were obtained for homogeneous elements and an equivalent homogeneous wall (21) was defined for multilayered constructions. Air temperature and solar radiation impinging on an opaque element were combined into a single input known as the sol-air temperature (22) . Internal masses were

not considered and transmitted solar radiation

and other internal radiant loads were considered

as cooling loads directly. Degelman(23) has computerised this method for year round usage

from first principles so as to obtain greater

flexibility in the choice of material properties,

surface coefficients of heat transfer and the computation of solar radiation data input as compared to the ASHRAE method(3), the earlier

version of which was based on this theory.

Nottage and Parmelee (24, 25) removed the limitations of constant indoor air temperatures

and the internal radiant loads not being linked

to internal masses by applying the harmonic inputs

to a lumped network representation of the building. Periodic types of inputs necessitated

the solution of only one set of simultaneous

algebraic equations for each of the harmonics as against a very large number for numerical methods,

even though lumping errors were introduced as before.

Van Gorcum(26) obtained an exact solution for homogeneous slabs subjected to harmonic inputs and showed that by analogy with passive four terminal

networks of electrical circuits, the analysis

could easily be extended to composite slabs in series. By considering any building as a combination of heat paths in parallel, each of which may consist of a number of homogeneous

slabs in series, Muncey(27) devised a technique

quoted as the matrix method to predict variable

internal air temperatures, which did take into account the internal masses. For a specified

indoor air temperature, which may be constant or variable, this method could also be used to predict heat gains. Pipes (28) reformulated the method in terms of hyperbolic functions using an electrical analogy. Gupta(29) introduced the delta network representation of indoor radiative

convective exchanges into the method due to Muncey(27) so as to obtain indoor air and surface

temperatures simultaneously and to allow the transmitted radiation to be linked to internal

masses. Muncey and Spencer (30) showed that the errors caused by taking a combined surface

coefficient of heat transfer at the indoor

surface instead of introducing a delta network

were not more than those caused by neglecting the furniture. Depending upon the value of this coefficient used, the calculation gave a mean

radiative-convective space temperature rather

than the air temperature. This temperature is akin to the environmental temperature proposed by

Loudon(31). Rao (32) devised a set of thermal

system functions to calculate cooling loads by

the matrix method, which provided for temperature

swings and internal radiant loads. Gupta (33) extended his earlier (29) scheme to take into account multidimensional heat flow through the ground so as to provide suitable inputs for floors

laid on ground. Muncey and Spencer (34) developed

an alternative technique to take into account internal radiant loads without having to introduce

a delta network for indoor radiative exchange.

This extension(34) also showed how heat flow within paths and various parallel branches in the individual heat flow paths could be taken into account. Gupta(35) has also interlinked the matrix method with daylight requirements so as to assign suitable values to Internal radiant loads due to artificial lighting during daytime as these acquire critical significance in determining

peak loads for open plan office buildings of large

floor areas.

The matrix type of harmonic method after

Incorporating the extensions outlined above, can handle all types of thermal problems stated in section 2. The requirements of system linearity

and invariability are to be observed and as such variable networks and non-linear boundary

conditions cannot be handled. Further, the length

of the periodic design climatic cycle should be

at least twice the thermal time constant of the enclosure(36) or more simply twice the largest

thermal time constant value amongst the heat flow paths (37) and not merely a day if a steady

periodic regime has to be obtained inside the enclosure.

6. Response Factor Methods

When energy requirements over a fairly long

period of time are to be assessed, the climatic

data are expected to be non-periodic and harmonic

methods are no longer applicable. Numerical

methods can still be used, but these must

introduce lumping errors. Response factor methods

have been devised so as to handle periodic, non- periodic and intermittent Inputs equally well

without necessarily being subject to lumping

errors. The essential strategy is to determine

the system response to a unit excitation under

identical boundary conditions as for the actual

inputs. Numerical integration of the convolution

integral (10) is then carried out and the system response is determined by superposing the unit responses or their scalar multiples over a significant period of time prior to the time in question such that the actual excitations are approximated by a succession of scalar multiples

of unit excitations. The unit response may be

characterised by a set of numbers giving the response at equally spaced points of time or by an influence function. These numbers or response

factors depend only on the construction and not on

the climate and can even be tabulated for different types of constructions for handbook type

calculations. Since the principle of superposition has to be used, the requirements of system linearity and invariability are still to be

met. Step by step calculation, however, makes it possible that the implications of these requirements are not so stringent in the actual

applications as in harmonic methods. It is usual

practice to take hourly or half-hourly intervals

for load estimation but shorter Intervals may be

desirable for control systems evaluation.

107
The earliest of such techniques, due to Nessi and Nlssole(38), calculated two influence

functions corresponding to heat flow at the internal surface of a wall when there is a unit

step change either in the external or in the internal air temperature. For a complete room, the heat flows are added after being multiplied

by appropriate areas. This gives the total heat

flow at the inside surface corresponding to a unit rise in external air temperature when the internal air temperature is constant or else to maintain a unit rise in internal air temperature

when the external air temperature is constant. The former case is used to calculate cooling loads

for constant internal air temperature and the latter by a process of inversion to determine the rise in internal air temperature for a constant heat flow indoors. Multilayered constructions

are approximated by a lumped system and there is no provision for internal radiant loads. Recently, Pratt and Ball (39) and Choudhury and Warsi(40) have derived unit response functions by

exact analytical procedures for enclosures having

heat flow paths containing up to a maximum of three layers.

Brisken and Reque(41) were the first to consider response factors as a set of numbers

denoting values of a unit response function at equally spaced intervals of time. They took the unit excitation function as a rectangular pulse

of unit amplitude and unit time step duration and treated the individual paths of the building as double lump networks. Combined surface

coefficients of heat transfer were taken at the indoor surfaces and included as part of the networks. Heat balance methods were used at each node to derive transfer heat admittance and control point heat admittance parameters similar

to the influence functions of Nessi and Nissole

(40). Provision was made for internal temperature

swings but the transmitted solar radiation and internal radiant loads were linked directly to the indoor air. The calculations were done in two steps namely determining the heat gains for constant indoor air temperature and then determining the change in indoor air temperature

for a given plant capacity or for a different

control setting. The climatic data sequences were approximated by a succession of rectangular

pulses. The method, however, cannot handle

temperature and time dependent boundary conditions

as these form part of the lumped network

representation of the heat flow paths.

Mitalas and others have presented an improved

version of the response factor method in a series

of papers (42,43,44,45). The major points of difference from Brisken and Reque(41) as enumerated in (42) are that the individual layers

constituting heat flow paths are treated by exact analysis as distributed systems, the unit

excitations are triangular pulses of unit

amplitude and twice the time step duration and

the heat transfer at the indoor surfaces of the enclosure is represented by a delta network. The first improvement removes lumping errors and the computation for multilayered constructions

involves Laplace inversion of the transmission

matrix for a composite slab (43). This matrix is the same as used for harmonic methods (26) except

for the presence of the transform parameter S.

These time series are truncated when a desired

degree of precision is obtained. Unit triangular

pulses approximate the external climatic cycles

and internal convective flows much better than rectangular pulses as the former are equivalent to trapezoidal approximations. However, a switching

type of input such as an artificial lighting load could be better approximated by rectangular pulses.

The linking of Internal surfaces by a radiative

network makes the surface temperature response

factors dependent upon enclosure geometry as a simultaneous set of heat balance equations are to be solved. However, the surface temperatures are calculated as part of the computations, the internal radiant loads are distributed to the Internal surfaces and non-symmetric elements can be handled more easily. Also non-linear boundary

conditions (44) due to condensing or evaporative

heat transfer or due to temperature dependence of the radiative component or due to variable wind

affecting the convective component of surface

coefficients of heat transfer can be taken into account in this method.

The number of sets of surface temperature

re:3ponse factors is equal to the number of excitations plus one for the room air temperature.

Cooling load response factors can be calculated

from the surface temperature response factors both

for constant air temperatures and variable air

temperatures. Once the response factors are known, they can be combined with any set of excitations to obtain cooling loads, air

temperatures and surface temperatures by simple

arithmetical processes. An example showing how

the time series method can be used to compute

cooling loads and to predict temperature swings

for a given capacity or for intermittent running

of the plant or to determine indoor air

temperatures is given by Stephenson and Mitalas

(45). The conditions of system linearity and invariability still require the thermal properties

of the materials to be constant. However, variable

ventilation can be handled as the calculations of air temperature are done step by step.

Kusuda(46) has recently extended the response

factor method due to Mitalas, Stephenson and Arsenault to multilayer structures with various

curvatures of finite thicknesses such as spherical

and cylindrical systems and to semi- infinite

systems, such as ground. Formulae for evaluating

interfaclal temperatures and heat fluxes in multilayer constructions have been derived and the evaluation of response factors for multilayered

constructions has been described in detail.

Muncey(47) proposed an alternative approach

to the computation of thermal response factors of multilayered slabs and their application to the determination of the transient thermal response

of enclosures. Instead of finding numerically the roots of a com-plicated transcendental equation for

the entire composite structure (43, 46) , he computed

the matrix elements for composite structures at prespecified frequencies and used a precalculated

matrix to determine the coefficients of a large

series of exponential terms with prespecified

exponents. By selecting suitable values and a sufficient number of the frequencies and exponents, any desired degree of precision can be

obtained. Thus, the time consuming procedures

108
used for the Laplace inversion in the other

methods are avoided by making use of the fact that frequency response curves in the case of buildings are smooth and stable and point by point

matching is in order. This is because there is no thermal analog of series capacitance or inductance in electrical circuits.

All the previous methods use individual

response factors to obtain separate heat flows

for constant indoor air temperature and then add them to determine cooling loads. Changes in indoor air temperature or cooling loads permitting

temperature swings need to use another set of response factors for the indoor air temperature

variation. Muncey et al(47,48) have developed a procedure, which determines the response factor

for the total building pertaining to each of the climatic sequences and internal heat loads or air

conditioning flows. This is done by determining

the indoor air temperature first and using a combined coefficient of surface heat transfer at the internal surfaces. However, provision exists

for linking internal masses to internal radiant

loads and accounting for heat flows occurring

internally to any path, as in the harmonic case

(37). All four types of problems mentioned in

section 2 can be handled. Both triangular and pulse types of unit excitations are used for the appropriate types of inputs (48). In this

method, however, it is not possible to consider

non-linear boundary conditions or variable

networks. Experience has shown that if the calculation for sol-air temperatures takes into account the variable outdoor coefficient of heat

transfer, using a time averaged constant value

for it in the calculation of response factors is sufficient. Further, if the internal radiant

loads are linked to internal surfaces and not to the air temperature, using a combined and constant value of surface coefficient of heat

transfer at the internal surfaces is expected to be satisfactory for building problems. Variable

ventilation can be included with certain

restrictions but only at the cost of analytical

rigour,

7. Conclusions

A wide variety of computer oriented thermal

calculation methods pertaining to buildings have

been considered in relation to the concepts they

use, the assumptions they employ and the limitations in regard to their applicability. No attempt has been made to compare their validity

with respect to actual buildings or their

efficiency in terms of computer time. This can only be done by using all of them for the same large size actual building and comparing the estimates with the experimentally observed data

and the actual computation costs incurred,

i.e. by instituting some sort of round robin

test. In a fast developing discipline, like the subject of this survey it is very likely that some conceptually significant methods may have

escaped the notice of the authors and the omissions, if any, are not intended to reflect on

the methods.

8. References

(1) Milbank, N.O. and Harrington-Lynn, J., Estimation of Air conditioning Loads in Air Conditioning System Design in Buildings,

p. 41 (Elsevier, 1969).

(2) Gupta, C.L., Heat transfer in buildings - a review. Arch. Scl. Rev. 21,1 (1970).

(3) ASHRAE Handbook of Fundamentals, New York,

(1967).

(4) Carrier Handbook of Air conditioning

System Design (McGraw Hill, 1965).

(5) Boeke, A.W. , New developments in the computer design of air conditioning systems,

J.I.H.V.E, 35,195 (1967).

(6) Korsgaard, V. and Lund, H. , Air conditioning

load calculations by means of a passive

electrical analogue computer. World Power

Conference, IV-B, Paper 63 (1964).

(7) Button, D.A. and Owens, P.G.T.,

Considerations for the optimized fabric

design. Engineering in the home, p. 64 (Allen & Heath, 1969).

(8) Euser, P. , De Toepassing Van Analogons Blj Het Oplossen Van Warmteoverdrachts-problem,

De Ingenieur J_7, (1961).

(9) Stephenson, D.G. , Methods of determining non steady state heat flow through walls

and roofs of buildings, J.I.H.V.E. 30,64

(1962),

(10) Carslaw, H.S, and Jaeger, J,C, , Conduction

of Heat in Solids (Oxford University Press,

1959).

(11) Beckman, W,A, , Solution of heat transfer

problems on a digital computer.

International Solar Energy Society

Conference, 7/66 (1970),

(12) Kusuda, T, and Achenbach, P,R. , Numerical

analysis of the thermal environment of occupied underground spaces with finite

cover using a digital computer. Trans. ASHRAE 69,439 (1963).

(13) Buchberg, H, , Bussell, B. and Reisman, A.

,

On the determination of optimum thermal

enclosures, Int. J.Brodim.Bromet _8,103

(1964).

(14) Sheridan, N.R. , Energy conservation applied

to the rational design of a dwelling for

the tropics, World Power Conference, IV-B, Paper 54 (1964).

(15) Buchberg, H. and Roulet, J.R. , Simulation

and optimization of solar collection and storage for house heating. Solar Energy

22,31 (1968).

109
(16) Wheway, R.T. and Vahl Davis, G.De.

,

Calculation of transient heat flow into

buildings, ASHRAE Jl.8,67 (1966).

(17) Bobco, R.P., Radiation heat transfer in

semi-gray enclosures with specularly and diffusely reflecting surfaces. Trans. ASME,

Ser.C. 86,123 (1964).

(18) Hamming, R.W. , Numerical methods for scientists and engineers, (McGraw Hill,

1962).

(19) Guillemin, E.A. , Mathematics of circuit

analysis, (John Wiley, 1964).

(20) Mackey, CO. and Wright, L.T. , Periodic

heat flow - homogeneous walls and roof, Trans. ASHVE 50,293 (194A).

(21) Mackey, CO. and Wright, L.T., Periodic

heat flow - composite walls and roof. Trans. ASHVE 5^,283 (1946).

(22) Mackey, CO. and Wright, L.T. , The sol-air

thermometer, a new instrument. Trans. ASHVE _52,271 (1946).

(23) Degelman, L.O., The development of a mathematical model for predicting solar

heat gains through building walls and

roofs. Better building report No. 6, (Penn. State University, 1966).

(24) Nottage, H.B. and Parmelee, G.V., Circuit

analysis applied to load estimating Pt.I,

Trans. ASHAE 60,59 (1954).

(25) Nottage, H.B. and Parmelee, G.V. , Circuit

analysis applied to load estimating Pt.II

Trans. ASHAE _61,125 (1955).

(26) Van Gorcum, A. , Theoretical considerations

in the conduction of fluctuating heat flow,

App.Sci.Res A2,272 (1951).

(27) Muncey, R.W. , The calculation of temperature inside buildings having

variable external conditions, Aust.J.Appl.

Sci 4_,189 (1953).

(28) Pipes, L.A. , Matrix analysis of heat

transfer problems, J.Franklin Inst. 263 , 195 (1957).

(29) Gupta, CL. , A matrix method for predicting

thermal response of unconditioned buildings,

J.I.H.V.E. ^,159 (1964).

(30) Muncey, R.W. and Spencer, J.W. , Calculation

of non-steady heat flow : considerations of radiation within the room, J.I.H.V.E.

34,35 (1966).

(31) Loudon, A.G., Summertime temperatures in buildings without air conditioning, BRS

cp 46/68.

(32) Rao, K.R. , Accurate estimation of airconditioning load of buildings, Proc. Third

Aust.Bldg Res.Congr., Melbourne, 1967,

162 (1968).

(33) Gupta, CL. , Some heat transfer problems

with application to buildings. Chap. 8. Ph.D. Thesis, University of Roorkee, 1967.

(34) Muncey, R.W. and Spencer, J.W. , Calculation

of temperatures in buildings by the matrix

method : some particular cases, Bldg.Sci.

3,227 (1969).

(35) Gupta, CL. , A systems model for environmental design of buildings (in this

symposium)

(36) Raychaudhuri , B.C., Transient thermal response of enclosures : the integrated

thermal time constant. Int. J. Heat Mass Transfer 8,1439 (1965).

(37) Billington, N.S., Building Physics - Heat,

p. 68 (Pergamon, 1967).

(38) Nessi, A. and Nissole, L. , Fonctions

d' influence de flux de Chaleur des parois

de construction. Rapport . Comite Tech.

Indus. Chauffages (Paris, 1967).

(39) Pratt, A.W. and Ball, E.F., Transient

cooling of a heated enclosure. Int. J. Heat Mass Transfer 6^,703 (1963).

(40) Choudhury, N.K.D. and Warsl, Z.U.A.

,

Weighting function and transient thermal response of buildings. Int. J. Heat Mass Transfer 2,1309 (1964).

(41) Brisken, W.R. and Reque, S.G., Heat load

calculations by thermal response. Trans. ASHVE 62,391 (1956).

(42) Mitalas, CP. and Stephenson, D.C, Room

thermal response factors. Trans. ASHRAE,

Paper 2019 (1967).

(43) Mitalas, CP. and Arsenault, J.C, Fortran

IV program to calculate heat flux response ^ factors for multilayer slabs, DBR computer program no. 23 (NRC Canada, 1967).

(44) Mitalas, CP., Calculation of transient heat

flow through walls and roofs. Trans. ASHRAE

74,181 (1968).

(45) Stephenson, D.C and Mitalas, CP., Cooling

load calculations by thermal response

factors. Trans. ASHVE 23, Paper no. 1028,

(1967).

(46) Kusuda, T. , Thermal response factors for multi-layer structures of various heat

conduction systems. Trans. ASHRAE 75,246

(1969).

(47) Muncey, R.W. , The thermal response of a building to sudden changes of temperature

or heat flow, Aust.J.Appl. Sci. 14, 123

(1963).

(48) Muncey, R.W. , Spencer, J.W. and Gupta, CL. , Method for thermal calculations using total building response factors (in this

symposium)

110
Method for Thermal Calculations using Total Building Response Factors

by R. W. R. Muncey*, J. W. Spencer"*" and C. L. Gupta"*"

Thermal calculations for buildings may be conveniently undertaken by

multiplication of the time sequence of climate parameters and the response factor

of the building for each parameter. The true response factor is the sum of an infinite number of exponential terms which may be approximated by truncation

directly or by matching the response with a chosen number of exponential terms having prespecified time constants.

Computationally the latter method is attractive because it may use the response values for the building to sinusoidal changes of a number of prespecified

frequencies. The combination of the behaviour of the various heat paths is then relatively simple irrespective of the number of layers in any one path and even if branches or heat flows occur within some of the paths.

The process involves calculation of the thermal response of the separate heat

paths relevant to the climate parameters at the steady state and at a set of 18 frequencies, the combination of these responses to determine the total building

response to any one climate excitation and multiplication by a precalculated matrix

to give the exponential series for the response factor. It has been found that

the errors introduced in the matching process are insignificant when compared with

the inaccuracy in knowledge of the building's thermal properties and of climatic

data.

Because, in the normal heavy building, the response factor even at 10 days is not completely negligible, some method is desirable to reduce the data bank

necessary to store the total building response factor. This is achieved by

calculating and retaining the values at hourly intervals to 6 hr and at times in the ratio of l:/2 upwards from 0.177 days (and including h, h, 1» 2, A ....days).

Results will be shown as obtained by use of a Control Data 3600 computer and

an indication given of approximate means for overcoming the inherent shortcomings

of this and comparable methods.

Key words: Building, computer, exponential series, harmonic, indoor

temperatures, matrix, response factors, step function, thermal.

1. Introduction

The growing desire to understand the internal

thermal environment of buildings and the greater

need to tailor the capacity of air conditioning

devices have led to notable improvements in the calculation methods available. With the advent of electronic digital computers giving improved

speed, complexity and reliability in comparison

with earlier methods, it is no longer necessairy to restrict investigation to simple cases or to adopt

simplifying assumptions of doubtful validity.

The data commonly available for use in specific cases consist of a knowledge of the structure and its orientation, the dimensions and

thermal properties of its components and the climatic variables expressed as time sequences, generally at hourly intervals, of the parameter

values. These inevitably relate to past cycles

and the calculation may use a set derived from an earlier specific occasion or a set representative

of earlier occurrences averaged by a selected

method not relevant at the moment. Sequences for external air temperature, sol-air temperatures of various surfaces, sunshine penetration of windows

and internal heat loads are the most suitable and will be used hereunder although other series

defining comparable climatic variables could be

used.

*Division of Forest Products, CSIRO, Melbourne, Australia

"'Division of Building Research, CSIRO, Melbourne, Australia

111
Several assumptions are implicit in even the most sophisticated methods presently of interest.

It is almost universally assumed that the transmission through the various paths

(e.g. walls, floor, roof) is unidimensional and that the effects of corners and lumped

construction such as wall studs and roof rafters may be ignored. Constancy of thermal values of conductivity and heat capacity is assumed even although these are known to vary somewhat with

temperature and moisture content. Film

resistances are commonly also assumed constant

and current work by the authors suggests this

assumption does not introduce errors of an unacceptable magnitude. Muncey and Spencer^

showed that the transfer of heat between the bounding surfaces of a room could be treated

adequately by a star network connecting each

surface to a "mean convective- radiative

temperature" for the errors thereby introduced

are less than those caused by neglecting the presence or the location of furniture.

2. Overall Strategy

A fonvenient method, when one has available

sequences describing climatic data, is to determine response factors which connect the temperature or heat flow to be calculated with

the climatic data by a relation

internal temperature = 2 (response factor x climatic data sequence)

(1)

/ 9 l A well known method (Nessi and Nissole^ -'j Brisken and Reque' , Stephenson and Mitalas^^-^ Kusuda^^O determines the response factor relating

the heat flow (with a constant internal

temperature) for each path separately and thence evaluates the total heat flow. By finding the response of the internal temperature to a step

function or unit pulse heat flow to the inside,

it is readily possible by an Inversion process to evaluate the internal temperature conditions

within or following a given climatic data

sequence.

This paper will describe a method which

evaluates the response factor for the total building, there being a particular set of response

factors corresponding to each external climatic sequence and to internal heat loads or air

conditioning heat flows. The response factor for

a total building derives from the sum of several

sets of an infinite series of exponential terms, the number of sets being n I if there be a total

of n "slabs" within the several paths for heat

flow within the structure. As the value of n might easily reach 20, and since the exponential

decrements are related to the solutions of

transcendental equations with values dependent on

the thermal properties of the structure, the complexity of the exact solution needs no emphas is

One method that might be used in a search

for simplicity is to truncate the series

described and it is common to find that, except

for very short intervals (i.e. soon after the initiating pulse) appropriate accuracy can be

achieved with only one or two terms. An

alternate method is used here. In this the response is calculated for the steady state and

for cases where the external driving stimulus is sinusoidal. The building can readily be treated

as a whole (i.e. the effect of the several paths may be combined) even if parallel paths occur as arms within a particular identified path or heat

flows occur at points internal to the path

(Muncey and Spencer^S)). By suitable choice of the frequency of the stimulus and by using an adequate number of frequencies, the response may

be characterised with any desired degree of precision. It will then be shown that, from

these sinusoidal responses, by multiplication by

a precalculated matrix, the coefficients of a large series of exponential terms with

prespecified time constants can be evaluated. Again, any desired degree of precision can be

achieved by using sufficient exponential terms.

In the work being described, 18 terms are used

with the (angular) frequency of the sinusoidal

variations ranging from 1 in 768 hr to 170 2/3 per hr and the time constants ranging from

768 hr to 3/512 hr. The total errors introduced by the use of only 18 terms are of the order of 0.01 per cent, for cases where the time constants are of the order of 1 hr to

1 day.

3. Harmonic Response

An individual homogeneous slab of infinite

area with sinusoidal temperatures on and heat

flows across the faces can be considered using

the same mathematics as for an electrical

"four pole" (Van Gorcumt7}, VodickafSl), The

surface temperatures T^^ exp(jojt) and T^ exp(ju)t) and the heat flows Wj^ exp(j(jot) and W2 exp(jiot) are related as follows:

cos H -(R sin H)/H Tl

W2 (H sin H)/R cos H

wherein R is the thermal resistance of the slab per unit area, c is the thermal capacity of the slab per unit area and H = (jaiCR)'^.

*Figures in brackets indicate the literature references at the end of this paper.

112
Van Gorcum further showed that, if slabs were

placed in series with intimate contact over their

surfaces, the matrix connecting the temperatures

and heat flows over more than one slab could be

found by multiplication of the individual

matrices.

An individual heat path in a building can be

represented by a number of slabs in series and

the total building with its several heat paths by

several of these groups in parallel. If the matrix for a typical heat path of area A

connected to an external climatic element be

^11 ^12

p = ^21 ^22

and that of a typical neat path

connected to a face over which no heat flows

(e.g. half a symmetrical wall exposed on each side

to the same temperature) be

Qll ^12

^21 ^^22

and if the value of the sinusoidal temperature be

exp(ju)t) externally and T exp (jiut) internally

and the heat flow to the inside (air) be W exp(ju)t) then

IAT^(1/P^2) - W

IA(P^^/P^2) + 2:b(Q2i/Q22)

shown by Muncey^9,10} and Pipes'-

(3)

Step Function Response

Consider a thermal circuit as shown in figure 1 with a driving stimulus at D and a response at R. The stimulus may be an imposed

temperature or a heat flow and connecting

circuits may have any configuration (series,

parallel or series-parallel) and some may not be

present in the specific case. The steady state response x^ at R due to a unit stimulus at D and

the periodic response Xq + + iV-^) exp(ja)j^t) at R due to a stimulus exp(j(i^t) at D can be

found for relevant by the method outlined in the previous section. It is desired to find the response g + f g exp(-b t) at R corresponding

0 n=I n n

to a unit step function at D. Consideration of the response at large values of t will show that The periodic stimulus exp(ja)^t) may be considered as the result of innumerable

infinitesimal step- function stimuli ju^^exp (ju^^t) 6t occurring from infinite time past.

Applying the step-function response to each stimulus and adding, the harmonic response is

ja)j^exp(ju)^t') [Bq + I^^ B^exp(-b^(t-t'))] dt'

3<\

i.e. BQexp(ja)^t) + B^ exp (jiJ), t)

Equating the response from the two methods and

ons remain

Each equation

removing B^ and x^, a series of equations remain

for evaluation of the values of B has the form ^

n=l

0, + ib 0), k n k + to, ~ \ = \ j^k

and the whole may be represented in matrix form

|R|.|B|=|x| and |s|.|B|=|y|

Presuming that the nxjmber of n's and k's are the same, the values of the B's may be found from

either set of equations as

iBl = IR 1

B

The same problem is handled by an alternate

{ 1 ?} method by Muncey .

5. Practical Evaluation

The method outlined would be merely

theoretically interesting if a number of conditions

are not fulfilled. It is desirable that, to achieve an acceptably accurate result in

representing the thermal change;

(a) the number of harmonics and exponential

terms is not excessive

(b) the range of frequencies and time constants adequately covers the area of interest

(c) the elements in the inverted matrix | R| or I S are not excessive

(d) the exponential coefficients are not large

compared with the thermal change.

An early choice, which has been found to satisfy these conditions very satisfactorily, is as follows:

113
(a) the values of bj and ui-^, i.e. the inverse

time constant of the exponential and the angular frequency, to be equal

(b) the ratio between successive b's and u's

to be 2:1

(c) the total number of harmonics (and

exponential terms) to be between 10 and 20.

In the presently used calculation the number is cfiosen as 18. This choice gives an angular frequency from 1/768 hr to 170 2/3 per hr

and time constants from 768 hr (32 days) to 3/512 hr (21 sec) which adequately covers the range of interest. The |s| matrix is symmetrical

and |s|~^ matrix has values up to 30.07. The quarter matrix is given in Table 1. It should be

noted that by calculating the matrix inverse for increasing sizes, it can easily be seen that each row in the infinite matrix would have the values

given in Table 2 in order from the diagonal to the left and right and thereafter the ratio from

one element to the next is -0.5. In a matrix of large order the elements close to the top left and bottom right corners (within say 6 rows or columns) are very close to those given in

Table 1. All this implies that the coefficient b

is largely fixed by the values y of the harmonic

response at frequencies to close to b, a result

that is not really surprising. . ,

The above treatment relates to the response

to a step function excitation. It is more

suitable, in representing the external climate, to assume a linear change to occur between successive

values of the climatic data. This can be achieved

by transforming the step function response to give

the response to one of the excitation patterns of figure 2 for temperature or heat flow.

It can readily be shown by Integrating the response at time t from t-1 to t (fig. 2 (a)), by

differencing the responses at times t and t-1, each being integrated from t-1 to t (fig. 2(b)), or by differencing the responses at times t and t-1

(fig. 2(c)) that the factors by which the term

exp(-b^t) must be multiplied are

t = 1

Figure 2(a) (exp(b )-l)/b n n

t > 1

(exp(b^)-l)/b^

Figure 2(b) (exp (b^)-l) /b^ -(exp(b^)-l) /b^

Figure 2(c) 1 - exp(b^)

Table 1. One Quarter of the Symmetrical 18 x 18 Inverse Matrix

, 7. 75597

-10. 34130 21.54437

6. 89420 -19.53356 27. 67254

-3. 72068 11.85510 -22. 84083 29.45742

1.,89682 -6.24977 13. 54116 -23.75077 29.92131

-0.,95304 3,16754 -7, 09692 13,99835 -23.98384 30.,03842

0.,47710 -1.58918 3. 59163 -7.32579 14. 11503 -24.,04247 30.06776

-0.,23862 0.79527 -1. 80129 3,70610 -7.38415 14., 14435 -24.05713 30,07507

0.,11932 -0.39772 0.90133 -1.85853 3.73528 -7..39879 14.15166 -24.06074

-0..05966 0.19887 -0. 45075 0.92994 -1.87311 3..74258 -7.40241 14.15338

0.,02983 -0.09943 0. 22538 -0.46504 0.93721 -1.,87671 3.74430 -7.40309

-0.01491 0.04971 -0. 11268 0.23250 -0.46863 0.,93893 -1.87740

0.,00745 -0.02484 0. 05631 -0. 11620 0.23421 -0.,46932

-0.,00372 0.01240 -0. 02810 0.05799 -0.11688

0.,00185 -0.00615 0. 01394 -0.02877

-0,.00089 0.00298 -0. 00676

0..00039 -0.00131

-0..00012

30.07679 -24.06143

Table 2. Major Elements in the Infinite Inverse Matrix

30.07756 -24.06204 14.15414 -7.40371 3.74507 -1.87801 0.93969 -0.46993 0.23498

114
It should be noted that these factors can range in magnitude from 10"^ to lO^^^ and that

the steady state term Bq remains at all times

when using the pulse shape of figure 2(a), but

cancels at times later than t = 1 for the pulse

shapes of figures 2(b) and 2(c). The authors

have found it most convenient to use the pulse

type of figure 2(a) for temperature changes, that

of figure 2(b) for solar heating through windows

and that of figure 2(c) for "air-conditioning"

and internal heat flows.

With exponential time constants ranging up

to 32 days it is obvious that the steady state may not be approximated satisfactorily even at

50 days. Storage of behaviour at hourly intervals

would require 1200 memory cells for each heat

path in each building and a similar storage for either each temperature sequence or future temperature accumulation. This huge store demand

has been reduced by the following device. The response factor for each path of the building and

the accumulation of future temperatures is undertaken for 1, 2, 3, 4, 5 and 6 hr and for

3 X 2^ 3 X 2^'\ 3 X 2"\ 3 x 2^'^

18/2 3x2 hr and the future accumulator for

3 X 1^^'^ and 3 x

2^°''^ hr (90.5 and 128 days) set

18/2

equal to that at 3 x 2 hr (64 days).

Acciunulation at each future time is made by

adding the product of the climate parameter for

each path by the response factor for the relevant

path and time.

Following suitable "thermostat" procedures,

the time marker is moved one hour and the new accumulator values are found as follows

by substitution from

previous 2 to 6 hr values

by interpolation as described later

1 to 5 hr

2/2 3x2' hr to 64 days

64/2 and 128 days by copying the 64 day value

2/2

6 hr by copying from 3x2 hr

\, 3 X 2

^ hr by second order Bessel

interpolation using linear

time and the values for

3, 4, 5 and 6 hr.

In the series from 6 hr to 64 days the value

for (3 X 2"'/2 + 1) Q^d time (i.e. 3 x 2TM/2 hr

new time) is found by second order Bessel

interpolation with a logarithmic time scale. Calculations for cases recognized to be difficult

to match with the chosen exponential series and operation of the repeated interpolation process

have been shown to introduce errors of the order

of 0.01 per cent, in conditions normally of interest in buildings.

Implementation

Computer programs to enable such calculations to be undertaken have been written

for an Elliott 803 computer and more recently a Control Data 3600 computer. Since only time

units are implicit in the program, it is capable

of operation in any consistent system of units.

Refinements allowing detailed data checking,

calculation of solar position, sol-air

temperatures and heat flows consequent on radiation transmitted by windows have been

included. Very lengthy climatic sequences can be handled and the total memory required for the program is of the order of 28K cells. Allowing

for heat path groups and 12 heat paths plus

thermostat ventilation, heating and cooling paths,

10 buildings can be accommodated at one time. The whole calculation for one building with say

10 heat paths and a 21 day sequence considered

hourly requires about 40 seconds computational

time.

7.

{1} Muncey, R. W. and Spencer, J. W.

,

Calculation of non-steady heat flow; considerations of radiation within the

room, J.I.H.V.E. 34 35-38 (1966).

{2} Nessi, A. and Nissole, L. , Fonctions

d' influence de flux de chaleur des parois

de construction, Rapp.Com.Tech.de I'Ind. du Chauff. et la Vent Paris, (1947).

{3} Brisken, W. R. and Reque, S. G. , Heat load calculations by thermal response, ASHRAE

Trans. 62 391-419, (1956).

{4} Stephenson, D.G. andMitalas, G. P.,

Cooling load calculations by thermal response factor method, ASHRAE Trans. _73^ III. 1.1-7 (1967).

References

{5} Kusuda, T. , Thermal response factors for multi-layer structures of various heat

conduction systems, ASHRAE Trans. 75 246-270 (1969).

{6} Muncey, R. W. and Spencer, J. W.

,

Calculation of temperatures in buildings

by the matrix method : some particular cases.

Build. Sci. 3 227-229, (1969).

{7} van Gorcum, A. H. , Theoretical considerations

on the conduction of fluctuating heat flow,

Appl. Sci. Res. Hague A2 272-80 (1950).

{8} Vodicka, V., Conduc tion of fluctuating

heat flow in a wall consisting of many

layers, Appl. Sci. Res. Hague A5 108-14

(1955).

115
{9} Muncey, R. W. , The calculation of temperatures inside buildings having

variable external conditions,

Aust.J.Appl.Sci. _4 189-96 (1953)

{10} Muncey, R. W. , Calculation of heat flows

and temperatures in slabs in series,

parallel and series-parallel,

Appl.Sci.Res. Hague A5 461-62 (1956).

{11} Pipes, L. A., Matrix analysis of heat

transfer problems, J. Franklin Inst. 263 195-206 (1957).

{12} Muncey, R. W. , The thermal response of

a building to sudden changes of temperature or heat flow, Aust.J.Appl.Sci.

14 123-128 (1963).

! •

D R

Figure 1. Generalised thermal circuit,

driving stimulus at D, response at R.

Figure 2. Temperature or heat flow excitation pulse shapes.

116
Calculation of Building Thermal Response Factors (BTLRF) as Wiener Filter Coefficients

T. Kusuda

National Bureau of Standards

Washington, D, C.

Recent advances in the application of computers for environmental engineering

problems have brought forth a number of sophisticated computer programs for simulating the hour by hour thermal performance of buildings. These programs not only

calculate hourly thermal load of the building spaces, but also simulate the opera- tion of energy distribution systems and mechanical equipment. When applied to a large building, however, the amount of computations to be performed become formi- dable even for the modern high speed and large memory computers. One way to reduce

the computational requirement and to save the computer time (and cost) is to use building thermal response factors, (BTLRF), which are secondary sets of numbers

derived from the limited amount of detailed calculations which are obtained from

the exact thermal analysis. Presented in this paper is a preliminary attempt to apply time series analysis for obtaining BTLRF of a single room building. It is pointed out that BTLRF could also be obtained from measured thermal performance

data or energy consumption data.

Key Words: Building thermal load response factors, energy requirements,

heating and cooling load calculation, Wiener filters

1. Background

Calculations to determine the heating and cooling load for use in predicting building energy re- quirements can now be done by many digital computer programs. Although differing in minor technical

details, most of the current computer programs for energy calculation obtain the hourly thermal load

in conjunction with hourly weather tape data as provided, for example, by the National Weather Record

Center.

This hour by hour calculation of energy requirements, based upon detailed simulation of building

thermal response, has been considered more accurate for a wider type of buildings than other simplified

techniques, commonly known as the "degree day method", the "equivalent load factor method" and the "bin

method"i!l/. These simplified methods are based upon the assumption that the building thermal performance

can be calculated by a simple linear function of outdoor air temperature, particularly the temperature

difference between the out- and indoor air. The temperature difference concept of the simplified tech- niques ignores the fact that the building thermal load is also dependent upon the other factors, such

as solar radiation, moisture content of air, internal heat generation, and heat storage of the building

structure. The simplified methods based upon the linear temperature difference concept have been, however, considered relatively accurate for use in residential applications, mainly due to the fact that

the effect of solar radiation is relatively small and the internal heat generation is small and relatively constant as compared with commercial or industrial buildings.

Senior Mechanical Engineer, Environmental Engineering Section, Building Research Division

Although numerous references are available for these traditional methods, the most convenient one will be the ASHRAE Guide and Data Book, Systems 1970, Chapter 40, pp. 619-634.

117
The factors that have justified the use of the simple temperature difference concept become increasingly inappropriate as the building becomes larger and operational and occupancy characteristics grow

complex. For example, the solar radiation effect becomes extremely important when an exterior wall of

a modern office building is largely glass. For another case, internal heat generation due to the heavy

lighting power per square foot of floor area tends to eclipse the indoor-outdoor temperature difference

effect on the thermal load. Added to the complexity of these characteristics of the modern large scale building is the sophisticated nature of the heating and cooling system and its controls, for distributing

excess internal heat of the building core to the periphery to limit the heating requirements during the winter.

The hourly load simulation method with the use of computers performs an algorithmic operation which

is designed to follow the actual thermal performance of buildings under realistic or randomly fluctuating

outdoor weather conditions. One of the difficulties involved in using the sophisticated and exact hourly

calculation of building thermal performance is that a large amount of computer and memory time is needed.

For example!./, the computer program developed by the U. S. Post Office Department requires a 100 K core storage computer (if applied to large postal facilities) and approximately 2 minutes of UNIVAC 1108 time

to obtain an energy requirement estimate for heating and cooling of one room for a period of 365 days.

If the calculation is to be performed for a large building consisting of, say 100 different rooms, the total computation time becomes prohibitive. This is particularly so when the building characteristics

under consideration are complex, and when the accuracy requirement is such that the simplification of

the computational efforts may be risky. The reduction of the computational effort is usually accomplished

in two different ways. The first is to simplify the algorithms such as to delete refined calculation

routines (thermal storage effect and infiltration effect). The second method is to simplify the building structure such as to treat a multi-room building as a single room building by ignoring the heat ex- change among rooms and by ignoring details of the building structure. However, it has not been wellestablished xinder what conditions these computational shortcuts are justified. But in addition to these two, also presented in this paper is a preliminary attempt to study a third alternative for the reducing computational requirement, with a reasonable accuracy. Its objective is to obtain a secondary

set of numbers called the building thermal load response factors (BTLRF) from the results of a limited

number of detailed calculations.

2. Building Thermal Response Factors (BTLRF)

These building response factors are basically regression coefficients as it becomes clear in the later discussion. The primary assumption imposed upon this technique is that the building thermal

loads are a linear function of various excitation parameters such as outdoor temperature, solar radiation, internal heat generation and as well as the indoor temperature^'.

It is also assumed that the stochastic characteristics of the thermal load as well as the excitation time parameters are stationary, meaning that their basic means and standard deviation do not change

with respect time.

As a matter of fact, it is important to point out that the basic technique used to derive these building response factors can be applicable to any time series relationship, whether it be the heating/

cooling load, energy requirement, space thermal load or building thermal load. The time series, therefore, could be the observed energy usage values rather than the calculated values as mentioned previously. The idea is to derive regression coefficients from any input and the output time series by a suitable regression technique.

For example, the hourly room thermal load may be calculated by a detailed computer program for a predetermined period (say N hours). The calculated hourly thermal load is then the desired output time series whereas the dry-bulb temperature, solar radiation and the internal heat generation may be con- sidered input time series or the excitation time series.

Denoting the hourly values of the thermal load, outdoor dry-bulb temperature, room temperature,

solar radiation and the internal heat generation by q, DB, T, SOL and LT, respectively, it is assumed

that the following linear relationship exists among them.

M / DB - T

t-s t-s

Lt-s ''t ~I (fi(s), £^(3), f3(s)) I SOL 1 , t - 1, 2 ... N (I) LT^

t-s

- The constant factor relating the degree days data to the energy requirement is a simplified

BTLRF when the temperature difference is the major contributor to the energy requirement.

118
In this expression fj^(s), £2(3) and f^Cs) for s = 0, 1, 2 ... M are the regression coefficients for the excitation parameters, temperature, solar radiation and the internal heat generation respectively. Sub- script t in eq. (1) refers to the hour at which q is calculated and t-s refers to DB, T, SOL and LT evaluated at t-s hour.

These regression coefficients are called the Wiener filters [1] if they are determined in such a way that N 6=Y(q^-q;)' (2) t=l

in minimum, whereby the q' is the value obtained by the exact calculations taking into account the building details and, or the desired output time series, whereas q^ is the value approximated by eq.

(1) solely on the basis of time series analysis of participating variables.

In eq. (2) N is the total number of data points to be analyzed to arrive at the least squares re- gression coefficients or Wiener filters. For example, if the two weeks data were used for the hourly

thermal load calculations, N should be 336.

A computer program to obtain the Wiener filters coefficients has been developed and published by

E. A. Robinson [2]. The progrcun utilizes a recursion type solution of multi-channel normal equations

of the data to be processed. Given in the following section are examples of the application of the Robinson's computer program to the heating and cooling load calculation by the thermal analysis pro- gram [2] of the U. S. Post Office Department (USPOD).

3. Sample Calculations

In order to examine the feasibility of the use of the Wiener filter routine to obtain BTLRF as the

least square regression coefficients, hourly heating and cooling loads of a one-room building was first

computed for 336 hours by the USPOD program. The weather data used for the calculation were for Janu- ary 1949 of Washington, D. C.

Figure 1 shows the trend of the excitation functions, namely the dry-bulb temperature, solar radiation and internal heat generation during the computation periods.

In order to simplify the calculation, the room temperature, T^ , in eq. (1) was assumed constant at

75 °F. When the calculated thermal load was plotted against the outdoor temperature and against the solar radiation, they showed very much scatter as shown in figures 2 and 3 respectively. Figure 2, for example, suggests a danger of estimating hourly thermal load by a linear relationship with outdoor

air temperature alone.

The Wiener filtering technique was applied to the calculated thermal load regressed with

(DB-75) , SOL and LT^ for eq. (1) for s = 0, 1, 2, . . . M. t-s t-s t-s 1 K J

The value M in equation (1) is called the filter length and is related to the delayed reaction of

the thermal load q^. with respect to the excitation parameters. A satisfactory value for M may be deter- mined by letting M = o, 1, 2 ... in eq. (1) until further increase does not significantly decrease the value of 6. In this particular example, values of M up to 20 have been tried and it was found that the optimum value is 3 for all the practical purposes.

In order to illustrate building response factors for M = 3, the filter coefficients for a one-room

building are listed as follows:

f^iO) = 31.913 f2(0) = 3.807 f^CO) = 4.308

fj^(l) = -.426 f2(l) = -.056 f^d) = 1.809

fj^(2) = -.267 f2 (2 ) = 1.777 f3

(2 ) = 1.762

fj^O) = -.245 f2(3)= 1.110 £3(3) = 2.639

119
Normalized values— of 6 for M = 0, 1, 2 ... 10 respectively for a similar analysis are 0.219, .137,

.093, .067, .062, .057, .054, ,053, .050, and .047, which show the diminishing return for M beyond 3. It should be pointed out that it is difficult to draw physically meaningful conclusions from these coefficients, since they were derived solely by numerical data manipulation. Nevertheless, they simulate thermal load very accurately for the period where the original data were analyzed. Also to be pointed out is the reduction of mathematical operation manifested in a simple algebraic formula of equation (1) against a detailed thermal analysis program consisting of approximately 2000 Fortran

statements.

It is, however, to be expected from the theory of heat conduction equation that the absolute

values of BTLRF should start to decrease steadily—' as the value of s increases beyond a certain value,

say S , such that max

.... fj^ (S+3)

when S > Smax

This decreasing trend was not observed for this sample calculation even when M was carried up to 20,

although it is possible that filter coefficients of more physically consistent nature might have been

obtained, had a suitable smoothing technique been applied to the input data.

Although these response factors did reproduce the original data very well, a true test of the res- ponse factors would be when they are applied in a predictive manner. Figure 4 shows the same response

factors applied to eq. (1) for the climatic data beyond the period when the original thermal load was calculated. Figure 5 is in turn the thermal load calculated by the USPOD program for the same weather

record period. If the response factors are ideal, figures 4 and 5 should match each other well for the entire period.

By overlaying figure 4 on figure 5 it can be shown that the two curves match almost perfectly for the first 336 hours during which period the response factors were generated. The same two curves, however, begin to differ considerably as the time goes beyond the first 336 hours and particularly during

the summer period, although general trend of the increase of the mean thermal load is obtained by the response factor calculation. The increase of the diurnal amplitude of the thermal load during the

summer, however, was not well represented by the calculation using BTLRF.

The similar calculation repeated for 336 hours (two weeks period) data of thermal load and accom- panying weather data during the last week of June yielded another set of building response factors

such as

fj^(O) = 39.497 h

(0) = 11.558 f3(0) = 7.2 06

f^(l) = 15.488 h

(1) = -4.362 f3(l) = 1.668

f^(2) = -50.894 h

(2) = -4.177 f3(2) = 1.789

f^(3) = 38.594 (3) = 10.768 f3(3) = 1.650

These values were in turn used again to calculate the hourly building thermal load from January to June by eq. (1), results of which are shown in figure 6.

The agreement between the thermal loads obtained by the detailed calculation with use of USPOD program and those approximated by eq. (1) is poor during the winter this time. The decrease of the average values and amplitudes of the building thermal load during the winter is not well reproduced.

These dwo sets of calculations and figures 4 and 6 suggest that the BTLRF can be made a function

of time.

It is assumed that they will change from set (3) to (4) by a linear fashion such that:

[f(t)] = [fj + [fj (1 - 5^) (5)

where [f ] and [f ] represent the winter and summer building response factors and [f] is those adjusted

with tune.

f^ (S+2) f^ (S+1) (S)

120
The value of §^ in eq . (5) was assumed to be a step time function representing:

P = Integer part of (t/336) . . 5t 12

for the 12 bi-weekly periods spanning the beginning of January through the near end of June.

The result of this calculation is shown in figure 7, and indicates a better agreement with the detailed calculations (figure 3) obtained by the USPOD program throughout the period than figures

4 and 6. The agreement should be further improved if the values of BTLRF were made a more complex

function of time than a simple linear function.

4. Summary

A possible new approach to enhance the use of computers for calculating building thermal load is the application of Wiener-type filter coefficients which are called in this paper the BTLRF or the building thermal load response factors. It is pointed out in this paper that BTLRF can be obtained

either from the heating/cooling load calculated by the very comprehensive computer program (simulating

entire building heat transfer processes) or from the experimentally observed values for a limited

period of time, say two weeks. Once determined, these BTLRF can permit the calculation of the thermal

load by one simple linear algebraic equation. This results in drastic reduction of the computational

effort as well as the core requirement on the computers, from a computer program needing a few thousand Fortran statements and 100 K core storage computer to a program of a few Fortran statements that can be executed on a mini- computer . A rough estimate of computer time reduction is from 2 minutes per room of

a building to a few seconds per room for a computation covering 365 days.

This paper presents one result of an exploratory investigation to derive BTLRF by the use of Wiener Filter Technique to the heating and cooling load calculated by the U. S. Post Office Energy

Analysis Computer Program,

The BTLRF were found to be dependent on time if they were to be applicable for the calculation

of hourly building thermal load over as long as a half year's period. This consideration is necessary

because building thermal load characteristics cannot be considered stationary if the time span is as long as a half year.

The time span of the hourly data used to determine the BTLRF was 336 hours for the calculation

illustrated in this report, although it could most possibly have been shortened to 168 hours or even

less, A satisfactory length of the filter appeared to be 4 terms (j =0, 1, 2, 3).

Although BTLRF provide a relatively good estimate in load calculation by a very simple algebraic

operation, the coefficients obtained by the Wiener filtering technique did not follow the expected

trend that the absolute value would eventually start decreasing steadily. Further work is being per- formed at the Environmental Engineering Section of the National Bureau of Standards to obtain building

thermal load response factors which do follow this expected trend and which are therefore more amenable

to physical interpretation.

5, References

[1] U. S. Post Office Department Report "Computer Program for Analysis of Energy Utilization in

Postal Facilities", Copies obtainable from J, M. Anders of the U. S. Post Office Department,

Washington, D. C. 20260, 1970.

[2] E. A. Robinson, Multi-channel Time Series Analysis with Digital Computer Programs, Holden-Day, San Francisco, 1967, p. 249.

[3] T. Kusuda, "Thermal Response Factors for Multi-layer Structures of Various Heat Conduction

Systems", ASHRAE Transactions, pp. 246-271, 1969, Chicago, Illinois,

121
J

Dry-bulb Temperature,

Solar Energy, Btu per 3q.ft,hr

I 1

J J }

Internal Heat Generation, Btu per hr

J L r~i . 48

Men Tue

96

Wed Thu

144

Prl Sat

Hours

192

Sun Mon

240 288

Tue Wed Thu

Figure 1. Excitation functions used for the thermal load calculation by USPOD computer program for the first two weeks of January.

122
-3000

-2500

^-2000

QQ

Q-1500

a:o

_j

CD-1000

en

>-

_i

ZDO

WfiSHINGTON. 0. C JflNUflRY 1-7. 1949

-500

0

500

100[|

o

a B

i a

g BI

g : i i ;

i s ^

§

° ° ° = B

S B i

°

° =. ° B

^ ° a

B

O

ID 8

S

Q

Ip

ID

15 20 25 30 35

DRY BULB TEMPERniURE, F

40

Figure 2. Relationship between the calculated hourly thermal load and outdoor air dry-bulb temperature.

123
Q

cro

CD

en

LU

>-

_jen

ZDo

3000

2500

2000

•1500

1000

-500

0

500

1000

WRSHINGTON, D- C, JflNURRY 1-7, 1949

0

a o a % o

a

o «

a o ° o °

B a Q Q

20 40 60 80

SOLAR HERT, BTU/HR. SO. FT.

100

Figure 3- Relationship between the calculated hourly thermal load and solar radiation over the south

facing wall.

124
1/nte 'awn nvraiaHi

125
126
Thermal studies by

electrical simulation.

Application example to the study

of the heating equipment of an apartment building heated by electricity.

J. Anquez and L. Bertolo

Centre Scientifique at Technique du BS.tiraent

Paris - Prance

For the study of- trasient heat flow problems we dispose of a simulateur composed of an electrical model with resistors ant capacitors, a direct current analog computer fitted with a logical console

and the necessary input and output devices.

The electrical model allows to represent a group of three rooms.

The time contraction on this model is in the ratio of 0,2 second for

24 hours.

The direct current analog computer allows to : - feed on the model the climatic or occupancy data,

- represent heating and its control.

The input device allows to store for instance the climatic or occupancy data throughout an entire heating season.

The output device includes a fast recorder and a group of digital

counters allowing an analysis of resuits.

The following problems can be treated : In artificial climatization (heating or summer air conditionning) : - Studies on the power required in the course of sequences of the

hottest or coldest day. - Studies on the consumption in the course of a season of heating or air conditionning.

- Studies on the efficiency of a control system during typical sequence

of several days or months.

In natural climatization : - Studies on the variation of the interior temperature in a room during

typical sequence of several days or months.

- Studies on the frequency curve of the temperature in a room throughout

a season. As an exqmple are given some results relating to the study of the

heating device in an partment building heated by electricity.

The heating system selected for the study includes a base heating

by storage in the solid concrete floors where the energy is supplied

principally during the night hours and a additional forced air heating

which is controlled by a thermostat in each room.

We have studied the influence of the heating device and its con- trol on the comfort condition and the energy for heating (base temperature, power capacities, etcetera).

127
Key Words : Electric heating, accumulation

heating in the floor, blowed air heating,

consumptions, power, control, comfort.

1 , Introduction

To solve conduction heat transfer problems in vmsteady state conditions we make

use of an analog method to represent thermal characteristics of walls and floors by

networks of resistors and capacitors. The simulator we have developed on this basis

is specially suited for buildings problems. Below we give a brief description of this

simulator and as an example the study for the electrically heated system of an apartment

building.

2, Description of the simulator

The simulator is composed of three basic section : - RC network

- a direct current analog computer fitted with a Logical console,

- the data input and output devices.

The photograph of figure 1 shows the overall view of the simulator and also indicates names of the major components of all the sections described below.

2.1, RC network

The model is based on the analogy between heat transfer in wall having thermal

infertia and propagation of electricity in a circuit having distributed resistance and

capacitance. In pratice it is difficult to design such an electric medi-um. So the

distributed constalit equivalent circuit representating a wall is obtained by combining

quadripoles in serie, each of them representing a slice of the equivalent circuit,

therefore a layer of the wall.

To determine the thickness of the slices, the heat transfer of a sinusoidal signal

in an homogeneous wall has been stiidied. The mathematical resolution of this problem

being known, it is possible to calculate the temperature and the heat flux in each plane

parallel to the faces of the wall. It is also possible to calculate, for the same signal,

the temperature and the heat flux at the interface of each section of the lumped circuit

equivalent wall. By comparing these two calculations the error introduced by the slicing

is determined ; this error is mainly a function of the frequency of the signal. Thus,

knowing the highest frequency present in the problem and the acceptable error, the

thickness of each slice can be determined. In case the highest frequencies present in

the problem are introduced a on-off thermostat for instance (the cycle of the transient phenomenon being of the order of fractional hour) and with an acceptable error of on per cent, the thickness of the slice must be about one centimeter. Thus it requires a great number of slices. Still hight frequency signals transmitted through the wall are quickly damped, and it is not necessary to keep the same slicing over all the thickness.

In practise, after four of the thinest slices, it is possible to double the thickness and

so on.

To al].ow an easier operation, fifty walls, each one including six sections have been

prewired, thus the coupling between plug-in type resistors and capacitors were ma.de once for all.

The surface resistances network in a room is also pre-wired. In this network the

convective heat transfer between each wall and air and the radiative heat transfer from

each wall to the others have been distinguished. Three networks, allowings to represent a group of three rooms, are pre-wired in this way. The value of the convection coefficients

on the horizontal walls changing with the sense of the heat flux, these coefficients

are represented in the model by circuits of the type shown on figure 2. The ratio of electrical time to thermal time used in the model being of the order

of 2 to 4 X 10-D, the duration of one day is 0.2 to 0.4 second. The ratio of electrical

resistance to thermal resistance is of the order of 10-6 ohms for 1°C W-^but can be changed. Taking into accoxmt the time ratio above, the ratio of electrical capacitance to

thermal capacity is of the order of 2 to 4.10-6yU.F for 1 J°0-K

128
2.2, The direct current analog computer.

Fifty operational amplifiers are used to perform the following fvinctions : - Impedance matching of the generators supplying the clims.tic and occupancy data. to the

network and also impedance matching of the network to the device recording the voltage

at several nodes.

- Data summation : for instance summation versus time of voltages representing outside

temperature and solar radiation on a wall to obtain a voltage representing sol-air

temperature.

- Current generators ; for instance current generator representing solar heat flux

entering in a room by openings.

- Representation of heating, air conditionning control systems.

The logical console is composed of logical modules (AND, OR, NOR, NAND, comparators

etcetera) and electromechanical relays or electronic switches, this system, supplied

with pulses or square signals recorded on the input device (magnetic recorder) described

in the section below, allows to control at predetermined times the following functions,

for instance : - generation of a heat supplied by the heating or air conditionning equipment or by the

occupancy,

- change of a ventilation rate.

2,5, Data input and output devices.

The data input device is composed of a punched tape reader, a digital to analog

converter and a fourteen tracks magnetic tape recorder. Each climatic data is recorded

on a punched tape in fifteen minutes steps. The same operation is made for the occupancy

data if they are functions of the time only. During the reading of the punched tape the

digital data is converted to analog signal and recorded on a track of the magnetic tape.

All the data relating to a building in a given locality outside dry bulb temperature-, so lar radiation on the walls, humidity rates of the outside air, etcetera, are stored in

this manner.

Two output devices can be used. The first one is a twelve tracks ultraviolet photographic recorder fitted with two types of galvanometers ; the three decibels bandpass of

which are four hundred of fifteen hundred cycles per second respectively. The second one

is a system of digital counters allowing an analysis of the results ; consumption statements, statements of the number of times a temperature is reached or exceded, etcetera.

3, Scope of the simulator.

The design of the simulator has been made to match at best the study of the following problems :

3.1, Natujal climatization.

- study on the variation of room temperature during a typical hot or cold spell, for

instance.

- study on the variation of temperature in a room throughout a heating or cooling season

In such a case, real climatic data of a given locality are used and the maximum daily

temperatures frequency curve, or the curve giving the total time during which the temperature stays at a given value may be determined.

3.2, Artifical climatization

(heating or summer air conditionning) - Analysis of the power required in a room throughout the coldest or hottest days

sequences, to determine the heating or air conditionning equipment.

- Analysis of the power consumption in a room throughout an entire heating or air

conditionning season, to determine the energy requirement or the frequency curves of the room temperature (air temperatxire , floor temperature in the case of floor heating or the

air relative humidity in humidifying climatization systems, for instance),

- Analysis of the efficiency of a control system throughout the season or a sequenc

of clear but sunny days in mid-season heating. The efficiency of the control system may

be judged by taking into account the energy requirement and comfort conditions obtained

by the system.

129
4, Stiidy of the heating device of an apartment building heated by electricity

Reported here is a study of a heating device of an apartment building, the power

source being electricity'

The building had a large thermal inertia and a good thermal insulation.

The system analyzed includes : - A base heating by storage in the solid concrete floors, the power being supplied

principally during the night hours.

- An additional forced air heating controlled in each room by a thermostat. The air taken

from outside, is pre-heated to a temperature Tp before supplied to the room ; this principally is to allow sufficient amount of humidifi cation is neoassary.

The heating system and its control system (capacities, base and preheating temperatures, ...) were studied to determine the best balance comfort conditions - energy consumption.

4.1, Climatic data

Prom the records obtained by the national Meteorology Office in Le Bourget station, near Paris, we have chosen two sequences (Fig 3) : 1^"*^ sequence (february 1963. 15 th to 28 th)

this is a typical sequence of cold and sunny days, the outside air mean temperature being near the base temperature of the place (- T°C) for several days.

2^*^ sequence (march 29 th to april 11 th, 1964)

this is a typical raid season sequence, the outside air mean temperature being rather high,

the diurnal variation and the direct solar radiation being also higho

For these two sequences : - The outside air temperature is the real one recorded in the station.

- The solar radiation has been computed by means of the curves giving the intensities of

the direct normal radiation and of the diffuse radiation on an horizontal plane with clear

atmosphere, of the sunshine hours and of the cloud cover factor. The shading effect crea- ted by the balcony has been taken into account.

- The long wave radiative exchange balance is a linear approximation of the following formula : B = a u(4-©'3 )

b : heat balance (W m~^

)

a : absorption coefficient of the wall

0s ^nd Tre : respectivelv wall surface temnerature and environment radiant temperature

(°K) " _o _4

^0 : Stefan - Boltzmann constant (W m " ° K ) Tre is approximated only as a function of the cloud cover factor. We have, for a vertical wall : Tre - Tae - 2^0 for a cloud cover factor greater than 3 Tre = Tae - 6°C for a cloud cover factor lower or equal to 3,

(cloud cover factor is in the range of 0 to 8)

Tae being the outside temperature.

4.2, Description and characteristics of the studied rooms (fig. 4)

The building includes about 200 apartments of a single surface exposure. It has a symmetry plane parallel to the facades and its orientation is E.W.

We consider a slice of the building bo-unded on two sides by the west frontage and

the symetry plane and on the other sides by the adjacent rooms.

We assume that the slice being studied and the adjacent ones have the same operation

characteristics therefore, the same inside conditions.

1, Inside Wall OomDOSition (1) - Horizontal walls : they are made of heavy aggregates solid concrete, 15 cm thick ; the floor can be covered with a velvet pile with or whitout coarse haire cloth.

130
- Vertical walls : they are either of heavy aggregates solid concrete 15 cm thick as the

horizontal walls or, plaster slabs 7 cm thick.

2, Fagade Composition

The faQade panel is of the light type. Its mean thermal transmission coefficient K is

1 .68 W m-2 oc-1 . m

The opening is fitted with double glazed windows (1), externally screened by shutters and internally by a light-coloured blind.

The shutters are always closed during night from 9 p.m. to 8 a.m. and on occasions

during the day. The opening thermal transmission coefficient is dependent of the position

of the shutters : o i Shutters open : K = 3 W m "C"' . Shutters closed : K = 2.4 W m-2 OQ"'

3, Occupancy

The heat generated by the bed-room occupancy has been fixed at 90 W from 9 p.m. to 8 a. next morning.

4. Exchange coefficients.

The radiative exchange coefficients were calculated by the standart formulas while the

convection exchange assumed the following values : - Vertical walls : 5-4. W m-2 _2 _^ - Horizontal walls, upward flux : 6.3 W m~ °C

^ - Horizontal walls, downward flux : 0.6. W m~2 oc~

4.3, The heating device (Fig 4 bis)

1 , A preheating of the force circuDated ventilation air to a temperature Tp,

The primary purpose this preheating is to be able to maintain the water content in the

ventilation air above 6 g for 1 kg of dry air. The forced air rate is constant at 30 m3 h-1 .

2, A base heating by a cable embelled in the concrete floors allowing a storage. The

energization of the embelled heater is made during the off peak usage hours, at the maxi- mum during night hours. Heating and preheating alone vould give a mean temperature Tf

of 10 to 18°C according to the time of the heating season taken into consideration.

3, A supplementary heater installed in the air supply system to the individual room

complements the base heater system to provides 20 +o 22 °C with a control thermostat in

each room (thermostat threshold ± 0,5°C, response time 10 minutes).

The power capacity of this supplementary heater is fixed at 500 w, much higher than

the room needs, to take into account losses by the adjacent rooms and to allow a greater

flexibility to the heating system.

The air is exhaused in the passage-room, where the heat losses by the adjacent rooms

and to allow a greater flexibility to the heating system.

The air is exhaused in the passage-room, where the heat loss from the forced air sup- ply duct is taken into account.

The power consumpted in the supplementary heater can be billed individually and its

rate structure is different from that of the base heating, which is billed collectively.

4.4, Results

The control system of the base floor heating is an open-loop system (no feedback

from the air temperatures obtained inside). The night hours are divided in a number of

equal intervals of time. In each of these intervals the connection of the heating resistances is commended in such a way that the ratio time of connection is a function f

length of interval

(0 ^ f ^ 1 ) of outside weather parameters : this is approximately equivalent to supply continuously a heat power ^ equal to f. ( | = installed power).

131
Here we limit ourselves to the comparison of two control systems : - one taking into account the instantaneous value of the outside temperature during the

time when the baseheating system is energized,

- the other including the mean values of the outside temperature and the solar radiation

on the room facade.

The comparison will made on the max:i miun temperatTxres attained in the room and on the

energy consumption.

We will consider only the case where the power is supplied to the floor heater dixring

night hours, that is to say from 10 p.m. to 6 a.m.

a, Control from the instantaneous

value of the outside air temperature,,

Assume first that the power heat supplied to the base floor heater was controlled to

the following expension :

f (t) = Tf (t) - k2 Tae (t) - k3 Tp (t) (2)

- Coefficients k1 , k2, k3 are defined as functions of the thermal characteristics of the room and those of the heating and ventilating equipment.

- The preheating is set on a particular temperature Tpo : if T i T , T = T ae po ' p po

if T > T , T = T ae / po ' p ae The resTxlts which are presented are those obtained when the preheating is not switched off during the peak hours.

From the first it is know that the control mode cannot be satisfactory, on the one hand because it does not take into account the solar radiation contribution and on the

other hand, because the outside air mean temperature measured between 10 p.m. and 6 a.m. may be quite different from that of the day. This leads to a base temperature drift, this

drift becomes more significant as the preheating is low and the diurnal variation of air

temperature becomes large.

During the february sequence, this drift is very low, as shown on the air temperature

records of figure 5 where the base heating is working alone. Otherwise it is of about 2,5''(

at the end of the april sequence, for Tf = 16°C and Tp = 6°C, where the solar contribution are not taken into account by the control ; this drift is increased due to the fact

that hight solar heat gain are coincident with hight diurnal variation of the outside

temperature.

Minimization of this drift is possible only by lowering the base temperature during

mid season. Figures 6,7 and 8 show the inside air temperature when the thermostat is set at 200C«

In february, and in the case the solar, contribution in the room is less important

because of balcony structure, the inside temperature, 21 °C mean value, is still acceptable

for a base temperature of 16°C, preheating to a temperature greater than 6°C improves the

comfort conditions (air and floor surface temperatures in the morning) and lowers very

appreciably heating energy requirement during the night hours ; so when Tf = 16°C, Te =

- 5°C and if 22°C inside temperature is wanted by heating dxuring the off peak hours, one must have ; if T = 6°C : Power capacity = 1500 W

P floor = 25.5°C

ceiling = 30°C

if T = 16°C : Power capacity = 1100 W

P floor = 24.2. °C

ceiling = 27,5°C

At the end of the april sequence and for Tf = 14°C, are still recorded very incomfortable air temperatures, of the order of about 240C mean value (without balcony). In

132
fact, windows woiild be opened to restore more acceptable comfort conditions, but the

consumption waste would be increased.

b, Control from mean outside

air temperature and solar

radiation.

The heat flux supplied is of the form : T

'

1 f-t-t2 f t-t4

$ t = (Tf )t - t2ltr" I Tae d © - k6 (Tae)t - k7 t4ltT~ ^ ^ /t-t1 /t-t3

- k8 (Tp)t

- The time intervals t^ - t2and t^ - t- being included in a cycle which may be daily.

- Coefficient k^to kg are defined as functions of the thermal characteristics of the room and those of the heating and ventilating equipment.

- R is the solar radiation on the fagade.

- Tp is defined as in 4.4, a, but the preheating is switched off during the peak hours.

The improvement attained by this type of regulation over the former one is very distinct for the april mid-season sequence.

On the fig. 9 some results are reproduced, the base heating working alone, with and

without controls taking into acco-unt the solar . radiation

- In case the controls does not take into account the solar radiation, the drift is slightly greater than 0,5°C at the end of the sequence with solar factor zero and,

- In the case the controls takes into account the solar radiation, the drift stays sensibly in a bracket of + 0,5°C.

On figures 10 and 11 one can read the inside air temperature variation for different

values of Tf, the thermostat being set at 20°C.

At the end of the april sequence, heat gain from the solar and occupancy contributions

are greater than the losses ("Tf being between 10 and 16°C), inside air temperature does

not change much, staying in mean value around 21 to 22°C, the peaks not exceeding 24 °C,

The difference is much significant in relation to the relative values of the power

consumed ; with a balcony in the case corresponding to figures 10 and 11, the consumptions recorded during the fourteen last days for base and supplementary heatings are the

following :

T _ igoc ( ^ase : 60 kWh

f (Supplementary : 8.1 kWh

T - mop (Base : 22.1 kWh

- lu I. (Supplementary : 48.9. kWh

For comparison with the control scherae defined in 4.4, a, the energy requirement

recorded in the some conditions are :

T _ (Base : 82 kWh

^ ~ (Supplementary : 4 kWh

The results for the february sequence are given in fig. 12.

5, References

(l) The thermal characteristics of the

building walls (thermal conductivity, mass

per unit surface, K coefficient, etcetera)

are extracted from the Docujnent Technique

Unifie : "Computation riiles for the serviceable thermal characteristics of the

building walls and off the basic losses

of the buildings".

133
1 m

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CO

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4J (1) a -H O O N -H • •H <^ C

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134
135
STAIRCASE

CIRCULATION

I

270

BEDROOM

ho

LOGGIA

15

255

370

135

« >• ^115 ^ 160 a1Q

40

Double glazed

window

130

80

250

Figure 4 , Studied Rooms and Facade Drawings

136
outdoor porometerp

outdoor Gir

Tp

Preheating contro

versus humidit/

control

Box

commutotion Box

embedded cables

Control in on r^ff thf»rmn<;tnt

t Supplementary heating

Ti

^

Figu.re 4bis - System schematic

137
FEBRUARY With Loggia Tj= 16°C

to

17

Tp 3 6*te

7

APRIL With Loggia T| = 16 C

Tp o 6"C 16

Pigure 5, Inside Air Temperat\ire.

Base heating only, regulated as a ftmction

of the outside air temnerature.

138
Figure 6, Inside Air Temperature. Base heating regulated

as a function of outside air temperature. Additional heating

thermostat setting : 20 °C

139
FEBRUARY With Loggia Tps.lft^C

If.

Figure 7j Inside Air Temperature. Base heating regulated

as a function of outside air temperature. Additional heating

thermostat setting : 20°C

140
FEBRUARY Without loggia Tp= 16 °C

IOC

21

16<»C 20

19

22.

27

OA

\J \

1 23 J

i7

Figure 8, Inside Air Temperature. Base heating regulated

as a fiinction of outside air temperature. Additional heating

thermostat setting : 20°C

141
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142
143
144
145
146
Analog Computer Simulation of an Air

Conditioning System in a Commercial

Building Incorporating Yearly Weather

Data

John L. Magnussen 1

Honeywell Inc.

Estimated operating costs of various air-conditioning systems is an important economic consideration in the design and selection of equipment

for a new building. Building construction, the heating/cooling system and

the controls must all be considered to minimize these operating costs and provide comfort control. To analytically accomplish this task, a small com- mercial building was simulated on an analog computer so that the building

orientation, construction and number of zones could be easily varied. Yearly

weather data for various U.S. cities was programmed on a 13-channel tape re- corder according to recommended ASHRAE procedures to simulate realistic en- vironmental conditions. Programming the analog computer for various heating/

cooling plants and control systems provides a quick analysis of initial cost,

operating cost and comfort performance.

Key Words: Analog, control system, digital, heat transfer, modeling,

simulation, solar radiation, system analysis, thermal capacity.

1. Introduction

Company sales and profitability can be significantly affected by employees' working environment. Maintaining the optimum environment at the least cost should yield increased productivity

and higher profits. The main factors influencing operating cost and thermal comfort are the building's construction, location and orientation, the heating/cooling system and the control

system. To analyze all these factors creates a complex problem requiring special tools such as analog and digital computers. Specifically, analog computers provide the dynamic results essential

to complete analysis of control system stability and performance. The analog computer can simulate

an actual heating/cooling system and illustrate the anticipated performance under various environmental conditions, building construction and controls. Cost performance data may be graphically

displayed in real time, permitting rapid dissemination and comparisons of various systems.

An optimum environmental system maintains a comfortable environment at the lowest operating

cost. This paper shall present a method for analytically determining system operating costs. The method utilizes an analog computer simulation of a small commercial building. Cost and performance

data from this simulation are then used to accurately define optimum system performance.

2. Cost Analysis

Heating/cooling system costs are composed of initial cost, operating cost and maintenance cost. Generally initial cost includes hardv;are such as the compressor, condenser, furnace, boiler, duct

work, piping, controls, etc., plus the cost of system installation. Once the system is installed, however, operating and maintenance costs are the main concern of the ovmer. This paper will be limited

to determining the operating costs.

The financial return of a building is highly dependent on the efficient operation of the heating/

cooling system. In dollars, this means the lowest possible total energy consumption necessary to maintain comfort conditions. Operating costs are generally those derived from operation of the condenser fan, delivery system, furnace and controls.

Senior Development Engineer, Residential Division.

147
An accurate calculation of yearly heating/cooling operation can be a simple summation of the heating/cooling plant's operating time if it is strictly on/off. If a modulating system is used, integration of the heat/cool delivered energy must be made. The energy requirements, together with the efficiency of the heating/cooling plant, can predict fuel consumption. Efficiency defined as the ratio

of output in BTU/hr. to input energy provides a functional relationship (between energy required and energy consumed) to incorporate into the simulated system. System operation can then be calculated

since the system is responsive to the outdoor conditions affecting efficiency, such as dry-bulb temperature (for an air cooled condenser) and wet-bulb temperature (for water cooling towers). All of these calculations may be made with an analog computer.

Numerous authors have proclaimed the advantages of computers, particularly in comparison to field

testing. For to rely on field testing only leads to added costs, development delays and inaccurate

results because of an uncontrollable environment. A computer-aided design, however, enjoys the benefits of a controllable environment, accurate definition of the effects of a single variable,

accurately defined results and hence lower total development costs.

Of particular concern in determining operating cost is the solution of dynamic problems. An analog computer was selected for this analysis because of the ease of simulating the transient be- havior of a heating/cooling system and the inherent dynamic problem solving ability.

The analog computer complements the passive electrical circuit simulating thermal properties of the small commercial building, automatically incorporating nonlinearities involved in total system

analysis. It thereby completely calculates the transient behavior of the heating/cooling system as the system responds to demands of the conditioned space, created by anticipated internal as well as external environment loads. For the simulation, the external environment was modeled using data from

the U.S. Weather Bureau.

The simulated commercial building is a 90' x 30' structure, 8' in height per story with a slab floor and a flat ceiling. Exterior walls are all opaque material, 50% opaque and 50% transparent, or all transparent. A floor may be divided up to 12 separate areas, each 15' on a side, to create separate 225 sq. ft. zones. An analysis of a multiple story building may be made by rerunning the simulation with appropriate adjustments for the thermal inputs to the floor and ceiling, changing the thermal characteristics of the floor and ceiling, and eliminating all heat flow between stories by

assuming the same control temperature for all floor sections. Thus the structure of the building, the number of zones and the type of exterior walls all may be varied.

The analysis of dynamic control performance and operating costs requires that the simulation include all thermal characteristics of the structure. Therefore all three modes of heat transfer - conduction, convection, radiation, and the thermal capacity of the structure must be included in the simulation. However, a given wall, floor or ceiling can never be perfectly simulated to produce an exact duplicate of the temperature profiles in the structure or the heat transferred. Therefore

assumptions are needed to bring the problem within the practical capability of present-day techniques

and technologies and be solvable with a realistic expenditure of funds.

In this simulation the lumped nodal point method of analysis was used. This analysis assumes

that for each wall, a uniform temperature is maintained on any surface, the wall is of uniform construction, and it has a linear temperature gradient between any two surfaces.

In an actual installation heat does not flow in a straight path through the wall but rather flows along the path of least resistance. There is also a discontinuity between wall material surfaces.

In this simulation a single temperature is assumed for the active wall and an average discontinuity is assumed between any two members (i.e. a uniform discontinuity is assumed between the studs and the plasterboard that is fastened to the studs). Assuming an average discontinuity an average thermal

contact resistance may be calculated. The thermal contact resistance is the resistance to heat transfer between two items fastened together.

From past experience, these assumptions should present a deviation less than 10 per cent between

actual and predicted heat flow characteristics of the wall, so that the dynamic effects on analysis

and total energy loss will be minimized. The anticipated difference is further minimized by using

one "T" section for each wall material and then building up the several "T" sections for an entire

wall (as shown in Figure 2) rather than just one "T" for the entire wall. The equation:

3. Computer Design of Temperature Control Systems

Simulated Commercial Building

148
(where 1 = thickness of material to be treated by one "T" section for an accuracy of 5Z, ft. a = thermal diff usivity , ft^/hr., f = frequency of the disturbance, cph), may be used to define the maximum allowable thickness of material that may be represented by a single "T" to achieve a maximum

deviation of 5% in a 24 hour variation of temperature (i.e. as would occur over an entire day). For

example, plasterboard may be 4" thick before more than one "T" is required to prevent a 5% deviation

of the response of an oscillating heat flow through the plasterboard.

The electrical circuit to model one zone (Figure 1) includes resistive elements representing heat

transfer due to radiation between the walls, floor and ceiling, convection heat transfer between the room air and the walls, floor and ceiling, and conductive heat transfer through the walls, floor and

ceiling. Figure 1 also shows the heat transmitted through the windows (this element is removed if glass is not present) and the capacitive elements simulate heat storage in the room air and walls, floor and ceiling. For a typical exterior wall (Figure 2) the resistive elements represent heat

conduction through the various portions of the wall and capacitors represent the heat storage of these parts. Values of resistors and capacitors are dependent upon the scaling used to model the structure. For this simulation the dynamic effects occurring during 24 hours of actual time are calculated in 14.4 seconds.

Air movement between sections is simulated by adding a special resistive network to the basic

circuit (Figure 1). The resistance network is connected to points representing room air temperature.

Thermal capacitance of each air space is represented by a single capacitor.

Figures 3 and 4 show the cabinet that contains the physical circuitry used to make this simulation.

The resistors and capacitors that form the "T" sections shown in Figure 2 are placed in a plug-in container. One container is used for each wall section (i.e. the container for an interior wall would in- clude the resistors and capacitors for an 8' x 15' area). These containers are visible on the front of

the cabinet (Figure 3). The containers on the lower panel of the cabinet are for the walls and windows; above these are the containers for the floor and ceiling sections. These containers may be easily

changed so that different types of wall construction may be simulated. For example, if concrete blocks were used instead of brick and plaster on the exterior walls, the exterior wall containers would be changed to those that include the resistor and capacitors sized for a concrete block wall. Since

these are plug-in containers, changes can be made quickly and the analysis continued to determine

the effects of the new wall construction.

5. The Simulated External Environment

To calculate the annual cost of operating a heating/cooling system, the external environment is simulated using weather data from the U.S. Weather Bureau. Weather variables are changed every hour

to closely approximate actual dynamic changes. Ten years of data are contained on a single reel of magnetic tape. The data are provided in a digital form from which the characteristics pertinent to the thermal simulation were converted into analog signals and recorded on an analog magnetic tape.

Environmental factors used were dry- and wet-bulb temperatures, relative humidity, wind velocity

and direction and solar radiation. Hourly values for the factors necessary to calculate the solar

radiation (cloud type and height, amount of cloud cover and the time of day and day of the year) were

read from the Weather Bureau's digital magnetic tape and then used according to ASHRAE procedures

outlined by the Task Group on Energy Requirements, providing a programmed method of calculating both

direct and diffuse solar radiation intensities for any wall. Additional statements were added to the digital computer program to read information from the Weather Bureau's digital tape. The re- sulting digital computer program read and calculated values for the solar radiation intensities and

5 other pertinent environmental factors. A total of 13 variables - dry- and wet-bulb temperature,

relative humidity, wind velocity and direction, the year, hour and week, solar radiation intensities

for an east- west- north- and south- facing wall, and a direct normal radiation intensity were

either calculated or read from the digital weather data tape. Hourly values for a 4-year period for these 13 variables were then recorded on a 13-channel analog magnetic tape. The analog tape is an

FM recording, although the output from the tape recorder is a voltage or analog signal. The outdoor

ambient temperature, reproduced as an analog or voltage signal, is connected to the appropriate

points of the electrical circuit (Figure 1). Since solar radiation intensities are directionally

oriented, the simulated building may be oriented in any direction by simply changing analog signals

in the cabinet (Figure 3).

Inside the cabinet (Figure 4) is the pull-out printed circuit board on the right hand side which

contains all the interior radiation and convection heat paths. Figure 5 illustrates the board used

for the one zone application. The six panels near the bottom of the cabinet (Figure 4) contain the resistive, capacitive network that simulates the heat transfer through the ground. Points from this

circuit are connected to the underside of the building's slab floor. This two-dimensional circuit

effectively simulates heat transfer to 16' where typically only 5% of the yearly outdoor ambient tem- perature oscillation is found. The circuit automatically provides for the complex heat loss from the building to outdoor ambient conditions through the earth by incorporating the dynamic nonlinear effects

149
of the ground, effects that would otherwise be next to impossible to solve by either digital or analytical solutions.

Air infiltration is accounted for by a direct heat transfer path between each point representing

the space temperature for a 225 sq. ft. area and an equivalent outdoor ambient temperature, simulated

by a representative resistance. Wind velocity defines the value of the equivalent outdoor ambient

temperature. Special analog circuits to achieve the correct direction for air flow and duplicate

wind direction heat gain or loss,

6. Simulation of the Heating/cooling System

Analog simulation of the building structure combined with the heating/cooling plant provides a system approach to analyzing the complete control loop (Figure 6). To simulate the heating/cooling

system, response characteristics of the physical components — the furnace, conveyance, cooling coils, — must be known. Once the response characteristics are defined - either by sinusoidal inputs (fre- quency response method) or step inputs (step response method) - the control loop may be established

(Figure 6).

Furnace time response may be found by measuring plenium air temperature from, a step input,

simulated by a transfer function of the form

, . T/Q = K/( -r s +1)

where T = air temperature rise in the plenum, Q = heat output of the furnace, K = steady state plenum

temperature rise per unit Q, s = the Laplace operator, and = the single order time constant characteristic of the furnace. Various types of furnaces - electric, gas, oil, coal, etc., may be modeled

using different time constants ('?'), Radiant panels or baseboard heaters may be simulated by

similar transfer functions, but with heat added directly to the ceiling surfaces for radiant panels

and to the walls and floors in addition to the air for baseboard heaters.

The cooling plant may be modeled similarly with the extent or complexity of the simulation

depending on the type of plant used, i.e., cap tube, absorption, reciprocating or centrifugal

chiller. Since the sensible-latent heat removal relationship is continually varying, the dynamics

of operation are more complex than the furnace simulation. Latent heating effects are necessarily

included to calculate realistic operating costs, since the efficiency of the air-conditioning unit

is dependent not only on the outdoor ambient conditions but also on the latent heat load across the cooling coils. The latent heat introduced by infiltration of outdoor air as well as that generated

by occupants must be considered.

Transient moisture storage of various materials found in typical furnishings was based on actual

field measurements of step-response tests from a humidity source. The data obtained from these tests defined the transfer functions used in the computer simulation. Dry-bulb and relative-humidity sensors were modeled and added to the control system circuit through appropriate transfer functions, taking

into account the respective time constants. If an Air Economizer provides free cooling by outside

air, another block must be added in Figure 6 and additional circuitry added to the simulation.

The heating and cooling conveyance, if present, should also be modeled because its relative time response may be significant to that of the total system, depending on its bcation and the time constants of other system components. A typical metal duct transfer function might be a lead-lag term

such as

Tg/Ti = K ( -PjT s+l)/( -^s +1)

where Tq = outlet temperature rise, T-j^ = plenum temperature rise or duct inlet temperature rise, K = steady state ratio of Tq/Tj^, = lead time constant, and "2^ = lag time constant. The time constants

reflect the relative duct length and the heat exchange between the air, the duct and the environment.

Last is modeling the control system. A simple on/off control is shown in the control loop

(Figure 6). The basic control system consists of a sensor to detect the current state or condition

a logic device to differentiate what is sensed from a preset or desired condition, and an actuator to trigger desired action from the appropriate equipment after receiving a command signal from the logic

device. Various auxiliary control components may be added to this basic model as demanded by the application. Controls simulated may be electric, electronic, pneumatic, fluidic, mechanical or any combination.

150
7. Computer Operation and Data Acquisition

The computer combines t;he simulated heating/cooling system with the commercial building in a control loop with the external environment provided by the taped weather data. Since these data form

the load on an unoccupied building, occupancy effects were added separately.

Solar radiation intensity adds heat to the structure. Since current is analogous to heat in the simulation, the voltage signal from the weather data tape must be transformed into current. These

current signals are then sent to the simulated building by connecting to the appropriate point in the simulated circuit using special analog current generators. Distribution of this absorbed heat (or current) is proportional to the voltages supplied from the taped weather data. Separate current

generators are used for the roof and each side of the building and to simulate heat transmitted

through the glass windows.

The voltage signal from the tape recorder representing the solar radiation intensity is a combination of direct and diffuse components, adjusted to account for average transmissivity or absorptivity of incident surfaces. This is obtained by time-averaging values for each direction (north,

south, east, west, or perpendicular to the earth). This averaging tends to smooth the daily cyclic

pattern somewhat; however, the difference between hourly changes and average transmitted heat is always less than 10% for any given day.

Sensible heating effects of lighting and occupancy in each zone are accounted for by injecting

convective and radiant heat into the simulated structure at the point that represents the room air

temperature and surrounding surfaces of the particular zone in question.

Output data is recorded by several instruments: A digital voltmeter with BCD (binary-coded

decimal) output capability, a counter timer with BCD output, an 8-channel oscilloscope, an X-Y plotter

or an analog tape recorder. In the present case a counter timer recorded yearly operating costs by

integrating total on time of an on-off system by pulsing a gate to allow the timer to count on its internal calibrated time base during the permitted period representing the system on time. If the system modulates according to demand, the heating/ cooling requirements must be integrated and the counter is then used to accumulate the number of integrations to a given value.

Dynamic performance of the system was recorded on an oscillosgraph where a graphic representation

of zone air temperature, along with other variables, was obtained, permitting dynamic temperature

swings of the zone to be easily determined. The performance and operational characteristics for a complete year are obtained in only 87.6 minutes, meaning several building types and various heating/

cooling systems can be examined in a single day.

8. Illustrative Example

For example, consider a single-story single-zone building 30' wide by 5D' long by 8' in height

with no internal walls or partitions, and the thermostat is mounted on one of several support columns.

All exterior walls have plate glass along the top half, opaque material on the bottom half. The building, located in Houston, is oriented so the long wall faces south.

A simple one-stage heat, one-stage cool system was simulated for the heating/cooling plant. To this was added a heat/cool space thermostat for control and an Air Economizer to use outside air for

free cooling whenever possible. The Air Economizer has two temperature sensors: One which senses outdoor air temperature and one which senses combined (or mixed) air temperature obtained from return

air and outside air temperatures. Two setpoints (one for each sensor) let the Air Economizer pull in outside air when outside dry-bulb temperature is below its setpoint and regulate the amount of outside

air entering through a damper according to the mixed air temperature (channel E, of Figure 7). The damper responds to loads on the structure and the control setpoint. For the illustration shown, the mixed air setpoint was 60°F and the outdoor air permit temperature setpoint was 70°F. The minimum

position of the damper was set to provide 10% outside air for ventilation purposes.

Figure 7 presents the typical oscillograph output of such a simulation. The time period shown

is the last 2 days of January and the first day of February, 1955. The two timing channels, D and H, are identical. Channel H is included only as a reference. Time is recorded in 1-hour steps from midnight through 24 hours, then resets. The cyclic pattern of outdoor air temperature, channel A, varies

from day to day. To approximate this pattern with an average condition that would produce the same response in space air temperature (channel B) would be extremely difficult as would trying to achieve

an average condition for the directional solar radiation intensities displayed by channels I, J, and K

151
The type of cloud cover (if any), the amount of cloud cover, haze in the atmosphere, ground re- flectivity and sky diffisuivity are accounted for in the values of these solar radiation intensities.

Infiltration effects of outside air are regulated by wind velocity, (channel F) and wind direction,

(channel G). The sharp swings on channel G are because of the scale used for the trace, from due north through a full rotation of 360 degrees. As the wind direction changes from north to south the oscillograph pen must traverse approximately one-half the trace. Outdoor relative humidity is recorded on channel L,

Variations in the cyclic space air temperature swings, channel B, coincide with the cycling rate

of the thermostat and the heating/cooling plant (channel C). These variations are In response to changes in the internal occupant and lighting load (present from 8 A.M. to 5 P.M.) and to changes in the outdoor weather conditions.

On time of the heating/cooling plant may be accumulated by a counter-timer to calculate the oper- ating costs for the time period and system in question. The effect of different components on the total system operating cost and performance may be easily determined by changing the simulated part

and rerunning the same weather data.

9, Conclusions

With this simulated small commercial building and weather data, yearly system operating costs may

be determined for a number of different types of building construction, composition, orientation,

location and use. A clear concise distinct analysis providing specific information on the effects

of a single variable may be made using analog computation. Effect of a single variable on total

system performance may be readily defined, as may various conceptual control ideas such as using outside air for free cooling through an Air Economizer. Multizone and single-zone systems may be readily examined by changing from a 12-zone to a 1-zone structure. The number of zones may be easily

changed. Various systems may be examined not only over long-term but also over short periods. Occupancy and lighting loads, as well as other internal loads, may be readily incorporated and the dynamic

effects examined. Geographical effects of a particular building and system may be determined for any location in the United States for which a magnetic weather data tape has been produced. The type of application a given heating/cooling system is to be subjected to may be readily evaluated. The type of control may be easily changed and the dynamic performance as well as the yearly operational cost resulting from the particular control defined. Knowledge of what the optimum control should consist of, and knowledge that the control parameter values defined are indeed the optimum values, may be graphical^

illustrated with this engineering approach. The information obtained here is not easily obtained using

field tests or other analytical solutions, especially not within a controlled environment that provides

a convenient and economical method of comparison.

152
10. References

II] Victor Paschkis, Periodic Heat Flow in Building Walls Determined by Electrical Analog

Method (ASHVE Transactions, Vol. 48, 1942,

p. 75).

[2] T. N. Willcov, et al. Analog Computer

Analysis of Residential Cooling Loads (ASHVE

Transactions, Vol. 60, 1954, p. 505).

[3] H. B. Nottage and G. V. Parmelee, Circuit

Analysis Applied to Load Estimating (ASHVE

Transactions, Vol. 60, 1954, p. 59).

[4] H. B. Nottage and G. C. Parmelee, Circuit

Analysis Applied to Load Estimating, Part II (ASHAE Transactions, Vol. 61, 1955, p. 125).

[5] Harry Buchberg, Electric Analogue Prediction

of the Thermal Behavior of an Inhabitable

Enclosure (ASHAE Transactions, Vol. 61, 1955,

p. 339).

[6] Harry Buchberg, Electric Analogue Studies

of Single Walls (ASHAE Transactions, Vol. 62,

1956, p. 177).

[7] J. L. Threlkeld: Thermal Environmental Engineering (Prentice-Hall, Inc., Englewood

Cliffs, N. J., 1962).

[8] Shao Ti Hsu, Engineering Heat Transfer, (D. Van Nostrand Co., Inc., Princeton, N. J., 1963).

[9] Handbook of Fundamentals, (ASHRAE, New York,

N. Y., 1968).

[10] G. P. Mitalas and D. G. Stephenson,

Absorption and Transmission of Thermal

Radiation by Single and Double Glazed

Windows (National Research Council of Canada, Division of Building Research,

Research Paper No. 173, 1962).

[11] G. K. Tucker and D. M. Wills, A Simplified

Technique of Control System Engineering

(Minneapolis-Honeywell Regulator Company,

1958).

[12] William I. Caldwell, Geraldine A. Coon,

Leslie M. Zoss: Frequency Response for Process Control (McGraw-Hill, 1959).

[13] Granino A. Korn and Theresa M. Korn,

Electronic Analog Computers (McGraw-Hill, New York, N. Y., 1956).

[14] Tyler Stewart Rogers, Thermal Design of Buildings (John Wiley & Sons, Inc., New

York, N. Y., 1964).

[15] Lorne W. Nelson, The Analog Computer as a Product Design Tool (ASHRAE Journal,

November, 1965).

[16] Met in Lokmanhekim, ed., (Task Group on Energy Requirements, ASHRAE, New York,

N. Y., 1968).

153
outside

film concrete studs and plaster coefficient block insulation board

outside

temperature -WW^ vAAA—r^AAAX

-vVVV

X

inside

wal 1 surface temperature

Figure 2. External wall simulated thermal circuit

154
155
SET POINT THERMOSTAT

SWITCH ON-OFF , OPERATIOIT

HEAT- COOL PLANT PLENUM TEMPERATURE CONVEYANCE OUTLET TEMPERATURE

AIR

SENSOR TEMPERATURE

SENSOR

TEMPERATURE

(8v WALL TEMPERATURE

SIMULATED COMMERCIAL

BUILDING

WEATHER FACTORS

ANALOG

CURRENT

GENERATOR

HEAT FLOW

from OUTLETS

SOLAR HEAT FLUX ANALOG

CURRENT GENERATOR

SOLAR RADIATION

ANALOG TAPE

RECORDER

Figure 6. Temperature Control Loop

156
Figure 7: Oscillograph Recording of System Variables

157
channel I —• —

|- 60,000 BTU/hr -

Solar Radiation Intensity - East VJall

|- 60,000 BTU/hr --|

0 BTU/hr

Solar Radiation Intensity - West Wall

Channel K i" -j" 750,000 BTU/hr

Solar Radiation Intensity - Roof

i Channel L 1 | - - 90% -j- - - -

- -

j --

- - Relative Humidity 1 r.i-^—r>-T~^—"1 ! t '-.^

[

'. 1 - 10% -A —j 4—

Figure 7: Continued

158
Experience with a thermal network analysis programme applied

to heat flow in buildings

* Norman R. Sheridan

University of Queensland, Australia, 4067.

After a brief discussion of the general features of thermal models for buildings, the paper

describes the general purpose network analysis programme that has been modified for use

in building heat flow calculations. The input data includes the dimensions and thermal

properties of the heat flow paths, the building orientation, the solar radiation on a horizontal plane, the ambient air temperature, the wind velocity and the rate of air infiltration. Sub-routines allow calculation of variable convective and radiative resistors. Calculated

output includes inside surface temperatures and heat flow into the building interior. As

an example, calculated values of the diurnal and daily heat flows and the maximum wall

temperatures are given for a simple enclosure with walls of various materials and different thickness. Factors affecting the alignment of the mathematical model with the prototype

are discussed with relation to a simple enclosure. The advantages and limitations of the method are critically examined and some comparisons made with the van Gorcum matrix

method, which has also been programmed for similar problems. It is concluded that the mathematical simplicity and the versatility of the general purpose thermal analyser give

considerable advantage for University type research. On the other hand, the long computing

time of this programme is seen as a limiting factor in its use for routine investigations.

Key Words: Air conditioned buildings, building heat flow, lumped parameter network,

optimum insulation, thermal design, thermal model, thermal network analysis.

1. INTRODUCTION

As a thermal shelter, a building acts to reduce the daily temperature range and to permit adjustment

of the temperature level by heating or cooling. Heat flow in the building shell is transient as a result of the periodic nature of the ambient temperature and the radiation received at the building surface. Thus,

predictions of the thermal performance need to allow for the unsteady flow and to account for the thermal

capacitance of the shell as well as its resistance.

For a naturally ventilated building, the problem is usually one of predicting the inside temperatures,

both of the surface and the air. On the other hand for air conditioned buildings , the net heat flow and

the wall surface temperatures will be needed.

Justification for a detailed thermal study of a building is usually made on economic grounds. For the

naturally ventilated case, the aim may be to decide the cheapest of various alternative ways of reducing

unwanted heat gains. For the air conditioned case, the aim may be to determine the most economical

structural system which will result from the lowest annual cost of owning and operating the building.

The unsteady flow analysis can be extended to cover the case of unsteady energy input into the air conditioner, such as is the case in the s^olar air conditioned buildings which have been the subject of re- search at the University of Queensland. Here, the problem is one of distributing the thermal storage between the solar collecting system, the air conditioning system and the building in the most economical

way.

2 . THERMAL MODELS

Thermally, a building consists of a number of different heat flow paths in parallel, each subjected to boundary conditions that may vary from path to path. A typical path through a homogeneous wall (Fig. 1) has distributed capacitance and resistance. It is affected externally by solar radiation, long-wave reradiation to the surroundings and convective heat exchange with the ambient temperature and internally by

long -wave radiative exchange within the interior and by convective heat exchange with the room air.

* Reader in Mechanical Engineering.

159
Fig • 1 . Homogeneous wall with boundary conditions

q = (1 - p) R AH.

It is assumed that heat will flow normally

to plane surfaces the dimensions of which are

large compared to the thickness, i.e. the flow

will be one-dimensional. Thus, each plane sur- face of uniform construction is considered to be a single path with the same set of boundary

conditions

a . Boundary Conditions . Short-wave radiation entering the surface can

be calculated from the insolation on a horizontal plane, a factor to allow for surface or- ientation to the sun and the surface reflect- ance .

(i) External long-wave radiative exchange will be governed by the usual Stefan-Boltzmann law with the assumption that some effective or average temperature can be found for the surroundings, T . 4 „ 4, q - ^^s2^ ) This equation can be modified to the form: [V q - 1

T^) ^2^

(ii) e„ F A(T + TJ(T

2 s2 s 2 s '+T ) where R^ is a temperature dependent resistance for a particular wall

Convective heat transfer will depend on the film resistance R^

the velocity in the case of forced convection or of temperature in the case of natural convection.

which will in turn be some function of The temperature difference is between the ambient temperature and the wall temperature. Thus:

T, q

L2 Rc

(iii)

Internal radiative exchange could be treated as above or alternatively by the matrix equation:

|b| |w| = IbT^^I ... (iv) [w[ is a matrix of leaving flux densities representing the response,

|bT4| is a matrix with terms of the form ^2 ^2 Tt'^ representing the excitation,

B is a matrix of system properties and is thus the transfer matrix.

2 For some studies, the boundary conditions can be simplified by the sol -air temperature concept.

(The sol -air temperature tg is that temperature of the outdoor air which, in the absence of all radiation

exchanges, will give the same rate of heat entry into the surface as would exist under the combination of heat exchanges in the model above (Fig. 1). A combined resistance R^^. , with temperature difference

taken to the ambient temperature, is usually used as:

q

= R

^2^ ' r (^s

r

T^) + a R A H =

2 g -(T^-T2)+aR AH

cr r(^e-^2^

cr

(v)

These boundary conditions may be available as a continuous record though more usually they will consist of a time-series with values at one hourly or three hourly intervals.

b. Thermal Response of Heat Transfer Path.

If the convective and radiative resistances can be considered as constants, the response of the system to the excitation can be calculated by superposition of the known response to simple components of the excitation function. Components that have been used are Fourier harmonics,"^ rectangular pulses,^

and triangular pulses.^

Each excitation function is resolved into components. It is sufficient to determine the response of the system to unit values of the excitation components since, for the assumed linear system, the magnitude of the response will be linearly related to the magnitude of the excitation. The response function

will be determined by adding the components of the response.

Mathematical manipulation can be conveniently handled in matrix form in which a transfer matrix containing fixed properties of the system is post-multiplied by a column matrix of the response variable and

equated to a matrix containing the remaining terms of the heat balance.

Application of this approach depends upon the ability to determine the transfer matrix and/or the unit response for the distributed parameter conduction path. These methods are detailed elsewhere.

160
Lumped Parameter Approximation.

The conduction path can be. approximated by a lumped parameter network of thermal resistances and

capacitances which gives a finite difference approximation to the partial differential conduction equation. The one -dimensional heat flow path of building problems is imagined as being divided into a number of slabs which have their heat capacity concentrated at their midpoints. The path for heat flow

is formed by the thermal resistance of each slab which is lumped to connect appropriate midpoints or nodes. For a reasonable approximation from 3-5 divisions of each conduction path should be made.^

Heat flows into or out of the path can be made by

I adding or subtracting heat from boundary nodes or by allowing heat to flow through convective or radiative resistances connected to the boundary nodes.

The interconnected circuit of thermal resistances

and capacitances is the thermal network.

1 ^

"c"

3 . SOLUTION OF THERMAL NETWORK

Electric analogues of the thermal network, essentially special purpose passive-network computers,

have been built. A large number of components

are necessary since all parallel paths must be in operation at the same time. However, the solution

„ „, 1 ^ , r , ^. ^1. time is short since the time constant of the electri- Fig . 2 . Thermal network of conduction path

cal path is several decades below the equivalent thermal path. Generally, the machines lack versatility

since the set-up time is long and inevitably special components are needed for most new applications.

Digital computer solution of the thermal network is a sequential process which, at each succeeding

time, calculates for each node in turn a new node temperature that results from the heat flows in the paths

connected to the node in the preceding time step. Thus a temperature history of each node is obtained.

There are two types of node - those with capacity and those without.

a. Nodes with Thermal Capacity.

In the general case, node i will be connected by resistances R^j to a number of surrounding nodes

jj, j2 , etc. The node will have a thermal capacitance C^, a heat input due to mechanisms other than

conduction or equivalent conduction q^ and a temperature Tq at the time 9 . Quantity of heat entering the node in the interval A© is given by:

Q = q^Ae

'^i ),i

R..

1]. This heat causes a rise in temperature of the node such that Q = C. (T„ . . „ . - T Thus,

= C. (T^ + A 6'i

S ^^e+Ae,i "^e,i^ '"^iA^

e,i

»,i

R.

1].

whence

n AS ^^e+Ae,i "^e,i^ "

'^i

+ A6/i C.

J=l R.

1]

n ;

fi, R^. -^6,1

fi, R^. + T.

b. Nodes without Thermal Capacity.

(vi)

These will frequently be surface nodes. The heat that enters the node must leave under the action of the temperature potential of the node.

T - T e+Ae,i e,j. T - T

e + AQ-i Q.h

q.Ae = Ae + AS +

161
a =T E - £

n

j=l R.

i=i ^

To ensure stability of the calculation, i.e. to ensure that the finite difference solution is convergent, the time increment A 9 must be less than the minimum time constant for the circuit, i.e. C,

Ae < (RC) = —^7 . . . (viii) £ Rij J=l Heat flows can be found from the heat flow in appropriate resistance paths for each time step.

When the heat leaving a conduction path is needed, it can be found from the heat flowing in the conductive resistance connected to a boundary node. For the heat entering the room air, the convective

resistance can be used.

For any given time interval, m A 9 - the average rate of heat transfer towards the node i will be

given by: TM ^i.m A9 " ^i.m AB

R m=l ij ,.

. q - ' . . . (ix) m

The computation of new temperatures by the node equations is simple and requires very short computing time but it must be repeated for each node at each time increment. Since with practical building systems, large networks of several hundred nodes may be involved and the allowable real time in- crement is small, maybe of order several seconds, the computing time for a run of several days is necessarily long, and several days must be run for each case since the error resulting from the assumption of initial temperatures takes two to three days to become negligible.

4. THE COMPUTER PROGRAMME

Though this programme is described as a general purpose thermal network analyser, it has been writt- en with the aim of allowing easy modification for the addition of special functions. Thus it consists of a simple main programme as shown on the flow chart (Fig. 3) with many of the operations representing subroutines which are on call. The input data for the programme is as follows:

Resistances - Identification by resistance number; nodes to which resistance connected;

dimensions of resistance element; thermal conductivity.

Capacitances - Identification by node number; dimensions of capacitance element; specific

thermal capacity.

Solar Factors - Latitude. Time of year. Node number; inclination and azimuth; area;insolation on a horizontal surface for each hour.

Cathode follower - Pairs of nodes i and j . (Temperature of node i will be replaced with

temperature of node j). Radiative resistance - Resistance number; value of e ^-^2' Convective resistance - Resistance number; area A; exponent m or n for free or forced convection

(Fig. 3). Table Association - Table number and associated node or resistance number.

Problem constants - Print interval. Problem cut off time . Initial time. Number of tables , etc. Heat flow calculations - Node number at which heat flow required; resistance number.

Temperature output - Node numbers at which temperature data required,

requirements

Tables - For each table: Table number; argument type; variable type; argument list; corresponding variable list. (Possible arguments: time, temperature.

Possible variables: temperature, resistance, capacitance, heat input).

The output consists of the temperature of specified nodes at required intervals of time together with

the rate of heat flow, during the previous interval, through separately specified nodes, e.g. the hourly

temperatures of any desired nodes with the heat flows for a separate list of nodes can be obtained.

162
5. TYPICAL PROBLEM

Q Calculations were made on a simple enclosure (Fig. 4) of fixed internal dimensions. The wall temperatures and total heat flow into the enclosure were determined for wall thicknesses in the range 1-6 inch.

Properties of the two construction materials used, viz. concrete and polystyrene foam, are given (Table I) as are the heat transfer coefficients and surface absorptance (Table 11). Table I Thermal Properties of Construction Materials

r UJ. ybLylcIlt: iUalll -3 Density, lb ft -1-1-1

Thermal conductivity, Btu h ft F Specific Heat, Btu lb~-^F"-^

140

1.0

40.02 2 0.21 0.27

Volumetric heat capacijiy, ^tu ft~~^ Thermal diffusivity, ft h 1-2-1

Overall heat transfer coefficient , Btu h ft F

29.4 1.08

0. 0340 0.02 04

(3" thick, vertical wall) 4.0 0.088

Table II Heat Transfer Coefficients and Radiation Absorptance Heat transfer Vertical wall Inside 2.18

coefficient

,

Btu h~^ft"2F~-^ Outside J 4.0

Horizontal wall Inside

Outside

2 .44 4.0

Absorptance Inside

Outside

1.0

0.8

As this work was part of a study of air conditioned buildings for tropical Australia, ambient conditions were chosen to be representative of a typical location. The data (Table III) is for an average sunny

December day in Cloncurry, Australia, an inland town at approximately 2 0°S latitude. Table III Time of day, h

Ambient Temp, F^

^ Insolation, Btu h ft

0 81.51 78.62 76. 7

3 76.4 76. 15 76.8

6 78.5

32

7 88.6

93

883.2

167

9 85.8

230

1089.3

276

11 93.0

3 05 Time of day, h Ambient Temp, F

Insolation, Btu h"-'-ft~^

12 97.4

315

13 100.0

300

14 100.0

2 64

1598.2

2 08

16 97.2

141

1796.5

72

1896.0

25

1993.5

20

90.2

2187.7

2285.62383.3

24

81.5

The thermal network (Fig. 5) consists of six circuits in parallel representing the paths through the

walls, roof and floor. These circuits are connected to a common node through a resistance network which

models the internal convective transfer. This common node, held at a constant temperature of 78°F,

stands for the indoor air. Other resistances connect the indoor surface nodes to allow for radiative

transfer

Outdoor surface nodes receive heat flows (Fig. 6) that have been calculated from the Insolation and

are connected through convective resistances to nodes which receive an input of the ambient temperature.

(It will be noted that long-wave radiation from the outdoor nodes is neglected for simplicity).

The floor circuit is connected to a node held at 74°F and representing the constant earth temperature.

The output from the analyses is the hourly temperature of each surface node, the hourly heat transfer rates from each inside wall to the inside air node and the daily heat transfer rate for each wall. A typical result giving the diurnal heat flow per square foot is shown (Fig. 7). It will be seen that the roof gives by far the highest rate and that the West wall is next. The North wall has no direct sunshine but is affected by diffuse radiation. The South wall shows an effect due to the direct component of radiation when compared to the North.

Integration of the heat flows on a daily basis was performed for each case (Table IV). For each wall

thickness, the heat flow through each wall was expressed as a fraction of the roof flow, called the relative heat flow. It will be noticed that, even though the roof flow ranges from 36 to 1080 Btu day~-^ft~^, the relative flows for each orientation do not vary significantly.

When wall flows are expressed as a percentage of the total daily flow (Table V), it will be noticed

again that the proportion through each orientation does not depend significantly on the thickness or the insulation of the wall. (There is a significant increase in the effect of the floor for the well insulated cases. Polystyrene 4 inch and 6 inch, but the total flows involved at this level of insulation are relatively

small.) • Total heat flows per day, appearing in this table (Table V), have been plotted against the overall

163
heat transfer coefficient U (Fig. 8). The result is an almost linear increase in heat transfer with increase

in the coefficient, as might be expected.

Table IV Heat Flow per day per square foot for each orientation

Material Th if-V - Heat Flow - Btu day ^ft ^ Relative Heat Flow

ness

-inch

N S E W R F N S E W R F

CD 1 370 540 670 620 1080 100 .34 .50 .62 .57 1.0 09

+-> 0) 2 340 490 590 550 990 89 .34 .50 .62 .56 1.0 09 u

c

3 320 460 550 510 910 78 .35 .51 .61 .56 1 .

09 oO

4 300 430 510 480 850 69 .35 .51 .60 .56 1.0 08

c0 270 380 460 430 750 55 .36 .51 .61 .57 1.0 07

1 67 93 114 107 173 -3 .39 .54 .66 .62 1.0 -0 02

olyene 2 37 51 62 59 95 -12 .39 .54 .65 .62 1.0 -0 123 25 35 43 41 66 -17 .38 .53 .65 .62 1.0 -0 26

4 19 27 33 31 51 -2 0 .37 .53 .65 .61 1.0 -0 39

U2 6 13 18 23 22 36 -23 .36 .50 .64 .61 1.0 -0 64 From the network analysis, wall temperatures are also available. The maximum daily temperature

and the time of occurrence have been tabulated for each orientation and two thicknesses of each material

(Table VI). The advantage of insulation is obvious as the temperature is reduced as much as 42°F when

comparing roofs of the same thickness but different material. A further point is the significantly higher

temperatures of the roof, west and east walls when compared with the north and south walls.

Table V

Wall Heat Flows as a percentage of Total Flow

1in 1

Materia] Thicknei inch N S E W R F

Total

Fk

Btu

day"

10"3 % %3

CQ

Crete

1 12 .3 17. 6 16. 1 15.0 35.6 3. 3 125 100 1.26

2 12 .4 17. 7 16. 2 15.

35.5 3. 2 114 91 1.14

3 12.5 17. 8 16. 2 15.2 35.4 3. 0 105 84 1.07

co 4 12.5 17. 8 16. 2 15.2 35.4 2. 9- 99 79 .96 O 6 12 .6 17. 8 16. 3 15.3 35.5 2. 6 87 70 .83

1 13 .7 18. 9 16. 9 15.9 35.1 -0. 6 20.3 100 16 .22

2 14.2 19. 7 17. 7 16.6 36.6 -4. 8 10.7 49 9 .12

3 14.8 20. 5 18. 5 17.4 38.5 -9. 6 7.1 35 6 .08

4 15.5 21. 5 19. 5 18.3 40.8 -15. 6 5.2 26 4 .06

cn 6 17.2 24. 1 22. 0 20.7 46.6 -30. 0 3.2 16 3 .04 Table VI Maximum Internal Surface Temperature

Material Concrete Polystyrene

Thickness

1 inch 4 inch 1 inch 4 inch

Time Temp Time Temp Time Temp Time Temp

North 14 93.7 16 89.3 14 80.8 15 78.8

South 17 97.5 18 93.

14 81.4 17 79.0

East 8 110.0 10 98.9 8 83.3 9 79.5

West 16 113.7 18 103.4 16 84.0 17 79.7

Roof 13 128.3 14 113.9 13 86.0 14 80.4

Floor 15 81.5 17 80.3 14 78.2 16 77.7

This data was si^bsequently used in an economic analysis of the cost of air conditioning buildings

of 1000 ft^ floor area. Cost data for Australian conditions was estimated as follows: Capital cost of building For U = 0.3 Cost = $7.8ft~^

U = 0.2 Cost = $ 8.6 ft "2 U = 0. 1 Cost = $10.8 ft"2 U = 0.05 Cost = $13.4 ft"2

164
Owning cost of building = 8% per annum

Capital cost of air conditioner = 94 0 t "^'2 8$ ton"-^ (t - refrigerator capacity in Owning cost of air conditioner = 10% per annum tons)

Operating cost of air conditioner = 22 0 t "'^•'^^$ ton The average cost levels thus obtained are designated levels A2 and B2 (Fig. 9). Levels and are approximately ±25% A, while levels B^^ and are approximately ± 45% 82- Thus the range of likely costs

is spanned. The results show that the minimum cost occurs for values of U between 0.1 and 0.2.

6. ALIGNMENT OF THE MODELS

Some experimental work and computation has been performed with the aim of proving the models.

Factors that have been investigated include:

a. One dimensional approach.

It is obvious from the different temperatures that can occur in adjacent areas, e.g. the roof and north wall, that considerable heat will be transferred in directions other than normal to the wall surface. Thus

the assumption of one dimensional flow must be evaluated. Other factors that can modify the approximation to one dimensional flow are discontinuities in the structure, such as with stud and panel wall construction, and the geometrical effect of corners. The effect is dependent, among other things, on the size of the building and is greater in scale models of buildings especially where the material thickness is not scaled. Errors greater than 5% can result. b. Fineness of the mesh.

Studies with electric analogues have indicated that dividing homogeneous conduction paths into four

to five lumps gives sufficiently accurate results. Our studies, using material properties as in Table Land

sinusoidal inputs for which the theoretical solutions can be obtained, indicate that using even three lumps

will enable calculation of heat flow within 5%. There may be greater inaccuracy in the amplitude ratio which varied up to -7% for the network with three lumps.

c. Heat Transfer Coefficients.

The outside heat transfer coefficient is usually considered as a function of the wind velocity which

varies with height and time. If wind velocity is taken as V^^ for the surface, it will have different effects on surfaces of different orientation.

The value of the coefficient has been adjusted within limits when attempting to align calculated and

measured results.

d. Size of the time step.

Since the time step can be of any value less than the stability limit, some results were taken to determine the improvement in accuracy for time steps as small as 0. 1 of the stability limit. It was shown that

for the system considered, reducing the step to 0.125 of the stability limit improved the accuracy of amplitude ratio by a factor of 4. Practically, this would also increase the computing time by almost eight

times and make such small steps uneconomic.

e. Damping of initial value transient.

Initial values of node temperature are usually assumed at some constant value though in practice some

distribution of temperature resulting from the previous variable input will remain. The transient from this incorrect assumption takes several cycles to become ineffective. The error in the amplitude ratio is reduced by 44% between the first and second cycle and by only 8% between the second and third cycles when it is approaching the long term value. Thus it would seem that only two to three cycles need be calculated

to remove this error.

f. Comparison with the van Gorcum matrix method.

The van Gorcum method was compared with the network analyser for some simple problems. Being a superposition method, it must be used with constant values of the resistances but, for most building pro- blems, separate averaging of these resistance values will usually give adequate accuracy. The calculation method does not suffer inaccuracy due to lumping since the distributed properties are used.

Since Fourier components of the input are required, it is somewhat less easy to deal with actual

weather data input over a long period.

7. CONCLUSIONS

A basic inaccuracy arises from the many approximations in modelling a real situation and this applies

to the mathematical model used to calculate the heat flows in a structure. Thus absolute accuracy in the calculation method is not of paramount importance as long as the calculation error does not unduly in- crease the overall expected error. The thermal response methods accurately model the conduction path of one dimensional systems and

can produce heat flows for periodic boundary conditions with a short computing time. Since superposition

is involved, variable convection coefficients and material non-linearities cannot be accommodated. Per- haps, pulse methods are more flexible in their handling of boundary conditions than Fourier methods.

Lumped parameter networks, analysed by solution of node heat balance equations at finite time steps,

are simple in concept. They are not restricted to one dimensional flow, can handle variable resistances

165
and internal radiative exchange. But, since sequential solution for each node is required at each time

step, the computing time is long. While they can approximate space-wise variations as accurately as desired by .decreasing thq spatial increments, computing time is increased as the space increment is decreased.

It would seem that the thermal response method may be more suitable for routine investigations with

programmes adapted for a particular class of work, e.g. routine calculation of heat flow into air conditioned buildings.

On the other hand, the thermal network analyser is suitable for investigational work on a wide variety of problems. It is particularly useful for University type research due to its conceptual simplicity,

its adaptation to parametric studies and its ability to model complex situations.

A

C

FH

qQ

R

area, ft _^

thermal capacity, Btu ft shape factor insolation on a horizontal surface,

Btu h ft"2 -1 heat transfer, Btu h heat quantity, Btu _^

thermal resistance, h F Btu

orientation factor, surface to sun

SYMBOLS

tTW

a6e

eep

a

SUBSCRIPTS

temperature, F temperature, R -1-2

flux density, Btu h ft absorptance

time increment, h emittance

time , h reflectance

Stefan-Boltzmann constant, 0.173 x 10 Btu h" ft"-2

convective

sol -air

i - any node

i - other node connected to i

REFERENCES

surroundings

at particular time

with time increment

Sheridan, N.R. and Carr, W.H. (1967) A solar air conditioned house in Brisbane, Solar Research

Notes No. 2, University of Queensland, Brisbane.

Mackey, CO. (1944). Sol-air temperature - a new concept, Heating and Ventilating, Vol. 41,

No. 12, p. 62.

Muncey, R.W. (1952). The calculation of temperatures inside buildings having variable external conditions. Aust. J.Appl.Sci. 4, 189-96.

Brisken, W.R. and Reque, S.G. (1956). Heat load calculations by thermal response, ASHRAE

Trans. , Vol.62, p. 391.

Stephenson, D.G. and Mitalas , G.P. (1967). Cooling load calculations by thermal response

factor method , ASHRAE Trans . , Vol. 73, Part 1, p. Ill 1.1. Paschis, V. and Heisler, M.P. (1944). The accuracy of m easurements in lumped R-C cable circuits as used in the study of transient heat flow. Trans. Amer. Ins tit. Elec. Eng. , Vol.63, p. 165.

Buchberg, H. (1955). Electric analogue prediction of the thermal behaviour of an inhabitable

enclosure, ASHI^E Trans., Vol.61, p. 339.

Sheridan, N.R. (1964). Energy conservation applied to the rational design of a dwelling for the

tropics. Proceedings VlAorld Power Conference, Paper 54, Section IVB. Sheridan, N.R. (1968). On solar operation of absorption air conditioners , Ph.D. thesis. University of Queensland, Brisbane, (unpublished).

166
Calculate Tg 4. ^ q Eqn . (vi)

Read input data I

Calculate fixed resistances

Calculate

capacitances

Calculate

solar input^

Interpolate in Tables

I

Calculate radiation

rpsi.qtancpq

q = (1 - p) R AH

iinear interpolation

1

(i)

R

= 2.^2 r eF _A (T + Tj(T + T ^

) (") s2 s 2 s 2 Calculate convective

resistances

R

=

1

Calculate

Z-k.T. T/R.A e

c BA ^T'

ir °^ R =^ c CA V

C. tQ < (RC) = —^J "^ij

-

. . . (viii)

. . . (iv)

Cathode

Follower

I T = T

e -^9 + A e

No

FIG. 3 PROGRAMME FLOW

CHART

(Counters, etc. are not shown)

167
ground

FIG. 4 VIEW OF SIMPLE ENCLOSURE

168
0 4 8 12 16 20 24

Time - h (from midnight)

FIG. 7 HEAT FLOW IN BUILDING WALLS

169
1.5 /

/

/

X

/

/ X

/

/ X

/

/

/

/

/

//

/

X

0 0.5 1.0 1.5 _ 1 _T -

Overall heat transfer coefficient 'U - Btu h ft F

FIG. 8 TOTAL HEAT FLOW IN STRUCTURE

lOOOl ' i ^ 1 0.4 0.3 0.2 0.1 0 -1 -2 -1 Overall heat transfer coefficient 'U' - Btu h ft F FIG. 9 OPTIMUM INSULATION THICKNESS

170
A Method of Computer Simulation

through Modified Signal Plow Graphs and Operator Concepts

and Its Application to Synthesis of Heating-Equipment Capacities

Shigeru Matsuura

Faculty of Engineering

Hokkaido University

Sapporo, Japan

In order to facilitate simulation of a physical system,

direct simulation on an analog computer through a signal flow

graph obtained directly from a schematic diagram in the physical

system Is used in this__ paper. Physical meanings of the method

are confirmed and modified in view of algorithm as follows: (1)

By creating a summing point which defines a signal, a wrong

signal flow graph resulting from two definitions of a signal is

avoided and an Inversion law and interconnection of subgraphs are clarified. (2) A scaling method in s-domain Is studied only by

the use of a translation of a modified signal flow graph; It is

made possible to obtain the completed program on an analog

computer in which mutual relations between a signal and a scaled

signal (a machine variable) are elucidated. (3) An operator

concept Is developed into the digital domain and a physical

meaning In a closed loop is confirmed, so that simulation on digital computers by same methods as in the above-mentioned

simulation on analog computers is made possible.

As an application, a synthesis of heating-equipment capacities is

performed together with the confirmation of troublesome points in

the actual operation, where not only a building but also automatically controlled heating equipments are simulated.

Key Words: Algorithm, closed loop, definition point, digital

operation, dynamic balance. Initial value, integral operator,

modified signal flow graph, operator concepts, warming up

load, scaling in s-domaln, space series.

1. Introduction

An environmental design related to buildings would be an optimization of the ways

of combination of components (said to be a structure of system) and their values in a buildings system containing equipments, which adjusts its entire balance under certain

specified conditions. Considering the use of a computer from the point of view of

design, therefore, it is desirable to use It synthetically rather than analytically,

that Is, It is necessary to be able to talk with the computer. As one of the useful

means for it, there exists such simulation as correspondence of components in a system

one-to-one, because a building system becomes large-scaled, complicated, high-priced

and made-to-order , so that experiments of actual systems are impossible. For the sake

of its usefulness, the technique of simulation has been widely used in fields of

electronics, automatic-control, chemical process and so on. The types of computers used in simulation are analog type, digital type and hybrid

type (which is the combination of previous 2 types). Considering them from the

standpoint of simulation, there, it shows the problems as follows: (1) There are differences of the models (expressions) as languages and ways of thinking depend on the

kind of computers. (2) Advanced knowledges and techniques are required for simulation.

(3) As the analog computer has the limited usages except for a differential analyzer or

Systems Engineer

171
a simulator, It Is necessary to consider simulation on the digital computer. However,

the large-scaled and high-speed machine is required in Its case.

As a countermeasure for the above mentioned, it Is necessary to consider the next

points: (1) Investigating programming-rules through models in use of the same concept

which Is Independent of the kind of computers. (2) Using symbolism with sufficient

informations in expression of system and its description. (3) A symbolism with

algorithm which leads automatically from description to program. (4) In synthesis, it

is necessary that a program one-to-one corresponds to a system in parts and the

program is newly made by Interconnection and division according to changing of the

structure In system by interconnection and division, and also values 6n the program can

be easily changed. (5) Finding out physical meanings and investigating calculation

rules which calculation accuracy is not less than it was before even if simple procedures are used for the purpose of using a small machine such as a mini computer or a desk calculator.

This paper deals with a new method of computer simulation with algorithm which

automatically gets to a simulation program through a model from an object system.

2. Method of Computer Simulation

It is well known that phenomena of system should be expressed in use of elements

and a pair of across variable and through variable with time. For instance, heat

conduction phenomena can be expressed as simultaneous differential equations using

thermal resistance and thermal capacity as elements, and using temperature and heat

flow as across variable and through variable with time. In these equations, relations

among components such as wall and boiler which actually construct the system, namely,

system structure is not clear.

There are graphical symbolisms as a way of expressing this structure, namely a physical network model, a block diagram, a signal flow graph, an analog computer

diagram and so on. These are diagrammed to emphasize different aspects respectively.

It is performed to symbolize many informations as to relations of actual components

and each element. However, Informations for the casual relation in each variable are not diagrammed. The signal flow graph and the block diagram are expressed in regard

to the casual relation, but the relation to the actual object becomes weak rather than

the physical network model. In the above expressions, direct Informations of time are

lost. The analog computer diagram has a nature of emphasizing element Itself, its own function in Itself and connection with other elements.

Observing these expressions from a view of simulation programming on the computer,

with respect to the analog diagram, simulation programming seems to have been

accomplished at one sight. However, as the analog computer diagram is usually

introduced in terms of an expression of slmulataneous differential equations, the

system structure is lost and the correspondence of system one-to-one in parts can not

be found. Simulation In use of this procedure requires to supplement informations

through thoughts of the structure. Therefore, it is very useful to obtain a simulation

diagram by making the best use of the characteristics of each graphical symbolism.

2 That is; at first, the physical network model is Introduced by a schematic graph [ 1]

which indicates actual system; and then, it is transformed into the signal flow graph

C 2] or the block diagram; and finally, the simulation diagram is obtained. However,

it is not always said to accomplish algorithm of final processes. Symbolism

applicable to both computers is, therefore, developed under considerations of terms

of physical concepts as follows:

2.1. Concepts of Signal and Operator

Observing the relations between variables and elements from a new standpoint,

variables are signals which transmit in a system and the signal is modified by the

element, so that it becomes the next signal in succession. Elements should be thought

as operators. Under such thoughts, what is diagrammed in s-domain Is a signal flow

graph. However, it should be noted that descriptions corresponding to a system have

many equivalent signal flow graphs, but physical meaning of the graph is clear only

when the graph is described in the form of 1/s concerning time, namely. In the form of an Integral operator, because physical phenomena may be said in general to depend on the past and the conservation of energy principle.

2 Figures in brackets Indicate the literature references at the end of this

paper

172
2.2. Modification of a Signal Flow Graph

As a simple example to clarify the above mentioned, it is considered that water

is discharged from water tank (across sectional area A) using a pipe (resistance R)

This is applied also to the case in which heat is discharged only by ventilation out

of the room. When the water level is h, its initial value is hj and outgoing water

flow is q, the modified signal flow graph expression of this system is given as eq (1).

where, the signal flow graph is modified as follows: The signals are enclosed by a large circle to be distinguished from transmittance (operator) and the new summing

points shown by small circles are made, they are also definition points in signals.

Observing the definition as to h, it is equivalent to the next equation.

h = + -ill sA g

By the modifications, the next merits may occur. By means of separating and

symbolyzing definition points in such a way as each a signal has only one definition

point (by elimination of signals on the way, it is not prevented that the signal has

sequentially two more definition points), misses in two definitions of a signal, when

the flow graph is drew, can be prevented. Physical meaning of interconnections in

system is in a concordance with across variables and a continuity of through variables.

An interconnection in sub-graphs (which correspond to sub-system) attending an interconnection of sub-system requires that In any Interconnection the across variables

are connected by a branch with transmittance 1 and the through variable is defined by

another through variables, connected by each branch so that continuity conditions may

be held. In this case, if a signal has two definition points through the interconnection, here, a branch of either definition point is inversed (in which 1/S is left as it

is) as a definition point for a different signal, and two definitions resulting newly

from it is Inversed in succession until reaches a signal having no a definition point.

Furthermore, by creating this summing point, the analog computer diagram can be easily

expressed by modified signal flow graphs. Namely, a potentiometer, a summing amplifier

and a summing integrator are expressed as eqs (3), i^) and (5). By using them, an analog simulation diagram corresponding to a system one-to-one can be made only by

equivalent transformations of the graph.

173
(5)

However, if a scaling change Is not done In the analog computer programming, it

is not that the program Is perfect. A perfect analog simulation in only a signal flow

graph is not always done. It means that there remains problems of algorithm. Next,

a scaling in s-domain is considered.

2.3. Scaling in S-domain

A scaling has two kinds, first is to transform variables in a system into machine

variables which are non-dimension and smaller than 1. Transforming them in s-domain

by considering a magnitude scale factor a with dimensions, it becomes as follows:

ax (6)

For the purpose of representing this relation on a graph it is necessary to add a new

rule, that is, by multiplying a signal by a , the procedure in such a way that a transmittance of incoming branch is multiplied by a and that of outgoing branch is

multiplied by 1/a is required so that the graph is equivalent to the original graph.

is equal to

(7)

(8)

Next, it is thought to transform concerning time in use of time scale factor

simulation within time or frequency adapted to the machine.

e for

At first, in t-domain

3t (9)

transforming (4) into s-domain

(10)

where t, s correspond to real time and t Mixnsky's expression [ 3]S to machine time. And according to

174
1 (11)

t = (12)

Observing both sides of these equations from the point of view of a dimension, they do

not coincide because 1/s is said to have a dimension of t.

The next po

result of operat

s-domain, operat

Therefore, this

impulse is though

be affixed to th

the dimension,

the signal is wr Considering phys

by 6 in time. A machine time is

ints are considered to clarify this problem. Observing a signal as the

ors acting on a unit Impulse, in a usual description of function in

ors alone are expressed and the unit Impulse is not expressed,

unit impulse having value 1 and the dimension 1/t (because the unit

ht as a limit of a pulse in the width At and the height 1/At) should

e right hand of eqs (11) and (12) and both equations coincide also in

Hereafter, to distinguish clearly a signal from a group of operator,

itten in the form of affixing I having a dimension of 1/t.

ical meaning of time scale change in eq (9), the phenomena is extended

s an area of a unit impulse must be always 1, the unit impulse 1 in

given as

(13)

A unit step function which results in one integral operator acting on the unit impulse

is expressed as, 1/s, 1/S, respectively. As this unit step function is an Infinite

step without concerning time scale change, they must be equal. And show them as 1/s.

1S

1 (14)

accordingly

16S (15)

From the above investigation, if time scale change is done directly in s-domain, it

will be done by affixing 1 to input signal and also by adapting eqs (iH) and (15).

For the purpose of showing a simple example of analog simulation procedures, the

graph of the tank model shown already in eq (1) Is transformed equlvalently in such a way as constructed by analog computer elements given In eqs (3), (4) and (5). And when

magnitude and time scale change are done with regard to the above mentioned, the analog

simulation program can be accomplished automatically and successively as follows:

<

1Ch

V

1 A —

6a,

(16)

1_

aq

>-

175
where, the values of H and Q are non-dimension and machine variables smaller than 1 and 1/R • /ahj 1/A 'Oih/Sciq are non-dimension and values smaller than 1 and indicate

potentiometer values'.' The newly added branches shown as dotted line indicate relations

between machine variables and variables of the original system (these do not become

the object of the simulation). Next, consider the case of digital operation.

2.4. Digital Operation

In the case of an operation on a digital computer, various numerical methods have

been developed in regard to information which can be obtained when it is sampled. That

is, information related to the structure is weak, so that they don't always adapt to

system simulation. For the purpose, the "time series" method [ 4] and the "thermal

response factor" method [ 5] were published. But it is difficult to adapt the methods

to the next cases; namely (l) when systems are Interconnected, (2) when the system- has

non-linearity, (3) when the system has the initial value which represents the past

effect, (4) when the problem having non-periodic intermitting heating including off

days is solved.

A digital operation of an integral operator is considered, observing that time is

represented only by the integral operator 1/S in the simulation diagram corresponding

to a system one-to-one. When values of a signal at t=0, T, 2T, etc. (T is time

interval) are xg, X]_, x-^j , etc., the signal x is approximated by straight

line segments at each interval. It is expressed as eq (17), which is named "space

series".

[ (Xo) , (Xj) , (x^) , (Xj) , (17)

The signal resulting from the integral in eq (17) is expressed by space series as follows

I

[(0) , (x, + xj (x,+ X, + X,Xo ) (x,+ x,+ x,+ (18)

Therefore, it is proper to replace all 1/s of the graph with the above equation and

calculate it step by step at each interval. However, as exceptions, when the signal

value is always zero in the previous interval and it rises to the value (xq), an operation of 0 + (xq) = (0) must be used, and in a unit impulse, the calculation is

such that instantaneously (1) will be preserved.

Next, consider adaptation of the digital operation in eq (1). When eq (1) is

solved theoretically with Mason's rule [ 6], eq (20) is given as:

ST.

1 + STr (20)

176
where, = AR Is time constant. Equation (1) Is expressed in the form of the digital

operator using sampling interval T as follows:

177
Table 1. Comparison between calculation values in use

of y= T/Tc = 0.25 and theoretical values.

Time Time (by T^) Calculation

Value

Theoretical

Value

0 0 1 . 0000 1 0000

T 0 25Tc 0 .7777 0 7788

2T 0 5 Tc 0 . 6o49 0

C r\ C r- 6065

3T 0 75Tc 0 .4705 0 4723

4t 1 0 Tc 0 .3659 0 3678

5T 1 25Tc 0 .2846 0 2865

6T 1 5 Tc 0 .2213 0 2331

7T 1 75Tc 0 .1721 0 1737

8t 2 0 Tc 0 .1339 0 1353

12T 3 0 Tc 0 . 0490 0 0497

i6t 4 0 0 .0179 0 0183

When M = 2 (namely the interval of 2 Tc), eqs (22) and (23) become zero (these

exact values are 0.135335 and O.OI8316). And when y> 2, they oscillate in +, -, +,

, etc., having values smaller than 1. Therefore, it is seen that y is an index

for modelizing a distributed system into a lumped system. That is, time constants in

each part should be divided to coincide as much as possible. In order to clarify

correspondence to the system, if divisions are done in such a way that time constants

in each part have considerable differences , the interval in calculation of each part

should be modified in such a way that y becomes equal in parts. For the purpose of

rough calculations, when the calculations are tried with large intervals, it is proper

to neglect heat capacities in the part of y> 2.

3. The Application to Synthesis of

Heating Equipment Capacitance

In use of the methodology mentioned above, it is reported to simulate hot water

heating in a building on an analog computer. A one-story house (100 m^ ) having

concrete walls of thickness of 15 cm affixed with glasswool 5 cm is heated by hot-water

radiator and the system is represented in figure 1 using physical network model. As the used computer is small, the building is one-room model with one boiler (with hotwater-supply tank inside) having one radiator, and a burner is controlled ON-OFF by room temperature and water temperature in the boiler.

3.1. Warming up load

As the results of simulation, figure 2 Indicates an intermittent operation in

which an operation is sixteen hours and a stoppage is eight hours. In this case, an average outside air temperature is -10°C and a calculation load in steady state is

10000 kcal hr~l.

Observing the results, at night the room temperature in stoppage of operation

falls from 20°C to 6°C, therefore, it seems as if fuel is saved in general. But judging

from figure 2, it is said that the sum of outgoing heat flow falls only a little. The reason is that heat stored in the wall is discharged at night and the heat is

coijipensated during warming up time. It requires about three hours until it reaches

20 C even when a burner of 20000 kcal hr (two times of calculation load) is used.

In this example, the intermittent operation has not saved even 10 compared to the

continuous operation and it is clear that the burner output from 2 to 4 times larger

than the steady state load, would be required, corresponding to the interval of

warming up time. Therefore, considering initial cost, the continuous operation is

profitable rather than the intermittent operation.

3.2. The Need of Dynamic Balance of System

Figure 3 indicates ON-OFF of the burner and the boiler water temperature, there.

178
the ratio k of the radiator capacity in steady state to the burner capacity is changed

to 1.0, 1.1, 1.2.

As the result, in spite of having no troubles in steady state, it is seen that

in transient state of warming up time, the boiler water temperature reaches a limit

and the ON-OFP operation begins before the room temperature reaches 20'^C. This ON-OPP

operation means that the burner output becomes smaller. Therefore, it is necessary to

consider not only static balance of system in steady state but also balance in

transient state.

3.3. The Drop in Hot Water Supply Temperature

and Additional Load in Hot Water Supply

Figure 4 Indicates the drop of the hot water supply temperature and an influence

on the room temperature when the hot water is supplied in thirty minutes at the rate

of 10 SL every minute. At that time, there are two cases such as the Intermittent

operation with the burner output in 20000 kcal hr"-'- and the continuous operation in

10000 kcal hr~l.

From the results of these simulations, it Is seen that when limit design of

equipment capacities and so on is done, each simulation should be done case by case because the characteristics are different because of the differences of the systems

and therefore limit design should be determined after confirmation and investigation

of problems.

4. Other Considerations

By means of the concept of the operator (the concept of the very system element

Itself which is the operator) and the modified signal flow graph (where it indicates

that signals are modified by the operators), algorithm was reported where simulation

will take place from the environmental system related to building to its simulation

automatically and continuously without regard to the type of computer. It will be

thought that the description method is also convenient for common expressions of

phenomena in fields of environmental engineering such as electricity, electronics,

dynamics, fluid dynamics, process and so on.

As the example of synthesis only the methodology using the small analog computer

was indicated . If a large-scaled analog computer is used, it is possible to indicate

each room. As digital computers occupy the major parts in general, simulation in use

of the digital computer should be indicated. Languages oriented conversations with

computers are in the stage of development in our laboratory. It will be discussed on another occasion.

5. References

[ 1] Samuel J. Mason and Henry J. Zlmmermann, Electronic circuits,

signals, and systems, John Wiley & Sons, Inc. (I96O).

[ 2] Louis P. A. Robichaud, Maurice

Boisvert, and Jean Robert, Signal

flow graphs and applications,

Prentice-Hall, Inc. (I962).

[ 3] Jan Mlkusinskl, Rachunek operatorow,

Panstwowo Wydawnictwo Naukowe,

Warszawa ( 1957 ) .

[ 4] A. Tustin, A method of analyzing the

behaviour of linear systems in terms

of time series, Inst. Elec . Engineers,

Vol. Part II-A, No. 1, p. 130-142,

(1947) .

[ 5] D. G. Stephenson and G. P. Mitlas,

Cooling load calculations by thermal

response factor, ASHRAE Transaction,

Vol. 73, Part II, p. 72 (1965).

[ 6] Richard S. Sanford, Physical networks,

Prentice-Hall, Inc. (I965).

179
Fig 1 Physical Network Model

6: temperature, C: heat capacitance, h: burner output,

q: heat flow, r: resistance

(Subscripts)

a: room, b: boiler, c: cold water, g: glass, h: heat water supply,

i: inside, o: outside, p: room wall, r: radiator, v: ventilation,

w: wall

Fig. 2 Response concerning h, Qqy,, Qy^ and

for Intermittent Operation

M/.

Fig. 3 Response concerning h and

6^ for Intermittent Operation when

k = 1.0, 1.1 and 1.2

1, 1"" i

A

1-^-

1

--1

1

1

>

i

i

- 1

1

i —

-r—

i

- j

1

Fig. 'I (a) Response concerning Gj^ and 6^ for Intermittent Operation with

h = 20000 kcal hr"^

(b) Response concerning 6^ and Oa for Continuity Operation with

h = 10000 kcal hr"-"-

180
Shared Time System Computer Programs for Heating and Cooling Energy Analysis of Building Air Conditioning Systems

Charles J. R. McClure and John C. Vorbeck

Mechanical Engineering Data Services, Inc. (Medsi)

Saint Louis, Missouri

Heating and cooling Energy Calculations are made by shared time computer programs using

Weather Data taken from Air Force Manual 88-8 and U. S. Weather Bureau Climates of the States covering 218 areas in the United States.

Three basic programs are used. Reheat, Heat-Cool-Off, and Multizone or Double-Duct to produce

net requirements of ton-hours and BTU x 10^. In addition to the weather file, 91 numbers are required

to describe building gains and losses, heating and air conditioning system and building use.

The output file of these programs are processed in another program to convert the ton-hours and

BTU X 10^ building requirements to KW, KWH and BTU x 10^ input to equipment by additional data of 32 numbers describing the equipment and efficiencies.

In addition to evaluation of the three basic systems, analysis may be made of the effects of many

variations of each system and programs schedule, such as:

Economiser system with or without reset of mix air temperature. Hot deck temperatures on cooling cycle.

Perimeter heating loads

Reduced temperature in unoccupied hours; intermittent operation in unoccupied hours.

Fuel conversion efficiencies; electrical demand.

Modifications and combinations of these basic programs may be used to evaluate Variable-Volume;

Variable Volume with reheat; Fan-coil units in exterior and Multizone in interior; etc. The programs have

also been used to analyze energy requirements of all electric and total energy systems. Mechanical and

electrical systems for schools, office buildings, hospital operating suites, hospital patient rooms,

apartment buildings, shopping centers and even a bicycle shop have been analyzed with the use of these programs

This system of calculation by computer is an outgrowth of many years of experience using manual

calculations. Programming, using Basic Language, was started in March 1968 and improvements continue to the present day.

Charles J. R. McClure and Associates, Inc., the developer of the system, has been making

practical use of the information provided for several years. Medsi' s customers have been using the programs on their own terminals since November 1969.

Approximately 25 seconds of processor time are used with about 30 minutes connect time for each

run; programs are available from a restricted library on SBC,Cal]/360 system.

Keywords; Energy, heating, cooling, air conditioning systems, shared time programs,

evaluation, gas, oil, electric, dollars.

181
1 . Objective

The Engineers associated with developing these programs have made many estimates of heating

and cooling energy requirements for building mechanical systems by manual calculations using degree

days, full load hours, average temperatures, typical 24-hour weather profiles for each month, etc. The last manual calculation in 1967 consumed over 2 ,000 man hours, most of which was spent in determining the net ton-hours and BTU x 10^ required by the heating and air conditioning system, without

regard to efficiencies of machinery. About this time, a computer time sharing system became available

and management decided to exploit the computer's ability to make many calculations in a very short time

The objective was a monthly tabulation of net ton-hours and BTU x 10 , as shown in Table 1, with high accuracy and requiring a minimum of repetitive manual calculation.

TABLE 1 . - Ton-hours and BTU x 10

SAMPLE! OFFICE BLDS. MINNEAPOLIS DEC 1.1969 FIN TOBE RADIATION AT EXTERIOR. CONVENTIONAL RETURN

SYSTEM #1 WITH ECONOMISER MULTIZONE OR DOUBLE-DUCT SYSTEM MONTH PERIOD TON HOURS BTUX10«5 INT BTUXlOtS EXT

JAN NIGHT 0.0 476.6 782. 1 JAN DAY 0.0 739.8 6 39.0 JAN EVNG 0.0 370.8 751.3

SUB TOT 0 3759 FEB NIGHT 0.0 417.3 656. 1 FEB DAY 35,0 644.9 494.0

FEB EVNG 0.0 326*6 614.7

SUB TOT 34 31 53 MAR NI GHT 0.0 414.5 * MAR DAY 249 • 1 671.2 MAR EVNG 6.3 549 5 SUB TOT 255 3004 APR NIGHT 139.1 333.6 402.6 APR DAY 3184.

49 1 . 3 885.

APR EVNQ 343.0 256.7 338.3

SUB TOT 3666 2047 MAY NIGHT 832.

249.6 855.8 HAY DAY 7645.9 318.9 100.9 MAY EVNQ 1047.2 176.2 198.8

SUB TOT 9525 1293 JUN NIGHT 1680.7 167.4 183.1 JUN DAY 10422.3 212.5 89. 1 JUN EVNG 1676.9 117.6 66.6

SUB TOT 13779 736

JUL NIGHT 8076.0 138.7 81.0

JUL DAY 11669.4 176.9 8.6

JUL EVNG 1912.0 99.4 45.5

SUB TOT 15657 550 AUG NIGHT 2092.2 146.9 88. I AUQ DAY 1 1842.8 180.9 10.1 AUG EVNG 1947.0 105.3 50.7 SUB TOT 15882 582 SEP NIGHT 1012.2 229.3 807.0

SEP DAY 8376.4 263.6 61.5

SEP EVNG 1071 .9 164.2 169.8

SUB TOT 10460 1095 OCT NIGHT 369.7 311.1 342.1 OCT DAY 5296.5 4S5.7 144.1 OCT EVNG 533.0 240.6 301.6

SUB TOT 6199 1765 NOV NIGHT 22.2 370.5 528.7 NOV DAY 592.2 639.0 396.7 NOV EVNQ 43.0 304.5 500.9

SUB TOT 657 8740

DEC NIGHT 0.0 441.0 696.0

DEC DAY 0.0 727.6 574.8

DEC EVNQ 6. 1 350.5 665.4

SUB TOT 6 3455

TOTAL NIGHT 8224.7 3696.7 4764.8 TOTAL DAY 59314.0 5492.2 3117.5

TOTAL EVNQ 8586.5 2845.4 4267.

ANNUAL TOTAL 76125.1 12034.3 12149.4

2 . Weather

Previous experience indicated that Air Force Manual 88-8, "Engineering Weather Data" (1), should be the weather source, since it was available, compact, included 8,750 observations per year, and covered many areas throughout the world. Weather observations in AFM 88-8 are grouped into 3

182
periods of the day, 1 A.M. to 8 A.M. (night), 9 A.M. to 4 P.M. (day) and 5 P.M. to 12 midnight

(evening). The accumulated monthly observations are also grouped into 5 degree dry bulb segments to- gether with the mean coincident wet bulb. In addition to the hours of dry bulb and wet bulb there is stored in the weather-file the hours of sunshine for each period of each month together with solar heat

gain factors for each period as compared to the maximum hour in July for 9 exposures (N, NE, E. . . NW,

Horizontal). Hours of sunshine for each locality are taken from U. S. Weather Bureau's "Climates of the States" (2) and solar intensity is calculated by computer using the method outlined in "ASHRAE".

Medsi has weather on file for instantaneous call for over 10 locations in the United States. Each

weather file takes 3 or 4 units of storage on Call/360. To prepare a weather-file for another location costs about $100, During each run the first part of the weather-file is read into a two-dimensional array, 45 by 125 maximum, and the second part covering solar gains is read into ten one-dimensional arrays

of 36 factors each. Review of many projects leads to the conclusion that these weather-files are the most accurate input of all the data that enters into energy calculations.

3 . Input Data

The input data required is shown on Medsi form No. 1 (Rev. 12-1-69) (Table 2). The data is entered into the program in the form of data statements together with job identification in the form of print statements. These are best prepared off-line by punch tape and then entered into the system. These

are entered, given a name (program file) and saved. It is then possible to 'WEAVE' this program of data statements with other programs such as a reheat program, multizone program, heat-cool-off program

etc. , to readily make comparisons.

3 . 1 Occupancy Schedule

Lines 1 through 4 of form No. 1 (Table 2) are the occupied hours expressed as a decimal part of the total hours of each period. These numbers can be changed for each month so that vacations and

holidays may be considered. The first number of line 1 is .2 08 and tells the computer that 20.8% of the January night time hours are occupied, that the outdoor CFM (3000) shown on line 16 is to be used, that

the room temperature is 75 degrees as shown on line 5 and that the first number of lines 24 (BTUH lighting gain), 26 (BTUH other sensible gain) and 28 (BTUH latent gain) are to be used for these hours.

Medsi form No. 2 (Table 3) is used to determine these numbers. Schedule C, occupancy, is filled in with X in the occupied hours of the week. The number of x (12) divided by 56 (8 hours per day x 7 days

per week) equals ,215. Multiplying this by 30/31, to allow for 1 holiday in January, gives .208.

3.2 Temperatures, Humidities and Enthalpies

Temperatures, humidities and enthalpies of the air throughout the system are entered on lines 5 through 14, and line 18. The room dry bulb (line 5) is used in both winter and summer calculations during occupied hours. To simplify calculations, enthalpies (BTU/# AIR) are used instead of Wet Bulb

Temperatures and specific humidities (Grain s/# AIR) are used instead of relative humidities. Lines 9, 10 and 11 are summer conditions of air in the supply duct of a terminal reheat system or the cold deck

of a multizone or double duct system. Lines 12, 13 and 14 are winter conditions at the same points

when cooling by refrigeration is used in winter.

3 . 3 Air Quantities

The total air quantity circulated is entered on line 15 and should be the actual air quantity circulated. The actual minimum fresh air is entered on line 16, The use of outdoor air for cooling in winter,

instead of using refrigeration, is called an economiser in this set of programs and is considered later. Line 17 is unoccupied CFM or infiltration and is applicable to all unoccupied hours. However, since

the refrigeration is usually turned off in unoccupied hours, the unoccupied CFM should be typical of

the heating season.

(1) Figures in parenthesis indicate the literature reference at the end of this paper.

183
TABLE 2 Medsi Form No. 1 M EDSI Form No. Ifflfl/. 12-1-69i

DATA STATEMENTS (91 NUMBERS! OCCUPANCY

SCHEDULE

Project JAMlPte. '^FlCt 3u»/l.P/A/g.

Location MI t^l^t. k Pt\ I f^iiJiy Date I^/i/L^

Night Day Evng.

Jan. April July 77

Oct. ,X,f

NiEht Day Evng. Feb. May 11

Aug. .11 r r.j

Nov. •'1

Night Day Evng.

IMar. .(fi> June .r»» nx Sept. .i«y .'71

Dec. r'l* DESIGN CONDITIONS:

5 Room Dry Bulb WINTER & SUMMER) 7S

6 Room Enthalpy (SUMMER) ly.i.

7 Room Minimum Humidity, Grains / lbs. e

8 Outdoor Enthalpy Max, (SUMMER DES.I

9 Summer Supply Dry Bulb

10 Summer Supply Humidity, Grains / lbs. .TK' n Summer Supply Enthalpy

12 Winter Supply Dry Bulb

13 Winter Supply Humidity, Grains / lbs. 14 Winter Supply Enthalpy

16 Total CFM

16 Outdoor CMM Occupied 3 < 0 »

17 Outdoor CFM Unoccupied y * »

18 Summer Mode Hot Deck Temp, ts

19 Max, Trans, Loss in BTUH Sit oo

20 Heat Loss Design Temp, Diff, fS

21 Max Trans, Gain in BTUH

22 Heat Gain Design Temp, Diff,

(ZERO IF NO WINTER HUMIDIFICA TION)

USED WHEN

THERE IS NO

ECONOMISER CYCLE

(NOT LESS THAN ROOM OR Y BULB)

SOLAR GAINS (Maximum in Julyl SE S SW Horiz. tr»co

LIGHTING GAIN

Occupied Unoccupied OTHER SENSIBLE GAIN

Night Night 171006

S/ eta

26 Occupied Night 27 Unoccupied Night 0

LATENT GAIN

28 Occupied Night 29 Unoccupied Night •

Day

Day

Day

Day

Day Day

Evening

Evening

Evening

Evening

Evening

Evening

/7 e eto

i-y too

DECIMAL OF

TRANS. HEAT LOSS DECIMAL OF

LIGHT HEAT APPLICABLE EXTERNAL AREA

INTERNAL AREA

RETURN AIR

DECIMAL OF HORIZONTAL SOLAR GAIN TO RETURN AIR DECIMAL OF TRANSMISSION GAIN TO RETURN AIR SUPPLY FAN HEAT IN BTUH RETURN FAN HEAT IN BTUH

to v»e

3.4 Building Gains and Losses

The transmission (conduction) loss is put in line 19 and the temperature difference used in the calculation is put in line 20. The transmission gain, not including solar gains, and the temperature

difference are entered in lines 21 and 22. Solar gains are placed on line 23. They are not coincident

solar gains but rather, are maximum gains for the peak hour for each exposure. For example, solar gain for East occurs about 8 A.M. and for West about 4 P.M. but the values would be the same if they were similar in glass area, shade factor, etc. These gains and losses should not include any safety

factors or pick-up allowance that might be normal considerations for apparatus sizing.

3.5 Internal Gains

Lines 24 through 29 are internal gains applicable in night, day and evening periods when occupied

and when unoccupied. These values (BTU/Hr.) are calculated manually using the schedule charts shown in Table 3. as follows. The schedules are filled in with percentages of maximum for each hour

for each day of the week. The occupancy schedule C shows 12 x "s representing 12 occupied hours in the night period. The percentages of lighting for these 12 hours shows 6 hours of 15%, 5 hours of 100%

and 1 hour of 50%. The average occupied night hour has 50.5% of the lights on and if the maximum heat

gain from lights is 340,000 BTU/Hr., the heat gain for each night occupied hour is 172,000 (the first

184
number on line 24 of Figure 2). People gains, sensible and latent are determined in a similar manner. Miscellaneous gains, if the energy source is electrical energy, such as an air cooled electric refrigerator in the space, should be included in with lighting gains since these loads will later be connected

to ?CWH. Otherwise, include appliance and intermittent equipment loads in other sensible and/or latent gains

TABLE 3 - Medsi Form No. 2 MEDSI FORM N-:2. ENERGY LOADS PROGRAMS: SCHEDULE A SCHEDULE B SCHEDULE C

o

« Hours

Peopla As Percent Of Max.

Lights As Percent Of Max.

Occupancy

Occ." )f , Unocc.= 0 Period 1

S M T w T F s S M T W T F s S M T w T F s

1

Night

01 0 0 o o 0 e a .li .IS .if If

Night

1

02 0 * 0 » o 0 •0 .If i< .If .If .ir li* 03 0 0 (9 e • o 0 If /< .11 ;« 04 0 0 O 0 • « o // .(f iS .>{ .if f

05 e « e 0 0 0 If »r .li .iS .If .If vf 06 « • • o » 0 jf jf ii' .if .1% .if 07 0 0 o 0 0 j% .If .if .if .if ./> X X X X

08 e .y ,¥ i .iS /. 1. A >! /. .f X X X X X

Doy

09 0 /. / A /• I- /. I. / /, /, .i ?(. / X X X X

OO

10 « /. /. /. l. 1, .if / / /.

/,

. { X X X X X X 1 1 e /• (. /. /. /. .r /. /. /. /. f X X X^X 12 « /. 1, /. / i. 6 /. /• /. A .i X X X XX 13 e 3 .3 .•J .3 .3 0 / /. /. A /. f X X X XX 14 • /. /. / / /. 0 /. /. A 1. if X X ^:^

IS /• / / /

/. /. A A /. .li X X X X

16 0 /. /. / /. /. o /. /. /. /. .n A X X

1

Evening

|

17 0 /. /. /. / /. e .f .5 .f .li X X X

Evening

|

18 • ,x t .X .X 0 .r .r .r .If X X X X

19 e 0 « 6 0 0 e £ s .r .l! 20 0 0 O 0 » 0 0 .r .s .r .r ••f 2 1 c 0 e 0 0 0 « .f .r .r ,»f 22 » o » o o 0 6 •If .f .r .r .r Jf

23 0 « « » e 0 6 .f .i ,f .r ,f ,ti 24 • 0 « 0 t 0 b .If .>s Ji

Max. People Sensible ^o. o Schedule)

Mox. People Latent i*e . a »0 (a Schedule.)

Max. Lights Sensible ?V«;.*«0 (b Schedule.)

3.6 Division of Building Heat Losses

and Light Heat Gains

Figure 1 represents the floor plan of a building with area 5 being an office with a window and

area 7 being an interior office. It is apparent that the lights in area 7 cannot be expected to aid in the heating of area 5; neither can the cold glass in area 5 help cool area 7. Consider also, figure 2 which

represents a store with only the window and roof exposed to the weather. The lights in this instance can be expected to help offset heating load. However, if fin tube radiation is added to offset heat

losses of the glass (Fig. 3) then the light can only be applied to the heat loss of the roof. It is necessary that some consideration be given to this problem and lines 30 through 34 have been provided for entering percentages of heat losses, and applicable light heat gains. Lines 32, 33 and 34 are used primarily for ceiling return systems.

185
3.7 Fan Heat

Heat of the supply fan and return fan are entered on lines 35 and 36. The brake horsepower times

2545 should be used unless the motor is in the air stream in which case KW input to the motor times

3400 should be used.

4.0 The System Programs

The programs that process the input data to produce ton-hours and BTU x 10^ are: *HCE1RH - Reheat System

*HCE2HCO - Heat-Cool-Off System

*HCE3MZ - Multizone or Double Duct System

Basic procedure common to all three programs is illustrated in the logic Diagram, Figure 4. As

indicated in the diagram, each of the 36 time periods that make up the weather year are printed after the influence of each weather incident is calculated with the input data . The programs determine solar heat gains, external heat losses and gains, and internal gains and losses, process this raw building

load in the unique features of the selected system program, calculate part load hours and accumulate

the totals of the various out put information.

4.1 Reheat Program

Figure 5. Logic Diagram, Reheat Program (*HCE1RH) illustrates the considerable complexity of analysis used to reflect the performance of this system in meeting the building loads. When the out- door temperature is lower than room dry bulb, the program accounts for the effect of economiser cycle. A determination of the mix air temperature is made, based on input data concerning reset range of mix

air if used, and, if the O.A. temperature is lower than the adjusted mix air temperature then the cooling

effect of the O.A. is calculated. The quantity of reheat is calculated for conditions when the space

needs additional heat and added to the heat required to preheat O.A. and to humidify. This program

allows for 3 degree shift in room temperature before the reheat load is figured to account for thermostat

throttling range. These calculations are done for each different weather condition.

If there is no economiser cycle, the program calculates required reheat for the mix air temperature

resulting from the introduction of the minimum quantity of ventilation air. The refrigeration load re- quired to cool the supply air down to the design supply temperature is adjusted to reflect the cooling

effect of minimum O.A. If the space does not require the full available cooling effect, then the program

calculates the necessary reheat and determines required heat for humidification . A separate loop is pro- vided to account for a special control cycle that will use 100% O.A. when the outdoor wet bulb temperature is below return wet bulb. When the outdoor temperature is above room dry bulb, the program calculates the reheat needed

in the same manner as with the economiser cycle. However, the refrigeration requirement is determined

as the sum of the minimum O.A. sensible cooling, return air heat gain, supply fan heat, space heat

gains and the heat added as reheat plus the latent heat load from internal loads and outdoor air dehumidification. The same loop as above is available to reflect 100% O.A, when outdoor wet bulb is below return wet bulb. The program also accounts for the scheduled mode of operation during unoccupied

hours

4.2 Heat - Cool- Off System

Logic Diagram Heat-Cool-Off (*HCE2HCO), Figure 6, illustrates the calculation procedure for this system. When the outdoor air is below room dry bulb temperature, and the building internal gains

exceed the heat losses, the program accounts for the cooling, heating and humidification required for minimum O.A, , and then determines if the system is in occupied mode and if there is an economiser

cycle. The heating needs for humidification and building refrigeration loads are calculated. When

the outdoor temperature is below room temperature and the building internal gains are less than the heat

losses, the program calculates the heat required for treating the minimum fresh air and supplying heat

to offset the losses. When the dry bulb is not lower than room dry bulb, the computer determines the

186
cooling required to offset sensible and latent gains, including minimum O.A. , and then adjusts this figure to reflect a reduction in latent load proportional to the ratio of total load to the size of the cooling

system. A loop of computer operations will take account of a special control cycle that provides 100%

O.A. when outdoor wet bulb is below return wet bulb. The program also can determine the refrigeration

load in unoccupied cycle if desired.

4.3 Multizone or Double Duct System

Figure 7. Logic Diagram, Multizone or Double Duct System shows the analysis employed to account for special considerations inherent with this system. Separate modes of calculation are used to reflect the system performance when the relationship of outdoor air temperature to room temperature

changes as in *HCE1RH and *HCE2HCO. By-pass factor is the percentage of supply air that goes

through the heating coil and this value is determined for each weather condition. The influence of the economiser cycle on cooling and heating energy use is calculated; heat required for humidification is determined for each new condition of outdoor air quantity, enthalpy and internal latent gain. The influ- ence of 100% O.A. when outdoor wet bulb is lower than return wet bulb is calculated. Refrigeration re- quired is calculated using the adjusted by-pass factors and including the latent heat load of outdoor

air. (The factor .633 is a constant converting grains per pound of air to BTU per CFM) . Use of the recalculated by-pass factor reflects the changing conditions of face and by-pass control and is valid

when the by-pass is merely untreated mix air, as when no heat is added to a hot deck in the summer

cycle, and when there is heat added to the by-passed air.

5 . Running the Program

As a check on number of entries and to provide a permanent record of the input data used for the

run, it is good practice to weave *HCEDATA program with the data entered. If the number of entries

checks, the Form 1 data will be listed in full. After this check, the data program is then weaved with

the appropriate system program, *HCE1RH, *HCE2HCO or *HCE3MZ. An outfile must be established

to receive the output and, when the "Run" command is given, the program will ask the following series

of questions

"Enter Input File Name": Response is the name of the desired weather file.

"Enter Output File Name": Response is the name assigned for the output data. "Do you want hours and part load": If the response is negative, the program by-passes this portion of calculation and some computer time is saved. A positive reply causes the program to calculate the percentage of boiler and chiller load required for each weather incident and

to accumulate the number of hours of each part load increment

"What is the tons of refrigeration machine": Respond with actual machine size selected.

"What is the MBH output of boiler": Respond with actual boiler size selected.

"What is the unoccupied winter room temperature setback": Response is the net difference from

occupied room temperature (Form 1, Item 5). There is no allowance built in for "Spindown" or "Pick-up". It is as- sumed that adequate controls are provided to prevent establishing peak demand for heat pick-up by staging ventilation

loads or similar control over load segments

"Is there economiser cycle": Response indicates whether outdoor air will be used to remove excess heat gain during the heating cycle. In Heat-Cool-Off

program the amount of outdoor air above the input minimum

ventilation air is determined by room heat gains only. In both

the Reheat and Multizone programs, the quantity of additional

outdoor air is the amount required to m.aintain the input mix

air temperature.

187
"What is the economiser mix temperature at 0° outdoors": Response is to indicate the upper limit of mix temperature reset if a variable control is used.

"What is the economiser mix temperature at 55° outdoors": Response must be 55° or higher. If variable mix temperature is used, the program will calculate

the specific temperature for each weather condition, as a linear function.

"Is CFM all outdoor air on cooling cycle when outdoor wet bulb is below return air wet bulb": Response should indicate if this control feature is used.

"Is system off in unoccupied hours when outdoor dry bulb is above room dry bulb": Response

should indicate if system is stopped in unoccupied mode

during cooling season. When the last question is answered, the computer will print out the ton hours and BTU x 10^ as shown in Table 1 . These values are the net load requirements of the building for the system selected

and operational program used.

6. *HCENERGY Program

The outfile created by the *HCE System program may be used in a supplementary program, *HCENERGY, along with additional input, to produce the total fuel and electrical energy input required

for the apparatus selected for the project,Table 5. Output of this supplementary program is illustrated

in Table 4 and is arranged to facilitate comparative analysis of several alternatives of equipment

selection and fuel source.

Additional input information describing the characteristics of the apparatus to be used in serving

the building loads must be entered on Medsi Form 3, Table 5. The reduced load performance characteristics, capacity and quantity of boilers, chillers, towers and pumps is related to the part load hour

calculations made in the HCE System program to account for variable energy conversion efficiency.

Additional data concerning domestic hot water loads other electrical loads that are not considered in heating-cooling calculations and some further operational schedule data as included in the 32 entries on Form 3. Methods of loading the data and running the programs are the same as described above.

- 6.1 Part Load Hours *HCENERGY has another option that will print out the list of hours of part load of the refrigeration

plant and the heating plant as illustrated in Table 6. The information printed shows the number of hours

the plant will operate at, for instance, 50% and 66% of full capacity and may be used to select incre- ments of plant size in multiple machine installations.

6.2 Dollars

An additional supplement in the Medsi library will read the output of *HCENERGY into a cost of energy program. This routine is developed to permit use of utility and fuel rate features peculiar to the project location. The local data must be written into the program by the user, or it can be programmed

by Medsi.

7, Alternatives and Variations

Since one complete run as outlied above uses so little computers time, it is economical to compare other systems and combinations of systems to evaluate alternatives available. One such combinaticn, illustrating the flexibility of these programs, might be a multizone system in the interior with fan

188
coil units at the exterior. This is easily run by separating the data into two segments as though each

system were serving a separate building and running the appropriate data with *HCE2HCO and *HCE3MZ.

TABLE 4 - Output of KW, KWH and BTU x 10^

SAMPLEI OFFICE BUILDING. MINNEAPOLIS DEC 1>1969

FIN TUBE RADIATION AT EXTERIOR. CONVENTIONAL RETURN

SYSTEM *l WITH ECONOHISER MULTIZONE OR DOUBLE-DUCT SYSTEM LIGHTING BOILER ACC SUPPLY t MISCEl^EOUS

( HTS PIMPS EXHAUST FANS O.ECTRICAL

KV KWH KW KVH KW KWH KW KWH

OAN 100 34376 0 557 18 5280 10 3355

FEB 100 31363 0 503 18 4875 10 3083

MAR too 34724 0 557 18 S398 10 3413

APR 100 33604 0 536 18 5224 10 3303

MAY 100 34376 0 538 18 5880 10 3355

JUN 100 33604 0 477 18 5824 10 3303

JUL 100 34376 0 458 18 5880 10 3355

AUG 100 34724 0 469 18 5398 10 3413

SEP 100 33867 0 511 18 5110 10 3847

OCT 100 347E4 0 553 18 5398 10 3413

NOV 100 33S67 0 539 18 5110 10 3847

DEC 100 34376 0 557 18 5880 10 3355

TOT 406783 6e6e 68863 39846 ABSORPTION ELECTRIC TOTAL TOTAL REFRI6 REFBIG ELECTRIC ABSORPTIOH ELECTRIC PUMPS.FANS PUNPS,FANS REFRIG REFR18 REFRIfl « AUX t AUX MACHINE SYSTEM SYSTEM KW KWH KW KWH KW KWH KW KWH KW KWH

•J*^" 0 0 0 0 0 0 188 43570 188 43570

0 6 0 3 0 34 188 39833 188 39865

7 45 4 88 46 255 136 44139 180 44378

^ 634 4 403 70 3666 136 4330S 803 46738

^ '> «029 70 9585 136 45169 803 54105 JW 7 8184 4 1350 70 13779 136 44733 803 57740

JUL 7 8250 4 1431 70 15657 136 45721 203 60559

AUG 7 2290 4 1456 70 15882 136 46296 203 61344

SEP 7 1696 4 1078 70 10460 136 43838 803 53675 OCT 7 1069 4 680 70 6199 136 45159 803 50969

"OV 7 119 4 75 46 657 136 48883 180 48897

DEC 0 1 0 0 0 6 188 43571 188 43577

TOT 11857 7540 76185 587613 599481 FUEL INPUT BTU X 10>6 RESISTANCE KWH AT IOCS err HTS U.W . A6S0RP. TOTAL HEATING TOT HTS « H.W. KW KWH KWH

JAN 575 8 0 583 862 110515 112136

FEB 492 7 1 501 868 98787 94198 MAR 485 8 9 503 816 88343 89965 APR 355 7 136 500 198 60807 61776 MAY 842 8 345 595 198 38087 39649

JUN 143 7 455 607 126 81644 83814

JUL 109 8 499 616 186 16170 17791 AUG 115 8 509 638 126 17111 18738

SEP 207 7 361 577 140 38804 33774

OCT 317 8 888 553 198 51895 53516 NOV 447 7 85 481 816 80567 88136

DEC 539 8 0 547 862 101585 103807

TOT 4031 96 8573 6701 711000 730093

As the maximum cooling or heating calculated by the programs during any period is not limited to the cooling capacity of the total CFM, the reheat program may be used to evaluate an induction system

by letting the total CFM be equal to the primary air CFM and using the proper temperature, outdoor

CFM etc.

Medsi's library contains program variations for evaluating:

Variable Volume systems

Variable Volume with reheat

Internal Source Heat Pump

These programs have been used as a base for evaluating simultaneous energy requirement for Total Energy Plants and heat with light systems, and recently, one user is estimating the air pollution

caused by fuels for various systems.

189
TABLE 5 - Additional Input Data to produce KW, KWH and BTU x 10°

MEDSI INPUT DATA -«r».c -

Form No. 3 R«. 12/15/69 .HCENERGY »^W*'t/»pot . 'V'At

1. BOILERS: Efficiency As Decimal at 100% Capacity .ITol t

2. Efficiency As Decimal at 10% Capacity .1 To 1

3. KW Requirement Of Boiler Accessories 0

4. HEATING PUMPS: Quantity (0, 1, 2, 3, Or 41 1

5. Total KW Of Heating Pumps

6. CHILLED WATER PUfUPS: Quantity 10, 1, 2, 3 Or 4) y

7. Total KW Of Ctiilled Water Pumps

8. ABSORPTION REFRIG. SYSTEM: Total KW Of Accessories .

9. CONDENSER WATER PUMPS: Quantity {0 1 2 3 Or 4) /

10. Total KW Of These Pumps H y

11. TOWER FANS: Quantity (0, 1. 2, 3. Or 4|

12. Total KW Of Tfiese Fans 3.3

13. REFRIGERATION: MBH Boiler Input Per Ton At 100% Capacity . .

14. MBH Boiler Input Per Ton At 10%Capacity . . sv

ELECTRIC REFRIGERATION SYSTEM:

16. CONDENSER WATER PUMPS: Quantity 10 1 2 3 Or 4| rr

16. Total KW Of Tfiese Pumps . . Z.6C

17. TOWER OR CONDENSER FANS: Quantity 10, 1 2 3 Or 41 18 Total KW Of Tfiese Fans REFRIGERATION:

19. KW Per Ton Input To Compressor At 100% Capacity . . . 1

20. KW Per Ton Input To Compressor At 10% Capacity 1

21. SUPPLY & RETURN FANS: Total KW ...

Do Supply Fans Run Continuously (1), Intermittently To Maintain

22. Temperature In Heating Season (2), Or Not At All (3), In Unoccupied Hours . IT

23. EXHAUST FANS: Total KW 3

24. LIGHTING: Total KW Demand yao

25. OTHER ELECTRICAL LOAD: KW Demand /o

26. KW/Hours During Occupied Hours

27. KW/Hours During Unoccupied Hours 1

28 DOMESTIC HOT WATER: Gallons Per Day

29. Numtier Of Days Per Week

30. so

31. Leaving Water Temperature

32. Efficiency of Water Heater As Decimal ITol .tlf

8 . Future

At the present time, utilities are doing most of the energy calculations as a part of utility sales

promotion. Because of the competitive nature of fuel supplies, design engineers will be required to take more responsibility and to perform more of these calculations and evaluations. Medsi is available to assist engineers in this work and will be improving and adding to its library of shared time computer

programs. The opportunity to evaluate other details of design with computer accuracy and speed require the progressive designer to develop skills in this area.

9 . Summary

The primary objective in developing these programs has been achieved. Medsi programs give accurate answers with minimum manual calculation. The program and an application manual are available now to qualified subscribers.

190
TABLE 6 - Part Load Hours

SAMPLEI OFFICE BUILDING. MINNEAPOLIS DEC 1.1969

FIN TUBE RADIATION AT EXTERIOR. CONVENTIONAL RETURN

SYSTEM #1 WITH ECONOMISES MULTIZONE OB DOUBLE-DUCT SYSTEM HOURS OF PER CENT OF 70 TONS

80 75 66 50 33 85 20 10 TOT JAN 0 0 0 0 0 0 0 0 0 0 FEB 0 0 0 0 0 0 0 0 0 0 HAR 0 0 0 5 0 0 0 0 0 5 APR 1 5 22 51 0 0 0 0 0 81 HAY 16 22 53 114 0 0 0 0 0 207 JUN 92 34 61 83 0 0 0 0 0 272 ML 136 31 43 77 0 0 0 0 0 286 AU6 134 33 42 62 0 0 0 0 0 293

SEP 46 26 52 92 0 0 0 0 0 217 OCT 8 0 47 60 0 0 0 0 0 137 NOV 0 0 0 14 0 0 0 0 0 IS DEC 0 0 0 0 0 0 0 0 0 0 TOT 436 155 324 603 0 0 0 0 0 TOTAL HOURS OF REFRIG. REO'D. 1520.:23 HOURS OF PERCENT OF 893 MBH

60 75 66 SO 33 25 20 to TOT

JAN 127 83 74 160 280 70 6 1 0 743 FEB 96 16 48 131 250 105 12 7 0 671 79 1

40 101 231 189 43 34 3 743 APR 30 22 28 60 9S 151 96 176 56 715 HAY 3 8 27 16 46 59 73 283 196 717 JUN 0 0 9 2 31 35 45 182 330 637 JUL 0 0 1 0 16 41 36 116 396 610 AUG 0 0 2 0 16 43 37 125 397 626

SEP 0 5 25 9 45 36 59 27 5 223 681 OCT 15 18 37 26 85 88 101 267 96 738 NOV 66 20 36 106 172 197 57 56 5 719

DEC 106 15 73 130 266 124 14 10 0 743

TOT 530 150 404 746 1541 1144 584 1S3S 1706 TOTAL HOURS OF HEATING REQ'D 8350.59

10. References

(2) U.S. Department of Commerce - Climates

of the States, for the State involved.

Superintendent of Documents, U. S. Government Printing Office, Washington

D. ©. , 20402

(1) Engineering Weather Data , Department of the Air Force Manual AFM

88-8, Chapter 6, Superintendent of Documents, U. S. Government

Printing Office, Washington D.C.,

20402

(3) ASHRAE Handbook of Fundamentals,

1967, Chapter 28. American Society

of Heating, Refrigeration and Air Conditioning Engineers , Inc., 345 East

47th Street, New York 10017

191
Figure 1 . Floor plan showing application flight heat to heat loss.

192
No Heat Gain Or Loss Through

Partitions And Floor ^ii miii i giTTTT

Retail Store

ii i )i i i i nmi iiiiM i Muiuih ii ii i mi lu i i iiiiiuniiiiiiiiiiiiiniiiiiiinii iiiMiiii mi in 7

Roof-^

'^Lighting Fixtures^-^

Retail Store

Figure 2. Retail store with lights applying to all of heat loss,

193
No Heat Gain Or Loss From

Partitions And Floor~^^

'liMjjiui mm imiim iiiiimi iiiniiiiiiii \ ni il II 11 lllll I li l i lllllHi I 111 111 II ill llilliigmT

"^^ Retail Store

[Ho o o ("J"^ Fin Tube Radiation

mimiinillllTTTTTrWTTTT

Roof-^

5 5

©Exterior Zone 'fh^^ifnt!,®

^Thermostat Thermostat-^

Figure 3. Retail store with lights applying to some of heat loss.

194

196
197
198
The Program of the ASHRAE Task Group

on the Determination of Energy Requirements

for Heating and Cooling Buildings

K. H. Tull''" Consulting Engineer

A description is given of the work being carried out by the ASHRAE Task Group

on Energy Requirements for Heating and Cooling of Buildings. The Task Group's work

is being done by four subcommittees. Subcommittee #1 is responsible for developing

methodology and calculation procedures for hour by hour determination of heating and cooling loads . Subcommittee #2 has the task of developing a new calculation tech- nique which will apply the heating and cooling loads to the equipment components and determine the energy requirements. Subcommittee #3 has the job of combining load calculation and system energy determination with weather data, building operating

schedule and other factors affecting system performance to develop overall annual

energy requirements of the building. Subcommittee #4 is responsible for instrumenting buildings to measure energy requirements and refine the calculation procedures

A summary of the progress made to date is presented.

Key Words : Task Group on Energy Requirements , building energy requirements

,

calculating energy requirements

1. Introduction

At the present time, for most engineers, the calculation of the energy required for heating and cooling a building is more of an art than a science. The ASHRAE Guide and Data Book in Chapter 54 of the 1968 Applications [1]^ volume describes calculation procedures which are not claimed to be exact but

which, based on experience and the application of good judgement, can give reasonably accurate estimates

for residential buildings . Not even this limited claim is made for any calculation procedure for commercial and industrial installations. A single paragraph on page 656 covers the subject and plainly

states

"To properly evaluate the energy requirements for commercial and institutional buildings, it is necessary to establish the character of all thermal load sources, the resultant magnitude of each of these specific heat release mechanisms, and their relationship to the most effective method of load re- moval. A thorough analysis of both the total energy balance and the character of the system operating

cycle must be made in order to accurately establish the energy requirements for each specific building".

This statement may be a good general description of the problem, but it provides little help to the engineer faced with determining the energy requirement for his specific building.

Yet the accurate determination of the energy required for heating and cooling a building is one of

the most important, and also one of the most difficult problems for the air conditioning engineer. It is important because the energy cost is an essential and significant element of the building's overall owning and operating cost. Accurate or not, it may be the determining factor in the selection of the air

conditioning system or the energy source for a new structure. The problem is difficult because of it's

complexity. It involves not only an accurate determination of the heating and cooling loads, taking into account the varying influences of the weather and the building operating schedule, but the even more

complex problem of determining the performance of the heating and cooling system under varying conditions

of partial load. The complexities of the problem have led to solutions based on approximation, experience,

judgement, rules of thumb, judge factors, or just plain guess.

In recognition of the need for ASHRAE to develop better engineering information on this subject, a

Chairman of ASHRAE Task Group on Energy Requirements for Heating and Cooling Buildings.

Figures in brackets indicate the literature references at the end of this paper.

199
Presidential Committee on Energy Consiamption was established in 1965. This committee reviewed the problem in considerable detail and then, typical of Presidential Committees, recommended the appointment of another committee, a special Task Group, under the Research and Technical Committee, to "develop accurate methods for determining annual or seasonal energy requirements for heating and cooling, taking into ac- count all energy sources and all sizes and types of buildings".

The original Task Group carried the analysis of the problem further until the resignation of the chairman at the end of 1966. The Task Group as presently organized met first in March 1967. It has

been meeting on a schedule of about two days every two months since them.

At our first meeting it was recognized that other engineering groups were already working on new

load and energy calculation methods based on computer techniques. It was decided to take advantage of

this work, in so far as possible, in the development of the ASHRAE calculation procedures. Subsequently,

several organizations, particularly the National Bureau of Standards, the Post Office Department and

the National Research Council of Canada, have contributed to the Task Group's program.

The work of the Task Group is carried on by four sub-committees. A description of their assignments

will outline the plan of operation being followed.

Subcommittee //I on Heating and Cooling Load Requirements is responsible for developing the methodology and calculation procedures for determining Heating and Cooling Loads for energy calculations.

Subcommittee #2 on System and Equipment Energy has the task of developing a new calculation technique

which will apply these heating and cooling loads to the equipment components of an air conditioning system

and determine the corresponding energy requirements.

Subcommittee #3 on the Overall Logic Pattern has the job of combining the load calculation and the corresponding system energy determination with the weather data, the building operation schedule, the requirements of auxiliaries and any other factors affecting the system performance, to develop the overall annual or seasonal energy requirements of the bulding.

Subcommittee #4 on Field Validation Studies is responsible for plans to instrument one or more buildings which will be used to refine and validate the energy calculation procedure.

The whole Task Group periodically reviews the work of each subcommittee to provide coordination and direction for the total program.

2. Calculation Procedures

The first step in such an energy calculation program is obviously the development of an accurate heating and cooling load calculation procedure. Taking advantage of computer capabilities it is now

possible to work with more sophisticated calculation procedures and gain in basic accuracy as well as speed. It was decided at the beginning of the program to take fullest advantage of the newest calculation

concepts, which require the use of computers, in order to make the ASHRAE procedure the most advanced

possible

For accurate energy calculations a continuous, or hour-by-hour calculation of the building heat

transfer, instead of the conventional, single point, design load calculation, is necessary'. The heating and cooling energy requirement responds to the everchanging dynamic heat loss and gain of the building as it is influenced by the continually varying outdoor air conditions, the position of the sun, the cloud pattern and wind effect, and by the operation schedule and the heat generating characteristics of the building. The air conditioning system responds to this changing load as it appears inside the building and is picked up by the heating and cooling distribution system.

The current methodology of design heat load calculation presented in the ASHRAE Book of Fundamentals (1967) [2] has to be modified for the hour-by-hour load calculations, especially with reference

to the transient thermal response of the building structure to the outdoor weather conditions and changes

in internal space temperatures. The total-equivalent-temperature-difference concept employed in the Book of Fundamentals is only applicable as long as the hour-by-hour pattern of weather conditions re- peats prescribed design cycles. The actual weather pattern, however, is puite random, or non-steady

periodic, so that the design equivalent-temperature-difference concept is not valid for a real weather

situation.

A new methodology, called the Thermal Response Factor Technique is better suited to the calculation

of non-steady periodic heat transfer. The application of this technique to cooling load calculations was proposed by Stephenson and Mitalas [3]. The ASHRAE Task Group adopted this new methodology for calculating the transient heat transfer of exterior walls and roofs, and to some extent, the heat storage effect

of the internal mass of the building. The subcommittee on Heating and Cooling Loads has completed

development of a new calculation procedure based on this technique which will be used as the basis for our energy requirement calculation. '

200
The details of this load calculation procedure were first released for limited distribution to engineers working in this field in June 1968 at the ASHRAE annual meeting at Lake Placid [4]. Comments,

criticism and suggestions were rec^uested and these were reviewed in a Forum at the January 1969 ASHRAE

meeting in Chicago. On the basis of these comments, and some further work by the subcommittee, some revisions have been made and a revised version has been prepared for general release. This revision includes an interesting and valuable short cut procedure which will considerably reduce the computation

time involved. Instead of calculating each category of load for all 8760 hours of the year, it has been

found practical to develop combined response factors for the whole building, or for a zone, based on approximately 100 hours of the year. Then the combined response factors can be used for a very rapid

calculation for the total 8760 hours. This technique has been tested at the Bureau of Standards.

The output of this load calculation will be the hour-by-hour heating and cooling loads to which the air conditioning system responds. We know of no present calculation procedure that attempts to accurately

translate this load, through the system performance characteristics, into the system energy requirements.

At this stage all calculations resort to some approximation procedure to relate the heating and cooling

load to the partial-load performance characteristics of the system. Such an approximation has been

essential because of the tremendous complexity of any more rigorous determination.

Here again the availability of computer capability and new calculation techniques presents a challenge arid an opportunity to develop a new methodology. Rather than attempt to refine present approximation procedures, the Task Group decided to take a more fundamental approach. The subcommittee on System and Equipment Energy is developing a new system-simulation technique which will make it possible to calculate the response of the complete system to the hour-by-hour load changes. It is believed that this new technique will open the way to improved methods of evaluation of heating and air conditioning systems

and their controls. This work is in the early development stage. Sample simulation techniques have been

developed for some typical systems. Other systems and system variations and a generalized simulation

procedure are now being developed.

A bulletin covering the preliminary work of this subcommittee was released for limited distribution

in June 1969 [5] at the ASHRAE meeting in Denver. Comments on this procedure were reviewed at a Forum

in January 1970. Further work on this technique is now underway looking toward the release of a revised

and more complete bulletin.

3. Overall Logic Subcommittee

The work of the subcommittee on the Overall Logic Pattern will begin in earnest when the system

simulation procedure is well in hand. We can, however, already visualize some of the problems involved

in bringing this whole program together into a unified calculation procedure. One of the major problems

is related to weather data. The heating and cooling load calculation for this procedure requires the coincident hourly readings of dry-bulb temperature, relative humidity or dewpoint or wet-bulb temperature,

wind velocity and direction and direct and diffuse solar radiation. Further, the performance of many system components is related to these same outdoor weather parameters. Existing ASHRAE weather data,

which covers only Design Load weather conditions, are clearly unsuitable for the needs of this procedure.

The Task Group is working with the ASHRAE Technical Committee on Weather Data to obtain the necessary

data in the form needed for this program.

Another weather problem is the determination of a typical year for use in calculating predicted

energy requirements. Out of ten or twenty years of weather data, how does one determine what a typical

year would be for calculating energy requirements and operating costs? ASHRAE has sponsored two research

projects aimed at eventually providing Typical Year Weather Data for a number of locations. One of these projects follows what might be called "conventional, meteorological approaches". Loren Crow

has made a study of the weather at one location and by the "scientific and careful use of meteorological

factors" has developed a typical year's weather data made up of 12 typical months, each selected to bring it within acceptable tolerances to the long-term average condition and the total climatic range

for that particular month.

In a parallel project with the same ultimate objective, Z. 0. Cumali is developing a mathematical analysis of the weather data at the same location to determine if it is possible to develop

mathematical relationships whereby a typical year's weather data, including all the variables needed in

the energy calculation can be generated within the computer as a part of the load calculation procedure.

This unconventional approach shows distinct possibilities and indicates long range benefits in other

areas of weather information.

Subcommittee #3 is made up of engineers who are regularly working with and operating computer programs for determining energy requirements. It is in effect our user's committee and provides a very

valuable and practical viewpoint and criticism of the theoretical work of the Task Group. Since this

subcommittee represents at least seven of the most advanced computer programs used in the United States

today, it provides a unique opportunity to check the calculations of these programs against each other.

To do this a project called "Operation Cross Check" is being carried on in which all of the programs

calculate the same building using the same input information. The results are then analyzed in considerable detail to evaluate program differences. The understanding gained from this project will provide

201
an invaluable input in helping to standardize the ASHRAE calculation procedure.

We can see ahead that this energy calculation procedure is going to require more information on the partial-load performance of some system components than is ordinarily available now. Moreover, we can see that this information will be needed in forms suitable for use by the computer. It is commonly

recognized that all heating and air conditioning systems only operate at their design of full-load con- dition for a very few hours each season. Most of the operating hours are at varying partial-load conditions, significantly different from full-load. To determine the system response to these partial-load

conditions we must have data on the partial-load performance of the system components. Moreover, for optimum use in the computer program, this information is needed in equation form suitable for use by the computer. A preliminary step in setting up this kind of performance information was taken by subcommittee

#2 in the bulletin released in June 1969 [5]. This bulletin included examples of the equation forms proposed for expressing performance information of the major components of the system.

The Task Group is now requesting manufacturers to provide such information. At the ASHRAE meeting

in San Francisco, the Task Group requested the Research and Technical Committee and the Board of Directors of the Society to approve a statement setting forth this future requirement for component

partial-load performance information. Responding to that request the attached statement was approved.

The need for this information has also been recognized by the members of APEC and that organization is also urging manufacturers to provide this kind of performance information.

We see this as the beginning of a long range and long term program to revise the performance information issued by manufacturers on the system components they manufacture. We believe that the ready

availability of such information is essential for the future, more accurate, calculation of building

energy requirements.

4. Field Validation

Subcommittee #4 on Field Validation Studies has the responsibility for setting up and conducting

one or more field tests on actual buildings to validate and, or, refine the overall calculation procedure.

This program is considered too complex and too vital to the interests of the Society and to the engineering field to be released as an ASHRAE approved procedure without a well supervised field check.

The field study plan proposes to set up instrumentation in one or more buildings which will measure

the local weather and other inputs required for the calculation. Each building will then be set up on

a computer by the local research contractor, using the calculation procedures developed by the Task

Group. Then each month the measured input data will be processed and the calculated energy requirement

will be checked against the actual , measured energy use of the building. It will be the responsibility

of the local research organization to analyze the monthly data and, working with the Task Grour , refine

and validate the calculation as indicated.

As a first step in this program, four test sites were selected and preliminary studies wure made to develop the costs of instrumentation and carrying out the proposed two year test program. At the ASHRAE meeting in San Francisco, in January 1970, the Research and Technical Committee recommended, and the Board of Directors approved, going ahead immediately with the field test program at one site, the one

at Ohio State University in Columbus, Ohio.

The work of the Task Group has already indicated areas where present ASHRAE engineering information

is inadequate. Through the Director of Research, the Task Group has requested that research studies be

undertaken in the following areas:

1. An up-to-date determination of the energy distribution from lights, including the effects of thermal storage.

2. A study of the effects of moisture absorption within the conditioned space on the cooling loads; i.e., the effect of latent heat storage on the latent cooling load.

3. A study of the transient heat transfer response of walls, ceilings and floors, including

non-homogenous sections

4. Guidance from weather experts in establishing typical year weather data.

5. A study to relate reported cloud cover to solar radiation.

5 . Summary

The work of this Task Group is considered by many responsible members of the Society to be one of

the most important and far-reaching undertakings of the Society. Based on it's work we now can make

heat-loss and heat-gain calculations which adequately and accurately reflect the actual transient heat

flow due to the varying outdoor weather and also the varying indoor space temperature and load conditions.

Through the thermal response and weighting factor technique we can take into account the heat storage

effects of the structure and determine the hourly, actual heating or cooling load imposed on the heating

and air conditioning system. By means of a general simulation technique we then expect to be able to

202
calculate the system performance based on the performance characteristics of the system components. This

will not only allow us to more accurately predict the operation of a given system and determine it's operating cost, it will provide a calculation basis for design optimization studies of both the structure

and the heating and air conditioning system. Other forward looking engineers see the work of the Task

Group as laying the foundation for more accurate and comprehensive computerized control of the heating

and air conditioning systems of large buildings, with resultant significant savings in operating cost.

As for the Task Group, we have our work cut out for us for sometime ahead. The revised bulletin

on load calculations has been released within the last few months [3]. Within a year we expect to re- lease a revised bulletin covering the work on system-simulation and component and system energy calculations [5]. Our work will then continue on the field test programs and in efforts to improve, simplify

and refine the procedure. We expect this program to generate other research activities, within and outside Society, as it has already done, to develop the engineering information needed for the program.

Hopefully, as a result of all this effort on the part of a dedicated group of Society members, we

can look forward to the day when air conditioning engineers can precalculate the performance of their

system designs and determine the energy requirements with confidence and accuracy, based on standard

ASHRAE calculation procedures.

Appendix A

A prediction of the energy required to operate the heating and air conditioning system of a building is essential to a complete and realistic evaluation of a heating and air conditioning system design.

Such a prediction requires not only an accurate calculation of the heating and cooling loads but also

a determination of the response of the H & AC system to those loads as they vary with the weather and with the changing conditions of building operation.

The ASHRAE Task Group on Energy Requirements for Heating and Cooling Buildings is developing

calculation procedures to accurately determine and predict such system energy requirements. The Task

Group program is being carried out under the supervision of the Research and Technical Committee in res- ponse to a specific authorization of the Board of Directors of the Society.

An essential element of this calculation procedure is a determination of the energy requirements

of the various system components in response to the partial load conditions under which they operate.

The performance information presently available on many system components Is Inadequate for such a determination. In addition to the performance information normally provided for equipment selection at design load conditions, performance data are required covering the partial load conditions under which

the components normally operate. To facilitate the use of this information in computer calculations,

it is desireable for these data to be expressed in equation rather than tabular form.

The Task Group on Energy Requirements is requesting that equipment manufacturers move as rapidly

as possible to provide such information in this form. It further requests all ASHRAE Technical Committees to work with the manufacturers and the Task Group in developing this information.

6. References

1) ASHRAE Guide and Data Book (1968 Applications)

2) ASHRAE Handbook of Fundamentals (1967)

3) Stephenson, D. G. and Mitalas, G. P., "Cooling

Load Calculations by Thermal Response Factor

Method". ASHRAE Semi-Annual Meeting, Detroit,

Michigan, January 1967, Paper No. 2018.

4) Proposed Procedure for Determining Heating and Cooling Loads for Energy Calculations, Edited

by M. Lokmanhekim. ASHRAE Task Group on Energy

Requirements for Heating and Cooling, 1968.

5) Proposed Procedure for System Simulation, Edited

by W. Stoecker. ASHRAE Task Group on Energy

Requirements for Heating and Cooling, 1969.

203

Successful Applications of Energy Analysis Programs

K. M, Graham

Southern California Gas Company

Los Angeles, California 90017

The lessons learned in bringing several environmental computer programs to a successful operating state can be used to make this process easier for others.

Several suggestions such as attempting to make operations as foolproof as possible,

allowing for development time, documenting data and creating a set of accessory

packages should be beneficial to others when they first implement their new programs. The mistakes of oversimplifying and over complicating several different

environmental programs have proven that a good engineering assessment of the time context and data available are essential in the successful application of these

programs. In the successful use of several in-house developed programs, G.A.T.E.

programs, and A. P. E.G. programs, each has always required considerable initial effort. The use of approximation techniques is essential as experience is gained.

The use of the "Sol-Air" method used in the A.P.E.C.-H.C.C. program with the G.A.T.E. energy analysis is one example of such approximating techniques. These experiences, which have been gained over a period of years, should prove valuable

to anyone involved in making an environmental program operationally successful.

Key Words: A. P. E.G. programs, energy analysis programs, environmental

computer programs, G.A.T.E. programs, Sol-Air, approximating techniques.

The key to most successful operations is experience. We all want to be immediately successful in all things, but unfortunately we are not. This is especially true with new computer programs in the

field of environmental control. The first few times one works with any new computer program might be compared to the first few times a laborer attempts to work a new kind of hand tool. It takes time to

learn how to be effective. The amount of time depends upon many variables including the knowledge

available from others who have experienced a similar process.

In the last few years, we have had the opportunity to analyze and work with many computer programs

associated with environmental control. As a result of this experience, the following suggestions can

be made:

1. Make all operations as simple and foolproof as possible . Most people are short tempered

when trying to understand someone else's work. When something doesn't work easily, people

naturally assume it is someone else's fault. Programs will not be successful if you assume

that everyone else has your intelligence and patience. No one really cares that the reason

your program is considered useless is because people were stupid in the way they applied it. You will be the one blamed simply because the program was unsuccessful. It is up to you to

insure against this. Use charts and graphs plus plenty of redundant information whenever

possible. Keep input data and the calculations for input data to a minimum. You'll be surprised that often when you aim the operating procedures so that they can be performed by

idiots, people will claim that you are a genius. If you aim your operating procedures toward

geniuses, many people may claim that you are an idiot. We will see later how charts and graphs can be used to easily collect what might otherwise amount to rather extensive data.

2. Allow for plenty of time . Experience indicates that if a time limit is imposed that might

be restrictive that that time limit will almost always be exceeded. In fact, it seems the more desperately something is needed,, the more certain you can be that a good printout cannot

be obtained on time. There is a good scientific explanation for this phenomenon. The

successful application of a computer program requires many successive operations. Each

of these operations like correctly filling in the data sheets or having a computer in running

condition when you are ready, will not cause any problems nine times out of ten, but when

taken in successive steps Baye's Rule of Probability takes effect. We know from Baye'sRule

Energy Systems Sales Supervisor

205
that if only seven steps were required, each being 90% certain of being done correctly, that the

overall probability would favor an incorrect computer run. This Is because the total probability

is the product of each step's probability. In your enthusiasm to successfully apply a new program, always allow for plenty of time. Nothing else but time and experience can be used

to reduce the number of operations and the chances of error to a minimum. It is far better

to do without than to try a program in a critical situation which has to be resolved in a limited time. People can become very bitter with a program which fails them in their first

involvement. Early users must understand that some experience is necessary before definite

time commitments can be made. Even then it is wise to allow for plenty of insurance time when making your time commi hnents.

3. Be certain of your data . So many different numbers are used in an environmental program

that it IS extremely easy to forget which units are being used and how these numbers and units

relate to the calculations in a program. One of our first steps when working with new programs

is to add units and explanatory remarks right into the printout. Often the originating pro- grammer is so familiar with the program that he forgets that these numbers can be very difficult

for others to understand. Another device which adds certainty to your data is intermediate

printout of calculations. In other words, before summing key calculations, provide an intermediate printout. This is a great help in the successful application of a program because

usually the user does not have the programmer's ability to dump the whole program in order to

look for why a calculation went wrong. A user also is more confident in a final answer if all the component parts of that answer appear in the printout and seem to be of the right

magnitude, if they are not of the right magnitude, it makes it easier for him to trace down which input data applies so that it may be reanalyzed. These precautions may seem like a lot of drudgery compared to developing the logic which is the heart of the program, but the greatest program in the world isn't worth anything to others if it can't be successfully

applied to solve their problems. Make the input and output data easy to understand.

4. Provide a good program package . A real key to any program's successful application is in having a good package for it to operate in. All sorts of provisions which can help a user successfully apply a program are often neglected when a program is given to a user. A good

documentation in both common english and the language of the program can save the user much anguish. The user should have good records of the control cards needed and other data which

relate directly to the use of the program on his particular computer. As soon as is practical,

at least two copies of the program should be made for insurance purposes. Plenty of clearly

labeled folders and covers for input data and printouts also need to be provided. Without

these labeled devices, soon all the input data and printout data from various projects can get mixed. This can lead to some frustrating situations, especially in multiple runs of the

same project. A little effort to insure that the program will be operated within a well managed and equipped package is well justified.

One of the ways we learn is by mistakes. Some of our mistakes were costly and time consuming. It

is hoped that a discussion of them will help others in avoiding these pitfalls. The first environmental energy analysis program we worked with was probably one of the world's worst applications of the computer. This program was basically a set of imperical formulas and rules of thumb that had come from various sources. Some of these formulas were obtained from generalized experience, some from prejudice

or pure myth. Instead of capitalizing on the computers capabilities to handle large amounts of data

and many calculations, we simply had a program which made the same mistakes we made in hand calculations,

only faster. This program was very unsatisfactory. Rules of thumb have their place when related to human judgment but some very strange answers can develop when they are unmercifully applied by a machine. This program was discarded soon after it was developed.

Our next program was more scientific and in fact was a series of programs. The first in this

series was a program which determined the energy requirements of a facility hour by hour for one year. Once this data had been obtained, it was given to a second program which contained equipment char- acteristics and calculated the amount of gas and electricity various systems would require in order to heat and cool a building. The third program was simply a rate cost program which solved for the cost of gas and electricity used. This annual cost data could then be compared to the initial cost

for an economic analysis of which system offered the best investment to a potential owner.

We made many mistakes with this program also, almost all of which were related to the input data

for the first program in the series, the energy requirements program. We found that we had limited data which could be given to the program. As a result, the program did not accurately reflect the

real requirements of many facilities. Basically we tried to obtain the input for this program from

the heat load calculations done manually by the consulting engineer. For the entire facility, we broke the calculated heat load into time dependent loads and temperature dependent loads. The computer could then take each of these loads plus a time schedule and temperature schedule and produce

an approximation of hour by hour energy requirements.

206
The time dependent loads wb re basically the solar component, the people component and light com- ponent of the heat load, fach of these loads described in a profile format of how they varied hour

by hour for different day types was provided as input data. (See fig. I and fig. 2)

The temperature dependent loads were transmission, outside air (both sensible and latent) plus

infiltration. Each of these loads were given at at least two different temperatures in order to provide a method of linear interpretation for loads at other temperatures. (See fig. 3)

As you might guess, this type data was far better than a rule of thumb approach but still was rather gross. In most facilities, a significant load is found from the effect of zoning. Many times

both heating and cooling are going on simultaneously creating an artificial internal heat load. Some distribution systems deliberately mix heating and cooling energy under certain conditions. We call this artificially produced load balance or trim heat. Transmission through walls of any real thickness

is not strictly linear. Latent outside air loads are wet bulb dependent, which was not being accounted

for. The solar load is affected by clouds and adjacent buildings which had also not been accounted for.

We made our biggest mistake at this point. We decided to have a program written which took into account every possible factor which we thought would effect a building's energy requirements. This awesome task was undertaken by Southwest Research Institute for 25 member gas utilities and the result,

after many years work, was known as the G.A.T.E.^ long form program. This program was fantastic. It took into affect temperature of street water, leakage around air handler coils, every control setting

in the building, wind direction and speed, and every other conceivable piece of data which might affect

the building's energy requirements.

Although this program was technically excellent, operationally it was a great mistake. We found

that the data needed by the program was not usually available until the building was well under con- struction. By that time, the answers it provided were of no practical use as most of the decisions

which these answers would effect had already been made. If we assumed and guessed at input data at

an earlier date in construction, we found that so many variables had such wide error margins that the resulting data in many cases was meaningless.

Upon discovering this dilemna, we gave a lot of thought to how we might ever obtain a successful

Energy Analysis Program. There seemed to be a paradox. By the time accurate data was available, the decisions which might be affected by that data had already been made.

We now realize that our mistake was in the degree of accuracy which we were trying to obtain.

The computer can be so very accurate, it is hard not to try to obtain all the accuracy that is available. But practical engineering tells us that ground temperature and air-handler leakage usually

have little effect compared to major loads like outside air temperature and solar radiation. We can usually determine the following major loads to within plus or minus ten percent at a relatively early

stage of construction:

1. Transmission heat load

2. Outside air sensible heat load

3. Outside air latent heat load

4. People sensible and latent heat load

5. Lighting heat load

5. Solar heat load

7. Distribution system balancing heat load

These loads are sufficient for us to obtain data upon which practical decisions can be made. A program starting from this data coupled with the data available from a year's weather data from the

U.S. Weather Bureau provides a pretty good picture of the facilities energy requirements. The Weather

Bureau data use has hour by hour records of dry bulb temperature, wet bulb temperature, cloud cover

and other factors which might affect these basic loads. This data like the other data may only be within ten percent or so of what any future weather year will be like.

When we had settled upon a ten percent or so allowable error, we found that the program became

very much more workable. Users could provide answers that were in this range from rough calculations

and experience. We also limited ourselves in most cases to the outside shell of the building which

greatly simplified matters. The effect of zoning and other internal imbalances was then loaded as a

^Group to Advance Total Energy, Inc.

207
function of the type distribution system plus whatever the designer's experience indicated. This saved

many very complicated calculations that otherwise would have been required for this relatively small

load. We also carried loads forward as stored heat when equipment capacity had been exceeded. A simple calculation allowed us to also determine the drift from inside design temperature when stored

heat was in effect. Once we had settled upon a lesser degree of accuracy in our input data, we found that we actually had not given up much at all. When compared on the same building, we found one program gave answers within five percent of the other. In addition, when it came to using this data

to select systems, every system compared in exactly the same relationship in either program.

This program was initially known as the G.A.T.E. APPROX program. For the last year, the old long form program has been dropped and the newer program is now the official G.A.T.E. program. We have run this program well over 100 times in the last year and found that it can provide very meaningful data concerning the use of various energy systems in all types of buildings.

We took this program and worked hard at making it as operationally successful as was possible.

We simplified the input data and printout into an easily understood format. We allowed for plenty of time when making studies. We also built up a good package of accessories to insure good management

of the program. For example, rather than collect data directly on key punch sheets, we used the forms

in the figures at the end of this paper for ease of understanding. Later we transferred this graphical

data to input sheets as numbers and reproduced it in that format in the printout.

We still had an occasional timing problem. Often decisions are made concerning a facility even before the basic heat load calculations have been done. The consulting engineer usually will not start his calculations to determine the component heat loads needed by the G.A.T.E. program until plans

are fairly firm. Yet decisions whether to use a central plant or to use gas or electricity as an energy

source might be made before that time. Sometimes a consulting engineer has not even been retained when

these basic decisions are being made. We found that we were having to do many heat load calculations

ourselves. This caused us to become interested in an organization known as A. P. E.G. We joined

A. P. E.G. and began using their H.C.C. program which provides heat load calculations from the basic

plans of a building. Again we had many start up problems, but each time we found it a little easier to bring a program to an operational state.

We now are in a position to obtain the data necessary for decisions on building energy systems at

a very early stage. We can even do a fair job of approximating energy requirements from as little data

as a plot plan and an artist rendering. These give enough physical data in conjunction with other data we have gained from past experiences to begin a preliminary study. As new data becomes available at

later dates, the study can be updated as required.

A surprising bonus developed out of our work with the A.P.E.C.-H.C.C. program. We found that this program could not only describe the hour by hour load from solar radiation quite accurately, it could

also calculate the non-linear portion of transmission and handle the effect of hour averaging. These calculations are quite sophisticated, but can be done by the computer. The results provide far greater

accuracy than is usually provided by manual calculations. This fallout has provided us with a solution

to a very perplexing problem. We knew that a better heat load calculation method would be possible if we used the "Sol-Air Method" as described in the 1967 A.S.H.R. A.E.^ Guide. The use of the "Sol-Air

Method" allows for the consideration of the dynamic nature of heat transfer in a building. This method

is used in the A.P.E.C.-H.C.C. program for a 24-hour day but it is very difficult to use for a 8760 hour year-long energy analysis. We were neglecting this effect in our energy analysis and using only

linear relationships for our temperature dependent heat loads. Through a modification to the A.P.E.C.-

H.C.C. program, we are able to extract the non-linear portions calculated when using the Sol-Air Method

for a typical day for each month of the year and then we created a time profile of these non-linear

components of transmission loads in an hour by hour printout. What we actually did was add a step to the A.P.E.C.-H.C.C. program which calculated what the transmission would be on a straight linear basis and then subtracted this quantity from the more sophisticated quantity calculated using the "Sol-Air

Method" and hour averaging. This represented the hour by hour differences for a typical day in one

month. The A.P.E.C.-H.C.C. program was also looped so that we obtained an hourly table of typical days

differences for each month of the year. In other words, we are approximating a very complex temperature

dependent load into the G.A.T.E. program as a more simply handled time dependent load. This is only an approximation of what is really happening but it has proven to be a satisfactory way to handle this complex load. In the energy analysis program, we adjust the hour by hour data calculated without using

the Sol-Air Method by the total correction factor derived for that hour by the modified A.P.E.C.-H.C.C. program for a typical day of each month. In practice, since the G.A.T.E. program requires an hour by hour solar table for typical days of each month, we simply have the A.P.E.C.-H.C.C. program add the solar and non-linear component of the transmission load together before printing our a yearly table of these values. (See fig, 2)

'Automated Procedures for Engineering Consultants, Inc. ^American Society for Heating, Refrigeration and Air Conditioning Engineers

208
With continuing experience, our capabilities continue to grow. We have learned how to make haste

slowly and not to expect too much too soon with new programs. We have also learned that in order to be successful, we need to truly have a good understanding and feeling for the data that we are dealing

with and have a system to manage and contain our work. The overall result is the successful application

of these programs, but we had to learn many lessons first. It is hoped that some of these lessons

will be helpful to you in your applications of environmental control and energy analysis programs.

209
Thermal Loads:

(Each day type must be described. Number functions in each

graph by day type rwmhex .) ft titifjffmS , A' *vetr^yS

Heat from electrical appliances (primarily lights) : @ 100% = il&SQ—MBtu ^ s wArn/ftH x 835.? /Ct4/

xuu

SO

80

B3

e 70

X 60

ffl S 50

>(-i o 40

30

20

10

0

6> 3.«#aMW/ifH/» ^^s/?

i

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[

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:

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r J

1

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j —f-" —

i

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1

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1

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i

ji .1 12 34 56 78 91D 11 1212 34 56 78 9101112

AM PM

TIME OF DAY

Heat from people:

/OO NU^US & ISO *

100

90

80

70

60

S 50

o

VP5v

40

30

20

10

0

i

!

1 1

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1

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1

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1

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..... .... ... j . .....j... 12 34 5 678 9 10 11121234 5 6 78 91011 12 AM PM

TIME OF DAY

Figure 1. The form used for collecting data regarding time dependent heat loads from people and from

lights with example data filled in.

210
Heat from Other internal sources: (Lt^tOfitn^^/ 8VdtJf^S*'F(*^^^^)

@ 100% = MBtU

100

90

80

70

60

50

40

30

20

10

0

1 1 '1

i

.

.

j ;

1

1

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1 -H) 1 23 4 567 8 9 10 11 12 12 34 56 7 89 10 11 12 AM PM

TIME OF DAY

Heat from solar radiation:

@ 100% = MBtU

(The percentage solar radiation by hour at 34° latitude for a facility of uniform sides has already been included in the

program- If actual conditions will be greatly different from

this, please note below.)

Time Dec Jan -Nov Feb-Oct

6 0.000 0.000 0.000

7 0.000 0.086 0.495

8 0.581 0.698 0.857

9 0.857 0. 906 0.988

10 0.970 0.980 0. 989

11 0.999 0.989 0.963

12 0.984 0. 979 0. 92 9

1 0.999 0. 989 0. 963

2 0.970 0.980 0.989

3 0.857 0.906 0.988

4 0.581 0.698 0.857

5 0.000 0.086 0.495

6 0.000 0.000 0.000

Mar-Sep Apr -Aug May-Jul June

0 .000 0 .435 0. 662 0 .733

0 .689 0 .867 0. 959 0 . 980

0 .966 1 .000 1. 012 0 . 990

1 .001 0 . 959 0. 905 0 .887

0 . 918 0 .824 0. 710 0 .680

0 .815 0 .653 0. 507 0 .457

0 .778 0 .573 0. 368 0 .353

0 .815 0 .653 0. 507 0 .457

0 .918 0 .824 0. 710 0 .680

1 .001 0 .959 0. 905 0 .887

0 .966 1 .000 1. 012 0 . 990

0 .689 0 .763 0. 959 0 .980

0 .000 0 .435 0. 662 0 .733

Figure 2. The form used for collecting data regarding time dependent heat loads from sources other

than people and lights plus data regarding the solar heat load with example data filled in.

211
Temperature Dependent Variables:

All temperature dependent variables are assumed to be linear. At

least two points are needed to define a straight line and therefore to describe any single temperature dependent variable. Up to

five different points may be used to describe all the variables

being considered.

(§) Design

Heating

* d Inside

Design

* (§) Design

Coolinq

Dry Bulb

Temp. (°F)

Dew Point

Temp. (°F) ( )** 1 Transmission

(MBtu) o

Outside Air

Sensible (MBtu) o

Outside Air

Latent (MBtu) 0 0

Balance or Trim

Heat (MBtu) 0 o

Other Heat

Loads (MBtu) 0 0

* If an economy cycle is used, each temperature point where the

outside makeup air percentage is changed must be described.

** Leave blank and make outside air latent equal to zero in these

columns if humidity control equipment will not be used when

heating.

Air Handling System Size = \L^,QOd CFM S> ifOO C, f: /H. /7QN

Outside Air Makeup Rate = % = OOC C F, &I

Installed Heating Capacity = ^X^^ MBtu® HS QTU/FT^

Installed Cooling Capacity = i/j^Q Tons Heating System Shutoff Temperature = Cooling System Shutoff Temperature =

Figure 3. The fom used to collect data regarding temperature dependent heat loads and data regarding

the equipment system used with exanple data filled in.

212
Comparison of a Short Form Load

and Energy Program with the Detailed

Westinghouse Load and Energy Programs

B. G. Liebtag and J. R. Sarver P. E.''^

Duquesne Light Company Westinghouse Electric Corporation

Pittsburgh, Pa. Pittsburgh, Pa.

Comparisons have been made between two heating and air conditioning load and energy programs. The purpose of this comparison was to determine the proper ap- plications and usefulness of these programs. Using the same input data necessary

for each program, typical buildings were analyzed by both programs. The results

of these programs were then compared to determine the accuracy of the short form

program. Each building was divided into the required number of zones. The re- quirement being that each zone had the same basic physical and operating characteristics. The short form program is basically a computerized A.S.H.R.A.E. Guide [1]^

method of load calculation. The energy calculations are handled with a modified

heating degree day method and an equivalent full load hour method for air conditioning. These modified methods allow for the evaluation of internal heat gains from

lights, people and equipment. The load section of the Westinghouse Electric

Corporation's program uses the thermal response factor method of calculating the

loads on the structure. These loads are determined on an hourly basis. The energy program can use any defined weather year and will calculate the energy requirements

for all the building functions for each hour of the year. The results of these

hourly calculations are then summarized to give the annual energy requirements of

the structure. The final results indicate that the short form program can be a useful tool for the engineer in properly evaluating building environmental systems. The results also indicated the advantages of using the more detailed program for larger structures.

Key Words: Electric heat, load profiles, control set points, ASHRAE method,

degree day approach, equivalent full load hours.

1. Introduction

Only in recent years since electric heat has made an impact as a practical method of heating a building has it been necessary to properly estimate the annual energy requirements of a building. Many

times the need for an accurate estimate must be made long before final plans of the building are completed. In fact, in order to properly utilize the various advantages of the available fuels, the decision as to which fuel is to be used must be made while the architect is doing his early stage planning.

Very accurate and elaborate computerized methods of predicting the energy consumptions for a proposed building have been developed in the past five or six years. One of these methods is the Westinghouse Electric Company's energy program. The program is divided into three sections. Section one

is a load model into which you feed the building characteristics, hourly environment specifications,

and actual hourly weather records. From this input data the program prints out the hourly zone load

profiles. Part two is the mechanical supply system design. From data obtained from part one the

Sjfinior Heating and Air Conditioning Engineer and Construction Systems Engineer, respectively. Marketing Services Department Major Projects and Urban Syste

2 . Department

Figures in brackets indicate the literature references at the end of this paper.

213
engineer sizes and selects the equipment he intends using in part three. Part three is the systems

operation simulation. It simulates the performance of the system selected in part two. The simulation

takes into account such items as equipment performance curves at partial loads, control set points,

lighting system interface with the space conditioning system, etc. Various systems may be inserted in part two and their operation simulated in part three. The final print out of all three sections is,

hourly electrical requirements, hourly fuel requirements, maximum percent heating plant load, maximum

monthly fuel use, and monthly maximum electric demand.

For large buildings the accuracy of this type of program is necessary. However, for small com- mercial buildings this type of program is not normally used.

In this study the results of a smaller, less sophisticated program were compared to the West- inghouse program. This program is a computerized manual calculation which took approximately 540 man- hours to develop. The program was designed to analyze the small commercial buildings which were being

done manually. The program uses the ASHRAE method of load calculation and combines this with a mod- ified degree day approach to arrive at the estimated heating energy consumptions. The air conditioning energy consumption is based on equivalent full load hours for the equipment.

The final print out of the Duquesne Light Company program gives the design heating capacity for

each zone, the estimated air conditioning capacity at two hour intervals from 8:00 a.m. to 8:00 p.m.,

the monthly electrical requirements and associated costs based on Duquesne Light Company's rates for all the electrical usages in the building.

2. Description of Input

For the same building, the Westinghouse program has about 40 sheets of input data with approximately 1,000 pieces of input information. It takes about 12 man-hours to fill out the input sheets.

On the other hand, the Duquesne Light Company program only has 3 pages of input sheets per zone (maximum of nine zones) with approximately 500 pieces of input information. It requires up to 8 manhours to fill out all of the sheets.

3. Description of Cases Studied

In order for a valid comparison to be made, three buildings were used in the comparison. The same

input data was supplied to both programs. The first building studied was a 10 story office building

with about 60,000 square feet. The second building was also an office building. This building had a floor area of approximately 300,000 square feet. The third building was a large two, and in some places, three story structure, with over 700,000 square feet of floor area.

No energy consumption data was available for building number one. The second building was opera- ted on an 8 to 10 hour per day schedule. The third building was occupied 24 hours per day, except for

a small portion of it which was used as offices.

The buildings are larger than what the short form program was designed to handle. However, these three buildings were the only ones available for comparison.

Since the Westinghouse program has the capacilities of performing hourly calculations, building

operation simulation was straight forward. However, judgment had to be used when using the Duquesne

Light Company program, since it simulates the operation as either day or night operation, and average

conditions must be assumed.

The accuracy of the Westinghouse program has been established in several comparisons apart from

this paper. In one case where actual weather data and building characteristics were put into the computer after the building had been in operation for a year, the computer was within 0.3% (three- tenths of one percent) of the actual consumption. In other studies similar results were obtained.

Therefore, for the purposes of this paper, the short form program was compared to the Westinghouse

program.

4. Results

Tables 1, 2, 3 and 4 show the results of the short form program as compared to the Westinghouse

program.

214
Table 1. Comparison of short form capacities to the Westinghouse heating and cooling capacities

for building number 1. Heating Cooling Duquesne Light % Duquesne Light % Westinghouse Company Difference Westinghouse Company Difference

1. 44,425 42,763 -3.9 112,191 120,390 7.3

2

102, 807 98, 240 -4.4 184,552 157,726 -14.5

3. 44,425 42,763 -3.7 100,204 100,429 0.2

4. 137,573 131,340 -4.5 204,214 175,473 -14.1

5. 1,394,776 1,311,305 -6.0 2,366,416 2,245,000 - 5.1

6. 205,137 199,605 -2.7 309, 110 296,203 - 4.2

7.

8.9.

1,354,725* 1,264,409* -6.7 1,077,100 802,800 -25.4

Total 3,283,868 3,090,425 -5.9% 3,927,000 3,812,000 -2.9

Ventilation load of building

Table 2. Comparison of short form capacities to the Westinghouse heating and cooling capacities

for building number 2. Heating Cooling

Westinghouse Duquesne Light Westinghouse Duquesne Light

Company BTUH Deviation BTUH Company BTUH Deviation

1. 1,079,488 1,068,852 -1 % 1,069,377 1,328,687 +24 %

2. 498,806 336,823 -32 % 562,590 894,505 +59 %

3. 1,194,213 1,178,269 + 1.3% 1,228,649 1,890,470 + 55 %

4. 402,907 369,908 + 8.2% 491,790 534,139 + 8.5%

5. 1,413,635 1,119,166 -21 % 1,923,085 2,123,450 +10.5%

6. 65,801 693,781 + 11 % 686,005 477,152 -30 %

7. 528,107 567,818 + 7.5% 573,527 870,900 +52 %

8. 206,400 256,383 + 24 % 264,581 289,649 + 9.4%

9. 3,020,613 3,203,347 + 6 % 4,045,156 4,781,861 +18.3%

Total 9,701,524 8,794,347 -9.4% 11,257,705 11,820,000 + 5 %

Table 3. For building number 3. Heating Cooling

Westinghouse Duquesne Light Westinghouse Duquesne Light 0, B.T.U. Company B.T.U. Deviation Tons Company Tons Deviation

1. 2,116,178 2,267,999 + 7.2% 365 376 + 3 %

2. 6,164,014 6,559,231 + 6.4% 823 845 + 2.7%

3. 2,507,617 2,724,041 + 8.6% 172 187 + 8.8%

4. 3,246,680 3,484,565 + 7.3% 237 246 + 3.8%

5. 2,925,500 3,074,979 + 5.1% 332 344 + 3.6%

6. 3,547,782 3,731,313 + 5.1% 336 360 + 7.1%

7. 795,753 940,095 + 18 % 36 42 +16.5%

Total 21,303,500 22,782,176 + 7 % 2,301 2,362 + 2.6%

Table 4. Compari sons of annual consumptions

HEATING COOLING TOTAL

Duquesne Duquesne Duquesne

Westinghouse Light Co. Westinghouse Light Co. Westinghouse Light Co. Difference

9,598,000 1,912,000 2,507,000 11,593,000 41,725,000 47,675,000 +14 % 6,920,000 3,155,000 2,386,000 3,185,000 22,449,000 19,064,000 -12.5%

Bldg. 2 Bldg. 3

215
For large complex buildings with complicated environmental systems it is felt that the accurate

results obtained from the Westinghouse program make it far superior.

The comparative tests show that for capacity comparisons the short form program is fairly accurate

for total building capacity. The biggest difference of the three test cases was only -9.4% and the smallest +2.6%. This comparison did point out, however, that on certain zones, due to their orientation, the short form program can be as much as 59% high on cooling. This value, one for 55% and one that is 51% high are shown on table 2. These errors resulted from all of these zones peaking early in the morning. The short form program assumed maximum temperature differential at this time. Due to the ability of the Westinghouse program to look at each hour of the year, it was able to determine more accurately the number of people in the zone and the ventilation for that hour. The Duquesne Light

Company short form program has only the ability to decide between day occupancy and its ventilation

rate or night occupancy and its ventilation rate.

The results of the annual energy consumption were much different. Although the total consumption

was 12.5% low for building number two and 14.0% high for building number three, the Kwh usages for the various components were way out of line. The heating consumption was estimated as much as 90% low. The cooling consumption was as much as 300% high (see table 4).

These large errors are due to the equations used for estimating the energy consumption which are:

Annual Heating Consumption

,,

, (Heat loss day - Internal load day) Degree day at change % day , Day Kwh = ^r^cZ 7--—1 z

t. i x* ^

' ^ x ^:x24 hours per day Temperature differential at which over temperature operation ^ heat loss was calculated

Ni ht Kwh - ( Heat loss night - Internal load night ) ^ Degree days at night % night 24 hours

Temperature differential at which temperature operation ^ per day heat loss was calculated

Annual Cooling Consumption

Cooling Kwh = Tons cooling x Kwh/ton x Effective full load hours**

24 X D X C **Effective full load hours = — -t— tm - td

D = Cooling degree days on base temperature equal to change over temperature

^ J ^ ^ Daily Range,

tm = (outdoor design temperature - ^ ^)

td = change over temperature

c = % time space is air conditioned

The above equations do not adequately handle the large internal zones of major buildings with

their high internal heat gains, and the short form method appears to work best in smaller exterior zones having more standard heating requirements.

The hourly analysis is far more accurate in estimating annual consumption for large complicated

buildings than these empirical formulas. These formulas were developed from test data obtained from samplings of offices and commercial buildings located in large metropolitan areas. For small offices

and commercial buildings these approximations are reasonable. For the larger building with large

interior zones, known also as core areas, these formulas do not yield accurate estimates.

5. Conclusions

This study shows that for estimates of heating and cooling, the short form, when used with judgment, can be fairly accurate.

However, this study pointed out that for an annual estimate of energy consumption, a program that i analyzes the building systems hourly is far more accurate than one using the old empirical equations.

This becomes even more important on very large buildings with many large internal zones.

6. References

[1] American Society of Heating, Refrigerating and Air-Conditioning Engineers, New York, (1968).

216
Energy Estimating - How Accurate ?

Robert Romancheck, P.E.

Pennsylvania Power & Light Compajny

Allentown, Pennsylvania

The Heating and Air Conditioning Engineer has , during the past five years

,

endeavored to utilize the vast capabilities of the computer to synthesize highly

sophisticated mathematical models for use in problem- solving. This paper is an attempt to relate (1) How we designed a building load and energy estimating com- puter program and (2) Propose the hypothesis that greater programming sophistication does not necessarily mean better estimating of energy consumption.

Work to computerize heating load and energy calculations was initiated in 196h and the implementation of computer studies began in 1965- The complete

system as it has evolved to date includes five programs:

1. A sort routine.

2. A design heat load and an energy estimate based on degree day data.

3. A design cooling load with an hourly synthesis of the projected

thermal requirements integrated with U. S. Weather Bureau Data.

h. Hoinr-ly energy summation routine

5. An on-site generation, total energy analysis, hourly computation.

Engineering studies relating to energy costs are usually undertaken in order to determine the most economical fuel to use. Many computer programs

have been written and will be written in an attempt to make this complex

task easier. We often wonder where does one choose to end their program

development and what "K" factor is used to account for this decision.

Key Words: Air conditioning, computer methodology, computer program

evaluation, energy determination, heat loss, heat pumps, solar effect.

Weather Bureau data.

1. Introduction

The ability to predict, within predetermined accuracy limits, design loads and energy consumption

of a building's environmental system can now be reliably accomplished on a dynamic, rather than static

basis, through the use of computers. Complexities of conditioning systems, capital costs and the com- petitiveness of energy suppliers have become so interrelated that the designer must now have this capability. At the same time, however, computer routines must be realistic in the amount of input data

required and the relative accuracy of the results generated. The computer programs that are discussed

here are written in both Fortran II and PL/1 programming languages, and are operational on IBM 707^,

lOK storage, or an IBM 360 , Model 60 525K storage computer.

2. Program Methodology

2.1 Philosophy

In 196k studies were undertaken to determine the feasibility of using an IBM 707^ computer to provide estimates of energy needs for space heating installations. This was necessitated because engineers in the sales group were spending most of their time preparing owning and operating cost analyses

This severely limited their ability to penetrate the bulk of the space heating market which, in turn,

led to our basic philosophy with respect to this computer application — development of a routine that

didn't need an engineer to supply the input data, but which would still yield results that were more

accurate than any method available. This concept would allow preparation of the greatest number of

operating cost studies, thereby effecting maximum market penetration.

217
The initial reasoning was to write a computer program capable of integrating "building heat losses and gains, and heating and cooling energy requirements. This idea was soon discarded because of the com- plex logic and the time delay required for debugging a program of this magnitude. A sequential program

system was then investigated and subsequently proved to be the best solution to our problem. In selecting

this method the first program would be written to generate design load calculations and energy use by the degree day method. Calculations from this program could then be stored on a tape file for use as input

data in subsequent routines. It is believed that program debugging was considerably reduced by this

sequential system. It was also determined that routines must be compatible for residential, commercial,

and industrial estimating use.

2.2 Heating Program

Program #1, Design Heat Loss Determination, has as input the various building design characteristics

such as :

1. Wall, roof and floor constructions

2. Window and door constructions

3. Building orientation

k. Design temperatures

5. Wall, roof and floor areas by zone

6. Internal heat gains

7. Ventilation rates

8. Occupancy schedules

Figure 1 illustrates the input data form used for this routine. All heat losses are calciilated by

zone, according to the methods outlined in the "ASHRAE Guide." Internal heat gains are also calculated

for both the occupied and unoccupied periods and are used to adjust the building heating load requirements. Cooling load determination was not part of the original operating system design. The occupancy

schedule input sheet, figure 2, can be as complex or as simple as the application requires. A file of

resistance values for the more common building materials is also on call. Simply by inputting a 3 digit

number and the material thickness, coefficients of transmission (U values) can be generated. The user

also has the option of developing his own "R" or "U" value and inputting this number on the data sheet. Building ventilation needs can be determined by one of three methods, number of air changes, cfm per

occupant or infiltration by zone. Infiltration values are based on the most representative data cur- rently available. It is a personal observation that additional work needs to be done in the area of infiltration rates based on varying wind speeds and the newer types of windows and doors currently used

in construction. One other element of Program #1 is the calculation of an energy requirement based on the degree-day method. Initially, this was the quickest way to get our system operational and since

studies were at that time calculated by using degree days, accuracy could only improve. The use of this routine was placed into production in the spring of 1965. Computer outputs (fig. 3 and 'k) were generated

for residential, commercial and industrial installations at the rate of 20-30 per day.

2.3 Air conditioning program

Program #2, Air Conditioning Load Determination, was designed to complement the first routine by

providing cooling load information. Calculated values from Program #1 were written on a tape file for use in this program and without any additional input, air conditioning design loads were provided. This was an interim procedure, however, since the programming efforts to provide this information was minimal

compared to hourly energy requirement determination.

In order to provide the optimum result it was of course necessary to integrate weather data into

the system to obtain a reliable synethesis or projected hourly thermal requirements. We had at our disposal 5 years of data from the U. S. Weather Bureau. An attempt was made at averaging the data

(discarded this method because of the loss of temperature extremes) or creating a typical year (discarded becaiise of definition, what is "typical"). The final decision was to use the year that was most

in line with the normal n\mber of degree days for the area. The hourly observations used, temperature,

specific humidity (obtained by calculation from the dew point temperature) and cloud cover (50^ cloud

cover or less constituting a sunny hour), were recorded on a tape file. Because of computer core limitations of the lOlh computer, it was necessary to average two hours of observations into one hour.

This use of weather data will probably prove interesting and hopefully will provoke some deep

thought and your consideration. First, each building zone is analyzed hourly, to determine whether

it requires heating or cooling. Solar load is an important consideration at tliis point. If the sun

is shining, (50^ or less cloud cover) a calculation of the solar effect is made. The design solar

load, as calculated by the sol-air temperature difference method developed by Messrs. C. 0. Mackey and

L. T. Wright, Jr. with additional work by Mr. J. P. Stewart, is used to predict the hourly BTU gain on the various building zones. The energy gain is then calculated to equal, the design solar load multiplied by the ratio of the temperature occurring at that hour, divided by the cooling design temperature.

218
Solar Heat Gain (BTU's) = Design Solar Load x Amjlent Temperature

Cooling Design Outdoor Temperature

This solar effect is applied to the building energy needs in the heating as well as cooling season.

Since input energy to a refrigeration machine varies with load, outdoor temperature, design of con- ditioning system and majiufacturer , some assumptions had to be made with respect to equipment energy use. Our entire problem-solving system, as we previously mentioned, is based on a production basis philosophy

It was therefore necessary to provide an equation, obtained from a regression analysis, to recognize the different characteristics of various manufacturers' equipment. This does not preclude the ability to

input a curve based on a specific piece of equipment and generate results relative to its use. An

output was then generated (fig. 5) which contained summations of hourly heating and cooling energy re- qmrements. Additional information was included in the output as an aid to the system designer.

2.k Heat Pump Option

Since the determination of a heat pump Coefficient of Performance (CO. P.) is obtainable only by

an hourly analysis, the routine posseses this facility also. We do not compute heat pump feasibility

studies on a production basis, but rather on an individual need, using a specific manufacturer's inputoutput energy relationships

Residential dwelling unit studies are not included in the hourly energy analysis. Much time and

effort was spent in trying to correlate known operating energy usage with the hourly routine projection.

Constant internal heat gains, variable gains, various occupancy schedules, set back temperature con- ditions were all tried without success. The EEMA equation, in our estimation, still yields the best

solution of heating energy determination for residential units.

2.5 Total Energy Routine

Since we are constantly developing and overlaying hourly BTU building thermal needs, it is a relatively simple procedure to create a file storing these values and use them as input to a so called,

"Total Energy," isolated generation routine. The BTU values are initiaiized positive, if heating, and

negative, if cooling, for identification purposes, before being placed on this file.

Additional input required for this run consists of the specified engine or turbine fuel rate

c\irve, waste heat availability curve, hourly electrical demands (weekly, monthly, etc.) and hourly process steam loads, if any. This data is then merged on an hourly basis with the building thermal requirement and an output generated (fig. 6) which lists hourly KWH generated, cooling or heating BTU

requirements, process heating BTU requirements, if any, and ciibic feet of gas or gallons of oil required. A summary is also developed which includes annual KOT, gas or oil needs and an overall thermal

efficiency of the isolated generation system. The hourly output is generated in order that any doubter would have the ability to verify the calculated quantities.

3. Program Evaluation

3.1 Industry Interest

The accuracy of these programming routines , we believe , has been demonstrated not only by actual

billing records, but also by the acceptance of electric heating in the residential, commercial and in- dustrial markets. The present total-electric customer breakdown within our Company area includes

jit.OOO residential units, k,000 commercial units and 2h0 industrial installations out of a total of

820,000 billed accounts.

There are numerous organizations that have heating and cooling design and energy calculation com- puter programs available and in use. Some of these include: The Electric Heating Association,

^ American Electric Power, Westinghouse , American Gas Association, Automatic Procedures for Engineering

Consultaats (APEC) , Post Office Department (TACS) and numerous consultants and utilities . The degree

of complexity varies widely and in all probability the results also. This leads into the next discussion.

3.2 The Unknown Factors

a

In 1967 after making a presentation to an ASHRAE Task Group on the procedures we had m use

,

letter was received which in part stated, "the Task Group is attempting to develop a veiy sophisticated

calculation program that will take into account all significant factors affecting the heating and

219
cooling loads." The initial reaction to this statement was to recall oior own experience when we began

to define and analyze the many variahles in this problem. Which of these variables do you choose to exclude and which do you include and a directly related question, how long will it take to provide the

input data and obtain the results?

Who will decide what is significant and what isn't? Where will new data be supplied for infiltration values or isn't it significant? U. S. Weather Bureau data is recorded at the airport. Must all new buildings be built on a runway for the data to be applicable or isn't this significant. Some weather data, such as cloud cover, are only observations. What factors do we use to account for this?

In the preli m inary design state of a mechanical system all components, ducts, etc. must be engineered

for the various systems in order to be able to select the best. Who will do this or "Isn't it significant?" Contractors build structures in varying degrees of soundness. What "K" factor is used to

adjust the estimate, particularly since we don't even know who the low bidder will be. Building

occupancy schedules in actual operation rarely, if ever, agree with the preliminary objectives. How

do we adjust the energy estimate. Do we continually adjust the resistance values of building materials

relative to outdoor temperatures or do we neglect this? How do we compensate for thermostat settings

ranging from 69°F to 78°F or isn't this Important? Control systems must be designed to properly

monitor the system. But control system contracts are given to the low bidder as are most other con- tracts, what's the "K" factor relationship here?

The basic problem being introduced should be obvious. What real value is there in computing the

sun's exact angle relative to a new building when someone comes along and builds a structure adjacent

to it. The building unit is a dynamic living entity not a static dormant box. The complexities of any program input must be justified by the accuracy of the program output. It is also the moral obligation

of the industry to honestly evaluate all , not just some, building energy needs, whether the structure

contains 200 square feet or 2,000,000 square feet. It is seriously doubted that these evaluations can be made for all clients unless the cost and program input are reasonable.

3.3 A Comparison

We recently compared the results of a study with one of those complex routines, which hourly com- putes the solar altitude, azimuth and incidence angles, and requires a various assortment of other input

data. In no case did a zone heat loss, heat gain, heating or cooling energy requirement vary by more

than 5/? and in most cases, the difference was negligible.

Energy analyses are necessary in the preliminary planning stages with preliminary design data

since this is when decisions are made. Deeper analyses of systems and designs are necessary, and should be done on operating systems, in order to determine what is the optimum system design.

^ The^ ability of computer programs to generate reliable and accurate results by using complex relationships

with numerous unknown inputs must at least be questioned.

220
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221
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Figure 2

;,i>ennsvlv6n(4 power c light company

[electric space heating estimate

PPf.L PIST. I ESTIMATOR JKS

OFFICE BUILPING BETHLEHEH PA NORMAL DEGREE DAYS 5-lCO RATF HS OATf TF SURVEY l2/l2/l-<)

CONSTRUCTION PES. GROUND FLOOR A - FLOOR 3EL0H GRI) 34,00 EXTERIOR WALL B - U VAUIF CE INSULATION .lOCO ROOF C - U VALliE HF INSULSTION .10^0

WALL BELOW GRO 0 - BELCw r.RAOE

OLSKN Tfso.

IN -ISf StT8M,»; INT IXI INT iXT

WINDOWS c nriiRS pts. infil.

A - PICTURE GLASS VFRT. 0.99 1.2^

B - COM" nOOR GLASS VFRT. O.H? b.C:

SCHfcOULE OF USE WEEKS ''0^ TUf WED THU FP I SAT SUN

i. A 0 5? 7 2C 7 ?0 7 20 7 2C 7 20 3 13 0 0

Figure 3

222
•eNN'iYiviNio POMFR c trr.HT cn. fLECTOIC SPACE ffATING ESTIMATE

IBM OFFICE BUlLDINr,

BETHCEHE'' PA

OUTSIDE

AREA EXPOSURE OIHENSirNS TYPE

FIRST FCR HALL

UALL FinnH WIN»nw/DR,

1 1 Norw/nR. KlNnrw/DR.

KiNOrw/OR.

ul NUnu/OR. ulNCnu/OR.

u I Monj/nR

H INDOW/nP HiNnnu/nR. iNLPw/nR.

rtlNnOri/OR.

I NF IL IR AT ION

V F N T 1 1 A T I ON rCCUPANCY

( ir.HT ING OTHER r.AINS

536.

536.

168.

1 W,

!<)(•;

I 71 '.

St:65

-70000

-?a6<iC6

7J)«

?'J'H') IMS',

1 IT,', 101)90

I 7n^<".

1 I..Trj

S'.'ii

•l';7'J T)79

S >6S

S

HEAT RfO.

I M WATTS

0

SUB-TOTAL J13264

StCON'l FtP KAIL

37 HINOOW/OR.

1 wiNnow/riR.

P WINOCW/PR.

1 UINDOU/DR.

2 wINOnw/np.

-^3 >iiNonw/nfl. 26 WINOrw/OR.

26 «iNnnH/nR.

INF IL IRAt ION VfNI IIAI ION

I Cf UPANCY

L irn ING TTHER GAINS

536. C K 12.0

2.0

3.0

<..r

3 "! M 3 9

1 1 >> 1

'.772

1 193 3579

51163^

35'i5^t 35^.54

i Ibl 2 272159

-2^1 OC

331139

3 1 H I 4772

1193

35 79 5M536

:'5454

'5',5<.

SU3- TOTAL 2 74 320

a WALL 5 '3 WINOOH/nR.

'.3 VJINDCW/OR.

26 WINOCW/OR.

26 HINCOW/OR.

INF IL TRAT ION VENI 11 AT ION OCCUPANCY

L IGHTING OTHER GAINS

31679 51636

5 363 6 35454

35454

1291(1 272159

-200O0

-2 )64C6

35 ,54 35454

I2 90C

265614 2 32 761 FOORTH FLR WALL OVERHE AC

4J hINUCh/DR.

43 VIINnOW/nR.

25 MlNDCW/OR.

25 vrlNOOw/OP.

I NF IL TRAT ION VENTILATION

OCCUPANCY

L ICHTING OTHER GAINS

536.

16fl.

3 1679

1 25999

53636 53636

1 54 5 4

3 5 4 5 4 12 9CO

2 72159 -'OCCO

-2 )64C6

31679

125999 53636 55636

35454

35454

1 290C

0

SUB-TOTAL

ESIIMATEC ANNUAL KyH eSTIMATEC ANNUAL COST FOR HEATING

TOTAL NET HALL AREA 16960 SQUARE FFFT.

TUTAL FLOOR AREA IS 672CC SQUARE FEET. COST PER SaUARE FOOT IS S 0.13

TOTAl VOLUME IS 806400 CUBIC FEET. COST PES HUNDRED CUBIC FEET IS I 1.12 NOTE. THE HEAT LOSS CALCULATIONS AND EST!"AIF OF OPERATING CISTS

IN THIS PROPOSAL ARE flASEO ON ACCEPTED PPACIICtS OF THE HEATING INDUSTRY. THEV APE OETrRMINFC ON THE BASIS OF NORMAL CONCITICNS WITH NO ALLOWANCE FOR UNUSUAL WEATHER CUNDITICNS OR VARIATIONS IN INDIVIDUAL LIVING HArtlTS, SUCH AS MAINTAINING UNUSUALLY HIGH TFMPERATUkES OR EXCESSIVE VENTILATION. IT 15 RtCUXMENOELl THAI THE INSTALLED WATTS RE INCRFASEE IN CAPACITY WHENEVER lEHPEPATURE SETBACK IS PLANNED.

Figure 4

223
PENNSYLV4NIA POWER UNO LIGHT COMPANY PPCL DIST. I ESIIMATOB JKS HOURIY HEATING E COOLING ENERGY ESTI'<ATE AND

AIR CONDITIONING LOAD ESTIMATE

NO. 11 OFFICE BUILDING BETHLEHEM PA AREA

THIRD FLPCHANGEOVER TEMPERATURE 50 MALL aru GAIN 7603 ROOF BTU GAIN 0 WINOOW/DOOR BTU GAIN VENTILATION BTU GAIN SENSIBLE 5'i<i32 VENTILATION BTU GAIN LATENT 96766

FIRST FLRCHANGEOVER TEMPERATURE 62 HALL BTU CAIN 6762 PEOPLE BTU GAIN LATENT 30oor ROOF BTU GAIN C OTHER BTU GAIN J26435 WINDOW/OOOR 8TU GAIN 2I«626 VENTILATION BTU GAIN SENSIBLE 5«'i32 TOTAL BTU GAIN 639364 VENTILATION BTU GAIN LATLNT 96 768 TONS 53.28 PEOPLE BTU GAIN LATENT 30000 ROOM CFM REOUIRFD 214f 3 OTHER BTU GAIN 2?6'i36 COOL ING K«H 65538

TOTAL 8TU CAIN 62902^ l-EAI ING KWH U1533

TONS HEAT ING BTU 3S0^^C736

ROOM CFM REQUIRED ?r,9fis HOURS IN use 36 40 COOLING KHH 65C97 HEATING KWH 12 9>57 HEATING BTU FOURTH FLR HOURS IN USE 36'. 0 CHANGEOVER TF-PEPATURE 5B WALL BTU GAIN 76C3 ROOF BTU GAIN a90'tf' WINDOW/DOOR BTU GAIN 22<il26 SECOND FLR VENTILATION BTU GAIN SENSIBLE 5'.'.32 CHANGEOVER TEMPERATURE 51 VENTILATION BTU GAIN LATENT 9676B WALL BTU GAIN 7402 PEOPIE BTU GAIN LATENT 300GC ROOF BTU GAIN C OTHER BTU GAIN 2264'!? WINDCW/OQOR BTU CAIN 226035 VENTILATION BTU GAIN SENSIBLE 5<i<i32 TOTAL BTU GAIN 72 '14 12 VENTILATION BTU GAIN LATENT 9676S TONS 60. 70 PEOPLE BTU GAIN L4TENT 3000C ROOM CFM REQUIRED 25586 OTHER BTU GAIN 226'V35 COOL ING KWH 70730 TOTAL BTU GAIN 6'il072 FEAT ING KWF 13U78

IONS 53. «2 Ff AT ING BTU 6 I » ROOM CFH REQUIRED HOURS IN USE 3640

_ COOLING KMH 6556-; „ HEAI INS KMH . 125399 HEATING BTU *27986'.32 HOURS IN USE .36'iO CASE TOTALS

TONS REQUIRED 2I9.R2 TI'N'j BTU CA IN 2637973 fllH CFM RtCUIRED 576 Cf

EFFECT IVE SENSIBLE HFAT 545 IT') Figure 5

HEAT ING KWH 73^.6 KV.M con ING KWH ^^^ 930 KWH ESIIMAIEO ANNUAL HEATING CrsI RAStn ON lEGWEFH^^UFS * 6S4H ESTIMATED ANNUAL CCOl I \G Crsl 9ASFC ON CfGaFFHOIIhS 1 12i'

NOTE. THIS STUDY IS BASFO ON A 15 nfCREE ''ESlsN I ' "Pf F A T ija f HFcfurMC

ANO ROOM CFH AIR ENTERING AT ?C OEGoFFS l^SS IH«N tT"

TEMPERATURE. A 10 PERCENT BYPASS FACinn HSS Mffv tSIt'

IN THIS STUDY. THIS STUDY IS TO BE USED FCP ESTIMATING PURPOSES ONI

ANO NOT AS DESIGN DATA

PENNSYLVANIA POWER & LIGHT COMPAHV

SHOPPING CBNTBR 800,000 SQUARE FEET TYPICAL

HOURLY KWH ffiffiRATED HOURLY HEATING/COOLING BTU'S HOURLY GAS CONSUMPTION Ft.^

4000. 3808. 3832. 3904. 6831691. 6831691. 9564367. 9564 367. 44800. 42650. 42918. 43725.

3832. 3792. 886. 664. 9905952. 3277612. 3745642. 3745642. 42918. 42470. 16346. 11637.

592. 592. 568. 568. 4026780. 4026780. 4401364. 4401364. 10830. 10830. 10892. 10892.

568. 592. 592. 880. 4775949. 4775949. 4641984. 4641984. 11391. 1 1516. 11338. 18256.

920. 928. 936. 936. 4397789. 4397789. 2810524. 2810524. 18704. 18794. 18883. 18883.

928. 920. 888. 920. 1955842. 1955842. 1345355. 1345355. 18794. 18704. 18346. 16704.

936. 944 . 624. 624. 1589550. 1589550. 3090320. 3090320. 18883. 16973. 1U89. 11189.

624. 696. 624. 624. 3277612. 3277612. 3652196. 3652196. 11189. 1 1995. 11189. 11189.

664 . 664. 592. 624. 3652196. 3652196. 3558550. 3556550. 11637. 11637. 10630. 11189.

592. 664. 696. 1168. 3090320. 3090320. 2444232. 2444232. 10830. 11637. 11995. 21482.

2944. 3424. 3408. 3704. 2200037. 8198029. 6831691. 6831691, 49773. 38349. 38170. 41465.

3656. 3736. 384 8. 3904. 5123766. 5123768. 5123768. 5123766. 40947. 41843. 43098. 43725.

4000. 3 806. 3832. 3904. 5465353. 5465353. 6831691. 6831691. 44800. 42650. 42918. 43725.

3832. 3792. 888. 664. 6831691. 2434797. 24347972434797. 42916. 42470. 18346. 11637.

664. 664. 592. 624. 2528443. 2528443. 2434797. 2434797. U637. 11637. 10830. 11189.

592. 664. 696. U6B. 2341151. 2341151. 1223258. 1223258. 10630. 11637. 11995. 21482.

2944. 3424. 340 8. 3704. 734869. 3757430. 3074261. 3074261. 49773. 38349. 38170. 41465.

3656. 3736. 3846. 3904. 2391092. 2391092. 1366338. 1366338. 40947. 41843. 43098. 43725.

4000. 3808. 3832. 3904 . 3415845. 3415845. 5465353. 5465353. 44800. 42650. 42916. 43725.

3832. 3792. 688. 664. 6146522. 2247505. 2341151. 2341151. 42918. 42470. 18346. 11637.

664 . 664. 592. 624. 2528443. 2526443. 2528443. 2528443. 11637. 11637. 10830. 11189.

592. 664. 696. 1168. 2903028. 2903026. 29030282903028. 10830. 11637. 11995. 21482.

PENNSYLVANIA POWER C LIGHT COMPANY

ISOLATED PLANT GENERATION STUDY FOR SHOPPING CENTER 800,000 SQ.FT. TrPICAL ANNUAL TOIAL KWH GENERATED, 19347744 ANNUAL TOIAL CUBIC FEET GAS REQUIRED, 245677260

j.g TOTAL PLANT THERMAL EFFICIENCY 40.92 PERCENT

224
Instantaneous Cooling Loads by Computer

based on ASHRAE'S time averaging method

R. V. THOMAS^

Naval Facilities Engineering Command

Washington, D.C. 20390

Variables affecting cooling load calculations are numerous, often difficult to define precisely, and always intricately interrelated. Many of the components of the cooling load vary in magnitude over a wide range during a 24 hour period, and

as the cyclic changes in load components are not usually in phase with each other

careful analysis is required to establish the resultant maximum cooling load for a building or zone. There may be an appreciable difference between the net instan- taneous rate of heat gain and the total cooling load at any instant. This differene

is caused by the storage and subsequent release of heat by the structure and its contents. This thermal-storage effect may be quite important in determining an economical cooling equipment capacity. This computer program uses the ASHRAE method

of calculating cooling loads. It takes the instantaneous heat gain and breaks it into radiation and convection components. Convection components are added directly

to the room space and instantaneous cooling load. The radiation components are summed and averaged over a given time period (dependent on building construction) up to and including the time of the desired load« They are then changed into convected

components and added back into the room space as part of the instantaneous cooling

load (See figure 1). Therefore, a cooling load calculation at any given time is actually taking into account the radiation build up that has been taking place

several hours earlier. The program will print out a building's cooling load, at any

location, room by room, for any hour between 8 AM and 5 PM and contains a psychrometric

routine for calculating moisture content, latent heat and relative humidity. The building itself can also be rotated to find the optimum orientation. Built into the program are eleven types of roofs, eight types of walls, six activity levels of people and six room lighting levels.

Key Words: Convection, direction cosines, fenestration, heat lag, latent

heat, radiation, relative humidity, sensible heat, solar heat gain factor,

thermal-storage, total equivalent temperature differentials, "U" factor.

1. Introduction

Calculation of a cooling load by hand using ASHRAE'S methods becomes very tedious and

lengthy, especially when the process has to be repeated to find the hour of the maxium load or

the orientation for minimum load. Lengthy and repetitious calculations such as these lend themselves very well to solution by computer and in this case the problem was programmed in fortran for a Burroughs 5500 time sharing computer.

2. Basic Considerations

Heat lag should be carefully considered in the cooling load calculations. In certain

types of buildings the effect of solar radiation is still apparent several hours after the sun

has shifted from that exposure. In other types having a much lighter construction, the heat gain due to solar radiation decreases markedly with the passing of the sun. Some walls, warqaed

by the sun, may radiate heat long after the passing of the sun. In these cases the greater

mass may be used to your advantage by pre-cooling it below the room design conditions prior to

the hour of peak load and much of the sun's radiant energy will go into raising the temperature

of the walls. (see figure 1).

'Mechanical Engineer, mechanical design.

225
2.1 Fenestration Areas

Solar heat gain factors were used in calculating heat gain through fenestration areas. These solar heat gain factors were developed from the equations found in Chapter 28 of [^l] which locate the sun's position in the sky with respect to the surface in question. These

equations express the radiation from the sun on a surface as a function of the date, time of day,

latitude, and direction cosine of the surface receiving the radiation. To further simplify the input

and eliminate the need for putting in direction cosines of building surface, direction cosines for

the most commonly used directions (N, NE, E, SE, S, SW, W, and NW) were built in to the program so the user need only supply the direction ("N", "NE", ...etc) the surface is facing. By using a looping

method and advancing the hour each loop, the sun's position is advanced across the sky and the resulting solar heat gain to each building surface is calculated. In the early stages of development, the solar heat gain factors thus calculated were then checked with the standard ASHEAE solar heat gain

tables for various latitudes.

The program then time averages these factors (length of time lag average depends on building con- struction )and breaks them into convected and radiant components. It then multiplies them by the fenestration area and adds the resultant heat gain to the room load. Shading devices such as drapes,

blinds, sun screens, etc. are handled by inputing the proper shade factor.

2.2. Walls and Roof

Heat gain through the walls and roof is calculated by using total equivalent temperature differentials (heat gain divided by "U" value). These quantities have dimensions of temperature and take

into account the solar radiation heat gain and heat gain from the difference between inside and outside

design temperatures.

'Total heat transmission from \ /Total equivalent \ /Heat transmission coefficient)

solar radiation and temperature\ =^temperature differential] *^Btu hr"-'- ft~^ difference between outside and

.room air, Btu hr"-'-

Total equivalent temperature differentials for eight types of walls and eleven types of roofs from ^l]^ have been stored in permanent files in order to reduce the amount of input data required.

Since these differentials are based on a daily outdoor temperature range of 20 degrees, a routine for correcting these equivalent temperature differentials for daily ranges other than 20 degrees has been

built in.

Heat transmitted through the walls and roof is broken down into components similar to the method

used above for glass. The convected portion is obtained by multiplying the total temperature differential of the time of the desired load by the "U" value and the area. The radiant portion is obtained

by averaging the total equivalent temperature differential several hours leading up to and including

the hour of the desired cooling load (the exact number of hours time lag is determined by the program

depending on the type of construction ). These values are then multiplied by the "U" value and the area.

Following the methods of ASHRAE, iA-0% of the convected and 607o of the radiant heat gain are added

to the instantaneous cooling load.

2.3. Latent Heat

Heat and moisture are given off by humans at different rates depending on their level of activity

and these sensible and latent heats can, in many instances, become a large fraction of the total load. Six different activity levels of occupants with their associated lighting Watts ft"^ and ventilation

requirements were built into the program so the user need only specify the type and number of persons who will be occupying the space. An exception code was also built in which allows the user to insert any values of sensible and latent heat, lighting or ventilation CFM which differ from the standard

values

A subroutine using computer developed equations from ^i] was then written to express relative

humidity and moisture content as a function of the dry bulb and wet bulb temperature. This routine is used to calculate the moisture content of the ventilation air, the resulting latent load, and the relative humidities of the air at indoor and outdoor design conditions.

The daily outdoor temperature is varied from morning to night by a routine based on a "time" versus "outdoor temperature" chart from [2\ ,

Figures in brackets indicate the literature references at the end of this paper.

226
3 . Output

A sample of the programs output (see figure 2) shows a typical search for a building's peak load. The following is an explanation of headings over the printout:

RM ID - This is the ID. No. of the various rooms for which the cooling load is being solved. The entire building may be looked at as one room for a quick analysis of a building cooling load.

PiSH - This is the room sensible heat. It is composed of radiation and convected

heat through the glass, doors, wall, roof, lights and the sensible gain

from the people plus the sensible load from the ventilation air that bypasses the coil plus any miscellaneous load.

RTH - This is the room Total heat. It is composed of HSH plus the latent load

from the people and the latent load from the ventilation air that by-passes

the coil.

OA SH - This is sensible heat of the outside air that is not by-passing the coils.

It is calculated for the given time of day.

OA TH - This is the OA SH plus the latent heat of the outside air that is not bypassing the coils. It is calculated for the given time of day.

OA CFM- This is the amount of outside air that is being supplied to the room. Usually based on local codes and ordinances on ventilation requirements.

GTH - This is the grand total heat and is the sum of RTH plus the OA TH.

BUILDING TOTAL - This is the sum of all the GTH's from each room. In the case where the building is treated as a single room, GTH will equal BUILDING

TOTAL.

L,. References

1 ASHRAE, Handbook of Fundamentals 1967.

2 Trane, Solar Tables for heat gain

calculations, 1966.

Fairfax, J. P. and Tung, J. S-T "Construction of a ^sychrometric

table by use of a digital computer", ASHRAE JOURNAL . March 1968, 59-61.

INSTANTANEOUS

HEAT GAIN

INTERIOR FURNISHINGS

RADIATION AND STRUCTURE, ^ CONVECTION

VARIABLE HEAT STORAGE

(DELAYED IN TIME)

CONVECTION

AIR IN SPACE AND

CONDITIONING

EQUIPMENT

INSTANTANEOUS

COOLING LOAD

THE RADIATION ABSORBED BY THE INTERIOR FURNISHINGS AND STRUCTURE

REACHES THE CONDITIONING EQUIPMENT AFTER A CONSIDERABLE TIME DELAY

Figure 1. Origin of the Difference Between the Magnitudes of the Instantaneous Heat Gain and Instantaneous Cooling Load

227
***BUILDING COOLING LOAD AT TIME= 1500 OUTSIDE DSGN DB & WB TEMP= 95.0 78.0 RH%= 47.4

INSIDE DSGN DB & WB TEMP= 7 5.0 60.5 RH%= 43.2

RM ID RSH RTH OA SH OA TH OA CFM GTH

10798. 16563.

13588. 10442.

12117.

18718. 15698.

11761.

935. 748. 1496.

935.

2741.

2193. 4386.

2741,

50. 40.

80.

50.

14859

20911 20084

14503

BUILDING TOTAL= 70357.

WHAT TIME NEXT

?1600

***BUILDING COOLING LOAD AT TIME= 1600 OUTSIDE DSGN DB & WB TEMP= 95.0 78.0 RH%= 47.4

INSIDE DSGN DB & WB TEMP= 75.0 60.5 RH%= 43.2

RM ID RSH RTH OA SH OA TH OA CFM GTH

11450.

16625. 13774.

10815.

12769.

18780. 15884,

12134.

907.

726. 1451.

907.

2713,

2171, 4341.

2713,

50.

40.

80.

50.

15483 20950

20225

14847

BUILDING TOTAL= 71505.

WHAT TIME NEXT

71700

***BUILDING COOLING LOAD AT TIME= 1700 OUTSIDE DSGN DB & WB TEMP= 95.0 78.0 RH%= 47.4

INSIDE DSGN DB & WB TEMP= 75.0 60.5 RH%= 43.2

RM ID RSH RTH OA SH OA TH OA CFM GTH

11493. 16325.

13810. 10973.

12812.

18480.

15920.

12292.

842. 673.

1346.

842.

2648.

2118. 4237.

2648.

50.

40.

80.

50.

15460

20598

20157 14939

BUILDING TOTAL= 71154.

Figure 2. Building Cooling Load at Time = 1500

228
Computer Method for Estimating Net Energy

Requirement for Heating Buildings

Nathaniel E. Hager, Jr.

Armstrong Cork Company

Research and Development Center

Lancaster, Pennsylvania IjGoh

The net energy needed to maintain constant building temperature is estimated

by subtracting cost-free heat gains from external losses. This quantity is integrated over the heating season by a ccmputer programmed to combine data on climate,

structure, and occupancy. The method is based on straightforward application of

the energy conservation principle, and does not depend on arbitrary choice of a degree-day base or other such factor requiring previous experience with similar

situations

Key Words: Architectural heating, building heating, computer,

environmental engineering, fuel consumption, heat gains, net energy

beilance, residential heating, space heating.

The degree-day method [l, 2, 3] has long been used for computing annual heat loss from buildings

and estimating resultant fuel consumption. It seemed practical to use this method when fuel was plentiful and homes were not well insulated. Because the total energy use was so large, cost-free internal

gains were relatively unimportant, and there was little incentive for handling them in a sophisticated

way. Lack of adequate weather data and computer facilities added further discouragement. Thus, these

small internal heat gains were handled by using an arbitrary degree-day base of 6^"?, which amounted to assuming that the heating plant kept the building temperature up to 65°F while the internal gains did

the rest. For buildings with higher gains, lower base temperatures were selected on the basis of experience with similar biiildings.

With the growth of electric heating it became apparent that the degree-day mentioned gave results

too high for electric heating estimates [k, 5, 6]. Consequently, the National Electrical Manufacturers

Association (NEMA) recommended that electric heating specialists adjust the degree-day results downward

by using a multiplying factor determined from previous experience [7]. This recommendation served a practical purpose, but, from the analyiiical viewpoint, compounded the arbitrariness of the degree-day

method. Both the degree-day method and the NEMA recommendation were unsatisfactory for handling

unconventional situations, and failed to provide a sound basis for theoretical evaluation of new heating and insulation methods.

In a 1962 publication [8] the writer showed that the growing inadequacy of these methods rose from

two important trends in residential structure. First, houses were becoming better insulated and

tighter, reducing the total energy used in heating. Second, more appliances and higher lighting levels were being used, causing an increase in available internal heat gains which did not need to be supplied

by the heating plant. As a result, it was no longer practical to ignore these gains, nor was it en- lightening to handle them with indirect and arbitrary approximations. It was then shown that the gains

co\rld be taken into account by direct application of the law of conservation of energy. A procedure

vas described which only counted internal heat gains during periods when they are profitably used to

offset heat losses.

Several subsequent workers recognized the need for taking into accoiont cost-free heat gains in

order to obtain better estimates . Thomas [9] subtracted the gross annual heat gain during the heating

1. Introduction

'igures in brackets indicate literature references at the end of this paper.

229
season frcm the gross anmial loss during the same season, without taking Into account whether or not these gains were profitably employed. Later, Blllington [lO] described a method for modifying the degree-day method to account for "miscellaneous sources of heat other than the heating system". In

1967 an ASHRAE proposal Cll] sioggested that a modification of the degree-day method be used for homes

and that a "heat balance" method be used for commercial and industrial buildings.

One purpose of the present paper is to show how straightforward inclusion of estimated internal

gains in the overall heating pictvire produces reasonable results without the use of arbitrary degreeday factors, and without having previous experience with similar buildings. A second purpose is to show how the previously described procedtire has been extended to take advantage of high-speed computers

and improved weather data. The present procedure makes it feasible to predict the economic conse- quences of using new components or systems, and to design heating pleints for unconventional structures.

The method is sufficiently general to be applied to any type of structure including homes, commercial

or industrial buildings, mobile homes, and computer facilities.

Present emphasis on minimizing pollution should ultimately lead to spending more money on insulation in order to minimize consumption of fuel. Thus, the effort to reduce pollution from heating

plants will cause internal heat gains to assume even greater relative importance in the overall space heating pictiure, and will add further emphasis to the need for properly including these gains when

estimating heating requirements.

2 . Theory

At first glance, it might appear that the net heat loss for the heating season can be estimated by

subtracting the total heat gain for the season from the total heat loss. Brief reflection makes it

clear that this approach is incorrect because it assumes that all heat gains are profitably employed.

Actually, these gains are only of value when they offset losses and help maintain the desired indoor

temperature. Usually, when the gains exceed the losses, windows are opened or cooling is employed;

potential heat gains are thus discarded, and are not used profitably. It is recognized that some portion of the excess gains can be stored by heating of massive parts of the structure, but this process is not included within the scope of this analysis. This omission is of little importance when

dealing with light weight structures where there is relatively little heat storage.

The following analytical proced\ire is developed for the pvirpose of taking into account cost-free

heat gains when, and only when, they offset losses. The procedure consists of selecting an interval

of temperature, say 5 degrees wide, and computing the rates of loss and gain when the outdoor temperat\ire falls within that interval. If the resialtant net rate of heat loss is negative it is discarded.

If there is a net loss, this is multiplied by the number of hours during the heating season when the temperature falls within this interval. This is done for all intervals of outdoor temperature encountered, and the results are summed to get the total loss which must be replaced by the heating system

during the heating season.

Therefore, data are needed describing the number of hours per year when the temperature falls within each defined intejrval. Such data are available for over 200 locations in the United States [12]. An example of these data is given in table 1 which shows the statistical distribution of dry-bulb

temperatures for Pittsburgh, Pennsylvania. The distribution is given for 5-degree temperature intervals. The distribution is further broken down into three equal periods of the day corresponding to the periods when people normally sleep, work, and engage in recreation, and the following procedvire is especially tailored to make good use of this additional breakdown.

(S) If At3 ' designates the aggregate time per heating season during the sleeping period, when the indoor -outdoor temperature difference falls within the interval centering on ATj, then the rate of

heat loss during these hours is given by

H^.^^ (LOSS) = uATy^tJ^) , (1)

where u is a smnmation of all losses expressed in the form

u =U^A^ +U2A2 +U3A3 + ... =/^U.A. . i

It is assumed that each loss item is expressible as a product of fixed factors which, when

mviltiplied by the indoor-outdoor temperat\ire difference ATj, will give the rate of heat loss during

those periods included within the aggregate time period

At(S).

230
Table 1. Mean frequence of occurrence of dry bulb temperature in hours per

year for Pittsbiirgh, Pennsylvania; data obtained from reference [12].

Period of Day

Temperature Range Sleeping (S) Working (w) Recreation (r) 1:30 a.m. -9:30 p.m. 9:30 a.m. -5:30 p.m. 5:30 p.m.

95/99 0 1 0

90/9it 0 15 0

85/89 0 107 11

80/84 6 264 57

15/19 34 317 l4l

lO/lh 151 286 276

65/69 291 239 319

323 204 296 55/59 277 174 24o

50/54 263 163 217

45/49 225 166 192

4o/44 219 192 213 35/39 242 215 223 30/34 291 217 276

25/29 218 152 171

20/24 l4l 93 112 15/19 91 57

rrO 78

10/14 74 37 52 5/9 37 15 30

0/4 22 5 13 -5/-1 11 1 3 -IO/-6 4 0 0

-I5/-II 0 0 0

-20/-I6 0 0 0

The heat gain during this same time period is calculated from the eqiiation

H^.^^ (Gain) = q^^W^^^ , (3)

where q is the sum of the contributing sources of heat gain during the sleeping period, given by the

expression

Therefore, the net loss is obtained by subtraction of eq (3) from eq (l), giving the equation

H^^^ (NET) = (uAT.-q^^b At^^^ . (5)

Similar expressions can be written for the working period (w) and the recreation period (R). The

net heat loss H for the heating season is obtained by summing over all three periods of the day, and

over all temperature intervals in accordance with the following equation:

H =

2^ (uAT^-q^^b^t^^^ + ^

(l^T^-q^"))At^(") + ^(uAT^-q(^))Atj^) . (6)

j j 0

It is understood that only positive terms from each of the summations are to be included in obtaining H.

231
2.1 Proposed Extension of Method

The form of the above method was influenced by the form of presently available tabulations on

the statistical distribution of climate conditions. That component of u accounting for infiltration

loss, represented above by a constant average value, would be better described if the distribution of

wind velocities were taken into acco\int. It has been shown by others [l3, iW] that the infiltration

loss from a building can be correlated with wind velocity. The U-factors for the various parts of

the structural shell also depend on wind velocity. Likewise, the ccmponent of heat gain q(S) which

accounts for solar gain, would be better described if the frequency with which the solar energy level

falls within arbitrarily selected ranges were taken into account. The attached appendix gives

further details on how these modifications can be accomplished.

3. Application to Representative Home

3.1 Insiilation Systems Defined

The above method is applied to a representative l-l/2-story house insulated to four different

degrees described in table 2. Instilation System I represents the case where the house is virtually

uninsulated; no materials are used which involve cost exceeding that required for structural strength.

System II represents a typical contemporary insulation installation usually considered adequate when

conventional heating plants are used. System III is a superior installation of the type specified

for electrically-heated houses. System IV is an even tighter installation which is slightly futuristic but, nevertheless, technically feasible.

Table 3 lists areas and air-to-air conductance factors pertaining to the various components

of each system. The U-factors are determined in accordance with usual handbook procedvires [15]. For

simplicity, so that the heat loss associated with the floor can be computed using the same temperature

difference used for computing the other losses, the U^A^ values for the floor are taken to be one- fourth of the actual value when the floor is not insulated, and one-half of the acttoal value when it

is insialated. The UiA^ values listed for infiltration are fictitious values which may be treated

like the real values for walls, ceiling, etc., in that multiplying them by the same indoor-outdoor

temperatiire difference gives an appropriate estimated value for the infiltration heat loss.

Table 2. Definition of thermal insulation systems for representative house.

Heat Loss Item I II III IV

Ceiling Plaster on lath; Same as (l) with 2-in. Same as (l) with Same as (l) with

no insulation; glass wool insulation. 6-in. insiilation. 6-in. insulation,

attic vented.

Walls

Floors

Plaster on lath; no insulation; gypsum sheathing;

brick or wood siding

2 layers of wood; no insulation.

Same as (l) except

2-in. glass wool.

Same as (l).

Same as (l) except Same as (III), use 3-5/8-in.

glass wool.

Same as (l) with

2-in. glass wool. Same as (ill)

Doors

Windows

Infiltration

Description of

Insulation System

Wood.

Single glass

weather stripped.

2 air changes per

hr.

No insxilation.

Wood with storm

doors

Same as (l) with

storm windows or thermopane

I-I/2 air changes per hr.

Good contemporary

insulation.

Wood with storm

doors

Same as(ll).

1 air change per

hr.

Superior contem- porary insulation.

2-in. cellularplastic -insulated

core in laminated

door.

Triple glazed; or double-glazed

with storm windows.

0.5 air change per hr; air

processed.

Futuristic insulation.

232
Table 3. Heat loss factors for representative hoiise; dependence on insulation system. Ai is in ft^, u^^ is in Btu/hr-ft2-°F, and u is in Btu/hr-°F.

InsiLLation System

I II III IV

Heat Loss Item \ "i "i^ "i U.A,

1 i "i

U.A.

1 1 "i "i\

Ceiling

Walls

Floor

Doors Windows

Infiltration

900 1800

900

i+0 180

0.70

0.3h

0.35

1.13

630

612

(79)

c.\) 203

(260)

O.lit 0.10

0.35

(J. J5 0.55

126 180

(79)

lU

99

(195)

0.05 O f)7 0.10

0.35

0.55

126

{k5)

99

(130)

0.05 0.07

0.10

O.UO

126

(i^5)

72

(65)

Total u = / U.A.

i

I80ii 693 1^59 357

3.2 Internal Heat Gains Described

Table h shows estimated values for the most important internal heat gains during each of the three

periods of the day. Because the solar heat gain through the roof depends on the degree of insulation,

separate estimates must be made for each insulation system.

The solar heat gains for roof and windows are estimated on the basis of data given for Pittsburgh,

Pa. They are estimated by the usual method shown in the ASHRAE Guide; the values shown are estimates

of averages for the entire heating season. Note that the solar gains are estimated to be zero during

the sleeping and recreation periods; it is assumed that significant solar radiation is spread evenly

over the 8-hour working period of the day. Solar heat gain due to sunlight falling on vertical walls

is neglected; this gain is probably less inrportant than the others because of the presence of shrubbery,

because of the common use of light-colored paints, and because a good fraction of the vertical wall

area is devoted to windows taken into accoimt separately.

At the present time, the average home uses electrical energy at an average rate close to 0.5 kw; this

figure is used for the representative house with Insulation Systems I and II. The electrical energy

usage is distributed unevenly during the three periods of the day such that the average value for the entire day, expressed in Btu/hr, is equivalent to the 0.5-kilowatt average. When it is assumed that

the representative house is insulated in accordance with System III, which is a superior contemporary

insulation system, it is assumed that there are more heavily powered electrical devices in the house, and that the electrical power is used at an average rate of about 1.0 kw. Similarly, it is assumed

that homes of the fut\ire, ones with insiilation systems like System IV, will use even more power for

ptirposes other than space heating; therefore, it is assumed that the representative house with Insulation System IV uses power at a rate of about I.5 kw. Figures given in the table are obtained by

noting that 1.0 kw is approximately equal to 3,1+000 Btu/hr.

The average human radiates body heat at a rate ranging from approximately kOO Btu/hr when at rest

to as much as 1500 Btu/hr when exercising. For purposes of estimating heat gain from hvnnan occupants,

it is assumed that there are four people at rest during the sleeping period, one person rather active

during the working period, and four people moderately active during the recreation period.

k . Res\ilts

The im 360 computer is programmed to perform the calculations indicated by eq (6). Punched cards

are prepared containing climate data such as shown in table 1 for each of 60 locations in the United

States. Once these cards are prepared there is no further need for the estimator to be concerned with

climate data. The heating energy requirement for the representative house is determined for any location by running the program using the appropriate climate card. To make estimates for the representative house values of u are taken from table 3 and values of q(^), q(^), and q(^) frcm table k. This completes the description of the insulation system and the conditions of occupancy. The program also

peimits entering £my desired indoor tenrperature (thermostat setting)

233
Table k. Estimated heat gains in Btu/hr representative house in

Pittsburgh, Pennsylvania.

Insulation

System

Period

of Day

Solar

Roof

Solar

Windows

Electrical

Gas Human

Total

(Btu/hr) Symbol

II

III

IV

sw

R

SW

R

Sw

R

Sw

R

7500

1500

600

600

2k00

2k00

2kOO

2k00

300

2000

3000

300

2000

3000

600

1+000 6000

900

6000

9000

1600

1000

2800

1600

1000

2800

1600

1000

2800

1600

1000

2800

1900

12900

5800

1900

6900

5800

2200

8000

8800

2500

10000

11800

W

,(w)

,(s)

,(")

,(»)

The printout shows the annual energy reqiiirement for heating the house for each of the four insulation systems. It also prints out, for each insulation system, estimates calculated by the degreeday method and by the NEMA method using the 18. 5 C-factor commonly employed in electric heating

estimates

k.l Comparison With Other Methods

Assuming that the representative house is located in Pittsburgh, Pa., whichhas a 5356 degree-day

heating season, and that it is occupied by four people with the thermostat set at 70°F, calculations

are run for the four described insulation systems . The results are shown in figure 1, the annual energy- requirement being plotted as a function of u, the insulation system parameter. Also plotted are theoretical curves obtained by the degree-day and NEMA methods for the same insulation systems. The net energy method gives higher estimates for poorly insulated (high-u) houses. When the house is moderately

insulated, however, the net energy method gives results very close to those obtained by the degree-day

method; it is this type of home for which the degree-day method has been most successfully employed. For heavily insulated homes, the type designed for electric heating, using Insulation System III, the net energy method produces an estimate lower than the degree- day method and more nearly in agreement

with the NEMA method, using a C-factor of 18. 5. In other words, the net energy method agrees with the degree-day method where the latter is most valid, and agrees with the NEMA method in situations where

it gives the best results. With insulation systems similar to System IV, the net energy method predicts

that the annual energy requirement is approximately half of the value predicted by the degree-day method

and substantia ll y lower than the value predicted by the NEMA method. Therefore, the net energy method

agrees with the traditional methods where it shoxild agree, and gives a rational basis for predicting

requirements under conditions where neither of the traditional methods should be applied.

The correlation between the net energy method and the traditional methods is further substantiated

by running the calculation for over 60 different locations. Fig. 2 shows a comparison between points

calculated by the net energy method and lines calculated by the traditional methods. The upper curve

shows how the annual energy requirement vsiries with climate according to the degree-day method. This is done for the representative house with Insulation System II, a situation in which the degree-day

method should give valid results. The circles plotted in the graph represent calculations made by the net energy method for the same house with the same insulation system. Each circle represents the annual energy requirement, when the house is located in a particular city, plotted against the degreeday climate factor for the same location. Similarly, the lower cwcve shows results predicted by the NEMA method, using a C-factor of I8.5. This cxirve is for the same house, but with Insulation System III. This system Is the type used for electrically heated homes for which the NEMA method is ordinarily used. The triangular points represent calculations made by the net energy method for the same situation.

234
It is evident that the net energy method consistently gives the same result as the degree-day

method for moderately insulated homes, and the same result as the NEMA method for heavily insulated

homes. The agreement covers a wide range of climate conditions ranging from 1,000 to 10,000 degreedays .

Next, csilculations are run for the representative house, the conditions of occupancy being as described in table k, in order to estimate the effect of changing the thermostat setting. Results are shown in figure 3 for three of the insulation systems described. Die results show clearly that estimating methods can lead to very large errors if they ignore the possibility that occupants might enjoy

keeping the house at 80°F.

Calculations are run for the representative house having Insulation System III located in the Pittsburgh area. The resiilts, shown graphically in figure k, predict the effects of varying thermostat

setting and nimber of occupants. With 8 occupants, the heat gain values Eire taken to be twice as large

as those shown in table k. With 2 occupants, the values are taken to be half as large as those shown

in the table.

The results shown in figure h indicate that two elderly people who like the thermostat set at 80°F

will use twice as much heat as a family of 8 occupying the same house with the thermostat at 70°F. This

may be a rather extreme comparison, but it serves to emphasize the important effect that occupeincy con- ditions can have in modifying the heating requirements for a building.

Because the net energy method is based largely on using conventional estimating methods for taking

individual factors into account, it cannot be claimed to be more acctirate than traditional methods in

cases where extensive experience has established reliable correction factors. However, the net energy method has a considerable number of advantages enumerated as follows:

1. It produces results in agreement with the degree -day method for moderately insiilated homes, and with the NBIA method for well-insulated hemes.

2. It is free of arbitrary "experience" factors. It shoxild, therefore, give valid

results for unconventional structures, or structiires with vinconventional insulation

or occupancy factors, for which insufficient experience is available.

3- It is useful for theoretical or economic studies of the space heating problem. For

example, it can be used to ccaiipute the most economical ins\ilation thickness, or how

fuel usage is affected by a number of appliances, thermostat settings or other occupancy factors. For another example, suppose one wants to decrease pollution

by increasing thermal insulation (to reduce fuel use) and adding a cleaning system to

the chimney: the net energy method makes it possible to design such a system in the most economical way.

h. The net energy method shows how badly traditional methods can be in error under slightly unusual occupancy conditions, and makes clear the need for explicitly accounting for

internal gains.

5. Finally, the computerized net energy method, is, for all practical purposes, as easy to use as the computerized degree-day method. In one case, when the energy requirement was computed for the representative house in over 60 different locations, the lEM 360 took

only a minute or two for the whole series of computations.

k.2 Effect of Thermostat Setting

h.3 Effect of Nianber of Occupants

Summary

6 . Appendix

eq (6) expands to

' a constant average value for solar radiation is assumed, but k different intervals of wind

are assumed, leading to k different values of u for each of the three periods of the day.

235
0 k

(R) (7)

where Atjj^ now represents the number of hours during which the wind velocity falls in the kth interval,

while the temperature falls within the jth interval.

Variations in the solar radiation level are taken into account by assuming that the degree of cloud cover or the normal-incident solar intensity falls within 1 different intervals. It is asstmied that

solar radiation is negligible except during the working period of the day. Equation (7) is modified to

include variations in the solar heat gain by writing an equation as follows:

H=^X(u(S)AT-q(S))At^,(S) ,

j k j k j k 1

,(W)n.+(w)

(8)

U. S. Weather Bureau data are available [ll] giving hourly values for temperature, percentage

cloud cover, and wind velocity. Using such data, analysis can be done to fit the needed values for Atju^ and Atjjj. If, in addition to the I5 temperature intervals, one uses three wind velocity intervals, and three cloud coverage inteirvals, the frequency of 135 different sets of conditions must be taken into account in order to evaluate the net heat loss during the working period.

' . 7- References

[1] "ASHBAE Guide and Data Book; Applications",

(Am. Soc. Heating, Refrigerating, and AirConditioning Engineers, Inc., New York, I968)

[2] N. S. Mllington, "Building Physics: Heat",

(Pergamon Press, London, I967) p. hO.

[3] J. L. Threlkeld, "Thermal Environmental Engineering", (Prentice -Hall, Inc., Englewood

Cliffs, New Jersey, 1962) p. hl6.

[U] R. L. Boyd, Heating, Piping and Air Conditioning, 30, 113, (1968).

[5] L. Lessing, Architectural Forum 3, I69 (1959)-

[6] S. L. Forsyth, Westinghouse Engineer 18, li+O (1958).

[7] "Nema Manual for Electric House Heating"

(Nema Pub. No. HE 1-1957, AIA File No.

30-C-i+4, 1957).

[8] N. E. Hager, Jr. ASHRAE Journal, Vol. h, No. 8, p. i+O (Aug. 1962).

[9 ] C. C. Thomas, Air Conditioning, Heating and

Ventilating, Vol. 60, No. 11, p. 6I (I963)

[10] N. S. Billington, J. Instn. Heating and Vent. Engrg., Vol. 3^, 252 (Nov. I966).

[11] "ASHRAE TC 2.6 Proposal" ASHRAE J. Vol. 9, No. 10, p. 45 (1957).

[12] "Engineering Weather Data," Depts. of the Air Force, The Army, and the Navy, (U. S. Gov't. Printing Offices, Washington, D. C,

(1967)

[13] R. C. Jordan, G. A. Erickson. and R. R. Leonard, ASHRAE Trans. 69, 3^U (1963).

[l4] J. Gabrielsson and P. Perra, J. Instn. Heat- ing and Vent. Engrg. Vol. 35, ?• 357 (March

1968).

[15 1 "ASHRAE Handbook of Fundamentals", (Am. Soc. Heating, Refrigerating, and Air-Conditioning

Engineers, Inc., New York, 1967).

236
iHA/niaNl A8II]N] IVnNNV

237
Figure 2. Correlation between estimates made by net energy method with estimates made by degree-day and NEMA methods for representative house under different climate conditions. The upper line

represents the degree-day estimate with Insulation System II, aind the circles represent net energy estimates with the same insulation system. The lower line represents NEMA estimates

with Insulation System III, and the triangles indicate net energy results with this insulation system. All estimates assume 70°F indoor temperature.

238
THERMOSTAT SETTING [1]

Figure 3. Effect of thermostat setting on annual heating requirement for representative house with

Insulation Systems I, II and III. House situated in Pittsburgh climate, occupied by four

people.

239
240
The Practical Application

of Sma 1 1 Computers

for Heating and Air Conditioning

Load Evaluation

Tlios . B . Rom i ne , Jr .

Romine & Slaughter, Inc. Consulting Engineers

Fort Worth, Texas

Although digital computers are ideal for heating and air conditioning load eval- uation, their practical application for the majority of engineers involved requires

establishment of appropriate restrictive parameters, for consideration of a wide

range of load types and sizes, but with small to medium-sized installations. Mini- mum requirements include orientation to current ASHRAE methodology, utilization of basic formulae versus tabular or approximated data, sophisticated evaluation of

t i me- va r iable factors, controlled flexibility for various system types, load accumulation into designated sub-systems with varying conditions and diversities,

simplified input data, calculation of "end-use" data for equipment selection, and printout of input factors and results in complete, concise form for record purposes

plus immediate engineering use. Limitations include tailoring software to readily

available hardware with limited core storage, compressed overall time-frame per load calculation, and availability in terms of low acquisition and operating costs. The

APEC HCC program, with certain modifications, solves this particular problem superlatively. It operates efficiently on an IBM 1130 8K single disk system, and is available to APEC members for under 2% of development costs. It determines simul- taneous peak loads from 24 complete hourly calculations, each involving time lag and

thermal storage factors, calculated solar shading variables, hourly temperature and humidity profiles, time-variable internal loads, external and internal surface loads,

ventilation and infiltration, interrelation of varying space requirements, etc. A single "Building" calculation is limited to 39 individually variable "Zones" (air

systems), and 1000 "Rooms" (basic areas). Exterior and interior load surfaces are

limited to 20 "Types" each, accessible to any "Room" being evaluated. Output presents

detailed cooling, heating, and humid i ficat ion totals and supply air cfm for each

Room, Zone, and Building level, arranged for "stand-alone" 8^" x 11" permanent

record of the load evaluation, and adaptable as input for various planned systems

analysis programs.

Key Words: APEC, calculated shade ratios, design load calculation, diversity

data, HCC, hourly evaluation, input simplification, minimum personnel qualifications, operational output variations, output self-explanation, practical

considerations, small computers.

1 . I nt roduc t i on

The application of digital computers to the solution of heating and air conditioning load evaluation problems is ideally suited to the needs of concerned practicing engineers. In today's glass

buildings and with the transient nature and varying requirements of building occupancies, there is simply no other practical way to arrive at a true simultaneous peak load condition.

The difficulty is obviously not one of technique, since the basic heat transfer calculation methods

have been worked out for some years and found to be both reliable and easy to use. These procedures are

also continually being polished and honed by the standard of the industry, ASHRAE, which carries out the parallel benefit of physical testing for theoretical correlation.

The only real problem of course is time, which from the standpoint of the consulting engineer in particular is all that he has to sell and therefore all important. Any good engineer, given enough

time, could come up with just as valid and as accurate a load evaluation as the most sophisticated

computer program on the largest installation. Both his design and the building itself would have be- come obsolete in the meanwhile, however.

241
2. Problems £ Prospects

2.1. Pre-Computer Compromises £ Pitfalls

Tlie practice in the past, therefore, has of necessity been one of educated compromise. The ex- perience and judgment of the engineer have been the controlling factors, without benefit of a myriad of comparative calculations, each taking into account a variety of changing conditions. Pre-calculated

tabular data has taken the place of detailed formulae. Single-run load calculations for an assumed

peak load period, with liberal safety factors to stay out of trouble, have been the order of the day.

Time-lag, storage-effect, and variations in effectiveness of external shading on glass have been mis- trusted, guessed at, or ignored. Only rarely has the importance of the project - and the size of the

fee - been such that any significant amount of detailed comparative calculation could be considered.

Since most systems do work, it therefore must be concluded that the building owner historically has bought, unknowingly, an environmental control system to some degree larger and more expensive than the circumstances actually justify.

Another continuing problem for the consulting firm, or for anyone else with a necessity to calculate heating and air conditioning loads, has been that the very personal nature of this type engineering

task is extremely vulnerable to both individual and parochial habits - not always to the best interests

of either the firm doing the calculating or the ultimate client. Even with standardization of pro- cedures and careful checking of results, undesirable deviations are bound to creep in undetected from

time to time. Thus we find the second major practical benefit of using digital computers, where the approved procedures can be "frozen" in a program and thereby remain beyond the misapplication or forget- fulness of the individual user.

Not to be ignored is the aspect of accuracy. No engineer has failed to experience the misplaced

decimal, the incorrect addition, or the inverted slide rule operation. Too often the ultimate detection

of an error of this type results in a vast amount of lost time and duplicated effort for its correction,

not to mention those errors which remain hidden until after they are constructed and in unsatisfactory

use. If just one error of the latter variety can be eliminated, a considerable amount of money and effort toward a computerized operation can be justified.

2.2. Computer Use Deterrents

If all this be true, then why not an immediate conversion by all engineers to automated procedures?

The controlling factor is really the same, in a slightly different form - overall cost, or perhaps the assumed probable cost.

It is obvious of course that many, if not most, engineers would find it difficult or impossible to afford even the smallest computer installation at today's market prices. Similarly, even if acquisition

cost weren't a factor, only the largest firms could keep even a small installation busy enough to justify the day to day expense of its existence. It therefore follows that in most cases the average engineer will have to rely initially on service bureaus, time-sharing terminals, or time-rental on available installations in nearby offices. The probable result is that experienced, capable, computeroriented personnel will not be continuously available as staff members.

A parallel factor is that, since most computer use by engineers for HVAC load evaluation will represent only a relatively small amount of his total work time regardless of the circumstances, he normally will have neither the opportunity nor the inclination to become more than superficially in- volved in either computer operation or computer programming. Similarly, his use of computers in any

form is likely to be less than constant or day-to-day, which reduces the complexity of details he can

be expected to master and retain for such operation.

2.3. Computer Use Requirements

Still another aspect is that of the short supply of technically proficient and experienced man- power in general. Since experience can only be gained as a direct function of time, it follows that

the most desirable program will have much of the necessary "experience factors" built in, so that less experienced personnel can be used in "feeding" basic and easily understood data to the computer. If successful, this approach frees the most experienced men for other more pressing duties, while expanding

the overall work-producing capability of the firm.

The type and arrangement of output information is also a critical factor. The very nature of engineering, as related to the construction of systems from engineering design, requires the engineer

to be an inveterate record- keepe r . Limits of legal liability for an engineer's work vary from place to place and from a few years to forever, which requires that old records be clear and self-explanatory

regardless of the passage of time. Another and happily more frequent need for good design records is for the intelligent and efficient future expansion of projects. A third factor arises on those projects

where a design analysis must be presented to the client as part of the engineer's service. All of these however are secondary to the basic first need for the data, which is to present to the engineer the

242
answers required to complete his design, in a form directly usable by him without extensive further

manual manipulation, and arranged in such a way as to minimize the possibility of data misinterpretation

by the engineer or his subordinates. In this same vein, the engineer should have some degree of control over the volume of output for any given calculation, consistent with the importance of the project and

the necessity for in-depth data presentation.

The problem of available software cannot be overlooked. Most engineers know exactly the type and amount of design data they must create and retain for any project, and largely because of ASHRAE's

influence over the years, these details are reasonably similar from office to office. Most HVAC engineers however are not programmers and most programmers are not HVAC engineers. The costs associated

with developing an adequate program in-house are completely out of the question for any but the largest

firms. The average engineer must therefore obtain his software from some outside source, and must search out the available programs for the one most suited to his taste, budget, and method of operation.

Once found, of course, any program must be sufficiently studied and tested by the engineer to make him

comfortable in its use and confident of its results.

From this combination of benefits to be obtained versus overall costs and other limitations there evolves a pattern, within which any automated procedure must fit before it can be considered a practical

application for general use in heating and air conditioning load evaluation by the majority of engineers.

It will be helpful at this point to summarize these factors.

a . The Sys tem Mus t

(1) Be based on the latest proven procedures and techniques, preferably ASHRAE oriented.

(2) Concentrate on the use of accurate basic formulae, versus tabular data or shortcut approxima t ions .

(3) Be capable of analyzing simultaneous load factors, both internal and external, at time intervals not exceeding one hour throughout a typical day, and determining by the use of such data the

peal load condition.

{k) Be sufficiently flexible to permit the engineer a wide range of options in establishing type

of system, space relationships, time variables, load diversity at various levels of load accumulation,

and special internal and external factors, in addition to the physical properties of the environmental

surfaces

(5) Be fast, not so much from the standpoint of program run time (although this is important) as from that of overall time required from beginning of input data assembly to receipt of final printout.

(6) Be sophisticated in operation, but simple to input, to make maximum use of the capabilities of

lesser trained personnel for input purposes, with automatic elaborate evaluation of basic information by

the program.

(7) Be complete but concise in output data, with basic input factors as well as final results presented in a self-explanatory mannor, and with optional additional output of detailed backup data whe re des i red .

(8) Be available, both hardware and software, at a reasonable cost and in a form capable of producing useful results from the moment of acquisition and/or access.

2.k. A Practical Solution

Fortunately, these very problems have been substantially solved by one of the organizations

sponsoring this symposium - APEC, or Automated Procedures for Engineering Consultants. This group, with

cooperative effort and financing, commissioned the writing of a unique heating and cooling load calculation program by Bruce E. Birdsall, William 8. Deeming, and Tseng-Yao Sun (l)'. The program, known as HCC, is excellent, easy to use, sophisticated, ASHRAE oriented, designed to run on as small an installation as the readily available IBM 1130, and is distributed to members at approximately 1% of the program development costs. Released in source deck form with complete documentation, it obviates the "black box" onus sometimes associated with canned programs which may be used for a fee but which are not revealed in detail. It is this program, with numerous user-oriented modifications developed by the author, that is presented herein as a practical application of small computers for heating and air

conditioning load evaluation (similarly limited to APEC members).

Figures in parentheses indicate references at the end of this paper.

243
3. Description of HCC

3.1. Genera I ly

The technical authenticity of HCC is its almost total dependence upon ASHRAE for methodology. All

of the basic load calculation algorithms are based on the ASHRAE 1967 "Handbook of Fundamentals" as the

latest and most complete generally accepted and available source of reliable information. Tabular data

is scrupulously avoided except for empirical values used as input in various formulae, such as values of

t ransm i ttance and absorptance for different glass types, pre-ca leu lated "U" factors for combinations of building and insulation materials, sensible and latent heat generation of occupants for different types of activities, and the like.

The program is design oriented for peak load determination, as opposed to an energy analysis tool. Hourly cooling calculations are made for all 2k hours of a typical design day for a selected month,

with varying solar loads, temperatures, ventilation, infiltration and internal loads, and with peak load selection and printout. Heating calculations are made and output for a single given set of conditions.

Loads are calculated and presented in a form primarily suited to some type of constant volume air system.

3.2. Input Capabilities

Flexibility and simplicity of use in practice can best be explained by reference to the program in- put da ta as fo 1 1 ows

a. Permanent Data

Permanent data is input one time, and stored in protected disk files for use by all calculation runs.

Its use is geared to the input simplification philosophy of the program, in that while remaining readily

available for possible future revision, this data can normally be taken for granted after initial input. Included in this category are:

(1) Solar Radiation data including Equation of Time, Solar Declination, apparent solar irradiation

at air mass = 0., atmospheric extinction coefficient, and a surface to sky radiation constant, for the 21st day of each month, for use in calculating hourly values for such days of direct normal intensity,

direct i ntens i ty , and diffuse intensity on horizontal and vertical surfaces (2).

(2) Absorptance and transmi ttance coefficients for up to 20 different types of single and double

glaz ing (3) .

(3) Transmi ttance and shading coefficients for four profile angles of each of four representative

types of solar screen material.

b. Semi -Permanent Data

Data in this group is permanent in the sense of its relationship to a specific geographical loca- tion, and may optionally be left on disk file or read anew for each different project. In practice, the data requires preparation only once for any given site with its own unique conditions, and the cards re- tained on file for re-input on subsequent runs in the manner of control cards. Input includes:

(1) Project Latitude, in degrees, for solar angle calculations.

(2) Ground Reflectivity Factor, for use in calculating solar heat gain factors.

(3) Inward Flow Fractions, for use in calculating overall heat transfer coefficients for glass, as affected by interior air motion. Fractions are input for still air, an increased factor for air being

supplied under the glass at the sill line, and a further increased factor for sill supply located be- tween the glass and a drapery.

(k) Clearness Factor, for calculating solar intensities in various atmospheres; ranging from 0.8

in smoggy industrial areas to 1.2 in very clear regions.

(5) Maximum Solar Heat Gain Factor, in Btu/hr/sq. ft., as an arbitrary limit for consideration of interior shading of glass surfaces. When interior shading devices are specified (with window data,

later) such as Venetian blinds, draperies, etc., the program assumes they will be left open when their

use is not required for interior comfort. Only when the solar heat gain factor reaches this pre-set

limit does the program assume the occupants will close the shading device, and thereafter takes it into account until the heat gain without it is once again less than the limit.

(6) Degrees from Standard Meridian, to allow a true sun time and hour angle to be calculated.

244
(7) Daylight Saving Time input factors, as signals as to which months, if any, are so affected,

for calculation of true sun time values.

(8) Temperature and Humidity Ratio Data, in deg. F. and lbs. moisture/lb. dry air respectively

are 2k hour cooling load outdoor weather profiles for a typical design day in each of the 12 months,

c. Master Data

Master Data is input once for each job, and stored in temporary disk files. It is similar to the permanent data in that, as its name implies, it is geared to input data simplification by establishing

master factors for an individual project which can either be accessed by a space unit being analyzed, or which will apply automatically in all cases unless specifically over-ridden.

(1) Job Identification Data, in alphameric form, is used to prepare a title sheet for the printout,

and to identify each printout page as to job number, job description, and date of calculation.

(2) General Building Design Data (fig. l).

(a) Hours for Calculation. Any 12 hours may be selected, inputting numbers from 01 to 2k. Although load calculations are made for each of the 2k hours to account properly for hour averaging,

only the results for the 12 hours selected will be stored and used in final load determinations. This

is a compromise to permit the program to run on a small installation.

(b) Hour Average, as the number of hours over which all radiant portions of the heat gain are

to be averaged, due to storage effect. Convective load components are considered as instantaneous

loads

(c) Heating Design Month, to designate a heating month for calculation of solar gain so as to indicate when such heat gain can exceed heat losses.

(d) Winter Outs i de- I ns ide Temperature in deg. F. and Humidity Ratios in lbs. moisture/lb. dry

air are for heating and humid i f i cat ion design calculations in the conventional sense.

(e) Cooling Design Month, to cause the program to use that temperature and humidity ratio

profile stored for such month, as originally input as semi -permanent data (par. 3-2. b).

(f) Cooling Outs ide- I ns ide Temperature and Humidity Ratios are design values, with inside

conditions considered to be fixed. The data input for outside conditions however are considered to be peak values of the respective profiles for the selected month, and such profiles will be raised or de- pressed by the difference between the input peaks and the stored peaks. This permits minor adjustments

of stored data without re-input of the entire weather file.

(g) Rotate Building Off South. To facilitate data input, all building exposures are taken

off as though "Plan North" were true north, in terms of azimuth deviation from south as 0°; i.e., north =

180°, east = -90°, west = +90°, etc. This master correction factor is then input so as, when added to

the assumed take-off azimuth, to result in the true azimuth, and is used by the program automatically to correct all related data. This is particularly useful in site-adapting buildings for various orientat i ons .

(h) Master Wall Height is a data take-off simplification factor, to permit the input of wall

lengths only for the various areas to be considered, and allow the program to calculate areas and volumes automatically with the master height. This factor can be over-ridden in several ways for nontypical situations.

(3) Master Internal Data (fig. 1)..

(a) Occupancy Load Factors, as Sensible and Latent BTU/ Nr. /Person (5).

(b) Hour In, "From-Through". The numeric hour designation, 01 to 2k, of the first and last hour in which the occupancy load is to be included. Hours used do not have to fall within the selected

calculation hours. Also applies to lighting and appliance loads.

(c) Occupant Loading. An optional factor to assign occupants to Rooms on an area basis, and

an optional over-ride limit for total simultaneous occupancy in the project. The program will pyramid occupancy data in accordance with other restraints, but will reduce the aggregate to this limit if exceeded .

(d) Lighting. An optional input reducing factor, to assign lighting load on the basis of

area, and an optional factor to relegate the input percentage of the lighting load to return air, rather than have it become a part of the room load and thus affect the room cfm calculation. The deferred load is re-added after the affected room loads and cfm's have been summed into zone groups as

later discussed.

245
(e) Infiltration. An optional factor for inclusion of infiltration in the load calculation

for each room, both heating and cooling, based on the calculated room volume, and a multiplier which will

be used to diversify a pyramid total of infiltration loads at the building summary level.

(f) Ventilation. A series of factors, each used to calculate an outdoor air cfm value for a specified air system. The program will compare the results, and use the largest value for load purposes.

J.. Air Changes Per Hour, Cfm Per Sq . Ft., Cfm Per Person. Conventional ventilation rate factors .

2^. Maximum Sq . Ft. Per Person. A form of diversity factor which can be used to reduce overall ventilation on a cfm/person basis, by limiting the density of occupancy for purposes of ventilation calculation only. The result of this calculation, if less than that resulting from the calculated occupancy on any other basis times the cfm/person factor, will supersede the latter.

(g) Diversity Factors. A series of optional decimal multipliers which will be applied to the respective building totals for lighting, people, and appliances, to prevent unrealistic pyramiding of

loads for the entire project.

(h) Supply Air Master D.T.R. A fixed dehumidified air temperature rise in degrees F. for supply air Cfm calculations. Admittedly, one of the practical compromises in the program in its present

form, but effective for most applications.

(i) System Type. An optional factor, to differentiate between system types as to chilled water or direct refrigerant expansion. If the former, the program will add 2.0% of the total project

sensible load to account for pump horsepower; otherwise, no effect.

d. Master Building Shell Data

Data for the various environmental surfaces, or the building "shell", are input once for each type

as master data and stored on disl<. Up to a maximum of twenty (20) different types for each shell classification can be considered, each accessible by assigned type number as needed. Alphameric descriptive

data is input for each shell data type for identification listing in the output (fig. I).

(1) Exterior Walls. Any vertical opaque fixed surface between the conditioned space and the outs ide weather

(a) Decrement Factor; Time Lag. Data for calculation of equivalent temperature differentials

(6).

(b) Color. Color of exterior surface, as "L" (light), "M" (medium), or "D" (dark), for varying effect of solar intensity on wall load.

(c) "U" Values. Conventional heat transmission coefficients in BTU/Hr./Sq. Ft./Deg. F. for

the particular wall construction involved, winter and summer (7).

(d) Below Grade BTU/Hr./S.F. Direct heat loss factor for sub-grade walls, used in lieu of

"U" factor and temperature differentials (8). Not used in cooling load calculations.

(2) Exterior Roofs. All data similar to that for walls, without of course any sub-grade factors.

(3) Interior Partitions. For the purpose of evaluating heat transfer to or from adjacent interior

unconditioned spaces. Doors in interior partitions are considered insignificant, and included as a part

of the gross wall area.

(a) "U" Value. As for walls and roofs.

(b) Temperature of Non-Conditioned Space. The arbitrarily selected temperature, winter and summer, of the adjacent space, in deg. F. Different temperatures for the same partition construction in different locations would be considered as different partition types.

(h) Floors and/or Ceilings. Any horizontal surface between the conditioned space and an adjacent

unconditioned area.

(a) Air Space Beneath, Winter and Summer. "U" values are conventional for the floor and/or

ceiling construction. Temperature inputs are those of the unconditioned areas, above and/or below the conditioned space, assumed as outside design values if left blank.

(b) Slab Below Grade. Direct heat loss factor in Btu/H r . /Sq . Ft . as for sub-grade walls (8),

in lieu of a "U" value and temperature differential calculation.

246
(c) Slab on Grade. Direct heat loss factor for exposed slab edges in Btu/h r . / 1 i nea 1 ft. (9).

(d) Both Floor, and Ceiling Exposed. An indicator signal that the same exposure occurs both above and below the conditioned space, causing the calculated load to be included twice.

(5) Exterior Doors. "U" value and door area input are used with exterior design temperature values

for load calculations. Areas are also used to facilitate calculation of net exposed wall areas as dis- cussed later. Cfm infiltration input is optional, for heating calculations only, and will supersede

other infiltration values if greater (10).

(6) Windows. Any vertical glass surface between the conditioned space and the outside weather.

Each unique combination of glass size, material, and interior and exterior shading factors constitutes a separate window type.

(a) Glass Type. Input is a type number which calls up Alpha and Tau coefficients for a particular glass material, thickness, and/or multi-pane combination from storage in permanent disk data

files. For glass types other than those on file, the Special Glass Shading Coefficient is input alternatively as a compromise method of approximating glass solar characteristics (11).

(b) Height and Length dimensions, in feet and tenths, are for the gross window size and are

used for transmission loads and for the mathematical framing of the glass area for calculation of sunlit and shaded portions thereof. Net glass area for solar gain consideration is calculated by use of

the Percent Open Area input factor applied against the gross area.

(c) "U" values are for transmission calculations for winter losses (12) and for summer gains

with and without interior shading devices (13). Values are increased for wiping effect of air stream

(14) on inward flow fraction of transmission coefficient, if input indicates supply air will be ad- mitted below the glass or between the glass and an interior shading device.

(d) Inside Shade Coefficient. The decimal effectiveness of the interior shading device, if any, in reflecting solar radiation (15)-

(e) Exterior Shading effectiveness of overhangs and attached side fins or projections is a calculated value. Sizes of such devices and their dimensional relationships to the glass surface are

simple input distances in feet and tenths, and are used to complete the three-dimensional mathematical

representation of the window and shading surfaces. This model is then used with the various glass

orientations and hourly solar angles for the selected load month to calculate the actual shade pattern

under any condition, and to reduce the solar radiation load component representatively (16).

e. Space Relationships and System Definition

As a program oriented to a constant volume air system, loads are accumulated and individually time- evaluated in three levels, "Room", "Zone", and "Building".

(1) The "Room" is the basic space unit for which specific input is defined as to size, internal

loads, and number, type, and orientation of any exposed surfaces.

(2) The "Zone" is a group of "Rooms", input specified, to be considered as a single air system,

at which level ventilation rates and loads are calculated and considered.

(3) The "Building" is a grouping of all "Zones" for overall consideration.

During initial planning the sponsoring organization, APEC, determined after considerable study of available hardware, that the best interests of most engineers would be served by a program which could

be run on a relatively small installation (and with relatively simple modifications on larger systems as well). The IBM 1130 was found to be the machine most frequently being installed or considered in most engineering offices, and one which could accommodate most of the desired and all of the necessary

features of HCC. A minimum configuration was thus established to include an 8K memory, single disk

drive, card reader-punch, and 1132 line printer. This decision dictated the principal program restrictions to a maximum of 39 Zones, 1000 Rooms, and 320 Rooms per Zone.

The assignment of "Room" areas to specific "Zones" or air systems is also master data in the sense

of pre-defining the space framework, and placing the information on disk file for later access at the time of Room load calculation. Individual characteristics of each Zone are included in such access for application to Room conditions.

(1) Zone Definition. Each Zone is given an individual number from 1 to 9999, as is each Room. Desired groupings of Rooms into specific Zones is accomplished by a series of input cards (fig. 1), each

listing a Zone number and up to five Room numbers. Each Room number is followed by a group of 10 alphameric characters to serve as a Room name, which data is stored on disk for output purposes whenever the

247
corresponding number is printed out. The principal value of room names is of course to enhance the "stand-alone" characteristics of the output, both for engineering use and for permanent record, by

eliminating the necessity of referring to plans or other related documents for identification.

(2) Duplicate Rooms. All Rooms must be defined as being included in some Zone. Input, run time, and output are all conserved however, in the case of two or more Rooms which are duplicates in size, exposure, orientation, and other load factors, by designating one of the group as a "Master" Room, and

listing all others as "Duplicates" of that Master. Having done this, it is necessary only to input Room

data for the Master Room, and the resultant load values will be assigned to the respective Zones for each duplicate Room as well. This procedure is reflected in the output in several meaningful ways.

(3) Zone Diversity Data. In most projects, such as hospitals, schools, office buildings, etc.,

the various air systems (Zones) are normally subject to some deviation in individual requirements from

the master data input. To account for these differences, each Zone is separately listed by number and identification name, and any deviations are noted.

(a) Zone Load Diversity Factors are optional decimal multipliers to be used on pyramid totals

of lighting, occupancy, and appliance loads for all Rooms in that Zone. If left blank, no diversity will

be taken at the Zone level.

(b) Zone Ventilation Factors, with regard to Air Changes per Hour, Cfm/Sq.Ft., or Cfm/Person,

are optionally input if it is desired to over-ride the building master factors for that Zone. If desired,

a fixed cfm value can be input for ventilation purposes, or the ventilation cfm may be set equal to the supply cfm, either of which will supersede any other ventilation data.

(c) Zone Inside Design Conditions. Master data input for Summer and/or Winter Inside temperature and/or humidity ratio may be over-ridden for any Zone as desired, and will apply to each Room in that Zone.

(d) Maximum Zone Occupancy may be input if desired, as an upper limit to the number of occupants accumulated from the individual Room loads. Final zone totals, on whatever basis, will be used in the initial Building summary.

(e) Zone Dehumidified Temperature Rise, in deg. F, may be optionally input if desired to supersede the master data value. Cfm values for each Room in any Zone will be calculated on the controlling DTR basis.

(f) Miscellaneous Factors. Indicator signals may be optionally input for the purpose of omitting either the heating or the cooling calculation for any Zone, which will apply to any Room in such Zone. A Safety Factor percentage may also be input for any Zone, should load data uncertainty warrant it, which will be applied to the Room load totals. A System Type indicator signal is used for recognition of duct heat gains and leakage and fan Hp load, as "1" for a low pressure system (adds k% to Room Sensible Heat), "2" for a high pressure system (adds 12% to Room Sensible Heat), or "0" for a room unit system (adding no additional load, and omitting cfm calculation) for all Rooms in that Zone.

f. Room Data

The "Room", as previously indicated, is the basic load building block upon and around which all other load data is built. It is the final phase of input, in which the specific load factors applying

to each basic space unit of the project are defined. As such, while complete and normally the most voluminous part of the input, Room data is strongly oriented to input s impi f i cat ion

One set of Room data is required for each Master Room defined, numerically identified, and con- sisting of one or more input cards depending upon the complexity of exterior exposure and extent of deviation from the master load factors. Input cards fall into three categories; Type I for Basic Room

Data, Type 2 for Special Internal Load Data, and Type 3 for Exposure Data (fig', l). An interior Room, with no vertical exterior exposure and which conforms to the cnaster internal load factors, requires

only a Type 1 card for complete input. Exterior Rooms with non-standard internal loads would require a Type 2 and at least one Type 3 card as well. Although there is no actual limit to the number of Type 3 cards which may be used for a given Room, most Rooms need just one, and only unusual exposure circumstances require more than two or three.

(I) Basic Room Data includes the minimum information required for spacial definition of the Room

to be evaluated, and to establish the calculation framework.

(a) Exposure quantity and Special Internal Load card indicator signals are input as required,

for the purpose of specifying the number and format of additional input cards which are to be read for this room.

(b) Room Dimensions are for area and volume calculations, and require lineal input only in ft. and hundredths. Room height need not be input unless it deviates from that in the Master Data.

248
(c) Roof, Floor, and Partition exposure is indicated by Type Number, if any, thus calling out

of file the stored thermal characteristics and/or related data for the material or materials in question.

Area inputs for Roof and/or Floor exposures are required only if such data is not equal to the product

of Room length and width. Partition length input calculates area with room height.

(d) Cfm Infiltration is an optional direct load factor superseding any other input. Cfm

Exhaust does not affect load calculations as such, but is accumulated at the Zone level and compared

with ventilation calculation results, causing output of a warning message if exhaust exceeds ventilation.

(e) Number of People, Lighting Watts/Sq.Ft. and Special Hour Average are optional input

factors, to over-ride Master Data if desired.

(2) Special Internal Load Data is optional throughout, and necessary only to over-ride various Master Data factors for non-typical situations.

(a) Lighting Data. In addition to over-riding master values for hours of operation and/or

percent of light heat to return air, the exact Room wattage may be input if available which will supersede all other data. If lighting is incandescent, rather than the normal fluorescent predicated by the program, the indicator signal causes 80% of the lighting load to be considered radiant heat for hour averaging rather than 50% (17).

(b) Appliance Loads, in addition to "appliances" in the conventional sense, can represent any

form of sensible and/or latent heat generation within the conditioned space. Input is directly in Btu/hr., with specified percentages of the load to be considered as radiant for time averaging, or con- vective as instantaneous room load. Hours of operation may be input if varying from Master Data.

(c) Occupancy over-ride values may be input for non-typical load periods or metabolism rates.

(d) Minimum Room Circulation Rate may be input in Minutes/Air Change, which will increase the calculated Cfm value accordingly if Room sensible heat requirements are inadequate for the desired air

movement. If no input, the program assumes 30 minutes per air change to be the minimum acceptable rate.

(3) Exposure Data takes into account all vertical exterior exposures. Nominally, one card per specific orientation is used, except that complicated walls with a multiplicity of shell types may

require several cards for complete input.

(a) Wall Azimuth Angle is the exposure orientation in degrees variance from "Plan South" as 0° (west = +90°, east = -90°, north = 180°). The program will correct this input for actual orientation

of the surface by adding the Master Data deviation factor, and will use the corrected value for calculation of all solar angles for this exposure.

(b) Length of Exposure in ft. and hundredths is used with Wall Height to calculate gross area

of the exposed surface. It is also used directly to calculate slab edge losses, if so indicated by Floor

type input.

(c) Walls are input by Type number, to access stored thermal transfer data. Two different

wall types may be input per exposure card, but if so must also include individual net wall areas of each

in sq . ft. and tenths. If only a single wall type is involved, as is normal, area input is not re- qu i red .

(d) Windows and Doors are input by Type number (which includes area in stored data), and quantity count. Two different window types may be input per exposure card. The effect of external shading on windows may be approximated by input of time period during which complete shading is to be assumed in the calculations.

3.3. Output Capabilities

For best overall response to the goals of efficient immediate design use, presentation in design

analysis form, and permanent record keeping, all printout is formatted to fit on standard 85-" x 11" paper with binding edge allowances. A summary of Master Data (fig. 2) and Master Building Shell Data

(fig. 3) input, suitability identified, appears at the beginning of the printout. This is followed by a summary of Zone Diversity Data (fig. ^) , indicating the factors to be used by each Zone, whether

specifically input for it or the Master Data value if not over-ridden. All Room numbers are sorted in ascending order, and so listed along with the Master Room and Zone number associated with each.

The amount and nature of printed output for Room, Zone, and Building calculations is subject to considerable control by the engineer. Room calculation results for example may be printed out on a single line per Room, including Room number and name, hour of peak load, peak cooling values of sensible

and total heat gain in Btu/hr., supply air cfm and minutes/air change check figure, and heating losses

in Btu/hr. This type printout, although comparatively rapid, is somewhat limited in usefulness since

the associated input data and load component breakdown is not presented.

249
The normal Room printout (fig. 5) is considerably more useful, giving a complete record of all input factors (specific input and/or Master Data) contributing to the calculation as well as a thorough breakdown of the results. The underlying concept of practical, "stand alone" output format is perhaps best illustrated by this single sheet record of the basic load calculation unit.

(1) Complete Identification. The page heading identifies the firm or engineer responsible for the work, job number, job name or other related information, date of calculation, and page number in the overall data. Room number and name appears both at the top of the sheet as a conventional heading and

at the lower right corner for rapid location in bound form. Zone identification and the total number of Rooms for which this is a Master Room appears in the lower left corner.

(2) Complete Record of Load Factors. All input data from Room cards is printed out with appropriate headings, together with calculated results where standard factors or other parameters were

ut i I i zed .

(a) Areas are mirrored when input, or calculated as appropriate when not. Room area for ex- ample represents the product of input length times width, as do roof and floor areas if not specifically

input otherwise, and if a roof and/or floor type number was input. Partition areas are the product of

input length times wall height (input or master) as are exposed wall areas, except that related window

and/or door areas are deducted from the latter leaving a net value. All areas are represented in sq.ft.

(b) People are listed as the input quantity or the calculated quantity by Master factor if not

input. Lighting is presented both as total watts and wa tts/sq . f t . , with values deriving from whatever

specific input or Master data was permitted to control by the engineer.

(c) Hourly load factors for people, lights, and appliances are indicated as the input values

or Master data if no specific input. The value used for hour averaging purposes is indicated, re- flecting either a specific input or the Master value, including in the latter case a reduction of one hour for each exposure more than a single exposure (but never less than I hour).

(3) Complete Breakdown of Load Components. The peak cooling hour is indicated, and load values

for that hour listed for window, wall, roof, partition, floor (and/or ceiling), door, infiltration,

lights (% to room), people, and appliance load components, together with fan Hp and safety factor allowances if any. The percent of light heat to return air, if any, is deferred to the appropriate

Zone load as later discussed. Heating load components are similarly listed for exterior exposure

losses, with separate compilation of internal gain factors for comparative purposes. Winter solar gain

is also presented to permit complete evaluation as to when internal gains may exceed winter losses.

(k) Cfm supply air calculation is based on satisfaction of Room sensible heat with Zone dehumidified air temperature rise (DTR) . Result is compared with Room volume and minimum minutes/air change

factor (input or master), with the larger selected and rounded off to the nearest 10. cfm.

(5) Check Figures, for Load Verification. Cooling data includes Btu/sq.ft., Btu/cu.ft., and

sq.ft. Aon of refrigeration, as well as supply air checks by Minutes/air change and Cfm/sq.ft. Heating

data includes Btu/sq.ft., Btu/cu.ft., and Sq . f t . /MBtuh

In addition to this data, an option is available at the Room level for printout of hourly load values, by load components, for each of the 12 load hours selected (fig. 6).

After all Room calculations have been completed and hourly load totals assigned to the appropriate

Zones, the Zone printout occurs. Each Zone is presented on a single sheet (fig. 7), identified in a manner similar to that of the Room sheet. Since Zone diversity data is already an output record it is not repeated here, but is used to perform load evaluation as a complete air system serving a designated

group of basic load units.

(1) Ventilation Calculations. As an air handling system, the introduction of ventilation is assumed to take place at the air handling unit. Accumulated area, volume, and diversified people

quantities are utilized with the appropriate input factors to calculate ventilation cfm values. In the latter case, a comparative occupancy density is also calculated from the Master input limit value and

used with the cfm/person factor to produce an upper limit cfm for this basis. The highest cfm value is then selected as the ventilation rate for the Zone, unless over-ridden by a fixed Zone input value as zero, some finite amount, or 100% of the accumulated Room supply air cfm. The ultimately selected cfm quantity is then used for calculation of sensible and latent heat gain values for each of the specified

load evaluation hours, and for winter heat loss.

(2) Load component diversity input factors for this Zone are next applied to the accumulated

hourly load totals for lights (both Room load and return air components), people, and appliances.

(3) Hourly Zone cooling load totals are then created as summaries of Room load components (including diversification effect, if any), ventilation load values, and the return air segment of light heat. The peak total value is selected and printed out in complete load breakdown form. For reference

purposes, the accumulated load values for lights, people, and appliances before application of diversity

factors are also printed out. 250
(k) Heat loss load components are similarly printed out, including a separate accumulation of

internal heat gains. Btu/hr. equivalent of humid i ficat ion requirements is calculated to offset effects

of ventilation and infiltration air, and added to the heating subtotal for a comparative comprehensive

value. As with the Room loads, further comparative totals reflect the effects of internal heat sources

and external winter solar gain for the Zone.

(5) Checl<. figures for both cooling and heating values are presented in the same form as for Room

loads, but at two load levels; the Room total accumulation, and again after the inclusion of ventilation

and return air heat loads. Total tons of refrigeration is also indicated at the lower left sheet corner,

for rapid comparative evaluation by the engineer.

(6) Total supply air cfm to be provided by the system fan is indicated, representing a pyramid

total of supply air requirements for all Rooms in that Zone. A "Coil Air" cfm figure is also printed,

representing the ideal cfm required to offset the sensible heat requirements of the Zone at its peak

load condition, using the same dehumidified air temperature rise value.

As for the Room level, an optional printout is available for hourly values of all cooling load components, for each of the selected load hours (fig. 8).

An additional optional Zone printout is an "Air Side Analysis, by Rooms" for that Zone (fig. 9).

As such, it is principally geared to the practical use of the output data in the production of engineering design. Each Room in the Zone, whether Master or Duplicate, is listed on consecutive print lines by Room number, name, Room size in sq. ft. area and cu. ft. volume, supply air cfm, and minutes/air change

check figure. Zone totals for area, volume, supply air, and cfm check figures are indicated following

the final Room listing. Space is also provided for manual insertion of the inevitable Room number

change, as well as any desired change in supply air value. This sheet, together with a one-line duct

routing indication on a floor plan, is all the information required by the duct designer to produce his work.

As each Zone is printed out, its significant physical data and hourly load component values are

summed into the Building level for final diversification and evaluation. The type of data and pre- sentation format (fig. 10) is very similar to that for the Zone level. Building master diversity

factors and/or over-ride limits are applied to Zone totals, whereas cfm values for supply air, exhaust

air, and ventilation air are direct summaries of Zone results without modification. Infiltration totals

are diversified or not according to the input data. Check figure data are similar to Zone figures, and

based on the true simultaneous total loads. An hourly printout similar to that at the Zone level is available as an option for presentation of Building cooling loads.

k. Future Potential

The entire thrust of HCC is to solve the design load calculation problem in a comprehensive manner,

with output geared to direct and immediate use by the engineer. In this achievement however it is obvious that the present useful results, no matter how valuable, are only a weak distillate of the powerful data within the program not yet directly usable.

The physical space definitions for example need little else to be suitable for lighting calculations, with resultant wattage data then available for original load calculations or the refinement of

pre-ca leu lated data. With a minimum of supplemental space relationship definition and operating

parameters, the Room, Zone, and Cfm data can be used for design of duct systems, as can the Zone and Building load data for design of piping systems. Spacial comparisons are a logical next step, with pre- diction and/or avoidance of interferences between ducts, piping, lighting fixtures, beams, etc. From

this point, the useful extension of interrelated data to embrace all building design disciplines is in- evitable, and the benefits to be obtained virtually limitless.

The bridge to this development is the creation of a comprehensive computing system with a common

data base, with entry available at a number of different points, each having access to data created by other disciplines and with the capability to modify and/or supplement such data appropriately with its own output. Just such an approach, known as the Computer Aided Building Design System (CABDS) is currently in initial development by APEC, and descriptions are appearing in current literature. Although of necessity geared to considerably larger hardware for full implementation, the system will also

be capable of partial operation on the small 8K installations and thus retain a practical availability

to the entire user spectrum.

Along parallel lines, the new ASHRAE response factor algorithms present an improved technical approach to both design load calculations and thermal energy analysis. This approach is under continuous

evaluation by APEC, and will without question be incorporated into HCC as it is adapted toward use in CABDS. In the meanwhile, the current usefulness of HCC as a practical design tool is a substantial step

forward in the development of the art, and a reassuring plateau upon which to regroup forces for the next breakthrough.

251
5. References

Birdsall, Bruce E., Mechanica) Engineer, (10) Technical Director, APEC, Dayton, Ohio;

Deeming, William 8., Architectural Engineer

and Programmer, Skidmore, Owings & Merrill, (II) San Francisco, California; Sun, Tseng-Yao,

Mechanical Engineer £• Vice President, Ayres,

Cohen & Hayakawa, Los Angeles, California. (12)

Table 8, p. 476, and intensity formulae,

p. his, ASHRAE Handbook of Fundamentals (13) (1967) .

Table 10 and solar heat gain formulae, p. 479, ASHRAE Handbook of Fundamentals (1967).

Table 20, p. 486, ASHRAE Handbook of Funda- mentals (1967).

Table 30, p. 497, ASHRAE Handbook of Funda- mentals (1967).

Table 27, p. 492, ASHRAE Handbook of Funda- mentals (1967).

Fig. 5, 6, 7, p. 412, 413, ASHRAE Handbook of Fundamenta Is ( 1967) .

Table 12, p. 480, ASHRAE Handbook of Funda- mentals (1967).

Table 18, p. 453, ASHRAE Handbook of Funda- mentals (1967) .

Table 9, p. 477, ASHRAE Handbook of Funda- mentals (1967).

(14) Discussion, p. 477-480, ASHRAE Handbook of Fundamenta Is (1967)

(15) Tables 15, 16, 17. p. 482; fig. 7, 8, 9,

p. 482, 483; Table 19, p. 485, ASHRAE Hand- book of Fundamentals (1967).

(16) Sun, Tseng-Yao: Shadow Area Equations for Window Overhangs and Side Fins and Their

Application in Computer Calculation.

(ASHRAE Transactions Volume 74, I968)

Table 29, p. 496, ASHRAE Handbook of Funda- mentals (1967).

Tables 4, 5, 7, 8, p. 435-440, ASHRAE Hand- (17) book of Fundamentals (1967).

Table 1, p. 460, ASHRAE Handbook of Funda- mentals (1967).

Table 2, p. 460, ASHRAE Handbook of Funda- mentals (1967).

(15)

252
HEATING DESIGN DATA SPECIFY HOURS FOR CALCULATIONS

lEMPERAtURE

COOLING DESIGN DATA GENERAL

BUILDING DESIGN DATA

OCCUPANCY LIGHTING INFILTRATION VENTILATION TYPE t ^

MASTER

INTERNAL LOAD DATA

MASTER DATA

DESCRIPTION

EXTERIOR WALLS

DESCRIPTION MI EXTERIOR ROOFS

OESCRIPTlON WINTER SUMMER

INTERIOR PARTITIONS

DESCRIPTION AREA OF C FM

DOOR INFIL SO FT {WINTER)

EXTERIOR DOORS

TYPE DESCRIPTION

AIR SPACE BENEATH NOT USPENDEO WINTER SUMMER

9 ^ 6l 7

1 1

1 1 FLOORS AND/ OR CEILINGS

MATERIALS, CONSTRUCTION. OR

OTHER SPECIAL COMMENT

DIMENSIONS "U" VALUES

SHADING HEIGHT LENGTH COEfF SUMMER WINTER

Z 9 1-0 5 ft 1 1 if

WINDOW

DESCRIPTION

OVERHANG LEF T F IN RIGHT FIN

eOTTOM

s \ 9 \ 1 -

MASTER BUILDING SHELL DATA

ROOMS N ZONE ( 0 ZONE NUMBER 1 Z 3 4 5 NUMBER NAME NUMBER NAME NUMBER NAME NUMBER NAME NUMBER NAME

1

ZONE

DESCRIPTION

ZONE LOAD

OlVERSTY FACTORS (OPTIONAL )

ZONE VENTILATION FACTORS ZONE NUMBER

ZONE NAME OR nF^rRiPTioNTO OVER- RIDE BLOG MASTER DATA WINTER SUMMER OMITC (ADD) ff f 1 t r

DUPLICATE ROOM NUMBERS DUPLICATION

SPACE RELATIONSHIPS S SYSTEM DEFINITION

ROOM DIMENSIONS (FEET} AREA (FT)

3

ROOM

1 0

LIGHTI NG APPLIANCES OCCUPANCr C F M

HOUR ON TOTAL WATTS HOUR ON SENSIBLE LATENT HOUR ON

1 1 - 4

>5 s

BASIC ROOM

DATA

SPECIAL

INTERNAL LOAD DATA

3

ROOM

1 0.

AZIMUTH

+ WEST

LENGTH

OF EXPOSURE

(FT )

WALLS WINDOWS

DOORS EXTERNAL SHADE

A B a A HOUR 8 HOUR

3 ;5 t

EXPOSURE DATA

NOTE: HEAVY VERTICAL LINE INDICATES DECIMAL LOCATION ROOM DATA

Figure 1. Room Data

253
MARGIN FOR TOP BINDING

o

ROMINE & SLAUGHTER. INC. » CONSULTING ENGINEERS FORT WORTH, TEXAS

JOe 565/e NBS/ASHRAE/APEC SYMPOSIUM * SAMPLE PROBLEM 11/30/70 »* PAGE 1

GENERAL BUILDING DESIGN DATA ««»»»«««»«»*«»«««#«»*«»»«

HOURS TO BE CHECKED FOR PEAK COOLING LOAD 9 10 11 12 13 14 15 16 17 18 19 HEAT ING MONTH OUTSIDE

(SUN DB HUMID.

LOAD) TEMP. RATIO1 10.0 0.0013

INSIDE

DB HUMID.

TEMP. RAT 10- 75.0 0.0092

COOLING

MONTH OUTSIDE

OF DB HUMID.

CALC. ThMP. RATIO8 100. U 0.0156

INSIDE

DB HUMID.

TEMP. RATIO78.0 0.0103 MASTER CONSTRUCTION FACTORS

HOUR ROTATE BLDG. OFF SOUTH. WALL

AVG. DEGREES (EAST-. WEST+) HT.

5 -19.0 9.0

(NOTE —HTG. CALC. MADE FOR LISTED DATA ) (ONLY. COOLING CALC. MADE FOR EACH HOUR I (IN CALC. MONTH (OUTSIDE DATA INPUT ARE ) (UPPER LIMITS OF DAILY WEATHER CURVES). )

o

MASTER INTERNAL LOAD DATA

**-ft*******it*************»

OCCUPANCY

BTU/PERSON— HOURS IN- SF PER SENS. LATENT FROM THRU PERSON

220. 230. 9 17 100.

LIGHTING

WATTS PERCENT-

/SF— TO RET.

5.0 60. AIR

INFILTRATION CHANGES MULT. FACTOR

PER HR. FOR BLDG TOTAL 0.0 1.00 VENT ILATION CHANGES CFM PER CFM PER MAX SF PER

PER HR. SF PERSON- PERSON

2.0 C.25 25.0 125. BUILDING LOAD DIVERSITY FACTORS

MAX. PEOPLE MULTIPLIERS. TIMES SUM

IN BLDG. OF ZONE TOTALS

(OVER-RIDE) LIGHTS PEOPLE APPL.

90. 0.90 1.00 0.75

DEHUMID

TEMP RISE. DEGREES

22.5 SYSTEM TYPE0 = D.X.

1 = CH. WTR.

(NOTE —ALL MASTER INTERNAL LOAD FACTORS. PLUS HOUR AVERAGE AND WALL HEIGHT ) (FACTORS. MAY BE OVER-RIDDEN BY SPECIAL DATA INPUT ELSEWHERE. IF NO SPECIAL)

(INPUT. THESE FACTORS WILL BE USED. DIVERSITY FACTORS ARE OPTIONAL. )

MARGIN FOR STANDARD 3-HOLE BINDING

o

8 '/2" c^STANDARD SHEET SIZE

Figure 2. Typical Printout - Master Data

254
ROMINE & SLAUGHTER* INC. *# CONSULTING ENGINEERS FORT WORTH* TEXAS (^JOB 56b/B NBS/ASHRAE/APEC SYMPOSIUM * SAMPLE PROBLEM 11/30/70 »* PAGE 2

WALLS

## * # #

TYPE GENERAL DECREMENT TIME WALL- U FACTORS OL. " U r\ C NO.- DESCRIPTION FACTOR LAG- COLOR WINTER SUMMER 6TUH/SF~

1 4. BRICK, 8. TILE 0.39 5. D 0.33 0.31 0.0

2 LIKE 1 + PLASTER 0.39 6. D 0.29 0.28 0,0

3 12.C0NC. TO GRND 0.00 0. M 0.00 0.00 2,0

ROOFS

««•««»

TYPE GENERAL

NO.- DESCRIPTION FACTOR LAG- COLOR WINTER SUMMER

1 2. CONC. 2. INS. 0.69 5. D 0.12 0.11

2 LIKE 1 W/ CEILG. 0 • 6 9

a0 • ur\ r\u»iu^ r\ nno u»uy

PARTITIONS

»»««#»#»*

TYPE GENERAL U r-ACTOKS UNCuInD* AKcA ItMr* NO.- DESCRIPTION BTU/HR/SF WINTER — SUMMER

1 4. TILE TO STOR. 0.40 40 • 90 •

FLOORS »*»«

FLR. GENERAL U FACTORSf UNCONDlTIOiMEO SLAB LOSS FLR» CLG TYPE DESCRIPTION DlU/nK/or— AKtM It. nr. DLW oK UN oK — 0NLY=1

,

NO.- OF FLOOR WNTR sumr WNTR. SUMH. BTU/SF BTU/LF B0TH»2

1 4. CONC. » INS. .CLG 0.08 0.08 10. U. 0.0 0.0 0

2 4. CONC, CLG. 0.27 0.22 40. 90. 0.0 0.0 2

3 4. CONC. TO BSMT. 0.44 0.60 60. 83. 0.0 0.0 1 SLAB ON GRADE O.UO O.UO 0. U. 0.0 42.0 0

5 SLAB BLW. GRADE O.UO 0.00 0. U. 1,0 0.0 0 6 4. CONC. TO STOR. 0.44 0.60 60. 9U. 0.0 0,0 1 NOTE —ZERO OR BLANK INPUT FOR WINTER OR SUMMER TEMPERATURE

WILL BE CALCULATED AS OUTSIDE DESIGN n D V Q 1 1 1 Q o

Figure 5. Typical Printout - Master Building Shell Data

255
o

ROMINE 6 SLAUGHTER* INC. » CONSULTING ENGINEERS FORT WORTH. TEXAS

JOB 565/B NBS/ASHRAE/APEC SYMPOSIUM * SAMPLE PROBLEM 11/30/70 «* PAGE 7

ZONE DIVERSITY DATA »»»«««»-»«»»**«<«»

ZONE ZONE NAME- MULTIPLIERS. TIMES SUM VENTILATION FACTORS- NO.- OF ROOM TOTALS- CH6S CFM CFM- FIXED ALLDESCRI PT ION LIGHTS PEOPLE APPLI

/HR. /SF /PER VENT-CFM O.A. 1000 ENGINEERING AREA 1.00 0.90 1 .00 2.0 0.25 30.0

2000 REPRO. 6 MAILING 1.00 1.00 0.75 2.0 0.25 25.0 X 3000 PERSONNEL MNGMNT 0.95 1.00 1.00 2.0 0.25 25.0 0. ^000 SERVICE & STORES l.OU 1.00 1.00 2.0 0.25 25.0

5000 EXECUTIVE SUITE 0.85 1.00 1.00 2.0 0.25 25.0 2000.

6000 DISTRIBUTION 1.00 0.80 1.00 2.5 0.30 25.0

ZONE MAX I MUM ZONE INSIDE DESIGN COND.

ZONE AIR SYSTEM MISCELLANEOUSNO.- PEOPLE- WINTER — SUMMER DTR- 0=RM UNIT. OMIT PERCT

IN TEMP HUMI D. TEMP HUMID. DEG. 1=L0W PR.. CALC.

SAFT.

ZONE DEG. RAT 10- DEG. RATIO- F.— 2=HIGH PR. HTG CLG FACT. 1000 35. 75. 0.0092 75. 0.0092 22.5 1 10.0 2000 5. 75. 0 .0092 78. 0.0103 25.0 1 0.0

3000 «• 75. 0.0092 78. 0.0103 22.5 0 X 0.0 4000 «. 60. 0.0013 78. 0.0103 22.5 0 X 0.0 5000 60. 77. 0.0090 72. 0.0100 22.5 2 15.0 6000 18. 75. 0.0092 78. 0.0103 22.5 2 0.0

(NOTE—ALL ZONE DIVERSITY DATA IS OPTIONAL INPUT. TO OVER-RIDE BUILDING MASTER ) (DATA. AIR SYSTEM TYPE SHOULD ALWAYS BE SPECIFIED. TO ACCOUNT FOR APPROPRIATE ) (AMOUNT OF FAN HEAT. DUCT GAIN. + DUCT LEAKAGE — 0 FOR ROOM FAN AND COIL UNIT.)

(4 PERCENT FOR LOW PRESSURE DUCT SYSTEM. AND 12 PERCENT FOR HIGH PRESSURE DUCT ) (SYSTEM. ADDED TO ROOM SENSIBLE LOADS. SAFETY FACTOR IS A PERCENT FIGURE TO BE)

(ADDED TO ROOM SENSIBLE. LATENT. AND HEATING LOADS. = SUM OF ROOM TOTALS. ) (MASTER DATA LISTED IF NO OVER-RIDE INPUT. )

o

Figure 4. Typical Printout - Zone Diversity Data

256
JOB NO.

FIRM NAME

CALCULATION DATE

PROJECT TITLE

CALCULATION

PAGE NO;

R-QMINE £r SLAUGHTERt INC. »* COiNSULTIiMG ENGINEERS / \ FORT WORTH. TEXAS

JOB 565/8 NBS/ASHRAE/APEC SYMPOSIUM SAMPLE PKOBLEX 11/30/70 * PAGE 16

ROOK 201 PRINT ROOM DIMENSIONS

LENGTH WIDTH HEIGHT

16.00 12.00 10.00

ROOF- AREA TYPE 192.00 1 AREA

192.00

FLOORTYPE

4 AREA

192.00

PARTI TIGN

TYPE AREA

1 UO.OO

CFM

INPUT MIN

INFL EXH. A/C

0 1000 30.0

PEOPLE

IN HOURS- BTU/HR EA. RM IN OUT SENS LAT

2 9 17 220. 280.

LIGHTING

WATTS

TOTAL W/SF

960. 5.0

HOURS- PCT TO I^INCAND

ON OFF RETURN 0=FLUOR

9 17 0.0 0 APPLIANCES

HOURS- SENSIBLE HT PERCENT TO- LATENT HT PERCENT TO- HOUR

AVG.

ON OFF BTU/HR ROOM- RAD. BTU/HR ROOM- RAD. USED

9 17 12000.0 70.0 30.0 4000. 100.0 0,0 3 EXPOSED

AZIMUTH ANGLE EXPOSD WALL A WALL B WNDiv A WNDW a DOORSINPUT- ACTUAL LENGTH TP AREA TP AREA TP NO TP NO TP NU 180.0 161 .0 16.00 1 119.00 0 0.00 3 1 0 0 2 1 90.0 71.0 12.00 1 120. UO C 0.00 0 0 0 0 0 0

(NOTE - TIME (FIGURES ARE

( INCLUSIVE

EXT. SHADEFR TO FR TO

0 0 0 0

0 0 0 0 o

peak; LOAD DATA FOR ROOM 201. OCCURRING AT HOUR NO. 17-

HEAT GAIN —

SENSIBLE

WINDOW 1122. WALL 1733. ROOF 1412.. PARTITION 384. FLOOR 0. DOOR 216.

-INF ILTRATION 0. LIGHTS 3263. PEOPLE 439.

APPLIANCES 8399.

FAN HP(0.04) 678. SFTY FAC(O.OO) 0. SUB-TOTALS 17652. TOTAL HEAT 22212. DEHUMID TEMP RISE 25. RM CFM = 653. 7» 650. ««»»»

- HEATING

INT. GAIN

.{ B.TU./HR. )

CHECK FIGURES

( TOTAL HEAT 1 COOLING

115.7 BTU/SF

11.6 BTU/CF

103.7 SF/TO-\

HEATING

57.6 BTU/SF

5.8 6TU/CF

17.4 SF/M6H

0. 4560. 12782.

11057.

-1724. LOSS LESS INTERNAL GAIN

415. WINDOW SOLAR GAI>N -2140. NET LOSS—LESS INT. + SOLAR ««»»» FOR 3.0 MINUTES/AIR CHANGE. AND 3.4 CFM/SF

O

ZONE 2000 ROOM 201 PRINT ROOM

<

I-<Q

OO

<

I-<

Q.

IZ) >°

<

o

o

o

ir

Figure 5, Typical Room Load Printout

257
oJOe 565/B NBS/ASHRAE/APEC SYMPOSIUM « SAMPLE PROBLEM 11/30/70 * PAGE 17

LISTING OF ZONES IN WHICH ROOM 201 APPEA

-fi- * -& * ^t * <^ »t * * * J> -i.- * *- -R- kS (MASTER OK DUPLICATE). AND HOW OFTEN

ZONE ROOMS

2000 1 HOURLY COOLING LOADS. ROOM 201

;: * « •» PRINT

^t « * * ROOM

HOUR WINDOW

WALL

ROOF FLOORDOOR

L I GHTS

. PEOP ( S )"^APPL ( S ) I\FIL(S)

^PEOPiL) APPL(L) INFILiL)

TOTAL(S)*

TOTAL ( L )

ROO.V- TOTAL*

8 1^6.

105'*. 137.

0. 30.

0 .

0 . 0 . 0.

0 .

0 . 0. 1802.

0. lo02 .

9 310. 1020.119.

0. 61 . 2176.

244.

560 . 6719. 4U00 . 0.

0 . 11477. 4560 . 16037.

10 535. 1005.113.

0. 92 . 2720 . 342 . 560. 755V. 40U0 . 0.u

13267. 4560. 17827. o

1

723.

1002.

111.

0. 123 . 3263.

439.

560 . 83 9V . 40 JO . 0.0 . 15032. 4560. 19592 .

12 885.

1020.

119.

C . 154. 3263 . 439.

560. 6399 . 4000 . 0.

0 . 15254. 4560. 19o 14.

1 3 1012.

1127.

269.

0. 185. 3263. 439.

560. 8399 . 4000 .

0 . 0 . 15685. 4560. 20245.

lA 1086.

1273.

538.

0. 205. 3263.

439.

560.

3399 . 4000 .

0 . 0 . 16221. 4560. 20781 .

15 1113. 1A45.

859 . 0. 216.

3263 . 439 . 560 . 8399. 4000 . 0.0 . 16767. 4560. 21327.

16 1117.

1599.

1165.

0. 226. 3263.

439.

560. 8399 . 400U .

0 . 0 . 17259. 4560. 21819.

17 1122.

1733.

1412.

0. 216. 3263.

439 . 56U. 8399. 4000 .

0 • 0. 17652. 4560. 22<;i2.

1 8 1262.

1858.

1587.

0. 205. 1088.

195.

0 . 1679.

0 . u.

u

8592.

0. 8592.

19 1379. 2124.1672.

0. 185. 544.

97.

0. 839.0.

0.

0. 7516. , 0. 7516. o(» NOTE — SENSIBLE TOTAL AND ROOM TOTAL FIGURES

AND SAFETY FACTOR. LATENT TOTAL INCLUDES SAFETY

INCLUDE PARTITION LOAD

FACTOR.

, FAN HP.

HOURLY COOLING LOADS

ROOM 201 PRINT ROOM

(-^NOTE HOUR AVERAGING EFFECT)

Figure 6. Optional Cooling Load Hourly Printout

258
o

ROMIiNE f, SLAUGHTEKt If'iC. «* CONSULT liMG ENGINELKS

JOB 665/B NRS/ASHRAE/APEC SYMPOSIUM »

FORT WORTH. TEXAS SAMPLE PROBLEM 11/30/70 * PAGE 33

ZONE 2000 — REPRO. 6 MAILING

nt -/r if --t a * « * a ;! -K « s -f. it -ft *n

PEAK LOAD DATA.

WINDOW

WALL

ROOF PARTITION

FLOOR

DOOR

INF ILTRAT ION LIGHTS TO RM

PEOP( 6.) APPL I ANCES

FAN HP ( 0 . O'*

SFTY FACIO.OO

ROOM TOTALS

TOTAL HEAT SENS. RATIO (^VENTILATION ^ TOTAL VENT

LT HEAT TO RA ZONE TOTALS GRAND TOTAL

SENS. RATIO

OCCURK ING HEAT GAIN - SENSI BLE 2239.

5272.

1253.

959. 1344.

226.

0. 11402.

1099. 9899.

1347.

0. 35046. (S)

AT HOUR NO. COOL I NG LATENT

0.

1306. 3000.

4306. ( L )

16 HEAT LOSS - HEATING

LOSSES

293B . 15971

1622 . 2800.

4632 . 666 . 5264.

INT. GAIN

CHECK FIGURES

I TOTAL HEAT I

0. 33897. (H)

11402. + 1099. + 9899. + 1369. ++ - 2 37 72 . ( I ) +

CCOLING( T

38.4 BTU/SF

H.3 6TU/CF

312.2 SF/TON

HEAT 1 NG ( H

33.1 BTU/SF

3.7 BTU/CF

30.2 SF/MBH

39353. (T=S+L) 0.891 ( S/T

34689. (VS) 37451. (VL)

7 2 1 4 1 . ( V ) 783. (RA) 70519. (Z) 41758. (ZD

112277. (GT=Z+ZL) 0.628 (Z/GT

33897. (H)

102492 . ( Vri

136389. ( TH) 136389. I TH=H+VH

783. (R 783. IR

COOLING(GT

109.6 BTU/SF

12.2 BTU/CF

109.4 SF/TON

HEATING! TH) 133.2 BTU/SF

14.8 BTU/CF

7.5 SF/M8H

PYRAMID TOTALS

LIGHTS TO RM LIGHTS TO RA PEOPLE! 8.) APPLIANCES

BEFORE DIVERSIFICATION

11402.*

783.*

1759.*

13199.*

2090.*

4000.*

58692. WINTER HUM I D I F I C A T I ON ( WH

195081. TOTAL. WITH HUMID (THH=TH+WH)

111833. LOSS LESS INT. GAIN (TH-l-R)

822. WINDOW SOLAR GAIN

111011. NET LOSS —LESS INT. AND SOLAR

AIR UUANTITIESAREA VOLUME PEOPLE!* X D.F. P£OPLE(SF/125. )

1024. *SF AT 9216. CF AT

) 5. MAX. AT

8. MAX. AT

0.25 CFM/SF

2.00 CHANGES/HR

25.00 CFM/PERSON

25.00 CFM/PERSON

256. CFM.

3U7. CFM.

125. CFM.

204. CFM. !CFMPP LIMIT) VENTILATION AIR SET EUUAL TO SUPPLY AIR ! ALL U.A.) EXHAUST REQUIRED (NOT INCLUDED IN ABV

1460. CFM (FOR VENT LOADS) «»«»»»»•»»

LOADS) = 1650. »CFM (WARNING - EXHAUST EXCEEDS VENT CFM) INFILTRATION o

0.»CFM (COOLING)

75.*CFM (HEATING) SUPPLY AIR

ZONE PEAK LOAD

1460. *CFM, ««»»«»*»«*

9.3 TONS

!NOTE -

AND TOTAL COIL AIR =

SUM OF ROOM VALUES)

1300. CFM (AT ZONE PEAK.) *»««««*««« (D.T.R. = 25.0)

ZONE 2000—REPRO. £, MAILING

Figure 7. Typical Zone Load Printout

259
ROM I ^iE {, SLAUGHTER. INC. » CONSULTING ENGINEERS FORT WORTH > TEXAS

* * * ft » (^JOH 56b/B NBS/ASHRAE/APEC SYMPOSIUM * SAMPLE PROBLEM 11/30/70 «* PAGE 34

HOURLY COOL ING LOADS, ZONE 2000 — REPRO. & MAILING

F I RST SIX HOURS (SEE NEXT PAGE FOR LAST SIX HOURS)-

HOUR W I NDOW WALL ROOF FLOOR DOOR PARTN ZO.mE LTS ( RM

PEOP (S) APPL ( S ) INF IL t S) VENT ( S ) 1 0 I I KM • S 1 10 1 I ^ N O J GRAND

LTS( RA) PEOP ( L

APPL ( L ) INFIL(L) VENT ( L ) TOT(RM.L) TOT(ZN.L) TOTAL

8 237. 3054. 149. 1344. 30. 959.

0. 0. 0. 0. 4730. 6 007. 107 3 7. 0. 0. 0. 0. 37451

0. 37451. 48189.

9 blh. 2937. 130. 1344. 61 . 959. 560. 8099 . 0. 9460. 22286

3 2216. hlO. 1306. 3000. 0. 37451

4306. 41758. 73975.

10 9B^. 2887. 123. 1 344. 92 . 959.

S'+yi. 754. 8909. 0. 14191

25609. 40248.

548. 1306. 3000. 0. 37451

4306. 41758. 8 2006 >

11 13a 5. 2360. 120. 1344. 123. 959. o 10182. 948. 9719 . 0. 18921

28751. 48299.

626. 1306. 3000. 0. 37451

4306. 41758. 90057.

12 129. 1344. 154. 959. 113&0. 1081 . 9899. 0. 23652 . 30721. 55078.

705. 13U6. 3000. 0. 37451

4306. 41758. 96836 .

13 1987. 3558. 291 . 1344. 185. 959. 11402. 1099. 9899. 0. 28382 . 31957. 61123.

783. 1306. 3000. 0. 37451

4306 . 41758. 102881

(NOTE--TOTALS INCLUDE FAN HP + SAFtTY FACTOR AS APPROPRIATE. )

o

HOURLY COOLING LOADS

ZONE 2000 — REPRO. & MAILINC

Figure 8. Optional Zone Cooling Load Hourly Printout

260
ROMIiME 6 SLAUGHTtR, IMC. » CONSULTING ENGINEERS FORT WORTHi TEXAS QjOB 565/B NBS/ASHRAE/APEC SYMPOSIUM « SAMPLE PROBLEM 11/30/70 »* PAGL 36

AIR SIDE ANALYSIS BY ROOMS. ZONE 2000 - REPRO. & MAILING

ROOM IDENTIFICATION... ROOM SIZE. .

ROOM CRM.. Ml NUTES PER FNL. CALC NAME OR... AREA VOLUME VALUES. . . . AIR CHANGE.

NO. 'JO. OESCRIPTN. SF CF CALC ADJ. CALC. ADJ.

#»« * »*»» «****#&#*# » * * « * **** ««#**

201 PRINT ROOM 192. 1920. 650. 3.0

202 MAIL ROOM 32U. 3200. 520. 6.2

203 MEN TOILET 192. 1536. 50. 30.7

204 WOMENS TLT 320. 2560. 240 . 10.7

TOTALS 1024. 9216. 1460. 6.3

REMARKS ««**»»«**«»

o

-( note: all rooms in this zone listed,

with appropriate data, whether

master or duplicate.)

O

AIR SIDE ANALYSIS FOR ZONE 2000 - REPRO. & MAILING

Figure 9. Optional Additional Zone Printout

261
ROMINE & SLAUGHTER, INC. « CO-\SULTlrMG ENGINEERS (^JOe 565/8 N6S/ASHRAE/APEC SYMPOSIUM

FORT WORTH, TEXAS SAMPLE PROBLEM 11/30/70 * PAGE hi BUILDIMG RECAP »»»»»«*»•»*«»«

BUILDING PEAK

WINDOW

WALL

ROOF PARTITION

FLOOR

DOOR INFILTRATION

LIGHTS TO RM PEOP ( 90. ) APPLIANCES

FAN HP SAFETY FAC. ROOM TOTALS

TOTAL HEAT SENS. RATIO r^VENTI LATION ^ TOTAL VENT

LT HEAT TO RA PUMP HP BLDG TOTALS GRAND TOTAL

SENS. RATIO

LOAD DATA,

HEAT GAIN - SENSI BLE

3905it. 45672,

44746.

959,

H957.

926,

0. 60906,

19799, 7904. 22191.

24852. 278973, (S)

OCCURRING AT HOUR — COOLING

LATENT

0.

NO. 17 HEAT LOSS LOSSES

42411.

110036.

46631 . 4400 . 25762

3622. 32669.

- HEATING

INT. GAIN

Check figures

(total heat)

20810.

2250.

2874. 25935. ID

22318. 287853, (H)

60906. + 19799. + 10424. + 22191. +

+ - 113322 . ( I ) +

COOLING(T)

27.1 dTU/SF

3,0 BTU/CF

442,0 SF/TON

HEATINGIH)

25.6 BTU/SF

2.8 BTU/CF

39.0 SF/MBH

304908. I T=S+L

0.915 IS/T

115700. (VS)

235621. (V) 68410. (RA) 9261. (P) 463083. ( BS

119920. ( VL

145856. ( bL

287853. (H)

3 17411 . ( VH

605265 . ( TH

6841U. (R ) + 68410 . ( R ) +

COOLING(GT)

55.0 BTU/SF

6.0 BTU/CF

218.0 SF/TON

HEAT INGTH ) 53.9 BTU/SF

5.9 BTU/CF

18.6 SF/MBH

613201. (GT=BS +BL

0, 749 ( B/GT ) 605265 , ( TH=H+VH

PYRAMID TOTALS

LIGHTS TO RM LIGHTS TO RA PEOPLE( 126, APPLIANCES

GRAND TOTAL

AIR QUANTITIES

AREA VOLUME PEOPLE(« X O.F PEOP, (SF/125.0

BEFORE DIVERSIFICATION

67674.*

76011.*

) 27939.* 29366.*

10539.* 3000.*

651610,*

181979.

787244.

423532.

56050.

367481

WINTER

TOTAL , HUMI DI FICAT ION ( WH

WITH HUMID ( THH=TH+WH

LOSS LESS INT. WINDOW SOLAK

NET LOSS—LESS

GAIN (TH-I-R)

GA I N INT. AND SOLAR

11232. «SF 103024. *CF

. ) 90. MAX.

) 89. MAX

ATAT

ATAT

0.25 2.00 25.00

25.00

CFM/SF

CHANGES/HR

CFM/PERSON

CFM/PERSON

2808. 3434.

2250. 2246.

CFM,

CFH.

CFM,

CFM, TOTAL BUILDING VENTILATION, FOR ALL ZONES 446 0. CFM

-********«**

-+ NOTE —

+ * = SUM OF

+ ZONE VALUES

(TOTAL BLDG EXH

("= 1650. CFM)

o

INFILTRATION 75. CFM, AT 499.*CFM. AT 1.00 FACTOR

1.00 FACTOR

75. CFM (COOLING)

499. CFM (HEATING) TOTAL FAN AIR 12750, *CFM,

***«»**«*

BLDG. PEAK LOAD 51,5 TONS

AND TOTAL CUlL AIR = 11740. CPM AT BUILDING PEAK »«******

BUILDING RECAP

Figure 10. Typical Building Load Printout

262
Accuracy Requirements For Computer Analysis of Environmental Systems

R. . Cook and J. A. Serfass

Power Systems Planning Department

Westlnghouse Electric Corporation

East Pittsburgh, Pa. 15112

The difference between the actual energy requirement for an environmental

system and the energy requirement as calculated by a computer program is termed

error. The usefulness of such a computer program in selecting between alternative

systems is a function, in part, of the magnitude of the error. The total error is considered in two parts - bias error that has the same percentage effect on all systems considered, and random error that is unpredictable from one system to another.

The effect of error is quantified by assuming a uniform probability distribution of random error between limits, and then calculating the probability that the lower total cost system has been identified by the computer calculation. The evaluation of this probability is accomplished by means of a simple decision tree analysis.

Key Words: Accuracy, competitive analysis, computer program, decision,

economic analysis, energy, environmental system, error.

1. Introduction

Most computer programs that calculate energy requirements of environmental systems in buildings

have been developed to aid in the choice between alternative competing systems. Important examples in- clude the choice between energy sources, i.e., gas, oil, or electricity, and the choice between energy

conservation systems. Certainly there are other uses for energy calculation programs, such as the study

of physical properties of a system, and perhaps the use of energy calculations as an integral portion

of a computerized control system. The accuracy requirements developed in this paper, however, apply

only to the use of the programs to select between alternative systems or subsystems and do not apply

directly to other uses.

In the past, little consideration has been given to the relationship between the accuracy of energy programs and the cost of using them. This paper presents such a consideration and should give

some insight into the answers of the following two questions: What is the expected accuracy? Does

this accuracy, combined with the result, justify the cost of the computer run? Precise answers to these questions applicable to a specific situation are difficult to obtain. It would be necessary to calculate the energy requirements for the various systems, construct a building with each of the systems

and measure the results over a period of years. Obviously, this is not practical. The purpose of this paper, therefore, is not to permit the absolute determination of accuracy requirements, but rather to permit some quantification of accuracy, based on estimated calculation errors, and the resulting value

of studies. Then, at least, users of building energy computer programs can begin to develop adequate

evaluations of their own use of such programs. In addition, and perhaps more important, it Is hoped

that developers of new programs can gain more of a feel for the accuracy required of their computer

programs.

2. Types of Errors

The errors that occur in the computer calculation of building energy requirements may be categorized as either bias or random errors. Bias errors are those that have Idehtical percentage effects on

all alternatives and, therefore, on the differences between alternatives. For example, if the cal- culations result in energy requirements that are 10 percent high for all alternatives, then the difference between any two alternatives will also be 10 percent high. Bias errors tend to occur in the portions of the calculations that are the same for all alternatives, such as heat flow and weather

factors. Random errors are those that are unpredictable (within limits) between alternatives. For

Engineering Section Manager and Electrical Engineer, respectively.

263
example, the calculated energy requirements for one system may be five percent high, and for another

alternative, five percent low. Obviously for random errors, the percentage error in the difference

between alternatives can be vastly greater than the percentage random error in each alternative.

Neglecting bias errors, the actual value of energy consumption for a building system alternative

will be the calculated or expected value, plus or minus some random error. The probability distribution of the actual energy consumption about the expected value is some type of curve whose shape is unknown at this time, but which probably peaks near or at the expected value. In other words, if the random error is plus or minus five percent, then the probability of the actual value being five percent

above the calculated or expected value most likely is less than the probability of the actual value

being the expected value. The limited experience to date, however, indicates that within the expected

limits of random error, the curve of probability distribution is relatively flat. For the purposes of

this paper and to facilitate analysis, the probability distribution of random errors is assumed to be

flat between the random error limits, and equal to zero outside the random error limits.

3. Effects of Errors

The effects of random and bias errors can be visualized by means of Figure 1. "A" is the energy

cost for system A and "B" is the energy cost for system B. The lines about A and B represent the actual values, which equal the calculated values plus or minus a random error of 10 percent, with no consideration of the bias error. The calculated values of A and B are 1.0 and 0.6 respectively. Thus,

the calculated value of (A-B) is 0.4. Considering only random errors, the actual value of (A-B) can be any value within (1+ 0.1) - (0.6+ 0.06) with the entire population of (A-B) being contained in the parallelogram in Figure 1. It should be noted that the breakeven differential cost between A and B (BEAC) is defined as the annual cost (excluding energy) of B minus the annual cost (excluding energy)

of A. If (A-B) (calculated) is greater than BEAC, then B is the apparent choice. The probability that

the actual value of (A-B) is greater than BEAC is equal to the shaded area of the parallelogram divided

by the total area. In Figure 1, BEAC is 0.3, and the probability that (A-B) (actual) is greater than 0.3 is 92 percent. Thus the probability that B is the correct choice is 92 percent. Similarly, if (A-B)

(calculated) is less than BEAC, then A is the apparent choice.

The effect of bias error is assumed to move the parallelogram to the right or left by an amount

equal to the product of the bias error and (A-B) (calculated) . This is equivalent to adding the same product to BEAC. In Figure 1, if the bias error is expected to be plus 10 percent, then BEAC becomes

0.34 instead of 0.3. Thus the probability that B is the correct choice becomes 77 percent instead of

92 percent.

4. Probability Curves

The relationships described by Figure 1 were calculated for a^wj^de range of values of the difference in annual energy costs of alternatives A and B, shown as ("J^)

> breakeven difference in energy

costs (BEAC), and random errors. The results are plotted in Figure 2 through 11. Note that each figure

contains a different family of curves which applies to one value of the relative closeness of the cal- culated annual cost differential (A-B) and the breakeven cost differential (BEAC). The different

curves within a family apply to different values of the relative closeness of the annual energy costs of each alternative. The abscissa is the random error of the energy calculations and the ordinate is the probability that the more economical choice has been correctly identified by the calculation. A-B

The proper curve is chosen by calculating ("~^) and BEAC, and finding the closest applicable parameters on a curve in the available families of curves. Then, knowing the approximate random error of the energy calculations, one can find the probability that his choice is correct. This probability, of course, is one measure of the relative usefulness of energy calculation computer programs in selecting

between systems. However, there is a need to relate the probability to economic factors, as will be shown in the next section.

5. Maximum Acceptable Study Cost

Figure 12 is an elementary decision tree analysis illustrating the decision that must be made as to whether or not to use an energy analysis computer program, and the chance events that occur after

the decision is made. For simplicity, it is assumed that there are only two alternative systems (A and

B) , but the same analysis could be expanded to include any number of alternatives, chance events and decisions. In order to choose between two alternative systems, it is necessary to utilize either a computer evaluation, at some expense, or an individual's own judgement which is assumed to be free. In either case, a decision is made, presumably in favor of the less expensive system, and with the decision

is associated a certain probability that the correct choice was selected. When only judgement is used,

it is assumed that the individual making the decision is inexperienced in choosing between these two systems, so there is a probability of 50 percent that he will select either system. This probability

could be adjusted to any expected value.

264
The total cost of each decision Is the cost of making the decision plus the equivalent cost of each

chance event, using the calculated expected value costs. The equivalent cost of a chance event is equal

to the summation of the products of the probabilities and the costs of all possible outcomes. The total cost of an outcome must Include both the energy and the capital (including all other costs). Obviously,

all costs must be on either an annual basis, or a present worth or capitalized basis. Such a decision

tree analysis shows that the maximum allowable expense of a computer study is that expense which results

in the two decisions being of equal total cost.

Unfortunately, the decision tree analysis of Figure 12 cannot be used to evaluate a computer study

that Is yet to be done. The reason for this is that the computer study results are required for the decision tree analysis. Its use, instead, is to evaluate the worth of past computer studies which, in turn, should help in developing policies for future situations.

In order to account for variations in the accuracy of the calculations for energy costs, it is necessary to add an additional term in the total decision cost. This is the "Evaluation of Risk of Loss" in Figure 12. Its value is equal to zero, if the calculations are absolutely precise, and of

such a value that the acceptable computer cost is zero, if the computer results are very Imprecise.

Analysis will reveal that this is equivalent to replacing the expected total cost of the coinputer selected system with a chance event. This chance event has a probability (P) of selecting the less expensive system with its expected total costs, and (1-P) probability of selecting the higher cost system with its expected total costs. (P) is the probability determined from the families of curves.

6. Hypothetical Example

The analysis approach developed in this paper can be illustrated by means of the following

example:

Alternative Calculated Annual Energy Cost Capital Cost A $100,000 $400,000

B 80.000 535.000 A - B $ 20,000 - $135,000

In addition to the above parameters, assume a capital recovery factor of 0.1175 (based on a 20 year recovery period with a 10 percent interest rate), a bias error of (+) five percent, random error of

(+) five percent and a study cost of $5,000.

The breakeven differential cost between A and B (BEAC) is $15,900, on an annual basis. The ap- parent choice is B, since BEAC is less than (A-B)(l-Bias Error) or $19,000. The use of Figure 9 (since + Bias error = 0.85) shows that there is a 75 percent probability that if we choose system

B, we ha^e^chosen the more economical system. The use of a decision tree analysis, adjusted for risk

of loss, with this probability of 75 percent, indicates that the breakeven cost for the computer study

would have been $9,000, on a first cost basis. This means that the expenditure of $5,000, in this situation, for the computer study has resulted in a net savings of $4,000, and thus, the decision to use the computer analysis was correct. It also indicates that the accuracy of the computer analysis

was adequate.

7. Appendix-Equations

Definitions: A - annual energy cost for alternative A

B - annual energy cost for alternative B BEAC - annual costs (excluding energy) of B less same for A

F - capital recovery factor to convert

capital costs to annual costs

RE - random error in energy -cost cal- culations - per unit

BE - bias error in energy cost calculations - per unit

P

- probability that calculations will

identify more economical alternative

SC - maximum allowable study cost (that cost which will result in no basis

for using computer calculations com- pared to the toss of a coin to choose

between alternatives A and B)

265
Equations

If: Then:

If: Then:

BEAC ^ (A-B)(I-BE) - (A+B) RE P = 1 that B is economic choice

(A-B)(1-BE) - (A+B) RE ^ BEAC ^ (A-B) (1-RE-BE)

^ , CbEAC - (A-B)(1-BE) + RE(A+B)]^

8 RE2 (A)(B) that B is economic choice

(1)

(2)

(3)

If: Then:(A-B) (1-RE-BE) £ BEAC ^ (A-B)(I-BE)

, BEAC - (A-B)(1-BE) + RE(A)

2 RE(A) that B is economic choice

(4)

(5)

If: Then:

(A-B)(1-BE) - BEAC ^ (A-B) (1+RE-BE)

, (A-B)(1-BE) - BEAC + RE(A)

*^ ^ " 2 RE(A) that A is economic choice

(6)

(7)

If: Then:(A-B) (1+RE+BE) ^ BEAC ^ (A-B) (1-BE)+(A+B) RE

, [(A-B) (1 -BE) - BEAC + RE (A+B

8~REMA)(B)

that A is economic choice

(8)

(9)

If: Then:

BEAC - (A-B)(1-BE)+(A+B) RE P = 1 that A is economic choice

(10)

SC _( P-0.5 ) F (A-B)(1-BE) - BEAC (11)

8. References

(1) Hertz, D. B. , Risk Analysis in Capital (2) Hammond, J. S. , III, Better Decisions with

Investment, Harvard Business Review, Jan-Feb. , Preference Theory, Harvard Business Review,

1964, p. 95. Nove-Dec, 1967, p. 123.

266
NO SCALE

0 .2 .4 .6 .8 1.0

ANNUAL ENERGY COST - pu

Figure 1. Illustration of the effect of random and bias

errors on differential (A-B) energy cost.

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278
Calculation of Energy Requirements vri.th the Proposed ASHRAE Algorithms for U. S. Postal Buildings^

Metin Lokmanhekim

General American Research Division (GARD)

General American Transportation Corporation (GATX)

Niles, Illinois, USA

The accurate calculation of the energy requirements and heating and cooling

equipment sizes for buildings is one of the most important, as well as one of the most difficult, problems facing the air conditioning engineer. It is important

because energy cost is an essential and significant element of the building's

overall owning and operating cost and very likely could be the determining factor

in selection of the air conditioning system for a new structure. The problem is difficult because of its complexity. It not only requires accurate determination

of the heating and cooling loads, taking into account the varying influences of weather and operating schedules, but also determination of the performance of heating and cooling systems under vaiying conditions of partial load. The application of digital computers for solution of these complex problems has made more

accurate and thorough treatment of a total building analysis possible and has made practical the comparison of all types of systems and energy sources that an engineer wishes to consider. An analysis of the type discussed above would nor- mally take from a week to many months if performed by hand. Now it can be done in a matter of a few hours or a few days, depending upon the size of the building

and the degree of analysis desired. The computer program described in this paper

utilizes proposed ASHRAE algorithms and accomplishes all of the above items along

with economic analysis.

Key Words: ASHRAE algorithms, digital computers, economic analysis, energy requirements, heating and cooling equipment sizes, operating

schedules, partial load, performance of heating and cooling systems,

varying influences of weather.

1. Introduction

Calcialations of energy requirements and heating and cooling equipment sizes for buildings by con- ventional methods is and always has been more art than science. The most important element in any calculation has been the experience factor, and the man whose experience permitted him to realistically

select an appropriate value is perhaps as much an artist in his own right as Picasso is in his.

Unfortunately, art and truth are not necessarily the same. With good reason, heating and cooling

equipment has generally been specified substantially oversized as a hedge against a poor guess. What's

more, energy requirement calculations in themselves are little more than guesswork, irrespective of the

effect of any experience factor.

Such inexactness in determining energy requirements and heating and cooling equipment sizes for

buildings is rapidly becoming a problem. First , rising construction costs and the increasing value of floor space are driving building owners to insist that equipment be no larger than absolutely necessary. Second , competition between energy suppliers is stiff and their claims are often conflicting,

which means that more refined methods of comparing energy sources are needed. Third, energy utilization equipment and methods are more varied now than at any time in the past . Again, accurate cost

The work described in this paper was sponsored by the Bureau of Research and Engineering of

U. S. Postal Service (Contract No. RE ^9-6?) under the Technical Monitorship of James M. Anders.

The details of the complete project are given in Reference 5- Manager, Thermal, Mechanical and Computer Systems.

279
comparisons are necessary. Fourth , architects and building owners would like the flexibiltiy of know- ing quickly and accurately the effects of changes in such factors as design, materials, and building

orientation on heating and cooling costs. Not having this information inhibits progress in building

design. Last , and perhaps most important, many experts are predicting that the United States is head- ing for an energy shortage which will boost energy costs substantially. Energy requirements, which

entail the greatest amount of guesswork in conventional calculations, probably will become the dominant factor in the selection of heating and cooling equipment

2. Fundamentals of the Computer Program

The solution to the present dilemma is to upgrade and refine heating and cooling load calculations

by making them more reflective of the actual conditions taking place in the building. This entails

switching from present calculation methods based upon the physical impossibility of steady-state or steady periodic heat transfer to a new calculation method which evaluates transient heat transfer "like

it really is".

The computer program developed by General American Research Division (GAE?D) of General American

Transportation Corporation (GATX) for the United States Postal Service (USPS) does exactly this.

Further, it doesn't stop at heating and cooling load calculations; it carries right on through to system simulation and final economic analysis . Known as the Computer Program for Analysis of Energy

Utilization in Postal Facilities, the program specifically will

(1) Evaluate total building design and the effects of size, shape, orientation, wall

and roof constructions, and window design on the heating and cooling demands.

(2) Evaluate system selection and the effects of equipment capacity, schedule of operation,

and choice of components on the ability to maintain design requirements in every space of the

building for each hour of the year.

(3) Evaluate owning and operating costs and the effects of the type of equipment, the type of energy source, and maintenance and overhaul costs on maximizing return on investment.

The USPS desired such a program so that it could determine exactly which energy source/equipment

combinations provide the lowest overall owning and operating cost for each one of many thousands of new postal facilities planned for constmction throughout the country.

To account for the thermal storage effect of a building, the heating and cooling load calculation

portion of the computer program utilizes the most advanced method of load determination, the "Convolu- tion Principle ". The mathematical theory behind the Convolution Principle is not new in itself. It has been known and applied in different engineering problems for a number of years . However, its

expansion into a practical and workable computer program which provides a wealth of design information

for building heating and cooling equipment selection has resulted from the research and development

carried out by the ASHRAE Task Group on Energy Requirements for Heating and Cooling [1, 2] 3, the National Research Council of Canada [3] , the National Bureau of Standards of USA Lh] , and GARD/GATX

[5, 6, 7, 8, 9] . The computer program developed by GARD/GATX for the United States Postal Service

utilizes the full analysis outlined in the ASHRAE booklet Ll] and applies the convolution principle

in two different places. First, the transient heat conduction through a multi-layer wall (or roof)

is calculated by convolving the outside and inside surface temperatures with the wall (or roof)

"response factors ", and secondly, the space cooling load is calculated by convolving the instantaneous

heat gain with its "weighting factors "

In heating and cooling load calculations, the hourly weather data obtained from the U. S. Weather

Bureau is used. The weather data utilized includes dry and wet-bulb temperatures, wind velocity,

barometric pressure, cloud tjrpe and amount. At this point, it is worthwhile to emphasize that in

addition to the utilization of the Convolution Principle, use of coincident dry and wet-bulb temperatures, modification of calculated solar radiation data by cloud type and amount, and calculation of

time- dependent outside film coefficient as a function of wind velocity and type of surface are further

features of the computer program.

Figures in brackets indicate the literature references at the end of this paper.

280
3. Description of the Computer Program

The computer program consists of four main sub- programs performed in sequence, with the output

one becoming the input to the next. The function of each sub-program is summarized below.

(1) Load Calculation Sub-program . Calculates sensible and latent components of hourly

heat losses and heat gains, for each space in the building for a desired period of time. This program is supported by wall and roof selection sub- programs

(2) Thermal Loads Plot Sub- program . With the support of the Punch Sub-program, plots

the load profile of any space for any period of time. Comparisons between plots

permit the grouping of compatible spaces into fan system control zones. This is achieved by the use of Editing Support Sub-program.

(3) Systems Simulation Sub-program . Simulates the operation of each fan system by

combining the heating or cooling requirement of each zone with ventilation air

requirements, thus obtaining the hourly heating and cooling requirements imposed

on the heating and cooling equipment. These thermal requirements are then con- verted into hourly energy requirements based upon partial load machine characteristics . Depending upon building floor area, Central or Packaged Systems

Simiilation Sub-programs may be utilized.

A. Central Systems Simulation Sub-program: The thermal distribution systems

which this program analyzes are:

• single zone system

• multi-zone system

• dual- duct system

• unit ventilator

• unit heater

• single zone reheat system

• radiant floor panel heating.

Heating and Cooling Plant combinations that the program can handle include:

a) Conventional Systems

• Hermetic Reciprocating Chiller with Gas, Oil, or Steam Heat

• Hermetic Centrifugal Chiller with Gas, Oil, or Steam Heat

• Open Centrifugal Chiller with Gas, Oil, or Steam Heat

• Steam Absorption Chiller with Electric or Steam Heat

b) Total Electric Systems

• Hermetic Reciprocating Chillers with Electric Heat

• Hermetic Centrifugal Chiller with Electric Heat

• Open Centrifugal Chiller with Electric Heat

c) Total Gas Systems

• Steam Absorption Chiller with Gas Heat

• Steam Turbine Driven Open Centrifugal Chiller with Gas Heat

d) Total Oil Systems

• Steam Absorption Chiller with Oil Heat

• Steam Turbine Driven Open Centrifugal Chiller with Oil Heat

281
e) On- Site Generation Systems

• Total Gas with Steam Absorption Chiller, Gas Heat or Gas EngineGeneration Sets

• Total Oil with Steam Absorption Chiller, Gas Heat or Diesel Fuel Engine- Gene rat ion Sets

B Packaged Systems Simulation Sub-program: The systems which this program analyzes

are

• Electric Air Conditioning (DX coil) with Oil Heat

• Electric Air Conditioning (DX coil) with Gas Heat

• Reversible- cycle Heat Pump with Electric Resistance Heating

• Gas Air Conditioning with Gas Heat

{h) Economic Analysis . Calculates the annual owning and operating costs of various com- binations of heating and cooling plants.

k. Sequence of Sub- programs Use

The sequence of using sub-programs depends upon the information the engineer wishes to obtain

and if he can initially break the buildings into fan system control zones rather than just spaces . Figure 1 illustrates the paths of sub-program sequencing that can be taken as a function of the engineer's decisions. As the engineer becomes more adept at breaking a building directly into

control zones, the need for space load plots and/or re-grouping of spaces will diminish.

The card input data required by some of the sub-programs cannot be prepared until the output

of another sub-program has been examined. For example, the proper grouping of spaces into control

zones, and then control zones into fan systems required for the Systems Simulation Sub- program

probably cannot be done until the results of the Thermal Load Plot Sub-program are reviewed to es- tablish which spaces have similar load profiles . Neither can monthly energy costs be calculated

and inputted to the Economics Analysis Sub-program until the monthly energy consumption summary has been received from the Systems Simulation Sub-program. Kor can the engineer collect the necessary

equipment cost data required by the Economics Analysis Sub-program until the Systems Simulation Sub- program tells him the quantity and capacity of the chillers, boilers, cooling towers, etc. Figure 2 illustrates this dependence of input upon output for a large Post Office building analysis. Figure 3 illustrates the same for a small Post Office building (less than 35^000 square feet of floor space)

analysis where use of all sub-programs is probably not required. For small buildings, the engineer

can elect to use only the Load Calculation Sub-program, the Packaged Systems Simulation Sub-program,

and the Economics Analysis Sub-program. If experience indicates no need for economic evaluation of fuels, energy and equipment variations, then the engineer can elect to rxin only the Load Calculation

Sub-program for the peak heating and cooling months. This would indicate maximum and minimum heating

and cooling requirements for proper capacity equipment selection.

Load Calculation Sub-program

The inputs to the Load Calculation Sub-program are the geometry of the building and its surroundings, thermal and physical properties of wall and roof constructions, operating schedules of the

building, i.e., occupants, lighting equipment, etc., schedules, hourly weather data from U. S. Weather

Bureau tapes, and internal loads.

The mandatory output on paper is the facility identification, weather data and station identification, building thermal and infiltration loads summary, and spaces maximum and minimum heating and cooling loads summary. The mandatory output on magnetic tape is the hour of the year, sun index,

dry and wet-bulb temperatures, wind velocity, humidity ratio, pressure, enthalpy, and density of outside air and for each space, space number, space sensible load, space latent load, plenum return

air lighting load, and space lighting and equipment power.

Optional outputs on paper are the wall and roof specifications, shadow pictures, and if desired,

the same information on magnetic tape.

5. Inputs and Outputs of Each Sub- program

282
Thermal Loads Plot Sub-program

The inputs to the Thermal Loads Plot Sub-program are the space number^ the number of days to be

plotted, the starting date, and the loads data.

The output is a strip chart graph detailing the heat gain or loss for each hour plus the maximum

heat loss and gain for the period.

System Simulation Sub-program

The inputs to the System Simulation Sub-program are the output tapes of the Load Calculation

(or Editing Support) Sub-program, fan system characteristics, chiller operating characteristics,

and types of heating/cooling combinations and energy sources to be analyzed.

The output on paper includes a summary of fan system characteristics, a summary of zone air flows,

a summary of equipment sizes, and energy consumption analysis.

Economic Analysis Sub- program

The inputs to the Economic Analysis Sub- program are the monthly energy costs, the installed

equipment costs, equipment life, maintenance and overhaul costs, and anticipated annual percentage

increase of labor and material.

The output on paper gives the monthly and yearly energy, machine, and equipment costs and total

owning and operating annuity.

6. Closing Remarks

As a result of different experiments performed, it can be stated that the Convolution Principle

used in heating and cooling load calculations gives more realistic values of the peak loads and the associated times of occurrence. Because the effects of heat storage are included in the calculations,

the program clearly shows that peak loads occur several hours after the hottest time of the day, at which time generally there are no occupants in the building. For practical purposes, this means that cooling and heating equipment can often be specified smaller than would normally be selected, and elusive demand figures for utility services can be pegged accurately, which is vital to achieving

realistic energy costs. It is also worthwhile to mention that the computer program can be utilized

in different ways, such as:

(1) Pre-design selection of the basic system and energy source. This includes total electric

systems, total gas or oil systems (on-site generation), purchased steam- absorption systems,

and combinations of the above systems and energy sources.

(2) During the design stage, utilize various subroutines or sub-programs to evaluate specific

design concepts and modifications

(3) During the construction stage, evaluate contractor proposals for modification or deviation

from the construction plans and specifications.

(h) After completion of the building, use the "ideal building", as finalized by the computer

program, to evaluate the maintenance and operation of the facility and the utilities

systems. This will completely optimize total owning and operating costs and provide the greatest return on utility dollars

At the present time, the computer program has different versions to run on Control Data 36OO,

6k00 and 66OO, Univac IIO8 and IBM 360 computer systems. Input data preparation and computer running

times depend on the complexity of the building under consideration. Both data preparation and com- puter running times decrease as the engineer gains experience. Depending upon computer system used

and the complexity of the building, the running time on the computer varies between 1/50 to 1/200

second per space per hour.

283
7. References

"Procedure for Determining Heating and Cool- ing Loads for Computerized Energy Calculations - Algorithms for Building Heat Transfer

Subroutines", compiled and published by the ASHRAE Task Group on Energy Requirements for

Heating and Cooling, Edited by Metin

Lokmanhekim

Tull, Robert H., "ASHRAE Program on Energy

Requirements for Heating and Cooling", ASHRAE

Journal, April, I968.

Stephenson, Donald G., "Calculation of Cool- ing Load by Digital Computer", ASHRAE

Journal, April, I968.

Kusuda, Tamami, "New Heating and Cooling

Load Calculations Procedure", published by

NBS.

Lokmanhekim, Metin, et.al., "Computer Pro- gram for Analysis of Energy Utilization in

Postal Facilities", published by GPO:

Volume 3 - Operation Manual - GPO Pub. No.: 889-665

Volume h - Fortran Listing

L6J Groth, Charles C, and Lokmanhekim, Metin,

"A New Technique for the Calculation of Shadow Shapes and Areas by Digital Computers", Proceedings of the Second Hawaii

International Conference on Systems Sciences,

Januaiy I969, pp. kYl-kjk

[7J Milnark, Sam W., "TAGS - A New Approach to System Design", Air Conditioning & Refrigeration Business, February I968.

[8] Milnark, Sam W., "TAGS - Computer Workhorse

for Sale", Air Conditioning & Refrigeration

Business, Januaiy 1969-

[9] Milnark, Sam W., "Computer Program of the Future ... Now'.", Air Conditioning & Re- frigeration Business, January 1971.

Volume 1 - User's Manual - GPO Pub. No.: 889-667

Volume 2 - Engineering Manual - GPO Pub

No.: 889-666

284
( START 1

LOAD CALCULATION

SUBPROGRAM

YES

NO

' r

PUNCH

SUBPROGRAM

r

THERMAL

LOABS PLOT SUBPROGRAM

NO

LOAD

EDITING SUBPROGRAM

SMALL —4—

PACKAGED

SYSTE-IS SI^^ULATION SUBPROGRAM

SYSTEMS SIMUWTION

SUBPROGRAM

ECONOMICS ANALYSIS

SUBPROGRAM

END ^

Figure 1 The paths of sub-program sequencing

285
LOAD CALCULATION

CARD INPUT

1 LOAD PRINTED LOAD CALCULATinW — CALCULATION

SUBPROGRAM OUTPUT

f

SYSTEI4S SIMULATION

CARD INPUT

SYSTEMS SIMULATION

SUBPROGRAM

ECONOMICS ANALYSIS

CARD INPUT

r

ECONOMICS ANALYSIS

SUBPROGRAM

PUNCH SUBPROGRAM

PUNCH SUBPROGRAM CARD INPUT

LOAD PLOT CARD INPUT

t

THERMAL

LOADS

PLOT SUBPROGRAM

LOAD

EDITING SUBPROGRAM

HOURLY

I-JEATHER & SPACE LOAD TAPE

Figiore 2 Analysis of Large Post Office Buildings

286
WEATHER

TAPE

INPUT

LOAD CALCULATION

CARD INPUT

LOAD

CALCUI.ATION

SUBPROGRAT'I

PKIMTliP LOAD CALCUI^TION

OUTPlIl'

HOURLY

WEATHER & SPACE LOAD

TAPE

PKGD SYSTEMS SIMULATION

CARD INPUT

PKGD SYSTEML- ^^IMULATION SUBPROGRAM

PRINTED

PKGD SYSTEMS SIMULATION

OUTPUT

ECONOMICS

ANALYSIS

CARD INPUT

ECONOMICS ANALYSIS

SUBPROGRAM

PUNCH

3JBPR0GRAM PUNCH

SUBPROGRAM

CARD INPUT

LOAD PLOT CARD INPUT

THERMAL

LOADS PLOT

SUBPROGRAM

Figure 3 Analysis of Small Post Office Buildings

287

An Accurate Computing Method for the Analysis of the Non- Steady Thermal

Behaviour of Office Buildings

S.W.T.M. Oegema and P. Euser

Institute of Applied Physics TNO-TH

Delft, The Netherlands

For the calculation of room temperatures and cooling loads in buildings a computer program has been made that meets certain special requirements in respect

of accuracy and flexibility. The room model chosen has five inner walls and one

facade. Each inner wall may consist of several layers, the possible cavity in the ceiling can be ventilated. The facade has a non-transparent part and a transparent

part with glazing and sun shading. The transparent system may consist of three

planes, each of which may be a glass plane (common, tinted, coated), a Venetian

blind (inside, in between, outside) or a screen (inside, in between, outside). It is possible to ventilate the cavities between these planes. The computing procedure

is based on an implicit difference method with time and space discretisation. The

number of nodes with both resistive and capacitive heat flow is 71, distributed

over inner and outer walls. Input data refer to solar radiat ion , outdoor temperature,

inner heat gain from occupants, lighting and apparatus, furthermore air and water

inlet temperatures as well as air flow. The incident solar radiation, divided into

direct, sky and ground radiation, is calculated depending on latitude, date,

orientation, time and sky dust factor. The solar radiation fractions absorbed in glazing and shading planes are calculated from reflection, absorption and trans- mission property data, and thus also the transmitted solar radiation. Indoor air

temperature may be free or controlled at a prescribed curve. Output data are indoor

air temperature, indoor surface temperatures and cooling load. When the discrete

time interval is a quarter of an hour the computing time will be about 5 minutes

on a IBM 360/65.

Key Words: Conduction, convection, discretisation, glazing, implicit

difference method, solar radiation, solar absorption, solar reflection,

solar transmission, sun shading, thermal behaviour, thermal radiation.

1. Introduction

Some years ago the accurate calculation of room temperatures and cooling loads in buildings could

only be made by using electrical simulation methods. References are [1 ]

' » [ 2] , [ 3] , [4] .Afterwards

computer programs were developed for air conditioning plant calculations [ 5] , [ 6] in which however the heat transfer process in the rooms, expecially the heat conduction in the walls, had to be approximated

because of theextait of these installation programs and the frequency of the computations for each

project. Meanwhile some programs for the analytical calculation of the non-steady heat transfer in separate composite wall constructions became available [7,8,9].

For the calculation of the non-steady heat transfer in a room we developed a program by means of which accurate and extensive parameter computations are possible, especially as regards the solar trans- mission, the heat transfer at the glazing and the heat accumulation in the walls.

In this paper a description is given of the program, involving the possibilities of this program

for research purposes and for plant capacity calculations.

'Figures in brackets indicate the literature references at the end of this paper

289
2. Description and Formulation of the Heat Transfer Processes in Rooms exposed to Sun Radiation

When the glass planes of a room are sun radiated various planes of this room will be warmed up through absorption of sun radiation and heat transfers occurs by conduction in the walls, by convection

between surfaces and room air, and by radiation between the surfaces of walls and planes. We refer to more detailed descriptions, for instance [1], and shall confine ourselves here to the formulation of the heat transfer equations to be solved.

2.1. Heat Transfer by Conduction

Non-steady heat conduction in a homogeneous medium is described by the partial differential

equation of Fourier. When T(x,t) is the temperature at place x and time t, then

where X is the thermal conductivity and pc the volumetric heat capacity. To calculate the temperature

^ 9T

T(x,t) and the heat flow -X ^ (x,t) the boundary and initial conditions must be known:

T(x,0) = f(x) (2)

3T 1

I + aiT(xo,t) = g(t) (3) X=Xo

where a^ and a] are constants.

When the medium is not homogeneous but consists of different layers, then eq (1) is valid for each layer

and additional conditions occur on account of contineous heat flow at the internal boundaries. For the numerical evaluation of the partial differential equations of type eq (1) in case of composite wall

constructions, place and time discretisation is applicable by using explicit or implicit difference

methods. We chose an implicit method on account of its total stability. A homogeneous layer is supposed

to be divided in M segments. Let the temperature in segment k at time nAt be Tj^^j^, then:

BT ^ ^k,n - Tk,n-1 , at

(5) 32t ^

T]^-! ,n " ^'^k,n + '^k+l,n

cG? (Ax) 2

Substitution of eqs (4) and (5) into eq (1) gives the following implicit difference equation:

Ax „ ,2Ax PcAx + _ PcAx

for k = 1,2,3 M, with Tq and T]j[+\ ^ as boundary conditions,

and witfi Tq^q* '^1 ,o> '^2,0 ''^M,o initial conditions.

With eq (6) it is possible to set up a computation model as shown in fig. 1 , where

R, = R2 = ^ and R3

with F being the area of the segment. The advantage of this model is that Rj and R2 truly represent the heat resistances. Resistance R3 is a fictitious heat resistance representing the heat capacity of the segment divided by At. Other heat resistances (see par 2.2 and 2.3) and the various heat sources (see par 3) may easily be joined

imaginarily with this model.

Eq (6) may also be written as a recurrent matrix equation:

290
A z(n) + B u(n) = C £(n-l) (7)

where z_(n) is a vector with temperatures Tj "^2,11' "^M.n*

u(n) is a vector with boundary conditions Tg^n ^M+l,n>

A, B and C are coefficient matrices of equation (6),

z(o) is the initial condition.

The solution of eq (7) is obtained by applying matrix inversion:

z(n) = A-'[C z(n-l) - B u(n)] (8)

By repeated substitution eq (8) passes to

n £(n) = A-'C £(o) - 2 (A-'oI-'A"' u(1) (9)

1=1

Thus the solution zin) only depends on the initial condition z^(o) and the boundary conditions u(l).

2.2. Radiation Heat Transfer

The radiation heat transfer between two grey surfaces is described by the Stef an-Boltzmann law,

written in its technical form:

*rl2 = ('FeA,F]2(Ti^-T2^) (10)

where 'I'j-12 is the heat radiation flux from surface 1 to surface 2,

o is the Stef an-Boltzmann constant, Fg is an emissivity factor dependent on emissivities £] and 62 of both surfaces and on the geometrical arrangement, Aj is the area of surface 1, F]2 is the configuration

or geometric factor defined as the radiation fraction leaving surface 1 which falls on surface 2, T] and

T2 are the absolute temperatures of surfaces 1 and 2. If (T1-T2) = AT is small, eq (10) can be approximated by:

<I>rl2 = 4aFeAiFi2T3AT (11) - T,+T2

where T = —^— . Then the heat resistance for radiation Rj- for two surfaces 1 and 2 follows from:

AT 1 " (12) *rl2 4aFeA,F,2TJ

When the temperature range is sufficiently smaU as by approximation in most cases of radiation transfer

in rooms, R^ will be a constant. Moreover for most room wall surfaces Fg^l, so that then R^- = constant x -r—— . AiF,2

The geometric factor F]2 for heat radiation between the wall surfaces of a room is calculated

applying well-known formulae. For perpendicular planes, indicated by 1 and 2, use is made of (fig 2):

F12 = (E,+E2+E3) (13)

with El = L arctg (1) + N arctg (i) - vP+lT arctg ( , ' ,„)

291
- 1 1 r (1+l2)(1+n2) l2(H-l2+n2) l2 ^2 = ' 1" I ,^j^2+l2 (,+l2)(i2+n2)^

E = [ n2(1+l2+n2) j n2

^ (1+n2)(l2+n2)

and for parallel planes (see fig 3):

Fl2 = (E4+E5+E6) (14)

Er = y \/l+x2" arctg (-7=^=57) + x VT+y^ arctg (-~?tO

VI VI +y'^

Eg = -y arctg y - x arctg x

Radiation at the blades of Venetian blinds is a special case. For both heat radiation and the reflection,

absorption and transmission of solar radiation, several geometric factors were to be calculated. They

are indicated in fig 4 and formulated below:

FA(z,i/',m) = I - -r^ V'l+z2+2z+2z sin ^' + ^r-l— Vl + (

1 -m)2z2+2z (

1 -m) sin i/f" (15) ^ ' ' zmz zmz

where z = W/S, m is the part of W which is radiated by the sun, 4/ is the position of the blades. If the blades are fully radiated by the sun then m = 1. Furthermore:

Fc:(z.i/'.m) = TT— Vl + z2+2z sin \//' + -ir^ Vl+m2z2-2zm sin ii - v/l + (

1 -m)2z2+2 (1 -m) z sin 1/'' - -r-^ (16) ^ ' ' 2mz 2mz 2mz 2mz

F5(z,i//,m) = { - [ V'l+m2z2-2mz sin i/- ' - 1] (17)

The factor F], F2 and F3 are special cases of F4, F5 and F5. When the whole blade is sun radiated then

F], F2 and F3 must be applied (m=l):

F](z,*) = Fi.izJ,]) (18)

F2(z,i/') = F5(z,./',1) (19)

Y^iz,^) = F6(z,i//,i) (20)

It is to be noted that

F4(z,i/',m) + F5(z,i/',1) + F(^(z,^|J,]) = 1 (21)

2.3. Convection Heat Transfer

At the various wall surfaces of a room convection heat transfer occurs. The heat flow between wall

and room air is, as usual, described by:

*^ = a^A(T^ - T3) (22)

where o.^, is the convection heat transfer coefficient, A is the area of the wall surface, T^ is the wall surface temperature, T^ is the room air temperature. Thus the heat resistance for the heat transfer

between the wall surfaces and the room air may be presented by

^c=fe = ^ (23)

292
The convection heat transfer coefficient generally depends on the air velocity v and the temperature difference AT. In case of room wall surfaces a useful approximation for is:

a = 2 + 6Vv for v < 5m/

(24)

= 6,5vO»S for v > 5m/s

V in m/s and in W/(m2.°C).

3. The Room Model

In paragraph 2 the simulation of conduction, radiation and convection heat transfer by a computation

scheme or network consisting of heat resistances and fictitious heat capacity resistances has been

explained. In figure 5 the computation scheme of the applied unit room is shown schematically. In this figure the resistances drawn represent the convection resistances between the (numbered) nodes for the surface and air temperatures, and some of the radiation resistances between the surface temperature

nodes. The other radiation resistances has been left out for clearness' sake. The blocks represent the capacitive walls or layers. The figures in these blocks correspond to the segments in which the walls

are discretised. The complete room model consists of 71 nodes. Some detailed parts of this model are given in figures 6, 7 and 8 referring to the schemes for the facade wall and for one of the various

possible glazing and sun shading constructions. The various resistance symbols are explained below fig 6.

For each node the heat balance equation can be written, containing the occurring heat fluxes, each

of which as a quotient of temperature difference and resistance, as described in par 2. The 71 nodes

equations together form the matrix equation (7).

4. Boundary Conditions

In this section the boundary conditions are described, such as the outdoor air temperature and the solar heat sources in the room derived from the incident solar radiation.

4.1. Outdoor Air Temperature

The outdoor air temperature may be approximated by a single sinus function or by the sum of some

sinus functions. For suanner conditions in The Netherlands a useful approximation is:

Tao = 23.0 + 5.0 cos ^ (tg - 14) (25)

where T^q is the outdoor air temperature in °C and tg is the solar time in hours.

If sufficient meteorological data are available more accurate functions for T^^ can be obtained, for instance the following form computed by Halahyja [ 10] , which is valid for Hurbanovo (Czechoslovakia),

July:

t„-14.6 t„-16.3 t„-9.0 t„-13.2

Tao = 22.06+7.38 cos 2n )+0.45 cos )+0,96 cos 2^ (-^ )+0. 1 1 cos(-^-^ ) (26)

4.2. Direct Solar Radiation

The direct solar radiation on earth, normal to the radiation direction, Sjj-j is generally considered

as a function of the altitude of the sun (h) and the sky turbidity (T). Using Nehring [ 13] the following

relation we derived:

Sdr(h,T) = Sdr max(T)(sin h)0.09T+0.14 (27)

with

Sdr max(T) = exp[ In 10(log S^r o-T/24.06)] (28)

where S^-j. q is the (direct) extra terrestrial solar radiation, normal to the radiation direction. The altitude of the sun (h) is given by:

2v sin h = sin 6 sin V + cos 6 cos 'P cos yT-(tg-I2) (29)

293
where 6 is the declination of the sun and 'f is the latitude on earth. If k is the k*-^ day of the year

then:

« = 27r sin (k-80)] (30)

For vertical surfaces S^j- must be multiplied by cos 4), where * is the angle of incidence.

4.3. Diffuse Radiation

The diffuse sky radiation is caused by the scattering of direct solar radiation in the atmosphere.

After numerous measurements for the diffuse sky radiation on a horizontal plane Bernhardt and Philipps

[ 1 4] derived:

Sdf,h = 0.33(Sdr o-Sdr)sin h (31)

The diffuse sky radiation on the vertical plane (Sjf y) depends, of course, on Sjf j,, but also on the position of the sun in respect of the vertical plane in question. Threlkeld [ 15,16/ derived the latter

relation by investigation [ 16]. We approximated this relation by two polynoms:

Sdf h 0.560 + 0.436 cos * + 0.35 cos^* , for cos * > -0.3

' 0.473 - 0.043 cos * , for cos * < -0.3

is angle of incidence)

In fig 9 the computed diffuse sky radiation on the vertical plane is given as a function of the altitude of the sun, with the azimuth of the sun with regard to the facade, as a parameter. Here the turbidity factor T = 4.0.

Another part of the diffuse radiation on facades is caused by reflection of solar radiation by the ground surface and by the adjacent buildings. The solar radiation reflected by the ground which falls on

a facade can be approximated by:

Sg = ^Rg(Sdr,h + Sdf,h) (33)

where R„ is the reflection factor of the ground surface for solar radiation.

4.4. Absorption and Transmission of Solar Radiation

at Glass Planes and Sunshading Surfaces

At the glazing and the sun shading devices the direct solar radiation and the diffuse radiation

fluxes are partly reflected, absorbed and transmitted. Thus the solar heat sources in the room are activated (see fig 8). In order to calculate the various absorbed fractions, the properties of the glass

planes and sun shading elements must be known as a function of the so called profile angle [ 12] . For

this purpose the basic calculation method is taken from Parmelee [ 11,12].

Besides the properties of the separate glass planes etc , also the absorption, the transmission and the reflection factors of the combined glazing and sun shading systems must be calculated. Here a distinction must be made between direct solar radiation, diffuse sky radiation and diffuse radiation

from the ground and any surrounding buildings.

In the calculation of the (spread) solar heat sources in the various solar radiated surfaces, all

the above mentioned effects are taken into account.

Till now the calculation of seven combinations of ordinary glass with different sun shading devices

have been carried out. They are;

a) single glass

b) single glass with indoor blinds

c) single glass with outdoor blinds

d) double glass

294
e) double glass with indoor blinds

f) double glass with blinds in between

g) double glass with outdoor blinds

Glazings with sun absorbing planes are provisionally calculated in another way. For each plane the absorption, reflection and transmission fractions for a mean incidental angle of 45° is applied. If necessary these quantities are determined experimentally with the aid of a spectrometer.

Glazings with reflecting coatings, which are however as a rule slightly tinted, are calculated

while taking into account the dependence of the reflection and transmission on the angle of incidence.

The part of the incident solar radiation, which is transmitted through the glazing and sun shading

system which enters the room is spread over the various wall surfaces, in general homogeneously, if necessary unhomogeneously.

4.5c Internal Heat Sources

In an office room in general heat is produced by occupants, the lighting (light flux, equipment heat)

dissipation) and any apparatus present. The heat fluxes produced are partly transferred to the air or when the air temperature is controlled, they are added to the cooling load. Another part of the internal

heat load, however, is radiated to the walls and can partly be accumulated. Therefore the internal heat fluxes must always be separated into a convection and a radiation part.

5. Survey of the Program

5.1. Possibilities

The units of the calculation model discussed in the former paragraphs are so built up to permit

murhvariants can be carried through. These variants refer to both the composition of the inner walls and

the facade and sun shading elements. Besides the diversity of glazing and sun shading systems, it may

for instance, also be assumed that the blinds may be drawn up during a certain period of the day.

Furthermore it is possible to calculate the point of time at which artificial illumination should be switched on, on account of the computed visuable solar radiation flux that enters the room. Shading

effects caused by surrounding buildings or by overhangs and side fins may also be taken into account

[17].

Between the various capacitive layers of the walls cavities may occur, which may be ventilated. The temperature of the ventilation air may either be prescribed or free. The room air may be ventilated with

outdoor air or with air of another (prescribed or free) temperature.

The temperature of the room air may follow a precribed curve, in which case the cooling load results

as a function of time. On the other hand the capacity of the cooler may be prescribed; then the room air

temperature is calculated as a function of time.

Besides the mean room air temperature respectively the cooling load, all the temperatures in all the nodes are calculated. The heat fluxes between the nodes may be calculated if necessary. For indoor

climate analysis the radiant temperature at certain points in the room may be calculated. It is of course

possible to combine these quantities with the room air temperature, in order to calculate the so-called

dry resulting temperature.

5.2. Flow Diagram

In fig 10 a simplified flow diagram of the program is given.

The computing time of the program on a IBM 360/65 computer for one situation (room, facade,

sun shading, date, orientation, latitude) is about 5 minutes, subdivided in 2 minutes compilation time,

1 minute matrix inversion and 1 minute temperature and heat flux calculations when At = 15 minutes.

The core memory required is about 300 K oktades.

5.3. Test Results

In fig 11 and 12, some test results are given. In the case under consideration, the glazing con- sisted of two normal glass planes, with Venetian blinds between these planes. As to the incident solar

radiation, the following data were chosen: latitude 52°, orientation SW, date July 23, sky turbidity

factor T=4. The internal load amounted to 800 W. The ventilation rate was three room changes per hour.

These results, and others, will be checked by means of an RC . network simulator.

295
6. Further Development

Several other variants as the above mentioned may. be included in the program through relatively

small modifications , such as a second facade with glazing, a separate ceiling part for lighting equipment,

a second non-transparant outer wall or roof.

For technical calculations, which must as a rule be carried out frequently, a reduced program will

be made, based on the same concept, with about 20 in stead of 71 nodes. Since the computing time is nearly proportional to the third power of the number of nodes, then a reduction of the computing time

of about 30 times will be obtained.

7. References

[ 1] Buchberg, H. , Trans. ASHRAE No 1543 (1955).

[2] Parmelee, G.V. , Vance, P., Cerny, A.N. , Trans. ASHRAE, No 1595 (1957).

[3] Korsgaard, V., Lund, H. , Publ. No 10 , Techn,

Univ. Danmark (1965).

[4] Euser, P., De Ingenieur (The Netherlands) 17, 63 (1961).

[5] Bordes, H.J., Heiz.-Lilft . -Haus techn. j_8, 300

(1967).

[6] Boeke, A.W. , J. Inst.H.V.E. , 35, 195 (1967).

[7] Shirtlife, C.J., Stephenson, D.G., Techn. Paper

No 1 14 Div. Build. Res. N.R.C. (1961).

[8] Kusuda, T. Trans. ASHRAE 75_ (1969), Part 1, No 2108, p. 246.

[9] Boer, J.H.de, Euser, P., Int. Inst. of Refrig.,

Comn. II and VI, Liege (1969).

[10] Halahyja, M. , Ges.-Ing. 2, 42 (1962).

[II] Parmelee, G.V. , Aubele, W.W. , Huebscher, R.G. Trans. ASHVE 54_. '65 (1948)

[12] Parmelee, G.V. , Aubele, W.W. , Trans. ASHVE

_58, 377 (1952).

[13] Nehring, G., Ges.-Ing. 83_, 185, 230, 253

(1962).

[14] Bernhardt, F. , Philipps, H. , Abh.Meteorol.u.

Hydrol.Dienstes der DDR, 45 (1958).

[15] Threlkeld, J.L., Thermal Environmental

Engineering, (Prentice-Hall, 1962).

[ 16] Threlkeld, J.L. , J. ASHRAE - nov. , 43 (1962).

[17] Tseng-Yao Sun, Trans. ASHRAE, No 2059, I. 1 . 1

(1968).

296
297
Figure 3. The configuration quantities in case of parallel walls, used in eq(14)

298
outdoor^sgV

air

]— 1 -13

front wall

venti lation

]— 15-19

glazing and sun shading

21 - —ceiling

(n) = temperature of node n

A3-r52

part ition walls

54-66

passage

wall

passage

air

floor

@

Figure 5. The thermal model of the unit room (for clearness the radiation resistances

are omitted)

detai I see f ig. 7

indoor

air

Si

I—omnD—@)

S2 —fflnnn—(si)

S3 —mm—(67) —iMD—(20)

Conduction resistances

Fictitious heat capacities

Convection resistances —tiiiiiiiiiii— Radiation resistances

Convect ion +radiation resistances

(nj Temperature at place n

at time t+At

©Temperature at place n at time t Q^^Heat sources

Figure 6. The thermal model of the front wall

299
Figure 7. The computation scheme for a part of the front wall (for symbols see fig. 6)

300
Figure 9. The diffuse sky radiation on a vertical plane (S ) as a function of the altitude of the sun for different horizontal positions of the sun (=) with

regard to the facade. Turbidity factor T=4.0

301
Start

jinitializatiorTI

read room

data input data

print room

data

1 calculate

matrices

A, B, C

1 matrix

inversion A~'

read boundary

condit ions

control output

input data

print boundary

conditions control output

are stated figures

contradictory ?

calculate

initial

conditions x(o

lk=k+ 1

print

j,ves ^ wrong

data

1

stop

control output

Axj,+ 1 + Buj,+ , = Cxj,

3c+l = A~'(Cxj<. - Buj^+i)

calculate

boundary con- ditions uj^+i

calculate

Xk+ 1

' (Cxjt-Buj^+ 1

)

print and plot resultt output

yes / calculation with x^io (another boundary condi- \ tion?

yes calculation with othei room data?

stop

Figure 10. Simplified flow diagram of program arrangement

302
ty cr <r rr. C cr. r^j C ^, C- -T ^ ^ T or- iT' 'y ^ (T ^- 'Z- '-' o c—<—irct cMcrr^n-J^^r ^

• ..«..

X f»i ,t .J- .J- IT u^- ir- < nO \C h c C —' 1^1 c —' f\ rv. cr ^ J j rvi c or h < sc X tf* if. (V (Vl f\' rvi (\; fv' <\J !\j fvi fNj CM 0.J (Ni t\j n- ^1 n- vj- >} -J ^ si' -f rtv rr, m <^g tvj (\ r>j (M r' fv (Vl

(- 0,- r- ^ t-i lt, o <; o '-r o sT (^i G .'^ f^' r- c r j r<-' r^i c >c c f»j >r ^ rvj or sj c •£ 'V' c in

f\| ^ fV (VI r ' f\j rsi fvj f\. ;v| r^: t\l r\j (V OvJ r^. p-i re (Vi r** 'O •^'^ rc^ m Ti r*"! (V ^N; r," rvj r^j o.; cm

/

area 75%

without cooling

-inside glass

temperature

indoor air

4Jp

CO

4J

03

QJ 4J

<u

to

rn to

,—

tlO o

0) •H -o -u •H •H

to •o C C

•H O

o

13C 1-1 to 0) U 4-1 •H !-i to D

)-i O

O

T3 OB C C

•H •H

0) O

X. O

O

* it * XT

X K

C: o L*^ C IT C C ir O J- o in O in C >••• • I- 'n rf LT < vc r- r- o- X c cX 'J U" o O ^' C in O I."

—I -Vl ^ ~-' <t- v!- \r u^. >r -T 1^ c-

.~ m i.^ -j; ir ^ —1 r^j r^. <j r .: a; X' r-j rv rvj

303
cr -J- c- f^; LT -S" ''^ »c >c X or vc f C vC' iNj (V sC' a- O" ir, o vr x —i (^; o- ^ r- a- < O (v r<" ro a c lo vO sO cr cp co oc h o

I I I I I I I I I I I I I I I I I I II I I O O c- c- O C' C' —' rj C en h- or <t r^.' '/^ O >t CW- -f O CC h- ^ IX c C O o c- o c c o c> c. C/ o

* C' o C' o o c: c o c cr CT f-H vT vc CO vc in or c- c LT, cr> tv; cr o o o o o c c- o o o o o c o

--'r\J<:^a:(yccO"aOr-((\jr'"i>j^j-irir, ir-LTxir-t

/

/

area 75% -cooling Load

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304
A Successive Integration Method

for The Analysis of

the Thermal Environment of Building

N. Aratani, N. Sasaki, M. Enai

The Department of Architecture

Faculty of Engineering

Hokkaido University

Sapporo, Japan

This method is to calculate the room air temperature or the

heating (cooling) load variations for each At step with repetition of simple multiplications and additions by utilizing

both the nature of an exponential function which decreases by

equal ratio for each At step and the fact the indicial response

of the room, wall and/or the heating equipment to a thermal

input of unit step function is approximate to the sum of ex- ponential functions.

The method is effective not only for the ordinal transient heating (cooling) load calculations but for the simulations of such cases as ; when the system has multiple rooms

of different conditions, when the ventilation rate of the room or the heat transfer coefficient of the wall varies, etc..

As another distinctive feature of this method, it is easy

to change At in the way of calculation whenever it is necessary,

therefore when the heat capacity of the building is quite large

and the actual outdoor conditions (including solar radiation)

should be considered, it is nossible to calculate with fewer

times of calculations with high accuracy by this method.

In the report the authors deal with the principle of this

method, method to change At ,some considerations for setting

the initial conditions to minimize the time of calculations and some examples of calculations.

Key Words : Thermal environment. Successive integration

method, Indicial response, Temperatxire excitation.

Heat flow response, Duhamel's integration formula.

Heating load, Non-linear factor. Heat transfer coefficient, Radiation, Ventilation, Change of At ,

1. Introduction

The factors related to precise analysis of the thermal environment of a building

are numerous as follows.

• Outside conditions ; fluctuations of temperature, solar radiation,

atmosriheric radiation, wind velocity, movement of sunlit and shaded area,

etc

• Inside conditions ; regulation of temperature and zoning, intermittent

heat supply, effect of unconditioned space, distribution of air temperature and radiant heat transfer in a room, rate of ventilation or infiltration and its change, etc.

1 Associate Irof. (M.E.), M.E. (Takasago Netsugaku Go.) and Research Assistant

(M.E.) respectively

305
• others ; two or three dimensional heat flow at the bea^as, columns or wall

corners, ther-^al canacity of furnitures and room furnishings, dynamic performance of heating equipment, etc.

Detailed studies on the weighting function for the analysis of thermal environment

have been carried on for a long time by Dr. T. Maeda, Dr. S. Fujii, Dr. F. Hasegawa

and others.

This successive integration method is one application of these earlier investigations, the intention is to make analysis more flexible and make calculation easier.

This method would be applicable for many kinds of problems in which the factors listed

above are concerned and depending on the purpose or the requisit accuracy of the analysis various conbinations and simplifications would be possible.

2. Duhamel's integration formula

Consider a system (such as a room, a wall or a piece of equipment) as illustrated in fipui'e 1 and assiime the heat flow response of the system to a unit step

function of temperature 0u.(t) is given by , then the neat flow response consequent on the arbitrary temperature excitation 0(t) is obtained by the use of

Duhamel's integration formula as follows ;

HCt) =

where

Jo (1)

T : variable of integration

e'(t) : the first derivative of ©(f)

"^(•t) : indicial response of heat flow to a unit step function

of temperature

however when i: <o em = 0

For example, heat flow at the inner surface of the wall under the conditions of

arbitrary inside and outside air temperature variations Q^Ct) and 6o(±') are expressed

by the sum of the responses which are excited by both excitation of St'Ct) and ^of-t) as follows ;

H(t) = HiC-f) - Hc(t)

(* ' ft

Jo where HUt) : heat flow at the inner surface of the wall when the inside air

temperature is and the outside air temperature is kept at

0°C

Hott) : heat flow at the inner surface of the wall when the outside air

te-nperature is Soft) and the inside air temperature is kept at

0 °G

-^i(X) , iieit) indicial response of heat flow at the inner surface of the wall

as seen in figure 2 ( Wa-r 4ej-' )

3. Approximation of an indicial response of heat flow

The indicial response of heat flow of the system to a unit step function of

temperature can be obtained by several ways, and in so far as the linear characteristics of the system are kept, it would be expressed by the s;im of the infinite series

of exponential functions. And in actual use it can be sufficiently approximated by

several terms as follows ;

-ic-t^ = Bo + Z Bm e^"'^ ^ S'm (3)

306
Bo

f

the term for steady state heat flow ( Watr deg-'

)

delta function

imaginary thermal capacity of the system ( ¥aTr -fi deg"' ) ySm becomes larger in order of suffix

The imaginary ther-iial ca-nacity ^ is the amount of heat to be supplied to the

system instantly when the temr erai-ure of excitation is raised suddenly/ from 0 °C to 1

°G at t = 0. However, for the approximation of the indicial response of heat flow at

the inner surface -fto(t) , it v;ould be advisable to approach it so as to satisfy the

following conditions from the nature of thermal response to an outside excitation.

"fto(t=o) = 0

i t = 0 , Bo + Z Bn. = o

There are many studies concerning tae approximation and simplification of the indicial response as shown in the reference.. 4.>.5),<)

4. Approximation of temperature variation by linear

eauation and the successive calculation metnod

of heat flow

By substituting eq.. (5) for (1), the heat flow response of the system H(t) to an

arbitrary temperature excitation Bit) is expessed as ;

ft , H(t) = e(T) • dt i- e(t=»v-^cf)

Jo

= Poem +Z[^%'(t:) &m €'''"'*''^^dT + ^H.o) Bn, e"^"*] + ^^Sc-c)^- 5"(-i-T)^T W "»"<*) ——

The heat flow H(-t) is expressed as the sum of steady state term Y(t) , transient terms

XmCt) and impulsive term p(t) . Now, let's assume the temperature variation 5c+) is approximated by a linear

equation within the time of tn 4 -t ^ tn+^t as seen in figure 5 and expressed as ;

= Ok-i^ + 02 rt) (5)

where ©,(+) = Q^t^ t « tn

0jf+) = 0

= 6h = const.

02ft) = A(»^^o (t- 1„)

/l(».»i> : temperature gradient ( deg • h~' )

Substituting eq. (5) for (^) the heat flow at the time ( tn a± ) will be ;

o defined as follows ;

307
e-'c^ = 0 < It < t. i-/it

I fCTTV i'C-t-T^ ^^T = f(t) -t>o

Equation (6) becomes

In equation (7) the underlined portion is the same as the transient term Tim at the

time of tri . Thus the following simrle calculation method is obtained ;

= Bo a-.) + /Icn.o B» 4t + ^ I Z«.(..:. "ETM +/!(«,.•, Xm }-+ /l(n*l) (8)

where = ^'^"^^ = const. (9)

^"='1^^'"^''^'"^*^ = const. (10)

If we take the time interval of each section /i"fc to be the same as seen in figure 4

then the coefficient of and Xm. becomes constant and the calculation of eq. (8)

becomes very simple. It is also easy to change At by only changing E« and x». whenever necessary.

This eq. (8) gives the rate of heat flow at the end of each interval so that we

are able to analyze the heating load or the temperature variations by substituting

this-for eq. (15) and it may be som^-what easier to understand but the following method

(which uses the quantity of heat flow during the interval instead of the rate of heat

flow at the end of the interval) would be more accurate in calculation.^'

3' Integration of heat flow in each interval

The quantity of heat flow durinf? an interval of tn ~ ( -v 4+ ) can be obtained

by integrating: eq. (7) with respect to Atr as follows (by using a variable of integration 1 instead of 4t ) ;

= 0w/3t + Z 4Z«<'«) /I (11)

where 4Xo= [ -^^^ ^

{ ^t- -i-

( , - e'/'-'S } + /-^t ] = const. (12)

^Z«(.,= Z.(«, (13)

If the time interval At is invariable after the time of tn as seen in figure 4 then

eq. (12) becomes constant and from eqs.(15) and (8) the follov/ing equation results ;

308
= /dZh.(«)-E„ + /A(»+o ilXm (1^)

where ^1 Xh, = ~ (\ -

^'^"'^'^ f (15)

= const.

If the temr^erature gradients A(n*<-> , yic-n^ « are known, each A2m(n*\) » ^Zmcntz) can be easily calculated in succession by eq. (14), and each AHcx^n , 4Hc"«) » is also obtained from eq. (11) by the repetition of sim];le calculations.

6. Equation of heat balance

( 'vhen the heat transfer coefficients of the room do not change ) Consider room k which is_ adjacent to ronms K = 1, 2, 5, where room air

teT.peratures are different from each other as seen in figuie 5« The follov;ing

equation of heat balance can be e'iven ;

<^k^^^^= V(t) - Hk(+) + Z [ Hh-rt) + 9 T^(t) { ©K(f) - 0fe«) n (IS)

where ©j, : thermal canacity of t ie air of room k (F4tr--fi- deg''

)

including that of furnis'iings of which the temperature change

is considered the same as that of the air temp.

, ©KCt) : temperature of the room and adjacent rooms

^(•t) : heating rate supplied to room air (TJa-H-) including axixiliary heat from human bodies and equipment

Hk(+) : heatloss through the surrounding walls of the room, where the

air temp, is 0fe(t) and the ad,''acent room air temp, is 6k(t) = 0

Hk(+) : inflow of the heat from the inside surface of the partitions

ad.jacent to the room K under the condition of 6k(.f)= 0

ad,iacent room Gxa)

Tk-C+) : air volume infiltrated from room^( outflow air is not related)

: specific heat of the air for unit volume CJVect -fi- deg '• m')

Assume the divisions of time aj'e the sa"ie as in figure 4- and assume the temperature

variations within the time interval ±n ^ (-tn ^'t ) are as follows ;

e(t.irt)= e<Hto = 6(.) A(x*n At (17)

And assume the heating rate and the infiltration rate T(t) are constant during

the time interval of At . Then by integrating eq. (16) with respect to "fc from in. to

(tii + ^"t ) and substituting eq. (11), the following relation is obtained ;

0K-4tJk(H«.) = lfr„(„^,y- At - ekcn-, Ai -Z.AZ''W(n) - /lX^^-Ak(-r<-^,) (continue)

309
(18)

5.1 When the temperature is known

In eq. (18) the teraperatui-e gradients ^kfot.) and ^frCn+o are known so the total

heating load "Vrkch-to is obtained easily. By subtracting the aiixiliary heat from this

result, the net heating load is obtained.

5.2 When the temperature is not known

As for unconditioned space or when intermittent heating or cooling is a factor,

the tenirerature gradient ftkcn+n is obtained from the following equation.

+ Cf /it Oh-Cn) - (9l»(a1 + ^/)(r(„+,))|- Tk- ^ [ii Qk +4Xok + "^^^ Z Tk: (r. * . ) ] (19)

6.5 'Vhen the temperatures of adjoining rooms are not known

A'hen the building has wny rooms or spaces of ^hich tenrera-ure variations are not given, we have to solve equation (19) as a sinultaneous equation of unknown temperature gradients.

Hovi^ever, from the nature of the tnprnal response to a outside excitation, the

influence of the te-iperature variation of the adjoining room is gradual as seen in

figure 2. Therefore the accuracv of the teirerature gradient of the ad-ioining room

^k("+<) is not toe important for the calculation of /^kci+o and this is a very foi'tunate

characteristic of this calculation net'iod.

In this case it would be gc^d to assume that the temperature variation of the

adjoining ro'~im is the same as that at the time At before. That is to use /Ihrcn-i which

was alrea 'y calculatpd instead of the unknown quantity Axcn-n^ in eq. (19).

7. 'Vhen the heat transfer coefficient varies wit:, time or temperature

Actually a fairly larp:e rart of the heat from a huiian body, electriciT:y , radiators

and window sunlight, transfers by radiation to the surrounding walls and moreover the

convection heat transfer coefficient varies with the wind velocity or with the temperature difference between the wall surface and the air, so that for the precise analysis

of the problem it is necessary to treat the heat transfer coefficient as a vaiiable.

In this case, it is alse possible to use the sarne method as above by considering

each surface of the wal] , of which the heat transfer coefficient is a variable, as a kind of a room where the temperature is not known. The order of the calculation is as follows ; Step 1. heat balance of the surface of the wall

An equation of heat balance of tne surface of the wall at time ± and during the

time interval of At would be v/ritten as follows ;

(Xm (t){ei,(t)- ekt(t) }- HkJ (t) + HkiCt) + Jte^a) = o (20)

(Xki

I ^kCf) - C-t) } d.t - z!Hw + 4Hit; (n+i) + Iknn+i) it =o (21)

where (Vit^fn+o = heat transfer coefficient of wall " j[ " of room k and which is

constant iuring the time of tn^C^-n + ^f)

Ji?j!(n+o : effective radiation to the surface of wall "

Jt "

0k (t) : air temperature of room k

310
0kii(t) : temperature of wall surface " Jl " of room "fe

Jo Jtr. ft , rtn+At

•^(fitt) : indicial response of heat flow of tne inside surface of

wall " S. " to a linit step function of temperature of the same surface

iM(t) indicial responce of heat flow of the inside surface of

wall " j2 " to a \init step function of temperature of the

outside surface

temperature of outside surface of wall " Jl "

By substituting the following relations to the eq. (21)

©kftt) = QkiW + (n-nT(t-tn')

&MH-) = ©W(n) + AkiCn+O (-t-tr,")

whereby

(Xwcn^o [ { ©fecn) - ew(r.) } 4t i- { Akcn^o - Ahicn^o } 4^'

]

- 0Wfn) Bokfi • -^t - Z Zwm Cn) — iiyok« • Afei!(» + |->

+ 6W(n-) fecW -^t + Z. Zk-im(r.) + ^Xotri /Iwfn+O + JkiCd+o^t = 0 (22)

If the tenperature gradients Akfn+o , AK-jfff+o are not known, assuming that Ak<n+o is

Ak(K> , and Awtnto is /lw(«) , the temperautre gradient of tie wall surface ^ktcn+n is

obtained from eq. (22).

Step 2, Equation of heat balance of the room air

After the te^iperature gradients of the surrounding wall surfaces Ak^c«+o are obtained the heat balance of the room air will be expressed as follows ;

= Zj Sf 0^HS('>*'1 4t

I 6(fi(n) - fikCn) + ^ ( Aki(«tO " AkCi+n)}

+ I [Cp Tk(«+0 ilt

I Sm-) - ek(h-, + y ( Alc(r.+n -yll,(«-o")\] +¥'k(i.tiv4t (25)

From eq. (23) the luiknown value of the temperature gradient Ak(M+o or the heating load

"Wkcn+o obtained.

8. Initial conditions of calculation

Figure 6 shows an example of the room air temperature variation of a flat house

which is built with reinforced concrete and is heated intermittently. As seen in the

example, if the thermal capacity of the system is large it will take many calculations

311
to eliminate the influence of inadequate initial conditions. Therefore , to minimize

the number of calculations, the setting of initial condition is important and the

following methods can be used.

8.1 To assume a steady state condition

One of a simple method is to make the initial condition of temperature of each room as close to the mean daily temperature of each room as possible and assume a steady state as in case 2 in figure 6, then the initial value of A'Zmw becomes 0.

8.2 To assu-ne 'ceriodical variation of temperature

vi/hen the temperature variation is aprroxiraated to a sine function as seen in

figure 7 then the value of z3 7".(ni becomes as follows ;

tn

P'" Bm +10 L / J

(24)

(25)

By using eq. (25) for the initial value of ^Zwcni at the time of fn , high accuracy

of analysis can be obtained with fewer calculations.

8.3 To chanp e the time interval of calculation

One of the distinctive features of this method is the easiness of changing At . Thus by at first using a large At and rough calculations, much detailed analysis

can be done later as seen in figure 8.

To change the time interval Air to At' , we have to recalculate the new constants

AXo , Em sind Xm and replace the terms A'Zinx) with AZ^i'i as follows

Figure 9 shows a comparison of two cases A and B.

A : calculated by i^t = 0.25('6') from the bigining to the end

fa dotted line)

B : calculated by At = 1.0 till the 13th day and change to At = 0.25 C"^) thereafter (a broken line)

The results agree peneccly after the 14th day. It will be also seen that if there

is a sudden change in neat supply and the time interval At: is large then the calculated te-iperature fluctuates for a while. However, from the nature of this integration method the calculatre.'i tempera^•u^e approaches an accurate value rapidly ana even when it is fluctuating the average value or the integrated value of the results

over the several intervals is always accurate. And of course wrien t^.e variation of

excitation is contenuous or when an interval ^t is short theie is no trouble like

that.

For the system in which thermal capacitor is quite large, such as for the underground structure, or when a synthetic effect of the syste-.s is in consideration, such

as a heating system and a room in which time constants are very different for each

other, the considerations of this sub-section are v-ry important.

Acknowledgement

This report is a summary and some extensions of the papers listed below.

The authors would like to acknowledge the continuing guidance and enco\iragement of Dr. G. Hone.

312
References

1. N. Aratani,'N. Sasaki and M. Enai ; Continuous calculation method for the

analysis of room air temperature variations, Part 1 and Part 2,

Extra Report of A.I.J. (Oct., 1968)

2. Same as above, Part 5, Extra Report of A.I.J. (Aug., 1969)

3. N. Aratani, N. Sasaki and M. Enai^ A successive integration method for

the analysis of room air temperature or thermal load variations,

Bulletin of Faculty of Sng. , Hokkaido Univ., No. 51 (Dec, 1968)

4. T. Maeda^ Some simplifications for the calculation of room air temperature variations. Report of ^.I.J., No. 2? (195-4-)

5. T. Maeda, M. Matsixmoto and '-P. Naruse ; Simplification of the weighting

function refered to heating in concrete room. Trans, of A.I.J. No. 66

(Oct., I960)

6. P. Hasegawa ; Three methods in room temperature analysis. Trans, of a. I. J.,

No. 69 (Oct. , 1961)

(Papers above are written in Japanese)

313
excitation

System

response

0n(t)=i'c h(t) e (t) H(t)

Pig. 1 Thermal system

©(t) = ei(t) + ejct)

Girt) = e<n> ft(^ ® —^

1

° th tn-»/lt Pig. 3 Approximation of temperature

314
K- 1

fk K-2

K-4 K= 3

Fig. 5 Room k and adjoining room K

Ist day 2nd day Jrd day IJth day periodical steady state

O 24 48 72 312 Fig. 6 Intermittent heat supply and calculated room adr temperature;

315
t=0 tn Pig. 7 Assuming of periodical steady state

Pig. 8 Change of time interval

13th day Uth day

Hi Hi

2n 304 312 320 328 C*^

Pig. 9 Examples of calculation when A t is changed

316
Digital Simulation of Building Thermal Behaviour

M. J. Wooldridge''

Division of Mechanical Engineering

Commonwealth Scientific and Industrial Research Organization

Highett, Victoria, Australia

The mathematical modelling of building thermal behaviour to predict transient

temperatures and humidities within it is presented in this paper The subdivision

of the building into thermally-independent regions, each comprising up to five zones, each of uniform air temperature, is the initial step. Heat and moisture

transfer to or within these zones is then described mathematically. In particular,

the heat transfer through walls is traced by using finite element techniques. The

solution of the assembled equations has been programmed in Fortran IV. Boundary

conditions for each heat transfer path within a zone are compounded within the calculation from the basic input data of external air temperature and solar radiation

(external boundaries) or internal radiative loads and solar radiation penetration

(internal boundaries). Occupancy, direct convective-to-air internal loads,

ventilation and infiltration variations may all be included as functions of time. The

program may be used to calculate either internal zone air temperature from a knowledge of cooling or heating effect supplied, or zone cooling or heating load

required to maintain a specified internal air temperature profile. Test results

from two buildings are compared with post test simulations and reasonable agreement

between measured and calculated temperatures is demonstrated.

Keywords: Building, digital simulation, heat transfer, internal air

temperature, cooling or heating load, test results, thermal behaviour.

1 . Introduction

The creation of a mathematical model for whole or for part of a building in order to study its thermal behaviour is a task now commonly practised in the air conditioning field [1 , 2, 3] 2. The

model may be relatively simple, amenable to hand calculation, or more complex, requiring digital

computing aids. That there is a use for such models is emphasized by the fact [4] that in the U. S. A. , for example, which itself accounts for 35% of the world's annual power consumed, a third of this is expended on providing environmental comfort for people. Such considerations justify work aimed at

(a) generating more confident estimates of building cooling /heating / air- c onditioning

requirements

(b) allowing quantitative assessments of the more effective use of building properties,

(c) enabling more effective programming of installed plant.

The task of creating such a model was commenced during 1969 utilizing the digital computing

facilities of C S I R O. It was divided into two phases: initially a description of the heat transfer

aspects of building performance was attempted and secondly an extension to humidity prediction was

incorporated. The first phase is complete, the second is in progress and may be commented upon

during the Symposium.

Part of the material contained in this paper was presented [5] to the 1970 Annual Conference of the Australian Institute of Refrigeration, Air Conditioning and Heating to whom acknowledgement is made

2. Modelling Technique and Assumptions

2. 1 Building Subdivision

Any part, or the whole, of a building may be divided into a number of discrete zones not

Senior Research Scientist. Figures in brackets indicate the literature references at the end of this paper.

317
necessarily thermally isolated from one another, but possessing different distinguishing thermal

characteristics or boundary conditions. For example, inner and perimeter modules of a large

building, or rooms associated with north and south walls, would possess sufficiently different

boundary conditions to make them identifiable as zones. The choice of zones, in which the air

temperature is assumed uniform, is made by the user, and is, to a large extent, arbitrary. Such

zones form the coarse subdivision of the model: in each there are numerous heat transfer paths,

e.g. wall, window, betwe'en some source temperature and room temperature. These paths form

the basic elements of the heat transfer model.

The subdivision of a building into such zones is shown schematically on figure 1. This central

and peripheral configuration is the type of breakdown which might be employed for a storey of a multi-storey building. On the other hand, a residential structure would require different subdivision

for analysis, such as is shown on figure Z. It is emphasized that, although it is often convenient to do so, it is not mandatory to use zones identical to those of a particular air conditioning system.

It is the aim of the calculation techniques that, having established the model for any particular

building, the input of desired boundary conditions as a function of time may permit the output of either air conditioning sensible load for a prescribed indoor temperature profile or the converse. Later phases of the work will incorporate the moisture transfer processes and generate a more

complete air conditioning solution.

2.2 Model

The equation representing the balance of sensible heat transfer to the air within a zone may be

described thus :

Cooling or Heating Effect from plant

+ Direct-to-air convective load (e.g. equipment, people)

+ Fresh air load

+ Surface-to-air convective load from all exposed surfaces within zones

= 0.

Using symbols defined in the list this equation may be written

JJ QLS + QID + QSFA + I h. A. (T - T.) = 0 (1)

. , 1 1

^ w. i' ^

' J = 1 J

Figure 3 shows the situation schematically.

The calculation of building sensible load requires that QLS be made the subject of eq (1), thus

J J

- QLS = QID + QSFA + I h. A. (T - T.)

j - 1 ^

Considering each term on the right hand side individually, the first is derived directly from input

data on the number of people and their work rating and on the operation of equipment within a zone. These are both permitted as functions of time in the input information.

The second, fresh air, term may be re-expressed

QSFA = HFA (T - T.) (2) ^ o 1

^

'

where HFA is the product of a constant x fresh aii' ventilation and infiltration rates, and Tq and T^

outdoor and indoor air temperatures respectively. Again all parameters in this expression are permitted as functions of time.

The third term is more complex to derive: finite difference numerical procedures are used to solve the diffusion equation for each path from the individual boundary conditions for that path; hence

the inner wall temperature and convective flux is obtained.

The establishment of boundary conditions for each path at each integration interval is performed

318
within the program from input data of outside air temperature, solar radiation, shading and of internal

radiation and air temperature. It is in this fashion that radiation is introduced; that is, radiation,

be it long wave or short, is allowed to fall on the appropriate surface, be absorbed and ultimately

appear as a convective load to the indoor air. In this way both the thermal capacity of each heat

transfer path is accommodated and radiation is handled in the manner in which that mode of heat

transfer occurs in practice Thus the radiant contribution to load does not appear explicitly in the results of the load calculation, nor is any factoring of radiant heat required.

In order to predict indoor air temperature, given a specified heating or cooling effect, Tj^ must

be made the subject of eq (1). Thus

QLS + QID + HFA . T + Ih. A. Tw

T. = ^ ° J J (3)

1 HFA + y h. A.

^ J J

Latent loads are also handled within the program. A simple calculation of latent heat gain due

to equipment, people and fresh air is calculated from the input data according to the practice of the ASHRAE Guide [6]. If internal humidity is to be calculated simultaneously with indoor dry bulb

temperature, the increase in moisture level over the integration interval is assessed and combined

with the internal air dry bulb temperature to calculate relative humidity.

The whole calculation proceeds on a step-by- step basis in time, each time increment being

equal and determined from the building properties, which do not normally change with respect to time. There are always an integral number of time steps to the hour and results are normally output

every hour. The maximum integration increment is 1 5 minutes.

The facility has been provided for the user to include the characteristics, including thermostat

operation, of an air-conditioning system when they cannot be expressed independently as input data

in the form of cooling effects.

2.3 Assumptions

Both diffuse and direct solar radiation (incident upon any surface) are calculated as a function

of time, either from total and diffuse radiation for a horizontal surface, which must be input in tabular form, or from the expressions of reference [7]. A test is made at each time interval to determine whether any path is in shadow: those in shadow are exposed to the diffuse and reflected

direct components, whereas those in the sun receive all components.

Long wave radiation is assumed to be incident on all external paths according to the product of a coefficient hj^ and the difference between surface temperature, T.^ . and the mean radiant temperature, Tj^. (Tj^ - Tq) may be input as a function of time. ^

Any radiation passing through the windows of a zone is assumed to be incident on and wholly

absorbed by the floor of the zone. Internally generated radiation is apportioned to each path of a zone according to an input form factor. Thus we may create a forcing or source temperature on the path boundary remote from the room

and a sink temperature on the room side boundary

Q + h (T - T ) T = T + — ^ (4) source o ^v, + h

"rsink - ^1^ IT1

These temperatures are analogous to the sol-air temperature [6] and are derived from a defining

equation of the type

K ' ^r) (^3,,,,, - T^) = (T^ - T^) + Q3 + h^ (T^ - T^)

where T.^ is the wall temperature of any path.

319
Internal paths either wholly within a zone or separating two adjacent zones are permissible.

Both source and sink temperatures are defined by equations of type (4) above for such paths.

All paths are assumed homogeneous in the direction of heat transfer so that they possess the properties of a uniform medium in that direction. Later stages of the study will enable nonuniformities to be modelled more exactly.

The building thermal model, including its boundary heat transfer coefficients, is not permitted

to vary as a function of time. Again, later stages may permit some variation of these coefficients.

3. Applications

3. 1 Test Building

Experimental data from two different test periods has been taken to illustrate comparisons of temperatures measured and predicted within a fairly heavy two storey office building. Curves are

included on figure 4 illustrating these comparisons. Further work on this aspect is continuing, but agreement in these tests is considered encouraging.

3.2 Examples of Use

Two hypothetical buildings in Sydney have been chosen to illustrate the calculation of air

conditioning sensible load, under normally imposed design climatic conditions and under measured

severe climatic environments. The normally-used design dry bulb of 32°C has been adopted to perform a load calculation by the ASHRAE Guide method for both an 1 8 square brick veneer residence

and for a typical storey of a city office building. Maximum sensible space loads (excluding fresh air)

of 8. 5 kW and 83 kW respectively, for a constant indoor dry bulb temperature of 24'-'C, were deduced

from this approach. The computer model for each building was fed with climatic data from the three

hourly Commonwealth Bureau of Meteorology readings on magnetic tape for Sydney. Heatwave

periods were input for the hottest spell in the ten years (1955-1965) on record and for the spell

containing a maximum dry bulb exceeded only 10 times during that period. Clear day solar radiation was input for these spells being calculated by a method [7], previously described by the author.

Figures 5 and 6 show how the sensible space load of the office storey varied with time during these

spells. The difference between the once - in- 1 0 -year maximum and the once-in-a-year maximum is significant, the latter amounting to 93% of the former. A comparison is summarised in table 1 below

for both the residence and the office buildings.

There are substantial differences between the cooling calculated from the transient thermal

model and from the ASHRAE Guide quasi- steady- state approach. However, it is not advocated that actual climatic sequences be used for design purposes: that would require far too much analysis. It is proposed to develop design sequences using a transient mathematical model to test for frequency

of load occurrence, but this will be the subject of a separate paper. At this time, these examples

are included to illustrate uses of the computational model.

Table 1. Maximum sensible coolings loads for

3 different external environments (kW)

Sydney Building

ASHRAE Guide

PRESENT

Once in 10 years

METHOD

Once in a year

Max.d.b.t. 32°C Max. d. b. t. 42. 2°C Max.d.b.t. 38.2°C

18 sq . Residence (167 m^)

Space load

People, Equipment and fresh air

TOTAL

8. 5

2. 0 10. 5

6. 4

2. 3

8. 7

5. 0 2.2

7. 2

Storey of Multi- storey block

Space load including people,

equipment

Fresh Air

TOTAL

83. 2 14. 4

97. 6

70. 6 31 . 4 102 . 065. 7 24. 3 90. 0

320
An alternative calculation on the above office building illustrates the Use of the program in predicting air temperature. Indoor air temperature has been estimated over a three day design

period for three levels of constant cooling effect, at 50, 75 and 100% of maximum required by the calculation for constant room temperature of Z4°C . Figure 7 illustrates the temperature profiles

obtained: from these it may be observed that, standby and pull down considerations aside, a somewhat smaller plant could still generate comfortable conditions. It is, of course, easy to examine the indoor temperature profile under any occupancy loading and after periods of shut down over weekends

say, so that better informed planning of standby and pull down requirements is possible.

4. Conclusions

It has been the aim of this paper to present a broad outline of the mathematical modelling procedure for the prediction of building thermal performance now set up at the CSIRO Division of Mechanical Engineering, and to illustrate some of the validation and uses.

While the experimental validation is continuing on larger buildings, the results obtained so far are sufficiently promising to suggest that the model is reliable.

Results of applications attempted so far indicate that, by being able to simulate correctly the heat diffusion process and by inputting radiation so that it is first of all absorbed, the part of a building thermal load transmitted via the structure to the air may amount to only some 75% of that predicted by conventional quasi- steady state methods.

The power of the modelling technique in being able to estimate indoor temperature excursions

for many varieties of input enables an investigation of the effects of different building properties or

of modes of operation of cooling or heating plant.

5. Refe

1 Stephenson, D. G. , Method of determining

non steady state heat flow through walls and

roofs of buildings, JIHVE, May 1962.

2 Stephenson, D. G. and Mitalas, G. P. , Cooling load calculation by Thermal Response Factor Method, Trans. ASHRAE, 73

(1967).

3 Boeke, A. , New developments in the computer-design of air conditioning systems,

JIHVE, October 1967.

4 Jordan, R. , Environment Control of Enclosed Spaces , Fed. Conf. Aust. Inst, of R. A. H. Melbourne, April 1970, Paper No. 4.

ences

5 Wooldridge, M. J. , The prediction of building

thermal performance. Federal Conference

Australian Institute of Refrigeration, Air

Conditioning and Heating, Melbourne, April

1 970, Paper No. 6.

6 ASHRAE Handbook of Fundamentals,

Chapter 28 (1967).

7 Wooldridge, M. J. , Solar radiation and its effect on air conditioning load. Paper delivere

to AIRAH S. A. Division, November 28th 1969. To be published as Division of Mechanical

Engineering Report E. D. 13.

6. Notation

Symbols

A - area

h - heat transfer coefficient

HFA - = constant x fresh air flow rate from

both ventilation and infiltration JJ - Total number of heat transfer paths

per zone of building

Qg - Short wave radiation x path absorptivity

Ql - Long wave radiation x path absorptivity

Qj- - internally generated radiation

intensity x path form factor

QLS - sensible load for cooling and heating

QID - internally generated direct convective

load

QSFA - fresh air load

T - Temperature

t; - glass transmissivity

Subscripts

j - path identifier

i - indoor condition

o - outdoor condition

R - long wave radiation

W - wall

Source - external boundary layer forcing value

Sink - internal boundary layer forcing value

d - directional n - non-directional

321
FLOOR AND

CEILING

WINDOW

EXTERNAL WALL

INTERNAL WALLS

(INTER-ZONE )

INTERNAL WALL (INTRA -ZONE)

1. Schematic of Building Plan Subdivision into zones.

2 BEDROOMS

AND

BATHROOM

KITCHEN

LDRY. ETC. LOUNGE

ROOF SPACE IS ZONE 5

2. Typical Zonal Subdivision for Residential Building Analysis.

322
\

DIRECTIONAL

RADIATION.

CONVECTION

CONVECTION h,.T, ^ I CEILING ( PATH TYPE 2 )

EXTERNAL WALL /

( PATH TYPE 0 ) ^

INTERNAL

RADIATION a..

/ / J / /t/ 2 / / ^ / / ^ ^ /

CONVECTION

DIRECT TO AIR

a.

RADIATION V

NON DIRECTIONAL*

LONG WAVE

ADJACENT

ZONE L

PARTITION

(PATH TYPE 3 )

CONVECTION

T. (:T. )

COOLING

^^

EFFECT

a..

FLOOR

(PATH' TYPE 1 ) h,. T,

3. Schematic of Incident Heat Fluxes for Typical Building Zone.

16-

0 10 20 30 40 50 60 70 80

TIME - HOURS

4. Measured and Predicted Air Temperature Profiles for an office building in Melbourne.

323
DESIGN FIGURE BY ASHRAE GUIDE -300

^3 ' ' ' ' ' '

23JAN 24JAN. 25JAN 26JAN. 27JAN 28JAN 29JAN. 30JAN. 31JAN

DAILY MAXIMUM

DRY BULB TEMP.

I 1 23-3 'C

>. J

74 0 'f

310 880 393

1030

40-9 105 9

42-2 108 3

39'S 103 4

2S'S 78 0

23-8 750

255 780

5. Sydney Office Block - Typical Storey : Estimated Sensible space cooling load

for period 23 - 31 Jan. I960. (Maximum dry bulb temperature on 27 Jan. I960 never exceeded during 1955 - 65)

DESIGN FIGURE BY ASHRAE GUIDE

24 NOV. 25 NOV 2(NOV 27 NOV 28 NOV. 29 NOV 30 NOV 1 DEC. 2 DEC 3 DEC.

DALY MAXIMUM 1 22-1 "c 27-7 DRY BULB TEMP.1 22-1 "C 27-7 38-2 22-7 24-4 22-7 22 7 37-1 20 5 24 ( J

72 0 V 12 0 WI'O 73 0 70-0 73 0 73 0 W 89 0 77 0

6. Sydney Office Block - Typical Storey : Estimated Sensible space cooling load

for period 24 Nov, - 3 Dec. 1964. (Maximum dry bulb temperature on

26 Nov. 1964 exceeded 10 times during 1955 - 65)

324
THIRD DAY OF DESIGN SEQUENCE

7. Sydney Office Block - Typical Storey : Estimated Mean Air Temperature for

3 different (constant) applied cooling effects.

325

A Computer Programme for the Calculation of Individual Room Air

Temperature of Multi -Roomed

Buildings

1 K. R. Rao and Prakash Chandra

Central Building Research Institute Roorkee, U. P. , INDIA

In recent years the use of computers for the calculation of heating and

cooling loads and for the prediction of indoor air temperatures of buildings

has been well established and is in the increase. Many organisations in a number of countries have developed suitable computer programmes in accordance with their specific requirements and the computer facilities available.

Most of the programmes which are meant for the calcvdation of indoor air

temperatures of the unconditioned buildings, treat the whole building as a

single enclosure. However it is also of practical interest to determine the individual room air temperatures within a multi -roomed building. For this purpose a computer programme which is siiitable for a small machine like IBM 1620 digital computer with 60K memory has been developed. This

programme takes into account the orientation of the rooms, ventilation,

internal heat sources, internal mass and furnishings and solves a set of linear simultaneous equations for obtaining the indoor air temperatures of the individual rooms. Provision has also been made in the programme to determine the inside surface temperatures of walls, roofs and floors, mean

radiant temperatures and the heating and cooling loads of individual rooms,

if desired.

The main programme utilizes a good deal of precalculated data obtained

by a number of separate programmes developed for the calciilation of sol -air

temperatures, shade piatterns of overhangs and fins, solar heat transmission

through glass and frequency response characteristics of building sections.

Key Words: Computer programme, driving point admittance function,

Fourier analysis and synthesis, heating and cooling loads, heat trans- mission coefficient, matrix equation, non-structural heat gains, room

air temperature, shade patterns, sol-air temperature, surface temperature, transfer admittance function.

1. Introduction

The problem of determining the thermal response of bxaildings under any given climatic

conditions has drawn the attention of many research and industrial organisations the world over With the ever increasing use of digital computers, in all most all branches of building science,

the computational methods, which were earlier considered as unmanageable, are now finding wi

Scientist and Senior Scientific Assistant, respectively.

327
application. This trend is more evident for the problem of the calculation of inside air temperatures

and heating and cooling loads of buildings exposed to variable weather conditions.

In the last decade several computational techniques, which are specifically suitable for high

speedy machine calculations, have been evolved by various researchers in the field of Heat trans

fer(lf'(2) (3) (4). A number of computer programmes for the accurate estimation of heating and

cooling loads and the indoor air temperatures have also been reported (5) (6) (7) (8). However,

almost all of these programmes treat the building as a whole as a single enclosure and do not account

for the variations of temperatures of the individual rooms within the building. The present paper

deals with a method and a computer programme developed for the calculation of individual room air

temperatures of multi. -roomed buildings.

2. Factors Involved in Room Air

Temperature Calculations

In order to determine the thermal behaviour under a given climate, a large number of factors are to be taken into account. These factors can conveniently be grouped into three categories,

2. 1 Climatic Factors

(a) Diurnal variations of shade air temperature

( b) Solar radiation (direct and diffuse)

( c) Net low temperature radiation exchange

( d) Wind speed and direction

( e) Humidity

2. 2 Design Factors

(a) Thermal characteristics of building sections i.e. walls, roof, ceiling, floor, doors,

partitions etc.

( b) Surface radiation characteristics i. e. absorptivity, emmissivity and transmitivity of building sections

( c) Shape and Orientation of the building and internal layout

(d). Window design, number, location and type of glass areas

(e) External and Internal shading devices such as overhangs, fins, louvres and venitian blinds,

curtains respectively

2. 3 Utilization Factors

(a) Ventilation

(b) Internal heat sources and sinks

(c) Density of occupancy

(d) Living habits which influence (a), (b) and (c).

The complexity of the problem increases not only due to the large number of variables that come

into the picture but also due to the interactions between them.

3. Computational Method

As buildings are subjected to periodic variations of air temperatures, solar radiation and other

climatic elements, the inside air temperatures of buildings would also fluctuate periodically. Several methods have been developed for determining the thermal response of building elements (9) (10) (11). Of these the transfer Martix method of Van Gorcum (12) for the determination of periodic heat

flow through a homogeneous slab has gained popularity being well suited for high speed digital compuFigures in brackets indicate the literature references at the end of this paper

328
tations. The Matrix method was further extended by Muncey (13) for predicting indoor air temperature variations of a sj.ngle room. In this approach, the bounding elements of the enclosure are

taJcen as parallel heal/paths and the internal temperatures are computed by applying the principle

of heat balance for steady as well as harmonic parts.

The equations for indoor air temperature variations (14) can readily be expressed in terms of areas, sol -air temperatures of exposed surfaces, steady state heat transmission coefficients

(U values), transfer and driving point admittance functions of building sections, ventilation rate and internal heat sources and are given below.

t + la la, h Cos (wj^r -</)h) (1)

where t is the temperature at any instant, t and t are the steady state and periodic components

of the temperature waveform respectively, w is the angular frequency, (p is the phase lag and T is the time and the subscripts, ia, and h stand for internal air and number of harmonics respectively.

xa m

H1 A U t sa C V

t _

z: 21 A U + C V

1 (2)

where A and U are the area and the steady state heat transmission coefficient of a building section

respectively, C is the specific heat of air at constant pressure, V is the ventilation rate, W is the steady state component of the variable heat source, m and ^ are the number of bounding elements

and sources respectively and the subscripts, sa, oa and i stand for sol -air, shade-air and

internal respectively.

*ia,h ^ ATYj^

1 sa, h

+ t oa, h CV

I

1 W, y^ADY^ +^ADYj^+CV

1 1

(3)

where TY and DY are the transfer and driving point admittance functions of the building section

respectively, W is the periodic component of the variable heat source, k is the number of internal masses in the enclosure.

In the above case the internal elements such as partitions and intermediate floors are treated as slabs for which the heat flow at the central plane is zero. The assumption involved here is that the temperature fluctuations on either side of the internal elements are symmetrical. In other words

the building as a whole is taken as a single enclosure and the variations of air temperatures within

individual rooms are neglected. However, there can be situations where significant differences in

air temperatures from room to room within the same building occur. This is specially so in the case of multi -storey bviildings.

In order to make the solution of the problem more general, it is imperative that the heat

balance for each room should be considered separately. In a multi-roomed building, the air

temperature of any room will not only be a function of the exposed elements, but also of the air

temperatures of the surrounding rooms. As the air temperature of a room is in turn depends on

the air temperatures of other rooms these are reqmred to be determined simultaneously.

The heat balance eqviations for steady and periodic parts of any room in a multi -roomed

building are given below.

'la 2^ AU + CV

1 +1 Au H-^t^ Au +2:

t -

W. + t „ CV = 0 (4)

where e and i are the number of exposed and internal elements of the room

329
and

ia, h

m k

T' ADY, I- T' ADY, + CV

e

1 ^sa ATY

h 1 h ,

+ t oa, h

h

CV = 0 (5) On the total 'n' such equations for steady state and '2 n' equations for each harmonic component

(being complex quantities) of the periodic part will result for a building having 'n' rooms. For high speed computer applications it is more convenient to express these equations in

a matrix form, A typical matrix equation (for steady state component) that would result from

a set of 'n' simultaneous equations is given below.

"11 "l2 "l3 - -

-

- - ''In ha, 1 Cl

^21 ^22 X23 - - -

- - "2n t. T la, 2 ^2

"31 "33 "33 - -

-

- - "3n

X

^ia, 3 ^3

X 1 nl ^n2 ''n3 - - ^nn *ia, h _Cn_

(6)

Similar matrix equations for real and imaginary parts for each harmonic component of room

air temperatures can be formed. The Fourier components of the air temperatures of individual rooms will then be obtained by solving these matrix equations. The hourly air temperatures for

each room can also be obtained by Fourier synthesis.

4. Computer Programme

A generalised computer programme for the determination of individual room air temperature

variations in a building, should naturally take all the factors involved and their mutual interactions

into account. A schematic diagram of the stages in the calculation is given in Figure 1. A flexible computer programme has been developed in FORTRAN II language for the above

said purpose. The main programme consists of a number of sub-programmes which would

calculate the sol -air temperatures of differently oriented surfaces, shade patterns of overhangs

and fins, solar heat transmission through glass and thermal system functions of the building

sections from the climate and design factor input data. A separate programme has also been

prepared for the precalculation of solar radiation data for differently oriented vertical and sloping

surfaces, which is required for the calculation of sol -air temperatures, Non structural sensible

heat gains are computed by the hourly variation of the loads due to ventilation, internal heat sources,

(lights, fans and other appliances) and room occupancy. The directly transmitted solar radiation

through glass area as modified by the internal shading devices, is considered as an internal heat source in these calculations.

The programme is made flexible and will determine the surface temperatures (inside and

outside) of wall and roof sections and the air conditioning loads of individual rooms, if desired.

As a small machine (IBM 1620, with 60K memory) is only available, all the sub-programmes

mentioned above are used as separate programmes to calculate the required input data for the main

programme. However where larger macliines are accessible all these sub-programmes can be

clubbed with the main programme as CALL type sub-routines.

330
4. 1, Flow chart

The sequential steps in the computation of room air temperatures, surface temperatures and

air conditioning loads are shown in Figure 2 in the form of a flow chart.

In this programme the number of rooms (N) in a building, significant harmonics (L) to be

considered and hourly shade air temperatures are first read. The following operations required

for determining the heat flow through vari ous parallel paths into each room are performed.

(a) Shade air temperature waveform is Fourier analysed.

(b) Number of exposed (NE), internal (NI) elements and number of internal masses (NK)

for each room are read.

(c) Hourly sol -air temperatures for each exposed element (precalculated) are read and

Fourier analysed.

(d) Shaded and sanlit areas of exposed elements due to the presence of overhangs and

fins, for each hour of the day, (which were precalculated) are fed.

{e) Steady and periodic heat flow characteristics for each harmonic, which are obtained

by a separate program, are read and the corresponding harmonics of the heat flow

into the room are computed.

(f) The non-structural heat gains viz. , lighting, ventilation, occupancy loads etc. , which were also precalculated are added harmonic wise.

^g) Driving point room admittance coefficients at the internal surfaces, due to the periodic

parts of the indoor air temperature fluctuations, are computed.

(_h") Transfer and driving point room admittance coefficients for the internal elements and masses of the room concerned are then calculated.

^i) The elements of the matrices for the steady and periodic (in terms of real and imaginary)

parts are generated.

0^ The steady state and harmonic components of the air temperatures for all the rooms

in the building are obtained by solving the matrix equations with the help of a call subroutine SOLEQN.

(k) The hourly temperatures of the rooms are obtained by a call subroutine FSS.

The inside surface temperatures of the building elements of a room are required in cases where radiant heat gains to the human body is to be estimated. For such situations additional

computations are required and a provision has been made in the program to calculate these

quantities by a call subroutine SURTEM.

If the estimation of hourly variation of cooling and heating loads of each room is also required,

the call subroutine LOAD provided in the program would perform the necessary computations.

5. Conclusions

(a.) The limitations imposed by the assumption of considering a large multi -roomed b\ulding as a single enclosure in calculating the indoor air temperatures and air conditioning

loads are removed by the method and the program presented in this paper.

(b) It is now possible to determine the temperature variations within the individual rooms

and thus to evaluate the effect of various design factors on the thermal performance of bmldings on room by room basis.

331
(c) These long felt refinements in thermal calculations for buildings are only possible because

of the speed and accuracy provided by the digital computers. However, it maybe stres- sed that the accuracy of the computer estimation basically depends upon how accurate

the input data is.

(d) The approach of using considerable precalculated data obtained by a number of subprograms is not the inherent limitation of the method but was only adopted to suit a small

machine like IBM 1620. The program can be made more versatile by linking all the subprograms as call subroutines of the main program, if large sized computers are easilyaccessible.

6. Acknowledgement

The work reported in this paper forms part of the program of Central Building Research

Institute, Roorkee, India and is presented with the permission of the Director,

7. References

(1) Pipes, L. A, , Matrix analysis of heat transfer problems, J. Franklin. Inst. Vol. Z63, No. 3, p. 195 (1957).

(2) Dusinberre, G. M. , Numerical analysis

of heat flow, McGraw ffiU (1949).

(3) Brisken, W.R. , Reque, S. G. , Heat load

calculation by thermal response, AshraeTrans, Vol. 62, p. 391 (1956).

(4) Vadica, V, , A contribution of heat conduction in composite continue, Appl. Sc. Res.

A., Vol. 11, 473-477 (1963).

(5) Holden, T.S. , The calculation of fluctuating heat flow in buildings, Aust. Computer Conf. , Melbourne (1963).

(6) Rao, K. R. , and Prakash Chandra, Digital

computer determination of thermal frequency response of building sections.

Build. Sc., Vol. 1, p. 299 (1966).

(7) Mitalas, G. P. , and Arseneatilt, J. G. , Fortan IV programme to calculate heat

flux response factors for multi -layer slab,

NRC Canada, Computer programme 26,

(1967).

(8) Buchberg, H. , and Nasuishi, J. , A rational evaluation of thermal protection

alternatives for shelter. Build, Sci, Vol.

2, 37 (1967).

(9) Rao, K. R. , Thermal system functions of building fabrics by matrix method. Seventh

Cong. Theo and Appl. Mechanics, New

Delhi (1962).

(10) Mitalas, G. P. , Calculation of transient

heat flow through walls and roofs, Trans

Ashrae, Vol. 74, Part 2, p 182 (1967).

(11) Kusuda, T. , Thermal response factors

for miilti -layer structures of various heat

conduction 3 ysterrs , Ashrae- J., Vol. 11, No. 1, p 64 (19 69).

(12) Van Gorcum, A. H. , Theoretical considerations on the conduction of fluctuating

heat flow, Appl. Sc. Res. A2, 272-280,

(1951).

(13) Muncey, R.W., The calculation of tempe

ratures inside buildings having variable

external conditions, Aust. J. Appl. Sc. 4_ p 189 (1953).

(14) Rao, K. R. , and Prakash Chandra, Application of thermal system functioris in predicting thermal behaviour of buildings,

14th Cong. Indian Soe. Theo and Appl.

Mechanics, Kurukshetra (1969).

332
Design

Factors

Climatic

Factors

Utilization

Factors

Calculation

of

1 . Sol -air Temperatures

2 . Shade Patterns

3. Thermal System

Functions

4. Non-Structural Sensible

Heat Gains

Computation

of Hourly Air Temperatures

of Individual

Rooms of a Building

Calculation

of

1. Surface Temperatures

2, Air Conditioning Loads

Figure 1 Schematic Diagram for Digital Computer Determination

of Temperatures within Buildings

333
Start _JR ead

N, L,

CALL FAS

DO I =

/ Read \

^ NE, NI, NK J

Tsd /

CALL FAS

No

Read

Shaded and

Sunlit Areas

DO J = 1. L

Read \ U, TY, DyJ

Compute and Sum

Heat Flow, SUM (J)

Compute

Driving -point Room

Admittance Coefficients

Read

NSHG, V

CALL FAS

DO J = 1, L

SUM (J) = SUM (J) + NSHG (J) DO K 1, Nl

DO J = 1, L

Read

A, U, TY, DY

Compute

Transfer and Driving Point

Room Admittance Coefficients

DO K = 1, NK

DO J = 2, L

Read

A, DY

Compute

Driving Point Room

Admittance Coefficients

DO J = 1, L

Generate

Matrix

CALL SOLEQN

DO I = 1, N

CALL FAS

Yes

CALL SURTEM

^o

Yes

CALL LOAD

Ns <

Stop

Figure 2 Flow Chart for the Main Programme

334
A Practical Method for Calculating

Room Temperature, Heating Load

and Cooling Load of Multiroom

Kiyoshi Ochifuji

The Faculty of Engineering, Hokkaido

University, Sapporo 060 Japan

It is possible to set up heat balance equations representing

the dynamic thermal characteristics of a multiroom by using

weighting functions, if the system is linear and invariable.

With the advent of the digital computer, it is now possible to solve them directly, even if there are numerous rooms with different thermal behavior. However, as the number of rooms increases,

the cost of calculation and the capacity of the computer required

increase rapidly. Therefore, it may not be practical to solve

the balance equations directly, when the number of rooms is large.

This paper proposes a practical method for calculating room

temperature, heating load and cooling load of a multiroom by means

of a digital computer of relatively small capacity at reasonable

cost. Rooms constituting a multiroom system may be divided into

two groups; one has a stronger influence on the relation between

the excitation and the system's response, the other has a lesser

influence. Then, the response to the system consisting of only

the former group may be good approximation to the response to the

original undivided system. The accuracy is not known exactly at

this stage, but it is shown that the effect of neglecting the

latter group of rooms can be easily investigated on the principle

of superposition or Thevenin's theorem. Also the improvement of

accuracy can be made to any desired degree by a relaxation method

on the same principle. Many examples for obtaining the room temperature of a multiroom by this method were studied and it has

been found that, with an increasing number of rooms, the usefulness of the present method for analysis and synthesis increase

rapidly.

Key Words: Multiroom digital computer, room temperature

heat source, Thevenin's theorem.

1. Introduction

It is possible to set up heat balance equations rei3resenting the dynamic thermal

behavior of a multiroom system by using the linear theory. Actually, it is difficult

to obtain analytical solutions for room temperature because of the complexity. With

the advent of the digital computer, it is now possible to obtain numerical solutions

with any desired accuracy, even if there are numerous rooms with different thermal

performances. It may not be worthy to get the solutions more accurate than required

for practical problems. To avoid such worthless calculations, it is necessary to simplify the system's elements and the mathematical models. However, as the number

of rooms increases, the cost of calculation and the capacity of the computer required

increase rapidly. Therefore, it may not always be practical to solve the balance

equations directly when the number of rooms with different thermal behavior is large.

Our method is practical for engineering and application problems because calculations

can be made by hand, by desk calculation or the digital computer of relatively small

capacity. Also, it can be done at a reasonable cost, depending on the amount of

calculations needed.

This method has been applied to obtain the room temperature of a multiroom system

335
consisting of two rooms, five rooms in parallel, and fifteen rooms in series. To

explain the present method clearly, the mathematical models are simplified by assuming

a one dimentional heat flow, by uniform room air temperature, and by a combined heat

transfer coefficient which would approximate the radiant heat interchange, between

the inside surfaces, and the convective heat interchange, between the inside surfaces

and the room air. Attempt is made to calculate the indoor temperature variation

caused by air conditionin"?; , taking the initial temperature 0 °C and assuming the

outdoor temperature always being 0 °C . These calculations are carried out using an electronic digital computer with the capacity of 2-K words.

2. Practical Method

2.1 Connection and Division of Systems

There are two systems; one has some heat sources, and the other has none. Therefore, there can be temperature variation in the former. Nov/, we attempt to connect the latter to the former at any boundary position with a constant temperature

of 0 °C . Consequently, different responses will occur because of the effect of the

connection. To investigate the effect, an artificial heat source is supplied to the

combined position. The magnitude of this heat source is equivalent to the heat fluxes

at the same position of the original system, which is caused by t he original heat

sources. The response of this artificial heat flov/ to the combined system represents

the difference of the responses betv/een the original system and the combined one, that is the effect of the connection. This will be described here in terras of the

superposition principle as follows.

First, a couple of artificial heat sources, heating and cooling with the same thermal quantity, is supplied to the combined position of the total combined system,

as shown in figure 1-A. Then, there is no change in the thermal performance, since

their total heat fluxes supplied artificially become zero. Second, a couple of heat sources is decomposed by the superposition principle.

Two cases result; one is an artificial heat source with the original heat sources,

the other is only an artificial heat source, as shown in figure 1-B,C. If the temperature of the divided position in the former case is kept at 0 °C at all times, this

system should be equivalent to the original one shown in figure 1-D, The magnitude

of the artificial heat source producing such a condition is equal to the heat fluxes

at the marked position in the original system. Therefore, the effect of the connection is obtained by calculating the temperature distribution in the latter case shown

in figure 1-D. V/hen the artificial heat source is less than the original one, it can

be very practically ignored. Thus, the response to the original system can be used

as an approximation of the response of the combined one. This approximation can be

directly applied to the system in which addition of rooms is made.

Furthermore, we can attempt to divide a system into two parts by the principle

mentioned above. It is possible to simulate the divided system to the original one described above, so that the effect of the division can be obtained by the same method

of the connection, as shown in figure 1.

2.2 Practical Method

Rooms constitution a multiroom are divided into two groups; one has a stronger

influence on the response, the other has a lesser influence. Then, the response to the divided system of the former may be an approximation to the response to the total

undivided system. The effect of neglecting the latter can be easily obtained by the

method given in the foregoing paragraph. If the effect is negligible, the accuracy

at this stage is sufficient for engineering purposes. In order to obtain an accurate

solution, the improvement of accuracy must be made by calculating the response to the

total system caused by the artificial heat source supplied for releasing another one

at the divided position, as shown in figure 1-i^. This system is also divided into

two grou-S different from the previous ones. Then, the response to the divided system

consisting only of the group having a stronger influence on the thermal behavior can

be an approximation to the response to the total undivided system. The second approximation is obtained by adding the improved result to the first one. It is then

deciri.ed wliether or not to continue the improvement of accuracy. It is necessary to continue successively the process of division and connection, until the accuracy

becones good. Then, the final solution is obtained by adding the result of each

process. If the improvement is continued to infinity, the complete solution is

obtained

336
The divided system should be as simple as possible. It is convenient to take a unit room, since there will be no trouble in how to divide a system, and since the

thermal characteristics required for this method are only of a unit room, and not of

a multiroom system.

Summarizing, calculation by this method may be performed in some very distinct

stages as follows.

1. First stage

a. The divided system is taken to be the heating or cooling room. The air

temperature caused by the original heat source is calculated under the

condition of the air temperature of 0 °C for all adjoining rooms.

b. The magnitude of the artificial heat source for producing the temperature

0 "C must be calculated for every adjoining room. It is then decided whether

or not to improve the accuracy.

2. Second stage

a. The divided system is taken to be each adjoining room. The air temperature

caused by the heat source mentioned in 1-b is calculated under the condition

of the air temperature of 0 °C for all neighboring rooms.

b. The magnitude of the artificial heat source for producing the temperature 0 °C must be calculated for every neighboring room. It is then decided whether or not to improve the accuracy.

3. Third stage

a. The divided system is taken to be each neighboring room. The air temperature

caused by the heat source mentioned in 2-b is calculated under the condition

of the air temperature of 0 °C for all adjoining rooms.

b. The magnitude of the artificial heat source for producing the temperature 0 "C must be calculated for every adjoining room. It is then decided whether or not to improve the accuracy.

4. Fourth stage

It is necessary to continue the procedure successively until the accuracy is

sufficient for engineering purposes. Then, the final solution is obtained by adding

up the result of each process.

The frequency of calculation required in this procedure depends upon the structure of a system and usually it may he a small number. The temperature caused by the

ar+i-f icial heat source may be negligible at early stages of the procedure, since the

magnitude of the heat flow decreases radpidly with increase of the distance from the source

2.3 Procedure of 5-Rooms in Parallel

In the case that the heat is supplied only to the center room as shown in figure

3, we will attempt to obtain the air temperature of 5, rooms in parallel by the method

described above.

1. First stage

a. Air temperature of heating room.

Ti (1) = Gi X Q (1)

b. Magnitude of the artificial heat source at every adjoining room.

Q2(l) = F|.2X Ti (1) (2)

337
Q3(l) = F1.3 X Ti (1) (3)

Q4(l) = Pi-4 X Ti (1) (4)

Q5(l) = Fi-5 k Ti (1) (5)

2. Second stage

a. Air temperature of every adjoining room

T2(l) = G2 X Q2(l) (6)

T3(l) = G3 X Q3(l) (7)

T4(l) = G4 X Q4(l) (8)

T5(l) = G5 X Q5(l) (9)

b. Magnitude of the artificial heat source at every neighboring room.

Qi (2) = F2-I X T2(l) + P3-I X T3(l) + P4-I X T4(l) + F5-I X T5(l) (10)

Q2(2) = F3-2X T3(l) + P5-2X Ts ( 1 ) (11)

Q3(2) = F2-3X T2(l) + F4-3X T4(l) (12)

Q4(2) = F3-4X T3(l) + P5-4X Ts ( 1 ) (13)

Q5(2) = F2-5X T2(l) + P4-5X T4(l) (14)

3. Third stage

a. Air temperature of every neighboring room.

Ti (2) = Gi X Qi (2) (15)

T2(2) := G2 X Q2(2) (16)

T3(2) = G3 X Q3(2) (17)

T4(2) = G4 X Q4(2) (18)

T5(2) = G5 X Q5(2) (19)

b. Magnitude of the artificial heat source at every adjoining room.

338
Final results.

Ti = Ti (1) + Ti (2) + Ti (3) +

T2 = T2(l) + T2(2) + T2(5) +

T3 = T3(l) + T3(2) + T3(3) +

T4 = T4(l) + T4(2) + T4(3) +

T5 = T5 (1) + T5 (2) + T5 (3) +

(20)

(21)

(22)

(23)

(24)

Where

Ti(j) : air temperature of No.i room at J stage of calculation.

Qi(j) : magnitude of the artificial heat source of No.i room at J stage of

calculation.

Gi : transfer function between the magnitude of No.i room heat source

and No.i room air temperature.

Fik : transfer function between No.i room air temperature and the hept

fluxes from No.i to No.k room.

i,k : subscript denoting room number. No.i is the center room, No. 2,

3,4.5 are the others.

J : subscript denoting the frequency of calculation in the procedure

given in the foregoing paragraph.

Q : magnitude of the original heat source at No.i room. T,Q,G,F : these functions are represented by the Laplace transformation.

3. Calculation and Solution of Examples

3.1 Description of Examples

This method is applied to some multirooms; two rooms, five rooms in Parallel,

and fifteen rooms in series. The module of each room is an office, 10x10 l\ meters,

without any windows and any furniture. It is constructed of concrete with a thickness of 0.15 meters. The thermal condition and structure of every story are similar, with a ceiling and floor slub which seems to be insulated. The heat source with a unit step function is supplied to the corner of two rooms, fifteen rooms, and

the center of five rooms. The inside cojnbined heat transfer coefficient for these

calculations is taken to be 8 Kcal in hf'm^deg C and the outside one to be 20 Kcal in

hr"'m2deg C.

3.2 Results

The results of these calculations are given in figure 2,3 and 4, where the room temperature is plotted versus time at every stage of this method. In figure 2 and 3 the curves are represented for the grade of improvement for every room, and in fie-ure

4 it is represented for the frequency of calculation by this method described in

foregoing paragraph.

The results for two rooms shown in figure 2 indicate that as the frequency of

successive improvement increases, the temperature degree to be improved becomes

smaller remarkably. For instance, the second improvement ratio between the true

temperature of each room and the improved supplementary one, X3/X and Y3/Y in figure

2, is less than one per cent. in the fi^rst stage of improvement, good accuracy is

obtained. It is thus possible to finish the calculation when it reaches the fourth

stage described in foregoing paragraph. The approximation is given by summing up the

first and second temperatures, XI and X2 or Yl and Y2 in figure 2. The computer capacity required for approximation by this method is about one- half as small as the one required for the complete solution by working out the balance

equations directly. In the case of a multiroom with just a few rooms, the time

necessary for calculation does not differ greatly from that of the complete solution.

The results for five rooms in parallel shown in figure 3 indicate that the

339
approximation with good accuracy is obtained when the frequency of calculation

reaches the fourth stage, so that it is given by summing up the first and second

temperatures, XI and X2 or Yl and Y2 in figure 3. The computer capacity required for approximation by this method is about twofifths as small as the one required for the complete solution by working out the

balance equations directly. The time necessary for calculation of this method is

about one-fiftieth as short as that of the balance equations. It is possible to calculate them by hand or by a desk computer.

Tht results for fifteen rooms in series shown in figure 4 indicate that as the

frequency of successible calculation increases, the temperature degree to be improved

decreases remarkably. For instance, the temperature at the fourth stage, curve 4 in

figure 4, is about one-hundredth as small as that at the first stage, curve 1 in

figure 4. Therefore, the terape-^ature seems to be zero for rooms with a room number

larger than 5, and the approximation of the rooms numbering from 1 to 4 is obtained

by summing up two curves representative of each room. The computer capacity required is about one-fifteenth as small as that for solving the balance equations, and the time necessary for calculation may be about

one-two hundredths as short as the latter. It is also possible to calculate them

by hand or by a common desk computer.

4 . Summary

The practical method for obtaining room temperature of a multiroom has been

proposed. Kany examples; two rooms, five rooms in parallel, and fifteen rooms in

series, v/ere studied, and it has been shown tha,t the present method is excellent for

engineering and application purposes because these calculations can be made by hand,

by a desk computer, or by a digital computer of relatively small capacity. This can

be down at p reasonable cost.

It has also been demonstrated that with an increasing number of rooms, the

usefulness of the present method increases remarkably. For instance, in the case of

fifteen rooms in series, the time necessary for calculation of this method is about

one-two hundredths as short as that of the balance equations method. The computer

cap-:>city for the former is about one-fifteenth as small as the latter.

It It^p also been found that this method is useful to obtain the effect produced

by an addition of rooms.

It is obvious that this method is also useful for obtaining the heating load and

cooling load.

340
341
7

6

5

4

3

2

I

0

(

7

6

5

4

3

2

I

0

I

X

1 Kcal-Hr

20 40 60 80 100 120

Time (Hour)

140 160 180 200

Room air temperature of 2-rooms resulted from heating in the furm of a step function at X-room.

342
Figure 3 Room air temperature of 5-rooms in parallel resulted from heating in the

form of a unit step function at X-room.

343
344
simulation by Digital

Computer Program of the Temperature Variation in a Room

G. Brown

The Royal Institute of Technology

Stockholm, Sweden

A computer program has been developed at the Royal Institute of Technology,

Stockholm, Sweden, capable of calculating the temperature variations that occur in a room subject to variable internal and external heat gains. The program offers a very

flexible choice of the quantities that are to be calculated. The air temperature in the room, the temperature and supply volume of the ventilating air, and the capacity

of the heating or cooling units in the room can either be calculated separately, or

in pairs when the limiting values of both quantities are known.

The program solves a system of heat balance equations which take into effect

surface heat transfer by radiation between the room surfaces, by convection between

the room air and room surfaces, and by conduction between the different material

layers of the walls and floors. Not only is the temperature of the room air calculated, but also always that of the room surfaces and the material layers and outside

surfaces of those walls and floor slabs which enclose the room. This practice has proved to be valuable when using the program in connection with studies of different

types. When an operative temperature is to be determined, the temperatures of the different surfaces in the room must be given, in addition to the room air temperature. The calculated temperatures on the outside surfaces of the walls and floor

slabs which enclose a room come into play in connection with studies of the function

of temperature control systems in adjacent rooms having different temperatures due

to different heat gains. An example of this is given in the article.

Key Words: Absorption factors, ALGOL, choice of unknown variables, daylight

distribution in rooms, digital computer program, finite-difference method,

heat balance equations, operative temperature, temperature control, temperature variation in a room.

1. Introduction

Use of computers in the study of non-uniform temperature variation in buildings began rather early

in Sweden. The first example of such use dates from 1957 when a method was described for computer cal- culation of the temperatures in an external wall exposed to solar radiation /I/. In the same year another investigation was presented dealing with design outdoor temperatures for heating load calculations

HI . The temperatures proposed in the survey were determined on the basis of computer calculated tem- perature variations in different types of buildings with temperature variation out of doors. In both

these cases, the calculations were made on the Swedish computer BESK which was installed in 1953.

The equations on which the present program is based were first published in 1963 /3/. Since this

date, the program has been developed in order to make it more versatile, cheaper, and easier to use. It has thus been supplemented in such a way that the quantity which is to be calculated can be chosen from

among several different variables. By revising the program, which is chiefly written in ALGOL (except

for a lesser part in internal computer code), and by modernizing the computer itself, i.e. the Swedishmade TRASK, the cost of computer time has been decreased. For a normal case, it costs, at present, about

US $ 10 for the calculation of a 24 h period of variation in one room.

A special alternative for easy use of the program has been developed in the form of the "engineer's

version" and enables the calculations to be made with less work, especially concerning the presentation

of data since the data need not be presented on special forms. The complete program version described

in this article allows, however, greater flexibility concerning the choice of variables.

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The calculation method, which is an iterative, finite-difference method, has been developed with

respect to its application for the dimensioning of plant for cooling and heating rooms, but also for the study of how buildings should be constructed in order to provide a comfortable thermal environment at

the lowest cost. It should be possible to use the program both for design and for research and investigation work. In view of the fact that it is essential to be able to explore the effect of all factors

which may arise, the complete program version is so written that no material constants or values for temperature and incoming radiation are stored in the computer memory. Furthermore, there are no limitations regarding the definition of the surroundings of the room, i.e. its position in the building.

To date, the program has been used in a fairly large number of cases in connection with the design

of hospitals, hotels and office buildings. Further, the program has been used in a survey concerning a design guide for school buildings in the study of the effects of different factors on classroom temperature. The investigation resulted, among other things, in a proposal for a standard for calculation of the temperature in classrooms for design of school buildings throughout Sweden. According to the proposal, such calculations will involve the use of the program presented here, or a program giving the same result /4/.

2. Input Data

Data for the calculations is recorded on eight different types of forms: 1 Room, 2 Wall or floor,

3 "Facade", 4 Window, 5 Lighting unit, 6 Heating unit, 7 Time dependent data, and 8 Constants. Time

dependent and time independent quantities are differentiated, see table 1. The time dependent quantities

can be assigned variable values during the calculation period, i.e. the time period under which the cal- culation is considered. They are identified on forms 7 and 8 by numbers assigned to them from forms 1-6. A form of type 7 can be used to record the values of a given quantity at different time points, while a form of type 8 is used to record data for such quantities which are in principle time dependent but which

for the present case do not vary with time.

The room is assumed to have parallelepiped shape. Forms of type 1 contain a sketch of a room in- cluding a coordinate system enabling the addition of sub-surfaces. Such sub-surfaces are windows and lighting units and even heating units which emit thermal radiation and therefore need to be included as surfaces in the room.

Values of outside air temperature and radiation from the sun and sky are found from tables or diagrams. The tables used here are computer calculated and based on Finnish measurements /5,6/. They give

sun and sky radiation against vertical facades and horizontal roofs as well as radiation transmitted

through vertical and horizontal windows with double-glazing of ordinary window glass. The radiation re- flected at the ground is included in the radiation values. In cases where a facade falls within the shadow of surrounding buildings a separate program is used to calculate the portion of the day when the different windows in the facade are sunlit. Computer drawn diagrams are used in determining the incoming radiation through windows which are shaded by overhangs or which are set back from the external plane

of the facade.

The shading coefficients (tab.l) give the transmission through the fenestration in question in relation to the total radiation energy transmitted through a double-glazed window of ordinary window glass

ni. These coefficients are determined under the assumption that the surface heat transfer coefficient

for the exterior side of a double-glazed window is 16 and 8 Wm~2deg-1 for the interior side.

The thermal resistance of the interior side of a window is not included in the calculations since

the temperature of the window surface towards the room is included in the programmed heat balance equations .

Shading coefficients and thermal resistance of windows are listed in table 1 as time dependent quantities since these values are not constant for windows having drapes or Venetian blinds which are used for only part of a 24 h period.

The word "facade" is taken to mean the exterior side of each wall or floor for which incoming radiation, surface heat transfer coefficient, and air temperature are known. Thus a "facade" is not necessarily the outside of an exterior wall. It can just as well be the outer surface of a roof or of a wall

giving onto a corridor.

A form of type 6 is used to designate a heating or cooling unit whose surface radiation or thermal

capacity must be taken into consideration. Furniture can be considered as such heating units of effect

0. For convective heating units with no thermal capacity, the data is instead listed under "heat direct

to room air". Heat from persons present in the room is often listed under this variable.

Radiation from people can be introduced in the calculations in the form of radiation from a lighting

unit which is located on the floor. The amount of body heat given off decreases with an increase of temp- erature. The program can simulate lower convective heat radiation when the calculations indicate a higher

air temperature.

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Table 1. List of quantities in the computer program.

Type of data or number i

form on which

identification

s given Time independent quantities Time dependent quantities

Type 1 Room

Length, width and height of room. Sub- surface dimensions in x-and y-directions and coordinates for their lower

left hand comers. Reflectance for room surfaces and sub-surfaces.

Outside air temperature, volume of air leakage, room air temperature,

ventilating air temperature, volume

of ventilating air, heat direct to room air. Unknowns.

Type 2 Wall or floor

Thickness, coefficient of thermal con- ductivity, density and specific heat

of different layers of materials of the wall. Thermal resistance of air

layer in the wall. Number of partial

layers of each material layer.

Absorptance of facade surface. Cloudiness

Type 3 "Facade"

Radiation towards "facade . Air

temperature. Surface heat transfer

coefficient

Type 4 Window

Radiation transmitted through double- glazed windows. Shading coefficient

for total and for direct transmitted

radiation. Thermal resistance. OutType 5 Percentage of radiation from lighting Lighting effect. Lighting unit units

Type 6 Heating unitVolume of heating or cooling unit,

density and specific heat of the material of the unit. Surface en- larging factor of the unit.

Effect of heating or cooling unit.

3. Unknowns

Those variables which may be unknown are room air temperature, ventilating air temperature, volume

of ventilating air, heat direct to room air, and effect of heating unit. The variable which is to be calculated is determined in the program by the code number given to "unknowns". Code numbers are listed

on the forms in the same way as the values for other time dependent variables. The code number gives

the different positions in the program where the sought variable is solved from the heat balance equation

for the room air.

It is sometimes desirable to seek a variable given the conditions that it lies within certain limiting values. If the calculated value is larger than a maximum value or less than a minimum value, then

the value for another variable must be found. Thus the program first tests a variable against its limit

value (which is not necessarily constant during a 24 h period). If this limit is crossed, the position

of another variable is found, the result is calculated, and the first variable is given its limit value.

4. Thermodynamic basis

4.1 Angle and Absorption factors

The equations for heat transfer between room surfaces take into consideration reflexion of short wave radiation (from the sun and sky) but not long wave radiation. Thus it is assumed that all long wave radiation which is emitted from a surface A^ and which meets a surface Aj is totally absorbed by Aj . Emission is furthermore assumed to occur diffusely and transmitted energy is determined by the angle factor , which is calculated using generally known equations and methods, see e.g. /8/ and /9/.

Transmitted radiation energy for short wave radiation is found by the equation system m

i;;..=cp..a. + Z cp. r ii . ij iJ J i-P P PJ

Here V^. is the absorption factor for radiation between A. and A., a. is the absorptivity of A.,

r is the reflectivity of some surface A of the m room surfaces, and^l- .^is the absorption factor ^for

radiation between A and A . The first tirm of the expression for t . . ii^that portion of radiation from A. which IS absorbed at A. and which has not been reflected by any inte^ediary surface. The sum term is ^ that radiation absorbed by A. which has first been reflected by the room surfaces.

347
In cooling load calculations it is useful to know at which time daylight is so weak that lighting units must be turned on. The equation system above has been used in the study of daylight distribution in rooms in this context, the program having first been extended so that the absorption factors for radiation from windows towards the top side of a small horizontal surface placed in different parts of

the room can be calculated. A condition for these calculations is that the radiation from the windows

is spread diffusely. Such is the case for windows with drapes or Venetian blinds as shown from previous measurements. These measurements have also shown that a calculation of the distribution of light from a window can be correctly performed only if room surfaces perpendicular to the window surface are divided

into sub-surfaces when angle and absorption factors are determined.

A. 2 Heat Balance Equations

Time variation of temperature in a room is calculated from the heat balance equations for the material layers on the surface and in the walls and floors, for the interior side of the windows, and for

the room air.

Walls are considered to be divided into layers which are parallel to the wall surface. The equation

for a layer yields the magnitude of temperature change in a layer of thickness Ax during a time interval

of At (ordinarily 15-60 minutes) caused by the surface heat transfer of both of the limiting surfaces of the layer.

Crank-Nicolson' s equation is used for an individual layer inside the wall in the form

K,9 , ^ + K„e ^ + K,e ^, , = K.e , + K,e + K,e (a)

1 n-l,t 2 n,t 3 n+l,t 4 n-1 5 n 6 n+1

where the temperatures at the beginning of the time period are written on the right side and the unknown

temperatures on the left side. The index n is used to denote the layer being treated while n-1 and n+1

are the adjacent layers.

If the three layers are of the same material, then K]^ = K3 = -1, K4 = Kfe = 1, K2 = 2 Ax2/a At + 2, K5 = 2 Ax2/a At - 2. The constant a here denotes the material's thermal diffusivity.

Equation (A) is also used for the limiting surface between two different materials as well as the surface of an air layer inside the wall. The coefficients then include the thicknesses, the thermal conductivities and the thermal dif fusivities for the layers of material on both sides of the limit surface, and, in the latter case, the thetnnal resistance of the air layer /3/.

The following relation is valid for a layer n at the surface of a wall : -^^ll,t ^ ^2«n,t - Vr,t ~ ^^^.t =

= ^^nll * ^5^n * ^3^ * ^^4^ * ^6

The index nil indicates the adjacent layer, r the room air, and u a room surface from which long wave radiation reaches the surface.

Equation (B) is applicable not only for surfaces of walls, floors and ceilings but also for the surfaces of heating units, interior sides of windows, and facade surfaces. Contrary to the K values of eq

(A), the F values of eq (B) are not all constant. The reason is that they include variables such as radiation from windows and lamps, effect of heating units, shading coefficients, thermal resistances of windows and the outside air temperature. For outdoor facade surfaces, Fg includes the sol-air temperature which contains the variables outside air temperature and radiation from sun and sky. It can be pointed out that the equation for the sol-air temperature is so formed that the dependence of long wave

radiation upon the degree of cloudiness is taken into consideration at roof surfaces /lO/.

The convective surface heat transfer coefficient hj. for a room surface is dependent upon the temperatures of the surface and air as given by the calculations. With each repeated application of the equations in which h^, appears, the most recently found value for h^ is inserted, during the calculation, in

the F coefficients.

Windows are assumed to lack thermal capacity. When eq (B) is used for the interior surface of a window, the temperatures ^n*}.* ®n' ^u "h^*^^ ^'^^ valid at the beginning of the time interval At

are all set equal to zero, since the surface temperature at the end of the interval is then independent

of these temperatures.

A third type of heat balance equation, type (C) , is used for the room air . This equation states

that the heat which is introduced convectively from heating units in the room and by ventilating air and possible leakage air is removed by the exhaust air and by convective surface heat transfer at the room

surfaces

348
5. Calculation Procedure. Steps and Tolerances

The temperatures in the material layers, at the interior surfaces of windows, and of the room air

are all calculated simultaneously from a system of equations of the types (A), (B) , and (C) . The calculation begins with assumed values for these temperatures at time point 0 o'clock if a 24 h period is to be studied, and then gives the temperatures after a first time interval of the calculation step's length At. These temperatures, in their turn, make up the start values for the calculation of the temperatures at the end of the following time interval of the same length. The same equation system as for the first

step is used here. However, the coefficients may have received new values. The calculation is continued

step by step until the variation for the whole calculation period has been found.

In general, the length of the period is 24 hours. It can however have other lengths, e.g. four times

as long. Stationary as well as non-periodic cases, where the start values are known and the input data

then varies at a known rate, can be studied.

Solution of the equation system which normally contains some fifty equations is done by relaxation. A calculation referring to one and the same time point is repeated time after time with increasing accuracy. The difference between the two values for the same variable from two consecutive calculations are compared each time with a predetermined tolerance, the relaxation tolerance. The calculations for the time point in question continue until this difference is less than the tolerance for all variables. This

tolerance is dimensionless and is expressed in such a way that it can be used for temperature as well as for air volumes and heating and cooling effects. ,

After the calculations have been carried out for all the time points during the period as determined

by At, they are repeated for the same time points during a new period. The difference between values for one and the same variable at the end of this period and the previous period are compared with a predetermined tolerance, the period tolerance. The calculations are now repeated for more periods until the differences for all the variables fall below the prescribed tolerance. The same expression is used here

as for the relaxation tolerance. The value for the period tolerance must, however, be larger than that

for the relaxation tolerance.

The values of the calculated variables are printed out at time points determined by the print step. The print out also includes the average values for the variables during the period. The pring step can often be made longer than the calculation step which is determined by technical factors. The normal

value for the calculation step is 0.3 hours, for the print step 1 hour, for the relaxation tolerance

0.1 % and for the period tolerance 0.2 %. These values are used if no others are motivated.

6. Application Examples

6.1 The Effect of Wall and Floor Insulation upon Temperature Variation in a Room

During a series of clear days with equal sunshine and outside temperature, the mean room air temperature for a 24 h period is not dependent upon an exterior wall being insulated from the outside or inside.

If the room is surrounded by similar rooms with the same temperature, this mean air temperature is also unaffected by the presence of a layer of insulation on interior walls and floors.

Both these measures, however, affect the magnitude of temperature fluctuation about the mean temperature. Heat storage in the structure has a dampening effect. Insulation of the heavier layers decreases

storage and results in stronger temperature fluctuation in the room. In this respect, insulation on the inside of exterior walls produces the same effect as the insulation of interior structures.

For an illustration of this, consider the curves in figure 1 which are drawn on the basis of calculations using the computer program. These refer to a clear July day in Stockholm (latitude 59°21'N) for an empty room without artificial lighting. The room was 2.7 m high and 5 m deep. It had a 3.8 m long window

wall and was ventilated over the whole daily cycle by 250 kg/h of outside air. The window had a glazed

area of 4 m2 with double glazing of ordinary window glass with light colored drapes on the inside, and faced S 60° E. The temperature in the corridor was a constant 24°C.

The dash-dotted curves in the figure indicate a room having a reinforced concrete exterior wall insulated on the outside with mineral wool. The floor is also of reinforced concrete and partition and corridor walls are of cellular concrete. Dotted curves indicate a room with the ssuae exterior wall but where the mineral wool insulation is located on the inside. The upper surface of the floor slab has been

covered by a wooden floor over mineral wool insulation, while the under surface has a suspended ceiling

with a thin layer of mineral wool insulation. The partition walls and corridor wall have also been in- sulated with thin slabs of mineral wool mounted on studs. All wall insulation is protected by 1/2 inch

thick plaster board. The thickness of the concrete and cellular concrete has been decreased sufficiently

so that the weights of walls and floors including the insulation are the same.

349
In the second case described, the quality of sound insulation between the rooms has been improved,

but the the rmal conditions have deteriorated* Mean air temperature under a 24 h period for both cases

is 2A°C, but because of the insulation, the maximum temperature for the second case rises by 2.4° from

25.9° to 28. 30c. Mean temperature here during the period 8-17 o'clock rises by 1.6° from 25.7° to 27.3°C.

Figure 1 also shows how the mean temperature for the room surfaces varies during the period 8-17 o'clock. The value is a weighted mean value with the surfaces as weights (the floor surface temperature

is not included). Because of the insulation, the maximum value rises by 3.2° from 27.5° to 30.7°C, while

the mean value for the period 8-17 o'clock increases by 2.2° from 27.0°to 29.2°C.

The example shows that the weight of the interior walls and floors and the weight and thermal trans- mittance of the exterior walls are not sufficient data on the building structure for calculation of the temperature variation in rooms.

6.2 The Temperature Variation in a Room as Affected by Heat Gains in Adjacent Rooms and the Type of Temperature Control (Individual or Central)

Given a building with several rooms of the same type along a facade and assume that a system is to be installed for regulating the temperature of ventilating air in such a way that the room air temperature during working hours has a desired value independent of whether the room is being used or not. If certain deviations from the desired value can be permitted, the problem is then to find out whether it

is necessary, under summer conditions, to provide controls in every room (individual temperature control),

or whether it is sufficient to feed cooled ventilating air of the same temperature to both unoccupied and occupied rooms (central temperature control).

Figure 2 presents the results of calculations for similar rooms of the same size as in the preceding

example. Whereas the walls and floors were of a different construction, the window had the same orientation and incoming radiation is thus the same. Outside air temperature was also the same. The ventilating air was supplied at a rate of 300 kg/h during the whole 24 h period. It was cooled only during the period 7-18 o'clock, and was 1°C warmer than the outside air during the rest of the time. Occupied rooms were used by two persons during working hours (8-17), and lighting units were turned on during the after- noon producing an effect of 25 W/m2 of floor surface. The windows in these rooms were double-glazed and had roller blinds which were kept down except for during the afternoon; there were also drapes inside the windows which were kept drawn during the whole 24 h period. The unoccupied room was assumed to be sur- rounded by occupied rooms, and the blinds in this room were not used. The desired air temperature in the rooms during working hours was 22°C. However, the ventilating air temperature was not allowed to fall below 15°C.

Under these conditions, according to figure 2a, the air temperature in the occupied rooms can be maintained at 22°C except for a slight increase in the afternoon. The ventilating air is then insufficiently cooled to wholly compensate for the heat release from people and lighting units.

Whereas the ventilating air to the occupied rooms need not be cooled so low as to 15° during the morning, it is necessary for the ventilating air to the unoccupied room (see fig. 2b). This is based

upon the fact that the roller blinds between the panes in this room were not let down.

In cases of central temperature control where the ventilating air for the unoccupied room has the same temperature as that for the occupied rooms the temperature during the morning and through the lunch

hour exceeds the desired value by ca. 1°. Contrary to this, the temperature towards the end of the working day is about 1.5° too low, as shown in figure 2c. On the basis of these deviations from the desired

value, it is possible to decide whether the cheaper alternative of central temperature control can be accepted.

In the calculations for the unoccupied room the heat conduction through walls and floors between

this room and the occupied rooms was taken into consideration. This was accomplished by using the pre- viously determined surface temperatures of the occupied rooms as the outside air temperatures at the external surfaces of the walls and floors of the unoccupied room. These surfaces were treated as "fa- cades" in the program. The surface heat transfer coefficient for them, were given a very high, fictive

value. This procedure involves approximations which, however, can be reduced by repeated calculations.

In this case, they proved to be insignificant.

Room air and ventilating air temperatures were considered as unknown quantities during the larger

part of the 24 h period in the calculations concerning the occupied room. Maximum values were then assigned to them for a part of this period and minimum values for anotlier part. During the night, the room air temperature was considered as the unknown.

During the calculations for the unoccupied room with individual temperature control,

minimum values were assigned to the temperatures of the room air and ventilating air during the whole 24 h period. In the case of the central temperature control alternative

the room air temperature was treated as the unknown during the whole 24 h period.

350
7. References

HI Brown, G., Utilisation de calculateurs

electroniques pour resoudre les problemes

de transmission de la chaleur en regime

variable, Chauff.- Ventil.- Condition. 33 (1957), No. 10. in Adamson, B., Brown, G., and Hovmoller, E., Dimensionerande utetemperatur . Statens Byggnadsbesparingsutredning. Stockholm 1957.

/3/ Brown, G., Metod for datamaskinberakning av varme- och 1 jusstralning i rum och av kyloch varmebehov. Nat. Swedish Inst, for Building Res., Reprint 4, 1964.

/4/ Antoni, N., Projekteringsunderlag for skolbyggnader for grundskolan. Nat. Swedish Inst, for Building Res., Report 50. Stockholm 1969.

/5/ Lunelund, H., Varmestralning och Ijusstralning i Finland. Svenska Tekniska Vetenskapsakademien i Finland, Acta 12. Helsingfors 1936.

/6/ Brown, G. , and IsfSlt, E., Irradiation from sun

and sky in Sweden on clear days. Tables and charts. Nat. Swedish Inst, for Building Res.,

Report 19. Stockholm 1969. PI Isfalt, E., A computer analysis of window shading coefficients by calculating optical and thermal transmission. Contribution to this symposium.

/8/ Kollmar, A., and Liese, W. , Die Strahlungsheizung. R. Oldenburg. Miinchen 1957.

/9/ Squassi, F., Die Einstrahlzahlen in Wohnraumen. Ges.- Ing. 78 (1957), No. 5/6.

/lO/ Hoglund, B. J., Mitalas, G. P., and Stephenson,

D. G. , Surface temperatures and heat fluxes for

flat roofs. Build. Sci. 2 (1967), No. 1.

Temperature, C

32

10 12 14 16 18 20 22 24 Time,hr

Mean temperature

of room surfaces Room air

" temperature

Outdoor air temperature

Radiation through unshaded window

1. Calculated temperature of air and room surfaces in two rooms whose walls and floors have the same weight but different insulation:

Exterior wall insulated on the outside,

non-insulated interior walls and floors Exterior wall insulated on the inside,

insulated interior walls and floors

351
Temperature, °C

12 1 , . . . . . . . ,

. 1 0 2 4 6 8 10 12 14 16 18 20 22 24

Tempera fure , °C

0 2 4 6 8 10 12 14 16 IS 20 22 24

I ernperoture , (_ 24

22

20

18

16

14

12 0 2 4 6 8 10 12 14 16 18 20 22 24 Room air temperature

VenKlaling air temperature

2. Calculated air temperatures in occupied and unoccupied rooms.

a. Occupied room

b. Unoccupied room, individual control

c. Unoccupied room, central control

352
Optimization of an Air-Supply Duct System

W. F. Stoecker , R. C. Winn , and C. 0. Pedersen

Department of Mechanical and Industrial Engineering

University of Illinois at Urbana-Champaign

Urbana, Illinois 61801

The design of a multi-branch air supply system is complex because there are

as many decisions to make as there are sizes of duct sections to specify. A fur- ther complication is that a decision on the size of one section affects the per- formance of the entire system. If an optimal duct system is sought, then, the design process becomes a multi-variable optimization.

The premise on which the mathematics of the procedure explained in this paper is based is that all of the available static pressure is dissipated in the duct and fittings with no artificial pressure drop due to dampers. Furthermore,

of the multitude of systems that would be balanced without the addition of dampers, the computer program selects the one with minimum cost.

The objective function is the total cost of the system based on a fixed

cost per pound of metal. The constraints appear because the pressure drop from

the fan discharge to each outlet must equal the available static pressure. Thus, there are as many constraints as outlets. The forms of both the objective

function and the equality constraints are preditable, so the optimization yields

itself to the method of Lagrange multipliers.

This paper presents the basis of a computer program which performs this op- timization for a circular-duct system. The user of the program provides the fol- lowing information:

(a) available static pressure at the fan outlet,

(b) the geometrical coordinates of each outlet, branch, and elbow,

(c) the flow rate at each outlet, and

(d) the cost of the metal per pound.

The printout includes the diameter, duct surface area, velocity, pressure drop, and cost for each section of duct for the optimum system.

Key Words: Air supply, duct system, optimization.

1. Introduction

An air-supply system is a requirement for practically every environmental control unit for a building. The design of the supply system is a complex one because the system has many components —each section of straight duct and each fitting is a component —and as is true of classical systems, component

performance is interrelated. The question might be raised, "How can such a complex system be designed

and constructed in practice by methods that are usually unsophisticated?" There are two answers

(a) The most popular design procedures afford a systematic way of arriving at a workable system, and

Professor of Mechanical Engineering.

Research Assistant, presently with U.S. Air Force at Columbus, Mississippi.

Assistant Professor of Mechanical Engineering.

353
(b) Most duct systems are not optimum.

The two answers are > related. The first task of the designer is to specify a system that will meet

the requirements, which for duct systems is to provide the specified flow rate at designated locations.

Furthermore, the designer must perform his task relatively quickly—he cannot make a career of one or two duct systems. To his aid come the standard procedures for duct design, such as the "velocityreduction method" and the "equal-friction method." The merits of these methods are

(a) that they result in workable systems, and

(b) that they provide methodical procedures for the designer to follow which simplify his task.

A further merit of the velocity reduction method is that it provides velocity limits which acknowledge

noise considerations. The equal-friction method, on the other hand, while it has no built-in procedures

for limiting velocities does come closer to achieving a duct system of minimum first cost.

One of the coverups for a non-optimum design is a high fan static pressure. Given an unlimited

static pressure at the fan and a generous supply of dampers , almost any duct system will provide the re- quired flow at designated locations. Unfortunately, the economies realized in reduced design time are sometimes dwarfed by unnecessarily high first and operating costs.

This paper presents the basis for a procedure for optimizing the first cost of an air-supply system. The procedure has been incorporated into an operating computer program. Specifically, the optimization

problem can be formulated as an objective function with equality constraints which is soluble by the me- thod of Lagrange multipliers. The computer program executes the optimization, solving the set of non- linear simultaneous algebraic equations by the Newton-Raphson technique.

2. Air-Supply System

A sample duct system (shown schematically in fig. 1) must supply Qj , Qj i

, and Qj j j cfm, respectively, at the positions shown. The optimization procedure presented in this paper determines the minimumcost duct system for a given available static pressure at point 1. The minimum cost system is the one which requires the minimum weight of metal, a proposition which conforms to the conventional method used

by contractors in making bid estimates.

An immediate question that emerges is whether the total system can truly be optimum if the static pressure at point 1 is arbitrarily assigned. Figiire 2 shows that when the static pressure is extremely

low, the duct cost will be excessive due to its large size regardless of the design procedure used. On the other hand, when a high static pressure is selected, the lifetime operating cost becomes the controlling quantity. There is a certain static pressure that results in minimum lifetime cost. For any static pressure there will be a minimum cost duct system. The program described in this paper designs

such a system. To obtain the information required to construct figure 2, this program must be used to find the optimum duct system pressures.

3. Premise of Optimum Design

From physical reasoning the optimum duct system is one where the available static pressure is dissiptated completely in each run. A "run" is defined as the path from the fan discharge to an air outlet.

The basis for this premise is that if a run should exist where the flow is too high, the flow should be

reduced not by throttling with a damper, but by reducing the size and thus the cost of some duct section

in that run. The consequence of applying this premise is that the resulting duct system uses all of the available static pressure to overcome friction in the straight ducts and fittings, and no static pressure is dissipated in dampers.

Obedience to the foregoing premise, however, does not describe a unique duct system. This fact could be shown schematically as in figure 3. Assume that the ducts shown by solid lines are of such

size that they deliver the desired flow rates of air to the two outlets when a certain static pressure

exists at the fan outlet. Another duct system tha^ has a smaller size trunk section and larger size in the branches and will also deliver the desired flow rates can be found (shown by the dashed lines).

One of those two duct systems undoubtedly will have a lower cost than the other. A conclusion, then, is that there is an infinite nximber of duct systems that consume the available static pressure, but only

one of these will have minimized cost.

4. Cost Function

The mathematical form of the duct optimization problem consists of two parts:

(a) the cost function which is the objective function to be optimized, and

35A
(b) the constraints.

For circular ducts the cost of a section is

Cost of section = ttDLWCCCP) (1)

where

D = diameter of the duct, ft

L = length, ft

W = effective weight per square foot of duct surface (includes allowance

for fittings, seams, hangers, and scrap), (lb)(ft)~^

CCP = cost per pound of duct, (dollars) (lb)

'

The allowance for fittings, seams, hangers and scrap in W is 20 percent of the weight of duct surface.

The weight of the duct per ft^ conforms to recommended construction for low-pressure ductwork (less than

2 in. of water static pressure) as recommended in Tables 11 and 15, Chapter 3 [1]'*. The gauge of the metal is thus a function of the duct -diameter. The total cost, COST, of the example system in figure 1

is

COST ^ =CtCtC+C+C+C+C (2) 1-2 3-4 S-6 4-5 6-7 S- 9 ^10-11 ^

When the costs of each section from eq (1) are substituted into eq (2), the variables for optimization

become the diameters. The other terms L, W, and CCP are dictated by costs and layout and are not variables of optimization.

Rather than choosing the diameters as the variables, it is more convenient for later manipulations

to express the diameter in terms of a pressure drop, Ap. The pressure drop in a section of straight

duct can be expressed by

2 p Ap = 12f ^^-f (3)

where

Ap = pressure drop, in. of water

f = friction factor dimensionless

V = velocity, fps

-1 -2 g = gravitational constant 32.2 (ft)(lb )(lb ) (sec)

c ml _3

= density of air, (lb) (ft)

_3

p = density of water, (lb) (ft)

Further, the velocity V can be expressed

60(t7D^/i+) (4)

4 . Figures m brackets indicate the literature references at the end of this paper.

355
where

Q = flow rate , cfm

Substituting eq (4) into eq (3) and solving for D results in

0. 2 D = constant/Ap (5)

Substituting eq (5) into eq (1) and then into eq (2) results in the objective function which is the total cost,

, - K K K K

^^r--. 1-2 3-4 5-6 4-5 COST = —- t —- + ——- + (^Pl-2^ ^^P3-4^ (^P5-6^ (^P4-5^

K K„ „ K

I I I 10-11

2 The constants K incorporate the length, flow rate, friction factor and effective weight per ft for each section

Equation (5) is the function that must be optimized subject to the constraints that will be pre- sented in the next section.

5. Constraints

The constraints essentially state that all of the available static pressure will be dissipated in friction in the fittings and straight sections. The number of constraints is the same as the number of

runs which also equals the number of outlets. The constraint equations for the system in figure 1 are:

APj., + Ap^ + Ap^ + Ap^_^ + Ap^_^ + Ap^_^ + Ap^_^ + Ap, = SP (7)

+ ^Pf ^ ^Pc + ^P2-4 + ^P4-5 + ^P5-6 + ^^6-7 + ^Pn = (8)

APl-2 + ^Pf + ^Pc + ^P2-4 + ^P4-5 + ^P5-8 + ^P8-9 + ^P9-10 + ^PlO-11 + ^PlII = O)

where

Ap^ = pressure drop in filter, in. of water

Ap = pressure drop in coil, in. of water

c

APj = pressure drop in terminal at outlet I

SP = static pressure at the fan, in. of water

The optimization procedures consist of minimizing eq (6) subject to the constraints of eqs (7-9).

6. Lagrange Multiplier Solution

The objective function, eq (6), and the constraints, eqs (7-9), are soluble by the method of

Lagrange multipliers. If an objective function y is to be minimized, where

356
y = y(Xj .•••><„)

subject to the constraints

0 (x -•••X ) = 0 ml n

the method of Lagrange multipliers [2] states that the optimum occurs where the following equations are satisfied:

Vy^11- A V(j) - ••• - XmmV(J) = 0 (10)

where

_ 3y -:- 3y — 3y —

dX, 1 dX^ 2 dx n

1 2 n

and are constants called Lagrange multipliers.

Equation (10) is a vector equation and in order for it to equal zero the coefficients of each unit

vector, such as ij must equal zero. Equation (10), therefore, represents n scalar equations which,

along with the m constraints, is a system of equations for the n + m unknowns, namely, x , •••x ,

1 m

Solving the equations represented by the vector equation, eq (10), along with the constraint equa- tions poses special requirements because the equations are often nonlinear. An iterative method for solving nonlinear simultaneous equations is the Newton-Raphson iteration [2]. In this process, trial

values are assumed for each of the unknowns. These trial values are substituted into the n + m equations. If all of the equations are satisfied the problem is solved. Usually, however, the equations

will not be satisfied with the first trials and the values of the variables need to be corrected. To determine how much each of the trial values should be changed, the Newton-Raphson technique prescribes

a set of simultaneous linear equations . The solution of these linear equations gives the corrections

which must be applied to the previous trial values to provide more correct values of the variables.

The fortunate circumstance which makes the method of Lagrange multipliers so applicable to the duct

optimization problem is that the form of eqs (6-9) is dependable —the objective function is a sum of terms, all of which have the same form, and the constraints are linear in the variables which are to be optimized, Apj . After the optimal values of the Ap's have been determined, the optimal diameters for

each section can be computed.

7. Computer Program

Robert C. Winn [3] developed a computer program to optimize duct systems automating the foregoing

mathematical procedure. The listing, flow diagram, and documentation of this program are found in [3].

To anticipate the eventual use of this program under coordinate geometry, the duct system is described

in terms of the coordinates of all elbows, branches and outlets. Once this information is entered, the computer determines the angle of turn of an elbow or branch. The complete list of input information re- quired is

(a) static pressure developed by the fan,

(b) type of each joint and its geometrical coordinates,

(c) pressure drop through filters, coils and outlets,

(d) upstream and downstream joint numbers of each outlet,

(e) air flow rate at each outlet,

(f) temperature of the air at the fan, and

357
(g) current cost of ductwork per pound.

The output, as example of which is shown in figure 4-, consists of the following information for

each section: diameter, velocity, flow rate, length, duct surface area, sheet metal gauge, pressure

drop, and cost. In addition, the total cost of the entire duct system is provided. The output corresponds to the duct system shown in figure 5

8. Strengths and Limitations of the Program

While the application of a standard mathematical tool and the computer program in which it is utilized are intended to be a contribution to improved procedures in the design of environmental systems,

the work is not to be considered complete. One of the obvious extensions would be to include the capa- bility to optimize a system of rectangular duct in addition to circular duct which the program now can accommodate. It would be realistic to encounter a dimensional limitation, such as the depth of the duct, and in such a case the program would determine the optimum width within this depth limitation.

The method for calculating cost used in this program multiplies the weight of metal by a factor. This practice oversimplifies the influences which contribute to the cost since the weight of metal alone

is not an accurate indicator of, for example, the labor cost. On the other hand, the most commonly used

method of estimating the cost of a duct system for bidding purposes is first to evaluate the weight of

metal and then multiply by a factor which varies somewhat depending upon the number and type of fittings

and ease or difficulty of installations. As long as bids are determined on this basis, the weight of

metal is the preferred quantity to minimize.

In its present status the program imposes no limits on velocity. In other words, a short run of

ductwork with the outlet close to the fan will optimize at an extremely small diameter because all of the available pressure must be dissipated in the duct itself. Standard practice calls for enlarging the

duct and installing a damper to accomplish the pressure drop. It should not be difficult to incorporate

in the computer program the provision for checking the velocity against some prescribed maximum, enlarging the duct if necessary to abide by the velocity restriction, and including on the output a statement

that dampering will be needed. Such a refinement of the program is planned. This practice, however,

raises a more basic question. Since the limitation of velocity is particularly to reduce the noise

level, which process would generate the most noise for a given drop in pressure, flow through a damper

or flow in a length of small diameter duct? There is evidence that a detached boundary layer (as in flow past a damper) generates more noise than an attached boundary layer (as in flow through a small

duct). A more thorough study of this question seems warranted.

The pressure drop through branch takeoffs and the straight-through portion of branch are computed

using data from [1]. The graphical data have been converted to equation form for convenience in the computer program. In air-duct systems the pressure drops in fittings will be of the same order of mag- nitude as that experienced in the straight sections of duct so accuracy in the fitting calculation is important. The calculation of pressure drops in straight sections is probably reliable, but the pre- diction of pressure drops in fittings is highly dependent upon the quality of craftsmanship of the fitting. The use of fittings manufactured in factories under controlled conditions and carefully tested

will add to the reliability of optimization efforts such as this.

The principal claim made for this method of duct design is that it results in the duct system of

minimum first cost for a specified available static pressure. A further benefit is that it results in

a balanced system. No one would be so foolhardy as to install a system designed with this computer program and omit dampers in each branch. The accuracy of the basic pressure drop data and the quality of workmanship is just too variable. It is likely, however, that the system will be more nearly balanced

than systems designed by other methods, so that the cost of balancing should be reduced.

9. Acknowledgments

During his graduate studies the work of R. C. Winn on this project was supported by an Industrial

Research Assistantship of Skidmore, Owings and Merrill.

10. References

[1] American Society of Heating, Refrigeration and [3]

Air Conditioning Engineers, ASHRAE Guide and Data Book , Systems and Equipment Volume , New

York, 1957.

[2] Stoecker, W. F. , "Design of Thermal Systems,"

McGraw-Hill Book Co., New York, (in press).

Winn, R. C, "Development of a Computer Pro- gram for the Optimum Design of Air Supply

Duct Systems," M.S. Thesis, University of

Illinois at Urbana-Champaign , Urbana, Illinois

1969.

358
0

Fan

Filter Coil

4-

2

3- 4

7 Q

E

cfm

cfm

5 8 -10

-11

o

IE cfm

Figure 1. A multiple-branch duct system.

Figure 2. Effect of fan static pressure on lifetime

cost of combined fan and duct system.

359
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360
5(30,60,0) 6(55,60,0)

IKFilter)

(7,0,0)

l(Fan)

(0,0,0)

12(Coil)

(10,0,0)

2000 CFM

3(30,20,0) 4(55, 20,0 )

' 1000 CFM

J 2(30,0,0)

A 7(50,0,0)

8(70,0,0) 2000 CFM

1500 CFM

9(50,-15,0) 10(70,-15,0)

Figure 5. Duct layout example.

361

Computerized Calculation

of

Duct Friction

H. F, Behls

Sargent & Lundy, Engineers

Chicago, Illinois 60603

With the duct friction factor known the pressure

drop due to friction in a pipe can be readily calculated

by the Darcey-Wiesbach equation. Colebrooks ' equation,

which relates the friction factors, Reynolds number,

diameter and material roughness factors, requires an iterative solution. This paper presents the Newton-Raphson

method for solving Colebrooks' equation, and all of the

pertinent subroutines to calculate the pressure drop in

straight air ducts. Presented also is an air friction

chart for an altitude of 5000 feet.

Key Words: Colebrook, computer, Darcey, density,

elevation, friction chart, friction factor, viscosity.

1. Introduction

Duct system simulation and design on the digital computer is becoming more and more common in the Consulting Engineer's office. At Sargent and Lundy we have modeled

exhaust ventilation systems in such a manner so as to obtain inherently balanced systems. In these systems the branch and main duct networks are designed so that both

networks have the same total pressure at the Junction of the tee. In addition to modeling systems we have generated friction charts for (1) air less dense than standard

air, and (2) fluids other than air.

A basic requirement for any modeling computer program is the ability to readily

calculate friction factors. As is well known the friction factor is a function of

Reynolds number, the material roughness factor, and the pipe diameter. The relationship between these parameters is illustrated by the Moody diagram (1)-^ which is presented in figure 1. Colebrook (2) developed the mathematical relationship, eq (1)

below, for these parameters. It is not the intent to discuss the development of this

equation, but rather, its solution, since Vennard (3) and others have excellent discussions on its development.

1V7

2 losio

12 E 2.31

(i;

where

f = friction factor, dimensionless

E = material roughness factor, feet

D = pipe diameter, inches

Rjj = Reynolds Number OoDVjui" ) , dimensionless

•'Figures in parenthesis Indicate the literature references at the end of this

paper.

363
>i = fluid viscosity, Ibs-ft"

"'"-hr"-'-

/o = fluid density, ibs-ft -3

V = fluid velocity, ft-mln""^

It is recognized that many organizations have in their computer program library a method for solving Colebrook's equation and calculating the pressure drops of fluids in

a pipe. Nevertheless, this paper is being presented for those who wish to initiate

modeling of duct and piping systems to meet their needs. The only limitation to modeling various types of systems is the fittings in your program library. More effort

needs to be expended in the correlation of fitting data. To assist in the correlation

of data. Dr. Inoue has an excellent summary of fitting data in his "Duct Design Handbook"(4).

In addition to presenting the program listings for determining friction factors

and calculating the pressure drop in a pipe the pertinent subroutines for calculating

the properties of moist air are presented for your convenience. Also Illustrated in

section 3 Is a friction chart for air at a density of O.062 lbs-ft"3, which Is equivalent to an altitude of 5000 feet.

2. Pressure Drop Calculations

2.1 Friction Factors

Of the numerical techniques analyzed to solve Colebrook's equation it was found

that the Newton-Raphson method requires the least computer execution time. This section presents an analysis of this method for solving the friction factor equation.

Rearranging eq (1) and setting the function of the friction factor, F(f), equal to zero yields eq (2). For fixed values of Reynolds number (Rj^j), material roughness

factor (E), and pipe diameter (D), the value of P(f) can be calculated for incremental

values of friction factors (f) and the results plotted as Illustrated in figure 2. In

Fffl + 2 log10

12 E 2.51 = 0 (2)

this example Reynolds

600,000 and 0.001, re numerical solution on Initiated by assuming

are unlikely since th

At the Initial value

lated by eq (2) . Aft

the Intercept to the

f (0.0159) In the sec the Intercept to the

point the difference

number and the dlmensionless ratio E/d (relative roughness) are spectively. The methodology is best illustrated by following the

this specific graphing of the function. The iteration process is

0.01 as a value for the friction factor f. Values less than 0.01

e Reynolds number would have to exceed 2.5 x 10° (refer to fig 1).

of f (0.01) the value of the function, F(f), is 2,988 as calcu- er calculating the derivative of function by eq (3), the value of

f-axis is calculated by eq (4) to be 0.0159- Using this value of

ond iteration process the value of P(f) is 0,892, and the value of

f-axls of a line tangent to the curve at O.892 Is 0.019^. At this

between the last two values of f is 0.0035- This difference is

F(f)

2 f1/2 1 + 12 E0,868590 2.51

(3)

NEW = fOLD LF'(f)

greater than the desired accuracy of 1/2 percent or difference of 0.001, therefore the

iteration process continues and f is reset to 0.019^- Using this value of f in the

next iteration the value of the next intercept to the f-axls is 0.0201. Since the difference between this value (0.0201) and the previously calculated value of f (0,019^)

is 0,00067, which is less than the difference desired, the iteration process is terminated. The solution for the friction factor, therefore, is 0,0201. By referring to

364
figure 1 the correlation of Colebrook's equation to Moody's diagram is readily demonstrated. To calculatb a friction factor three iterations are usually required, however

in a few cases, four iterations will be necessary to yield a solution. A listing of

the computer program for calculating friction factors is presented in figure 3. Figure

4 is a flowchart for this program.

2,2 Pressure Drop in Straight Ducts

The pressure drop in a pipe may be calculated by the Darcey-Wlesbach eq (5). This

relationship, used with the expression for velocity pressure (eq 6), may be used directly In your mainline programs, or as a subroutine. A Fortran listing of the pressure drop subroutine, naimed DUCT, is presented along with the friction factor subroutine (PRICT) in figure 3. These programs, in addition to your modeling programs, may

be readily used to develop friction charts for any fluid, fluid density and viscosity.

AP = f [§] (5)

where

Z\P = pressure drop. Inches water gage pressure (iwgp)

f friction factor, dimensionless

L pipe length, inches

D pipe diameter. Inches

Hv = velocity pressure, iwgp

/O fluid density, lbs-ft"3

V fluid velocity, ft-min"'''

2.3 Properties of Moist Air

To use the friction factor and pressure drop programs, the density and viscosity

of the fluid must be known. For your convenience in modeling air duct systems, or generating other air friction charts (see section 3)> the pertinent moist air subroutines are presented in the following sections.

a. Barometric Pressure

Altitude and barometric data by NACA (5) was correlated linearly by the method of

least squares between sea level and 5000 feet elevation. The resulting relationship,

eq (7), has a coefficient of determination of 0.999. Refer to figure 5 for the function subroutine of this equation.

BP = 29.841 - (0.9935) (10"3) (ELEV) (7)

where

BP = barometric pressure. Inches mercury

ELEV = altitude, feet

b. Moist Air Density

Function subroutines for the properties of moist air are presented in figure 5 and

are based on the "Algorithms For Psychrometric Calculations" by the National Bureau of

Standards (6). As may be noted the subroutine for calculating the air density (RHO) in

turn calls the absolute humidity (W), the partial pressure of water vapor (PV), and the

partial pressure of water vapor in moisture saturated air (PVS) subroutines.

365
c. Viscosity of Moist Air

Temperature-viscosity data for dry air at l4.7 psi from Jakob (7) is approximately

linear, and therefore the data was fitted by the least squares method to the regression

line between -60°F and +300°F. The resulting eq (8) has a coefficient of determination

of 0.991.

p. = 0.039^8 + (6.213) (10"5)T (8)

where

p. = dynamic viscosity, lbs mass-ft~-'--hr~"'' T = dry-bulb temperature, °F

Since the viscosity of moist air varies little from that of dry air at normal

atmospheric pressure (8), the above equation for viscosity is used to calculate the

Reynolds number of air flowing through the duct. The function subroutine for viscosity

is presented in figure 5-

3. 5000-Foot Friction Chart

An air friction chart for an altitude of 5000 feet using the subroutines in this

paper is presented in figure 6. Comparing these values to the standard air friction

chart in the ASHRAE Guide (9) the pressure drop for the less dense air at the higher

elevation ranges from 20 to 32 percent less than that at sea level (^=0.075 lbs-ft~3).

For example, for a flow of 1000 cubic feet of air per minute the loss in 100 feet of

6-lnch diameter pipe at sea level is 6.9 inches of water (refer to fig 6), while at

5000 feet ^=0.062) the loss is 5-5 inches of water. This decrease in air density re- sults in a 20,3 percent (based on standard air) reduction in resistance to air flow. As stated previously, other charts can be readily generated by developing a mainline program utilizing the friction factor (FRICT) and pressure drop (DUCT) subroutines.

4. Re

(1) L. F. Moody, "Friction Factors for

Pipe Flow", ASME Transactions, Vol. 66,

1944, p. 671.

(2) C, F. Colebrook, "Turbulent Plow in

Pipes, with Particular Reference to

the Transition Region between the

Smooth and Rough Pipe Laws", Jour.

Inst, Civil Engrs, London, Feb. 1939^

p. 133.

(3) J. K. Vennard, "Elementary Fluid Mechanics", 3i'd Edition, Wiley, New York,

1959. p. 193.

(4) U. Inoue, "Duct Design Handbook",

Waseda University, Japan, pp. I16-I37.

(5) "Tables and Data for Altitudes to

65,800 Feet", NACA Report 1235, Washington, D.C., 1955, pp. 66-81.

(6) T. Kusuda, "Algorithms for Psychrometric Calculations", National Bureau of

Standards, U.S. Department of Commerce,

Washington, D.C., Report No. 9818,

March, 1969.

rences

(7) M. Jakob and G. A. Hawkins, "Elements

of Heat Transfer", 3rd Edition, Wiley,

New York, 1959, p. 10.

(8) "Handbook of Fundamentals", American

Society of Heating, Refrigerating and

Air-Conditloning Engineers (ASHRAE),

New York, I967, figure 12, p. 109.

(9) "Guide and Data Book, Equipment",

ASHRAE, New York, I969, figs 2 & 3, pp. 26-27.

366
Figure 1, Moody Diagram (from ref 8, p. 87, fig 12)

367
JO saniBA

368
C NOMENCLATURE:

C E IS THE PIPE MATERIAL ROUGHNESS FACTOR, FEET (SEE REF. 8, P. 88, TABLE 4)

C DIA IS THE DIAMETER OF THE PIPE, INCHES

C CFM IS THE VOLUMETRIC RATE OF FLUID FLOW, CUBIC FEET PER MINUTE

C RHO IS THE DENSITY OF THE FLUID, LBS PER CUBIC FEET

C AMU IS THE VISCOSITY OF THE FLUID, LBS PER FT-HR

C ALGT IS THE LENGTH OF PIPE, FEET

C FRICT IS THE FRICTION FACTOR, DIMENSIONLESS

C DUCT IS THE PRESSURE FOR THE LENGTH OF PIPE (ALGT) INPUTED, INCHES OF WATER

C FRICTION FACTOR (FRICT) FUNCTION SUBROUTINE

FUNCTION FRICT(E,DIA,CFM,RHO,AMU)

RENNO= ( 916 . 733*RHO*CFM )/( AMU*DIA

)

F=0.01

10 C1=12.*E/(3.7*DIA)

C2=SQRT(F)

C3=2.51/(RENN0*C2)

c5=ci+c3

FF-1 . 0/C2+0 . 868589*ALOG ( C4

)

FDF= ( -0 . 5/( C 2*F )

) * ( 1 . + ( 2 . l801/( C4*RENN0 ) )

)

FNEl^=F-(FF/FDF)

DIF=ABS(FNEW-F)

IF(DIF-0.001)30,30,20

20 F=FNEW

GO TO 10

30 FRICT=FNEW

RETURN

END

C PRESSURE DROP (DUCT) FUNCTION SUBROUTINE

FUNCTION DUCT ( DIA , ALGT, CFM, RHO , FRICT

)

VP=RHO* ( CFM*0 . 1671/DIA**2) **2

DUCT=PRICT*ALGT*VP*12. /DIA

RETURN

END

Figure 3, Subroutine Listings for Calculating

Friction Factors and Pressure Drop

369
ENTER

SUBROUTINE

CALCULATE

REYNOLDS

NUMBER

ASSUME INITIAL

VALUE OF

FRICTION FACTOR

(f ) TO BE 0.01

FSNIO

-<

CALCULA'j

OF COLI

EQUATIOI

(see Nc

l?E VALUE

:brook

J, F(f)

)te 1)

NOTES ;

(1) F(f) = ^ + 2 log^o

(2) F'(f) = - _1

2f / f

1 +

12-i<-E + ^.5

D*3.7

0,

^NEW - f - F(f)

F'(f)

(h) FSNlO, FSN20, FSN30 are Fortran Statement Numbers, see listing, figure 3

CALCULATE VALUE

OF DERIVITIVE

OP THE FUNCTION,

F'(f)(see Note 2)

CALCULATE NEW

VALUE OF (f

)

BY NEWTON-RAPHSON

METHOD(see Note 3)

CALCULATE ABSOLUTE

VALUE OF THE

DIFFERENCE

FSN20 I SET (f)

EQUAL TO

LAST VALUE

CALCULATED

SET FRICT

EQUAL TO LATEST

VALUE CALCULATED

RETURN TO

CALLING

PROGRAM

Figure 4. Flowchart of the Friction Factor Program

370
c

c

c

c

NOMENCLATURE:

DBT IS THE DRY-BULB TEMPERATURE, DEGREES F

WBT IS THE WET-BULB TEMPERATURE, DEGREES F ELEV IS THE ALTITUDE ABOVE SEA LEVEL, FEET

C DENSITY OF MOIST AIR (RHO), POUNDS PER CUBIC FOOT OF DRY AIR

FUNCTION RHO( DBT, WBT, ELEV)

V0L=(0.75^*(DBT+459.688)*(1. +7000. *(W(DBT, WBT, ELEV)/436o. ) ) )/BP

l(ELEV)

RH0=1./V0L

RETURN

END

C BAROMETRIC PRESSURE AS A FUNCTION OF ALTITUDE (BP), INCHES MERCURY

FUNCTION BP (ELEV)

BP= ( 0 . 2984 11E02 ) - ( 0 . 993523E-O3 ) *ELEV

RETURN

END

C HUMIDITY RATIO OF MOIST AIR (W), LBS OF WATER VAPOR PER POUND OF DRY AIR

FUNCTION W( DBT, WBT, ELEV)

W=0 . 622* ( PV( DBT, WBT, ELEV)/( BP ( ELEV) -PV(DBT, WBT, ELEV) )

)

IF(W)10,20,20

10 W=0.

20 RETURN

END

C PARTIAL PRESSURE OF WATER VAPOR IN MOIST AIR (PV), INCHES MERCURY

FUNCTION PV( DBT, WBT, ELEV)

PV=PVS(WBT)-(0.000367*BP(ELEV)»(DBT-WBT)*(l.+(WBT-32. )/l571. )

)

IF(PV)10,20,20

C PARTIAL PRESSURE OF WATER VAPOR IN MOISTURE SATURATED AIR (PVS), INCHES MERCURY

FUNCTION PVS (TEMP)

DIMENSION A(6),B(4)

DATA A/-7 . 90298, 5. 02808, -1 . 38I6E-7, 11 . 344, 8 . I328E-3, -3 . 49149/

DATA B/-9 . 09718, -3 . 56654, 0 . 876793, 0 . 0060273/

T=(TEMP+459.688)/1.8

IF( T-273 . 16 ) 10, 20, 20

10 Z=273.l6/T

P1=B( 1)*(Z-1.

)

P2=b(2)*0.43429*AL0G(Z)

P3=B(3)*(1.-1./Z)

p4=0.43429*ALOG(B(4) ) GO TO 30

20 Z=373.l6/T

P1=A( 1)*(Z-1. ) P2=a(2)*0.43429*AL0G(Z)

P3=A 3 *(10**(A(4)*(1,-1./Z))-1.)

p4=a(5)*(io**(a 6)*(z-i.))-i.)

30 PVS=29.921*10**(P1+P2+P3+p4)

RETURN

END

C VISCOSITY OF MOIST AIR (AMU), LBS MASS PER FT-HR

FUNCTION AMU (DBT)

AMU=0 . 03948+06213E-4*DBT

RETURN

END

10 PV=0.

20 RETURN

END

Figure 5. Subroutine Listings for Determining

the Properties of Moist Air

371
®

0) -p3a

0)

.02 ,0U .06 .1 .2 .k .6 1. 2.

Friction Loss in Inches of Water per 100 ft

k. 6. 10.

Figure 6, Friction of Air at an Altitude of 5000 Feet

372
Friction Loss in Inches of Water per 100 ft

Figure 6. (cont'd) Friction of Air at an

Altitude of 5000 Feet

373

Pressure Loss Coefficients

for the

45-Degree Return Air Tee

H. P. Behls and W. K. Brown, Jr. Sargent & Lundy, Engineers

Chicago, Illinois 60603

For good design of duct system, the losses of the corn- components In the system network must be known. For the tee

there exists an Infinite number of combinations of throughflow and branch loss coefficients. Data for both the

through and branch coefficients have been correlated for

the 45-degree return air tee and the resulting family of curves presented. For those who wish to develop their own computer programs, the subprogram listings are provided.

In addition, the significance of the negative loss coefficients is discussed.

Key Words: Computer, design, exhaust, loss coefficients, pressure drop, return air, tee.

1. Introduction

The tee is the focal point in any duct system analysis because the resistance of

the main duct network, including the losses in the through portion of the tee, should

match at design air quantities the resistance of the branch network; otherwise the

system will not be in balance. Heretofore little emphasis was placed on the losses

which occur concurrently through both the main and branch sections of tees. For both

good design practice and modeling of duct systems on the computer the losses occurring

at the same time must be known. This paper presents the correlation of experimental

data for the 45-degree return air tee which has a circular cross-section, equal inlet

and outlet areas in the main, and a branch area equal to or less than the main. For

those who wish to develop their own duct system models for computer design, the program listings for the tee-through and tee-branch loss coefficients are Included herein,

2. Tee Loss Coefficients

Forty-five degree return air through-flow and branch to main loss coefficients

have been determined experimentally by Petermann( 1) 1 and the coefficients summarized

by Dr. Inoue in his handbook for duct design (2) as presented in table 1. Although this discussion pertains to the data correlation of the 45-degree tee

with a round cross-section, other data are available, primarily the 90-degree return

air tee (3j 4), and the supply air tees listed in table 2. These data should also be

correlated so that more diversified duct systems may be modeled.

2,1 Tee-Through Flow Loss Coefficients

Petermann's tee-through loss coefficients are best represented (least standard

deviation from the original data) by a family of parabolas as shown in figure 1. As

Figures in parenthesis indicate the literature references at the end of this

paper.

375
Table 1. 45-Degree Return Air Tee Loss Coefficients

Tee Configuration Flow Path Loss Coefficient (A)

Main

Area

Ratio

(D/B)

Velocity Ratio (U/D)

0.2 0.4 O.b O.B 1.0

1.0 -0.17 0.06 0.19 0.17 0.04

3.0 -1.50 -0.70 -0.20 0.10 0

8.2 -5.70 -2,90 -1.10 -0.10 0

Branch

Area

Ratio

(D/B)

Velocity Ratio (B/D)

0.4 0.6 O.B 1.0 1.2

1.0 0 0.22 0.37 0.37 0.20

3.0 -0.36 -0.10 0.15 0.40 0.75

8.2 -0.56 -0,32 -0.05 0.24 0.55

Table 2. Sources of Tee Data

Angle Type of Take-off Author Reference

450 Straight Petermann (1)

90° Straight Ashley (5)

90° Conical Ashley (5)

illustrated below, these parabolas can be correlated to the zero coordinates since the

location of their apexes is related to area ratio. This correlation is a straight

line going through the point (1.0, 0.0) with the area ratio approaching Infinity as the velocity ratio approaches 1.0. The resulting equations for the displacement of

the apexes from the (1.0, 0.0) coordinates are as follows:

376
H'(HPRIM) = 0.3015 (^^^ YK = 0,5978 - 0.5926 H (2)

where

H = 1.0 - H' ARDB = area ratio from the tee main to the

tee branch, dimenslonless

HPRIM = acronym used In computer program

The family of parabolas at the (0.0, 0.0) axis are represented by eq (3). It should be noted that the parabolas approach the negative Y-axis as the area ratio

approaches infinity.

COEP = [-1.461 ARDB°-9306j ^2 (3)

where

T = H - VRUD

VRUD = velocity ratio from upstream of the

tee main to downstream of the tee main,

dimenslonless

With the equation of the parabolas and their displacement known, the tee-through

loss coefficients can be readily calculated by eq (4). Using these relationships, the

data may be represented as shown in figure 2, or calculated utilizing the computer

listing presented in figure 3- For comparison purposes the parabolas for area ratios

of 1.0, 3-0 and 8,2 are superimposed on figure 1 to show the correlation to Petermannfe

original data. The coefficient of correlation of the curves to the original data is

0.987

Am (TEETH) = COEF + YK (4)

where

Ajy] = main loss coefficient, dimenslonless

TEETH = acronym used in computer program

2.2 Tee-Branch Plow Loss Coefficients

Along with data by Brown (6), Pettermann's tee-branch coefficients are shown in

figure 4. Since both sources of data correlate exceptionally well, confidence in the

data is high and Petermann's data was fitted to the general form of [Ag + 1 = VR2]

as suggested by Healy (7). The resulting correlation, with a coefficient or correlation of 0.962, is given by eq (6), and using this relationship the family of curves

in figure 5 were generated. It should be noted that as the area ratio increases the

loss coefficient approaches the ideal loss coefficient given by |^A-g +1 = VR^].

1 =

" 1.0276' "0,3405 (VRBD)' +

_ VARDB. L VARDB J [VRBD^-Oj (5)

where

Ag = branch loss coefficient, dimenslonless

ARDB = area ratio from the tee main to the tee

branch, dimenslonless

VRBD = velocity ratio from the branch to downstream of the tee main, dimenslonless

377
Figure 5 can be readily utilized by those who have a need for expedient data. For

those who wish to simulate and design their systems by use of the computer the program

listing for determining the branch loss coefficients is presented in figure 6,

2.3 Total Pressure Drop

With the loss coefficient known the total pressure loss in the through or branch

portions of the tee may then be calculated by the following expression.

AP = A[Vj/1097]^^ (6)

where:

AP = main or branch total pressure drop,

inches of water gage

Vj) = downstream velocity, feet-min"-'-

lO = moist air density, lbs-ft~3

A = main or branch loss coefficient,

dimensionless

2.4 Negative Loss Coefficients

By investigating figures 2 and 5 it may be noted that one or the other coefficient

may be negative. This can be best illustrated by the following example and sketch.

For an area ratio of 19.3 from the main to the branch, and a velocity ratio of 0,89

from upstream of the main (U) to downstream

-0,075; while the tee-branch coefficient is

of 2.15, In effect, the branch Jet at 8800

is moving at 3635 ft/min, has an asperating

ration phenomenon, also noted by Healy (7), are connected to relatively large mains.

(D) the tee-through loss coefficient is

+3.55 for a velocity ratio from (B) to (D)

ft/min coming into the mainstream, which

affect or acts like an ejector. This asplbecomes predominant as smaller branch ducts

This illustration actually occurred in one of our industrial power plants where

the noise generated due to the high velocities is not a problem. These relatively high

velocities are a result of our system design philosophy, which decreases the size of

the branch until the total pressure for the main and branch duct systems are approximately the same. For systems in which noise would be a problem the branch diameter

would not be decreased, but rather, resistance added in the branch by other means such

as obstructions. In most applications high velocities would not be encountered, and

both the main and branch coefficients most likely would be positive.

378
3. References

(1) F. Petermann, "Der Verlust In Schlefwlnkllgen Rohrverzwelgungen" , MHITHM

(Mlttellungen des Hydraullschen

Instltuts der Technlschen Hochschule

MUnchen), Heft 3, 1929, PP. 98-117.

(2) U. Inoue, "Duct Design Handbook",

Waseda University, Japan,

(3) G. Vogel, "Untersuchungen liber den

Verlust in rechtwinkligen Rohrverzweigungen", MHITHM, Heft 1, 1926,

pp. 75-90.

(4) G. Vogel, "Untersuchungen ifber den

Verlust in rechtwinkligen Rohrverzweigungen", MHITHM, Heft 2, 1928,

pp. 61-64.

(5) C. M. Ashley, et al, "Branch Fitting

Performance at High Velocity", ASHAE

Transactions, Vol. 62, 1956, pp. 279-

294.

(6) W. K. Brown, Jr., et al, "Friction

Loss Characteristics of Branch Duct

Fittings with a Fixed Duct Configuration", ASHRAE Transactions, Vol. 72,

Part I, 1966, p. 346.

(7) J. H. Healy, et al, "Pressure Losses

Through Fittings Used in Return Air

Systems", ASHRAE Transactions, Vol. 68,

1962, pp. 281-295.

4. Acknowledgement

We are grateful to Mr. Y. S. Chen of the University of Kansas for indicating the

availability of Petermann 's data as summarized by Dr. Inoue and the discussions with

respect to the significance of the negative loss coefficients.

379
o

sseiuoTSueuifp '{HJ,a3iL Jo Wy) ^jusf ofjjaoQ ssoi q3noj:qj,-88j,

380
381
C TOTAL PRESSURE LOSS COEFFICIENTS IN THE THROUGH SECTION OF A RETURN AIR

C 45-DEGREE TEE (TEETH), DIMENSIONLESS

C

C ARDB IS THE AREA RATIO OF THE TEE MAIN TO THE TEE BRANCH, DIMENSIONLESS

GC VT^UD IS THE VELOCITY RATIO PROM UPSTREAM OF THE TEE MAIN TO DOWNSTREAM OF THE

C TEE MAIN, DIMENSIONLESS

FUNCTION TEETH ( ARDB, VRUD)

HPRIM=03015/ARDB**0 . 6566

H=1.0-HPRIM

T=H-VRUD

YK=0. 5978-0. 59^6*H

C=-l . 46l*ARDB**0 . 9306

C0EF=C*T**2

TEETH=COEF+YK

RETURN

END

Figure 3. Fortran Function Subprogram Listing for

Detennlning Tee-Through Loss Coefficients

Velocity Ratio, Branch to Downstream (VRBD), dlmensionless

Figure 4. Comparison of Brown's and Petermann's Branch Coefficients

382

C TOTAL PRESSURE LOSS IN THE BRANCH OF A RETURN AIR 45-DEGREE TEE (TEEBR),

C DIMENSIONLESS

CC ARDB IS THE AREA RATIO OF THE TEE MAIN TO THE TEE BRANCH, DIMENSIONLESS

C

C VRBD IS THE VELOCITY RATIO FROM THE BRANCH TO DOWNSTREAM OF THE TEE MAIN,

C DIMENSIONLESS

FUNCTION TEEBR (ARDB, VRBD)

A=1.0276

B=0.3405

R= ( A/ARDB**0 . 5

) -

(

B*VRBD/ARDB**0 . 5 ) + ( VRBD»*2

)

TEEBR=R-1.

RETURN

END

Figure 6. Fortran Function Subprogram Listing for

Detennlnlng Tee-Branch Loss Coefficients

384
Automatic Design

of Optimal Duct Systems

M. Kovarik

Commonwealth Scientific and Industrial Research Organization

Melbourne, Victoria, Australia

A system of ducts for the delivery of air in an air-conditioning installation

subject to pressure-balance conditions is found to be indeterminate and thus capable of satisfying additional conditions. Upper bounds are imposed on the air velocities in some sections and the problem of economically optimal

diameters is formulated as a constrained non-linear programming problem.

This is transformed into an unconstrained problem capable of solution by

known numerical methods. A computer program based on the concept of Lagrange multipliers and the Newton-Raphson iterative method is outlined.

Techniques for acceleration of convergence are stated. Properties of resulting

optimal solutions are discussed.

Key Words: Ducted flow, friction losses, annual cost, capital cost,

running cost, kinetic energy, potential energy, static regain.

1. Scope and Definitions

The duct system under discussion consists of several sections, each of a uniform equivalent

diameter along its entire length. If a section contains bends, it will be represented by a straight

section of an equivalent length, according to conversion formulas summarised by Carrier and

others [ 1] ^ . Each section terminates either in a divided flow fitting or in a terminal outlet. Each

divided flow fitting has one inlet and two or more outlets. One of these outlets may be a terminal

outlet, others connect to the inlets of further downstream sections. There is only one entrance

section. From the description, it follows that there are at least as many sections as terminal outlets. A run is a set of duct sections commencing at a terminal outlet and continuing upstream to the

inlet of the entrance section. The number of runs is equal to the number of terminal outlets.

2. Balancing Conditions

To maintain the required flow of air at each terminal outlet, it is necessary that the sum of pressure drops along a run, plus the pressure at its outlet p is equal to the inlet pressure p^ for

all runs:

Pi = ^^Pjk + ^^Pl + Po

The summations extend over all sections 1 of a run and over all divided flow fittings connecting

section j to section k along the same run. The singly subscripted pressure drops result from friction

losses, doubly subscripted ones from the application of Bernoulli equation at the divided flow

fittings, as shown in Appendix 1. For given section lengths, flow quantities and fixed shapes of divided flow fittings, the pressure drops Ap of eq (1) are functions of equivalent diameters of the corresponding sections.

For a system with M + 1 terminal outlets, there are M + 1 equations of type (1), one for each

run. By subtracting the first of these from each of the remaining ones, the inlet pressure is eliminated and M equations are obtained in the following form:

Figures in brackets indicate the literature references at the end of this paper.

385
^APjk + ^^Pl - ( ^^Pxnn ' l^P,) - 0 (2)

These M simultaneous equations will be written as

H(D) = 0 (2a)

where H is an M x 1 matrix of the left hand side of eqs (2) and the argument D is an N x 1 matrix of the equivalent diameters of all the N sections. As the number of sections is at least equal to M + 1 and each section may have a different equivalent diameter, there are N independent variables

available to satisfy M < N simultaneous equations. Thus the balancing equations have no unique

solution. Consequently, a duct system corresponding to the description of Section 1 is always free

to satisfy at least one condition in addition to the balancing conditions.

3. The Degree of Freedom

The difference between the number of sections N and the number of balancing equations M will be called the degree of freedom of a duct system. In systems of one degree of freedom, only one

section diameter or velocity may be freely chosen, all others are determined by the balancing

equations. Where the degree of freedom exceeds one, the design problem is complicated and while

different feasible designs may be evaluated by comparison, it is difficult to estimate how much better

the best possible design might be. In the following, the problem of optimal duct system will be

posed, analysed, and a computer program for the determination of optimal dimensions will be

described.

4. Criterion of Optimality

A duct system which delivers required quantities of air at the required outlet pressures may

suffer from only two major shortcomings: excessive costs and noise. Standard reference literature

[3] suggests empirical rules for maximum permissible air velocity in various duct sections. The

computer program to be described provides means of incorporating arbitrary upper bounds on any

air velocity in the system.

Having satisfied requirements relating to noise, a duct system may be optimised with relation

to costs. For given layout, section lengths, air quantities, duty period, types of divided flow fittings

and unit cost factors, the total cost of the system depends on the transversal dimensions. It will be

analysed on the basis of equivalent diameters.

5. Costs

All capital costs will be reduced to their annual equivalents, following standard accounting

practice [2]. The annual capital cost of section j of length Xj and diameter Dj is

C.j^j^ollj22j' = q.X..(a + a,S,D. + a.,S,D^ ) (3) ^ '

where q is the capital recovery factor and the a's are unit cost factors. The first of these, a.Q, reflects costs dependent on the length alone, aj^ represents the component of cost related to the duct

surface area, a^^ stands for the rental value of the space occupied by the duct section. Any two of these three factors may be simultaneously zero. The factors S]^, S2 relate the equivalent diameter

to circumference and to the cross-section area; in a circular duct, they are 11 and n/4 respectively. For rectangular ducts, analogous factors follow from Ref. [4].

The annual capital cost of the duct system is the sum

C(D) =

I C. (4)

over all the sections. According to eq (3) it is a quadratic scalar function of the equivalent diameter

matrix D.

386
The running cost of a duct system is the cost of energy necessary to maintain the airflow for

the required time. The power applied at the entrance section is

P = Ql Pi(D) (5)

where Pj^ is the total pressure at the entrance of the system and Q^^ is the air flow rate. The

derivation of p;^ is in Appendix 1. For an overall motor-fan-diffuser efficiency e, the running cost is

r^D) = e"^ a3 t P(D) (6)

where a^ is the cost per unit of energy at the motor and t the total time of running per year. The total annual cost is then

C^(D) = C(D) + r(D) (7)

As the pressure increments which combine to determine the running cost are proportional to velocity to a power of approximately 2 (see Appendix), r(D) is a function of diameter raised to a power of approximately -4. The capital cost is a quadratic function of diameter and both C(D) and

r(D) are, of course, positive. Thus C.-p(D) of eq (7) is a convex function and satisfies second order

necessary conditions in the sense of Ref. [5] for the local uniqueness of the optimal solution.

6. The Constrained Problem

The problem of optimal duct system design may now be formulated:

minimise Crp(D) (8a)

subject to H(D) = 0 (8b)

and D. - B. > 0 (8c)

1 1 — ^ '

where Bj^ is the lower bound of diameter corresponding to the prescribed upper bound on velocity

in section i.

This is a non-linear programming problem with accessory conditions (8b) and unequality

constraints (Be). Techniques of solution are summarised by Fiacco and McCormick [5] , who refer

to this form as Problem A. A particular technique embodied in a working computer program for

iterative solution of optimal duct diameters will be described.

7. The Unconstrained Problem

The constraints (8c) are represented by ficticious costs; if, during the computation, any

diameter Dj^ becomes smaller than the corresponding constraint Bj^, the cost of section i is increased by a quantity proportional to the square of the excess Bj^ - D^. This increase is applied

with sufficient weight, so that the resulting optimal diameter is within a prescribed tolerance

interval of the applicable bound. Thus, the constrained problem is transferred into an unconstrained

problem with accessory conditions:

minimise C-p(D) (9a)

subject to ^j(-^) ^ °' 1 1 j £ (9b)

where C-p is the sum of actual and ficticious costs:

Cj, = Cj, + I k. (B. - D.)^ (9c)

387
being the ficticious cost factor

k. = 0 if B. < D. (9d)

k. > 0 if B. > D. (9e)

j The solution of problena (9) is a set of N diameters Dj^ constituting an N x 1 matrix D which

satisfies eq (9b) and the condition for extreme value

aw

aD, (10)

for all i's. Here, W is the Lagrangian

W = + u'^H (11)

consisting of the cost and the M balance condition Hj (D) = -0;- is the M x 1 matrix of Lagrange

multipliers, transposed. (For a brief outline of the Lagrangian technique, see reference [6])

The design problem now consists of finding the N values of and M values of Uj which

simultaneously satisfy eqs (10) and (9b); these are M + N independent conditions binding an equal

number of variables.

The numerical solution commences by choosing a tentative initial set of values for the Lagrange

multipliers Uj, solving eq (10) for the corresponding diameters Di(U) and substituting these into eq (9b). Due to an error in U, the left hand side of eq (9b) is not equal to zero, but to an error matrix E dependent on U:

H(D(U)) = E(U) (12)

A better set of multipliers is obtained from the initial one by Newton-Raphson method [7]. A

correction 5U in the values of U which reduces the error E is calculated from the first order

approximation:

E + -fg. 6U = 0 (13)

This equation is solved by inversion of the M x M matrix SH/ aU:

5U = -i-ff . E (14)

The original values of U are corrected by 6U and the procedure is iterated until the residual error E is reduced within prescribed bounds. The physical significance of E is the amount of pressure unbalance in the duct system.

The matrix BHI dU is obtained as the derivative of a composite function:

au ao dU ^

'

All elements of the M x N matrix dlil dD are available in analytical form following substitution

into eq (2a) from eq (2) and from the pressure drop expressions in Appendix 1 . The N x M matrix

ao/ au is obtained from the Lagrangian eq (10) by the rules for derivatives of an implicit function.

The typical element is

388
dD.

i_ dU.

az.

1^ au.

J_ az.

i_ ao.

1

(16)

where = , from eq (10).

i The denominator dZ^I dD^ in eq (16) is the second partial derivative of the Lagrangian W in respect of D^^.

8. Convergence

The iterative process converges slowly and it is necessary to use special precautions to ensure stability while the initially chosen values of U are far from the correct ones. The program

limits the step size and restricts, in the initial stages, all diameters by cost penalties based on a rough estimate of optimal diameters. These penalties are cancelled when stability is reached and

have no effect on the result.

9. Properties of Optimal Duct Systems

The duct system resulting from the above procedure differs to some extent from systems

designed by current methods. The difference is minimal in systems of one degree of freedom,

i. e. those where the number of sections is equal to the number of terminal outlets. The static regain method [8] uses physical concepts employed in the setting up of balancing conditions, eq (2a)

and eq (2c), Appendix 1 of the present study. With one degree of freedom, the system is determined

by any single variable being fixed; it follows that any such system is optimal for some set of design

parameters. However, these may equal the parameters actually applicable only by coincidence.

TABLE 1 SYSTEM OF ONE DEGREE OF FREEDOM

DESIGN A:aj = 1 . 50 $/ft^ DESIGN Btaj = 16. 70 $/ft^

DUCT

SECTION

LENGTH

ft Q, CFM DIAM.INCH

VELOCITY

ft / min

DIAM.

INCH VELOCITY

1 50 10, 000 38. 1 1,261 24. 0 3,185

2 40 8, 000 36. 3 1,115 23.4 2, 680

3 20 6, 000 32. 6 1 , 036 21.4 2, 412

4 20 4, 000 27. 8 949 18. 6 2, 127

5 20 2, 000 20. 9 837 14. 3 1 , 795

CAPITAL COST, at a^ = 1 . 50 $/ft

ANNUAL CAPITAL COST

RUNNING COST at 8750 hrs/year

0. 02 $/kWh

TOTAL ANNUAL COST

$1 , 957

$184. 74

$42. 11

$226. 85

$1 , 263

$119. 30

$294. 50

$413. 80

System of one degree of freedom, for Table 1

389
Table 1 compares two optimal systems of one degree of freedom, differing only in the capital cost factor aj , the cost per unit area of the duct surface. Both systems have been obtained as results

of the procedures described above. Design A is optimal for a realistic value of aj = 1. 50 $/ft^;

design B would cost 82% more to own and operate in the same cost environment. It happens to be

optimal for duct cost 16. 70 $ I it^ . Design B consists of sections 10 - 14 of an example given in Ref. [9]. The example quoted may, of course, be optimal for a lower capital cost and a shorter

duty period.

For systems of degree of freedom higher than one, the current design methods offer no unique

solution. Thus, there is no basis for economic comparisons between them and the present method.

It is true, however, that while static regain systems of degree one are inevitably optimal, even if perhaps for some unrealistic cost factors, higher degree systems may only be optimal by an unlikely

multiple coincidence.

To understand the shortcoming of existing methods, it is necessary to realise that a duct system

supplies two things to each divided flow fitting: the air to be distributed and the energy to drive it through the subsequent sections. This energy exists in two forms: kinetic and potential (static

pressure). The static regain method, consisting in a "procedure in which the duct is sized so that the increase of static pressure or regain at each take off offsets the pressure loss of the succeeding

section of the run" [10] transports all this energy as kinetic. This involves friction losses upstream

whereas transport in the form of potential, or pressure, is free from losses in systems without leaks. On the other hand larger ducts are required to reduce the kinetic energy content. The present

procedure optimises the proportion of kinetic to potential energy according to the criterion of minimal costs, subject to balancing conditions and velocity constraints.

10. Re

[1] Carrier, W. H. , Cherne, R. E. , Grant, W.A. , Roberts, W. H. Modern Air Conditioning,

Heating, and Ventilation, Third Edition,

pp. 256-7, (Pitman, 1959)

[2] Ibid. p. 513.

[3] ASHRAE Guide and Data Book, Systems and

Equipment for 1967, p. 37 (American Soc.

of Heating, Refrigeration and Air-Conditioning Engineers)

[4] Ibid. p. 29, eqs (6).

[5] Fiacco, A. V. and McCormick, G. P. Nonlinear Programming: Sequential Unconstrained Minimisation Techniques

(Wiley 1968)

:ferences

[6] Korn, G. A. and Korn, T. M. Mathematical

handbook for Scientists and Engineers

(McGraw-Hill 1968)

[7] Ibid, section 20. 2-8.

[8] Ref. 1 , p. 261.

[9] Ref. 3 , pp. 42 - 44, Table 9, sections 10 - 14.

[10] Ibid. p. 39, Col. 2.

390
APPENDIX 1 Pressure Drop Formulas

The following expressions are based on the ASHRAE Guide [3]. Equation (1) is the SI equivalent of formula Z5, p. 39. Equation (2) is a generalised form corresponding to formulas 14, 16-20

of page 35. Any of the guide expressions may be obtained from eq (2) by a suitable choice of parameters Cy, Cq.

The remaining equations of this Appendix are derived from eqs (1) and (2).

Symbols and Units

p air density (kg m'-^)

(m s V air velocity ) Di equivalent diameter of section i (m)

Li equivalent length of section i (m)

/ 3 -1> (m s Qi flow rate in section ) i Api pressure drop in section i (N m"^)

^Pkl pressure drop due to a divided flow

fitting connecting section k to section 1 (N m'^)

In a duct of circular c ros s - section the pressure drop resulting from friction is

Ap. - 0.0202 . L. . Q^-^^ . D"^-^^

1 111 (1)

The pressure drop corresponding to a transition from section j to section k would be, in a loss free system

f (^k (2a)

Introducing coefficients C-y and Cj-j to represent losses occurring upstream and downstream of the divided flow fitting, we have

_E_ 2 ^D ^k C., v^ U J Expressing the velocities by flow rates and diameters

V. = S-, Q. D'^

1 1

(2b)

(2c)

where 82 is the proportionality factor between D and c ros s - section area for the particular shape

employed

The total pressure at the entrance of the system consists of the velocity head and of all the pressure drops along any run.

2

'1 + I Ap. + I Ap.j^ + p

(2d)

(3)

and the necessary fan power is

Qj . P (4)

which leads to eq (5) of Section 5. The first and second partial derivatives of the running cost in respect of any diameter follow

after substitution into eq (3) for Vj and all the pressure drops from eqs (1), (2a) and (2d).

391

A System of Computer Programs

Widely Used in Europe for Designing,

Selecting and Analysing Different

Air Conditioning Systems

1 A.VJ, Bo eke and S. Larm

Delft University of Technology, Netherlands

and AB Svenska Flaktfabriken , Stockholm, Sweden

The ultimate object of using computer programs in air conditioning design is to make feasible an optimal choice and integration of building features and A.C.-

equipment that complies with indoor environment requirements. To this end it is necessary not only to compute heating and cooling loads in all individual rooms

for specified room temperatures and outdoor conditions, but also to obtain the data required for directly selecting all main central eurid peripherial components

of the A. C, -plant from maniif acturers ' catalogues and to assess the average yearly

energy consumption. These items are substantially influenced by the type of plant chosen and the interaction of the different loads handled simultaneously in all zones. Further, heat storage capacities cooperating with tolerated uncontrolled variations of room temperatures within specified limits, moving shadows

from other buildings, control systems and setting values, causing annihilation

and/or recuperation of energy etc., play an essential part. In this paper a set of computer programs is presented which yield all the information mentioned for

different kinds of A. C. -systems in addition to many other valuable data, such as temperature curves occurring in rooms without air conditioning. There is also a prograjn for the calculation of complete duct systems. Manuals and take-offsheets are available in different languages and units systems. Computer results

are printed in corresponding varieties. The programs are used in many countries

in Europe and several hundreds of projects have hitherto been calculated. As a result of these programs there is now a growing practice for architects, together

with civil, electrical, acoustical and A. C. -engineers, etc., to form a team as early as the financial stage of the planning, thus obtaining an optimal total

design without individual dominance of any part concerned.

Key Words: Air conditioning, A.C. central systems,

A.C. load calculations, A.C, plant design,

computer calculations.

1. Introduction

In articles and discussions about the application of computers in A.C. -design work one often

meets the opinion that this application would be identical with and confined to the computerized

calculation of maximum heating and cooling loads per room - and possibly the dimensioning of duct

systems.

Without denying the importance and extensiveness of these basic calculations, every A.C.-

designer knows very well that they constitute only a minor part of the entire work. They do not give him any ajiswers to questions such as total cooling and heating energy consumption in the entire

building - consisting of many different rooms - during a normal year, determination of size of room

units and central plant in such a way that room temperatures are allowed to glide freely within certain

specified limits, setting values of different control functions, etc.

These, and many similar items, are dependent on the way in which the calculated net heating and cooling demands are satisfied, and on the thermo-dynamic losses and regain possibilities inherent to the A.C. -system chosen. A complete package of application programs within the A.C. -field should therefore incorporate not only the necessary load computing routines, but also the digital simulation of

most current A.C. -systems.

Professor and Engineer, respectively

393
For this reason, in I964 we started to develop such a set of programs (see fig. I), the second

generation of which have already been in extensive daily use throughout Europe for several years and a third generation are now being completed and are already partly operative.

2. Survey of Computer Programs Developed

When planning a new building in moderate European climate areas the first qriestion posed by architects and principals is often whether an A. C. -installation is in fact necessary, or whether an acceptable

indoor climate could be maintained by a simple ventilation system. The prime decisive factor in this

case is the air temperature attained in the rooms during the hottest part of the year. Therefore a special prograjn has been established which calculates the course of daily room temperature variations

without air-conditioning, and without or with mechanical ventilation at a given rate and temperature.

Of course all given structural characteristics and specified conditions as regards the use of the building and the local outdoor climate are taken into consideration in this calculation.

If the need for aji A. C. -installation is found to exist, the necessary equipment can be determined

and the operating costs be evaluated by using the other available programs for the calculation of,

respectively:

A. Net heat gains and losses per building module for all relevant average ajid design

conditions such as normal workdays and holidays during clear aind cloudy weather

throughout the year (Program LK012).

B. Installation and operating data for: Two-pipe induction systems with variable primary air temperature (Prograjn LK022).

Four-pipe induction systems (Program LKO42). This program can also be used for

calculating two-pipe terminal reheat systems.

Ihial-duct systems (Program LK062).

C. Dimensions of duct systems made up of sheet metal ducts of circular sections and consequent fan pressures (Program LK002).

3. Particulars of the Programs

3.1 General Observations

When the work of calculating is entrusted to a computer it becomes feasible to take full consideration of such factors as non-simultaneousness of maximum cooling demands, heat storage in the building

structure in connection with irregular times of insolation due to moving shadows, etc.

The potential of the computer has not been fully utilized if it is merely employed to carry out the

same table references and calculations as the designer has previously performed manually. On the other

hand, the program designer should not seek theoretical perfection. This could easily result in the loss of other important attributes, such as wider usefulness, since there is a limit even to the capacity of

computers.

An excessively thorough treatment of certain factors in the calculation process may also frequently

result in the take-off sheets being so extensive in scope as to daunt the ordinary, practical design

engineer.

Moreover an unlimited refinement of the calculation methods entails a rapid increase of the CPU-time

in the computer and so a sensible balance between calculation costs and scientific perfection must always

be observed.

3.2 Meteorological Data

This philosophy is also apparent in the method we have adopted for the specification and subsequent

use of the meteorological data. The calculation requires a continuous course of outdoor temperatures

during an average and a design-day in every month under clear and overcast weather conditions. These

temperatures are calculated by the computer on the assumption that the daily variation describes a sine curve (vjith alternate long and short half-periods), the maximum and minimum points of which are given in a special meteorological data form.

When a calculation is to be carried out for a specific geographic area for the first time, the requisite climatic particulars must be entered on this form. The particulars are then filed for future reference.

394
The varying hvunidity of the outdoor air is treated in a similar majoner. For direct ajid diffuse

solar radiation intensity only information as to the maximum values for a clear day in each month is required. The variation in intensity during the day is then calculated by the computer for every required aspect by assuming that direct solar heat striking an external wall varies during the day from

zero to a maximum value and back to zero in conformity with the positive portion of a sine curve. The

half-period is equal to the time between the instant when solar radiation first strikes the facade and

that at which it ceases to strike it, regardless of whether these points in time are determined by sunrise

and/or sunset, or by the sun appearing and/or disappearing round the cprners of the facade.

3.3 Basic Calculation Method

The variation of room air and wall temperatures and of heating and cooling demaJids per module is calculated by determining the balance of heat stored in the building mass and trajnsferred to the room air. This balance is computed hour by hour and includes all internal and external heat gams and losses. The

heat balance at a certain point of time, called "the hour (CL+T)" is calculated with the assumption that outdoor conditions, solar radiation, as well as internal heat loads that do not vary with room temperature are constant from the preceding point of time, "the hour CL" for which they were given or previously calculated, until and not including the hour CL+T. If the room air temperature varies it is supposed to be subject to a sudden change immediately after the hour CL and then to remain constant until

and including the hour CL+T. Those heat loads which depend on room air temperature (e.g. transmission)

as well as the wall surface temperature and the wall core temperature are supposed to vary in the Scune manner.

The results of each heat balance calculation are new values of wall surface and wall core temperatures for the hour CL+T as well as a new room air temperature to be reached at that hour or, when room temperature is prescribed, a new cooling or heating demand. Thus a "backward discretization of time"

is applied avoiding any instability in the calculations.

Calculations are started from 1 a.m. on the assumption that both the air in the room and the walls

and floor have a temperature of 71°F then. After calculations have been completed for a full 24 hours,

the room and wall temperatures obtained are usually different and these new values are taken as starting

points for the next day, and so forth. Calculations are carried out in this way for four consecutive

days, in general, this being adequate in most cases to achieve a stabilized temperature history i.e. , the values for 12 p.m. are largely identical with those calculated for 1 a.m. the preceding night. In buildings with heavy structures, however, stabilization may not be achieved at the end of the fourth day

calculated and therefore the number of consecutive days can be changed arbitrarily. In most cases, though, this number is limited to four days in view of the fact that the majority of 'heat-wave' periods

(representing design weather) seldom last longer than four days, at any rate in Western Europe type

climates.

3.4 The Influence of Sudden Load Variations,

Manipulation of Blinds, etc

Using the method described, it is also possible to take account of sudden load changes, such as the switching-on or off of the lighting, the drawing or rolling-up of sunblinds, or the start and finish of office hours with the associated change in the required room temperature, occupant load, heat gain from

lighting, etc. The cooling requirement in an office, for example, is greatly affected by assumptions

such as that Venetian blinds will be drawn all day on sunny days, or that they will be drawn only when

the sun shines directly on the wall concerned during office hourse.

The take-off sheets provide for an indication of the times between which office hours may be assumed

to lie, and the temperature limits to be maintained during these hours eind at night or during holidays.

As stated previously, the solar heat gain through the windows is calculated for each hour. The program

maJces the assumption that when this gain exceeds a certain level the sunblinds will be drawn, as long as the room is occupied. Otherwise it is assumed that the blinds, etc., are not drawn. Outside office

hoxirs, the client may specify that blinds will always be drawn or open.

Similarly, the light intensity due to natural lighting at a given distance from the windows is calculated for each hour of the day. It is assumed in the program that when this falls below a certain

level the artificial lighting will be switched on and the heat gain from this source is then included in the heat balance equation for the hour concerned. It is taken for granted in this context that lighting

is likely to be switched on only during office hours. When the intensity of natural lighting in the room is on the increase, so that it exceeds the limiting value up to which supplementary lighting is required, then it is normally assumed that artificial lighting will be switched off. It is possible,

however, to provide for a degree of 'lighting negligence' by assuming that once the lighting has been

switched on it will be left on to the end of office hours, regardless of the subsequent need or otherwise.

395
' 3.5 Effect of Shadows from External Wall Projections

and Other Buildings

The reduction in the solar radiation through windows depending on shadowing by external wall

features such as balconies or columns, or to the recessing of windows is taken into due account. This

reduction will naturally vary according to the angle of incidence of the sim's rays, i.e. according to the time of day, and is calculated stereometrically on the basis of the sun's varying altitude and azimuth at the geographic latitude concerned.

The tables published in current A. C. -design manuals which are normally used to determine 'storage

factors' are limited, for practical reasons, to external walls on which there are no shadowing features. This meauis that in such manual calculations the same reduction factor for shadows is employed not only

for the direct solar radiation at the time considered, but also for the solar heat stored during the preceding hours. This may lead to tangible errors in certain cases, but these are completely eliminated

in the computer programs, which calculate the shadow factor and stored heat hour by hour.

The programs also permit moving shadows from other neighbouring buildings or parts of the same building to be taken into account. The edge of such shadows moves constantly and, at any given time, the different parts of the facade will have been in sunlight for different lengths of time. The stored

solar heat will therefore be different for these different parts and thus the resultant room temperatures,

or the cooling demand will differ also.

A maximum of 12 shadowing rectangular buildings can be allowed for. Buildings with complex shapes,

such as horizontally or vertically L-shaped structures, are considered to consist of two or more adjacent

single rectangular buildings. The locations of the corners of the shadow-throwing structures in relation to the facade investigated are defined by means o:" a co-ordinate system which can be laid

arbitrarily over a site plan of the building area (see fig. 2).

A division of the facade into a maximum number of 100 surface elements is then assumed by the computer.

The sequence of room air temperatures or thermal loads is calculated for one module in every such surface

element or group of elements. The different local successions of sunny and shaded periods on every part of

the facade are thereby taken into account and also the corresponding switching on and off of electric

lighting, the drawing and opening of sun blinds and the storage effect due to these factors.

4. Lay-out and Versatility of Take-off Sheets

For every program only two different kinds of take-off sheets are used. One of these contains all the data which are common for the entire building or describe the basic conception and central control of the A. C. -plant, whereas the other contains all the data pertaining to each individual "zone" or group of identical modules.

In addition to comprehensive instructions given in the "Program Users Manuals", the take-off sheets contain a considerable amount of guiding text to facilitate the filling-in. This is illustrated in figure 3 showing the "Common Plant Data"form for the four-pipe induction system program (LKO42).

Within each A. C—system many alternative variations can be specified such as different combinations

and consecutive orders of components in the central air treating unit, free cooling through "dry" or "sprayed" recovery coil, automatic or manual terminal unit control, etc. J:\Lrther, the user can specify

by how many deg. F personnel in a room should be able to regulate the room temperature upwards or downwards, by how many degrees the room temperature should be allowed to glide upwards above the normally

desired value in the event of exceptionally hot weather (at summer design temperature), whether 'lighting

negligence' is to be taken into consideration, ajid so forth.

5. Calculation Results

5.1 PLOom Temperature Program

The results of the room temperature program LKOI5 comprise one printed page for every building zone and month investigated. Vlhen moving shadows occur on a facade this page gives the daily range of room temperatures obtained in the two facade elements in which the highest and the lowest top values, respectively, of the entire facade occur on a clear day. Further, the print-out gives the temperature range obtained on a cloudy day during which all modules, of course, are subject to equal loads.

VJhen the computer, on the basis of prevailing solar intensity at any point of time, states that lighting should be switched on or that Venetian blinds, jalousies or similar devices should be shut, this

is indicated by the letters 'L' and 'J' respectively, after the room temperature value at the hour in question. In addition frequency tables are printed giving information on the percentage of the total

time of occupancy in the zone during which different room temperatures are reached or exceeded. The varying boimdary line of the moving shadows is also shown in the computer results, (fig. 4)'

396
5.2 Basic Load Calculating Program

The results obtained with th^ program LK012 include the heating and cooling requirements per module

during any specified month or all 12 months of a statistically normal year, as well as the maximum re- quirements occurring under outdoor design conditions. These results are based on room temperatures

being prescribed either at fixed values or between given limits.

The normal procedure following this calculation is to use the data calculated and stored by the computer for designing aji A. C. -installation with the aid of one of the "plajit programs". However, in many cases the result of the LK012 program has a value of its own - for instance when different

alternative building featiires such as size of windows, kind of blends, etc., are to be compared.

5.3 Plant Designing Programs

An example of one page of the results produced by the plaJit designing programs {LK022-LK062) is shown in figure 5. This page supplies, for one zone, the information necessary for the selection of the induction units in a four-pipe system (max. required unit coil cooling and heating capacities in connection with primary air supply). Comments are also printed as to the specified comfort requirement or some other consideration that has been decisive for the capacity values stated.

In addition, a number of tables are printed showing the varying thermal output of the induction unit

during the day together with room temperatures actually obtained for several critical running conditions

In the results of the dual-duct plant program (LK062) corresponding information is given concerning

the chao'act eristics of the mixing boxes.

When moving shadows occur on any facade a special table is printed indicating on which parts of

that facade it is possible to install terminal units with a lower capacity than the maximum required

capacity owing to the reduced solar heat gain in these parts. After determining the capacity of the induction units or the mixing boxes, the computer calculates the total heating and cooling energy consumption in the whole building for all consecutive hours of a clear, as well as a cloudy day in every

month. This is done both for normal and extreme ("design") outdoor conditions.

The highest value of the total momentary cooling demand (including all required sensible and latent cooling of outdoor air) which the computer encounters in the course of this calculation is stored and

later shown in the printed calculation result. The result, apart from the maximum total cooling load, also states the daily course of unit outputs and room temperatures in every zone during the day on which

this maximum total load occurs (fig. 6).

In addition to the design cooling load with the appropriate times and temperatures, the maximum

total heating demaJid and a large number of other data required for the design of the plant, such as central cooling ajnd heating coil characteristics, total water flow rates, etc., are also provided.

The total consumption of heating and cooling energy at every hour, calculated over the normal year

referrred to above, is collected in a number of items so that the totals may be obtained at the end of each month and of the whole year. These totals are composed of the summed-up hourly consumption

figures obtained in "real" (digitally simulated) over-all plant operation during clear and cloudy workdays and weekends in statistically correct proportions for every month. Apart from the yearly totals,

the over-all energy consumption is stated per hour and per month.

5.4 Duct Calculating Program

After determining all main thermal components in the way described above, the dimensioning of the

duct system and the fans remains to be calculated. This is done with the aid of the duct system calculating progrcun (LK002).

This program yields all the necessary information for each individual pipe section of the system

such as quantity of air passing, air velocity, pressure loss and, in the case where the pipe section

ends in a supply or extract point, the available static pressure at these points. Any throttling

devices required are indicated on the appropriate sections giving the pressure drop need. The diameters

of the pipe sections and the throttling devices that may be required at the main junctions are given

final values by the computer, often after repeated calculations in order that a certain maximum permissible pressure difference between the different supply points will not be exceeded. The table f\irther

indicates the total quajitity of air and the faji pressure.

Fiirther, the results of this program include a complete list of the total lengths of all ducts of different diameters used in the system, as well as the total number of bends, tees, etc.

397
When recfuired, the print-out can also include a sub-division of the list in accordeunce with the different stages of erection of the building. Each partial list then comprises the ducts and accessories required for one floor, wing or similar part of the building and the erection engineer is thus provided with means to order the duct parts for delivery to the building site in smaller portions just

when they are required.

6. Practical Applications and Consequences

Amongst air-conditioning engineers in Europe there is a general wish to be involved in the planning

of new buildings at as early a stage as possible in order that the architectural design and the lay-out

of the A. C. -plant should be co-ordinated from the very beginning, and this desirability is pointed out on every possible occasion.

However, this recommended teamwork has only too seldom been applied in actual practice. One of the main causes of this regrettable state of affairs has most probably been the difficulty for A.C.-

people to give immediate and correct answers to essential questions raised by architects and principals.

Such questions are, e.g., "How does the glazing percentage of facades influence costs and required space for cooling equipment?" or "What type of A. C. -system is the most advantageous m ajiy given case?"

During the last couple of years, however, a noticeable chaJige in this situation has taken place -

made possible by the development of computer programs such as those described in this paper.

An increasing understanding by architects and building owners of the importance of air-conditioning

and of the problems involved can be observed. Thus, there is now a growing practice for all the parties

concerned in the planning of a building to form a team already at the financial stage, resulting in an optimal total design.

398
ROOM TEMPERATURE

CALCULATING PROGRAM

LK015

2-PIPE INDUCTION

SYSTEM WITH VARYING

AIR TEMPERATURE

LK022

BASIC LOAD

CALCULATING PROGRAM

LK012

^-PIPE INDUCTION

SYSTEM

LK0/;2

DUAL DUCT SYSTEM

LK062

DUCT CALCULATING

PROGRAM

LK002

Pig. 1 Basic conception of a set of A. C. -design programs

399
Fig. 2 Configuration of buildings with site plan

400
SVENSKA

•l.AK 1 F VBRIKEN

EDP-calculation for air conditioning pJontu

Foiir pipe iniiijction ayBtem.

Ponii BK 0042 DEE

ProKroin LKO/12

CUMMON PLANT DATA

Cardn^ber I fl L | K| 0 | 4 | 2 | [3]

N^e or oo. Oi- Wildine iVl l^l I I I 1^

I I I I I I I TTTT" I I I I!

Reference- and job number (filled in by SP) .

Mark with 1 if!

Calculation of required capacities

and central control only (Part l)..

•0

Calculation of energy consumption and cooling plant only (Part 2). It is aesumed i—

that calculation of Part 1 has been made earlier L_J

COOLING PLANT AND REQUIRED COIL CAPACITIES

Mark with 1 if:

Cooling plant to be determined with r~~] regard to light load a clear day«"l I a cl

When dimensioning cooling plant and required coil capacities continuous running is assumed

Heating demand at design winte

period of holidays calculated for a workday after

sired number of holidays

0121 IBILIKI0I4I2I

•g

0

CETJTRAL UNIT AND CENTRAL CONTROL

Supply temp, old water to induction un

At outdoo

temp, lim

ALT. 1

AF CR PC HS CHP

n principle built up according' to alternative No

ALT. 2 r T «HiH!KM T4 T1 T3 N+ k'j T5 71 N+Jj T4 T5 T1 N+L'j

r T ALT. 3

AF CR PC HS CHR

r T

L J AF "Anti-freese" coil, if any CR = Cooling/Heat recovery coil

PC = Preheating ceil

HS = Sep. humidifying section

Temp, cf primary air at T1 Winter

If morning boost heating: Allowed

max. temp, of primary air at T2...

If "anti-freeze" coil: r Mi;i. air temp, after coil (at T4)-...*fL

HEAT RECOVERY

Mark with 1 if:

"Dry" recovery coil.

Temp, efficiency of cooling/heatrecovery coil ("dry" coil value)

if dimensioned principally with

regard to recovery function

Degree of humidificatic

•0

Central reheater, if any

Fan Reheaters, if any

At outdoor

temp, limit .

If alt.1 , Temp, of ,

r.tral reheating coil:

If alt.

after humidifying sect.

fter coil (at T3) "F

3: Mm. temp.

(at T5).

"Sprayed" recoveiy coil (Alt 2 if omitting sep. humidifying section).

Temp, rise fan .

0

Min. supply temp, of cold water

available to central cool, coil summer if cool./heat-rec. coil is

dim. only with reg. to req. cool. cap. . "'^l^45 V

IF IHMER ZONES SHALL BE CALCULATED

Total air supply

to inner zones . .

Number of working days per

Reheating temp, (at T2) fo

Shaded squares need not necessarily be filled in. When left open plausible data are put

the cor.puter. Blank (unshaded) sqiiares should aluays be filled in.

Pig. 3 "Common Plant Data" form for the four-pipe induction system program

401
SHADOW BOUNDARIES IN AUG ON ZONE 9 BEARING 166.0 DEGR.

- = SURFACE

" = SURFACE

ELEMENT

ELEMENT

IN

IN SHADOWDIRECT

OF NEIGHBOURING

SUN

BUILDINGS

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( X

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X X X X

X X X

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9: X 9! X X : : ; 9! ;( X X 9C 9: 9- X JC 9: X X 9{ it

9C 9: X

_ _ _ - _ _ 9: X 9: - _______xx_

Pig. 4 Calculated boundary of moving shadow

402
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403
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Pig. 6 Result of calculation of central cooling plant

404
standardized Method for Optimizing

Building Construction and Heating

and Ventilating Installations for Various Indoor Climate Criteria

by Arne Boysen and Sven Mandorff

The National Swedish Institute

for Building Research

Heating and ventilating Installations are used to create and mainta.in certain

room temperatures under variable internal and external heat loads. If these room

temperatures can be calculated for a given building, taking into account the thermal

properties of the building, the calculations may be used as a tool for an optimal

design of the building as a whole. It will be possible to choose between a building

with a high thermal storage and relatively simple heating and ventilating installations,

or a light building with more complex installations.

Such calculations are sometimes made for extreme climatic conditions. Those

conditions are, however, not representative of the accumulated heat stress during a long period of time, and calculation cost or time does not allow a greater number of calculations. A method will, however, be presented whereby a few calculations make

it possible to judge the resultant high room temperature over a period of one month.

The method is applied to classrooms.

In a building code this method can be used to regulate the heating and ventilating Installations. It is, however, then necessary to standardize most of the factors that go into the calculation and only vary those factors which have the most

direct influence upon the design of the heating and ventilating system. It is also

necessary to find a simple rating of the room temperatures, so that comparisons of different solutions will be feasible. This rating will be presented in addition to

a few calculations showing some, typical results. This paper is based upon part of a research project, which has been published as Report 50/69 from the National Swedish

Institute for Building Research [l^ ' . A more detailed report, also giving results

of calculations according to the method described in this paper, will be published

in the near future.

Key V/ords: Building construction, classroom, duration of heat stress,

heating and ventilation, indoor climate criteria, optimized design,

performance requirements, room temperature.

1 . Factors Affecting Room Temperature

Room temperature may be affected by many different factors. The correlations are perhaps shown most

clearly by a diagram where the factors can be arranged in four different categories; i.e. internal loads,

external loads, building and installations.

B

Internal loads are normally heat emission from persons, lighting, machines and equipment. The

internal loads for the type of premises to be discussed here - namely, ordinary classrooms - consist

mainly of heat from pupils and teachers and heat from lighting.

Figures in brackets indicates the literature references at the end of this paper.

405
External loads are solar heat, transmission losses or transmission gains, influence due to the dependence of the ventilation system on wind conditions and so on.

The influence of both external and internal loads is affected by the building through, for example,

its orientation, size of windows, thermal insulation etc. The heat storage properties of buildings are, however, at least as important; heat is stored, for example, in the structure of a building and in its

furniture, fittings and fixtures. The volume of air stores air pollutants but also to a certain extent

heat. The damping effect exerted by a building is thus in part fixed once and for all by the method of construction and the site, but can also vary, for instance, according to the use of adjustable sun shading devices and opening of windows.

However, the range of variation possible in a building is as a rule not sufficient to be able to compensate completely for the variations which occur in loads. The final compensation must therefore

come from installations, in this case heating and ventilation systems.

2. Calculations of Room Temperature

The traditional method of calculating the requisite thermal effect of these systems is to take account of external loads, the building itself and an assumed room temperature. The heat flow is assumed

to have attained an equilibrium, and it is further assumed that the values of the factors included in the calculations are not dependent upon time. This method involves great simplification of actual

conditions, simplifications which can possibly be accepted for calculating the requisite heating effect,

but which cannot be accepted for calculations of the necessary means of controlling temperature, or for

calculation of the required cooling effects.

In the case of these calculations the internal loads, the dynamic variation in these loads and the effect of the building must be taken into account. These calculations are complicated and time-consuming.

In the normal sequence of calculation it is, however, possible to make simplifications of varying extent. Different experts have suggested different simplifications, with the result that we have today a large

number of different calculation methods to choose between. The simpler methods are suited to manual

calculations, but the more detailed require computers. One problem is that different methods yield

different values and it is hardly possible to find such simple correlations between methods that results

from different methods can be converted and thus permit full-scale comparison. A method proposed by Dr

Gosta Brown j]2^ of the Royal Institute of Technology in Stockholm was used for the calculations in this

paper. This is probably one of the most com.prehensive methods and provides excellent scope for computing most of the data which can be required for estimating the temperature of a room.

The way in which people react to the temperature of a room is partly conditioned by personal

preferences and partly influenced by other factors, - for instance, clothing. Apart from this it is primarily three factors, air temperature, surface temperature and air velocities, which play a significant

part. Speeds of air currents are, however, low and hardly possible to calculate. An estimate of the temperature of a room - the operative temperature - is therefore based on the prevailing surface and air

temperatures.

In the case of the temperature levels dealt with here, heat exchange between a person and his

surroundings is generally assumed to occur as much by radiation as by convection. This means that the mean between air temperature and the average surface temperature of walls, floors and ceilings can be taken as the operative temperature of the room. In calculating the average surface temperature, the temperatures of the respective surfaces are weighed in relation to their solid angle, meaning that the average surface temperature varies from point to point within the same room.

Thus the original diagram can now be modified as follows;

where air temperature

different surface temperatures and

where K the operative temperature

406
3. Relevant Point and Time

The importance of taking into account the point in the room to which the temperature estimate refers

is Illustrated in figure 1 . The diagram shows conditions in the vicinity of windows whose surfaces

usually show the greatest temperature deviation from the others. The part of the body facing a window

does not experience the same operative temperature as the part facing away from it. The scale of temperatures gives the difference between these values.

The difference near to the window may be as much as 2°C, while at the wall of the room farthest

away from the window it is almost non-existent. A difference in operative temperature of approximately

1 °C is thus possible between these two points, which in view of the variations permitted in room

temperature is quite considerable.

Despite the fact that there may be considerable differences in temperature between different points

in a room it may be possible to disregard this complication when computing room temperature. In such a case the temperature of a point in the inner part of the room is calculated. Whether the value obtained

will have to be adjusted for other points need only be considered when the result is to be assessed.

Even with due consideration for the points of view which have been put forward, this is not sufficient to render calculations of room temperature meaningful. We must also be careful to decide for

which time calculations are relevant.

If calculations are to be used for dimensioning of air conditioning systems, they should, of course, refer to the occasions which make the greatest demands on the heat removal capacity of the system.

However, the problem is as a rule somewhat different in schools. There, it is hardly a question of complete air conditioning but of trying to achieve a reasonably comfortable room temperature by other

means. It is true that we may also wish to knov; the maximum value, i.e. the highest temperature likely

to occur, but discomfort is also a question of duration. It Is, for example, then possible to choose between calculating the frequency for days with different maximum temperatures or the true duration of high temperatures in hours.

The latter alternative is probably a better measure of the discomfort which occurs; i.e. in this

case, deterioration in the performance of the schoolchildren.

4. Results of Temperature Calculations on Sunny Days

We want to show some example of results of calculations of room temperature as a function of different parameters. The calculations were made for a sunny day in May at the same latitude as Stockholm

assuming a room facing due south and with an average outdoor temperature corresponding to the average

for the whole month. This date v;as chosen in view of the fact that the school year finishes at the beginning of June and that climatic conditions In May are therefore of particular importance.

The calculations are, of course, also dependent upon many other factors but since the aim is in

this case to present the method rather then the results, these factors have been omitted from this paper.

The influence of the structure is shown in figure 2. Case T represents a building with a high degree

of heat accumulation; external walls and floor slabs are of concrete, internal walls of double plasterboard panels enclosing a layer of mineral wool. Case M is a building in lightweight concrete and case L

a timber structure having mineral wool as thermal insulation. All the alternatives represent entirely

normal constructions.

Figure 3 shows the effect of the size of windows and sun shading devices in a lightweight concrete

building; window sizes were 4 7 and 10 glazed area (double glazing) and as sun shading devices

Venetian blinds between the panes or curtains on the inside were assumed. Compared to the solar heat

gain through unshaded double-glazed windows, these arrangements admit 40 % and 60 fo respectively.

The curves in this diagram are not entirely comparable if, for example, the minimum requirement is 300 lux at the desks with the poorest illumination. In some of the cases this value is not attained

unless the lights are switched on. In rooms with the smallest window size fitted with Venetian blinds

the lights must be left on all day which raises the corresponding curve so that it almost coincides with

that for the largest window with Venetian blinds. With curtains the lights need only be on for an hour

in the morning and the paradoxical result is that a less effective sun shading device gives a lower

room temperature. This result is, however, not generally valid; it is a consequence of the special

conditions which were assumed to prevail.

Figure 4 shows how different ventilation systems can affect room temperature. The building has a structure of lightweight concrete and windovjs with an area of T fitted with Venetian blinds (F^ = 0.4).

The five curves represent three different rates of air flow; 7-5 ""Vh per capita, 1 5 "'•Vh per capita

and 30111/h per capita, combined with supply air of different temperatures, the lowest temperature being

407
limited to + 20°C, or + IS^C, or outdoor temperature without a lower limit. The conditions thus illustrate

a number of interesting cases. The rate of air flow of 1^ rn'/h per capita is more or less the rate required according to current Swedish regulations. 7.5 ^/h per capita is approximately the rate that can

be expected in the case of many simple systems without mechanical ventilation or possibly with only an extract fan. 30 ni'/h per capita is the rate attained using ventilating equipment which is specially

designed for classrooms. In the latter case it is possible to supply air with a minimum temperature of + 15°C without risk of draughts; with the simpler systems air is supplied without preheating and thus without minimum temperature. In addition, central air conditioning plants are to be found; these supply

air to classrooms at room temperature, i.e. ca. 20°C, provided that the outdoor temperature is not

higher.

The last type of system mentioned has a poor cooling effect and induces high room temperatures. The simplest system {7-5'^ per capita) would seem to be better, but this is a consequence of the conditions

regarding outdoor temperature which were assumed for the calculations. As soon as the outdoor temperature

rises a degree or two the simplest systems will give the highest room temperatures.

5. Calculating for Longer Periods

The results published apply for school hours during just one day. These results, though limited,

have of course a certain interest but in the majority of cases the prime aim is to extend the analysis

to cover longer periods of time. This can also be done by determining for each day of the period the values of the calculation factors that tiave to be used.

Among the external factors it is primarily the temperature and the solar energy which vary. In the case of the internal factors the use of classrooms and the number of persons varies. As for the structural factors, it is conceivable that the use of the sun shading devices might vary or that windows

might be opened.

However, it is not sufficient to know how each factor varies individually; the simultaneous

variation must also be known. Since correlations do not always exist between the factors, it is impossible to try to find a logical pattern in the covariation of all these factors and it therefore

becomes necessary to make certain simplifications.

V/ith regard to sun shading devices, it is reasonable to assume that these are always used when the windows are sunlit during school hours, since this assumption is easy to handle mathematically and since

it is impossible from the practical point of view to maintain a reasonable room temperature on any other

grounds.

Opening of windows gives as a rule better ventilation and a lower room temperature. On the other

hand, v;ork in the classroom is disturbed by noise from outside and for this reason airing of rooms by

opening windows cannot be relied upon as being a generally acceptable method of controlling room

temperature. It is therefore reasonable in the case of the calculations we wish to make to assume that

windovjs are closed during lessons. During breaks, however, they are assumed to be opened to reduce the room temperature.

The use of classrooms is of course governed by a time-table and this may mean that on certain days

a room is used for a smaller number of school hours than on other days. The trend, however, is towards

an increasingly intensive use of rooms and minor variations or displacements do not affect the room temperature to any great extent. It is therefore safe to assume that in the case of these calculations

the daily schedule has not been changed. Similarly, it may be assumed that the number of persons present

in the room is the same from day to day.

Thus outdoor temperature and solar energy remain, for both of which extensive meteorological

statistics are available.

The mean temperatures per 24 h for four places over a period of thirty years are more or less normally distributed for each place vjlth a standard deviation of ca. 3.5°C for months which are of interest in this context as shown in figure 5. The same would appear to be generally applicable. We have at any rate found that the monthly means of JO places chosen at random vary considerably, but that the standard deviation lies between J.O and 4.0, Thus, using the monthly mean as a basis and having fixed

the standard deviation at J.S'C, it is possible to predict the average numbers of days that will have

higher temperatures. A still higher degree of precision can be obtained if the prediction is based upon

the temperature which represents the true standard deviation above the monthly mean temperature (Fig. 6).

As in the case of temperatures, differences exist between different times of the year and different

places for solar energy on clear days. Furthermore, differences in room orientation must be taken into

account. The difference for the same place and orientation are, however, not very great over a limited

period of time (Pig. 7).

If we examine the simultaneous variation of outdoor temperature and solar energy, we find that the

408
daily variation in the temperature Is greater on sunny days than the average, and that high daily mean

temperatures seldom coincide v;ith maximum radiation of solar energy. When temperatures are more than one

or two degrees higher than the monthly mean we can estimate the solar energy to amount to 8O-85 % of the maximum value.

[^5

Tiie position is thus in brief as follows:

1 . High classroom temperatures may be anticipated when a high outdoor temperature coincides

with solar radiation.

2. The high outdoor temperatures have a frequency corresponding to normal distribution.

3. At these high outdoor temperatures solar radiation on clear days is approximately 8O-85 io of the maximum radiation.

These correlations make it possible to obtain a good idea of the duration of the high room temperatures which can be expected by calculating the room temperature for the current outdoor

temperatures and then weighting the results according to frequency. Each outdoor temperature is given a weight corresponding to normal distribution with a standard deviation of 5.5.

As many as 8-10 outdoor temperatures may be current at any one time. The total calculation volume

is thus considerable. It can, however, be reduced by utilizing the fact that the correlation between

outdoor temperature and the room temperature on the whole is linear. It is then sufficient to make, for

example, three calculations and to interpolate and extrapolate the remaining values, figure 8.

6. An Aid to Construction

This method can now be used as an aid in the construction of school premises. It is possible to establish the temperatures that will occur at different orientations, the effects of the structure and

the building materials and the effect of different heating and ventilation installations etc. (fig. 9). It is thus possible to make a completely objective choice of the combination vjhich yields the best

results. If the costs of the different alternatives are also included we can judge which will be the optimum solution from the point of viev; of building costs.

The different results obtained from the calculations show quite clearly that different structural

factors can exert just as great an influence on room temperature as different heating and ventilating

installations. We realize that it is futile to try to guarantee a good room climate solely by drawing up standards for installations. This point has also been proved practical in a large number of schools built

in recent years. It is possible, though nowadays hardly economically motivated, to concentrate entirely

on structural measures for controlling room temperature. Installations are essential and with the calculation demonstrated it is possible to adapt them according to the building in question. The method

thus provides us v;ith a means of making demands on the room temperature and from these demands derive

the conditions for the installations. We have thus the chance of establishing highly functional

standardized rules for performance requirements regarding heating and ventilation systems. Such a rule

has been suggested, stating that "The classroom temperature, calculated according to this method, may

exceed 25°C during, as a maximum, 20 ^ of lesson time in months of May".

7. Functional Standard for Heating, Ventilating and Air Conditioning Plants

Such standardization can hardly be considered without first including model values for all the factors wherever possible. Some of these values have been already touched upon, but not all of them. It goes without saying that the model values must be chosen with great care; they must be realistic for modern schools and modern work routines in schools, while at the same time deviations from the model

values may not produce excessively large deviations in the final results. Nevertheless, however much

care is taken deviations cannot be entirely avoided.

Here we should like to draw attention to one such deviation. As v;e said earlier, the statement made

regarding the curve showing normal distribution for outdoor temperature is based on statistics from the years 1931-1960. This applies then for a long period of time but not necessarily for individual years. This means that in certain years the high outdoor temperatures may have longer duration, causing the high room temperatures also to last longer than intended. Conversely, it is possible to obtain shorter

values. In other words, there is very little chance of checking in an existing building, if the standard

is fulfilled. The standard will be purely for purposes of calculation.

It may be acceptable from the point of view of the community that a standard of this nature in the long run should give reasonable temperature conditions. For the individual pupil, however, this is un- satisfactory as he or she may be spending only one year in the classroom in question.

This weakness, if indeed it is to be regarded as such, would appear to be inevitable. It is, however,

possible to prevent the most unsuitable conditions through choice of temperature limit or duration value

in the standard. 409
Thus, In this case it is possible to use computer techniques for a standard concerning heating and ventilating installations in classrooms which is functionally constructed in that it adopts the permissible room temperature as a basis and compels us to take into account the thermal properties of the building and the purpose for which the premises are to be used. This standard is probably the first

of its kind and should represent a great step forward in comparison with other regulations applied to date which have been proved largely incapable of preventing unsuitable classroom temperatures.

8. Literature references

[l ] Antoni, Nils, Projekteringsunderlag for skol- byggnader for grundskolan, Statens Institut

for Byggnadsforskning, rapport 5O/69.

|^2j Brovm, G., A method of calculating heating and

cooling loads v;ith the aid of a digital

computer. WS 54 (1963) No. 11.

[5J Adamsson, B. , I968, Val av klimatdata vid be- rakning av hogsta rumslufttemperatur och even- tuellt kylbehov, Tekniska Hbgskolan, Lund. Institutionen for byggnadskonstruktionslara.

Arbetsrapport 1968:5.

DIFFERENCE IN OPERATIVE TEMPERATURE

•c3

2

1

0 0123^50123450123/.56

Figure 1 DISTANCE FROM WINDOW m

Difference in operative temperature (between two opposite directions) as a function of the distance from

windows and glazed area. The values have been calculated on the assumption that the difference between

the temperature of the glass and the mean of the room air and the temperature of the interior surfaces

is 5. 10 and 15°C respectively. Cases a, b and c show the conditions for different sizes of window (A = = 4 m^, 7^1^ and 10m^).The point of reference lies on the centre line in relation to the window and on a level with the lower edge of the window.

LESSON TIME

20 21 22 23 Ik 25 26 'C P^g^^^ g ROOM TEMPERATURE

Duration of room temperature during lessons in classrooms in neavy IT), medium-heavy (M) and light (L) structures; the prerequisites are among others a sunny day in May, due south orientation of the room and

the same latitude as Stockholm, Daily mean temperature + 1 1 °C.

410
LESSON TIME %

20 21 22 23 2U 25 "C ROOM TEMPERATURE

Figure 3

Duration of room temperature during lessons In classrooms with different sizes of v/lndow (A) and sun shading arrangements (F 1); the prerequisites are among others a sunny day in May, due south orientation

of the building and the same latitude as Stockholm. Daily mean temperature + 1

1 °C,

LESSON TIME %

20 21 22 23 2U 25 26 'C ROOM TEMPERATURE

Figure 4

Duration of room temperature during lessons in classrooms with different rates of air flow and supply

temperature; the prerequisites are among others a sunny day in May, due south orientation of the room

and the same latitude as Stockholm. Daily mean temperature + 1

1 °C.

411
DISTRIBUTION OF 2^h PERIODS %. .

Figur e 5 Frequency of different daily mean temperatures

during the period 1931-1960. The values refer

to four towns and the months of May (5) and

June (6).

0 2 ^ 6 8 10 12 U 16 18 20 22 2L 'Z MEAN TEMPERATURE PER lU h

Figure 6 12° 16° 20°

Isotherm map for May. The isotherms refer to the mean monthly value of the outdoor temperature + the standard deviation in the daily mean temperature.

412
kcal/24h

Oj , . \ , . ^

±180 ±120 ±60 0 ±60 ±120 ±180

ORIENTATION

Figure 7

Heat gain from direct and Indirect solar radiation through an unshaded double-glazed window. Values are given for two towns, one In southern- Sweden and one In northern Sweden. The diagram is valid for the 15th

day of each month, ground reflection r = 0.25.

TIME %

20 21 22 23 2i, 25 26 27 28 29 30 ROOM TEMPERATURE 'C top % OF TOTAL LESSON TIME

Ol . , ? , . . ^

20 21 22 23 2i 25 26 27 28 29 30 C top

Figure 8

Duration of room temperature during lessons at different values of the daily mean of the outdoor

temperature. The lower part of the figure is a sum of the curves in the upper part, account having been

taken of the relative frequency q ^ of different outdoor temperatures. Prerequisites are among others

sunny days in May, due south orientation of the room and the same latitude as Stockholm.

413
TOTAL LESSON TIME

^0 r-^^ ,

30

23 2^ 25 26 27 ROOM TEMPERATURE 'C

Figure 9

Duration of room temperature in classrooms with different combinations of structure and ventilation

systems. More or less the same results are obtained in a lightweight building with an air flow of ^0 n'/h per capita as in a medium-heavy building with an air flow of 1 5 "^'/h per capita. Prerequisites are among

others sunny days in May, due south orientation of the room and the same latitude as Stockholm.

414
Designing Installations by Computer in Sweden

1 Lasse Sundberg

Wahlin'g's Installation Development Company

Stockholm

Sweden

Designing buildings and their installations has become more complicated.

The building-time is shorter now than earlier because of improved buildingmethods. Increased demands for exterior and interior environment and more sophisticated installation equipments will increase the demands upon the designer. To make it possible for. him to follow this development he has to use effective means of assistance. The computer can offer the designer this

help, but first after a wide development work.

In 1968 the National Swedish Council for Building Eesearch commissioned

us to investigate the possibility for rational designing of installations

by computer. The purpose of the investigation was to make an inventory of

existing computer programs, to analyse and systematically compare them and

give recommendations for the continuance of the work of development. The

investigation showed that there are computer programs only for some routines

of calculation. However they are made in a way which makes it difficult to use them practically for designing. The programs are written in different

languages. There are also no standards for forms and documentations of

programs. Due to this investigation the coming work will be concentrated

on working out a basis for rational applications of data processing. The

work will be done with grants from the National Swedish Council for Building

Eesearch according to the following principles:

- A data coordination group for the building trade, including the

installation trade, has been appionted in order to investigate which program

language is giving the best qualifications for a flexible use of new programs.

Rules for description of programs, disposition of forms, presentation of

results and so on will be drawn up.

- On the basis of the recommendations of the coordination group the

calculation routines for designing installations will be programmed. This

work has already begun by collecting theoretical formulas etc. We shall also

investigate the possibilities how to use the computer for choosing installation components such as fans, pumps, boilers, valves and so on.

Key Words: Computer program, designing, electrical installations,

environmental engineering, installation in buildings, mechanical

installations, sanitary installations, Sweden.

1. Introduction

It is becoming more and more complicated to design buildings and the installations that go with them. Construction takes place more rapidly because of improved building methods. Future

buildings will probably require even more installations, and more advanced versions of them,

because of the increased demands that are being made on the indoor and outdoor environment.

Equipment installed today must be capable of future modernisation or replacement, within the use- ful life of buildings as a whole, because of the rapid development that is taking place in the

field of installation systems and products.

1 Mechanical Engineer

415
The above factors make great demands on the planning and construction of installations, and

will continue to do so. It is now more than ever necessary to plan well in advance, to make preliminary investigations and to carry out trial calculations to compare alternative systems with each

other in terras of installation and running costs. Naturally comparison should also be made with,

other possible technical solutions, based on different layouts or methods of construction. The

technical and economic calculations involved in planning a comprehensive and complex projekt can- not usually be carried out with the help of approximate formulae, diagrams and slide-rules alone. For these purposes computer techniques should be exploited to the full.

In 1968 the National Swedish Council for Building Research commissioned us to investigate

the possibility for rational designing of installations by computer. The investigation was car- ried out with the above background. The aim was to make an inventory of the computer-based

methods that are currently applicable to the planning of installations, and to suggest ways in which they could be developed. The results may be found in a report (I) that has been published, the contents of which are summarized in this paper. The investigation showed that there are computer

programs only for some routines of calculation. However they are made in a way which makes it

difficult to use them practically for designing. The programs are written in different languages.

There are also no standards for forms and documentations of programs. Due to this investigation

the coming work will be concentrated on working out a basis for rational applications of data

processing.

2. The Available Choices of Machine

The choice of machine depends firstly upon which program or programs are available for the

purpose. Programs owned by other users are often linked to some special type of machine, or even

to a certain machine. It is usually possible to obtain the use of programs stored at other data

centres.

Programs whose development has been supported by the Building Research Council are at present available without cost. The user must pay for the machine time that he uses in running the program. Certain non-recurring costs can be involved in adapting the program for use at the

chosen data centre. The following choice of machines is available:

1. Rent of machine time at data centre.

2. Rental of a small machine.

3. Terminal of teleprinter type.

The various alternatives are discussed in more detail in the report. It is thought, however,

that alternative 3 will prove to be the most useful, in the majority of cases.

3. Rationalisation using Computer Techniques

In the planning of installations calculations must be made at the various stages of construction. Shortage of time often leads to the acceptance of values based only on personal experience

as the basic criteria for various judgements that have to be made. Approximate formulae and rules

of thumb are often allowed to serve in place of exact calculation.

Such short cuts are often satisfactory, but they seldom allow alternative interpretations.

What influence would different solar screens or differently constructed windov;s have? How would

the air heaters and their control systems behave under different loads? What different lighting

effects would be achieved by combining three different types of lighting element with four diffe- rent floor coverings in a landscape office? How vjould the choice of ventilation system affect the heat dissipation from the light fittings? Naturally these questions can be ansv/ered by manual

calculation, but the necessary time is not usually provided in the schedule. Computer techniques

make it possible to weigh the different alternatives against each other, often for considerably

less than it would cost to have the calculations for a single alternative made by an engineer.

It is true that calculations can be made quite rapidly with the help of tables and nomograms but

these are always based upon certain constants that cannot be changed without drav;ing up a completely new table or nomogram. Changing conditions can render such constants inapplicable, but the

necessary changes are seldom made. The constants in a computer program can easily be changed,

which makes data processing by this method more flexible. Experience has shown that builders and

architects quickly realise that automatic data makes a more subtle analysis possible, even if they

have originally been sceptical.

Few programs that are both suitable for the present purpose and intended for use via a data

terminal are as yet available. Most of the available programs are very large and ambitious. Some

of them are also closely linked to a certain type of machine. A number of computer manufacturers

are interested in producing a "packaged program" for use via data terminals. For this to be realised, private users will have to make their programs available and further programs will have to be specially written for use via data terminals.

416
Existing programs

Several programs are currently available for programs written for the purpose of research, whi

inventory of programs in Scandinavia, in order to rams and their possible areas of use. They are de engineers a summary they can easily use.

The programs described in the report are

is given in parantheses.

the planning of installations. There are also

ch could be adapted for practical use merely by

give a systematic overvievj of all these progscribed in a simple v;ay in order to give design

listed below. The author or ovmer of each program

a. Room Temperatures; Cooling and Heating Loads

Calculation of cooling and heating loads for a building and design parameters for comfort

ventilation systems (AB Svenska Flaktf abriken) . - The program calculates the loads for one module

and one hour based on a sunny day and a cloudy day for each month of a metheorological normalyear and also for an extreme day in summer and in winter. The calculations are not bound to any special comfort system. The influence of moving shadows are also calculated.

Calculation of room temperatures (AB Svenska Flaktf abriken) , - This is a similar program to the first, but no cooling of the air and also no supply air flow can be simulated.

These two programs are presented in a separate paper by W Boeke.

Calculation of room temperatures and of cooling and heating loads (G Brown, KTH). - This

program calculates for one or more rooms during em arbitrary period of time, one quantity of

each: cooling and heating load, room temperature, sufficient air flow, temperature of supply air. Max and min values can be given to one or two of the quantities. This is a research program and

intended to be very flexible. It is presented in a separate paper by G Brown.

Calculation of room temperatures (C Allander, E Abel, KTH). - The program calculates the

room-temperature in a multi-room building. It is limited to rooms with a facade wall and mechanical ventilation and is designed for the summer period in the southern and middle parts of Sweden, especially Stockholm. The program is based on a method, described in the ASHRAE Guide and Data Book 1963, p. ^^9-30^.

Calculation of room temperatures and cooling and heating loads (Richard Nilssons Konstruktionsbyra AB) . - The program calculates the room-temperature, airflow, air inlet temperature,

cooling and heating load for one or more rooms in a building. The calculation is made for each

hour in ajiy chosen month. The input data can be chosen freely. Either can the cooling load be

calculated from a certain airflow, or the airflow can be calculated from the cooling load. The

calculation can also be done with regard to the influence of moving shadows. The outdoor temperature is approximated to a sinus function.

Calculation of cooling and heating loads and of the energy requirements of a building

(Ekono, Finland). - A series of programs have been developed by the Finnish company Ekono. One program calculates the heating load with regards to the wind pressure and unwanted ventilation.

This program is described in JIHVE, March 1968, p. 357-368. Two programs calculate the cooling

and heating load respectively the energy requirement. They are described in the ASHRAE Journal,

Sept. 1967, p. 63-68.

b. Temperatures in Structures

Calculation of temperatures in a structure of parallel layers (B Ludvigson Ingen jor sbyra AB)

The program is calculating the variation in temperature in a structure, consisting of parallel

layers. The temperature on each side of the structure must be known, either constant or as a function of time. Maximum 15 parallel layers can be used. For each Iciyer the temperature in the center is calculated. The program is specially written for testing different kinds of insulation.

Calculation of temperatures in a cross section of an arbitrary structure (Industridata AB).

This program is calculating the temperature in a structure and the layers need not be parallel.

The heat flow can be constant or suddenly changing. A heat source within the calculated zone is

allowed. The border of the zone and the heat transfer coefficient may be a linear function of

time. It is useful for complicated constructions.

417
c. Heating Systems

Calculation of the design parameters for one and two-pipe heating systems and their distribution netv;orks (AB Databerakning) , - The program calculates the type and size of the radiators,

the pipe dimension, the friction loss, the valve dimension and the size of the distribution pump.

A quantity list including all prices can also be calculated. Any make of radiators can be used.

The program is useful when deciding the hot water temperature, the pipe dimension regarding

energy consumption etc in order to find the lowest annual cost.

Calculation of the design parameters for single-pipe heating systems (Fellingsbro Verkstader).

The program calculates the size of radiators, valves, pump and a quantity list. The heating load

can also be calculated. The program is specially designed for radiators made by the company

Fellingsbro, Sweden.

d. Water-pipe Networks

Calculation of the pressure and flow conditions in a network of water pipes (Industridata AB)

The program is simulating a distribution network, e.g. a part of a town. The pressure and the

flow for every connection in the netv/ork is calculated for a certain moment. Alternative con- sumptions of water can be simulated, as well as alternative data for pumps and reservoirs.

e. Waste-pipe Networks

Calculation of flow conditions in a waste-pipe network (Industridata AB). - The program is

designed for a rather large network. The flow is calculated as a function of time, depending on the flow on every terminal point.

f. Stress in Pipe Systems

Stress calculations for pipe systems (Industridata AB). - The program calculates deformations,

loads and stress forces in a pipe system due to temperature alterations, inside overpressure, dead

weight, concentrated forces and moment, forces from flow of fluids, and forced deformations. The

network system is supposed to be anchored in one or more points, with or without springs or sliding support.

Stress calculations for pipe systems (IBM). - The program calculates the pipe system based

on an electrical analogical method and gives forces, moments, distorsion and stresses in diffe- rent joints. No respect is taken to dead weight or the forces from flow of fluids.

g. Ventilation Systems

Calculation of the design parajneters of a ventilation system for constant static pressure

(Wahlings Konstruktionsbyra AB) . - The program sizes ventilation duct systems based on the con- stant static pressure method. Duct types, dimensions etc are given in tables. The program calculates loss of pressure from the fan to each section and static regain. Friction loss can also be

calculated only regarding to highest air speed.

Calculation of the design parameters for ventilation systems (AB Svenska Flaktf abriken)

The program sizes ventilation duct systems regarding to less sheet area and most possible even pressure over air inlet or air outlet. The fan pressure can either be calculated or given as input. Necessary dampers are calculated. A quantity list can also be printed.

h. Heat Loss from Pipes

Calculation of heat loss from pipes, flooring or ground (Hugo Theorells Ingenibrsbyra AB).

The program calculates the heat emitted from hot water pipe loops embedded in concrete, sand etc,

for floors and pavements. The prograin can also calculate the necessary heat for melting the snow

on pavements.

i. Viscous Resistance

Calculation of viscous resistance in pipes (Hugo Theorells Ingeniorsbyra AB) . - The program

calculates the flow, the speed, the dynamic pressure and the friction loss pr lenght unit for any desired diameter and fluid in a pipe. The result is given in tables.

418
k. Sun, Shadow, Lighting

Irradiation from sun and sky in Sv;eden on clear days (G Brown, E Isfalt, KTH) . - The program

is calculating the irradiation together with the position of the sun in the sky for each hour

from sunrise to sunset on a clear day. The radiation transmitted through horizontal and vertical

double-glazed windows and the irradiation onto horizontal and vertical surfaces are also calculated.

Calculation on shadows moving across building facades (G Brown, E Isfalt, KTH). - The program calculates for any desired time on a sunny day the shadow on a facade, caused by narrow buildings or other objects. The facade is divided into an arbitrary number of squares, thus giving a picture in scale of the facade. The shadowed squares and the contour of the building are printed.

Calculation of the light distribution in a room (G Brown, E Isfalt, KTH). - The program calculates how the irradiation in the state of diffused light is distributed in a room. The light

source should be a part of a wall, e.g. windows and built-in fluorescent tubes. The irradiation

is given for a small area, the position choosen freely in the room.

1. Electrical Networks

Calculation of radial high and low voltage networks (Industridata AB) . - The program can be

used for continous control of existing radial high or low voltage networks or combined networks,

concerning potential drop, loads, fuses, response to sudden loads, short-circuit currents and currents to earth. It is also useful as a simulation program when planning a new network.

m. Lift Usage Patterns

Simulation of lift usage patterns (Asea-Graham) . - This program can simulate lift (elevator)

usage in office buildings, hospitals, hotel, department, stores and other similar buildings. The

simulation is made by a simulator, special built for this purpose. Due to the number of floors,

persons etc the waiting time after a call for the lift is calculated.

5. Suggestions for Future Development Work

5.1 Supplementary Research

Programs v/ritten for research purposes could often be of great practical use for engineering

work. However, most of them require certain additions before they can be taken into practical

use, e.g. data forms, program descriptions and adaptation to different machines. This kind of

program development can most easily be done by the original author in consultation with design

engineers familiar v^fith the proposed area of use.

5.2 Continued Work

A Review of the various routines used when planning installation projects was also included

in the report. In view of this, a proposal for new programmes was made. Example of programmes:

Heat exchanger system. Chimneys (dust distribution), Two-way valve system. Heat loss in pipe or duct network. Distribution of air within the duct system. Estimation of costs and quality. Optimum planning of a plant, Calculation of control circuits.

6. Selection of Products by Computer

6.1 Data Terminals

The day will probably come when each installation consultant will rent a data terminal, that

is connected to a data centre via the telephone network. In this way, with only a small capital

outlay, using the capacity of a large computer, one will be able to carry out very complicated

calculations'.

Details of the veirious products are needed continually during designing in order to facilitate selection of products. This information is generally obtained from catalogues and brochures.

It is often very difficult to find just the right product amongst such extensive material. Some

companies arrange their brochures in files; there is, however, a risk that some brochures are either missing or have become obsolete. There are so many pages for some code indexes, that it is

impossible to check the complete details for each of the products.

419
6.2 Selection Methods

In order to make selection quicker and more accurate, data terminals can be used. This makes

it possible to find the right product via an automatic selection system.

In order to utilize such a system, which should be based on an interchange of information

between computer and designer, details of every product given by the manufacturer must be available. These facts are keys to the selection system.

One condition for developing a selection system is that the user must be able to find his

product by freely specifying his requirements. He commences the dialogue with the computer by

giving a general classification, for example, "pump" or "valve". There must only be a few general

classifications to cover the whole range of existing products and any others that may be included

later.

The computer answers by supplying a list of the various sub-group, for example, "pump for

water", "pump for oil" or "manual two-way valves", "automatic controlling valve". The user then

chooses a sub-group. Thes,e sub-groups should be small but still it should not be necessary to go through more than one of them in order to find the required product.

Once the sub-group has been decided upon the process of selection really begins. The computer

then lists the various characteristics of the products within the group. With the help of these

the user can select the features he wishes to specify. It can be details concerning size, material,

media, geometrical design, sound, standard, brand etc.

It is the computer that does the selecting all the time, by giving information about the par- ticular characteristics of the vairious products.

Such a system of selection has to be very flexible. It must be possible to select a product

by carrying out a detailed dialogue as just explained, as well as being able to give merely the

sub-group and requisite features, in order to shorten the dialogue.

Any changes in the existing products or details of new products must be easily included so that a manufacturer can immediately inform all the customers using the data terminals.

6.3 Handling of Information

The selection system leads up to an identification of the products fulfilling certain requirements. The selection system does not include complete information about each product. However,

data techniques can even be used to help in this respect.

Three alternative methods for storing information entailing varying degrees of automation

will now be described.

a. Alternative 1

The information is stored as at present, in systematically arranged brochures and catalogues.

The selection system refers you to certain pages in the files by giving the code and name of the product and the manufacturer. The appropriate pages are then picked out manually.

In this case the selection system facilitates the use of the files of brochures, besides

which you are informed of products not represented in the files. In this way the files on relevant

products are kept up to date.

It is only necessary in this case, to have a data terminal for calculation routines.

b. Alternative 2

The terminal users need no brochure collections of their own. Such files are only kept in a pool, but in turn may be linked to a computer. All brochures are micro-filmed, thus enabling the

whole range of products and their various details to be stored conveniently in a number of microfilm cartridges.

Every terminal user has a complete set of cartridges. He also has a so-called "reader-printer", i.e. an apparatus which enables one to get an instant reference view of any desired frame

on a large screen. Prints of the relevant pictures can also be produced within a few seconds.

The contents of all cartridges are reviewed and up-dated each year.

420
Any changes that occur during the year can be immediately put into a supplementary cartridge,

which is distributed regularly to all customers.

The selection system is adapted to provide not only the name and manufacturer of the product

but also to give information regarding the cartridge number of the frame in the cartridge. This

alternative entails a certain amount of capital investment and some operating costs, but at the same time it cuts out the expense of producing and distributing brochures to all the terminal

users.

c. Alternative 3

The terminal user has no files at all. All information regarding products is stored centrally,

on video tape, microfilm or something similar, and linked to a computer.

The system necessitates selection by dialogue with the computer via the terminal. When selection has been completed, relevant frames are projected directly onto a screen after being trans- ferred from the data centre via the telecommunication network. Prints can also be obtained when

required.

This system completely eliminates the risk of getting obsolete information, as any changes

can be made quickly and are immediately available to all users.

Capital investment and operating costs will, however, be considerable. Despite this, there

are a few such systems in the USA at present and there is a wide general interest in this type of

system. As a result manufacturers of data and telecommunication systems are carrying out intensive

research.

7. References

(l) Allan Westrbm & Teddy Rosenthal. Computer techniques for the planning of installations.

National Swedish Building Research, Report R1:-1970, 100 p.

421

A Cost Analysis Service Helps

Optimize Building Costs and

Environmental Benefits

John T. Malarky''"

PPG INDUSTRIES, INC.

Glass Division

One Gateway Center

Pittsburgh, Pa. 15222

During the past decade architectural glass performance has

been improved to help achieve a comfortable indoor environment.

Lower shading coefficients reduce solar heat gain 75%. Lower U- values reduce heat loss 6 5%. This performance results in cooler

indoor glass surfaces in summer, warmer indoor glass surfaces in

winter enabling easier system control and a more comfortable

thermal and visual environment indoors.

A Cost Analysis Service has been developed to provide a direct cost comparison of the effect of improved fenestration on overall building costs. This service, called Building Cost

Analysis, utilizes a computer program, cost estimates and rough

project design criteria early in the design stage to obtain a first approximation of the effect of glass performance on construction and operating costs. This rough economic analysis obtained

before glazing and mechanical system design is firm, may indicate

that a more detailed professional study of glass selection best

suited to the needs of the project is warranted.

The program computes initial heating and cooling equipment

costs, annual heating and cooling operating costs and long term

owning and operating costs for each glass under consideration.

Two case histories, a two-story office building in Madison,

Wisconsin, and a 57-story office building in Columbus, Ohio,

illustrate the potential savings high performance architectural

glass products may have for the owner, greater design freedom for

the architect and for the engineer, summer and winter insulating

performance enabling more accurate control of the indoor system

creating a year-round comfortable environment.

Key words: Shading coefficients, U-values, approximation,

heating and cooling equipment costs, annual operating

costs, present worth, owning and operating costs,

potential savings, comfort.

Mechanical Engineer

423
A Cost

Building

Analysis Service Helps Optimize

Costs and Environmental Benefits

Building owners and managers who rent space to make money recognize that tenants

pay premium prices for offices with large window areas. They know also that sophisticated control of temperature, air movement, humidity and radiant temperature within the

comfort range is a necessity in the high rent district. Glare, condensation and drafts

long have been associated with simple clear glass windows.

To meet these comfort needs new types of windows have developed and the computer

has been put to work to provide an objective means for comparing glass performance and

economics on specific jobs.

During the past decade architectural glass performance has been improved to help

achieve a comfortable indoor environment. Lower shading coefficients reduce summer solar heat gain 75%. Lower U-values reduce winter heat loss 65%. This performance

results in cooler indoor glass surfaces in summer, warmer indoor glass surfaces in

winter enabling easier system control and a more comfortable thermal and visual

environment indoors.

A Cost Analysis Service has been developed to provide a direct cost comparison of

the effect of improved fenestration on overall building costs. This service utilizes

cost estimates and rough project design criteria early in the design stage to obtain a first approximation of the effect of glass performance on construction and operating

costs. This rough economic analysis obtained before glazing and mechanical systems

design is firm, may indicate that a more detailed professional study of glass selection

best suited to the needs of the project is warranted. Also, because it relies on a sophisticated computer program for processing and analyzing the data, it is quick and

easy to use. The Building Cost Analysis service utilizes 38 data input items. The program

selects a summer and winter design day based on typical weather data for 30 geographical areas throughout the United States. Then, considering building orientation,

materials, construction, energy systems and heating and cooling methods, determines the

peak and annual heating and cooling loads. With this information, mechanical heating

and cooling equipment size is determined and annual heating and cooling operating costs

are estimated.

Also, the program uses estimated initial costs of the building, land, interest and

taxes to compute the present worth and long term cost of owning and operating the

building

The Building Cost Analysis program is written in Fortran IV-G language and is run

on an IBM-360-40. The memory area required for the program is 140 K. Each run takes

approximately two minutes.

The program takes the input data (Chart I) , accesses the design program from

storage discs, calculates the latent (Design 1) and sensible (Design 2) heat loads thus

determining the peak heating and cooling loads. Next, it accesses the energy program

from storage discs and calculates the annual energy required for heating and cooling

loads. Then, for the type of energy used - all electric, electric air conditioning - gas heating, all gas, the program estimates the annual heating and cooling operating

costs. Finally, the program computes the building present worth and the annual cost of

owning and operating the building.

The Building Cost Analysis program is designed to accept multiple runs for any

geographical area or building variable.

Since the program has been designed to investigate the effect of various

fenestration materials on buildings, glass performance is the variable we usually

compare. Other building parameters for a specific product usually are fixed from run

to run. The same program could be used to make other comparative analyses.

By introducing performance properties of alternate glasses, such as single clear

glass vs. single tinted glass or clear insulating glass vs. reflective insulating

glass, the program provides a direct comparison of the cost effect of these glasses on building cost. The most significant difference usually occurs in the initial cost of

the mechanical equipment and the initial cost of the glass. Operating costs can be

significant too.

424
Two case histories illustrate the effect architectural glass in buildings may have

on initial and long term building costs.

CASE HISTORY #1

The first case history is a two-story building in Madison, Wisconsin. This

building consists of approximately 96,000 sq . ft. of rentable floor area. The proposed

building will be occupied by 450 people during the hours of 8:00 a.m. to 5:00 p.m.

Electric lighting will utilize 6 watts per sq . ft. Heating and cooling energy will be

all-gas. The building facade will be all-glass construction - vision and spandrel area totaling approximately 15,000 total sq. ft.

The owner, architect and engineer selected three glass alternatives which were compatible with the aesthetic design. The glass alternatives selected were: 1/4-inch

S0LARBR0N2E Plate, 1-inch LHR SOLARBRONZE TWINDOW (a fired-on reflective coating on

the air space surface of the outdoor glass in an insulating unit) and 1-inch

SOLARBAN (2) TWINDOW (an insulating glass unit with a metallic reflective solar control

coating on the air space side of the outdoor light)

Table I illustrates the performance properties of the architectural glass alternatives and the installed cost of the glass per sq . ft. (The installed cost includes

glass and installation charges)

Table II illustrates the Building Cost Analysis results. These represent building

heating and cooling peak loads for each glass alternative. Note the improved

performance (insulating value) of the more sophisticated glasses results directly in

reduced heat gains and heat losses.

Table III is a summary of each glass alternative which includes the initial cost

of the glass, the heating and cooling system costs and the cost difference between one

glass and another. Initial cost comparisons reveal a potential savings of $15,000 if

the more sophisticated reflective insulating glass - the SOLARBAN were used instead of

the 1/4-inch SOLARBRONZE Plate. Thus, the owner and architect may elect to use the more

sophisticated glass product at no increased initial construction cost.

Table IV summarizes the Building Cost Analysis program output on the building and

shows that though the potential savings (initial and operating costs) are significant,

the present worth and owning and operating costs remain relatively unchanged. This is

typical when savings due to sophisticated architectural glass performance offset

increased glass costs.

The principals used this information as incentive to investigate architectural

glass alternatives more thoroughly. They elected to use the SOLARBAN product realizing

that in addition to the potential savings, the glass provided added comfort due to warmer indoor glass surfaces in winter and cooler indoor glass surfaces in summer. CASE HISTORY #2

The second case history is a proposed 57-story office building in Columbus, Ohio.

This building will consist of approximately 645,000 sq. ft. of rentable floor area; 3,000 people occupy the building from 8:00 a.m. to 6:00 p.m., electric air conditioning

and gas heat are the energy requirements. The building facade is approximately 56%

glass - 210,000 sq. ft.

The owner, architect and engineer selected three glass alternatives which they

felt were compatible with the building aesthetic design.

The glass alternatives selected were: 1/4-inch SOLARBRONZE Plate, 1-inch

SOLARBRONZE TWINDOW (insulating glass with the outdoor light tinted bronze) , 1-inch

SOLARBAN (2-3) TWINDOW (insulating glass with the metallic oxide solar control coating

on the air space surface of both indoor and outdoor lights)

2 TWINDOW insulating glass construction consists of two lights of 1/4-inch clear or tinted glass separated by a 1/2-inch air space and retained in a stainless steel

compression channel about the perimeter of the unit. Solar control reflective

coatings normally appear on the air space side of the indoor or outdoor lights.

(Figure 1)

425
Table V illustrates the performance properties of the architectural glass

alternatives and the estimated installed cost per square foot.

Table VI illustrates the proposed building heating and cooling peak loads for each

glass alternative. The improved performance properties of the sophisticated architectural glasses result in reduced heating and cooling equipment requirements.

Table VII is a siammary of each glass alternative including the initial cost or the

glass plus the cost of the heating and cooling equipment. The initial cost comparison

reveals a potential savings of approximately $570,000 if the SOLARBAN TWINDOW were

selected over the 1/4-inch SOLARBRONZE Plate.

Table vni summarizes the Building Cost Analysis program output for the proposed

building and shows, in addition to the potential initial savings, an approximate $9,500

savings per year in heating and cooling equipment operating costs. Also, present worth

and owning and operating costs are shown.

The potential savings of over half a million dollars plus $14,000 per year in

heating and cooling operating costs encouraged the architect and engineer to enthusiastically conduct professional studies on the glass alternatives to demonstrate to the

principals' satisfaction that the potential savings through discriminate selection of

architectural glasses is realistic.

Often the Building Cost Analysis program shows that a potential justification for use of more expensive sophisticated glass products leading to increased indoor thermal

and visual comfort is achievable at little or no initial cost to the owner. "Potential savings" is used throughout because the results shown represent a savings of heating and cooling equipment based on estimated "installed heating and cooling

equipment" costs. Depending on the timing of a Building Cost Analysis, however, the

"achievable savings" may be somewhat less. Potential savings can be realized if the

architect and engineer conduct architectural glass studies early in the design process.

This service provides rough cost estimates early in the design stage to encourage

architects and engineers to conduct a professional design study of the economic

feasibility of sophisticated, aesthetically desirable architectural glass products.

The case histories illustrate the potential savings high performance architectural

glass products may provide the owner, the greater design freedom for the architect, and

for the engineer, summer and winter insulating performance enabling more accurate

control of the indoor systems creating a year-round comfortable environment.

The Building Cost Analysis program helps professionals relate an increased client awareness of potential savings with sophisticated high performance glasses which may

lead to improved occupant comfort and satisfaction of the client's needs.

426
CHART 1 BUILDING COST ANALYSIS

BLOCK DIAGRAM

INPUT FROM

ARCHITECT

AND/OR ENGINEER

DESIGN

1 DESIGN

2

ENERGY

DETERMINES SIZE OF HEATING AND COOLING

EQUIPMENT

DETERMINES ANNUAL

ENERGY REQUIREMENT

FOR HEATING AND COOLING

EQUIPMENT

FUEL

A

COST OF ANNUAL NNERGY

REQUIREMENT

PRESENT WORTH, ANNUAL COST

OWNING AND OPERATING A BUILDING

OUTPUT TO

ARCHITECT, OWNER OR

ENGINEER

427
FIGURE 1 - TYPICAL TWINDOW CONSTRUCTION

428
MADISON BUILDING

TABLE I • GLASS ALTERNATIVES

DESCRIPTION*

U - VALUE

SHADING

COEFFICIENT

INSTALLED

COST

S PER SQ. FT.

A. 1/4-INCH SOLARBRONZE PLATE 0.8 0.54 $ 1.25

B. 1-INCH LHR SOLARBRONZE TWINDOW 0.5 0.32 4.10

C. 1-INCH SOLARBAN (2) TWINDOW 0.30 0.16 3.60

*ALL WITH INDOOR SHADING

429
MADISON BUILDING

TABLE II RESULTS

DESCRIPTION*

COOLING HEATING

TONS $ X 1000 MIL-BTU $ X 1000

A. 1/4-INCH SOLARBRONZE PLATE 657 $ 657 n.6 $ 198

B. 1-IMCH LHR SOLARBRONZE TWINDOW 641 641 11.3 193

C. MNCH SOLARBAN (2) TWINDOW 631 631 11.1 190

*ALL WITH INDOOR SHADING

430
MADISON BUILDING

TABLE III HEATING & COOLING SUMMARY (SX 1000)

DESCRIPTION*

INSTALLED

G L A S^

COST

HEATING

& COOLING

EQUIPMENT

COSTS

TOTAL

RELATIVE

DIFFERENCE

A. 1/4-INCH SOLARBRONZE PLATE 10.6 855 865.6

D. I-INLH LMK iOLAKoKUN^t TWINPOW 34.8 834 868.8 3.2 INCREASE

C. MNCH SOLARBAN (2) TWINDOW 30.6 820 850.6 15.0 SAVINGS

*ALL WITH INDOOR SHADING

431
MADISON BUILDING

TABLE IV COST ANALYSIS SUMMARY

INSTALLED

GLASS

COST

($)

HEATING & COOLING

C WUI r Men I COSTS

(S)

HEATING & COOLING

U r C K A 1 1 nu COSTS

($)

PRESENT

WORTH

($ per »q.ft. rentable

floor area)

OWNING & OPERATING

COSTS

($ per sq.ft. rentable

floor area)

A. 1/4-INCH SOLARBRONZE PLATE 10,600 855,000 18,800 53.04 3.09

B. 1-INCH LHR SOLARBRONZE TWINDOW 34,800 834,000 18,300 53.36 3.11

C. 1-INCH SOLARBAN (2) TWINDOW 30,600 820,000 18,000 53.01 3.09

*ALL WITH INDOOR SHADING

432
COLUMBUS BUILDING

TABLE V GLASS ALTERNATIVES

DESCRIPTION*

U - VALUESHADING

COEFFICIENT

INSTALLED

COST

i PER S Q . FT

A. 1/4-INCH SOLARBRONZE PLATE

B. 1-INCH SOLARBRONZE TWINDOW

C. 1-INCH SOLARBAN (2-3) TWINDOW

0.8

0.5

0.28

0.53

0.42

0.10

3.30

4.50

5.59

*ALL WITH INDOOR SHADING

433
COLUMBUS BUILDING

TABLE VI RESULTS

DESCRIPTIONCOOLING HEATING

TONS $ X 1000 MIL-BTU S X 1000

A. 1/4-INCH SOLARBRONZE PLATE 3,114 3,114 23.21 371.4

B. l-INCH SOLARBRONZE TWINDOW 2,763 2,763 17.41 278.6

C. 1-INCH SOLARBAN (2-3) TWINDOW 2,226 2,226 13.06 209.0

•ALL WITH INDOOR SHADING

434
COLUMBUS BUILDING

TABLE VII HEATING & COOLING SUMMARY ($ X 1000)

DESCRIPTION*

INSTALLED

GLASS

COST

HEATING

& EQUIPMENT

COSTS

TOTAL

RELATIVE

DIFFERENCE

A. 1/4-INCH SOLARBRONZE PLATE $ 693 3,485 4,178

B. 1-INCH SOLARBRONZE TWINDOW $ 945 3,041 3,986 192 SAVINGS

C. 1-INCH SOLARBAN (2-3) TWINDOW $1,174 2,435 3,609 569 SAVINGS

*ALL WITH INDOOR SHADING

435
COLUMBUS BUILDING

TABLE VIII COST ANALYSIS SUMMARY

DESCRIPTION*

INSTALLED

GLASS

COST

($)

HEATING & COOLING

EQUIPMENT

COSTS

($)

HEATING & COOLING

OPERATING

COSTS

($)

PRESENT

WORTH

($ p»r »q.ft. rentable

floor arte)

OWNING & OPERATING

COSTS

($ per »q.ft. rentable

floor area)

A. 1/4-INCH SOLARBRONZE PLATE 693,000 3,485,000 75,300 44.79 3.76

B. 1-INCH SOLARBRONZE TWINDOW OAK (\(\r\ 0|U4 1 ,uuu A A A'i i.l i

C. 1-INCH SOLARBAN (2-3) TWINDOW 1,174,000 2,435,000 60,800 43.64 3.66

•ALL WITH INDOOR SHADING

436
Comparative Computer Analysis

of the Thermal Cost Performance

of Building Enclosures

Willard A. Oberdick-"-

Smith, Hinchman & Grylls Associates, Inc. Architects, Engineers and Planners

Detroit, Michigan 48202

The computer programs on thermal-cost performance of building enclosure systems developed to be used in computer-aided

architectural design are described as to logic, data structure

and man machine interaction. The solar-climatic simulation

approach using normal Weather Bureau data for predicting the

thermal performance is compared to an hour by hour computer

analysis of selected examples. A mathematical model of the

total thermal energy system of a specific building is described

and used to evaluate the relative importance of the building

enclosure as well as compare computed data with that of metered

energy. This study proposes that specific modeling of specific

building thermal systems can be used to develop simulation

packages for use in computer aided design.

Key Words: Building enclosures, computer-aided design,

initial wall costs, man-machine interaction, owning

cost, present worth, building mechanical equipment,

thermal performance, solar- climatic simulation.

1. Introduction

The objective of the computer programs on thermal-cost performance is to provide

the architect with information in the design development or selection of components

for the building envelope, i.e., the walls and roofs. The programs can be used for a variety of comparative studies involving thermal cost trade-offs. Initial and total

owning costs can be compared for specific building situations in specific locations.

The basic computer-aided design package was developed in 1967 and 1968 by

Smith, Hinchman & Grylls Associates, Inc., Architects, Engineers and Planners of

Detroit for use on an IBM1130. Subsequently, it was adapted to the IBM360/6 7 Time

Sharing System of the University of Michigan. This program package and video tape

instructions have been made available to the Department of Architecture for Educational purposes

The objective of this paper is 1) to describe and evaluate the programs as a computer-aided design method 2) describe and evaluate the use of Weather Bureau data

for such simulation and 3) to explore the concept of modeling of the total building

energy system as a means of checking simulation approaches used in computer-aided

design.

2. Design Development-Man and Machine

Many factors such as those related to the thermal, cost, luminous, sonic and visua

performance are considered by an Architect-Engineer in the design development of the

building envelope as part of the total building design. Of these, thermal performance

is particularly significant since it has implications from the standpoints of comfort,

direct and indirect costs and weatherability . The mechanical systems are dependent on

the nature of the envelope thermal loads. Therefore, not only are decisions by the

-'-Consultant; Professor of Architecture, University of Michigan, Ann Arbor, Michigan.

437
mechanical engineer required but effective design would indicate an optimizing approach

or at least consideration of interdependent trade-offs between building components and

mechanical equipment.

Since the computer program involves estimates of mechanical equipment costs, the

thermal loads must necessarily be compatible with the design practice of the mechanical

engineer, and as such he is logically involved in the entire process. Other facets of

the problem of program development involve the need for flexibility. Combinations of

advancing technology, changing building needs and variety of microclimates indicate a maximum of flexibility in any data structure. However, tempering this requirement is

the need for simplicity of imput. These points together with the lack of computer

background of many who might logically use the system indicates the nature of the

challenge faced.

Experience to date indicates that the remote terminal is an ideal device for learning to use the programs and, in effect, to understand the system. Effort has been made

to improve the man-machine interaction with these programs using conversational imput,

default files for physical property and cost data along with an editing system. Once

the user has learned the system he may exercise the option of using either batch or remote terminal as is appropriate in any particular case. Graphic display devices are

a logical next step when such are readily available. The user should in effect be a team of a mechanical engineer and an architect or possess the insight of both for

effective use of the computer programs.

The problem of computational cost must also be considered. The general objective

is to obtain accurate information fast and at low cost. At one extreme is the complete

design and detail evaluation of complete buildings for comparative purposes. The

approach to simulation used in this system is intended to give specific effective

information at a minimum cost. As an example, with the University of Michigan system

the time used for the simulation-study is one fifth of that required for the detailed

hour by hour analysis noted subsequently in this paper. On an IBM1130, runs will

consist of from 5 to 10 minutes for several comparisons.

3. Data Structure

The heart of the problem from the user's standpoint is identification of the

specifics of the building and finding required information for use in the system.

The required data can be divided into five categories: wall type, mechanical systems,

wall conditions, solar-climatic conditions and economic data.

The approach used relative to wall types is that of identifying separate components

such as brick, block and glass, as shown in figure 2. Air spaces are identified as separate components. Inside shading is included with the glass as a separate component.

A data assembly program TASSEM identified in figure 1, is used to select data from a master file. The data includes cost information and physical properties. As an example the user might type:

BRICK/EXTERI0R/4IN/

The computer would echo the data line with values in succession identified as: key

number, thickness, density, conductivity, specific heat, initial cost, maintenance cost

and maintenance interval.

14.1420 4. 130. 9. .18 1.73 .12 20. BRICK/EXTERI0R/4IN/

Transparent component are similar except the second, third, fourth items are, respectively, total solar energy transmission, solar heat gain factor and the "U" value.

The type of mechanical system is identified in similar manner: UNITARY /AIRCOND/HWBASE/

From the master file, figure 2, the following cost information is identified: key

number, cooling equipment costs, energy costs for cooling, heating equipment costs and

energy costs for heating all in dollars per BTU. The line would be echoed as:

81.1000 .04 000004 .024 .0000011 UNITARY/AIRCOND/HWBASE/

438
Wall conditions, figure 3, are defined with information on relative position, area, percentage of glass, nature of ground reflecting plane and exterior shading as noted in

figure 4. In the latter case the actual position of the glass needs to be identified

in relation to the projecting surfaces. All of this data is sequenced and stored in a Building Specifics File, figure 2. With the three groups of data the user in effect

identifies the building envelope and mechanical system.

The solar-climatic data is stored in a file and this is referenced in respect

to a particular location. The data is developed in accordance with the block diagram,

figure 5. The program identified as SOLCLIM in effect determines diurnal variations

from a year's data of drybulb temperatures, and cloud cover and with recorded normals

as input assembles the simulation data base of twelve prototypical days. The data for

the July day is shown in table 1. The first line from left to right consists of latitude, elevation above sea level, outside surface film coefficient, solar radiation

constant for that month, days from equinox, season, average percent of sunshine. The

second line consists of projected diurnal temperature data for a day with average

temperature values at 3 hour intervals corresponding to those days with an average

cloud cover within the range of 31 to 69 percent. The average temperature is the normal

value for the month. The third line is similar except it consists of expected highs

with temperature pattern corresponding to 0 to 30 percent cloud cover. The maximum

is average of normal daily maxima and extreme high as recorded. The fourth line is

similar except that the cloud cover is 70 to 100 percent and lowest temperature is the

average of normal daily minima and recorded extreme low.

Table 1. Solar climatic normals for a prototypical day in July.

1 General 42 750 4 344 68 1 39 Time 1 A.M. 4 A.M. 7 A.M. 10 A.M. 1 P.M. 4 P.M. 7 P.M. 10 P.M.

2 Average 64 63 64 72 77 77 75 67

3 Highs 71 69 69 80 85 85 82 73

4 Lows 63 62 62 68 70 71 68 63

The data noted here and subsequent information on wet bulb temperatures were keypunched directly from Local Climatological Data Summary sheets (1) . The same information could be obtained from the Environmental Data Center in Asheville, N. C. and processed for the immediate locale related to the observation station.

Information on long term costs are based on the concept of present worth of future

payments. Interest rate, years of anticipated use and the room temperature are entered

in running the simulation programs. Increasing attention is being placed on long term

or total owning costs. Although many more factors are involved in the total cost of

a building, the factors included in this system do permit effective comparative studies.

4. Program Logic

4.1 Basic Approach

Three concepts, thermal neutralization, solar climatic simulation and present worth

of future costs are fundamental to the logic of these programs. First, the concept that

mechanical equipment and energy will be considered to counteract any loss or gain from

the wall or roof; in effect, to obtain a thermally neutral surface. Involved are solar

and climatic effects on both transparent and opaque surfaces. Second; fundamental to

the prediction of the thermal performance is the simulation of the solar climatic

environment. The system included in these computer programs is intended to be microoriented, that is, local temperatures, radiation intensities and ground reflections are considered. Third, in order to compare future payments for maintenance or energy with

initial costs the concept of present worth of future payments is utilized. The equivalent of a dollar invested with identified interest for future payments is assumed to be

comparable to the initial construction dollar.

*Note : Figures in brackets ( ) indicate literature referenced at the end of the paper.

439
In general, the approach has been to minimize the use of tables, in effect, to

use the methods that originally were used to generate the tabular values. This

distinction is a logical step from that of handbook engineering to computer-aided

design. Further, it has been necessary to improvise from basic research certain projected empirical relationships to fill program "logic blocks" where such have not been

advanced to the Engineering level. As an example, the interrelationship of cloud cover

to direct and indirect solar radiation and related transmission through glass required

programming expediency. In the latter case a second problem occurs when technical data

on product performance is not available on the detail required.

The primary problem is that of using logic that accounts for changing parameters

and is consistent in complexity throughout the program with intended use of the information.

4.2 Solar Radiation and Heat Transfer

The basic program logic used for heat transfer and solar radiation was developed

in 1966 as part of research at the University of Michigan in reference to an evaluation

of polyurethane roof system (2). This was prior to publication of 1967 ASHRAE handbook

of Fundamentals (3) in which the first step was taken toward computer-aided design.

Direct solar radiation is computed for each of the hour-dates considered for

both a clear sky and a state of cloudiness as indicated. Factors considered are: latitude, elevation above sea level, changing earth-sun distance, wall solar azimuth,

wall vertical position and cloudiness. For indirect radiation, cloudiness, intensity

of direct radiation (4) altitude of sun, wall position and irradiation (5) from the

ground are considered. The distinction is kept between direct and indirect radiation

in considering gain through transparent surfaces. The effect of direct radiation is

considered only in sunlit areas as determined by exterior shading patterns.

Heat transfer through opaque walls is based on an adaptation of the exact method

proposed by Mackey and Wright in 19 44 (6) for determining periodic heat flow through

walls and roofs. Decrement factors and lag angles for the first and second harmonics

are utilized. Factors considered are absorptivity of outer surface, outside film

coefficient, ambient air temperatures for a 24 hour period, direct and indirect solar

radiation, the density, specific heat and conductivity of each component and the

inside air temperature and inside surface film coefficient in respect to direction

of heat flow and position.

The program logic now incorporated for solar effects on the glass has been adapted

to use the coefficients (3) for transmittance and absorptance of glass. Total heat

transfer is based on prorated square foot of wall accounting for the proportions of

glass and opaque surfaces. Heat transfer from solar radiation and air to air temperature difference are considered for glass at the particular hour under consideration.

Transfer through opaque is considered at a prior lag angle hour using solar radiation

and ambient air temperatures of that hour.

In the research on polyurethane shell roofs (3) noted earlier limited field

observations were made as a check on the logic related to solar radiation and periodic

heat flow. The prototype structure consisted of seven, 14 foot hexagonal shells. A

temporary enclosure and heating was provided for the test period. Iron-constantan

thermocouples were installed in the roof and monitored manually at selected times over

a two month period and hourly over selected days. Results for a typical day are shown

in figure 6, Observations of cloud cover, wind velocity, air temperatures, surface

absorptivity were intended to parallel the computer logic. On the basis of this

correlation the idea of an hour by hour analysis was initially used in the development of the concepts presently used in the solar climatic simulation.

4,3 Thermal Loads

In the simulation program heat transfer for expected high and low temperatures are computed and stored separately in 12 by 8 arrays. As each surface in an identified zone

is computed it is added to respective array. Peak heat gain and loss are determined by

searching the accumulative values in the arrays. These are based on a clear sky and

should, in effect, be the basis of design. Equipment costs are based on these values.

440
In addition, heat transfer under specified cloudiness with both highs and average

temperatures are accumulated for each wall at the 96 prototypical hours for annual

gross loads per se in these programs.

4.4 Costs

Initial costs of wall are the accumulative prorated sum of the costs of identified

components. Initial cost of mechanical equipment for thermal neutralization is the

product of peak loss and gain and the respective estimates of costs per BTU capacity

for the particular system.

Energy costs are based on annual costs for energy for heating and cooling and are

the products of accumulative loads and respective energy costs per BTU. The present

worth (7) of future annual payments is used for the comparative figures. As an example

for twenty equal payments the present worth equal 11,4 7 times the annual value.

Maintenance costs are based on the accumulated prorated sum of the present worth

of future payments for maintenance on each of identified components.

Total owning costs then are the sums of initial, energy and maintenance costs.

5. Simulation-Thermal Cost Performance

The first example used to illustrate the application of the programs and as a test

case for comparing the simulation programs with that of the detailed analytical program

is the Cooley Building located on the North Campus, University of Michigan. The two

story rectilinear building, figure 7 was built twenty years ago without air conditioning. The thermal performance of the building was such that an exterior shading screen

was subsequently installed on the south glass wall. The summary of the output, table 2 indicates the trade-off for changes in the south wall with and without air conditioning

It should be noted that the south wall accounts for only one-quarter of the total

envelope area and as such the substantial changes in heat gain from 124 to 5 8 BTUS

per square foot for the south wall without and with the screen, is reflected in reduced

values when considering the entire building surface. The total owning cost for air con ditioning with the exterior screening is $7.45 per sq. ft. of envelope as compared to

item 4 involving an alternate of Venetian blinds.

Table 2. Thermal Cost Comparison for the Cooley Building, North Campus,

University of Michigan, Ann Arbor, Michigan

No. Type

South

Wall

Mech

Sys

Initial

Wall Cost

Mech

Equip.

Cost

Maintenance Cost

Energy

Cost

Total

Cost

Gain/Loss

BTU/Sq.Ft

1 SN Basic Heating 2.67 0.75 . 39 1.28 5.08 28.5/-37. 3 Only

2 SN +Outside Heating 2.90 0. 75 . 39 1.27 5. 31 16.9/-37. 3 screen Only

3 SN Basic Air 2.67 3.60 . 39 1.96 8.61 28.5/ 37. 3 Cond.

4 SN +Venetian Air 2.78 2.44 0.42 1. 72 7.63 19.9/-35. 6 Blinds Cond.

5 S69 +Venetian Air 2.78 2.60 0.42 1.69 7. 50 19.2/ 34. 1 Blinds Cond.

6 A69 Venetian Air 2.78 2.99 0.42 1. 83 8.03 22. 2/- 38. 2 Blinds Cond.

SM - Simulation Normals ; S69 - Simulation Data Equivalent for 1969

A69 - Detailed "Year-Hour" Analysis

All values are for a prorated average square foot for the five surfaces

Basic south wall consists of brick and cinder block with 71% clear glass.

441
Items 4, 5 and 6 in table 5 are for the same building condition, in effect, the

same Building Specific File is used in each. The simulation data for Ann Arbor is used

in item 4 along with simulation program WTHERM, figure 8. Item 5 involves 1969 values

in a simulation form, figure 5. Item 6 involves results from program WTHERMA, figure 9, a detailed analysis for 1969. The results are not exact but reasonably close for com- parative purposes.

The second example the Institute of Science and Technology on North Campus,

University of Michigan, involves a unique shadow box shading device. Results from

the simulation study indicate an initial cost of glass of $3.10 and mechanical equipment cost of $10.20 and present worth of energy costs of $4.30 per sq. ft. of glass.

The minimum shadow during period of gain for the west wall is 22 percent, figure 10.

The cost trade-off for the shading device for the west wall is $2.57 per sq. ft.

of glass. This was obtained by another run omitting the exterior shading.

6. Modeling of Building Thermal Energy Systems

It is proposed that the accuracy of the simulation approach can be evaluated by

modeling the total thermal energy system for a building and comparing the prediction

of energy consumption with that metered. The Undergraduate Library, figure 11, at the

University of Michigan was used as a case study. The building has nearly a constant

year around occupancy, further, monthly turnstile figures, recorded electrical energy

consumption for the building and monthly recordings of condensate were available. The

computer program system used for this building is blocked out in figure 9. Program

WTHERMA referred to in the previous section was used to obtain the 1969 3-hour interval

heat loss or gain of the total building envelope. Although the building appears simple

in form, 12 separate surfaces were identified to cover combinations of brick and glass,

stone and glass and porcelain steel panels and glass combinations. The maximum heat

loss for the 63,600 sq. ft. of envelope is only 16.1 BTUS per sq. ft. and the gain of

7.1 BTUS, indicating a minimum influence of the envelope.

The program ULGUM in effect, is a model of the energy aspects of the air conditioning system. The system is a central system consisting of 6 supply fans with a total

capacity of 163,000 C.F.M., a reheat system for zone control, a hot water convector

system and a chilled water system using steam in Lithium Bromide absorption machine with

a cooling tower. Cooling equipment was turned on April 28 and off on November 2 in 1969.

On the same dates basic control of outside and return air damper were changed. Involved

in this program are predictions of room temperatures and relative humidity of room air.

For each of the 2920 three hour periods in the year, room conditions, percentage of

outside air, as well as required wall heat, reheat and cooling are determined. Lighting

and number of occupants are predicted for that specific hour. A summary for each month

is included in table 3. Several runs with different cold deck temperatures and slight- room temperature variation resulted in sufficient difference in total energy to indicate

that the preciseness of system control is essential for closer correlation.

Table 3. Thermal Cost Comparisons for the 1969 Operation of the Undergraduate

Library, University of Michigan

Month

Enve lope

Gain

-Energy

Loss

Occupancy

Gain-Energy

Reheat

Energy

Cooling

Energy

Total

Energy

Metered

Energy

Total

Cost $ Jan

0 494. 5 1,113.9 1,471.

0 1,963.9 1,600.0 3,224.

Feb. 0 395 .9 1,180.9 1,338.6 0 1,734.4 1,250.0 2,844.

Mar. 0.4 362 .2 1,053.9 1, 758.9 0 2,121.1 1,100.0 3,478.

Apr. 4.2 180 . 8 1,133.0 1,139 .9 0 1,319,7 1,821.0 2,164.

May 18. 7 103. 6 712 .6 1,632.5 577. 3 2 , 313.

2 ,120 .0 3,793.

June 36. 8 53.5 832.1 1,251,541 2,574.6 3,878.6 2,011.0 6 ,360 . July 72.6 7.1 705.0 1,340 ,173 5 ,200 .6 6,547.9 5 ,103.

10 ,737.

Aug83. 2 7.1 731. 9 1,222.5 4,523.0 5 , 752.

5,747.0 9,433.

Sept. 16 .6 66.1 873.6 1, 269 .0 2,293.3 3,628.4 6,246.0 5,949.

Oct. 0.8 197.

1,016 .2,563.5 614.9 3,375.6 4,449.0 5,535.

Nov. 0.1 330 .3 1,046.5 1,642.6 0 1,972.9 1,579.0 3,235.

Dec. 0 463 .1 1,083.1,661.4 0 2,124.5 2,266.0 3,484.

Total 233 . 3 2,661.1 11,483.

18,291.

15 ,783.

36 ,734.

35,292.0 60 ,244.

Note: Total energy equals the sum of envelope loss, reheat and cooling.

All energy values are noted in MIL BTUS

Costs are based on a projected steam cost of $1.65 per 1000 lb.

442
The relative influence on costs of the envelope are shown in table 4, for the

Library and a hypothetical library occupancy for the Cooley Building, Case II. The

latter having a larger wall to floor area ratio and a thermally responsive glass south

wall. The system cost figures used in this case have been adjusted to be consistent

with those used for equipment and energy in the Library, Case I.

Table 4. Comparison of Building Envelope and Mechanical Equipment Costs in Buildings

Case II. Case I. Cooley Bldg.

Undergraduate Library Hypothetical Library

Floor Area

Envelope Surface Area

Envelope Cost

Equipment Costs for Envelope Neutralization

Equipment Cost for Total Building

Energy Cost for Envelope Neutralization - Present Worth 20 Years

Energy Cost for Total Building - Present Worth 20 Years

136,680 sq.

6 3,363 sq

$ 1.46

$ 1.64

$10.08

ft. ft.

0.40

6.19

26,072 sq. 28,644 sq.

$ 3.06

$ 3.77

$10.99

ft. ft.

2. 30 8.23

Cost Values are in $ per sq. ft. of floor area.

7. Conclusions

The simulation approach for identifying wall performance is an effective computeraided design tool. Expansion of the concept to the total system is required to give

the design team an accurate cost performance picture of the building.

The use of normals from accumulative Weather Bureau Data for this simulation has

been compared to that obtained from a detailed year-hour analysis. The same procedure

should be used for a larger number of years to provide a statistical base for correlation. Detailed checking of program logic or blocks can be accomplished by isolating

the parameters for specific correlation with field measurement of temperatures.

The results of the total thermal energy study are inconclusive but do indicate

the potential not only as a check for this simulation approach but as a direct benefit

to the owner in optimizing the operation of his building. Further, idiosyncrasies of

the building operation, such as down time for cooling equipment; and accuracy of

metering must be taken into account.

8. References

[1] Local Climatological Data , Asheville,

North Carolina, U. S. Department of

Commerce, Data Sheets - Detroit,

Michigan, 1969.

[2] Oberdick, W. A., " Design and Evaluation of a PolyuretHahe Foam Shell Roof

System,

Ann Arbor, Michigan, ARL

Report, 196 6.

[3] ASHRAE Handbook of Fundamentals , New

York City, Am. Soc. Heat., Refr. , and

Air-Cond. Engrs. Inc. pp. 475-479, 1967.

[4] Robinson, N., Solar Radiation , Netherlands, Elsevier Publishing Co., 1966.

[5] Threlkeld, J. L., Thermal Environmental Engineering , pp. 356, 360,

(Prentice Hall, 1962)

[6] Mackey, C. 0., Wright, L. T. , Jr.,

"Periodic Heat Flow-Homogeneous Walls or Roofs , " Trans. Am. Soc.

Heating and Vent. Engrs ., Vol. 50

(No. 1255) , pp. 293-312 , 1944.

[7] Grim, C. T. , Gross, J. G. Ultimate

Cost of Building Walls . Washington,

D.C. Department of Engineering and

Technology, Structural Clay Products

Institute, 1958.

443
KEY WORDS

SELECTED INFO- INPUT

PROMPTING

ECHOED DATA

OUTPUT

WALL CONDITIONS

POSITION, AREAS

GROUND PLANE

EXTERIOR SHADING

T ASSEM

DATA ASSEMBLY

MECH- SYSTEMS

WALL TYPES

WALL CONDITIONS

MODES

TTY- CONVERSATIONAL

BATCH-NUMERIC

B UILOI NG SPECIFICS

INTERMEDIATE FILE

MECHANICAL

MASTER FILE SYSTEM COSTS

SELECTION a EDITING

SELECTI ON a EDITING

MATERIALS

MASTER FILE PROPERTIES a COSTS

Figure 1 Block diagram - data assembly of building specifics

FACE BRICK

• • • 1 •

f 1 • •

a

• • Wa • • • •

' • • • m' •

8

CINDER BLOCK

CLEAR GLASS

Figure 2 Wall types - Cooley Building South Wall

444
Figure 4 Exterior shading - data re^jresentation

445
WEATHER BUREAU DATA

SUMMARY VALUES

NORMALS a EXTREMES

SIMULATION DATA

NORMAL VALUES

12- PROTOTYPICAL DAYS

S 0 LCLIM

CONSTRUCTION OF

SIMULATION SOLAR

CLIMATIC FILES

DIURNAL VARIATIONS

HIGHS -AVERAOES-LOWS

WEATHER BUREAU DATA

DRY BULB TEMPERATURE

CLOUD COVER

I YEAR - 3 HOUR INTERVALS

SOLAR CLIMATIC

SPECIFIC YEAR

12 - PROTOTYPICAL DAYS

Figure 5 Block diagram - solar climatic data

REFERENCE PLAN SECTION (A)

£ 60

" 50

o/

//

-^tr 7

-h

O G

o e

100% SUNSHINE

H-7m N

OUTSIDE AIR

0 % SUNSHINE

(CO

G

MPUTED)

• 7m

6 AM 8 10 12 NOON 2 PM 4 EASTERN STANDARD TIME NOTES CURVES ARE FOR RECORDED VALUES EXCEPT AS NOTED

DATE MAY 2, I9«6 AVERAOE WIND VELOCITY = 7.9 M.RH. Figure 6 Correlation studies of diurnal variation of temperatures in a polyurethane shell roof.

446

CONTROL DATA

TEMPERATURE, YEARS

INTEREST RATE

INPUT

DETAIL THERMAL CONDITION

ELECTIVE SHADIN6

PATTERNS OUTPUT

SUMMARY OF COSTS

AND THERMAL CONDITIONS

OUTPUT

WTH ER M

ANALYSIS OF

ENVELOPEHEAT LOSS a GAIN

INITIAL COSTS

MAINTENANCE COSTS

ENERGY COSTS

BUILDING SPECIFICS

INTERMEDIATE FILE

SIMULATION DATA

12 PROTOTYPICAL DAYS

Figure 8 Block diagram of the thermal cost performance simulation program

CONTROL DATA

TEMPERATURE, YEARS

INTEREST RATE

LATITUDE, ELEVATION

INPUT

ENVELOPE OWNING COSTS

THERMAL LOADS

OUTPUT

ELECTRICAL ENERGY

OCCUPANTS

SYSTEM FACTORS

INPUT

CUMULATIVE ENERGY COSTS

BY HOUR, MONTH, YEAR

OUTPUT

WTH ER MA

ANALYSIS OF

ENVELOPE

- 3 HR INTERVALS

HEAT LOST a GAIN

INITIAL COSTS

MAINTENANCE COSTS

ENERGY COSTS

HEAT TRANSFER-3HRU G L U M

ANALYSIS OF

MECHANICAL SYSTEMS

ENVELOPE

LIGHTING

OCCUPANTS

VENTILATION

BUILDING SPECIFICS

INTERMEDIATE FILE

WEATHER BUREAU DATA

DRY BULB TEMPERATURES

CLOUD COVER

I YEAR -3 HOUR INTERVALS

WEATHER BUREAU DATA

WET BULB TEMPERATURES

I YEAR -3 HOUR INTERVALS

Figure 9 Block diagram of the computer programs for modeling of the thermal

energy system in buildings.

448
Figure 10 Shadow box window enclosure and line printer output of shadow pattern

Institute of Science and Technology, North Campus, University of Michigan

449
450
A Numerical Method for Computing

the Non-Linear, Time Dependent,

Buoyant Circulation of Air in Rooms

Jacob E. Fromm

IBM Research Laboratory

San Jose, California 95114

A method is described which solves the dynamic equations for air circulation

at Grashof numbers that are in the range of environmental temperatures of rooms. Previous computation techniques were limited to G ~10^, but environmental conditions require G ~10-'-^. The higher Grashof numbers are attained by improved non- linear approximation methods. Fourth order difference equations are discussed rel- ative to linear stability properties which determine the fidelity of the convective process in the finite net of points. Non-linear instability of time-splitting

methods is described and the means of overcoming this type of instability are given.

Key Words: Heat transfer, finite difference, computation, convective

approximations, air circulation, time dependent solution.

1. Introduction

In the past decade numerous advances have been made in the use of numerical means to solve coupled non-linear partial differential equations. The methods for obtaining solutions fall roughly

into two categories: i. Expansion methods which make use of orthogonal polynomials; 2. Finite difference methods. The former of these was used by Poots^ and the latter by Wilkes"^ for the particular problem of interest here. The success of the two methods of solution relative to the work

of the cited authors was about the same. Comparable solutions were obtained for the problems of buoyant fluid flow in a two dimensional enclosure with vertical walls at a fixed temperature difference

and horizontal walls either insulated or with a fixed temperature which varied linearly between the upright walls. These successes were important ones and led to the hope that the methods could readily be extended beyond the range of parameters of those studied into the practical problems of everyday engineering experience, in particular to the study of air circulation at environmental room temperatures or under fire conditions.

Both the methods indicated above do possess the potential of providing solutions to such problems.

Currently, the greatest emphasis is on finite difference methods because they may be applied in a straightforward manner if sufficiently accurate algorithms are known. Unfortunately, such algorithms

have been slow in realization. Here we have utilized higher order approximations that depend upon flow direction. This is essential in order that detail may be maintained without introduction of noise com- ponents which are of numerical origin. The nature of the flow in the rectangular enclosure is such

that the common weaknesses of non-linear difference approximations are very pronounced. Thus while the geometrical situation is fairly simple it provides a crucial test of the methods.

Our primary objectives here are to outline the numerical methods and to give details of the al- gorithms that are required. The general procedure of finite difference computation using the vorticity

and streamfunction as field variables is fairly well established^'**'^. Also, the evolution of thought

on requirements relative to reduction of phase error, which is the primary cause of computational noise,

has been documented^ ' ^ . The additional modifications of the basic algorithms that are pertinent for

the success of high Grashof number calculations are emphasized here.

As a result of these efforts toward minimizing numerical noise and numerical damping, the two-dimensional computation can reasonably be carried out up to Grashof numbers of 10^^. At these high values

there are uncertainties about the magnitude of viscosity and heat transfer coefficients relative to truncation errors. Further, very small time increments are required for computation. Hence, the limiting calculation of infinite Grashof number would not be a reasonable one.

Because turbulence is surely a factor in the real world, the present calculations using molecular

451
coefficients should be regarded as idealizations. This does not mean that they are of little value. On the contrary, we can analyze the flow behavior, explaining the flow features that occur and why

they occur. Further, gross properties of the flows can be given within the framework of the idealization. With this information it should be possible, with the help of experiments, to determine where

discrepancies occur between observation and computation. Information so obtained is pertinent to modeling efforts where turbulent diffusion and heat transport must be parameterized.

2. Governing Equations and Problem Description

The conservation equations to be solved in a two dimensional rectangular region are:

Mass: ^ + = q , (1)

Momentum: tt— +u — + v— = — + vVu, (2) dt dx 3y p 3x

o

3v , 3v , 3v 1 3P l'^ '^o^ + u — + V

3t 3x 3y p 3y ^ T

o \ o J + vv^v , (3)

3T ^ 3T , 3T „2„ Energy: _ + u — + v — = kv T . (4)

Here u and v are velocity components in the x and y directions respectively. The thermodynamic variables p, P, and T are the density, pressure and temperature respectively. The sub.- script o indicates constant reference values to be defined, v, k, and g are the kinematic viscosity, thermometric conductivity and gravitational constant respectively.

Numerical computation is carried out using the vorticity and streamfunction. We define

to = 7— - 7— (5) 3y 3x ^

and

" = 97 ' " = - •

Thus (1) is satisfied identically by (6), (5) becomes

2 2 —5" + —T = - 10 , (7) 3x 3y

and P can be eliminated from (2) and (3) yielding the vorticity equation

w'-u . (8)

3(1) , 3uu , 3vu 3^ +

.."Z 3t 3x 3y T

o

Our system of computation equations are then (7), (8), (4) and the definitions (6).

We take x as the horizontal coordinate and impose the boundary conditions for a square enclosure

u=v=o, T=T^ at x=o for o <_ y <_ d

u=v=o, T=T at x=d for o £ y £ d

at y=0 ,d for o _^ x

T=T,-x(T,-T )/d

1 1 o at y=o,d for o < x < d (9)

452
It is found more convenient to deal numerically in terms of the dimensional variables because of

physical interpretation and number sizes encountered in numerical solution. Following Foots we use

the nomenclature

a = v/k

as the Prandtl number and

A = a G = (T -T ) gd^/T kv

i o o

for the Rayleigh and Grashof numbers respectively.

While numerous gross properties could be evaluated to lend understanding to the flows, we here consider the dimensionless heat transfer for comparison with results by Foots and Wilkes. Heat transmission

through the cold vertical boundary is not the total heat transmission but is the value given by Foots. Numerically, one must also include the convection flux because the discrete description requires it. For the square region considered we define the Nusselt number

N = ^ . 1 o

The total heat transmission can be evaluated only by having the end points of the integration corres- pond to x=d/2 and y=o,d. Nevertheless, for comparison purposes we also measure the transmission at x=o with integration limits y=o,d.

3. The Numerical Approximations

We now describe the non-linear approximation method that was required for the success of the given calculations. For completeness we shall outline the numerical procedure, giving the numerical

approximations but postponing the convective flux methods for later discussion.

For small values of A or G it may be advisable to initialize calculation with no flow and an initially prescribed linear horizontal temperature variation inside the fluid region. If A is small,

steady state results are of primary interest and computation time may be preserved by relay type calculations, always using steady state results from lower values of A to proceed to higher values. However, beyond A=10^ the solutions are unsteady, in fact A=10^, 0=0.1 gives an oscillating solution.

While it is always useful to begin with an approximate solution to the expected solution at late time,

it is more reasonable to initialize calculation at high values of A with internal temperatures specified to be everywhere the mean of the given wall temperatures. If the initial interior temperature

is specified to be that of the low temperature wall, much computation would be required to approach

true late time conditions. In all cases reported here, we initialized the temperature field to have

the mean wall temperature value. The streamfunction and vorticity were perscribed to be everywhere

zero initially.

With all field values given at the time t=o we proceed by updating the temperature field toward

ultimate prescription of field values T, . = T(iAx, j Ay ,nAt) for n=l. Through convective flux com- putation we first obtain everywhere

i,j i,j Ax [ i'-l/2,J 1+1/2, jj Ay 1^^1,3-1/2 *i,j+l/2j (10)

where F is the flux at half cell distances from the point (i.jj. Using everywhere the tantative values

(except for fixed values at the boundaries) we add the conduction contribution to complete the update

j of T. Thus

T. . = T. . + ( T.^, . - 2T. . + T. , .

+ f T. - 2T . . + T. . , 1 . (11)

453
The use of tentative updated values in the conduction calculation provides for less restrictive

conditional stability of this explicit difference equation. This has been suggested in the work

ofMarchuk^ and has been observed empirically in the present calculations. Through this procedure the stability condition

KAt/ min[(Ax)2,(Ay)^] <l/4 (12)

is strictly applicable. For small A a more stringent condition would otherwise be necessary.

At this stage one proceeds similarly with the vorticity equation, first obtaining

1,1 i,J Ax 1^ 1-1/2, J 1+1/2, Ay ^ i,j-l/2 i,j+l/2j

where H is the vorticity flux analogous to F of (10) . Here two tentative updates are necessary because of the buoyancy term. For the diffusion update we write

* ~ VAt f~ ~ -l r ^ > i.J i>J (^2^)2 [ 1+1, J i,j 1-1, jj + —^ 1,1+1 1,1 1,3-lj. (14)

Finally the buoyancy contribution gives the complete update of to thusT

u! . = to* . + (t'^_^^ • - t"!" , .] (15) 1,3 i,j 2T^Ax V 1+1,3 1-1,1

j

Note that the values obtained in (11) are necessary in (15). If in (15) the old time values were used

instability would result.

With T and to both obtained for new times we next consider the streamfunction field. Simultaneous

solution of all net points is required to satisfy

1 11 1 11

(Ax) Ay"^

Because of the simplicity of the boundary conditions on ij; a direct method may readily provide solution. We have here made use of a program developed by Buneman^. Buneman's method involves cyclic matrix re- duction in two directions. It is applicable to an enclosed rectangular region with zero value specified for ijj at the boundaries. The program is fast, accurate to computer round off, and compact.

It is estimated that an iterative method would have taken more than ten times as much computation for equal accuracy.

The final step in computation of the field variables, to have a complete solution at the advanced

time step, is to apply no-slip conditions at the walls, i.e., obtain boundary vorticity values. The approximations here used are

1 /'I 1 '1 2

1 r 1 1 ^ , 2 ^i,i = ' - Vi,jJ/'^^

1 r 1 ,1 ^ , 2 ^,0 = -2 [^i,i- \,o] i^y

1 1 1^,2

where o refers to left or lower boundary and I and J refer to right and upper boundaries respectively. The equations (17) may readily be derived from (16). Comer values of to are always zero

as implied by successive use of appropriate parts of (17).

454
Stability of the explicit form of solution is tested at all time steps and provision is made to double or halve the time step. If the larger of uAt/Ax and vAt/Ay Is less than 0.4 the time step

is doubled. If the larger of uAt/A x and v At/Ay is greater than 1.0 the time step is cut in half. Applying these conditions along with (12) maintains stability throughout the forward marching problem.

While an initial estimate of At is not required by this procedure some early time rapid adjustment of

At does occur for large A. In these cases a maximum early time At should be used for the first se- veral time steps because a very large At is implied by the stability conditions. Eq . (15) is overstable and no test is necessary for this part of the procedure.

With a view of the overall procedure we now give further consideration to F of Eq. (10) or H of

Eq. (13). Both F and H are, in computation, handled by the same program. Prior experience led to fourth order one dimensional approximations for F on the assumption that "time splitting" methods would

be used to provide isotropic behavior relative to the finite lattice. "Time splitting" is a process which involves computation of tentative values through the addition of horizontal flux contributions

followed by additions of vertical flux contributions. Here the latter computation makes use of the ten- tative values derived from the horizontal additions. In a linear sense "time splitting" results in the inclusion of diagonal values of the field variable such that truly two dimensional flow is treated. It

is an efficient way to obtain isotropic behavior since without "time splitting" or some equivalent procedure one may, in the extreme case, experience instability in the flow direction simultaneous to numerical diffusion transverse to the flow direction. Often these two effects can hold the numerical com- putation in check but the results may be badly in error since distortion occurs here even if the flow

is uniform but not along the coordinate axes. In two-dimensions then we must in some sense bring in mesh values of the field variables that are diagonally distributed relative to the coordinate directions

at (i,j).

Unfortunately, while "time splitting" is an efficient procedure to use it has been found that

a new type of instability can occur. This instability is slow and occurs only in non-linear cases. In

the given problem a vortex originating from buoyant effects may grow in intensity in a non-physical manner. This difficulty is not very different from that of using non-conservative difference methods. It

is perhaps less severe. Its degree of severity depends upon the non-linearity of the problem and the am- plitude characteristics of the approximation. The difficulty has its origin in an inconsistency that occurs in the velocity values that are effectively present in the implied cross differences. Since the cross derivatives are implied through "time splitting", this shortcoming goes unnoticed until the slow

growing instability occurs.

Here the difficulty is circumvented by explicitly programming cross derivatives as required to provide the linear equivalent of "time splitting" procedures. By so doing the linear stability conditions

are maintained and the inconsistencies in velocity values are avoided. If one expands the "time splitting" equations into a single step the cross differences will appear. Using these terms as a guide,

final layout of conservative expressions are developed from a Taylor's series expansion*. Consider

T"+1 = T'^+At ^'^^ '^'^^

3t J 2 I ^ 2

Because we are numerically separating convection and conduction we take

il = _ IhI _ Ai^

at 3x 9y

If we make use of (19) in (18) and drop velocity time derivatives we obtain

(18)

(19)

3^T _ 9 12 3^T 3T I, 3 f 3T _|_ ^ j ^^q)

, 2

- 3x r + 3y ! 3y I - 2 - 2 3t ^ 3x ^ J

^ y 3y

Here the (uv) terms are the first cross terms that must be explicitly programmed rather than implied

as in "time splitting". The (uv) term has two parts, one part is regarded as a skew flow correction

to the flux in the x direction, the other part as a skew flow correction to the flux in the y direction. With similar expansion of (18) to eighth order all cross differences for fourth order approximation may be developed. Proper combination of these terms can lead to simple expressions and reasonably fast computation. The fourth order forms are giveft in the Appendix.

One further consideration in the convective approximation is phase distortion. It is particularly

This technique was first employed by S. K. Jordan in his Doctoral thesis "Numerical Solutions for the Time-Dependent, Viscous, Incompressible Flow Past a Circle," Department of Aeronautics and Astronautics,

Stanford University, 1970.

455
pertinent to the problem at hand since the usual difference methods would quickly lead to meaningless

results for A>10^. It is essential to success of such calculations to have leading phase errors and

these should be small. Upstream approximations may be used to achieve this and if necessary several

different approximations may be linked through different magnetudes of a = uAt/Ax. Here we have used a combined fourth order upstream and central approximation (flow direction must here also be tested) for

a >_ 0.5. For 0.90 ^ a _< 0.5 the fourth order upstream approximation alone is used. If a < 0.09 a second order upstream approximation is used. Central approximations are used only for flow away from

solid boundaries if data points for upstream calculation are not available. In these latter instances

lagging phase errors do not lead to noise. The use of second order upstream approximations for a < 0.09

has to do with an anomoly in fourth order characteristics that is not present in second order. The above procedure is not the only one that may be used. In the given case it was the most expedient on the basis of available data on phase properties of the methods. The choice made also included consideration

of amplitude properties to limit numerical damping.

4. Flow Behavior

At the time of this writing we have computed several cases to give an overall view of variation of

flows with different Rayleigh number and Prandtl number. Computations have been made for A = 10** through A = 10-^^ at intervals of a factor of 10 and with a=1.0 For even powers of A, runs were

also made for a = 10.0 and a = 0.1. From these computations the flows can be classed roughly

into three groups. 1. Steady state flows (G < lO'') ; 2. Transition flows, unsteady and highly variable in behavior (10^ < G < 10^) ; and 3. Single circulation, high Grashof number flows (109 < G < 10l3).

The steady state flows are also single circulation flows characterized by the presence of a vertical temperature gradient in the central region of the enclosure but little horizontal temperature

gradient. The temperature gradients increase strongly near the walls. This type of behavior is illustrated in the steady solution of A = 10^, a = 1.0 of Fig. 1.

In the transition flows the variable behavior includes sinusoidal behavior at the low values of G. Mid-transition flows deviate from sinusoidal to include random occurances of buoyant plumes along the horizontal boundaries. In the upper transition flows randomness is increased and boundary layer en- trainment leads to counter circulations mixed with buoyant circulations. Figure 2 is an example of upper transition range flow.

Members of the last group are classed together because visually they exhibit little difference in be- havior. A single circulation (in the square region) is the main feature and is common to the whole

group. The interior fluid is essentially isothermal at the mean temperature and vorticity is almost completely absent there. One can describe these flows as having an inner core of ideal fluid flow and

a highly variable boundary layer behavior. The thermal and velocity boundary layers are thin but comer

regions are involved in the flow related to these layers. In Fig. 3 we include an example from this group.

Returning now to Fig. 1 we consider this group in more detail. In Fig. lA the streamlines of the flow are given. The highest speeds, as expected, are of flow near the vertical boundaries while the flow near the center is slow. The separated centers of circulation are in the same direction of rotation.

They occur because of two regions of buoyant vorticity associated with the heated and cooled vertical

walls. They are separated by a reverse flow tendency which has its origin in a slight reversal in the horizontal temperature gradient. In Fig. IB one notes that the highest values of vorticity occur at the boundaries. The sign is opposite to the two buoyant vorticity extremals occuring near the vertical walls.

This is the boundary layer vorticity which follows from our no-slip condition. The central extremal of vorticity is also of opposite sign to the main buoyant contributions. It also has its origin in buoyancy

but here in reverse to the main circulation. This reversed vorticity contributes to the attainment of steady flow in this range, along with the dissipation or frictional restraining forces. The latter mec- hanism is of coarse strongest at the boundaries. In the isotherms of Fig. IC one clearly sees the slight

reversal in horizontal temperature gradient at the center (the slant of the isotherms is downward to the right) . Increased heat transfer relative to a non-fluid material is obvious from Fig. IC in that the

flow leads to high gradients in temperature at the vertical walls. Near the walls conduction is in- hanced by the high gradients and in turn the flow in the center leads to exchange of warm and cold fluid

through the convective process.

The results of Fig. 1 are not new,, similar results have been obtained by Wilkes and Foots. To es- tablish a point of departure from this earlier work we have compared a calculation of A = 10**, a = .73 with the results by Foots. The results are the same in all essentials in the visual sense of the solution. To further compare results we have numerically obtained the Fourier coefficients of our computed

result for the disturbance temperature field (the linear gradient with T-|^-T =1.0 must be added to ob- tain the equivalent of Fig. IC) . In Table I we compare the numerical coefficients with coefficients

given by Foots. Differences in the results cannot be construed as error in the numerical results because

the analytic solution is also approximate. The differences in the second group of coefficients of Table

I is puzzling and may be an error by Foots in recording the numbers. Consistencies for even smaller co- efficients is good. Measured heat transfer at the cold wall as obtained by Foots is N = 1.706. We ob- tained N = 1.75 3 numerically.

456
Table I. Fourier coefficients of disturbance temperature distribution for A = 10 , a = .73

Term (kx.ky) Poot's

Finite

Difference

1,2

2,1

-0.1875

-0.1874

-0.1868

-0.1840

1,4

2,3

3,2

4,1

0.0019

0.006 3 -0.0107

-0.0314

-0.0082

-0.0166

0.0034

-0.0359

1,6

2,5

3,4

4,3

5,2

6,1

0.0017

0.0026 -0.0004

0.0016 0.0017

-0.0071

0.0024 -0.0000

-0.0014

0.0014 0.0024

-0.0067

1,8

2,7

3,6

4,5

5,4

6,3

7,2

8,1

0.0009 0.0018

0.0008

0.0007

-0.0003

0.0006 0.0008

-0.0018

0.0010

0.0011

-0.0001

0.0006 -0.0003

0.0002

0.0005 -0.0015

1,10

2,9

3,8

4,7

5,6

6,5

7,4

8,3

9,2

10,1

0.0001

0.0004 0.0003

0.0003

-0.0002

0.0001 0.0001

0.0003

0.0003

-0.0006

0.0003

0.0004 0.0001

0.0001

-0.0001

0.0002 -0.0001

0.0001

-0.0001

-0.0005

I, 12 2,11

II, 2 12,1

0.0001

0.0001

0.0000 -0.0002

Proceeding to Fig. 2 we include results for A = 10^, a = 1. In this range we have passed considerably beyond the point where solution was previously possible. The results portrayed in Fig. 2 are a

sinf.le still portrait of a rapidly varying flow. Standing alone these photos do not yield much understanding of detailed behavior, nor do we necessarily need detail of the origin of every small vortex. Animations of these solutions have proved to be valuable. With motion picture films of various representations new insights into the behavior become possible. The most important mechanisms beyond those evident in Fig. 1 is that boundary layer separation occurs and counter circulations to the main buoyant

tendency can arise. IVhen these do arise they may influence the temperature field sufficiently to be enhanced by buoyant effects. Reinforcement of counter circulations by buoyant forces is present in the case of Fig. 2. The instabilities that occur because of these successive effects are probably only

part of the influences that prevent the emergence of a steady state. In the transition range, steady

state is probably impossible although resonant effects might possibly be achieved through a highly

critical choice of rectangular dimensions of the enclosure.

In Fig. 2A the separation streamline is given and counter circulations may be identified by tracing

this streamline. Those circulations falling in regions toward the boundaries (exterior to the separation

streamline are counter circulations). The remaining significant centers of rotation are in the direction

of the basic buoyant tendency. In the vorticity plots of Fig. 2B we note that the buoyant contribution

from the vertical walls is confined to a very narrow vertical strip and this strip may be broken up into

small concentrations. These concentrations move upward along the heated wall much like air bubbles in water and give a wave character to the streamlines. Dominant characteristics in this range of A, even

457
in the presence of the rapid time variation, are the strong circulations in the upper left and lower

right corners. These circulations are inhanced by the rising and falling concentrations of bouyant vorticity from the heated and cooled walls. Boundary layer separation occurs immediately downstream from

these dominant circulations. The counter circulations so developed usually migrate along the horizontal

boundaries. Buoyant inhancement of the counter circulation is most likely in the vicinity of the lower

left and upper right corners where thermal boundary layers become stretched into plumes. In Fig. 2C such a plume is evident near the left side of the lower boundary.

Measurement of the heat transfer in the transitional and upper range is difficult because the un- steadyness can lead to wide extremes (numerically we cannot measure transfer right at the wall). Long

term averages must be taken. Currently we are still in the process of dealing with these measurements

along with necessary work that must be done on overall data reduction. For the calculation of Fig. 2A

(A = 10®, a = 1) we estimate N~32.0. Numerical programs to give late time average heat transfer values

have not been employed at this writing.

Finally we consider the last group (Fig. 3) in greater detail. The single circulation behavior of

the high Rayleigh number flows is somewhat of a surprise because here the character of the flow is al- most the same for a very wide range of values of the parameters. Quantitatively the flows remain dif- ferent particularly in the speed of circulation at late times or the rate at which the circulation speed

increases from the initial no flow state. In this range the viscous and conduction effects are essentially absent at the central region but intense at the boundaries. The results show dramatically why

boundary layer theory has been so successful in manv theoretical studies of fluid flow. While the un- steadyness far exceeds that of the transition range it is almost entirely confined to a thin layer at the boundaries and to the corner regions. There is eccentricity in the flows that does not appear to diminish over the range of time covered by the calculations. An almost perfectly circular flow may be disrupted by migrating corner activity. Such a disruption may lead to increasingly eccentric flow but never a return to the type of flow of the transitional range.

In these flows it is not uncommon for plume roll up to occur so that a hot or cold spot is carried

out into the main circulation. Once caught up in the main circulation it may undergo several revolutions

before intermingling again with the thermal boundary layer or getting trapped in a comer of the flow region

The single circulation behavior must be a consequence of the very low dissipation and slow conduction process in the interior flow region. In the absence of some roughness or protrusion from the boundary to inhance mixing the interior region remains isothermal. It is also free of vorticity because

boundary generated vorticity does not penetrate to the central region and the isothermal fluid does not contribute buoyant vorticity.

Early transitional behavior from the no flow initial condition does involve similar behavior to that of the transitional range flows. It may however be of value to investigate the effects of the initial

state. Presumably late time solutions for an initial state of the interior fluid at the cold temperature

would ultimately be the same as the given solutions of Fig. 3, but no calculations of this type were

made

In Fig. 3A we note that counter circulations to the main circulation are very limited. The apparent

smooth appearance of this still shot is not indicative of the actual behavior. Small extremals of vor- ticity (Fig. 3B) or hot spots of temperature (Fig. 3C) that occur on occasion in the central part of the flow have been timed to estimate a mean speed of the main circulation. In an 8 ft. square enclosure

the circulation time is roughly 5 seconds. This is not unreasonable but much work still needs to be done

in comparing our results with experiment. It is uncertain to what extent the numerical result provides

for the mixing that Would occur in the turbulent flows as observed in the laboratory.

5. Acknowledgements

The author wishes to acknowledge the assistance of Donald E. Schreiber^° whose graphics programs for

the IBM 2250 made it possible to reduce many numbers to very meaningful pictures. Acknowledgement is also due William E. Langlois for his review and recommendations of the work.

6. Refe

[1] Foots, G. , "Heat Transfer by Laminar Free Convection in Enclosed Plane Gas Layers",

Quart. J. Mech. App. Math., 11, 257-273 (1958).

[2] Wilkes, J.O. , "The Finite Difference Computation of Natural Convection in an Enclosed

Rectangular Cavity", University of Michigan,

Ph.D. thesis (1963).

nces

[3] Deardorff , J.W. , "A Numerical Study of Two- Dimensional Parallel Plate Convection", J. Atmos. Sci. 2_1, 419-438 (1964).

[4] Fromm, J.E., "Numerical Solutions of the Nonlinear Equations for Heated Fluid Layers",

Phys. Fluids 8, 175 7-1769 (1965).

458
Aziz, K. , "A Numerical Study of Cellular Con- vection", Rice University, Department of Chemical Engineering, Houston, Texas (1965).

Roberts, K.V. and Weiss, N.O. , "Convective

Difference Schemes", Math. Comput. _20, 272-

299 (1966).

Fromm, J.E., "Practical Investigation of Con- vective Difference Approximations of Reduced

Dispersion", in High-Speed Computing in Fluid

Dynamics, International Union of Theoretical

and Applied Mechanics Symposium, American

Institute of Physics, New York, New York (1969).

[8] Marchuk, G.I., "The Automatic Construction of Computational Algorithms", translated by G.J. Tee, Technical Report CS30, Computer Science

Department, Stanford University, 1965.

[9] Bunemann, 0., "A Compact Non-Iterative Poisson

Solver", SUIPR Report No. 294, Institute of Plasma Research, Stanford University, Stanford

California (1969).

[10] Schreiber, D.E. , "A Generalized Equipotential

Plotting Routine for a Scalar Function of Two Variables", IBM Research Report RJ 499 (1968).

459
Appendix

In this appendix we describe the form of the convective approximation used in the calculations. We shall give the form of the flux term in the u direction only, but for the various ranges of a = uAt/Ax

as indicated earlier. It must be remembered that the flux as given is only half of the required compu- tation for a given mesh point . If the flux is added to the point on the right and subtracted from the point on the left the speed of computation can be reduced by half. Also the same convective program

can be used for both vorticity and temperature if these variables are defined the same relative to the

grid. The fluxes in the vertical direction may be inferred from those given here for the horir.ontal

We define

u , At V. , . At

a. ^ ,„ . = T

' and S. , . = ;•' 1-1/2, J Ax 1-1/2,3 Ay

where

Vi/2,j = ^*i-i,j+i + '^i,j+i - "^i-i.j-i - *i,j-i^ /

^-l/2,j = ^"^i-l.J-^.j^ /

If |a|<.09 we use an upstream second order approximation. We here write the central approximation

terms with the understanding that if a>0, a is replaced by (a-1) and i indices are reduced by 1. Further if a<0, a is replaced by (a+1) and i indices are increased by 1. To make addition and subtraction of flux contributions possible as previously mentioned the powers of a must further be modified. For example must be replaced by [(a-l)^-l] = a^-2a so that Eq. (11) does indeed

apply without a shift of index on the leading term of this equation. Cancellation of the appropriate

linear terms (terms that do not contain a) can readily be varified for the difference forms here given.

This however requires writing out the complete expression of both the flux into and out of the cell of interest

Define

_ = T. , . + T. . , D. - = T. , . - T. . 3,0 1-1,3 1.3 3,0 1-1,3 i.J

^6,2 ^i-1,3+1 '^1,3+1 ' °6,2 ^i-l,j+l ^i,j+l

and . = T. ^ . , + T. . . , D_ ,= T. , . , - T. . ^ 7,4 1-1,3-1 i>3-l 7,4 1-1,3-1 1)3-1

Here the subscript numbers follow a procedure of successively numbering points in a counter clockwise

direction starting with the point just to the right of a point of interest. The symbol Ci,3) and the symbol 0 are synonymous.

Now with index i-1/2 implied for a, 3 and F we write

7^ F = 1/2 a S- . + 1/8 a6(S, , - S, ,) Ax 3,0 7,4 6,2

+ 1/2 a2 Q + 1/12 aB2(s^ ^ - 2 ^ + 2^

+ 1/6 a2g(D^ 4

" °6 2'' -"-^^ a^e>^(D^ ^ - 2 ^ + ^)

For 0.9 <^ |a| _< .5 we use a fourth order upstream expression and for .5 < |ci| 1 we use the average of the upstream and central expressions. Here again we give only the central difference ex- pression. The same rules apply on replacment of a appropriately with (a-1) or (a+1) and shifting

indices as previously indicated.

Define in addition to the above sums and differences

460
T. + T. , D. = T. - T. 15,10 i-l,j+2 i,j+2 ' 15,10 1-1, j+2 i,j+2

T. + T = T. - T. . 18,12 i-l,j-2 i,j-2 ' 18,12 i-l,j-2 i,j-2

T. „ . + T. T. 11,1 i-2,j ,i+l,j ' 11,1 i-2,j i+l,j

T. + T . = T,. - T. 16,5 i-2,j+l i+l,j+l ' 16,5 i-2,j+l i+l,j+l

T. + T T. - T. 17,8 i-2,j-l i+l,j-l ' 17,8 i-2,j-l i+l,j-l

= T + T. 22,14 i-2,j+2 i+l,j+2 ' 23,14 i-2,j+2 i+l,j+2

and T. + T T. T. 23,19 i-2,j-2 i+l,j-2 ' 23,19 i-2,j-2 1+1, j-2

We may now writejwith index 1-1/2 implied for a, 6 and

42

Ax E1=1

Where the B's and X's are given in Table II (A and B) , and the numerical coefficients associated

with the B's are given in Table III.

Table II-A. Leading terms and differences of fourth order approximation.

B X

1 11 a ^3,0

2 ^21 " ^11,1

3 ^11^11 ° 6/2 ^7,4

- '6,2

4 ^11^21 <^ S/2 ^18,12 " ^6,2 " ^15,10

5 ^21^1 " 6/2 ^17,8 " ^16,5

6 ^21^21 " 6/2 ^23,19 " '17,8 ^16,5 " '12,14

7

8 ^2

A22 ^.0

°11,1

9 ^11^12 6^/3 '7,4

- 2^3,0+^6,2

10 ^1^22 ° 62/3 ^18,12 - ^7,4 - ^6,2 +

'15,10

11 ^21^2 ° 62/3 ^17,8

12 "^21^22 e2/3 ^23,19 " ^17, 8 ~ ^16,5 + '22,14

13 2 A A ^^12 11 a2B/3 °7.A

- °6,2

14 2A^2'^21 a^B/S °18,12 - °7,4+ '^6,2 - °15,10

15 2^22^11 a26/3 °17,8 - °16,5

16 2^22^21 a26/3 ^23,19 - °17,8+ ^^16,5 ~ ^^22, 14

17 A23 a3 X2 - X

1

461
Table II-A. continued.

B X

18 A A

11 23 4 3 19 ^21^23 ^6 - S

20 ^12^12 °7,4 - 2^3,0 +

21 A A 12 22 a2B2/2 °18,12 ~ °7,4

" \,2 +

^15,10

22 ^22^12 a2B2/2 °I7,8

- ^ ^16,5 23 ^22^22 a2B2/2 ^^23, 19 ~ ^17,8 - °16,5 + °22,14

Table II-B. Leading terms and differences of fourth order approximation, (continued)

B 1 X

25

^^23^11 "^'^^^ 3A„,A., a36/4

23 21 S - ^3

26 ^24 Xg - 3X^

27

28

^11^24 A„A-, oB'^/S 21 24 ^12 -^^11

29

30

2A, .A„. a2B3/5

12 23 2^22^23^4 ~ ^13

^16 " ^15

31

32

^^23^12 '^^^^^

3^23^22 "'2/5 hi ~ ho

33

34

^^24^11 ""^"^^^

^"^24^^21 "^^/^

h5 " ^^13 h6 ~ ^^14

35

36

A^2A24 "23^/3

^22^24 "^^''''3 ^21 " -^^20 X23 - 3X22

37 A23A23 a3B3/2 ^19 " ^18

38

39

2A2^A^2 ""^S^/S

2^24^22 "'''^^''3 ^22 " ^^20 X23 - 3X2^

40 3A2 3A2^ a 334/7 ^28 " ^27

41 4A2^A2 3 a'*s3/7 X30 - 3X25

42 ^24^24 ^36 " ^^35

462
Table III. Coefficients of fourth order approximation.

^1 7/12

hi 15/24

- 1/12

- 3/24

^21 - 1/12

^22 - 1/24

^2 3 1/12

^24 1/24

Figure lA. Steady streamxme solution for A = 10^, c = 1.0. The plot increment Aij; = 0.05ft^/sec.

i/j = 0 at the boundary and 0.025 at the first contour from the boundary.

Figure IB. Contours of constant vorticity for A = 10^, a = 1.0. The plot increment Ao) =0.2/sec. The

minimum displayed contour value is -0.5 and is the inner contour of the two symetric ex- tremals, oj maximum at the wall is 2.47.

Figure IC. Isotherms for A = 10^, a = 1.0. The plot increment is AT =0.5°F for the overall wall tem- perature difference T - T = 10.0.

453
Figure 2A. Late time streamline solution for A =10^, a = 1.0. The plot increment Atjj = 0.02£t2/sec.

The separation streamline ijj = 0 is given and is the reference contour.

Figure 2B. Vorticity contours corresponding to Figure 2A. Ato = 0.75/sec. u maximum at the wall is 12.9.

Figure 2C. Isotherms corresponding to Figure 2A. AT =0.5°F.

Figure 3A. Late time streamline solution for A = 10^^, a = 1.0. The plot increment Aijj = l.Oft^/sec.

The separation streamline i|; = 0 is given and is the reference contour.

Figure 3B. Vorticity contours corresponding to Figure 2A. Aoi = 10.0/sec. co maximum at the wall is 145.4.

Figure 3C. Isotherms corresponding to Figure 2A. AT =0.5°F.

464
Fortran IV Prograxn to Calculate Absorption

and Transmission of Thermal Radiation by

Single and Double-glazed Windows

G. P. Mitalas and J, G. Arseneault^

Division of Building Research

National Research Council of Canada

Ottawa

In the calculations of the heating or cooling load for a room,

it is necessary to know the fraction of the solar radiation incident on the outside of the window that is absorbed by the glass and the fraction that is transmitted to the interior of the room. This program calculates the absorptivity and transmissivity of windows

made of common glass. In addition the coefficients for a 5th degree

polynomial are calculated to allow rapid (although less accurate)

determination of these factors for a given window and given incident

angle of solar beam.

The calculations by this program are based on:

(a) Fresnel's formulae (relation between incident angle, refraction

angle and reflection of parallel and perpendicular polarization

components of radiation).

(b) Snell's law (relation between refraction and incident angles).

(c) Exponential extinction law (relation between glass sheet thickness,

extinction coefficient for glass and absorption of radiation in a

single pass).

The calculated factors for single and double glazed windows

account for the multiple reflections and absorptions that occur when

radiation passes through more than one air-glass interface.

The 5th order polynomials, that relate the factors and the cosine of incident angle, are fitted by the least-squares method

using the calculated values for incident angle 0° to 90° in one degree

steps. The coefficients of these polynomials are used to calculate

diffuse radiation factors assuming that the diffuse radiation from

the sky and the ground has equal intensity at all incident angles.

Key Words: Absorbtion, glass, radiation, solar trans- mission, window.

Research Officer and Computer Systems Programmer, respectively.

465
1. Expressions for Absorptivity and T ransmis sivity of a Window

The single air-glass interface reflectivity is given by Fresnel's formulae

tan^ (9^ - e^) " tan (6^ + e^)

sin^ {9^ - 9 )

sin (9^ + 9^)

where r // and r^ = the reflectivity for radiation that is polarized with the electric vector parallel and perpendicular, respectively, to the plane

that contains the incident beam and a normal to the interface.

1

The refraction angle is related to the incident angle by Snell's law.

incident angle

refraction angle

Sin 9^ = n Sin 9^ (3)

where n = index of refraction for the glass.

For normal incidence 9 = 9^ =0

2 fn - W ^""^ 7/ \

The fraction of the radiation that is absorbed in a single pass through a glass sheet of thickness

L. is given by

a = 1 - exp (-KL/Cos 9^) (5)

where K = extinction coefficient for glass.

The absorbtivity. A, transmis sivity, T, and reflectivity, R, of a sheet of glass and doubleglazed window are calculated for parallel and perpendicular polarization separately. The average

values of A,, and A , 1 , , and T , or R// and R are applicable for non-polarized incident beam.

The factors A, T, and R of a single sheet of glass (taking account of multiple reflections of both surfaces and multiple absorbtions) are given by

A . a(l - r) [1 + r(l - a)]

1 - r^ (1 - a)^

466
(1 - r) (1 - a)

1 - (1 - a)^

(7)

and R r +

r(l - r)^ (1 - a

)^ 2 2

1 - (1 - a)

(8)

where r and a are the single pass factors. The factors for parallel and perpendicular polarization

components are calculated when r - rjj and r = r respectively.

The double-glazed window absorptivity, ^-^-q ^'^'^ ^ZH' ^^'^ transmis sivity, T^^, are given by

2D 1 - R^R^ (9)

ID

^1 ^2

1 -R^R^ (10)

and

^1^2

"D 1 - R^R^ (11)

where the quantities with subscript D are for double-glazed windows and those without subscript D

are for a single sheet of glass. The subscript 2 denotes the factors for the outer pane and subscript

1 refers to the inner one.

2. Polynomial Coefficients

The 5th order polynomials, that relate the factors and the cosine of incident angle, are fitted by the least-squares method. For example, the polynomial that relates A and cos 9 , is

A IC , . (cos

A, 1 (12)

where ^ = calculated polynomial coefficients for an absorbtivity A.

Polynomials are fitted only to the non -polarized beam factors using the calculated values for

= 0° to 90° in one degree steps.

3. Diffuse Radiation

For heat -gain calculations through a window it is usually assumed that the diffuse radiation

from the sky or the ground has equal intensity at all incident angles. The factors for diffuse radiation

of this nature are given by

n /2

F = / F(e ) sin 29 d9 (13) diffuse

467
where F(9) is the factor for direct solar beam and is a function of the incident angle 6. The substitution of the polynomial e;fcpression for F(6) and integration gives

5 F

Ci

(14) diffuse i + 2

where Ci 5th order polynomial coefficients that relates the factor F and

cos 9 , .

4. General Description of the Program

This Fortran IV program is for an IBM -System/ 360 operating system.

The coding sheets, a sample of output and the flow diagram (fig. Al) are given on pages A-1 to A -7 of Appendix A.

Input:

Card 1 - columns 1-10 n, index of refraction

Card 2 - columns 1-10 KL inside

1 1 -20 KL outside.

Format: Floating point, 10 columns.

This paper is a contribution of the Division of Building Research, National Research Council of Canada, and is published with the approval of the Director of the Division.

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469
start

200 Print

input

data

Set Calcul.

1 W 01=0 Cos 01 —

Calcu late

Aj, 1 , A2, II T2 , II , Rj, 1 , "z- II A| , 0 . Aj, 0 and To

30

Calculate

C't s for A I and T

KL out *0

KL outN

= 0

Calcu late

A|,i , A|, ii,T|,x

T| , II , R I , x . R i . II T| and A,

Calculate

C'lS for A2

Print the factors

for selected incident angles

\8,t^0

30

Calcul.

rii and

r,

KL out = 0

Calculate

C, s for

R

180 Calcul.

diffuse

rad. factors

KL out = 0 Indicates single glazed window

Print Ct s and diffuse

rad. factors

Figure Al - Flow Diagram for Absorption and Transmission Factor Calculation Program.

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476
A Computer Analysis

of Window Shading Coefficients

ty Calculating Optical and Thermal Transmission

E. Isfalt

The Royal Institute of Technology

Stockholm

Measurements of solar heat gain through windows with different shading

devices are rather complicated and need a calorimeter or some other kind of

expensive equipment. The optical properties of a single layer can be found

quite easily by spectrometer measurements in a laboratory. The paper describes

a method to calculate the solar heat gain through combinations of layers

outgoing from the optical data for the single layers. The ALGOL-program

developed to solve this problem allows an arbitrary number of layers, anyone could be diffusing. The direct and total transmission through the combination,

the reflexion, and the shading coefficients eire calculated. The results of

a theoretical investigation of different window combinations are presented.

Key Words: Artificial lighting, daylighting, daylight distribution,

fenestration, light transmission, polarization, shading coefficient,

shading devices, solar heat transmission, soleir optical properties,

solar radiation, window shading coefficients.

1 . Introduction

For a correct choice of shading devices many different aspects should be taken into consideration.

Apart from the solar heat reduction, illumination demands, glare, operating possibilities, dirtying,

sound, aesthetical demands etc. should be paid regard to. In most cases these points of view should

be taken into account at the lowest possible cost. Information on shading devices is often restricted

to values of the solar heat reduction. Below it is indicated how calculations of the transmission

of sunlight as well as solar heat can be made starting from optical data for the different layers

of a window. Thereby it is possible to determine the heat flow into a room with regard to solar heat

and artificieil illumination.

2. Concepts and Definitions

The optical properties of a translucent layer is indicated by its transmission, T, reflexion ,R, and absorption. A, of incident radiation. For these quantities the following is edways applicable

T + R + A = 1 The optical properties are due to the wave-length of the radiation. Solar radiation is within a reinge

of wave-length with a certain distribution within this range.

On calculations of this kind it is presupposed that the optical properties are average values

for solar radiation, i.e. they are valid with regard to the distribution of wave-length of the solar

radiation and the properties of the layers (Solar-Optical Properties).

The part of the incident radiation which is absorbed, part A, causes a heating of the layer.

Hereby part of A will be transmitted into the room by long-wave radiation and convection, the secondary

transmission.

Thus the solar heat transfer through a window consists of two parts, the direct and the secondary

transmission.

The direct and total transmission is due to the angle of incidence of the radiation. For most window combinations curves of almost the same appeEirance are applicable. The curves diverge approximately by a constant factor. This implies that the transmission of a certain window can be related to

477
For continuity reasons this, is also achieved

= ^(2)

%ec = ^1)2

Finally this definition is made

m, ^ = m + m. + m. tot y f 1

From these equations , q^, t^ and t^ are eliminated and the secondary transmission is obtained from

the expression

t^ - t^ m m + Sec" m^ ^ ^1(2) ^ ^(1)2 * m, ^ tot tot tot

Here the first term constitutes the heat transmission owing to the difference of temperature between

the outside and the inside, the other terms aire contributions from absorbed solar radiation.

Similar derivations can be made for several layers . It can be observed that the inward-flowing

fraction of the absorbed radiation in a layer is always the ratio of the thermal resistance from the

layer to the outside air to the total thermal resistance of the window.

h. Arbitrary nmber of layers. Computer Program

The extensiveness of the calculations increases rapidly by the number of layers. The equations

for the course of radiation in the layer combination vary owing to where a possible diffusing layer may have its position. Instead of using different equations for different cases when calculating with

a computer the radiation components are followed and added successively until all contributions are exceedingly small.

The core of the ALGOL-program which has been drawn up for these calculations consists of a procedure which divides the radiation components at each layer into one transmitted, one reflected

and one absorbed part. The radiation components are stored in a two-dimensioned array

IN [from, to]

The layers are numbered 1, 2, 3 etc... NUMBER from the outside. (Capital letters for identifiers).

The calculations proceed by steps forwards and backwards through the window. At each step one element

is divided up according to the pattern below

ATOT [1] ATOT [2] ATOT [3] + + + etc. «- In[2,1] in [1,2] * m[2,3]-* etc.

etc. etc.

When the radiation has passed through or has been reflected against a diffusing layer the optical

properties of the different layers which are stored in the arrays T NR , R NR and A NR are exchanged for the values applicable to diffuse radiation.

The direct transmission constitutes the sum of all elements IN [NUMBER, NUMBER + 1] and the reflexion the sum of all elements IN [1 , o] .

When the calculation has proceeded so far that all contributions are smaller than a given tolerance,

the direct transmission, the reflexion amd the absorption in each layer are summed up. This sum should

be = 1 . Finally the secondary transmission is determined with the aid of the thermal resistances which

were given as data and the calculated values of the absorption in the different layers.

478
the transmission through a reference window and thus be characterized with the aid of one single factor

which is independent of the angle of incidence. This factor is called the Shading Coefficient.

If the solar radiation values are determined once for all with regard to the reduction in the reference window the angles of incidence of the solar radiation need not be determined any more.

In Sweden an unshaded two-glass window of ordinary window-glass is used as a reference. (The total

transmission when the radiation is falling in perpendicularly = 0,79).

The directly transmitted short-wave radiation and the secondarily transmitted solar heat are distributed in different ways in a room. The short-wave radiation is reflected between the room-surfaces

whereas the long-wave radiation broadly speaking interprets the room-surfaces as being black. When

calculating with our main program [2] this difference is taken into consideration. For this reason

two shading coefficients and F^ have been introduced: F^ mxiltiplied by the incident solar radiation

through the reference window gives the totally transmitted solar heat, F similarly the directly

transmitted part. If the spectral changes of the radiation are small at the passage through the window,

Fg is a value of the light transmission.

3. Double panes

3.1 Short-wave radiation

When several layers are combined they affect each other by reflexions between themselves. The

course of radiation when there are two translucent layers can be seen in Fig. 1, in which the denominations used below are also given. The repeated reflexions give rise to geometrical series, the sums

of which are included in the following expressions:

The direct transmission is achieved from the expression

T • T

1 2 12 1 - •

The reflexion

2 T • R

1 2

'12 " "1 1 - • R,^ = R, +

The absorption in layer No. 1 with contribution of layer No. 2 T • R ^(2) = \ ' 1 -'r^ \

)

The absorption in layer No. 2

A, ^1 • ^2

(1)2 1 - R^ . Rg

3.2 Long-wave radiation and convection

The secondary transmission can be derived from Fig. 2.

For the denominations introduced in this figure the following is applicable

t = temperature m = thermal resistance

q = heat flow

The heat flows are given by

y

479
5 . Applications

3•^ Influence of polarization

As to calculations including several panes the effect of the polarization is often taken into account. This is not the case in this program. Fig. 3 shows the direct transmission through a two-glass window

determined with as well as without regard to the polarization. It is evident that the imperfection

is not noticeable until the angles of incidence are larger than about kO . If the determination of

and F^ is made with layer data valid at an angle of incidence of for instance 30 the imperfection

is negligible.

5.2 Different nijmbers of panes

The availability of the program is first illustrated by the following example:

Calculations with the number of ordinary window-glasses (T = 0.86, R = 0.079) increasing from _^

2 to 6 have been made. Thermal resistances: outside 0.06, inside 0.11, between glasses 0.17 m^ °C W

Fig. k shows the result. The secondary transmission increases by the number of glasses. The direct

transmission, however, decreases more so that the total transmission decreases by £in increasing

number of panes.

5.3 Windows with drapes

The optical properties of a drape fabric is variable within wide limits owing to the fact that

the closeness of the texture as well as the color of the fabric can be varied. Calculations have been

made for varying types of drapes in combination with two panes of ordinary window-glass (T = 0.86)

placed on the outside, between the panes and on the inside. The direct transmission indicated by Fg,

is supposed to be the same for visible light as for radiation in the whole solar spectrum. Since

the primary purpose of the window is to let in the daylight it is natural to start from F^ as an independent variable, which is the case in the figures 5-7. The total transmission indicated through

F^ is a dependent variable and T and R of the drape fabric are parameters.

The following values of heat resistance in °C W ^ have been used:

outside 0.06 inside 0.11 glass to glass 0.17 glass to drape 0.13 when drape outside, else 0.15

6. Utilization of calculated data

The following example is intended to illustrate how the values which are achieved from the

diagrams can be used in a chain of calcxilations concerning the heat flow into a room due to sun and

illumination.

6.1 Assumptions

The example refers to a room with the dimensions

breadth = 2.5 m

depth = l+.O " height = 2.9 " 2 window area = 3>Zh m

Other pre-requisites

latitude 60°N orientation South

climate August, clear day

Window: drape between 2 ordinary window-panes

The shading coefficient F^ = U0%. This value is achieved according to Fig. 6 for instance

with combinations according to the table below.

480
Fabric Transmittance % Fabric Reflectance % %

11 38 10 21 50 20

29 60 30

The value of F^ is decisive for the daylight in the room. Owing to the demands of illumination

Fg therefore is determining for the heat energy from artificial illumination.

6.2 Solar radiation

through the refere

determined by a program from information about latitude, longitude, date and orientation

_2

The incident solar radiation, in ^fei , through the reference glass (unshaded double glazing) is

6.3 Visible radiation

The sunlight is supposed to be in keeping with the incident solar radiation and is indicated by

a luminous efficiency factor.

6.3.2 Distribution of daylight

The distribution of daylight in the room is achieved with the aid of a program which determines

the absorption factors for radiation from the window against horizontal surface elements placed

arbitrarily in the room. The calculations thus presuppose a diffuse distribution of the light. In the

result an infinite amoiont of reflexions between the room surfaces is included.

For the room in question the program gave the following values of the ratio of the lumance of

the window surface to the daylight illumination along the central line of the room at a height of 0.8 m

Distance from window, m ratio

1 0.212

2 0.108 (middle of room)

3 0.068

6.k Artificial lighting

The calculations made so far have given the incident solar radiation and the daylight hour by hour

in the room. Fig. 8 shows the incident solar radiation in W m"^ window area and the illumination in lux

in the centre of the room for = 10, 20 and 30^.

The consequence of different demeinds of illumination in the centre of the room can now be examined.

The calculations concern the time between 8 and l6. When the daylight is insufficient it is presupposed that the illumination is switched on. With different demands of illumination Fig. 8 gives the

following illumination periods for different values of F^ Artificial lighting, hours

Lux

^2 500 1000 1500

10 3.5 8.0 8.0

20 0.5 3.5 8.0

30 0 1.1* 3.5

6.5 Total load

Provided that the armature gives 20 lumens per watt the energy with which the room is supplied

from sun and illumination during the day gets the following values:

Energy from sun and

artificial lighting, W h

Lux

^2 500 1000 1500

10 6100 9200 11200 20 5300 6950 1 1200 30 5200 5900 7800

481
On the basis of these values Fig. 9 has been drawn. The figure shows the great importance of

considering the light as well as the solar heat transmission when choosing shading devices. The heat load as a result of sun and illumination at a demand of illumination of 1000 lux is about 30% larger

for a drape with F = 13% than for one vrith F = 30%. The incident solar heat is the same in both

cases (F^ = kO%)

References

ASHRAE Handbook of Fundamentals, Ch. pp U67-512 (1967) XXVIII Brown, G., Simulation by digital computer program of the temperature variation in a room. Contribution to this symposium.

482
M(2)

1-1

jtdoor indoor

^sec

M(2) Hm

'sec

2. Denominations used to derive the secondary

trajismission through a two-glass window.

transmittance , %

80

60

40

20

0

ith regard to | polarization

without reg<3rd to polariz 3tion\\

0 20 40 60 80

\' 100

angle of incidence

3. Direct transmission through a two-glass

window determined with as well as without

regard to the polarization.

483
1.0

I

total transmission

secondary trans- _

mission

I I I

Total and secondary transmission through

different numbers of panes.

5 6

number of panes

' 1 1.0

Shading coefficient F (for total transmission) as function of coefficient (for direct trans- mission) for double glazing with

drapes. Drape solar optical

properties are parameters.

0 V. 1 1 1 1 1 0 .2 .4 .6 .8 1.0 F2

484

4 000

10 20

F,-40%

30 40

486
Optimum Shape of External Shade for the Window

to Minimize Annual Solar Heat Gain

and to Maximize View Factor

K . Kimura

Department of Architecture

Waseda University

Tokyo , Japan

One of the most fluctuating components of space cooling load

is associated with solar heat gain from windov/s . Overhangs, side

fins or screen type of sun shades are v/idely used to avoid unwanted

heat from the sun. On the other hand the windov/ is expected to provide sunlight into the occupied space and allow people to look

outside through it. Considering that the design of shading devices

should be coordinated to both of these factors in conformity with

aethetics , the author developed a procedure to determine the

optimumshape of external shade for a rectangular window of a given

proportionfacing to a specified orientation so that it could intercept direct radiation as much as possible and be fabricated with

a minimum amount of material, providing a maximum possible view for

the occupants. Iteration process is required to obtain the geometry

of the sun shade composed of two pairs of horizontal and vertical

flat plates with optimum width and tilt angle. This is follov/ed

by the estimation of the annual total solar heat gain from the

window with the brise-soleil thus designed, talving account of

reflection and re-radiation from sunlit surfaces of sun shade as well as direct and diffuse solar radiation transmitted through the

shade. The heat exchange problem around the shade assembly is

approximately solved by the method similar to that to calculate

the weighting factors relating heat gain to cooling load. The

routines developed are intended to be incorporated with graphical

display system or plotter drawing system so as to be an effective

aid for the architectural design.

Key Words: Computer, optimization, brise-soleil, windov/,

solar radiation, shadow, overhang, side fin, view factor,

heat gain , design

1. Introduction

Design of sun shades for the building fa9ade is one of the most interesting phases

of architectural design associated with environmental engineering. In determining the

shape of sun shades the designer wants to Ivnow the actual effects of shading devices in

terras ofannual energy savings owing to the reduction of solar heat gain as well as the

cost to fabricate it. It is considered necessary, therefore, to offer the designer the

optimum range of key elements defining the geom.etry of sun shade so that he can determine

the shape of it with his idea and aethetical judgement, eliminating such unnecessary

steps that he has to draw many figures of obviously ineffective sun shades. Determining

the shape, the computer can calculate the cooling load for air conditioning engineers as well as the manufacturing cost to justify the installation of sun shades.

Conventional architectural design involves various phases of design process such as

v/orking on drawings, refering to informations, mailing discussions and so on. In order

to use the computer as a design partner the design procedure must be systematized aiid the

design operations be performed in a logical flow without losing artistic inputs. This

"Associate Professor, Department of Architecture.

487
is the general concepi; of computer aided design and the attempts made on the sun shade

design is based on it.

2. Basic Concept

2.1 Design Process and Use of Computer

The process of architectural design is too complexed to be thoroughly systematized,

but efforts are being made by computerists to seek the possibilities how far the design

process can be computerized taking various human factors into account. This approach is

being attempted by Negroponte (1)-^ and his colleagues in their program development for

urban design. For simplicity in this paper it is presupposed that the design process is

composed of the combination of various minor processes and they may be either inductive

or deductive depending on situations.

It is considered that the conventional process of architectural design consists of

multiple repetitions of making decisions based on various requirements and designer's

idea and judgement through the routines of deriving effects caused by the decision and

checking conflicts ajnong other decisions in reference to the design criteria. This is

shown on the left side of Fig. 1, Since it is always advantageous to use computer when

calculation involves a number of repetitive routines, the design process v/ith computer

should be so arranged as to include repetitive routines. The right side of Fig, 1 shows

a flow of the deductive design process where the computer gives a number of answers that

meet the requirements and suffice the criteria and the designer only has to select one

out of them based on his idea and judgement. If the computer gave only one answer, which

might be the most optimum, there would be no room for selection. It is desirable, therefore, that the optimum range of key elements defining the object should be provided,

because the most optimum one may be much inferior to another v/hen refered to the designer's idea.

On the other hand conversational or on-line type of design process with computer,

which might be called inductive design process , can go through the same routine as the

conventional one as shovm on the left side of Fig. 1 again. When the graphical display

system ;vere used, for example, the calculation of checking conflicts and deriving effects

can simultaneously be made by the main processor and the designer can change as many

decisions as he likes while sitting down at the C.R.T. console.

2.2 Basic Approach to Design of Sun Shades

The object problem for sun shade design presented in this paper is to determine the

optimum shape and to calculate heat gain from windows excluding the cost estimation routine. The overall phase of it is shown in Table 1 in the list up form of input and output items

,

Table 1. Input and output of object problem

I/O Description Symbol Item Unit

Location of building LAT

LONG

Latitude

Longitude

degrees

degrees

Input

Wall orientation V/0

Shape of v/indow to which B sun shade is to be attached

Normal direction to wall

surface

Proportion of v/idth to height of window

degrees

from south

Design criteria PSA Upper limit of sunlit area

per window area

Optimum Shape of sun shade

DL Projection of overhang per

windov/ height

FL Projection of side fin per — windov; height

Figures in brackets indicate the literature references at the end of this paper.

488
Output

Reference data

AA

AB

AM

AS

VF

HG

Tilt angle of overhang

Tilt angle of side fin

Drav/ings

Area of material per

window area

Sunlit area per

windov; area View factor

Heat gain through

fenestration

degrees

degrees

watt/mp or kcal/m h

Table 2 shows the overall flow of the object problem subdivided into three phases

for the conversational type of design process in the sequence form of execution routines,

v/here Enter means to enter the input data at the keyboard and Xeq. means to execute the

calculation routine marked after that. These three phases also can be applied to the

deductive design process v/hich does not necessarily require C.R.T. console or terminal

units

,

Table 2. Sequence of execution routines

Phase Operation Output

I Enter LAT,LONG,WO

Xeq. MAXSOL IDV Maximum direct radiation upon window

TIMAX Time when IDV occurs TPM Tangent of profile angle at TIMAX

TGM Tangent of wall solar azimuth at TIMAX

II Enter B, PSA

Xeq. SHAPE DL, FL, AA, AB

Drav/ings

Xeq. REFER AS, AM, VF

III Enter TIME

Xeq. DSOLT IDVT Direct solar radiation transmitted

through shade throughout the year

Enter IVEATA (weather data)

Xeq . HGAIN RDT Direct radiation transmitted through

shade and glass

RFT Diffuse radiation transmitted through

shade and glass

HTTR Overall heat transfer at inner surface

of fenestration

*MAXSOL, SHAPE, REFER, DSOLT, HGAIN are the back-up routines the programs of which

are loaded in the main processor.

The basic approach to the problem to find the optimum geometry of sun shade is, first

of all, that the sun shade should be designed so as to intercept the direct solar radiation as much as possible v/hen it amounts to its maximum for the orientation to which the

window is faced. It would not be probable that the total solar radiation transmitted

489
through the window plus the heat gain associated with outside air temperature at other

times of the year would exceed the rate when the maximum radiation occurs, but this must

be checked before the decision is made.

5. Description of Routines with Example Results

3.1 Phase I According to the above basic approach, the objective of Phase I is to find the

maximum rate of direct solar radiation upon the surface for the window orientation and

the sun's position relative to the v/indow surface when it occurs. Useful data on the

sun's position for the Phase II calculation are the tangent of profile angle as defined

by Parmelee (2) and the tangent of wall solar azimuth.

Example calculation results are shown in Table 3 for the window faced with southwest and for the building located in Tokyo (35°41'N, 139°46'E). This shows the maximum

radiation occurs in January. Considering that the total cooling load usually amounts to be higher in summer, the data for August were selected for the determination of optimum

shape of sun shade for Phase II calculation.

Table 3. Output data example of Phase I Direct solar radiation Tangent of Tangent of on vertical surface Profile angle wall solar azimuth

(kcal m~S-l)

January 1^ 677.9 0.52885 0.23383

February 13 675.0 0.49787 0.09798

March 15 595.1 0.72571 0.26333

April 15 522.5 1.03434 0.48731

May 15 ^81.2 1.36358 0.72624

June 15 3if2.5 1.52520 0.84353

July 15 385.4 1.36358 0.72624

August 15 455.3 TPM= 1.03434 TGM=0. 48731

September 15 581.5 0.72571 0.26333

October Ik 610.8 0.70200 0.14790

November Ik 610.9 0.52885 0.23383

December Ik 605.7 0.46956 0.26325

3.2 Phase II

The objective of Phase II calculation is to determine the optimum shape of sun shade

for a given rectangular window whose height is unity and breadth is B based on the output

information of Phase I. Studied in this paper is with an egg-crate type of sun shade

that consists of horizontal overhang and vertical side fins, both of which are made of

rectangular flat plates and may be tilted if desirable as shown in Fig. 2, where the

general shadow patterns are also illustrated. The design criteria adopted is the upper

limit of sunlit area of window when direct solar radiation reaches its maximum in summer.

The problem then is to find the optimum projection and optimum tilt angle of both over- hang and side fins.

Fig. 3 is the flow chart showing the actual routines of Phase II calculation and

the followings are the step by step descriptions.

(1) Input data:

B = 0.5 ( v/idth of v/indow relative to height of windov/ )

490
TPM = 1.03if3/f ( tangent of profile angle at 3 pm in August, cf. Table 3 ) TGM = 0.48731 ( tangent of v/all solar azimuth at 3 pra in August, cf. Table 3 ) PSA = 0.1 ( upper limit of sunlit area per v^indov/ area as design criteria )

(2) Initial set values of tilt angle of overhang and side fin:

AA = 0

AB = 0

(3) Calculate the tentative values of overhang projection DL and side fin projection FL

to have the sunlit area proportion AS made about 0.1 (PSA) v/ith the follov/ing formulas:

DL = 0.7 / ( tan AA + TPM ) (1)

FL = 0.7 / ( tan AB + TGM ) (2)

(4) Calculate sunlit area AS including the triangle area as shown in Fig. 2,

(5) Calculate area of material AM required per windov/ area as the sum of overhang area

and side fin area.

(6) Calculate view factor VF.

(7) Output data:

DL, FL, AA, AB, AS, AI'I, VF.

(8) Repeat calculation with the shape of overhang and side fin modified.

(a) Modify the tilt angle of overhang or side fin whichever gives larger shadow

area. Go to (3)

(b) Modify the projection of overhang or side fin whichever gives larger shadow

area. Go to (4)

Example calculation results for the window whose relative breadth to height B is 0.5

are shovrn in Table 4.

It can be seen that the area of material requires gets smaller as the tilt angles

of overhang and side fin increase , whereas view factor hardly varies regardless of the

shape as long as the sunlit area stays the same around 0.1 which is the specified- values

as design criteria.

All of these results shovm in Table 4 from the serial number I = 0 to I = 30 are regarded optimum as far as the design criteria adopted is concerned.

Fig. if shows the plotter drawings of section and plan of the four selected types of

brise-soleil with the shadow pattern casted upon the v/indow , assuming that the designer

made his selection based on his idea and judgement to see the actual shape of them. In Fig. Zf, (a) shows the figure of the type I = 0 in Table 4 , (b) I = 9 , (c) I = I9 and (d)

I = 29 • It would be more desirable to show the perspective drawings.

3.3 Phase III Calculation of heat gain from the glass window combined with the sun shade the shape

of which is determined in Phase II is to be made in Phase III, There are three basic

components of heat gain that appear inside of glass: direct solar radiation transmitted

through shade and glass , diffuse solar radiation transmitted through shade and glass including the reflected component from the sunlit surfaces of the shade and the heat transfer from outside across glass including the long wave length re-radiation from the shade

surfaces the temperature of which could get considerably higher than the air temperature

because of the absorption of solar radiation. Fig. 5 shov/s the overall phase of direct

and diffuse solar radiation that turn out heat gain through the combination of shade

assembly and glass.

The direct transmission component can be calculated using SHADOW routines (3)}(4).

The diffuse component including the reflected radiation at the shadow surfaces can be

calculated with the view factor formulas. As the rigorous calculation of re-radiation

component is very complicated and attempts were made to simplify the situation and

estimate it in the form of equivalent temperature rise based on sol-air temperature

491
Table 4. Output data example of Phase II

B = 0.50

T

I nU 1L ^ A A B A S AM V F A\J u . o o 0.72 0 . 00 0.00 0. 09 2.11 0.19

11 A 1 (1U . on'J u Cj . 0 9 1. 90 0.20

c 0. 74 0.61 0.00 5 . UO C. 0 8 1.97 0.18

-3

I'l VJ . Ao ^? 0.6 1 5.00 5.00 0.09 1.35 0.21

A*+ V ^ . O 7 ("i A 1 iJ n fi . u u ^ n n n 7 1 9

0 1 Q C U . o ^: J . J J

*=i T . nu nu 1 n nn 1 7 0 0 ? 1 o U. O 7 J . LI U in on 1 7 A 0) 1 M

f U.JO J . J J in on in nn 0 nq 1 . o6

o. 0. 64 0.53 10.00 10.00 C . 07 1.72 0.19

Q n ft 0.46 1 nn 15.00 G . 1

1.55 C . ? 1

1i. n\j U . O 10.00 15.00 COS 1.61 0.19

X i. 0. 54 0.46 15.00 15.00 0.09 1.52 0.22

1 7 n . 5 9 0.46 15.00 15.00 C . 08 1.57 0.20

11 3 0.41 20.00 0.10 1.43 0.2 2 0. 59 15.00 20.00 C. 09 1.49 0.19

0.41 2 0.00 20 .00 0. 09 1.41 0.22

1 O p. R S J . ^ 1 7 T no ?c\ nn 0.08 1.46 0.20

11 7f 0.5 0 TiJ . ^7J? ( 2 0.00 2 5.00 0.10 1.34 0.2 2

1 ft nU . sJ 3 fi ^7 ? 1 nn ? n n C . 0 8 0.20

1 Q ? s n n 0.09 1.32 0.23

C \J n s 1 0,37 2 5.00 2 5.00 0.08 1.38 0.20

7 1 0 47 0.33 2 5.00 30 .00 C . 1

1.2^ 0.22

n s 1 25 . 00 30.00 C. 03 1.33 0.20

2 3 0.43 0.33 30.00 30.00 0.10 1.26 0.23

24 0. 48 0.33 30.00 30.00 0 , 0 8 1. '31 0.20

25 0.43 0.2^ 30.00 35.00 0. 10 1. 22 0.22

26 0.-^8 0. 2<; 30.00 35.00 C. 08 1.27 0.20

27 0. 40 0. 29 3 5.00 35.00 C. 10 1.21 0.2 3 28 0. 44 0. 29 35.00 35.00 0. Oo 1.26 0.21

29 0. 40 0.2 6 35.00 40.00 0. 10 1. 18 0.22

30 0.44 0. 26 33.00 40.00 0.0 7 1.23 0.20

Table 5. Output data example of Phase III

Time V/eather data

Direct Diffuse Outside

solar solar air

radiatn radiatn temp. —(kcal m-2h-l)- degc

Output information

Direct Diffuse Keat

radiatn radiatn transfrd

transmtd transratd across

(kcal m-2h-l)

Squivalent temperature ris e Radiatn Re-radtn Atraosphrc

absorbed from radiatn

by glass shade

degC degc degC

_ 9 2 34 2u .c 0

10 3 49 29.6 0

11 ?1 56 30.3 0

12 215 57 30.7 0

13 340 56 31.1 0

14 425 54 31.0 23

15 455 51 30.7 29

16 416 47 30.5. 1 r

-LO 17 288 39 29.6 0

18 54 22 23.4 0

11 7 0.16 0.19 -1.28

21 16 0.28 0.49 -1.30

29 23 0.39 1.05 -1.31

34 31 0.46 2.02 -1.32

37 39 0.51 3.19 -1.33

37 47 1.27 4.13 -1.32

35 50 1.42 4 . 7^ -1.32

30 47 0.91 4.91 -1.31

21 37 0.29 4.41 -1.30

7 22 0.10 2.94 -1.28

concept against the glass surface (5) using the weighting factor technique (6) as used

for space cooling load calculation. Detail of this approximation process is described

in Appendix.

Results of example calculation with the brise-soleil whose type is I = 29 in Table

4 are shown in Table 5. It can be seen that the re-radiation effect can be quite large

and the equivalent temperature rise aiaounts to over 7 degC especially when the shade

492
intercepts a considerable amount of incident solar radiation. The author's experiments

previously made (5) showed that the equivalent temperature rise was 3 - k degC at maximum

in summer.

In the process of heat gain calculation it is desirable to check whether or not the

shape of sun shade determined in Phase II could effectively reduce heat gain at other

times of the year as well as other hours of the month. It sometimes happens in winter

that the transmitted solar radiation amounts so high that one cannot control the space

temperature. Two methods to check the possibility of this situation throughout the year

are conceivable: one is to calculate only the direct solar radiation transmitted through

the sun shade because it is a predominant factor and the other is to calculate heat gain

or cooling load including other excitation components to make an overall judgement. If

the heat gain for any month turned out too much, the alternative shape should be selected

and the Phase III calculation repeated until the conditions regarding both aethetical and

thermal effects are satisfied. If it is still unsatisfactory, Phase II routine must be

repeated with input data revised from the results of Phase I calculation.

Z+. Conclusion

(1) As an example of optimization problem with computer the procedure to determine the

optimum shape of sun shade is presented. This is based on the realistical design process

so that an architectural designer could use his aethetical judgement in the course of the

computer calculation which could be combined with graphical display system or plotter

drawing system.

(2) The basic routines developed can be used both for the deductive and inductive design

processes by a simple application technique so that they could be an effective aid in

the architectural design of building fa9ade.

(3) The procedure to calculate the heat gain from the window v/ith brise-soleil talking

account of reflection and re-radiation from sunlit surfaces is also developed so that

the results obtained could directly be used for air conditioning load calculation.

5. References

(1) Negroponte , N,, Towards a Humanism through Machines, Technology Review Vol.71 No. 6,

Massachusetts Institute of Technology, April 1969.

(2) Parmelee, G. V. and Aubele , V/. W. , The Shading of Sunlit Glass, ASHVE Transactions,

1952.

(3) Sun, T,, Shadov/ Area Equations for Windov/ Overhangs and Side Fins and Their Application in Computer Calculation, ASHRAE Transactions, Vol.7i+ Part I, I968.

Groth , C. C. and Lokmanhekim , M. , "SHADOW", Proceedings of the Second Hawaii International Conference on System Science, I969 , P.471-47A-.

(5) Kimura, K, , CoolingLoad Caused by Re-radiation from Sun Shade, Transactions of the

Architectural Institute of Japan, Special Issue, I965.

(6) ASHRAE Proposed Procedure for Determining Heating and Cooling Loads for Energy Calculations, ASHRAE Task Group on Energy Requirements for Heating and Cooling, I968.

6 . Appendix

6.1 V/eighting Factors to Estimate the Heat

which is Discharged from Sunlit Shade Assembly

Part of incident solar radiation transmits through the shade as shovm in figure 3

and the remainder naturally falls upon the surfaces of the shade. Part of the radiation

absorbed in the shade material is once stored but eventually discharged to the air by

convection and to the glass surface by radiation, the remainder being emmitted to the

sky. The radiation component from sunlit shade surface to the glass is defined as re- radiation and the effect of it can approximately be estimated using v/eighting factor

technique,

Refering to figure 6 the v/eighting factors W. relating the incident solar radiation

into the shade assembly to the heat discharged from all the surfaces of the shade can be

expressed by the following equations using the response factors of shade material X. and

493
Y^. Namely,

for j ^ 1 W = - ( X - Y )*a /a , (A-2)

J J J s so

where a is the absorptivity of shade assembly and OL is film coefficient along the

shade s§rface. ^°

Then HS the heat discharged from the shade surfaces per unit window area at time

t = ni\t, where At = time interval, can be obtained by

HS =E W * I . , (A-3)

n 3=0 J n-j

where I is the incident solar radiation into the shade assembly including the reflection

from glSss as shown in figure 5 per unit window area.

494
INDUCTIVE

DESIGN PROCESS

DEDUCTIVE

DESIGN PROCESS

N > I DECISION

DERIVE EFFECTSn^

CHECK CONFUCTS

CHANGE

DECISION

N N !

YES

CHANGE

I DEA

REQUIREMENTS

CRITERIA

IDEA

OBJECT

DESIGN

(Ho

OPTIMUM

RANGE OF

BJECT

«= SELECTION

Figure 1 Two basic types of design process

495
496
B , tan0, tony

1- o|

AA

AB

= 0

= 0

Calcu

DL

late

, FL

Calcu

AS, A

late

M, VF

AA= AA + 5

or AB= AB+5

DL, FL

AA, AB

AS, AM, VF

DL=DLx|.|

or FL= FLxl.l

DL,FL

Figure 3 Flow chart of Phase II calculation

497
Figure Z| Plotter dravifings of example shapes of sun shade

498
499
[watt/m2]

1 [kcal/m^h]

Figure 6 Weighting factors relating the incident solar radiation into the shade

assembly to the heat discharged from the shade surfaces

500
Calculation of Smoke Movement in Buildings

T. Wakamatsu

Building Research Institute Ministry of Construction

Hyakunin-cho 4, Shinjuku-ku

Tokyo, Japan

For the purpose of personal safety from the hazard of smoke in building fires, it is necessary to keep escape routes clear of smoke or to keep the smoke concentration on the routes thinner than allowable one until the evacuation of the occupants is completed safely. For this, it is naturally required to control smoke movement by some mean. There should

be a need for some design system, so called "smoke protection design

system", to plan the reasonable and effective system suitable for every

building to secure occupants from the hazard of smoke. Some calculation

to estimate smoke movement or to evaluate smoke control methods will be

indispensable to the design system.

Smoke movement is, needless to say, substantially caused by stack

and wind actions the same way as air flow in a building. The movement

is, therefore, practically under the influence of such conditions and

factors as burning severity in fire compartment, composition of vertical

shafts and other various flow paths and openings, temperatures on each

part of a building and the outside air, the air handling systems involving

the smoke tower or the pressurization method, and the outside wind.

If these data are given, calculation of smoke movement can be made using

a digital computer.

This paper presents a fundamental concept of the smoke protection

design system, computer techniques for calculating smoke movement and

computed results of sample buildings. A computer program has been formulated to calculate mass rate of smoke or air flowing through each path

or opening and concentration of smoke and to evaluate methods of controlling smoke movement under various conditions for various buildings.

Key Words: Air, building, computer, concentration, control,

design, density, escape, evacuation, fire, flow, movement,

path, pressure, rate, shaft, smoke, stack action, wind action.

Engineer, Dr. Eng.

501
1. Introduction

The increase in the number of high rise buildings and the tragic results of fires continuously

happened in Japan in recent years have attracted much attentions to the hazard of smoke and toxic

gases produced by fires in the buildings. As a result, various suggestions have been offered as counter-measures against smoke hazars, such as the restriction on the use of combustible linings, the effectivity of balconies on outside wall for escape, the necessity of smoke tower or the pressurization of escape routes as measures to control smoke movement and so on. These are surely

available for personal safety from smoke in its own ways, however it should not be easy in practice

to apply all of them in a building. To evaluate these measures, and to solve the problem how rationally and effectively to protect occupants against smoke, it will be the most important and necessary

approach to establish a design system enable to evaluate various measures mentioned above, by means

of estimating smoke movement or concentrations in escape routes and the time required to evacuate

the occupants. Since the calculation to estimate the time for the evacuation is now enabled to apply

practically (1), the only remained difficult problem to be solved is how to assume the conditions and

to calculate smoke movement under the conditions.

If a building has a perfect security to prevent an outbreak of fire, with all incombustible linings

and furnitures or some complete set of fire extinguishers as sprinklers, the building should evidently

need no further measure against fire or smoke. However, actually it is almost impossible to expect

to be that way. Therefore, the most important problem is how to make occupants escape safely in fire by some measure, and then how reasonably and effectively to provide and plan the measures or

the facilities. The system to solve this problem is, so to speak, the smoke protection design system.

Fig. 1 shows a flow chart illustrating a concept of the design system. When the conditions and

factors of a building are given or determined, one can estimate whether the occupants will be safe or not in fire, and one can take measures to meet the situation or consider how to plan facilities against smoke per the procedure shown in Fig. 1. The smoke concentration "Cs ( t ) " can be estimated

for each part of the building as a function of the time "t" after outbreak of fire by the calculation of smoke concentration or mass rates of smoke and air flowing through each opening. The smoke load to each compartment is given as the product of the mass rate by the concentration of smoke flowing into the compertment. The original concentration of smoke in a compartment in fire (3) can be assumed

from the combustibles and the temperature in the compartment (4). The evacuation time for the design

"Td" is given as a product of the minimum time required to evacuate the occupants "Tm" by a safety

coefficient " e " as Td = £ Tm. Tm can be calculated for each escape route based on width and length of escape routes and its number in quantity, type and quantity of fire alarm system, lighting and guiding

sign, constitution of the occupants, and human psychology in emergency. The allowable smoke concentration "Cs/^" may be given from the visible distance required for the occupants to escape (5). According to the procedure shown in the Fig. 1, we can predict from the values of Cs(t), Td and CsA,

whether the occupants will be safe or not in fire, or whether Cs(Td)<ICsA or Cs(Td)> Cs^. When

Cs(Td)> Cs^, it indicates need for some further consideration to reduce Cs{Td).

Smoke is probably not so much different from air in the nature such as the density (10), the viscosity and so on. To understand smoke movement in buildings, therefore, it is necessary to solve

the problem of how much air flows through each component and how much smoke is contained in the air.

2. Smoke Protection Design System

3. Analysis of Air Flow in Building

3. 1 Basic Pattern of Flow through a Path

In general, the mass rate of air through a path Q can be represented as.

502
Q = ±\/ j z^P I / R , or Z^P=R.Q2

where R: flow resistance of a path,

P: pressure difference across a path.

When two spaces adjoining each another with different temperatures, there is pressure distribution on the separation attributed to the density difference of the air. In the case of Fig. 2(a), where

the neutral plane exists between the levels of the top and the bottom of the opening, each mass rate Ql and Q2 of air flows through the upper or the lower part of the opening can be thought as, Qi= ±\/ I ^Pai I /Ri . or Q2= ±\/\Z\Pa2 l/Rj

where ^Pai= 4Z\Pi/9 , Z\Pa2= 4Z\P2 /9 , Ri= 1 /( 2gri ( aAi)^ ) , R2 = l/( 2 gTz ( aAa)^)

g: acceleration of gravity, : density of air, GA: effective area of flow path,

/^P;[ , Z\P2 : pressure difference at the level of the top or the bottom of the opening.

In the case of Fig. 2(b), where the air flow is one-way, the rate Q can be given as, Q = ±\/ \Z\Pa |/R where R = l/( 2g r 2K ( QA )^ ) , ^^=1^^+ (l + n)(; + n+2^) ^ "^^'Z*^^

^Pa.: pressure difference between two spaces at the center of the opening.

3.2 Wind Action

Wind pressure on a outside wall Pw is determined by wind velocity v and wind pressure coefficient C which depends on directions of wind and a wall face, that is Pw = C?'v2/2g. If the velocity

profile, surrounding conditions and the nature of wind are neglected, the wind pressure coefficient C

is given by an angle Aww between wind direction and the normal to a wall face as follows (9), C = 0. 75 when 0°^|Aww|<30° , C = -0. 021Aww + 1. 38 when 30 °<|Av/w|<;90 ° , C = -0.5 when

|Aww|>90°.

3. 3 Computer Technique for Flow Analysis

a. Basic Model and Computer Technique

Pressure in each part of a building and air flow rate through each opening or path can be obtained

by means of solving an air flow network composed of flow resistances of openings and such motive

forces as wind pressures and air gravities. There are two methods, so to speak, "loop method" and

"knot method", as computer techniques to solve these kinds of networks. Two basic patterns of the network simulating the electric circuit are illustrated in Fig. 3 and 4, relating to the both methods.

The loop method is to solve, based on the 1st and 2nd lows of Kirchhoff, the equation of the

through quantity on the knot ^ Q = 0 and the equation of the across quantity on the loop of the network

J/^P = 0. This method has already been described in (2), but the simplest model is shown in Fig. 3.

The knot method is to solve the network with the mass rate balance for each knot or the equation

of the through quantity 2' Q = 0, as shown in Fig. 4 where a basic model of the network is shown for this method. In this method, pressures on all knots are assumed at first, then they are corrected iter- atively until mass rate balances of all knots are satisfied. In Fig. 4, when static pressures p-^~ P4 arc

given, the pressure P to be solve is obtained as a root of the following equation;

£Q= I±s/ \Pi-Ei - P\ /Ri = 0 The flow chart shown in Fig. 5 illustrates an iteration procedure for correcting unbalanced mass

503
rates in the above equation.

b. Network for Practical Building

Fig. 6 shows practical patterns of the network of air flow in buildings. A computer program was

formulated using the iterative technique shown in Fig. 5, to solve the network composed of the patterns

shown in Fig. 6, by which it is enabled to calculate air and smoke flows under various conditions on various building. Fig. 7 shows a network of an actual building in Tokyo, as a simple example. The

results for this building, calculated by the loop method, has already been published (2), but a part of them is shown afterwards.

4. Smoke Spread and Smoke Concentration

To estimate the safety of occupants in escape routes, one must calculate the rising rate of smoke

concentration in each escape route. So it is necessary to obtain the time in which smoke appears at each escape route and to calculate smoke concentration after smoke reaches there. As a whole, it is very difficult to grasp the smoke movement in inicial stage of a fire, because temperature of smoke

is transient and under unsteady state. So, calculations was made based on the following assumptions;

(1) temperature in each part is constant during fire,

(2) smoke diffuses uniformly itself all over the space instantaneously except in vertical shafts and the corridor of the floor on fire.

4. 1 Smoke Movement in Corridor of Floor on Fire

The nature of smoke, particularly its temperature, in the corridor of the floor on fire is very

important for calculations of spread and diffusion of smoke to other floors. Layers of smoke and air are generally formed in the corridor, as shown in Fig. 8, the one of smoke flowing on upper part of the corridor from burning compartment, and the other of air flowing on the lower part to the compartment.

The temperature of the smoke layer varies according mainly to the distance from the opening of burning compartment and the temperature of burning compartment which varies not so much after the flash-over. Since the temperature as a function of the distance and the time after breaking out of fire is difficult to solve and not so much usable for the purpose of these calculations, one may assume

it as constant for the time, and then regard it as a function of the distance. Fig. 8 shows a cross

section of a smoke layer of thickness H and width W (equal to the width of corridor). Assuming that heat transfer coefficient to the surroundings h, the specific heat of smoke at constant pressure Cp

and the temperature of the air Q^^ are constant, a heat balance is shown by the following equation

(1) on the crosshatched finite slice of thickness dx and distance x from the opening of the burning

compartment.

dd

- Q • Cp-(

g,^

)

• dx-dt - 2h(H+W) ( e-(9o) ( 1-/?) dx dt = HWrCpdxZX^ (1) where Q is mass rate of smoke in its layer, d is the temperature of the slice or smoke x distant

from the opening, z\0 is the varied temperature of the slice after the elapse of a finite time increment

dt, and ^ = (^dsx — do ) / { 6— do) where ^ sx is the temperature on the surfaces of the surroundings at the position x from the opening.

Assuming the temperature to be constant or = 0, Eq. (1) becomes

dd _ 2h ( H+W) (!-/$') r ft_ ^ ) dx Q Cp

I. 0

;

504
Therefore, 0 is given as d=do+(dF-do) exp (-a0x)

2 ( H+ W)

where

(2)

a = Q Cp

X - c fl

h'exp(h2t/^ cp) erfc h s/t/Jcp

temperature of smoke in burning compartment

the time representing the elapse of fire heat conductivity, specific heat and density of the materials of surrounding walls of the corridor respectively

In Eq.(2), 0 can be obtained by assuming that the surroundings of the corridor are made of semiinfinite solid. Fig. 9 shows a graph of ®vs. t/^c/5 for the values 40 120 of h(Kcal /m^hr °C).

One may use 0 at an average time like the half of the evacuation time based on the assumption of steady state.

Assuming that t = 0 or <P = h for initial smoke flow, to calculate the time Tx in which smoke

arrives at a position x distant from an opening of the fire, the velocity Vx of the smoke head at x

is thought as

Q( ^0+ ( dp-Oo ) exp (-ahx))

Vx =

doTo HW

where To is density of air at temperature

(3)

(9o= 27 3 4- 00 (?F= 273+ dp

Tx= f X dx

'o Vx roHW , do + { dr-do) exp (-ahx)

( ahx+ ln( TT ) ) (4) cthQ Of Therefore the time Tc in which smoke head arrives at a shaft opening in the floor on fire can be

obtained by inserting the distance from the opening of burning compartment to the shaft into Eq. (4).

4. 2 Smoke Movement in Vertical Shaft

To obtain the smoke load and the time for smoke to reach other floors, it is necessary to analyse the flow in vertical shafts such as a staircase, an elevator shaft or a vertical duct for the HVAC.

Let's assume a simple condition or layout as illustrated in Fig. 10. The time Ti, in which smoke

flows through a duct from the burning floor "f" to any floor "i", and the concentration of smoke Ci in a shaft on the "i"-th floor level are:

/-I rHA , ^ ^ r j=irHA

"^^^ \<.i<f, or when iyf

Ck Qk

d = where Q is ( + ) for flow out of a shaft,

h Qk

k=\ or (-) for flow into a shaft

where H is floor height, A is effective cross section area of a shaft. When £(rHA/Q)<l 0 or T^ < 0 in the i-th floor, no smoke will consequently flow into the floor through

the shaft.

4. 3 Smoke Concentration in General Floors

If smoke enters into a compartment "j" in the i-th floor through openings n in number, the

505
smoke concentration will be

n 2Ck-Qk

Cji(') = £

4=1 21 Q;

( l-exp( - ALS^ (t_Tk)) )

where Cji (t) : smoke concentration in the compartment "j " in i-th floor for the time t after elapse

of fire,

Ck : concentration of smoke flowing into the compartment through the "k" opening,

: mass flow of the smoke,

Tk : the time in which smoke appears to the compartment through the "k" opening,

Tk = Tc + Ti,

Qj : total mass flow of air and smoke flowing in and out of the compartment,

V : volume of the compartment,

f : density of air in the compartment.

Transient smoke concentration of the equation assumes instantaneous mixing of smoke with air in the compartment.

Calculation of Example Buildings

Calculations were made of smoke movement on two buildings, using the techniques as mentioned

above. These calculations were assumed temperatures at steady state condition.

5 . 1 Example - 1

Assumptions: The example is of 9 story building actually existing in Tokyo, and a plan and openings of the building are shown in Fig. 11. The building has two duct systems for HVAC which are independent of each other. The one has air diffusers through which fresh air can be supplied into the center core in fire. The other has 8 air diffusers per an office roorrl in each floor - the total leakage area is 0. 072 sq m -, but fresh air does not be supplied through this system during fire. Fig. 7 shows

a simplified cross section and a simulated network of the building. The optical concentration of smoke

in fire compartment is Cs = 10 (1/m). The calculation is performed under 32 conditions composed of the followings

(1) floor on burning 2nd or 5th (floor)

(2) size of opening window of burning room (height x width) 2 x 1 or 2x5 (m)

(3) number of opening door leading to the outside on 1st floor 0 or 2

(4) season of fire summer or winter

(5) wind velocity (wind direction toward the opened window of burning room) . .0 or 10(m/s)

s eason

s ummer

winter

Temperature (°C)

the outside rooms and core duct burning room

30

0

24

1 7

27

17

727

727

Calculated results: The results are shown in Table 1 and Fig. 12. Table 1 shows mass rates of air or smoke flowing through each opening or path, and the safe time during that occupants are sequred

against smoke in each part of the building. These results show clearly that the mass rates and the

506
safe time are so much influenced by wind and stack actions. Fig. 12 shows the relationship between

volume of supplied air into the core and the safe time, under only no wind. Under every condition, as

the supplied air increases more, the powerful effect appears more as shown in the figure. The tendency is particularly appeared when the doors are closed. So it may be said generally that the effect of pressurization is more powerful to thin smoke concentration than one of ventilation. The highest pressure on a door under pressurized condition is calculated to be about 3kg/sq m or lOkg/leaf, which

suggests no difficulty for occupants to open the doors.

5 . Z Example - 2

This example has a purpose to calculate smoke movement under various conditions for a building,

using the computer program which is formulated on the pattern of network shown in Fig. 6, based on

the techniques mentioned above.

Assumptions: The example building is 10 story, and its plan and sizes of openings are shown in Fig. 13. This building is consisted of five rooms (j) - (5) , a corridor and a core on each floor. The core is consisted of two symmetrical parts, and each of them has a staircase, a lobby, an elevator shaft, a smoke tower, a HVAC duct, a return duct and a duct for air supply into a lobby or a staircase. During fire the return duct can be used for air supply only to a corridor of the floor on fire. Each smoke tower has two openings which are possible to open and shut to the lobby and the corridor of the floor on fire. The elevator shafts can be regarded as one shaft for the calculation by combining

their flow resistances. The smoke concentration in burning room is Cs = 3 (1/m). Room (T) of 2nd

floor is on fire. Temperatures of the corridor of the floor on fire smoke towers are calculated by

Eq. (2). Other temperatures are 0°C outside, 20°C in general part of the building, and 800°C in the room burning. The calculation was performed under eight conditions as shown in Table 2. Smoke

control measures as smoke tower and pressurization on escape routes are also included in the as- sumptions. The efficiencies can be evaluated by these calculations.

Calculated results: The details of calculated results for condition No. 1 are shown in Table 3 and Fig. 14 - 17. Table 3 shows mass rates of air and smoke flowing through each opening and

pressure on corridor of each floor. Fig. 14 - 16 show respectively the smoke and air flows through

the openings of burning room, smoke movement on the corridor of burning floor and vertical shafts - elevator shafts and staircases -. Fig. 17 shows smoke concentration on each corridor. Calculated

results for every condition are shown in Table 4 and 5. Table 4 shows the time in which smoke

concentration on each corridor reaches to allowable one Cs^ =0.2 (1/m), when visible distance is 10 - 15m. Table 5 shows the smoke concentrations in staircases (T) and <Q . From these tables, one can easily estimate whether occupants are safe or not in fire and evaluate how to control smoke.

6. Discussion

This paper described computer techniques to calculate smoke movement in building fires, are

an important and necessary approach to establish a smoke protection design system. For the background of this establishment, there have been done many valuable works on the smoke generation from

various materials in fire (3), the temperature in burning compartment (4), the allowable smoke concentration for occupants to escape (5) and the time required for evacuation (1). These research works

have already reached to the stage of practical apprication.

Therefore the only remained difficult problem was how to grasp the movement of smoke in fire,

though it has been possible to calculate air and smoke flows when the conditions are assumed (2), (6), (7). The difficulty in this problem is however how to assume the conditions for such calculations.

In practice, therefore, it should be required to simplify the conditions of the calculation particularly

the compositions of flow paths and to calculate only significant flows under various conditions such

as altering location of burning compartment, temperatures of the outside and the inside of a building,

the outside wind and so on (8).

507
References

(1) ''' Togawa, K. , Manual of High Rise Building

Engineering, (1967)

(2) Wakamatsu, T. , Calculation of Smoke

Movement in Building, BRI Research

Paper No. 34 (1968)

(3) Saito, F. , Study on Smoke Generation

from Building Materials (Part 1), BRI Research Paper No. 33 ( 1968)

(4) Kawagoe, K. , Estimation of Fire Temperature-Time Curve in Rooms (3rd Report),

BRI Research Paper No. 29 ( 1967)

(5)

'' Jin, T. , Special Issue of Architectural

Symposium ( 1969)

(6) Tamara, G. T. , Computer Analysis of Smoke Movement in Tall Buildings

,

ASHRAE Transactions ( 1969)

(7) Barret, R. E. and Locklin, D. W. , A Computer Technique for Predicting

Smoke Movement in Tall Building,

Presented at the Symposium at Hertfordshire, England ( 1969)

(8)

''" Wakamatsu, T. , Calculation for Smoke

Control System, Presented at the Symposium of Smoke Protection at Sapporo ( 1969)

(9)

''" Sekine, T. , Transaction of SHASE of Japan, Vol.36, No. 4 (1962)

(10)* Maeda, T. , and Terai, T. , Special Issue of Architectural Symposium ( 1970)

(*): Report in Japanese

508
a

•H

-IJO

a

o

fHP.

on u H

o -P

tw tfi a o

Id

r-Ha. 0)

condition in

^ burning comnartr.'.ent

condition of

the outside

general con- dition of building

condition of occupants

quantity and quality of the com- bustible in burning compartment

openings of burning compartment

'.;ind: direction and velocity

temperature in the outside

temperature in each part of building

forced ventilation

constitution of openings and

paths

use, scale and structure of

buildins'

-| constitution of escape routes

fire alarm system

lighting and guiding sign for

escape

constitution of occupsnts

human psychology in emergency

rate of smok;

-»>|-;eneration

air flows in building

safety coef- ficient; £,

smoke load

:-.;::0ke corjcen-'

tration in escape route; MO ,

minimum time for evacuation

to escape; Tm

evacuation

time for

design; Td

Td = e Tm

allowable

smoke con- centration;

CsA olan to make occupants escape safely (

s(Tq;

Fig.l Flow Chart of Smoke Protection Design System

A,

Oi (rBhO

' B

(a)

Fig. 2 Basic Pattern of Plow Through Opening

509
Pl.'iniclally assumed ptessure

ho - inicial increment ( CONStanK <-))

Q ; total of mass

flow in a SI

Q,= Gf(P,)|

yes

I h= -^hc I I h = K I

P==(P,Q2-PA)/(a -Q,

Q^^Qr (P)

P2 = PQ

2jJ-~- no P,= P2 , P2= P

, Q2= Q

SOLUTION

Pig. 5 Flow Chart of Interation Procedure for Correcting Ujibalanced Mass Flow in a Space

-f EW

-^Pb)T T

(b) Detail of Net Work on Burning Room and Burning Floor marks

:

0 : Outside air R ; Room(compartment

)

Rb: Burning room

C : ODrridor

L ; Lobby

(a) Net work of a Floor

S: Stair Ew.Wind pressure

VD : HVAC duct

ST : Smoke tower RD: Return duct at corridor AS: Air suply duct to lobby

or stair for pressurizntion SP; Air suply duct or vertical shot

Fig. 6 Net Work Shows a Pattern of Air Flow Paths under Wind and Stack Action

510
air Wb ""idx^

opening of burning room

smoke

air

Fig. 8 Smoke on Corridor of Fire Floor

511
Fig. 9 Heat Loss Factor on Surrounding Surface

^ T.Vi

h; Qi.

I ^' tCi

i-l Fl. Ci-l A : cross section area

H: -floor height

(a) Qi>0 ( b) Qi ^ 0

Vi - (Qi-1- Qi)

Ci = C i -1

Vi = (Qi-1^ Qi)

3-

P _ Ci-lQi-l*C'iQi

^' Qi-uQi

Fig. 10 Smoke Flow in Vertical Shaft

512
COMPARTMENT

(OFFICE ROOM )

TSP/MR q

»SE )

PLAN OF A BUILDING

EFFECTIVEWIDTH OF CRACK

olA - A - 0 00 3 ( m )

SCALE UNIT ; m

PARE GLASS

VENTILATION OPENING ; 52 ( PER FLOOR)

VENTILATION OPENING

(AT BOTTOM OF WINDOW )

Fig. 11 Plan and Opening of Example Building (Example-l)

Fig. 12

I 2 3 4 5 6 7 a 9 10 II 12 13 14 15 16 17 IB 19 20 Volume of Supplied Air ( kg /sec)

D 1

""2 ^2 "4 '1 Time ot Air Change ( I /h ) Relationship between safety time for escape and

volume of supplied air or times of air changes

in staircase

\30* Wind (velocity : 5m/s SSE 30°)

marks

RM

DS

RD

ST

A5

room

HVAC duct space

return duct

smoke tower

air supply duct

door's shut in fire

opening •.

wmdovv/ on burning RM; 2''2(m)

exhaust opening on ST ; 1.5 »l door of lobby on fire, 2*2

Fig. 13 Plan of tixample Building (Example - l)

513
out sfde

0.15

window

6.77

14. OA

Qvent.op. []

(N)

burninq rm.

0.8

2 22 opening ; (m) u

corridor

•8.37

4.83

window -.2x2 Q vent, op ;0.3»1 12 13 door ; 2«2 ^

transom window;1»2

1.76 7.46

Fig, I'll Mass Rates (kg/s) of Smoke and Air of Burning Room

burning rm. RMRM

15.7(3^

^5.5(2.K)

(D

,07(0)

RM0I

0,6 (0)i

2.5(0)

192 75

(3) (2.2) 20.5(3) — 75 (2.2)

1.3 (3)

( 2.K)

(ES) 25(0)

|l.2(2K)

r—• air supply -3.6(3) - 2.0(2.7)^

2.0 (2.65) (ii)

O.A ( 0 ) ^ SD

RM ; room ES . elevator shaft

Ll.in lobby 1,11 SI.SH : stair case 1 ,11 ST . smoke tw/er

755(2.1 )

STi-^

1.2(1.8) .9(0) in.

7.A (2K)

77(2.0)

027(0 ) 4 RM (T) 0.27(0T ^

Fig, 15 Smoke Flow on Corridor of Fire Floor

outside

m

1.97 ^ .

) zio i02S) 151 ^

7A0

(035) VAl

9.15 s(0.35) 1.29

1.2 35

-(035) 1.17

1 3.77 (035)

1.03 ^

^ 1170

,(0.A1) 086

y

12.76

(0.A1) 0.66^

836

(0.62) 0.36 ^

^70A 0=1

OA 3

air supply

duct

-338

corridor outside air supply .OA 5/^ 159 <^'^ct

-1.61

3.35

5.22

652

I

1 1-23^

t 2.0A

.(0.15) 1A9

-3. AO

-^729

(0.1 5) 1.38

' 895

(01 5)

1.26 -1,62

"^12.09

(0.15)

1.1 A "^^AO

(015) 0,99^

3.31

11,2A

(0.1 9>) 0.82^

-^121

(0.1 8) 0^^

5.21

' 73 A (030)

^ 737

JO.15) 0 55^ 6,50

(a) Elevator shaft, (b) Stair easel

I I time in which smoke head arrives at each

( ) smoke concentration ,( optical) , ( 1/m ) other figures : mass rate of smoke or air ( kg/sec

( c ) Stair case II

floor level, ( sec.)

Pig, 16 Smoke Flow in Vertical Shaft

514
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Season

Fire

Floor

Opening

at

two

door

at

1st

FL

Width

of

opened

window

on

burning

compartment

(hight :2

m) <u JZo

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CO in to CO cn

stair

way | e w 00

5* DC 2^ >. 1 a 2 ^ £

Ll

Safe

time

for

occupants (

min ) S:

safe

more

than

30

min

<D M

CI. e

0)o0

515
0 1 2 3 /. 5 10 15 20

* TIME (mm)

Fig. 17 Smoke Concentration in Corridors on Each Floor

Table 2 Conditions of Calculation (Example - 2)

Condition No. Marks

Outside wind, velocity(m/s)

direction

Window

on staircases

on corridors

Mass rate to staircases

of supply

air (kg/s) to corridors*

Opening of smoketower (T) smoke ,, /0\ tower

SSE 30

OP OP

OP OP

10

5

L.C.

OP

OP

10

0

CL

CL

10

0

OP

OP

10

0

L

L

OP

OP

10

0

C

c

CL

CL

5

10

- ; -: no wind

CL I OP: opened

CL : CL: closed

10

20

*: on fire floor

L: opened to lobby

I C' opened to corridor

516
Table 3 Mass Rate of Air and Smoke and Pressure on Corridor (Example - 2)

Floor

NO,

Qi Q2 Q3

Q4

Q5

® ® Qe

Q) (a) Q) U52

s N E s s s W N

] 1.28 -0.65 078 1.30 1.33 1. 41 -027 -0.27 -0.75 -0.70 -078 -061 -0.65 -0.60 -055 -0.27 -0.01 -030 -0.36 1.4 1

2 0 0 0 1.25 1.27 139 -0.37 -037 -080 -0.58 -066 -037 -1303 -067 -0.61 -0.27 - 1 28 -1.5ft -7.70 117 11/

3 1.18 -0.82 0.60 114 1.17 1.30 -0.61 -061 -043 -053 -061 -023 -0.53 -0.61 -0.56 0.1 4 016 -01 0 1.0 0

1.11 -0.91 0. A4 1. 03 107 1.21 -0.78 -078 -0.21 -0.45 -055 0.13 -0.42 -058 -052 0.22 — 0-8

0.21 00 9 0.78

5 1.02 -1.01 005 091 0. 95 1.12 -090 -0.90 027 -0.36 -047 0.35 -0.32 -0.55 -0.48 0.34 - 0.96 0.25 0.16 0.45

6 0. 92 -1.10 -0. 42 076 0.81 103 -1.00 -1.00 0. 45 -027 -0.«) 049 0.15 -050 -041 0.48 -1.1

0.25 0.17 -04 1 7

6

0. 83 -1.17 -0.59 0.58 0.66 0.95 -1.08 -1.08 059 -0.10 -028 063 0.35 -0.48 -0.37 0.58 -1.22 030 023 -07 6 0.74 -1.23 -0.70 028 0.44 0.67 -1.14 -1.14 071 0.21 -0.09 0.75 0.48 -0-49 -0.35 0.67 -132 0.34 028 -1.00

9 0.65 -128 -078 -0.1 4 0.01 0.80 -1.19 -1.19 0.84 0.50 0.33 0.86 0.56 -036 -033 0.73 - 1.40 041 036 -1.22

10 0.57 -1 32 -0.84 -038 -03 3 073 - 1.24 -1.24 0. 96 0.66 0.55 0.97 0.62 -029 -0.22 077 -1.46 049 045 -1.41

Floor NO. Qq O10 OlOO pressure on corridor Oqi Q42 Qi. Q 12 Qio. Q loi

1 -0.30 -0. 36 6. 52 6.53 0.43 0. 50 -082

2 -0.58 -0i29 -036 -023 -076

3 0.16 -aio 5.22 5.21 -066 -0.60 -0. 4 4

4 021 0.09 -0.86 -0.82 -017

5 025 016 3.35 3.31 -103 -0.99 010

6 025 017 -1.17 -l.U 0. 41

7 030 023 -1.61 -1.65 -1.29 -1.26 0.67

ft 034 0.28 -1.41 -1.38 0.92

9 041 -036 -3. 38 -3.40 -1.51 -1.49 1 .1 3 10 0.49 0. 45 -1.61 -1.59 1 30

out

side'

Q,

'^ .duct out staircase

(C) lobby Q,|

O5

shaft

outside ^ ©^0.0,

Table 4 Safe Time in Corridor (min.

)

^~"\.^ndition Ko.

Floor No.

1 2 3 4 5 6 7 8

1 s* s S S S S S S

2 S

3 s S S S S S 13.0 S 4 s S S S S S 13.0 S

5 s 5.0 9.0 S S S 8.0 3

6 s 2.5 4.5 13.0 7.5 13.0 4.5 S

7 8.0 2.5 3.5 5.5 4.5 6.0 3.0 S 8 6.0 2.5 3.0 4.5 3.5 5.0 3.0 S

9 5.0 2.5 3.0 4.0 3.5 4.5 3.0 S 10 4.5

1 2.5 3.0 4.0 3.5 4.5 3.5 S

S : safe constantly; Csa<0.2, 0 < t < c>o

517
Table 5 Smoke Concentration in Staircase (l/m)

—~_^ndition

siatr _ —^^ucose

NO.

floor N0>~~-1..^

1 2 3 4 5 6 7 8

(T) (T) (IT) \l> (Ti Kg)

1 0 12 0.05 0 0 0 09 O.OB 0.01 0-01 0.06 0-0 3 0-03 0 0-1 9 007 0 0

2 0.62 030 1.7 1 .2 048 0 45 0.06 0.06 0.44 0.1 9 0-17 0 0 58 0 22 0 0

3 041 0 18 1 .4 1 .1 0.31 0-2 9 002 0. 02 0.21 0-10 0 09 0 0-3 7 0.14 0 0

4 0 41 0-18 1 3 0-96 0-31 0-29 0-02 0-02 0 .21 0-10 0-09 0 0-3 7 0-14 0 0

5 035 0.15 1 .3 0 98 0-27 0.25 0-02 0-02 0-18 0-08 0-08 0 0-37 0-13 0 0

6 0.35 015 1 .3 098 0-27 025 0-02 0-02 0-18 0.08 0.08 0 0 -37 0-13 0 0

7 0.35 0 15 13 0.98 0-27 0-25 0 02 0-02 0-18 0.08 0-08 0 0-37 0-1 3 0 0

8 035 015 1 3 098 0-27 025 0 -02 0-02 0-18 0.08 0-08 0 0 .37 0-1 3 0 0

9 035 015 1.3 098 0-27 0-25 0-02 0-02 0-18 0,08 0-08 0 0-37 0-13 0 0

10 035 015 1 3 098 0-27 0-25 0-02 002 0-18 OX)S 0-08 0 0 37 0.13 0 0

)

518
Use of Actual Observed Solar Radiation

Values in the Determination of Building Energy Requirements

John C. Thies, P.eJ

Southern Services, Inc. Birmingham, Alabama 35202

The effect of solar radiation is one of the many items that must be considered

to properly determine a building's energy requirements for heating and cooling. The intensity of direct and diffuse solar radiation impinging upon a building's surfaces

depends upon many factors; the season, locality, time of day and various types of

sky contamination.

Numerous computer programs to determine the total annual energy consumption of buildings for heating, cooling and other uses have been written by various companies

and organizations. Different approaches are used in these programs to estimate the effect of solar radiation on a building's heat loss or heat gain which in turn affect

the energy requirements of the heating and cooling systems being evaluated.

This paper describes a practical, rather than theoretical, approach for estimating the effect of solar radiation on a building's heat loss or heat gain. The ap- proach described is incorporated in a computer program that calculates a building's

total annual energy requirements on an hourly basis. Basically, available solar ra- diation data as observed on a horizontal plate at several locations in the Southeastern United States over a period of years are converted to solar intensity values normal to the sun's rays for each hour of a year. The advantages and disadvantages

over the theoretical approach are discussed.

Key Words: Solar radiation, actual radiation, observed radiation, actual ob- served radiation, building energy requirements, heating and cooling requirements.

1. Introduction

Consulting engineers and utility personnel often are required to estimate the annual heating, cooling and electrical energy requirements and energy cost of different buildings. Such estimates can be much more difficult and time consuming to calculate than the design point heat loss or heat gain for sizing the building's heating and cooling equipment. Calculation of the annual energy requirements involves

a summation of the combined effect of many factors over a lengthy time period, and these factors may vary considerably with time.[l]2 Though the electrical requirements of a building are affected only by the building's mode of operation, the heating and cooling requirements are affected by five factors:

(1) building location, (2) building construction, (3) building mode of operation, (4) building thermal load and (5) weather at the location.

2. Complexity of Problem

Because of the complex and interrelated nature of the factors involved, no simple and quick, non- computerized method has to my knowledge yet been developed for very accurately estimating the energy re- quirements of various types of buildings; however, there are many- different analysis methods in use to- day that provide reasonably accurate estimates of this nature. Use of past operating records on a par- ticular building, when these are available, may provide a reasonably accurate prediction of future energy

requirements for a building being designed - provided that the factors affecting its energy requirements

are almost identical in every respect. Unfortunately, many new buildings will differ from those existing

in not just one, but in many ways. The use of averages of operating records available from similar, yet

Supervisor of Technical Services, Rate Department

"Figures in brackets indicate the literature reference at the end of this paper."

519
not identical, buildings can be misleading. There is no "average" building.

3. Digital Computer Offers Means

The most direct and reliable estimating procedure for determining a building's annual energy requirements to provide its heating, cooling and electrical needs is an hourly integration of the simultaneous

calculated loads of each item involved as a function of the weather and use schedules. The modern digital computer offers the means for handling the vast amounts of data and calculations associated with pre- paring such an estimate. Development of computer techniques together with improvements in the availability of the basic data needed for the calculations are making it possible to determine the annual energy

requirements with a high degree of accuracy. Numerous computer programs and methodologies have been written in recent years by various companies and organizations to perform this type of work. Different

approaches are used in the programs to estimate the effect of solar radiation.

4. Solar Radiation a Major Factor

The amount of solar radiation impinging on the exterior surfaces of a building has a significant ef- fect on its heating and cooling requirements. In many buildings as a result of a particular orientation

and construction, solar radiation can have a very decided effect on the heating and cooling requirements.

Due to the numerous factors that affect the total amount of solar radiation finally reaching the earth's

surface, the exact magnitude impinging on the exterior surfaces of the building can be difficult to predict.

The intensity of direct solar radiation on a surface normal to the sun's rays above the earth's at- mosphere is generally assumed to be approximately 445 btu/hour/square foot. In passing through the earth's atmosphere, the sun's radiation becomes scattered and absorbed to varying degrees by water vapor,

dust, ozone and gas molecules that are present. Thus, what was only direct radiation now becomes both direct and diffuse. The amount of total solar radiation reaching a particular surface is the sum of the direct solar radiation, the diffuse sky radiation and the solar radiation reflected from surrounding surfaces. Its magnitude at any given time is determined by the moisture, the amount of smoke and dust in the air, the type and thickness of cloud cover, the locality, time of year and time of day [2].

5. One Way to Calculate Solar Radiation

It is recognized that some of the approaches used in existing computer programs and methodologies

are a result of insufficient solar radiation data being available for the entire United States at the time the program was written. In other instances, the approaches used were probably thought to be, and may be, reasonably accurate. One of the more prevalent approaches has been to calculate assumed hourly

solar radiation values for cloudless days and to apply available percentage cloud cover hourly data in an attempt to compensate for the effect of cloud cover on radiation. With this procedure, values of solar

azimuth and solar altitude angles are input in table form on a one set of hourly values per month basis. Values for cloudless days of direct solar radiation received at normal incidence at the earth's surface

and values of diffuse or sky solar radiation assumed to be received by variously oriented surfaces for clear or industrial atmospheres are also input for the varying solar altitudes. The program then interpolates the data to determine the hourly location of the sun and to estimate the hourly values of radiation impinging on the various building surfaces.

6. Use of Observed Solar Radiation Values

Another approach that can be utilized to calculate the hourly effect of solar radiation on a building's heating and cooling energy requirements is to use actual observed radiation data on a horizontal

plate as an integral part of the program. This is the approach that was utilized in a computer program

developed several years ago for the group of electric utility companies in the Southeast with which I am affiliated. The program was developed by the Mechanical Engineering Department of the University of Florida on a research contact with Southern Services, Inc. It considers the various factors mentioned earlier

and performs an hour-by-hour synthesis of a building's heating, cooling and electrical requirements on a multi-zone basis, up to a maximum of 24-zones. After the hourly requirements are calculated, the program

simulates the performance of specific equipment to meet these requirements and determines the total monthly and annual energy consumptions and demands. From these values, the monthly electric, fossil fuel and/ or steam bills can be calculated.

This computer program was developed on the basis of having the capability to be used on any type of building. Its development was predicated on being able to obtain the most accurate answer that present

scientific knowledge and available information would permit, using basic equations. In keeping with this basis, it was concluded that the use of actual observed hourly solar radiation data on a horizontal plate

for energy calculation purposes would be preferable to calculating assumed hourly values and adjusting

them by the application of cloud cover factors. The actual observed horizontal plate values would already

520
include the effect of the type and thickness of cloud cover and the moisture, smoke and dust content of

the air. Use of these values would also eliminate any error due to an improper cloud cover percentage

being estimated by the observer. It was recognized that the effect of an industrial atmosphere would

still need to be considered.

7. Details on Use of Observed Radiation Values

Research efforts located eleven year averages of actual observed hourly solar radiation data on a horizontal plate for various cities. This data was developed through a joint effort by the Boeing Com- pany and the U. S. Weather Bureau [3]. Data was extracted from the report for the southeastern cities of

Apalachi col a , Florida, Lake Charles, Louisiana, and Charleston, South Carolina. (See figure number one for a comparison of the average values of solar radiation on which this program is based and the extremes

which occurred over a 14-year period.) From the mean hourly solar radiation data in the report for these

three cities, average values in Langleys were calculated for each sunlit hour of each month. One Langley

is equal to one gram calorie per square centimeter and one gram calorie is equal to .003968 btus. These

values were converted to btu/hour/square foot of horizontal surface. (See figure number two for curves depicting typical hours.) Then, these values were converted to intensity normal to the sun's rays, still

in the same units. A review of these values indicated that afternoon values were somewhat excessive due

to the higher level of diffuse radiation energy existing in the afternoon hours. To obtain more realistic values of direct solar radiation normal to the sun's rays in the afternoon, the morning horizontal

plate readings were subtracted from the equivalent afternoon hour's readings, with the difference considered as diffuse radiation energy. New afternoon values were then created by adding this difference to the morning values at the same solar altitude. Equations were developed to calculate these values as well

as the sun's location for each hour of the year. (See figure number three for typical curves of the solar

radiation normal to the sun's rays as used in the program.)

8. Other Considerations

The effect of atmospheric clearness is considered by the program and the effect of an industrial at- mosphere can be considered. An atmospheric clearness number of 0.95 is used in the equations rather than

a value of 1.00 because according to Threlkeld and Jordan [4] in the southeastern states there are rela- tively high concentrations of atmospheric water vapor. The effect of an industrial atmosphere on direct

normal solar radiation is considered as a function of the solar altitude angle and can be varied from 0 to 100 percent. Moon's data for 40 degrees North latitude on about August 1 relating the direct normal radiation and diffuse radiation of clear and industrial atmospheres to solar altitude is used as a basis

[5].

9. Concluding Remarks

The above comments reflect the treatment of solar radiation for hourly energy calculation purposes.

I have not discussed the procedure used for design condition energy calculation purposes. The procedure

used for these purposes is somewhat different. One may question the accuracy attained by use of eleven year averages of hourly solar radiation data for three locations as opposed to other analysis methods.

It was concluded that an analysis procedure predicated on being able to use long-term averages of actual observed hourly data for three locations covering The Southern Company service area was more factual and inherently more accurate than other possible methods.

10. References

[1] ASHRAE Guide and Data Book, Applications, Chapter 54, p. 645-656 (1968).

[2] ASHRAE Handbook of Fundamentals, Chapter 28,

p. 469-475 (1967).

[3] "Summary of Solar Radiation Observations", U.S. Weather Bureau Report Number D2-90577-1) December 1964.

[4] Threlkeld, J. L., and Jordan, R. C, "Direct

Solar Radiation Available on Clear Days", ASHRAE Transaction Number 1622.

[5] ASHRAE Guide, Chapter 13, p. 298, Table 4 (1958).

521
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(TYPICAL VALUES)

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(a) Based on Apalochicola, Fla.,

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gure number two: 11-Year Average of Observed Radiation For Southeastern U.S.A. (Typical Values)

523
524
Design of Direct-Expansion Evaporator Coils by Digital Canputer

Donald G. Rich

Senior Engineer, Research Division

Carrier Corporation, Syracuse, New York

Jack B. Chaddock

Professor, Department of Mechanical Engineering

Duke University, Durham, North Carolina

and Consultant, Research Division

Carrier Corporation, Syracuse, New York

Heat and water vapor transfer normally occur together in the use of an evaporator coil for air conditioning, making the process diverse and complex. As knowledge of this process has developed, together with the ability to describe it

analytically, so has the need evolved for more exact procedures in practical design. This paper describes how the digital computer may be used for this purpose.

Beginning with a discussion of overall program objectives with respect to input

and output, the development of a program logic for evaporator design is described.

Decision points within the program include a logical procedure for selection of coil

dimensions and refrigerant-side circuiting. Other decision points of particular

significance are those Involving iterative procedures for arriving at designs which

match coil load conditions. Problems of convergence of these procedures are discussed. Basic equations used for performing the calculations are outlined, including

methods of determining air-side, refrigerant-side and metal thermal resistances. The effect of variations in these resistances on overall performance is considered as re- lated to methods of circuiting and operating conditions.

Sample solutions illustrating use of the program and output format are given.

Keywords: Air conditioning coils, coils (plate -fin) , cooling and dehumidifying, computer design (digital), evaporators, heat exchangers, refrigerant

heat transfer.

1. Introduction and Objectives

The large volume production of finned-tube heat exchangers for the air conditioning and refrigeration industry provides strong incentive for improving their performance and lowering their cost. The computer program described here, as an aid to the design of direct-expansion coils, was developed to

assist design engineers in meeting these cost and performance objectives. The program should be viewed

as providing a tool for "computer-aided" design, rather than design by computer. Although many design

decisions are made automatically, key decisions, and a final choice among several alternative "good"

designs, are still required by the design engineer. Introduction of the program into actual use at the Carrier Corporation has shown it to be of considerable assistance as a time and cost saver in identifying

that "best" design. And its acceptance, even by experienced designers, has been excellent.

Specific objectives for the development of the computer program were as follows:

1. To permit more effective use of the accumulating data on heat transfer and pressure drop for re- frigerants evaporating inside tubes and air flow over coil surfaces.

2. To study the differences which would result from computer-aided design, using more detailed and

fundamental heat transfer relationships, as compared with existing design procedures.

3- To provide a tool which would permit the designer to arrive nearer the optimum coil configuration

for a given task.

h. To identify critical areas in which present information is not sufficiently precise to satisfactorily determine an optimum design, and to plan research efforts to overcome them.

525
2 . Overall Program Logic

The design of an evaporator coll, like most design procedures, is not a straightforward process. It

is necessary to make a number of initial assumptions regarding coil configuration, air flow rates, and

refrigerant conditions. The more experienced designer will have acqiiired certain rules and judgments

which make it possible for him to choose initial values that produce a near-optimum solution. Nevertheless, even he will have to make a few trials and adjustments to match satisfactorily the particular con- straints for a given system.

Our most challenging task in developing a computer-aided design procedure for evaporators was to bring into its logic relationships which express quantitatively the judgment of experienced designers.

In addition there was the overriding goal to make the program a flexible tool in the hands of the designer. While key assumptions and decisions could be made by the program, they must not be hidden frcm

the user. In fact it would be desirable for the designer to override key program logic, and to specify

particular constraints on certain variables where he desires. In general he should be able to guide the computer calculations, when desired, to confom with his experience and judgjnent in obtaining a satisfactory design.

2.1 What it does - general

The program determines the physical dimensions, leaving air conditions, heat transfer characteristics, and manufacturing cost of a direct-expansion air cooling and dehumidifying coil. As input it re- quires geometric data defining the type of plate-fin heat transfer surface, constants and exponents to calculate air-side pressure drop and heat transfer performance, required cooling load, system operating

conditions, and cost data.

The procedure is to make an initial assumption with regard to air quantity (about ^00 cfm/ton for

air conditioning applications) , and air face velocity (usually between hoo to 500 fpm) and calculate the coil dimensions. An iterative calculation then matches the heat transfer rate to the required cooling

load. The iterative procedure either adjusts the air face velocity or the coil size to match the loads to within one-half of one percent. Finally, the program calculates the leaving air conditions, the air

pressure drop, the sensible heat factor, and the coil cost. The program also has features to automatically index to another air velocity or coil size and repeat the above calculations. The designer is thereby provided with several alternate designs to assist him in either making a final choice, or re- specifying key conditions in a continued search for an "optimum" coil design.

2.2 What it requires

The user of the program must supply data on the plate-fin type heat exchanger surface, the system

operating conditions, and the manufacturing costs. Figure 1 is a typical input data sheet. The quantities appearing thereon are as follows:

a. Coil data

(1) Description, Refrigerant (12 or 22) , and Identification Number.

(2) Tube outside diameter and wall thickness - Dq and t^ (inches).

(3) Hairpins or return bends, and return bend inside diameter - Dj_-b (inches).

(h) Tube spacing (transverse and longitudinal) - and Pj, (inches)

(5) Fin spacing and thickness - Nf (fins/inch) and tf (inches).

(6) Surface heat transfer constants - C-^ and n^^ (for the determination of the air-side thermal

resistance, as explained in Section 5.2).

(7) Surface pressure drop constants - and n (for the determination of the air-side frictlonal pressure drop, as explained in Section 3.2 j.

By storing the heat transfer and pressure drop characteristics of a given type coil in a disc file,

items (6) and (7) can be replaced by an identification number which is related to the location on the disc

•where the information is stored. This number is 5 in the example given in Figure 1.

b. System operating conditions

(1) Cooling load - q(Btu/hr)

(2) Saturation temperature at suction - tyQ(°F)

526
(3) Subcooled liquid temperature at inlet

(k) Suction superheat

(5) Entering air dry-bulb temperature

(6) Entering air wet-bulb temperature

(7) Atmospheric pressure

(8) Safety factor (see Eq. l)

(9) Minimum air face velocity

(10) Air face velocity increment

(11) Maximum air face velocity

c. Cost data

The cost of materials for construction of the coil core can be expressed as the sum of the costs for

the tubing, the fin material, and the return bends. The tube and fin costs will depend on the weight or

volixme of material used. The total material cost is then written as

Cm = ^t ^t ^ Cf Vf ^ % \

The input data then requires

(1) Cost of tube material - C^ ($/cu in)

(2) Cost of fin material - C^ (t/cu in)

(3) Cost of return bends - C^ (t/bend)

More detailed cost calculations would bring into consideration costs of the refrigerant distributor

and feeder tubes, solder, labor, etc.

2.3 Decision Points

A first and major decision is where to start the design calculation. Other key decisions involve

the refrigerant circuiting of the coil, and how to direct the search to insure a final design choice

which is a near optimum one. The program logic which makes these decisions originally evolved from the judgment of experienced designers, and underwent refinements as it was put to use on a variety of evaporator designs.

a. Initializing coil dimensions

Three choices are possible as follows:

(1) Case 1 - Aspect ratio

Under this case, the ratio of coil length between tube sheets to coil height (aspect ratio) is specified by the designer. In iterating to arrive at the design cooling load the length between tube

sheets is varied, hence the final design does not correspond to the exact value of aspect ratio.

(2) Case 2 - length between tube sheets With this selection the program iterates on air face velocity so that the final design does conform

to the specified length dimension.

(5) Case 3 - Number of tubes in the coil face

This is equivalent to the selection of the face height of the coil. With this design constraint the program holds the given height and iterates on the length between tube sheets to match the design load.

If the user does not choose to select any of the above, the program sets the aspect ratio at a value

of 2, and proceeds as in Case 1.

- tsub(°F)

- Atsup(°F)

- *ai(db)(°F)

- tax(wb)(°F)

- Patm^'"-

- Fs

- V__, . X (ft/min) 70(min) ' ' - AV^o( ft/min)

- V_„, X (ft/min)

T^o(max) '

b. Air velocities

Air face velocities for DX evaporator coils have

coil size which may not be economically competitive.

and flow rates

a restricted range. Low velocities require large

High velocities may cause entrainment of condensed

527
water on the coil surface, and carry over into the discharge air stream. As listed above for the system

operating conditions - input data, the user must specify a minimum, maximum, and incremental air face velocity. Reasonable limits are 300 fpn and 600 fpm for the minimum and maximum velocities, although

velocities outside this range may be used in special cases. The incremental air velocity, AV^^, directs

the program to index upwards from ^yo(ja^±j^) to (max) that increment. A good initial selection would

be 100 fpm. In the final search for a best design tne increment may be made smaller.

An air flow rate of hoo cfm per ton has proven to be a good choice for starting the design in air

conditioning applications. This choice usually leads to an operating sensible heat factor of between 0.7 and 0.8 for a 3 row deep coil at ^00 to 500 fpm air face velocity. In iterating to arrive at the design

cooling load, and in automatically indexing to new design configurations, the cfm/ton changes.

c. Refrigerant circuiting

If the number of circuits is not given with the input data a subroutine is called which determines

circuiting automatically. In this subroutine the number of circuits is selected so that the refrigerant

flow rate is within the range of good design practice. In addition, circuiting selections are limited

to those which will provide balanced refrigerant distribution, a factor of considerable importance to good performance

For an air conditioning coil with l/2 inch tubes, experience has shown that a good starting point for determining the number of circuits is to assume a circuit load of l6,000 Btu/hr. At smaller or larger

tube diameters the loading factor of l6, 000 must be decreased or increased correspondingly. Changes in the pressure level also affect the loading factor because of density changes of the fluid. Relationships

to account for these effects are incorporated into the program logic to calculate an initial value for the number of circuits. The program next requires that both and the ratio N|-/Nc be integers. For example,

if = 2h tubes in the coil face, then the number of circuits, Nq, permitted is 1, 2, 3, 4, 6, 8, 12, or 2h. The selection will be the smallest of these numbers which does not exceed by more than 30 per cent the initial value.

The above procedure insures that a balanced refrigerant circuiting arrangement will result. The experienced designer may recognize a satisfactory circuiting arrangement not permitted by the simple program logic. In this case he may specify in the input data, and override the computer selection

procedure

d. Indexing to new designs

Depending upon the designer's choice of Case 1, 2, or 3 in Section (a) above, the computer is directed to iterate on either air face velocity or face length to match the design load. After the first

design has been found, provision has been made for autcmatically seeking alternate designs using the same method of iteration. The first method of indexing to a new design is to change the number of tubes in

the coil face by first two greater and then two less than that found in the initial design.

When the design is proceeding on the basis of aspect ratio (Case 1 or no designer specification)

,

or on tubes in the face (Case 3) , the design starts with the minimum air face velocity of V^^/ . x

After the initial design, and those at + 2 additional tubes in the face are completed, the compuier indexes to a higher face velocity by the velocity increment AV^^. Again at the completion of an initial

design for this velocity the program calls for designs at + 2 additional tubes in the face. The indexing

to increasing air velocities continues according to the equation

V^o = V^o + I (^V)yo

with I = 1, 2, 3, —, until V^^ exceeds '^jo^^nax)- In Case 2 where the length between tube sheets is specified, the procedure for indexing to + 2 tubes in face is used, but the incremental air velocity is not. If the number of refrigerant circuits is specified, or if the face area of the coil is fixed by giving both Lp and with the input data, then no

automatic indexing occurs

2.^ Flow Diagram for the Main Program

A condensed version of the main program flow diagram, labeled DX - 12/22, is presented as figure 2. As used on an IBM 1130 computer it calls on nine subroutine programs, designated: R, S, T, A, B, C, D, E, and H. Referring to circled numbers on this figure, the explanatory phrases below will assist in followthe program logic

,

528
(1) Subroutine program 'A' reads the input data of figure 1, and supplies index numbers to carry out

the automatic indexing to new designs, described in (d) above.

(2) Subroutine 'R' calculates refrigerant properties for either R-12 or R-22.

(3) Subroutine 'S' calculates air-side thermal resistance and pressure drop at standard air con- ditions for the specified plate-fin siirface.

(h) Subroutine 'T' calculates the metal resistance of the finned coil by the sector method.

(5) Subroutine 'H' calculates the enthalpy of moist air at the coil inlet. The other calculations

here are to make a temperature correction to the air-side thermal resistance, and set an initial

value of air flow by the rule of hoo cftn/ton.

(6) Subroutine 'B' calculates the coil geometry, including the number of refrigerant circuits.

(7) Subroutine 'C calculates refrigerant-side heat transfer coefficients and pressure drops, the mean temperature difference in the superheat section and the superheat length.

(8) Subroutine 'D' calculates the mean temperature difference in the evaporating section of the coil.

(9) The load calculation is made by determination of heat exchange in both the evaporating and

superheating portions of the coil.

(10) The convergence routine to match calculated to design load. (See Section h.2)

(11) Subroutine 'E' calculates the leaving air conditions, the sensible heat factor, coil apparatus

dew point, and materials or manufacturing costs.

(12) This is the automatic indexing sequence to set up for additional designs at + 2 additional

tubes in the face, and at incrementally higher air velocities.

5. Basic Relations

The flow and heat-transfer processes occurring in a direct expansion evaporator are exceedingly

complex. On the air side heat and water vapor transfer simultaneously between the air and the fin surfaces. On the refrigerant side a series of changing two-phase gas-liquid flow patterns occur due to the increasing ratio of vapor to liquid flow rate. These changing flow patterns and velocities profoundly

affect the heat-transfer coefficient and pressure gradient.

Figure 3 illustrates, in an approximate way, the heat-transfer coefficient and temperature behavior

of a refrigerant as it moves through an evaporator tube. Two sets of curves are shown, one for high

loading and the other for low loading. As shown in this figure, the heat transfer coefficient increases

to a maximum and then decreases sharply, eventually reaching a value corresponding to that for pure gas flow in the superheat section. The increase in coefficient is due to increasing shear at the vaporliquid interface. The decrease is due to the development of dry areas on the wall, a condition which

occurs at vapor qualities on the order of 0.8 in typical evaporators. Experimental determination of

these variations in coefficient have been reported by Anderson, Rich and Geary (l)"''

It is clear from figure 3 that an accurate calculation of the heat transfer in an evaporator cannot

be made using a single average value of the refrigerant coefficient. Ideally, a step-by-step calculation

could be performed such that local variations in coefficient, refrigerant temperature, air enthalpy, and

surface temperature are accounted for. Such a procedure, however, would be complex and time consuming.

As a first approximation, therefore, the present program divides the coil into two sections - an evaporation section and a superheat section - with average coefficients determined for each. Coil capacity

is then calculated as follows:

F S At \ F S At

s o m \ s o m

R + R / R + R

r m / r m , evap ' sup

(1)

where Sq = external surface area (prime plus finned)

Atjjj = mean temperature difference between the refrigerant and the wetted coil surface R^ = thermal resistance to heat transfer between the refrigerant and the inside surface

of the tube wall per unit of external surface area

Rjjj = thermal resistance of the fin and tube material per unit of external surface area

Fg = a safety factor specified by the designer

Procedures used for calculating At , R and R are described in the following sections.

m-" r m

""Figures in brackets indicate the literature references at the end of this paper.

529
5.1 Mean Temperature Differences - Surface Temperatures

Figure h presents two examples of circuiting arrangements which might be used in direct-expansion

evaporator coils. In kk (labeled thermal parallel flow) the refrigerant enters at the coil leaving air

face, flows through the coil generally counter to the air flow, and discharges at the entering air face. In (labeled thermal counterflow) the refrigerant enters at the entering air face, flows through the coil generally parallel to the air flow, but returns to the face for the final pass (tube marked S) . Both

of these arrangements have the advantage of providing superheating in the region where the air temperature

is maximum. The second arrangement has the additional advantage of providing an approximate thermal

counterflow relationship between the air and refrigerant. Although other arrangements may be used in practice, depending upon economic considerations related to the application, those shown in figure 2 are sufficiently typical to be useful as models.

Figure 5 is a simplified thermal diagram for an evaporator depleting the evaporation and superheat

sections and defining the various terminal temperatures and enthalpies used to calculate the mean temperature differences. Circuiting is the thermal counterflow type as shown In figure ^B, with superheating

assumed to occur in tubes at the coll face. In figure 5 this results in a discontinuity for the plot of air enthalpy (h^^) and coil surface temperature (t ) vs circuit length. As Illustrated the superheat tube section is in contact with entering air (h^^ = hg^^J.

Using temperature symbols as identified in figure 5, the following equations can be written for the mean temperature differences:

Evaporation Section

' *si

- V \ log

\ *S2 - *r2

1

thermal parallel flow

(t - t ) - (t - t J si rs S2 ri or At = ~ r (5) m / t , - t

' log (4^) ^ S2 ri /

Superheat Section

(t - t ^) - (t - t J

'm

thermal counter flow

At =— ^ (h) log

(t - t \ S3 rg \ t - t I S4 ra /

Referring to figure 5, note that tpo is the temperature at saturation corresponding to the refrigerant pressure at the coll outlet. This value Is an input to the program, as is the superheat, tj.^ - t^^^. The other refrigerant temperatures are direct functions of the tube-side pressure drop; t-^^ - tj,Q is the temperature drop due to pressure drop in the superheat section and t^x - t-^^ is the temperature drop due to pressure drop in the evaporation section.

The coll surface temperatures will depend upon the air flow conditions, the refrigerant conditions

and whether the surface is wet or dry. The computer program presented here assumes that the coll surface

will be completely wetted. This is not a serious limitation for a design program since evaporator coils

normally operate fully wetted at normal design conditions. With this assumption, each of the surface

temperatures can be related to a coll characteristic, C, by the equation(2)

where t^ = surface temperature

tj, = refrigerant temperature

hg^ = air enthalpy

t^ - t R + R

s r m r

has- h^ c paR

= C (5)

530
hg = air enthalpy- at saturation at tg

Cp = humid specific heat 0.2h'^ Btu/lb(ia Ra = thermal resistance between the air and surface per unit of external surface area

For the evaporation section of the coil circuit a single value of the coil characteristic is used,

based on an average value of the refrigerant-side thermal resistance. Values of tg-,^ and tgg are then determined from eq (5) using hai - and hg^^ and, respectively, tr^^ and t^^ ^rs ^"^^ ''^ri themal parallel flow)

For the superheat section of the coil circuit two values of the characteristic are used. At the entrance the surface temperature (tgg) is based on the evaporating coefficient and t^.^; at the exit the surface temperature (tg 4) is based on the superheat coefficient and t^.^. The entering air enthalpy, hai> is used in both cases reflecting the assumption that the superheating tube passes are located on the enter- ing-air side of the coil.

A computer procedure for solving eq (5) is given in Section h.l.

3.2 Air-Side Thermal Resistance

Because of the many geometric variables involved, the air-side thermal resistance for plate-fin coils

is determined by experiment. Fin spacing and thickness, tube spacing and diameter, number of tube rows and fin surface configuration are variables upon which the coefficient depends. Generalized relationships

which can predict the effect of these variables are lacking. Detailed procedures for experimentally determining the air-side thermal resistance of cooling and dehumidifylng coils are given in ASHRAE Standard

55-6^ (3).

For the small temperature differences and limited velocity range encountered in normal air conditioning and refrigeration applications, convectlve heat transfer data can be represented accurately by the Nusselt equation.

- f-^f' - (6) k ^

\

\x I r

Setting m = 0.*+, eq (6) can be solved for R^ (= l/h) , to give

^a - \~K k P

• r

where cp^is a properties function to account for variations from standard air conditions.

An approximate equation for q5^, normalized to standard air conditions of 70° F and 1 atmosphere, is

^1 " 1 + 0.00143 (1.109 + n^) (t - 70)

Equation (8) is accurate within + 1 per cent from -25°F to 175°F.

The frictlonal pressure drop can be calculated in a similar manner. Thus

Ap =

2P gp 2 g^ D

1 + m

m \ 2-m

G

or Ap C cp V

2 2 ^2 70 (9)

531
where qs^ accounts for variations from standard air conditions.

C-^, n^, Cg and n are empirical constants fitted to the experimental data for a particular geometric

coil configuration. A file of these constants for a variety of coil types can be stored for automatic

access by the computer. Alternately, the designer can supply values to be read as part of the input data.

5.3 Metal Thermal Resistance

The metal thermal resistance is the sum of the resistance of the fins and the resistance of the tube wall. The following equation relating the metal resistance, B^, to the fin efficiency f), is taken from

Reference 2.

R c a pD. S /S.

1 o' 1 2 k, log

D.

1 (10)

Herein, h^ = dhg/dtg; k^ is the tube conductivity; Dq and Ti^ are the tube OD and ID; and , Sf,

and Sj^ are the external prime, external finned, total external, and internal surface areas respectively.

Various methods have been proposed for calculating the fin efficiency. Where the fin shape associated with each tube is nearly square the efficiency of an annular fin of equal area can be used {h)

Otherwise, more accurate results can be obtained using the sector method (h) (5). The present program

utilizes a subprogram based on the sector method.

3-^ Refrigerant-side Thermal Resistance and Pressure Drop

Experimental measurements of evaporating heat transfer coefficients in tubes have been reported in

the literature, and several methods of correlating these data have been proposed. Reference 6 contains

a summary of experimental results and correlating equations which are applicable to forced convection

evaporation of refrigerants. None are completely satisfactory for the complete range of conditions en- countered in evaporators. As stated in Reference 6, "the single equation which can be recommended for

broadest application to refrigerant evaporation in tubes is that of Pierre (7) • Altman, Norrls and

Staub (8), and Chaddock (9), have fitted it to a wide range of Refrigerant 12 and 22 data."

Pierre's equation for exit qualities < 90 per cent is

Nu = 0.0009 (Rg^Kj.)°"^

or h^ = 0.0009

G D. H

J Ax h fg

(11)

where AxL

D.

1

J

change In vapor fraction

tube length

tube inside diameter

liquid thermal conductivity

liquid viscosity

latent heat

mechanical equivalent of heat (778 ft-lb/Btu)

unity.

In the present program a modified form of Eq. (ll) was used In order to cover vapor fractions up to

The heat-transfer coefficient for the superheat section can be calculated by the well-known methods

for single-phase forced convection in tubes. McAdams (lO) , after critically evaluating a large amount of data covering a wide range of conditions, gives three equations. One of these Is called the DittusBoelter equation, and is expressed as:

532
h D.

1 ,023

D. G' 1 0.8 0.4

Pr

or h = cp^ (02)

1

where cp^ is a function of the fluid properties.

Reference 6 tabulates values of cpg as a function of temperature for various refrigerants. The following simple polynomial expressions can be used to calculate cpg with a maxim\im error of 0.7 per cent over the temperature range 0 to l6o°F. R-32 vapor cpg = I.816 x 10"® + 3.2lk x 10"® t + I.786 x 10"^ t^ R-22 vapor cps = 1.97^ x 10"® + 3-039 x 10"® t + I.II6 x 10"^ t^

The pressure drop in a direct-expansion evaporator has several components. These include pressure

drop across the bends, pressure drop due to friction in the tubes, pressure drop within the suction

header, inlet and exit losses, and a pressure drop due to acceleration of the refrigerant as it flows through the coil. In the present program header losses are not included (pressure at the exit of the tubes has been chosen as a program input), and inlet and exit losses have been neglected. Of the re- maining losses (bends, friction and acceleration) the acceleration loss is generally smallest and friction

largest, although bend losses can predominate in very narrow coils.

Several methods have been proposed for calculating friction pressure drop for two-phase flow inside

tubes. The one proposed by lyfertinelli and coworkers (ll), (12) has received widest acceptance because of

its general applicability. A somewhat simpler method is that based on the friction-factor equation. It has proven to be satisfactory in correlating data for restricted ranges of conditions.

The basic form of the friction-factor equation is:

= —f ^ (13) 2 p i

where L is the total circuit length and G is the refrigerant mass velocity based on the total flow rate

(liquid plus vapor). Various definitions of the two-phase friction factor, f, and two-phase density, p, have been proposed. Pierre (13) uses an average between the liquid and vapor densities, and defines his

friction factor in terms of Kf/Rg (see eq n) . A similar approach was taken in the present program except the vapor density was used and the effects of inlet vapor mass fraction were incorporated in the friction factor.

In addition to the pressure drop due to friction there is also a loss in pressure to accommodate the acceleration of the refrigerant as it changes frcm a liquid to a vapor. The acceleration pressure drop

can be calculated by the relation proposed by Martinelli and Nelson (12) . For complete evaporation this

relation is

^2 r (1 - X )2 X

2

where R^ is the fraction of the tube filled with liquid at the inlet.

The following polynomial expression, based on the curve given in Reference (ll) , can be used to calculate R^L log^Q \ = " O.Shhl^ + o.ii555V - 0.1308 + 0.01929

533
Virtually no data is available in the literature for pressure drop of refrigerants in bends. As an

approximation, therefore, the pressure drop for the bends is calculated in the same manner as a straight

tube, using a length equal to 75 diameters. This practice is commonly used for single-phase flow (lO)

3-5 Leaving Dry Bulb Temperature, Sensible Heat Factor and Coil Costs

After the program calculations have converged to a coil design whose capacity matches the given load,

a final subroutine is called which calculates the leaving dry-bulb temperature, the sensible heat factor,

and an estimated cost.

Using the relationships recommended in Reference 2, the leaving dry bulb temperature is calculated

by first determining the saturated air enthalpy, ITg, at the coil surface by

(h - h ) ai aa al

where X = -S /w c R

o' pa

The surface temperature T corresponding to h" is readily found, and the leaving dry bulb temperature and sensible heat factor follow directly fran^the relations

_ -X

t = t +(t -t)e (15) as s ai s

'

SHF = c (t - t )/(h - h ^) (l6) p ai a2 ' ai as' ^

'

Once the coil size has been determined, fin and tube costs can be calculated based on unit material

costs furnished as input. Labor costs may also be included provided information is available which re- lates the time required for coil fabrication to the various gecsnetric parameters. Obviously, labor costs will vary greatly depending upon manufacturing methods, plant layout, production volumes and other factors

and generalized relationships cannot be given.

h. Iterative Procedures

An important consideration in the development of computer programs for designing heat exchangers is the selection of iterative procedures which converge quickly and consistently to a correct solution. In the present program iterative procedures are involved in solving eq (5) for surface temperatures, and also to find coil size or cfm to match the specified load. A discussion of these procedures is given below

^.1 Surface Temperatures

"When the derivative of f (x) is a simple expression and easily found, the real roots of f(x) = 0 can be computed rapidly by a process called the Newton-Raphson Method" (l^) . According to this method,

successive approximations to the root can be formed by the following steps.

a, = a - f (a )/f' (a ) 1 o

^ o" o'

a = a - f (a )/f' (a )

a^ = a - f (a ) /f' (a ) n n-i n-i'' n-i'

where a^ is the first approximation to the root. Applying this procedure to eq (5) we obtain

fCtg) = t3 - tr - C (h^ - hg) = 0

534
Therefore

f (t ) = 1 + C h.

-t - t - C(h ~h)

t (new) = - (-^ £ 5 '—\ (17)

s s 1 + C h

' s

Since f'(tg) is always greater than unity, a routine based on eq (l?) will always converge rapidly.

Following are a series of FORTMN statements based on eq (l7) which can be used to calculate surface temperature to within E degrees of its correct value.

C = (RR + RM)/( .2^3*RA) TS = TR

1 CALL HAIR (TS, P, HS, HSP) DT = (TR-TS + C* (HA. - HS) j/(l. + C * HSP) TS = TS + DT IF(ABS (DT - E) ) 2, 2, 1

' 2 CCWTINUE

In the above routine HAIR is a subroutine which calculates air enthalpy at saturation (hs) and its

derivative (HSP) as a function of surface temperature (ts) and air pressure (p)

h.2 Air Flow Rate

As previously described, the program may, in some cases, be called upon to match the load by varying

the coil length between tube sheets, with the air face velocity held constant. In other cases the air

flow rate is varied to match the load while holding the coil size constant.

Let us first consider the case where the coil size is fixed. Figure 6A is a graph showing for a typical case how the coil capacity q as calculated by the program will vary with the assumed flow rate w. Note that as flow rate increases the capacity asymptotically approaches a maximum value. This is the value corresponding to negligible air-side thermal resistance; it must be greater than the given load if

a solution is to be found.

As the air quantity decreases, the capacity approaches zero at a finite value of air flow equal to

Wq. This is due to a decreasing enthalpy difference (approach) at the leaving air side of the coil. This zero approach condition is possible because the leaving air enthalpy, hg^^, is calculated as a function of the given load, q^, rather than as a function of the calculated capacity, q, since the latter

is not known at the beginning of the computation.

Figure 6b is a similar plot to figure 6a for the case where the length between tube sheets is varied

to match the load. In this case the calculated capacity can reach a maximum and th^ decrease with increasing length and flow rate. The decrease occurs when the effect of refrigerant-side pressure drop becomes dominant. Obviously, the given load must be below this maximum value if a solution is to be found.

Depicted graphically on figure 6b is an iterative procedure which can be used in both of the above

cases to find the value of w for which q = q . The procedure calculates successive approximations to w

by interpolating along a straight line between the points (O, Wq) and (q^j, w^) . A general equation relating the new value of flow rate, Wj-^+j^, to the previous value, Wjj, follows directly.

w = w + (w - w ) —

n+1 o ' n o qn

Although convergence is not particularly rapid with this procedure, it offers the important advantage of insuring convergence for all values of w^ less than w^.

535
5. Sample Output

Figure 7 gives the output corresponding to the input provided in figure 1. In addition to the calciilated quantities for the dimensions and performance of the coll, most of 'the input data values are re- corded also. This is to assist the user in identifying the coil design and in making comparisons and

selections. Comparisons are also .facilitated by the columnar format used for output.

In the example given the program was asked for solutions at only one air velocity, ^50 ft/min. Three

solutions were given. As a first choice the prograjn arrived at a design with 2h tubes in the face and 12 circuits. It then increased the tubes in the face to 26 and selected 15 circuits. Finally, the tubes in

the face were reduced to 22 and a solution given for 22 circuits. In this last case 11 circuits was re- jected by the program as being beyond good design practice; the search for a solution at a greater number

of circuits resulted in 22 as the only number which would meet the requirements that N^/n^ be an integer.

The last case illustrates a situation where designer selection of the number of circuits may result

in an improved design. If, for example, space limitations dictate a maximum of 22 tubes in the face the designer may wish to override the program by specifying the number of circuits at some value between 11 and 22. While this may present a more difficult circuit balancing problem, it could result in a more

economical design.

An important constraint which frequently is imposed is the cfm/ton. As presently written the program starts with a value of cfm/ton dependent upon the refrigerant temperature and the entering air enthalpy. The final value will show variations from this initial selection, depending on the ratio of the design load to the first trial value of the calculated load. To arrive at or near a specific cfm/ton,

therefore, some trial and error computations may be necessary involving face velocity, fins per inch,

number of tube rows or face area. Here again the designer's experience and judgment plays an important

role in arriving at a good final choice.

From the foregoing it is clear that the program described here is a powerful design tool. It has made practical the application of improved fundamental relationships, and more accurate design procedures.

As our understanding of the fluid flow and heat transfer processes is increased through new research re- sults, modifications can be made to reflect that improved knowledge. In this way the program plays an

important role in accelerating the process of bridging the gap between research results and engineering

application

Acknowledgement

The authors express their gratitude to Mrs. Anna D. Mathill of the Mathematics Section, Research

Division, Carrier Corporation, for her major contributions to the development of this program.

6. References

(1) Anderson, S. W., Rich, D. G. , and Geary, D. F.: Evaporation of Refrigerant 22 in a Horizontal

5/^ inch 0. D. Tube. (ASHRAE Transactions,

Volume 72, Part I, I966, p. 28).

(2) Standard for Forced Circulation Air-Cooling and

Air-Heating Coils, (Air Conditioning and Refrigeration Institute, Standard ^10-64).

(3) Methods of Testing for Rating Forced-Circulation

Air-Cooling and Air-Heating Coils (American

Society of Heating, Refrigerating and AirCondi tioning Engineers, Standard ^J>-6h) .

(h) Carrier, W. H. , and Anderson, S. W.: The Resistance to Heat Flow Through Finned Tubing

(Heating, Piping and Air Conditioning, May

19^^, p. 504)

(5) Rich, D. G. : The Efficiency and Thermal Resistance of Annular and Rectangular Fins (Proceedings of the Third International Heat Transfer

Conference, Vol. Ill, I966, p. 28l)

(6) Handbook of Fundamentals, Chapter 3, Heat Transfer (American Society of Heating, Refrigerating and Air Conditioning Engineers, 1967)

(7) Pierre, Bo: (Kylteknisk Tidskrift, Volume 3,

May 1957, p. 129).

(8) Altman, M. , Norris, R. H. , and Staub, F. ¥.: Local and Average Heat Transfer and Pressure

Drop for Refrigerants (ASME Transactions,

August i960, p. 189)

(9) Johnston, R. C, Jr., and Chaddock, J. B. : Heat Transfer and Pressure Drop of Refrigerants

Evaporating in Horizontal Tubes (ASHRAE Transactions, Vol. 70, 196k).

(10) McAdams, W. H. : Heat Transmission, McGraw-Hill

Book Co., New York, 195^, 3rd Ed.).

(11) Lockhart, R. W., and Martinelli, R. C: Pro- posed Correlation of Data for Isothermal TwoPhase Two-Component Flow in Pipes (Chem.ical

Engineering Progress, Vol. 19*^-9, P- 39)-

536
(12) Martinelli, R. C. and Nelson, D. B. : Prediction (l^) Scarborough, J. B. : Numerical Mathematical

of Pressure Drop During Forced Circulation Analysis (The Johns Hopkins Press, 1950,

Boiling of Water (ASME Transactions, Vol. 70, 2nd Ed.).

19^5, p. 695).

(15) Pierre, Bo: Flow Resistance with Boiling Refrigerants (ASHRAE Journal, September and

October, 1964).

537
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538
DESieN OF DIRECT EXPANSION EVAPORATOR COILS PROSRAM 0X-I2/Z2

Figure 2 Main Program Flow Diagram

539
HIGH LOADING

LOW LOADING

CIRCUIT LENGTH

Figure 3 Heat Transfer Coefficient and Temperature Versus Circuit Length for an Evaporating

Refrigerant in a Tube

540
.REFRI6.

OUT

,REFRIQ.

OUT

REFRIG

IN REFRIG.

IN

THERMAL PARALLEL FLOW

B THERMAL COUNTERFLOW

(s « SUPERHEAT TUBe)

Figure h Two Evaporator Circuiting Arrangements

541
542
A FACE AREA CONSTANT

B FACE VELOCITY CONSTANT

Figure 6 Calculated Capacity Versus Assumed Air Flow Rate

543
COOLING MD DEHUMIDIPYING COIL DESIGN DX-12/22

DESCRIPTION' SAMPLE RAMPT.F

^ ur\ V J-j ui iDJ-jiv J

TDTT -po T(^Tjyp A Torn 22 22 Cel. FTWR X .l.AM 1—' J.P"R"R TNPH 1

1 wJ.i 1 ^ n J.^ «

"1 n

IMTTMRPP 1*1 CW PnWC; U r>~' r\ \Jr i\ UVv o

zJ J

TT TP.'W TP A CV ^ PA r TWTi 1 PRn X U TUBE ROW SPACING INCHES 1.083 1.083 1.083 TUBE O.D. INCHES .520 .520 .520 m 7 . Ul f

. 0065 . 0065

• i'? •

riXn ATR WTV Hi XiVA-f OPTTVC XIX \>J'^TTl'l XU J PPM" CVM( 9>TT)) CFM 7Q^P 7885 8236

A-TD PRRRRTTR'R IN . HG 2Q Q? PQ OP PQ OP

TVrriMR'F'R vi Ui"lXXtjX\ (W\J1: TTTRTilf? ± UlJX-iQ TTJ X-LN "PAfP Prl-'^ylj 2h 26 22 X3 00 NUMBER OF RETURN BENDS 24 26 22 COIL HEIGHT INCHES 30.00 32.50 27-50

LENGTH BETWEEN TUBE SHEETS INCHES 8i^.6l 77.61 95.84 SURFACE RATIO 20.3 20.3 20.3

RTTRTOPF /"PAPF /rDW Pli 7 pit 7

JjUHU I5XU / rlrv p iinnnri P iinnnn

SUCTION TEMPERATURE DEGF ^2 .^2 .

4-2 .

rOMD T.TQ TEMPRRATTTRF DEGF 110. 0 110 .Tin n

QTTpTTRHFAT DEGF 12 . 00 12 . 00 12 . 00

VJiVX / J.\J-JX X\ • X'XX U \ V"i / DEGF 10.23 10.81 1 56

iJQTIPP UX^X^ /pT?|TO MTTl f RTTPHTI / X\Xjr X\ • vi±U \ OU JTIIX y DEGF J-^ 1 ^

13.68 it 65

ENT. DRY BULB TEMPERATURE DEGF 80.00 80.00 80.00

ENT. WET BULB TEMPERATURE DEGF 67.00 67.00 67.00

LVG. DRY BULB TEMPERATURE DEGF fin LVG. WET BULB TEMPERATURE DEGF S7 4S S7 8q TADP DEGF 7il ss 66 sfi PO

AIR TH.RES.(STD) HR-SQFT-DEGF/ BTU (7777 0777 • (7777 '-'1(1 AIR PRESSURE DROP(ACT) IN. WATER .268 .268 .268 METAL RESISTANCE HR-SQJT?-DEGF/BTU .0172 . 0172 .0172 REFR.COEFF (EVAP) BTU/HR-SQFT - DEGF 655 6i4 451 REFR.C0EFF(SUEHT)BTU/HR-SQFT - DEGF 82 77 sn

REFR. MASS VELOCITY LBS/HR/SQFT

REFR. TEMP. DROP DEGF 6. 08 h 87 1. 08

FACE AREA SOFT 17.63 17.52 18.30

SUPERHEAT LENGTH FEET h nn SENSIBLE HEAT FACTOR 7SP .766 CFM PER TON 597 412

FIN MATERIAL COST DOLLARS 27.87 27.70 28.94

HAIRPIN TUBE COST DOLLARS 55.62 55.38 57.61 TOTAL MATERIAL COST DOLLARS 85.89 85.68 88.75

FIGURE 7 SAMPLE OUTPUT

544
Simulation of a Multicy linder

Reciprocating Refrigeration System

with Chilled Water Coil and Evaporative Condenser

E. Stamper and M, Greenberger'''

Newark College of Engineering

Newark, New Jersey 0 7102

A refrigeration system consisting of a packaged chiller, chilled water coil, and evaporative condenser was simulated mathematically in an effort to determine

it's performance under varying load conditions. While the simulation was done for

the above system only, the method used is sufficiently general to be applied to re- frigeration systems with other components. Components were selected from manufacturers catalogues to meet design load conditions for an assumed building whose

load is time dependent. The response of the refrigeration system to these changing

building loads is found by simulating the performance of each component by a polynomial function of two independent variables and solving for the balance point

by matching the polynomials.

The water coil's performance is expressed by finding its effectiveness as a function of air and mass flow rates. The chiller's performance is given in terms

of the leaving chilled water temperature and condensing temperature. The evaporative condenser's performance is a function of the condensing temperature and out- door wet bulb temperature.

Manufacturer's catalogue data were used with a computer program to determine the nine constants needed in the polynomial expressions for each system

component and the system balance was then established using a computer program

for each load on the system.

Key Words: Simulation, system simulation, refrigeration system simulation,

component simulation.

1. Introduction

The calculation of energy requirements of a building and the use of a computer to control the starting and stopping of components of the building's air conditioning system require the simulation of the performance of both the air distribution system and the refrigeration system. Methods for calculating

building cooling and heating loads via computer have been developed by the sub-committee on cooling and heating loads of ASHRAE's Task Group on Energy Requirements for Heating and Cooling and presented in the publication of this sub-committee [1]^. Suggested methods of component simulation and forms of the equations to be used were presented in the publication of the Task Group's sub-committee on System Simulation [2]. An example of the simulation of a dual duct system is also given in that publication.

This paper uses the methods suggested for component simulation to simulate the performance of a multicylinder reciprocating compressor water chiller, evaporative condenser and chilled water coil. The

output of the calculations give air flow over the cooling coil, coll bypass factor, coil effectiveness

as well as power input to the compressor, total heat rejection, condensing temperature as well as percent of the time that the compressor is running.

"Professor of Mechanical Engineering and Graduate student, currently Desalting Engineer, Mekorath

Water Co., Israel, respectively.

'Figures in brackets indicate the literature references at the end of this paper.

545
2. Cooling Load

2.1 Building

It is necessary to have cooling load data in order to select equipment to meet the design load as well as to determine how the equipment will perform under part load conditions. The fictitious building

shown in figure 1 was used to calculate the cooling loads . The building was located in New York City

and is three stories high with wall, roof and glass areas and construction indicated in the figure.

2.2 Cooling Load Calculation

The cooling load was calculated by hand at two hour intervals from 7 A.M. to 7 P.M. for two typical

days, July 21 and August 21. The calculations were based upon recommended procedures in the 1967 ASHRAE Handbook of Fundamentals [3]. A typical outdoor temperature variation was taken from figure 15.16 in Threlkeld [4]. The number of people assumed to work in the building Is 375, starting between 7 and 9 A.M. and leaving between 5 and 7 P.M. The lighting load was assumed constant at 4.75 watts ft."^. Outdoor

design conditions are 94F dry bulb and 77F wet bulb. To allow for vacations 80% occupancy was assumed

for the July 21 calculation. Outside air is introduced at the rate of 15 cfm per person and at the outdoor weather conditions.

Results of the load calculations are in Tables 1 and 2. These results were used in selecting the components and were used in determining the necessary operating conditions for each component under

part load.

Table 1

Sxjmmary of Cooling Load for August 21

Sensible Load 7 9 11 13 15 17 19

a. Transmission

Roof -18,202 -17,971 - 2,304 21,888 61,517 76,262 71,885

North Wall - 5,400 - 4,140 360 4,860 8,640 11,520 10,440 West Wall 840 2,040 4,200 6,360 8,280 9,720 11,760 East Wall - 9,083 ~ 6,896 841 8,746 14,968 17,491 15,809

South Wall -12,334 -10,765 - 9,157 2,018 10,316 17,268 19,062

b. Transmitted Solar Radiation & Transmission

East Windows 28,200 62,150 59,506 40,727 47,025 70,548 56,272

South Windows 15,635 16,592 40,743 67,864 71,682 50,330 27,709

South Door 10,992 13,552 33,440 59,904 57,320 39,136 20,304

c. Internal Load

Infiltration 781 540 1,404 1,836 2,052 1,944 3,384

Lights 471,400 471,400 471,400 471,400 471,400 471,400 471,400

Fan Motor 30,528 30,528 30,528 30,528 30,528 30,528 30,528

People - 93,750 93,750 93,750 93,750 93,750

Total Sensible Load 513,357 650,834 724,711 809,881 877,478 889,897 738,553

2 . Latent Load

Infiltration 12,481 4,889 4,017 3,533 3,340 3,436 8,515

People - 75,000 75,000 75,000 75,000 75,000

Total Latent Load 12,481 79,889 79,017 78,533 78,340 78,436 8,515

3. Ventilation Load 316,406 315,141 313,875 312,609 311.344 311,344 313.875

4. Total Cooling Load 842,244 1,045,864 1,117,603 1,201,023 1,267,162 1,279,667 1,060,943

546
Table 2

Sunvmary of Cooling Load for July 21

1. Sensible Load 11 13 15 17 19

Transmission

Roof

North Wall

West Wall

East Wall

South Wall

-28,570

-13,500

- 4,560

-16,651

-22,426

-28,339

-11,700

- 3,720

-14,464

-20,855

-14,285

- 9,000

- 1,680

- 7,905

-16,819

8,295

- 5,760

-720

- 1,177

-11,213

46,541

- 2,500

480 4,542

- 3,589

61,287

-180 1,920

6,560

2,691

57,830

0 4,800

6,063

5,382

Solar Radiation

and Transmission

East Window

South Windows

South Door

26,341

- 2,074 -588

52,877

5,599

5,536

59,383

27,139

22,680

35,821

43,359

36,752

61,482

29,939

24,376

57,601

11,897

9,352

30,540

3,525

2,804

Internal Load

Infiltration

Lights

Fan Motor

People

- 1,458

471,400

30,528

-540 471,400

30,528

75,000

108 471,400

30,528

75,000

324 471,400

30,528

75,000

540 471,400

30,528

75,000

432 471,400

30,528

75,000

208 471,400

30,528

Total Sensible Load 438,442 561,322 636,489 682,609 738,719 728,488 613,080

2. Latent Load

Infiltration

People

4,386 2,081

60,000

1,307

60,000

920 60,000

726 60,000

823 60,000

2,606

Total Latent Load

3. Ventilation Load

4,386 62,081 61,307 60,920 60,726 60,828 2,606

91,125 91,125 89,962 i,596 88,596 i,596 89,962

4. Total Cooling Load 533,953 714,528 787,758 832,125 884,041 877,912 705,648

3. Component Selection

3.1 Cooling Coil

The peak load occurs at 1700 hours (5 P.M. EDST) on August 21. The load is 1,279,667 BTU-hr""'' or 106.64 tons of refrigeration. Of this total the space sensible load is 889,367 BTU-hr"-'- and the space

latent load is 78,436 BTU-hr"-'-. To meet this load the water flow through the coil is given by eq (1)

Q = WC AT

P

(1)

where Q = total load (BTU-hr "")

, C = 1.0 BTU-lb °F

"'' p

^ AT = water temperature rise through the coil, F, taken as 10 for the selection made W = water flow rate (Ib-hr . From eq (1)

W = J-'279^667 ^ 127,967 Ib-hr = 255.9 gal-min

The air flow across the coil (cfm) is given by eq (2)

1.08(T T, ) Ivg.

(2)

547
. and T are the dry bulb temperatures before and after the coll ent . ivg

889897

1 1.08(75-56) A3270 cfm

432 70 500 ft^ where a face velocity of 500 ft-min Is used. The coil face area required is FA =

12 coils with a length of 36" and height of 30" and a total face area of 90 ft^ and face velocity of 480 ft-min ^ were selected. From a manufacturer's catalogue to meet the required '^'g^ a set of 12, 6 row, 80 fins per inch coils 36" x 30" were selected.

1.18 tons-ft

3.2 Chiller

With the required tonnage of 106.64, leaving water temperature 45°F, entering water temperature of

55°F, two chillers were selected as possible alternatives. The simulation was run with both possibilities

to show how the simulation is helpful in selecting the optimum chiller to meet the building load char- acteristics. The final selection is discussed under results. The two chillers selected had as full load characteristics , for chiller A; saturated discharge temperature 103. 7°F, compressor power input 93.4 KW, total heat rejection 133.4 tons; while for chiller B the corresponding values are 114. 3°F, 110.2 KW and 138 tons.

Each compressor is equipped with cylinder unloaders to operate at 100%, 75%, 50% and 25% of full load capacity.

3.3 Evaporative Condenser

The evaporative condenser chosen with a saturation temperature of 103. 7°F, outdoor wet bulb of 77°F would have a capacity of 133.2 tons with 20 sub-cooling. This was chosen to meet the conditions of chiller A. This condenser has a capacity greater than the required 138 ton heat rejection needed for chiller B at it's higher condensing temperature of 114. 3°F.

4. Component Simulation

Each component's performance is to be expressed as a function of two independent variables [2] in

the form:

Z = a^ + a2X + a^x + a^y + a^y

+ a^xy J.+ a^x2, 2_^22 y + agXy + a^x y (3)

The coefficients a-^ through ag should be chosen so as to predict the performance of the individual

component over a wide range of load conditions. It is hoped that the manufacturers will present the per- formance of their equipment in the form of eq (3). Currently this data is not generally available and

the coefficients used in simulating each component in this paper were computed from tabulated manufacturer's values (which are generally at or near full load). The equations so derived were used to predict

the part load performance. Clearly the results will be more reliable when more reliable part load data

becomes available.

4.1 Simulation of Chilled Water Coil

In accordance with the suggestions of Stoecker [2], the coil's performance should be given by the effectiveness expressed as a function of the air flow (G) and water flow (W) rates.

The effectiveness is defined as

h. h

in out Ah

h. - h Ah

in w w

548
where hj_^ and h^y^ are the enthalpies of the air before and after the coil and h^ is the enthalpy of saturated air at the entering water temperature, so that Ah^ is an enthalpy potential.

The maximum possible effectiveness E =h. -h/h, -h where h = enthalpy of saturated air at ^ max m w In w w

the average water temperature.

The effectiveness can be expressed in terms of G and W because

Q = GAh = GEAh (5) w

and q = W (T, - T ) = WAT (6) in out

where AT, the cooling range is the water temperature difference across the coil.

In terms of the coil face velocity and face area

G = pVA (7)

For this example the coil was used as a "wild" coil, i.e. the temperature of the water entering the coil and the mass flow of water across the coil is constant. Since the load on the coil is the building

load, and the outdoor conditions are known, and the water inlet temperature is constant, h^j^ is known and

h,^ is constant; the coil effectiveness can be computed from manufacturer's catalogue data. Therefore,

for a given coil with part load data given, the constants in:

2 2 E = a, + a„G + a-G + a.W + a^W

1 2 3 4 5

+ a^GW + a^G^ + a„GW^ + a.G^^ (8)

D / by

can be evaluated by solving nine simultaneous equations using manufacturer's data for G, W and computed

values of effectiveness based upon manufacturer's data.

4.2 Simulation of the Chiller

From manufacturer's data at full and part loads the chiller capacity, Q^-^ and power input, may

be expressed in terms of T^-^ and T^^^j, the temperature of water leaving the chiller, and the condensing

temperature of the refrigerant.

Q , = b, + b„ T , + b, T . ^ + b, T , + b, T ,^ ch 1 2 ch 3 ch 4 cd 5 cd

+ b, T , T + b_ T , ^ T , + b. T , T ,^ + b- T , ^ T ,^ (9)

6 ch cd 7 ch cd 8 ch cd 9 ch cd

2 2 P,=Ct+c„T+c„T, +c, T+c, T, +c, T,T, ch 1 2 ch 3 ch 4 cd 5 cd 6 ch cd

+ c, T . ^ T , + c„ T , T ,^ + c- T , ^ T ,^ (10)

7 ch cd 8 ch cd 9 ch - cd

Again, standard programs for solution of simultaneous equations evaluate the constants if nine data

points are given.

The performance of the chiller is complicated by the fact that the compressor is equipped with unloaders to lower the power requirements in steps to 75%, 50% and 25% of full load requirements. However,

to deliver the exact cooling load the compressor must cycle and operate only part of the time.

549
The starting current is higher than normal running current so that the effect of cycling is to in- crease equivalent power consumption; e.g. when the compressor operates say 80% of the time, the power

requirement is greater than 80% of the full time operating power. Manufacturers suggest that the ratio

of part time power required to full time power (RP) is expressible in terms of the percent time operating (RL) by

RP = R + .8 RL (11)

so that the heat rejected in the evaporative condenser is given by

Qrej = ^ + ^ (^ch^

4 . 3 Simulation of the Evaporative Condenser

The evaporative condenser heat rejection is given by:

QrEJ =

'^l <^2("^^) + + '^4(V

2 2 + d^ T J + d, (WBT) T „ + d^ (WBT) T

5 cd 6 cD 7 cD

+ dg (WBT) T^^^ + dg (WBT)^

(^cd^^ ^'^^

It is seen from eq.'s 10 through 13 that the power requirement of the chiller and heat rejected by

the condenser are functions of the condensing temperature, so that T^ will be determined by the relative

capacity of both components.

5. System Simulation

5.1 Control System

The coll was selected to operate without a control valve so that the water flow rate and entering water temperature are constant. To control the output some of the air is bypassed around the coil and then at low loads the amount of coll surface exposed to the air is decreased.

The blocking of part of the coll surface is necessary because at low air flow rates the leaving air

temperature becomes uncomfortably low.

In the mathematical model the requirement of blocking part of the coll may be sensed by values of E that are too high, approaching E^^^ (the DBT of the leaving air approaches the average water temperature).

5.2 Mathematical Model

At a given load eq.'s (8) and (5) must be satisfied simultaneously. Since W is constant, eq . (8) may

be rewritten as:

E = B' + F'G + D' G

where B ' = a.14+ a.W + a^W

5

(14)

F' - a^ZD+ a,W + a^W

o

D' = a^ + a^W + agW

550
GE Using the identity G = ^ in eq (14) we get:

E"' - B'E^ - (GE)F'E - (GE^)D' = 0

This equation is solved for E with constant G such that

0 < E < Emax

If no such root exists, G is reduced (part of the coil is blocked) until such a root is found. The operation of the packaged chiller and evaporative condenser is dependent upon the cooling load and the outdoor wet bulb temperature only. If the chiller leaving water temperature is fixed, the con- densing temperature T^^^ is the only variable.

The capacity of the chiller is: Q , = f(T , , T ,) , if T , is fixed at 45°. Based on the actual ^ chil ch cd ch load Q the number of cylinders required is found. For example if

RL = Q/Q , = 0.6 chill

so .50 < RL < .75, 75% of the cylinders are required and the percent operating time is:

RLI = (100) = 80%

The power ratio is then RP = .2 + .8RLI = .84 and the actual power required

PWI = P , X .75 X .84 = .63 P , ch ch

P , = f (T , T ^) and Q„^^ = Q + PWI

ch cw cD REJ

The capacity of the evaporative condenser is evaluated at T^^

Q = f(WBT, T „) and the two values are compared, evcon cD

If Q > Q . then T „ is decreased and if Q < Q . , T „ is increased, ^evcon rej cD evcon rej cD

A flow chart of the computer program is shown in figure 3.

6. Results

Typical results are shown in Tables 3 and 4 for the full load case on August 21 and 5 P.M. The

two alternate chillers chosen result in an input of 94.3KW with all cylinders in operation 100% of the

time, and 96.4KW with all the cylinders in operation 91.9% of the time. The result for the full load period are typical throughout. One chiller chosen generally has a smaller power input and cycles less

often. Thus, the simulation is helpful in equipment selection as well as in energy computation.

An exception to the first alternate giving better results is shown in Tables 5 and 6 where the out- puts at 9 A.M. July 21 are presented. Here alternate 2 has a lower power input and will cycle less.

The importance of examining the entire range of outputs is evident.

551
Table 3

Date - August 21 Time - 17.00 Cooling Load, BTU/HR 1279667. Outdoor Dry Bulb Teinp.,F 93.0 Outdoor Wet Bulb Temp.,F 77.0

Water Coil Data

Percent of Face Area Used 100.0 Water Temperature (Entering Cooling Coil) ,F 45.0 Water Flow In Cooling Coil,GPM 255.9 Air Temp. (Entering Cooling Coil) ,F 77.0 Air Flow Over Cooling Coil,CFM A2076. Coil Effectiveness Is 0.571 Bypass Factor Is, Percent 15.8

Water Chiller Data

Water Temp. Living Chiller, F A5.0 Condensing Temp, of Chiller, F 103.7

100 Percent of Cylinders are in Operation

Operating 100.0 Percent of the Time

Actual Power Requirements ,KW 94.3 Total Heat Rejection, Tons 133.4

Table 4

Date - August 21 Time - 17.00 Cooling Load, BTU/Hr 1279667. Outdoor Dry Bulb Temp.,F 93.0 Outdoor Wet Bulb Temp.,F 77.0

Water Coil Data

Percent of Face Area Used 100.0 Water Temperature (Entering Cooling Coil) ,F 45.0 Water Flow in Cooling Coil,GPM 255.9 Air Temp. (Entering Cooling Coil) ,F 77.0 Air Flow Over Cooling Coil,CFM , 420 76. Coil Effectiveness Is 0.571

Bypass Factor Is, Percent 15.8

Water Chiller Data

Water Temp. Living Chiller, F 45.0 Condensing Temp, of Chiller, F 103.7

100 Percent of Cylinders are in Operation

Operating 91.9 Percent of the Time

Actual Power Requirements ,KW 96.4 Total Heat Rejection, Tons 133.4

552
Table 5

Date - Ju;Ly 21 Time - 9.00 Cooling Load, BTU/HR 714528. Outdoor Dry Bulb Temp.,F 70.0 Outdoor Wet Bulb Temp.,F 67.0

Water Coil Data

Percent of Face Area Used 75.0 Water Temperature (Entering Cooling Coil),F 45.0 Water Flow in Cooling Coil.GPM 255.9 Air Temp. (Entering Cooling Coil),F 74.4 Air Flow Over Cooling Coil.CFM 20207. Coil Effectiveness Is 0.724

Bypass Factor Is, Percent 59.6

Water Chiller Data

Water Temp. Living Chiller, F 45.0 Condensing Temp, of Chiller, F 91.9

75 Percent of Cylinders are in Operation

Operating 68.1 Percent of the Time

Actual Power Requirements ,KW 48.9 Total Heat Rejection, Tons 73.4

Table 6

Date - July 21 Time - 9.00 Cooling Load, BTU/HR 714528. Outdoor Dry Bulb Temp.,F 70.0 Outdoor Wet Bulb Temp.,F 67.0

Water Coil Data

Percent of Face Area Used 75.0 Water Temperature (Entering Cooling Coil) ,F 45.0 Water Flow in Cooling Coil.GPM 255.9 Air Temp. (Entering Cooling Coil) ,F 74.4 Air Flow Over Cooling Coil.CFM 20207. Coil Effectiveness Is 0.724

Bypass Factor Is, Percent 59.6

Water Chiller Data

Water Temp. Living Chiller, F 45.0 Condensing Temp, of Chiller, F 91.7

50 Percent of Cylinders are in Operation

Operating 94.1 Percent of the Time

Actual Power Requirements ,KW 45.4

Total Heat Rejection, Tons 71.9

553
7. References

Proposed Procedure for Determining Heating and Cooling Loads for Energy Calculations. Task Group

on Energy Requirements for Heating and Cooling - ASHRAE , edited by M. Lokmanhekim

Proposed Procedures for Simulating the Performance of Components and Systems for Energy Calculations.

Task Group on Energy Requirements for Heating and Cooling - ASHRAE, edited by W. Stoecker.

Handbook of Fundamentals, 1967, ASHRAE.

Threlkeld, L. James, Thermal Environmental Engineering, Prentice Hall, 1962.

Naylor, T. H., Computer Simulation Techniques, W. Ley, 1966.

554
ROOF - MEDIUM CONSTRUCTION, 2" INSULATION

2" GYPSUM PLANK.

10* CEILING

1st FLOOR

13 BRICK

PARTY WALL X

80'

120'

WINDOWS

27 % GLASS

ENTRANCE DOOR

100% GLASS

EAST

8 CONCRETE

^ITH 5/8" PLASTER

2nd a 3rd FLOORS

WINDOWS

27% GLASS

Figure 1. Building Orientation and Structure

555
556
Use of Digital Computers

For the Heat and Mass Transfer

Analyses of Controlled

Environment Greenhouses

M. Kudret Sel^uk, Ph.D.

Environmental Research Laboratory

University of Arizona

Tucson, Arizona

Heat and mass balance equations for the controlled-environment

Greenhouses yielded simultaneous non-linear differential equations

that were modified to finite difference equations for computer

solution. These equations were linearized before attempts were made to solve them, using a CDC 6400 Computer. The unsteady state

analysis was carried out to determine the variation of temperatures

due to storage effects, especially that of soil. The plastic cover, plant and air temperatures responded to any change of radiation or external disturbance fast enough to justify a quasi-steady state

analysis in which the radiation level was modified step-by-step in

hourly intervals . Various programs were written to solve the problem

at different phases; namely, the analysis without any moisture effects,

studies with transpiration taken into consideration and, ultimately,

the model with evaporation from the soil, transpiration from the

plants and condensation over the plastic cover whenever its temperature drops below dew point of the air stream. Since the final phase

covers all phenomena involved, only its formulation and computer

programming are emphasized. The computer programs developed may

be used in predicting the controlled-environment greenhouse perfor- mance under continuous operation conditions for any locality, if

weather data are supplied. This information also will enable the

designer to determine the capacity of the packed bed humidifiers,

circulation fans and water requirements of humidifiers and irrigation purposes.

Key Words: Controlled environments, greenhouse energy

budget program, greenhouse heat and mass balances.

1. Introduction

The controlled-environment greenhouse is the vital component of the POWER-WATERFOOD complex developed by the University of Arizona. The principle of operation and

features of a large-scale scheme which is being applied in Abu Dhabi on the Arabian

Gulf already has been reported. [1], [2], [3]^

The present paper outlines the computation methods and details of the computer

programming of an extensive study of the heat and mass balances of the controlled

environment greenhouses [4].

'"Author is an Assistant Professor at the Mechanical Engineering Department

Middle East Technical University of Ankara, Turkey. This paper is based upon

a research carried out while he was on leave at the Environmental Research

Laboratory of the University of Arizona.

2 Numerals in brackets refer to references at the end of this paper.

557
2. Mathematical Models

The formulation of the heat and mass transfer in the inflated plastic controlledenvironment greenhouse was carried out at a number of stages, from simple to elaborate. The purpose has been to obtain approximate values of unknowns for use in the

iterative process to compute temperatures and moistures accurately.

Fig. 1) is a sketch of the greenhouse, its dimensions and definition of unknowns

investigated as well as initial and boundary conditions . The ambient db and wb air temperatures, outside wind velocity, inside air

velocity, solar radiation intensity and initial db and wb air temperatures are specified as input data for the computer program. The present analyses enable one to compute temperatures of the plastic cover, air stream plant leaf surface temperatures,

soil temperature at the surface and various levels below the surface, at selected

space intervals for a 24-hour operation period.

The following steps were taken in formulating the problem:

(a) The analysis of the system neglecting the moisture effects, steady state,

(b) The analysis of the system with plant transpiration only, steady state,

(c) The analysis of the system neglecting the moisture effects, unsteady state,

(d) The analysis of the system with plant transpiration only unsteady state,

(e) The analysis of the system with the effects of soil moisture evaporation,

plant transpiration and condensation on the cover, unsteady state,

(f) An analysis to predict the greenhouse performance for year-round operation

based upon the formulation (e)

Since the detailed description of these formulations would be too lengthy, only

the study which is covered in formulation (e) will be outlined.

It should be noted that formulations (a) through (d) are special cases of formulation (e) in which some of the parameters have been neglected and analysis is applied

to the steady state operation.

2.1 The Analysis of the System with Soil Water Evaporation,

Plant Transpiration and Condensation on the Cover

The model employed in this analysis is outlined in Fig. 2) . The computer program

is labeled KUD 81.

2.1.1 Heat Balance on the Cover

Neglecting the heat capacity of plastic cover and employing quasi-state analysis:

hc.PAx(T, - e ) + K PAxh^ (a)-aj)+hr E^e^A{e- e^)F ^ 1 1 c c fg a c p,c p,Lw c,Lw pr p c p,c

+ la PAx + hr e ^ e ^ F PAx{e - 0 ) = he PAxO - T ) c,sw s,cs,Lwc,Lws,c s c w c a

+ hr , PAx (9 - T , ) e ^ , -,

c,sk c sky c,Lw (i)

-1 -2

where K is the condensation rate in (lb hr ft ) c Taking F , F =1, and from F • e =p*.

^ p,c' s,c

Rearranging for the unknowns of 6 T, 6 and G and dividing by Ax:

c , 1 , p s [-hc.P - hr Fa /Ax - hr F P - he P - hr , pe , ]e

1 p,c p,c pr s,c s,c w csk'^ CLw* c + [hc.P]T, + [hr F A /Ax]6 + [hr F P]e = - k Ph^ (o) - (o ) 1 1 P,c p,c pr' -' p '- s,c s,c s c fg ^ a c'

- la P - he PT - hr , Pe ^ T , c,sw w a c,sk c,Lw sky (2)

558
Mass Balance of Airstream, enables one to obtain w in terms of w , o) , u and

the initial humidity ratio of the airstream (o) . ) . P

a / 1 n

2.1.2 Mass Balance on Airstream

Change of water vapor content of the airstream is

m(a) - oj .)=K(a)-a))A + KA(w -a))-K(u -w )PAx (3) a a a,in ssagpppa cac

The transpiration rate is proportional to:

K = —i

P

1 + R ^

-T-r 77; StOm (he /C

P Pm

o -1

and R ^ is stomatal resistance in (hr ft lb ) stom

Rearranging (3) and solving for (o) ) ; a

0) =(mio . +Ka)A tKAw + Ka) PAx)/{ra + KA + KA + K PAx) (5) a a a,in ssg PPP cc a sg pp c from the Psychrometric Relations, assuming saturation conditions at the cover, leaf

and soil surfaces

0)

[0.622 P ,„ , ]/[P - P ,Q , ] (6) V (9c) '

'- m V (6c)

[0-622 P„,«^J/[P^ - P,w«^J (7) p V ( Op) '- m V ( 6p)

0) s"-= [0.622 P ,9 ,]/[P - P ,Q x] (8) v(s) '-m vOs)-"

Equations (5), (6), (7) and (8), together with 4 heat balance equations correspon

ding to cover, airstream, plant and soil are 8 non-linear simultaneous equations

which should allow one to solve the unknowns a),a),a),w,6,T,,6 and 6 . p c s a' c l p s To ease the solution, u^, and to^ will be expressed as linear functions of temperature in the form of co = X9 + Y. Rather than using relations (6) , (7) and (8) , the

constants X and Y are to be individually determined within the temperature region of

interest.

For the cover at saturation conditions: u = X 6 + Y

c c c c (9

)

For the plant at saturation conditions: w = X 6 + Y (10) P P P P For the soil at saturation conditions: w = X 9 + Y (11)

s s s s

9 , 9 and 9 were approximately determined employing the analysis with plant transpi

ratioR only.^ Details of this analysis are described in another publication by the

author [5].' The coefficients X , X , X , Y , Y , and Y can be closely estimated

c p s c p s

^ from the saturation curve for air-water vapor mixture once 9 , 9 and 9 are known.

c p s Since the mass flow rate is:m = p vA : Ib/hr

a '^m s

'

The mass balance equation (5) for the airstream then could be written in terms

of temperatures alone:

'^a=[^(Pm^\/A^)'^a,in + (KsV^^^^ ^""s^s + ^s^ + ^Vp^^''^ ^""p^P ^P^

+ K P(X 9 + Y )]/[p VA /Ax + KA/hx + K A /Ax + K P] (12)

559
separating 9^, 9^ and 9^,

w = -, ^—77 , ^—y,-*- ^ ^—77 ^ ^, [X K P9 + (X K A /Ax) 9 + (X K A /Ax)

a (p msvA /Ax + K A /Ax + K A /Ax + KP)'-cc c PPP P sxg' Sg PP C r r r- c

+ (p vA /Ax) 0) . +YKP + YKA /Ax + Y K A /Ax] (13) m s a,in c c PPP s s g' '

Substituting u from equation (13) and w from equation (9) , into equation (2)

[ - hc.P - hr F A /Ax - hr 7^ P - ho P - hr^ „vPe^ n„]e + [hc.P]T.

1 p,c p,c pr' s,cs,c w CjSKclwc i i

+ [hr F A /Ax]9 + [hr F P]9 = -K Ph, [d{X K P 9 + (X K A /Ax)

'- p,c p,c pr p ^ s,c s,c s c fg'- c c c P P P P

+ (X K A /Ax) e + ( p vA /Ax)a) . +YKP + YKA /Ax + Y K A /Ax} - X 9 - Y ssg' s '^ms a, in cc PPP sag' cc

- la P - he PT - hr , Pe ^ T , c,sw w a c,sk c,Lw sky (14)

Where _ 1

p vA /Ax + K A /Ax + K A /Ax + K P ^m s' s g' p

p' c

2.1.3 Heat Balance on Airstream

For a system of Ax length: m C (T, - T, . ) = he A (9 - T,) + he A (9 - T, ) - he.PAx(T, -9 ) apm l l,in sg s 1 pp p 1 i 1 c For unit length:

(p v/Ax)A C (T, - T, . ) = he A /Ax(9 - T, ) + he (A /Ax) (9 - T, ) m s pm 1 l,in s g s 1 P P P 1

- he^P(T^ - 9^) (15)

(A /Ax) : The effective plant surface per unit length of the greenhouse has to

be worRed out separately for the plant under study and at various stages of growth.

2.1.4 Heat Balance Over the Plant Canopy

The plant canopy does not have a definite geometrical shape, nor uniform heat

and mass transfer coefficients. The velocity field around and across the canopy is

not uniform. Therefore, those coefficients, areas, temperatures and velocities

have been bulked in this analysis. For the unit length of greenhouse, Ax = 1.

1^1 „a ^A^ + I ,T ,a ,A, = he A (9 - T, ) + h- K A (w - co ) D c,sw,D p,sw,D D,p d e,sw,d p,sw,d d,p PPP 1 P P P a

+ hr F A (9 - 9 ) + hr F A (9 - 9 ) s,p s,p p s p p,e p,c pr p c

+ hr,T^e^A(9-T,, ,,,, p,sk e,Lw p,Lw pr p sky) (16)

where the subscript D refers to Direct, and d refers to diffuse.

(he A ) , (K A ) , (F A ) and (F A ) are bulked as indicated above.

P P P P s,p p

' p,c pr'

560
Substituting from equation (10) and co^ from equation (13):

n + I t a ,A, = he A (9 - T, ) Dc,sw,Dp,sw,DT),p ac,sw,ap,sw,da,p PP P 1

+ h _ K A [X e + y - D{ (X K P) 6 + (X K A /Ax) 6 + (X. K A /Ax) 6 fgpp'-pp p cc c PPP P ssg' s

+ (p vA /Ax)a) . + YKP + YKA /Ax + Y K A /Ax)] ^m s a,in c c PPP ssg-"

+ hr F A (9 - e ) + hr 'F A (9 - 6 ) s,p s,p p s p p,c p,c pr p c

+ hrp,sk,T^e^A(9-T,, c,Lw p,Lw pr p sky) (17)

2.1.5 Heat Balance on Moist Soil

The soil is assumed to be saturated to moisture. Evaporation from the soil surface

results in reduction of the soil surface temperature and affects the humidity ratio of

the airstream. The area of the exposed soil surface is the same for conduction con- vection, radiation H.T. and evaporation.

In case of one-dimensional heat flow into soil, for unit soil surface dividing

by A

gIt a = h^ K (w - 0) ) + he (9 - T, ) + hr , e ^ t ^ (8 - T , , c,sw s,sw fg s s a s s 1 s,sk s,Lw c,Lw s sky)

+hr e.e^F (9-9)+ (hr A /A ) (9 - 9 ) s,cc,Lws,Lws,c s c s,p s,ppgs p

+ (V63)(e3 - 9^1) + P^^^c^o^ - e3,i^)/At (18)

Substituting w from equation (8) and w from equation (13):

S 3. -h, K {X 9 + Y - D[X K P9 + (X K A /Ax) 9 + (X K A /Ax)

fgsss s 'ccc PPP P ssg s

+ (p vA /Ax)aj . +YKP + YKA /Ax + Y K A /Ax]} - he (9 - T, ) ^m s a,in c c PPP ssg' s s 1

- hr , e ^ T ^ (9 - T , ) - hr (9 - 6 ) s,sk s,Lw e,Lw s sky s,c s,c s c

- hr F A /A (9 - 9 ) - K (9 - 8 , ) /6 - p 6 C (8 - 8 . )/At

s,p s,pp g s p s s si s sss s s,in

= - It a (19) c,sw s,sw

2.1.6 Heat Balance on the First Soil Slab

The first soil slab temperature after the time interval of (At) (^gj^)' c^^i be

obtained from:

(9 . , 9 ^ . - 29 , . ) = -|r(e 1 - 6 1 • ) (20) s,in + s2,in sl,in aAt si si, in or

o 2aAt[(9 . + 9 „ . )/2 - 9^, . ] + 8^, . -. . 8 , = —r-z— s , m s2,in sl,in-' sl,in (^0-1; si 0 s Similarly for the second soil slab:

®s2 = ^fp'^'^sl,in + ^s3,in^/2 - 632,11,^ + ^s2,in (20-2)

For the kth soil slab:

= ^[(e.,,_,, + 9^,,^,, ,J/2 - 8^^ ,J + 8^^ (20-k)

561
where (k;=m-4), and m is the number of unknowns. 4 equations refer to the cover, stream of air, plant and the soil slab at the surface.

Those equations could be further simplified taking

(5 = /2aAt.

s For 20 slabs below soil surface:

si

((

(6 . + e . . )/2

s , m s2 , in

s2

^sk

=

^s20

si, in s3,in)/2

^^s,k-l,in + ^s,k+l,in'/2

3 -,„ . + 6 . )/2 sl9,in s21,in^

The initial and boundary conditions are;

"sky

1 , m

3 . e , . e „ e . s , in , si, in, s2,in s21,in

li a, m

(21)

(22-1)

(22-2)

(22-k)

(22-20)

The ambient air temperature

Effective sky temperature

Initial air temperature

Initial soil temperature profile

Initial humidity ratio of the airstream

Equation (14), (15), (17), (19) and (22-1) to (22-20) are 24 simultaneous equations

in which G , T,

,

C are 24 unknowns to be solved. "1' p' s' si' s2' s20

The solution techniques and features of various programs follow.

Since the

tion also was

00 Series

KUD 0 3

10 Series

KUD 12 KUD 15

20 Series

KUD 21

50 Series

KUD 5 3 KUD 55

KUD 5 7

60 Series

KUD 61

3. Computer Programming

formulation of the problem was carried out at various stages, the soluobtained for the corresponding steps as listed in Table I. Table I - List of Computer Programs

No-moisture Analysis, Steady State Printout + Variation of

(9^, T-^, 6^, 9^) along the Greenhouse, Computer Plotted

Analysis with Transpiration Only, Steady State Linear Interpolation for

the Plant Temperature Correction

Same as Above - Newton-Rhapson Method Used in Approximation

Same as KUD 15, Greenhouse End Effects Included

Unsteady State Analysis, No Moisture Effects 4 Equations + SchmidtBinder Technique

Same as KUD 53, but 4 Original Unknowns + 20 Soil Temperatures Solved

by 24 Equations

Same as KUD 53, but Design Modified for E.R.L. Tucson Greenhouses

Unsteady State with Transpiration only 4 Equations + Schmidt-Binder

Technique

562
Table I .- List of Computer Programs (Continued)

80 Series

KUD 81 Unsteady State, with Soil Moisture Evaporation, Plant Transpiration

and Condensation on the Cover 4 Equations + Schmidt-Binder Technique

KUD 82 Same as Above, Effect of Time Interval

KUD 84 Same as KUD 81, Effect of Stomatal Resistance

90 Series

KUD 91 12 Month Performance Prediction from KUD 81 Printout

KUD 92 Same as KUD 91, Result Computer Plotted

KUD 93 Same as KUD 92, Effect of Shading

3.1 The Analysis with no Moisture Effects

The formulation of the problem which is described elsewhere [4] yielded four

non-linear, simultaneous equations, due to the radiation terms of (9^ + 460)'' etc. These were linearized using the equivalent radiation heat transfer coefficients,

hr , ....etc. The program is labeled KUD 03. The solution of this and other models

C , SK was obtained using CDC Model 6400 computer, of the University of Arizona's Computer

Center.

(4x4) matrix A and 4 element column vector C were generated and the solution

of linear simultaneous equations was obtained using the Gauss-Jordan elimination

technique.

The computer program of the final model, however, includes the same matrix A

and vector C which is used to predict the temperatures of 6 , 6 and 9 . c p s

3.2 Solution of the Model with Transpiration Effects Only

The formulation with transpiration effects which allows prediction of plant

temperatures more accurately has been described in Reference [5].

Starting with an estimated transpiration rate based upon the enthalpy potential

between the plant interface at approximate temperature and the airstream, both

transpiration rate and the final leaf temperature were iterated until the assumed

and calculated leaf temperature agreed with one another. The convergence of the

iteration was accelerated utilizing the Newton-Rhapson method as shown in Fig. 3)

This process which utilizes the matrix E (4,4) and vector G(4) is included in the

second part of the computer program KUD 81.

3.3 Solution of the Model with Condensation on the Cover,

Transpiration from the Plant and Evaporation from the Soil

24 simultaneous equations previously derived were utilized. Those equations were arranged for the 24 unknowns mentioned, and the coefficient matrix Q(24,24) and vector

Z (24) which are presented in Table II, were obtained. q corresponds to the matrix

element of Q(M,N) and z to z (M)

563
Table II - Coefficient Matrix Q (24,24) and Vector Z(24)

for the Simultaneous Equations, Program KUD 81

Q{24,24) Z(24)

^11 ^12 ^313 ^14 0 0 0 0 0 0 . . ^1

^21 "323 ^324 0 0 Q Au u ^2

^31 cr^32 ^33 ^34 0 0 0 0 0 0 7^3

^41 ^42 q43 ^44 0 0 0 0 0 0 . . ^4

0 0 0 0 1 0 0 0 0 0 . . (6 . + e _ . )/2

0

1

0

1

1

0

\

1

0 0

1

1

1

I

1

0

1

1

0

1

1

0

1

1

0 . .

1

1

(e -, . +6 , . )/2 si , m s3 ,

1

0

1

1

I

1

0

1

1

1

1

0

I

1

1

1

0

1

1

1

1

0

1

!

!

1

0

1

1

1

0

f

1

1

1

0

1

1

1

0

t

f

1

f

1 . . .

1

1

1

1

1

1

(6 +6 ,,,.)

0 0 0 0 0000000001 =(e,„.+e^, .)/2 sl9,in s21,in

The coefficient matrix Q and vector Z yield the final solution by means of

Gauss- Jordan elimination technique.

The other alternative is to solve the original 4 equations written for the cover, airstream, plant and the soil surface slab, then apply the Schmidt-Binder method for

an hour's interval. The solar radiation intensity during an hour's period is assumed

to be constant. The soil surface temperature is determined starting with an initial

temperature profile following the method outlined in Reference [6].

Then, temperature profiles, at succeeding hours, within the soil are obtained at intervals defined by At = 6|/2a.

The logic diagram of the computer solution is presented in Fig. 4)

The ambient air temperature, solar radiation intensity, and the sky temperature

were supplied as boundary conditions.

The air outlet temperature from the control volume T, , was set equal to the

initial air temperature of the following control volume TT^^ in^ ' Similarly, the

solution of the present analysis w was introduced as the initial humidity ratio for

3. the adjacent control volume. This process was repeated until the length of the

greenhouse was traversed.

Comparing the results obtained using these two approaches suggested for the soil

temperature profiles, it can be concluded that the accuracy attained employing (n + 4) equations is not worth the excess computer time required.

Typical soil surface temperatures obtained using 24 equations with 24 unknowns,

which are 60.9°F, 95.8°F, 128. 0°F, 136. 8°F, were modified as 61.2°F, 95.4°F, 126. 1°F,

134. 9°F, respectively, using the simplified method based upon Schmidt-Binder Technique.

On the other hand, the variation of computed air temperatures using either method has

been less significant.

564
Typical air outlet temperatures obtained by 24 equations have been 58.69°F,

69.88°F, 85.75°F, and 93.76°F; whereas, using 4 equations and Schmidt-Binder

Technique, respective temperatures have been 58.81°F, 69.82°F, 85.46°F, and 93.54°F.

4. Results of the Analysis and Experimental Verification

24-hour tests were run to verify the theories developed. The same experimental

data was used for a variety of computer programs and computed values were compared

with measurements as listed in Table III.

Table III - Comparison of Computed Values for Various Programs and Measurements

at Puerto Penasco on November 21, 1969, 12 Noon

COMPUTER PROGRAM NUMBER

ITEM UNIT KUD03 KUD15 KUD21 KUD53 KUD61 KUD81 MEASURED

Ambient Temp. , DB o p 70 . 8 Ambient Temp., WB "f 63 .2 Air Inlet, DB °F 85 .2 Air Inlet, WB 'f 84 .2 Air Outlet, DB

(200 ft)

°F 95 90 .16 91 .2 89 .7 88 2 89 .6 89 .0 Air Outlet, WB

(200 ft)

°F 87 86 8 86 . 8 88 86 , 5 Wind Velocity mph AH Air Velocity ft hr-1 6870

Solar Radiation Btu _ hr -^ft"^ 208

Plastic Cover

Temp, at 50 ' °F 84 1 90 .16 87 09 81 5 83 .8 83 .7 Plant Temp. at 50 ' °F 93 6 85 9 86 03 89 8 86 1 86 8 87 . 4 Soil Temp. Surface °F 111 9 102 2 107 8 92 4 100 3 95 1 97 . 5 Soil Temp. , 2" *F 84 91 .4 88 .5 89 .9 Soil Temp. , 4" *F 79 5 84 5 83 9 83 .4 Soil Temp. , 7" "F 78 9 78 9 79 4 79 .4 Condensation on the Cover lb hr"-"- 25 9 53 .7

0) . lb

a, in v/l^da 0 0263 0 0263 0 0263 0 0263 0 .0255

"a, in (200 ft) v/^^da 0 0274 0 0273 0 0276 0 0291 0 .0271

The analysis with transpiration effects improves the computed leaf temperature

whereas considering evaporation from the soil allows to predict the soil surface

temperature more closely. The condensation rates could only be computed using the

program KUD81.

It should be noted that the analyses with no moisture effects and end effects were

developed for steady state operation; therefore, the typical radiation and ambient

conditions at 1200 noon were used to compare the computed temperatures. Soil temperatures below the surface are not available in the programs labeled KUD03, KUD15 and

KUD21.

The choice of program to be used depends upon the degree of accuracy desired, as well as the cost of computation time. Typical computation times have been 8.954

seconds for KUD03, 13.968 seconds for KUD15, 16.816 seconds for KUD21, 26.599 seconds

for KUD53, 71.660 seconds for KUD61, and 51.058 seconds for KUD81 , on a CDC 6400

computer.

565
The use of the advanced version of KUD 61 and 81 may be a drawback, especially in case of using a low-speed computer.

5. Discussions and Conclusions

The prediction of temperatures and humidities in a controlled-environment greenhouse enables the design engineer to maintain the temperature of air and leaf within

the safe and productive margins given by the horticulturalist

Determination of the fan capacity, cooling or heating load where required, should

also be possible. The present mathematical formulation of the problem has proven to

represent the actual performance accurately enough for any engineering application,

since test results have agreed with the computer program.

The physical phenomena of transpiration, condensation effects on the plastic cover,

turbulence over the plant canopy, flow field through and around the canopies, penetration of solar radiation through plant communities have been separately treated by

investigators in various disciplines [7], [8], [9], [lO]. However, the results of

those surveys are not directly applicable to the specific system under study, since

they mostly consider each component separately. Physical properties of plastic cover,

plant and soil are not exactly the same as the present system. Besides, heat and mass transfer coefficients must be determined for the surfaces under consideration.

Those studies would require sophisticated instruments and tedious experimentation

techniques while the present analysis aims to predict the overall performance of the

system rather than the detailed analysis of each component such as determination of

stomatal and boundary layer resistance of a single leaf.

The computer program developed however, is versatile enough to consider these

modifications on the analysis and in its present form, supplies the essential design

data on temperatures, humidities, and heating or cooling load.

Year-round performance prediction for the controlled-environment greenhouse has

been possible through the program KUD 91 which is virtually the same as KUD 81 except

the repeated number of runs and computer plotted curves. A typical set of performance curves for the month of July at Puerto Penasco and

year-round variation of temperatures, humidities and condensation at 11:00 AM and

5:00 AM are sampled in Fig. 5) and Fig. 6) , respectively.

An extensive program is being launched by the Environmental Research Laboratory

of the University of Arizona, to investigate all those interrelated parameters in a coordinated research effort. The findings of this survey should provide the most

accurate data for the prediction of the performance of an inflated plastic controlled

environment greenhouse.

Acknowledgements

The author wishes to express his thanks to Mr. Carl N. Hodges and the staff of

the Environmental Research Laboratory of the University of Arizona, for their help

during the different phases of the reseaich, especially the tedious experimental

program undertaken at Puerto Penasco, Mexico.

Dr. W. Gensler of the Electrical Engineering Department, deserves thanks for his

help in computer programming.

This work was carried out while the author was on leave of absence from the

Mechanical Engineering Department of the Middle East Technical University, Ankara,

Turkey

Funds and equipment that were provided by the University of Arizona, the Abu Dhabi

Government, and the Rockefeller Foundation are gratefully acknowledged.

566
References

[1] HODGES, C.N. and HODGE, Carle 0.,

Power, Water and Food for Desert

Coasts, an integrated system for

providing them, 66 Annual meeting

Am. Soc. Hot. Sci . , Pullman,

Washington, 1968.

[2] HODGES, C. N. and GROH, J.E.,

Controlled Environment Agriculture

for Coastal Desert Areas, 8th

National Plastics Conference, San

Diego, California, 1968.

[3] HODGE, Carle O. , The Blooming Desert,

Bulletin of Atomic Scientists

,

Vol. XXV, No. 9, pp 32-33, 1969.

[4] SELCUK, M.K., Heat and Mass Transfer

Studies of the Inflated Plastic

Greenhouses, unpublished report.

Environmental Research Laboratory,

University of Arizona, May 1970.

[5] SELCUK, M.K. , Analysis , Design and

Performance Evaluation of Controlled

Environment Greenhouses , paper for

A.S.H.R.A.E. National Meeting,

June 29-30, 1970, Kansas City.

[6] JACOB, M. , Heat Transfer, Vol. I, pp 292-304, John Wiley, N.Y., 1949.

[7] WALKER, J. N. and COTTER, D. J.,

Condensation and Resultant Humidity

in Greenhouses During Cold Weather,

Transactions A.S.A.E., pp 1968.

[8] LEMON, E., Aerodynamic Studies of CO2

Exchange Between the Atmosphere and

the Plant, Harvesting the Sun,

pp 263-290, Academic Press, N.Y. 1967.

[9] DECKER, W. L. Atmospheric Humidity

and the Energy Budget of Plant

Canopies, Jnl. Missouri Agr. Exp.

Station No. 26020 .

[10] COWAN, I. R., The Interception and

Absorption of Radiation in Plant

Stands, Jnl. App. Ecol. Vol 5,

pp 367-69, 1968.

Nomenclature

D,p

d,p

pm

Area of plant receiving

direct radiation

Area of plant receiving

diffuse radiation

Ground area (Exposed to Solar

Radiation)

Area of plant (convection H.T.)

Area of plant (Radiation H.T.)

Area of the cross section

Thermal diffusivity (soil)

Specific heat of dry air

Specific heat of moist air

Specific heat of soil

UNIT

ft^

ft^

ft^

ft^

ft^

ft^

ft' hr"i

Btu lb~^

Btu lb~^

Btu lb~^

FORTRAN

NOTATION

ADIRP

ADIFP

AGROU

AP

APR

CROSEC

THDIF

CEAIR

CESO

Radiation Heat Transfer Shape

factor

3- = F

' e Radiation H.T. Shape Emissivity Factor

Dimensionless

Dimensionless

567
p,c

(F ' e ^ ' e ^ ) Radip , c p , Lw c , Lw

ation heat transfer between

plant and cover

s , c

e T

* e T ) Radi- s,Lw c,Lw

s ,p

s , c ation heat transfer between soil

and cover

(F e T

' e T ) Radis,p s,Lw p,Lw

ation heat transfer between soil

and plant

Enthalpy of dry air

Enthalpy of saturated liquid

Enthalpy of phase change, evaporation

Enthalpy of saturated vapor

interf Enthalpy of air stream at

the plant interface

he.

1

he

he

he

Convective H.T. inside

Conveetive H.T. over plants

Convective H.T. over soil

Conveetive H.T. due to wind

w hr , ERHTC - cover to sky

C / SK

hr , ERHTC - plant to sky

P / SK

hr , ERHTC - soil to sky s,sk ^

ERHTC - plant to cover

ERHTC - soil to cover

ERHTC - soil to plane

hr

p,c

hr

hr

I

s ,p Solar radiation intensity

Direct solar radiation intensity

Diffuse solar radiation intensity

Mass Diffusion coefficient

Mass Diffusion coefficient at cover (Condensation Rate)

Mass Diffusion coefficient at

plant (Transpiration)

UNIT

Dimensionless

Dimensionless

Dimensionless

Btu lb

Btu lb

Btu lb

Btu lb

Btu lb

_ 1 _ 2 o _ 1 Btu hr ft F

1 2 Btu hr ft

_ 1 2 lb hr ft

FORTRAN

NOTATION

FRPC

FRSC

FRSP

HDA

HF

HFG

HG

HCIN

HCPL

HCSP

HWIN

HRCOSK

HRPLSK

HRSOSK

HRPC

HRSC

HRSP

RADI

RADIR

RADIF

OKC

OKP

568
bar

v,a

V, m

T.

1

stom

db

wb

"sky

1 , in

" 1 , in

Mass Diffusion coefficient over

soil (Evaporation)

Thermal Conductivity

Soil Thermal Conductivity

Mass Flow Rate of air

Perimeter : n ' R Partial pressure of air

Barometric pressure

Total (mixture) pressure

Partial pressure of water vapor

Partial pressure of water vapor

at ambient air

Partial pressure of water vapor

initially

Total heat transferred

Heat transfer rate

Greenhouse cross section radius

Stomatal resistance to mass diffusion

Time

Temperature

Temperature of air inside the

greenhouse

Ambient Air temperature

Dry bulb temperature

Wet bulb temperature

Equivalent sky temperature

Initial temperature (Dry Bulb)

(Wet Bulb)

Volume flow rate

Velocity

Wind velocity

UNIT

lb hr ft

_ 1 _ 1 _ 1 Btu hr ft °F

lb hr

ft

psia

psia

psia

psia

psia

psia

_ 1 Btu hr

_ 1 2 Btu hr ft

ft

_ 2 _ 1 hr ft lb

hrs

°F

°F

°F

Op

°F

°F

°F

3 1 ft ft"

FORTRAN

NOTATION

OKS

CONSO

PERIM

PBAR

PMIX

PVAM

PVI

RADIUS

RSTOM

TIME

TEAIR

TAM

ft hr

mph

TSKY

TINIDB

TINIWB

VEL

WIND

569
c , sw

C ,Lw

ap,sw

p,Lw

s , sw

s ,Lw

p,sw,D

p , sw ,

'c ,Lw

'p , Lw

's ,Lw

c,Lw

T c , sw

Ax

At

Nomenclature

Greek Symbols

UNIT

Absorptivity, cover shortwave Dimensionless

Absorptivity, cover longwave Dimensionless

Absorptivity, plant

Absorptivity, plant shortwave

Absorptivity, plant longwave

Absorptivity, soil shortwave

Absorptivity, soil longwave

Dimensionless

Dimensionless

Dimensionless

Dimensionless

Dimensionless

Absorptivity, plant shortwave, Dimensionless

direct radiation

Absorptivity, plant shortwave, Dimensionless

diffuse radiation

Emissivity, cover longwave Dimensionless

Emissivity, plant longwave Dimensionless

Emissivity, soil longwave Dimensionless

Cover, transmissivity Dimensionless

Cover, transmissivity longwave Dimensionless

Cover, transmissivity shortwave Dimensionless

Thickness of the soil slab

e. .

, init

Space interval (Length of the

System)

Time Interval

Humidity ratio

Humidity ratio of air

Initial humidity ratio

Humidity ratio of saturated

air, at the cover temp.

Humidity ratio of saturated

air at plant temp.

Humidity ratio of saturated

air, at soil surface temp.

Relative humidity of air

initially

ft

ft

hr

lb /lb , V da

Dimensionless

FORTRAN

NOTATION

ALFCSW

ALFCLW

ALFPSW

ALFPLW

ALFSSW

ALFSLW

AFPSWR

AFPSWF

EMCLW

EMPLLW

EMSOLW

TRAN

TAUCLW

TAUCSW

DELSO

DELX

DELTIM

OMEGA

OMEGIN

OMEGCO

OMEGPL

OMEGSO

PHIN

570
si

s2

Transparent cover temp.

Plant temperature

Soil surface temperature

Soil temperature 1st slab

Soil temperature 2nd slab

Soil temperature 3rd slab

Soil temperature kth slab

Density of dry air

Density of moist air

Density of the soil

UNIT

°F

°F

°F

°F

°F

°F

°F

lb ft m

FORTRAN

NOTATION

TECOV

TEPLA

TESOI

TSl

TS2

TS3

ROAIR

ROMAIR

ROSO

aam

c

D

d

da

db

i

Subscripts

air

ambient

cover

Diffusion, Direct for solar radiation

diffuse, solar radiation

dry air

dry bulb

inlet, inside

init.,in initial

interf. interface

Lw longwave m moist air

o outlet, outside

p plant

s soil

sat saturation

sk sky

sw shortwave

V Vapor w water

wb wet bulb

571
572
573
'READ

DATA

PROR

CALCULATE

MOIST AIR

PROPERT

101

A: MATRiX

CiMATRiy"

CALL

COZUM

(a>- PART PRES.

AIR AT

PLANT TEM

401

E: MATRIX

G: MATRIX

TECOV(M)CI

TEAIR(M)C2

TEPLNW C3

TES0L(M)C4

4 SI MULT

EQUATIONS

NO-MOIST

SOLUTION

SIMULTAN.

EQUATIONS

GAUSS-JOR.

4SIMULT

EQUATIONS

W/TRANS.

ONLY

SOLUTION

OF SI MULT

EQUATIONS

GAUSS-JOR.

A^p ERROR

ERR.=TEPL

NW-TEPLA

NEWTONRHAPSON

APPROX.

64

-<a)

PRINT

CORRECT

TEMPER.

RE-INITIAL

TINIDB=TE

AIR(M)OME

GINOMEKM

I

CALCULATE

AIR PROP

AT CORR.

TEMPER.

Fig. 3) Flow Chart for the Analysis with Transpiration Effects Only,

Program KUD 15

574
'READ

DATA

PROP.

'NO

MOIST.

ANALY.

APPROX.

J_

ANALYS.

W/TRAN.

ONLY

IMPROVED

COMF

Xc,x

'UTE

Y 5 ' 'S

GENERATE

Q, (4.4)

Z(4)

4 SIMULTA.

EQUATION

EVAP-TRAN

AND COND.

CALL

COZUM

SOLUTION

OF SI MULT.

EQUATIONS

GAUSS-JOR.

0

COMPUTE

CONDENS.

PRINT

TEMP

COND

EXAC

HUM.

EN.

COMPUTE

SOIL TEMP

PROFILES

SCHMIDT

BINDER

TECHNIQUE

PRINT

SOIL

TEMPER.

RE INITIAL

TINIDB,

OMEGIN

X=X+AX

AX: SYSTEM

LENGTH

X: DISTANCE!

TO INLET

Fig. 4) Flow Chart for the Analysis with Evaporation-Transpiration

and Condensation Effects

575
0 6 12 18 24

HOURS

Fig. 5a. Computer Plotted Performance Curves for the Month of July

at Puerto Penasco, Sonora, Mexico.

576
go

(D3 mo y

.08 8000 110

.07 7000 100

.06 6000 90-

.05 5000 80-

.04 4000 70

.03 3000 60-

.02 2000 50-

.01 1000 40-

0 30

X = GOV. TEMP.

O = AIR OUT. TEMP. • = PLANT TEMP

+ = SOIL TEMP

A = TOT. CONDEN.

JULY

12 HOURS18 24

Fig. 5b. Computer Plotted Performance Curves for the Month of July

at Puerto Penasco, Sonora, Mexico.

577
40 70

30 SO'

20 50

X = GOV. TEMP.

O = AIR OUT. TEMP. • = PLANT TEMP

+ = SOIL TEMP

A = TOT CON DEN.

0 30

J \M M J S /N

OQO

8000 110-

7000 100

6000 90

5000 80

4000 70

3000 60-

X = GOV. TEMP

O = AIR OUT TEMP

• = PLANT TEMP

+ = SOIL TEMP

A = TOT. GONDEN.

F A J

A.M. 5 A.M.

Fig. 6) Computer Plotted Performance Curves at Noon and Midnight

for 12 Months at Puerto Penasco, Sonora, Mexico

578
Automated Design Program for

Air-Handling Apparatus

M. Nagatomo^ S. Tanaka^ and N. Tohda'^

Kajima Corporation

Tokyo Japan

This paper describes a computer program that can be used to calculate

the heating and cooling load, the supply air volume, the psychrometric data,

and the specifications for an air -handling apparatus. The program is based

on equations that express the change in the state of moist air. The program

can be used to select the appropriate apparatus and calculate the required

air volume for either a non-reheat system or a reheat system. It also can

be used to quickly optimize the design by performing alternative calculations

for various hypothetical conditions.

Key Words : Air-handling apparatus, apparatus dew point,

automated design, cooling and dehumidifying coil, cooling load,

psychrometric chart, reheat system, single-duct air system,

supply air volume.

1. Introduction

The process of designing single- duct air systems requires the calculation of cooling-heating

load, a psychrometric analysis, the calculation of supply air volume, and the selection of the apparatus. The calculation of the cooling and heating loads by computers has been widely studied and many

programs have been developed. Programs that consistently treat the entire design process have not been formulated. Because it is difficult to treat the psychrometric analysis by computer and to establish and systematize a standard for engineering judgement during the design process. This paper

describes a program that consistently treats the design process by setting up approximate formulas

to express the state of moist air, simplifying the phenomena under several hypothetical conditions,

and establishing the standard for engineering judgment.

2. Program Outline

This program is to be used after the preliminary design of the air-conditioning facilities is completed and the types of systems, the zones, and the kind and conditions of the energy source are

determined.

Dr. Eng. , Chief of Environmen'tal Engineering Department, Kajima Institute of Construction

Technology.

Chief Engineer, Kajima Computation Center. Mechanical Engineer, Design Department.

579
The input data are as follows : a. Data for load calculation: outdoor design conditions, room design conditions,

thermal properties and quantities of the materials constituting the room, internal heat

load, etc.

b. Data for system-design : type of system, chilled-water temperature, steam

pressure, type of humidifier, type of filter, etc.

The program consists of three blocks. The first calculates cooling and heating loads, based on

the theory of periodic heat conduction, which assumes the room temperature to be constant. From

the input data of the load calculation, summertime cooling load and wintertime heating load for every room are calculated by hour and summed up by zones. The second block takes the results of load

calculation and calculates the states and the volume of supply air by the psychrometric analysis of system-design data. If no solution can be obtained by that process, the room conditions are auto- matically changed and the load calculations are repeated. The third block determines the specifications of air-handling apparatus, calculating the apparatus load as well as the energy source capacity

from the system-design data and psychrometric data, and selects the equipment. The data showing

the apparatus efficiency required for the apparatus selection are included in the program with the performance value stated in the manufacturer's catalogue converted into formulas.

The data to be printed out are as follows : • The peak load of each room.

• The supply air volume of the room.

• The hourly load of each zone.

• The specifications of air-handling apparatus,

the psychrometric data, and the capacity and

conditions of the energy source.

3. Algorithms of Psychrometrics

A psychrometric chart is generally used to obtain and analyze the data concerning the state of moist air. In order to do the same with a computer, all the characteristics of moist air have to be

expressed by mathematical formulas. The general psychrometric chart has enthalpy and humidity

ratio drawn as oblique coordinates, and dry-bulb temperature, wet-bulb temperature, and relative

humidity as constant lines. The data of moist air necessary for the calculations of supply air volume

and the selection of the coil can be expressed by dry-bulb temperature, humidity ratio, and enthalpy.

To simplify the numerical analysis, approximate formulas may be used, so long as no practical problem arises. In this program, therefore, the state of moist air and its changes are expressed by

using the enthalpy and the humidity ratio. The dry-bulb temperature of moist air employed in the following formulas ranges from 0°C to 40°C when the atmospheric pressure is 760mmHg.

Equations for obtaining humidity ratio with dry-bulb temperature and relative humidity, given:

PWS (T) = 735.557 * EXP (-7. 90298* (TS/T-1. 0) + 5. 02808 * ALOG (TS/T)

-1. 3816E-7*(10. 0**(11. 349*(1. 0-T/TS))-l. 0) + 8. 1328E-3* (10. 0** (-3. 49149 * (TS/T - 1 . 0))-l. 0) ) (1) W = 0. 0062 *RH*PWS (DB+273. 16) / (760. 0 - 0. 01 *RH*PWS (DB+273. 16) ) (2)

Equation for obtaining enthalpy with dry-bulb temperature and humidity ratio, given

H = 0. 240=1= DB+ (597. 3 + 0. 441 * DB) * W (3)

Equations for obtaining humidity ratio and relative humidity with dry-bulb temperature and wetbulb temperature, given:

PW = PWS (WB+273. 16) - 0.5*(DB - WB) * 760. 0/ 755. 0 (4) W = 0.622*PW/ (760.0 - PWS (DB+2 7 3. 16) ) (5)

580
RH = 100. 0*PW / PWS (DB+273. 16) (6)

Equation for obtaining humidity ratio Wo, when the air with dry-bulb temperature DBj, and

humidity ratio W-^ changes with the given A El A W constant and dry-bulb temperature becomes DB2 : ^ __ C+597.3+0.441=<-DBi ^ ^ ^

0. 24 MDB2+DB1)

^ C-597. 3-0. 441* DB2 C-597. 3-0. 441 * DBg

Equations for the approximate relation of enthalpy and humidity ratio when relative humidity is constant

(Within dry-bulb temperature of 0° - 30°C, the error is limited to + 0. 4%. )

HS(W) = -3. 32635 + 1673. 25* W - 49827. 4* W**2 + 1005561. 0*W** 3 (8)

H95(W) = -3. 13977 + 1669. 23* W - 49134. 4* W**2 + 983042. 0* W** 3 (9)

H85(W) = -2. 93914 + 1726. 00* W - 54017. 6* W**2 + 1128573. 0 * W ** 3 (10)

To obtain enthalpy H2 and humidity ratio W2 when the air with enthalpy H-^ and humidity ratio

Wj^ changes with the given constant A H/ A W, and relative humidity becomes 95%, solve the following

equation

H95(W2) = C*(W2 - W^) + (11)

Equation (11) can be solved by applying the Newton-Raphson Method.

To obtain dew-point temperature of air with humidity ratio W^, first obtain dew-point enthalpy

by eq(8) and then use eq(3).

4. Calculations of Supply Air Volume

4. 1 Fundamental

If the state of supply air and its volume can be set to satisfy eqs(12) and (13), the room temperature and humidity can be maintained under conditions similar to those of the design.

QT = 1. 2*AQ* (Hi - Hg) (12)

Hi - Hg 597.3

^^3j

Wi - Wg " 1.0- SHF

In determining the state of supply air and its volume, however, there are the following limitations :

• There is a lower limit of the supply air temperature which prevents

vapor condensation at the outlet.

• There are limits of the cooling and dehumidifying ability of the chilledwater coil.

• There are upper and lower limits of air volume for the air distribution within a room and for economic and health reasons. When the air volume within the range of the above limitations is minimized, the equipment will

be most economical. If such limitations are established and standaridized, it will not be hard to use

the computer for psychrometric analysis. The conditions set up in this program for such limitations

and the procedure for air-volume calculations are given in Figure 1. As to the change of the state of

air passing through the cooling -dehumidifying coil, A H/ A W is assumed to be a constant. It is also

assumed that the change of the state of air makes no change in the air volume.

The state of supply air should be above the dew point temperature of the room, to prevent vapor

condensation at the outlet, and below 85% relative humidity, to prevent the state of air leaving the coil from being too close to the saturation line.

581
The relative humidity of the air leaving the cooling-dehumidtfying coil is to be below 95% and the apparatus dew point temperature is to be above its specified dew point temperature. Considering the

coil performance, the variation of chilled-water temperature, and the value of A H/ A W of the air

passing through the coil, the designer must set the specified apparatus dew point temperature to be

higher than the chilled-water temperature by 3°C or more. As to the minimum volume of supply air, choose the larger one from either between outdoor air

volume or exhaust air volume, as is required by the. design. The maximum will be, as a rule, below

15 times of air changes per hour, but this can be ignored if it interferes with other factors.

The heat gain caused by the fan can be determined by the fan efficiency and its total pressure.

Their exact value cannot be estimated until the duct system is designed. So they most be assumed.

The centrifugal type is one of the most common types of fan used in the air-handling apparatus ; its efficiency is 0. 5-0. 65. Thus, if the efficiency is assumed to be 0. 5, the relation between the total pressure of the fan and the rise of temperature caused by heat gain is as follows:

FTD = 0. 0162*PT ^^'^^

The total pressure of fan will be assumed by the designer according to the layout of the duct

system and the type of filter. Since the actual temperature rise is 1. 0-1. 8°C, it is not necessary to maintain complete accuracy. It is assumed that the fan is located in the discharge-side of the airhandling apparatus.

The supply duct heat gain is ignored. It can, however, be estimated to be about 5 percent of the sensible heat load of the room and added to the apparatus load.

4. 2 Non-Reheat System

If the total heat load of the room, the sensible heat factor, the required outdoor air volume, and

the room and outdoor conditions are given, the psychrometric data and the supply air volume are cal- culated by eqs(7), (8), (10), (12), (13), and (14). In case the solution cannot be obtained or the apparatus dew point falls below the specified apparatus dew point, the room conditions are automatically

modified and the load calculation is repeated. The dotted line in Figure 2 shows such a case. As in the basement zone, where the cooling load is small, the supply air volume calculated in the above way may turn out to be too small. In this case, the temperature difference between supply

air at the outlet and the room air will be reduced so that the supply air volume can be equal to the re- quired minimum volume. In the example in Figure 3, the state of supply air changes from 6' to 6.

In modifing the room design conditions, the dry-bulb temperature and the humidity of the room

air will be modified to keep the effective temperature of the room constant. In this program the drybulb temperature is reduced by 0. 5°C and the relative humidity is increased by 5%. In the case of Figure 2, 1' is moved to 1. When the room conditions are modified, then the load calculation is re- peated under the new conditions. If the apparatus dew point is too low even when the conditions are

modified, reheating calculations should be performed.

4. 3 Reheat System

In the case of a reheat system, the specified apparatus dew point is initially set to be the apparatus dew point, and the relative humidity of the air leaving the coil should be 95% to maximize the temperature difference between the supply air at the outlet and the room air, and thus to minimize the supply air volume. In the case of Figure 4, if the supply air is assigned the room dew point 6', the apparatus dew point cannot be obtained, as indicated by the dotted line, because of the inadequate

selection of the state of supply air. If the total heat load, the sensible heat factor, the required out- door air volume, and the room and outdoor conditions are given, the appropriate state of supply air can be obtained by solving the following simultaneous equations :

1.2* (H^ - H5)*OAQ Wq - QT W2 - Wi ^

'

582
W4 = We (16)

H4 = H95(W4) (17)

"3 "7 - 114 n Y (18) W3 - W7 W4 - W7

Wovv 3

- Wivv 1 H3 ~ Hi

WoVV2 - Wi1 2 1

( 19)

He - Hi 597. 3 (20) We - Wi 1.0 - SHF

If the state of supply air is known, the state of air entering the fan or leaving the reheater can

be obtained by eq(14). When the volume of outdoor air and the latent heat load of the room are large,

however, the air temperature at the outlet approaches the room air temperature; consequently, the

air volume may increase and becomes greater than the specified air volume. In this case, the room

conditions must be modified and the calculations performed as in the non-reheat system.

5. Example of Computation

This program has been applied to the design of the equipment for a hotel, to be built in Tokyo.

The hotel is 47 stories high, has 3 stories underground, and has a gross floor area of 114, 600m2.

It has 44 cooling zones and about 330 types of rooms. Thirty of the cooling zones are to be serviced

by all-air systems, of which 18 will employ the reheat system. The other 14 zones will be serviced

by the primary air fan- coil system.

The input data to the program consist of about 2, 500 punch cards, mostly for load calculations ; the data cards for the computation of designing the system number about 50. The computer calculations take approximately 15 minutes.

The specifications of the air-handling apparatus and the psychrometric data are shown in Figure

5 as an example of the output. As can be seen from this example, the computation of psychrometric

data was sufficiently accurate as compared to the manual calculations using the psychrometric chart. The manpower required to prepare the input data was approximately 50 man-hours, or about the same

manpower required for the load calculations.

6. Conclusion

The formulas and the procedure for supply air volume computation and the psychrometric analysis can be applied to the computer design of not only a single-duct system but also a dual-duct system but also a dual-duct system or a primary air-handling apparatus of the water system.

The advantages of using the Automated Design Program are as follows :

• Great amounts of design labor and time can be saved, and engineers can promptly follow up on any change in the architectural design.

• The discrepancies arising from the designers' experience and personality can be eliminated, and even inexperienced designers can obtain

the same results with equal safety and accuracy.

• Comparative studies of computations with alternative design factors are easy, thus an optimum design can be achieved.

We express our deepest gratitude to the staffs of the Kajima Corporation Designing Department

and the Kajima Institute of Construction Technology for their assistance in developing this program.

583
7. References

(1) ASHRAE, The Task Group on Energy

Requirements for Heating and Cooling,

Proposed Procedure for Determining

Heating and Cooling Loads for Energy

Calculations (1968).

(3) Uchida, H. , Moist Air and Cooling Tower,

Syokabo, Tokyo (1965).

(4) Carrier Air Conditioning Company,

Handbook of Air Conditioning System

Design, McGraw-Hill (1965).

(2) ASHRAE, Handbook of Fundamentals (1967)

8 Notation

Letter symbols used in this paper are defined as follows:

A -= Supply air volume (m'^/hr)

C -- Enthalpy-humidity difference ratio, A H/ A W (kcal/kg)

JJJd - Dry-bulb temperature (°C)

Fi'P iJsr - Dew-point temperature (°C) FTD == Temperature rise caused by fan load (°C)

H --= Enthalpy of moist air (kcal/kg)

HS == Enthalpy of moisture saturated air (kcal/kg)

H95 --= Enthalpy of 95% relative humidity air (kcal/kg)

H85 == Enthalpy of 85% relative humidity air (kcal/kg)

OAQ -= Outdoor air volume (m^/hr)

PT == Fan total pressure (mroAq)

PW = Partial pressure of water vaper in moist air (mmHg)

PWS -= Partial pressure of water vaper in moisture saturated air (mmHg)

QT = Total heat load of room (kcal/hr)

RH = Relative humidity (%)

SHF = Sensible heat factor (non- dimension)

T = Absolute temperature (°K)

TS = Absolute temperature, 373. 16 (°K)

W = Humidity ratio of moist air (kg/kg of dry air)

WB = Wet-bulb temperature (°C)

Subscript symbols are used as follows :

1. refers to room design condition

2. refers to outdoor design condition

3. refers to condition of air entering coil

4. refers to condition of air entering reheater

5. refers to condition of air entering fan

6. refers to condition of supply air

7. refers to apparatus dewpoint

584
585
Fig. 2 Psychrometrics of Non-Reheat System.

Fig. 3 The Case where the State of Supply Air is Determined under the Limited Condition of Minimum Air Volume.

586
Fig. 4 Psychrometrics of Reheat System.

587
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588
Computer-aided System

for Preliminary Air Conditioning Design

E. Maki and Y. Okuda ^ Nikken Sekkei Komu Co. , Ltd. Mechanical Department

Japan

In preliminary designing stage of air conditioning system, there is a time

when the information necessary for deciding the zoning, type of system, general layout, types of equipment, cost, etc. must be obtained by preparing a schematic design of the proposed system to see if it will meet the basic design

requirements. The information thus obtained may be fed back to those con- cerned so that they can make necessary project coordination. In order to make it possible to deal with the work required at such stage effectively by

utilizing a computer, the authors developed a system titled COSMA which was

intended for continuous processing of heat load computation, equipment selection, pipe and duct designing, etc. Based on the experienced gained through

its trial use, COSMA is now being reorganized into SPACE (Subprogram and

Phrase for Air Conditioning Engineers) which is featured by the following

characteristics:

1. A variety of subprograms and files is available so as to enable the selection

of various equipment, basic design of ductwork and piping work, cost esti- mating of principal elements, etc. on the basis of heat loads.

2. The system is flexible and allows free combinations of phrases in accordance with thinking sequence of the designers.

3. Simplified input data are another feature of this system.

4. The system is composed of subprograms which are minutely divided into fxmctional units by well documented and classified files. These subprograms and files are designed to be easily expanded, modified or adapted to cope with varied conditions. Moreover, considerations have been given

so that they can, in future, be coupled with the computer-aided systems for

other engineering areas such as electrical, plxombing, architectural and

structural. This system enables the designers to obtain the basic data which are more concrete and objective in a shorter time, and thus makes it possible to study more

alternatives within the given time.

Key Words: Preliminary air conditioning design, computer-aided system,

equipment selection program, duct design program, pipe design program,

AC system design program.

echanical Engineers

589
1. Need of Developing a Computer Program

for Preliminary Design

At an early stage of architectural planning, an air conditioning engineer must propose a preliminary air conditioning design which will satisfy the given conditions. At this stage, he must make

necessary investigations and propose a creative design based on his professional intuition and experience. Then, he must check to what extent the aforesaid proposal will satisfy the given conditions,

decide whether the proposal shoiild be adopted, and, if it is to be adopted, determine the optimum

scope of the system. If not, he will have to make some alternative proposal, or request the architect

to restudy and modify the architectural design, or in some cases, he will have to ask to modify the basic design conditions and requirements in conformity to which he has prepared the original proposal.

The data required at this stage will include: (1) the initial instUation cost; (2) the operating cost;

(3) the physical size of each element of the system to give the basis for coordinating the relation of architectural and structural designs with the air conditioning design; (4) the data indicating the anticipated ambient conditions (including the values, changes and distribution of temperature, humidity, air

flow, etc. in each room and parts thereof) which will be created by the proposed system. The data

is important because they will enable the mechanical engineer to foresee if these conditions meet the design requirements.

The data described above need be prepared and evaluated by two methods: in the method (A), the evaluation of the data (1), (2) and (3) will be made through a statistic approach, namely on the basis of analyses of assembled data, while the data (4) will be assessed on the basis of professional experience;

and in the method (B), the data (1), (2) and (3) will be obtained by the schematic design studies of the proposed system and the data (4), by means of simulation. (It should be noted that the methods (A)

and (B) are mutually supplementary, and one is not enough without the other to insure an accurate and

proper determination. )

It, however, may be generalized that the method (B) is more direct and convenient in seeing

quantitative differences beween a number of proposed systems with respect to the data (1), (2) and (3).

Since a considerable part of the work required at this stage can be systematically structured, a utilization of a computer at this stage should enable a mechanical designer to evaluate a larger number of alternative proposals in a comparatively short time, and this should make it possible to make

feed-backs to the architect and the owner in a more effective manner. For this reason, the development of a computer-aided system for the aforesaid schematic design studies is highly desirable.

The firm of Nikken Sekkei took to the development of such a computered system in 1967, and

completed the first edition of the program in 1969. Based on the experience in using this program,

the firm began to revise the program at the end of 1969. In the following paragraphs, the authors

intend to describe briefly the first edition of the program, the advantages derived from it, the reasons why the first edition had to be revised, and the concept and present status of the new system now in the course of development.

2. Program Group for Schematic Designs

COSMA - First Edition

2. 1. General Description

The scope of COSMA First Edition is as shown in figures 1 and 2 and the program has been in use

at Nikken on some of the actual project on a trial basis.

Basically, COSMA is composed of the following three groups of programs:

(1) Programs for a continuous data processing from heat load computation to selection of various

equipment.

590
(2) Programs for designing duct and piping systems

(3) Programs which, for some typical perimeter zone and interior zone systems often adopted in practice, enable a continuous data processing, by means of simplified input data, for all design

stages such as heat load computation, selection of terminal \anits, pipe and duct design and cost estimation.

(1) Outline and features of program for heat load computations

and equipment selections

The first step in a series of processes described in this paragraph is to define space \mits and

zones in the building for the purpose of planning. The word "space-unit" may be defined as a minimum

unit of space which is used as a basis for the load computation. The term "zone" as used here de- notes a building space which is regarded as a minimum independent area in air conditioning planning,

and zones are classified depending on their load characteristics and the intended purposes. Each

zone is defined as a group of space units. The program to be discribed later in this paragraph use

the aforesaid unit space and zone as a basis. The program is capable of dealing with up to 36 types

of space units and 60 zones for one building.

The second step is to make heat load computations to give a basic data for the entire air conditioning system design which includes the selection of equipment and the designing of ducts and piping.

The program introduced here is so contrived as to enable numerous detailed computations required for large buildings with well-organized simple input data. The computation according to this program

follow the steps mentioned below: (1) data for calculation for the various types of interior are fed to the computer, each input data card representing one type; (2) next, various combinations of the perimeter

and the interior types and requirements for fresh air intake are fed for each space unit with two cards

per space \mit. Based on the foregoing input data, the computer calculates the heat loads for all space units and then sums them up to give the heat load for each zone. The zonal heat loads are further summed up to give the heat load for the whole building. Then, as the last step in heat load

computation, flow rates of air, chilled and hot water, steam and other media are computed for each

zone.

The third step in this program is for the user to assign a group of chillers, boilers, p\imps, air

conditioners, etc. to each zone according to the air conditioning system under consideration. Each

group of chillers etc. is given an identification niimber; and the zone or zones to be served by the respective group are indicated by the aforesaid identification number. Also, the nxomber of equipment

needed for each group is determined.

The input data are given in the form of cards, one card being provided for each zone. The niimber given at the equipment type coliimn on each card indicates the identification number of the set of equipment which takes care of the zone the card represents. The number of equipment for each group

is indicated on the same card. A pump may be designated to handle chilled water, hot water or con- denser water to meet seasonal requirement. Thus, if the chilled water pump column and hot water

pump column of the card are given the same number, it means that a single pump is to handle both

chilled water and hot water.

The fourth step is to select equipment on the basis of the heat loads, flow rates and system designations obtained in the previous step. At this stage, such requirements as types of apparatus are

also specified on the input data. The data necessary for specifying such requirements can be taken

from the information supplied by the manufacturers, arranged and stored on disks.

The output data give the information on the type, performance, size, weight, cost, etc. of each

equipment. For some kinds of equipment, this information is given in the form of a comparative

table showing performance etc. of various makes and models.

591
Sampl e input data showing zone-equipment-system relations (Simplified for explanatory purposes)

Zone Chiller Boiler Pump Air

Condenser Primary Secondary Hot Conditioner

Water Chilled Chilled Water

Water Water

1 1 1 1 4 7 1 1 2 1 1 1 4 8 1 2

3 1 1 1 4 9 1 3 4 2 1 2 5 5 10 4

5 2 1 2 5 5 10 5

6 2 1 2 5 5 10 6

7 3 1 3 6 6 6 7

The meaning of the above input data is: No. 1 chiller is for Zones No. 1, No. 2 and No. 3. No. 1 boiler is for all zones. No. 1 pump is for condenser water and hot water fo r Zones No. 1 , No. 2 and No. 3. No. 2 pump is for condenser water for Zones No. 4, No. 5 and No. 6. No. 6 pump is for primary- secondary chilled water and hot water for Zone No. 7.

(2) Outline and features of piping and duct programs

In the piping program, the locations of equipment, the required flow rates of water, the desired

flow resistance, etc. are fed as input data, according to which the computer calculates the appropriate

pipe diameters at respective sections of pipeline, and gives the pipe sizes, flow resistance, lengths

which are useful for cost estimation, etc. Pipe sizes are determined to equalize the resistances of

all branches. Input data are prepared by nodal description method. In the duct program, the design, cost estimate, outlet and mixing box selection, etc. are processed on the basis of input data which are prepared by nodal description method.

(3) Outline and features of the programs for AC system

The flow chart in figure 2 indicates what can be processed by this set of programs. In computerizing the process of obtaining necessary information through schematic designs of a fan-coil unit, an induction unit, a dual-duct or a single duct system, the greatest difficulty is usually enco\mtered in how to computerize the designing of duct and piping systems. This difficulty results from the fact

that the input data become, more often than not, highly complicated in proportion with the importance

of the information. To avoid this diffic\ilty, the nodal description method is dispensed with in preparing input data for duct and piping design as shown in figures 4 and 5.

Instead, a set of input sheets into which an architectural modular grid is entered in the form of matrices based on the elevations and plans is used. On these input sheets, the designer writes either

in symbols or in numerals, the designations as to the following: (1) the types of systems to be studied

(the name of systems and designation of the number of pipes, i. e. , 2-pipe, 4-pipe, etc. ); (2) the type

designation of duct and piping system; (3) the type of piping (reverse-return etc. ); the data necessary

for computations (computation method, friction loss per unit length, etc. ). The program is formulated in such a way that heat load computation, selection of terminal units, and further duct and pipe

computations and cost estimating can be performed by a computer. As shown in figure 3 , these

program requires only two input data sheets to study up to three different perimeter systems.

592
(4) Scope of the program

No. of Main No. of Sub- Steps Fixed Data Programs Programs (Sectors

)

Psychrometirc Chart 0 18 300

Heat Calculation and Flow Rate 8 1, 000 35

Equipment Selection 38 9 5, 000 715

Perimeter System 1 8 3, 500 23

Interior System 1 9 3, 000 28

Piping 1 1 500 1 Ductwork 2 7 2, 000 10

Altogether, these amount to one and one half disks in area.

2. 2. COSMA promoted design efficiency

The authors utilized COSMA when they designed the air conditioning system for a 20- storied

building having a floor area of about 10, 000 sq. m or 106, 500 sq ft. In this case, the computer

(IBM 1130) was used to process those data which are shown above the dotted line in figure 1 , or in other words, the data concerned with the steps from the heat load computation to the equipment

selection and study. The relevant information desired by the designers was obtained in less than five hours, the designers spending two to three hours for input data preparation and the computer personnel

spending about two hours for pimching, running, etc.

Also, COSMA was utilized in designing the air conditioning system for another 20-storied building with a floor area of some 30, 000 sq. m (318, 000 sq ft). In this case, it was assumed that the whole system was composed of 8 perimeter systems and 12 interior systems, and three alternative

system types (induction unit system, fan coil system and dual duct system) for the perimeter and also

three system types (single duct system, dual duct system and individual zone system) for the interior were considered. It took about 8 hours for input data preparation, 3 hours and 15 minutes for computer processing, and another 8 hours for manual assorting and editing of the output data. From these experiences, it was learned that all the data processing for COSMA System could be

done in one day if the output data were limited to the point of equipment studies, and in about three or

four days if the output data were to include those concerning duct and piping designs and comparison

of alternatives. With the efficiency thus achieved, the system was considered capable of serving the intended purpose satisfactorily.

2. 3. Some problems with COSMA

After having been used for the past year on a trial basis by some machinery engineers of our

firm, it is considered that COSMA should be improved with respect to the following:

a. COSMA consists of a niimber of subsystems; however, it is rather strongly characterised by its being one inseparable system. This character of the system makes it difficult to pick out and combine desired programs freely as the occasion demands.

b. The need is felt that the system should allow for a greater freedom in setting up the most desirable

flow of data processing for each individual project.

c. COSMA is capable of dealing with the air conditioning systems generally used at present. The improvement of the system to make it easily adaptable to new design situations, such as the development of new equipment or unique air conditioning system combinations, is considered necessary.

d. It is desired that COSMA have a means of output control so that the computer can give the specific
information reqmred at any given phase of the data processing,

e. It is desired that COSMA be made capable of aiding the design work from the earlier stage of design

than is possible with the present program.

3. Development an Assembly of Phrases for Schematic Designs

- Development of SPACE (Subprograms & Phrases for Air

Conditioning Engineers)

3. 1. Two approaches to the development

There appear to be two approaches to arrive at the solutions for the problems described in the paragraph 2. 4. , with the original system being used as basis of the further development.

(1) Developing a group of approximation formulas

In one way of approaching the solutions, the whole group of programs is regarded as a data generating system, with the conditions given to COSMA being changed systematically. The resxilting

output data can be handled and organized as in the case of statistic data. Then, a variety of approximation formulas can be obtained for these output data, and this group of formulas can be converted

into programs to obtain important information.

(2) Subprograms and phrases

Another approach to the improvement of original COSMA is to decompose it into as many minute

mono-functional subprograms as possible and, at the same time, to standardize all the files.

These subprograms and files can then be organized as required by application of IBM-plan technique (1) ^ into a set of phrases for air conditioning designs. It is expected that this process can

eliminate the drawbacks of original COSMA to a large extent without losing its features.

The air conditioning designers who use this system (SPACE) are not supposed to look at the input

data sheets and make entries for the necessary items disregarding the inapplicable optionals, all ac- cording to the designated processing sequence. Instead, the designers are requested to arrange the phrases and data as necessary for the designs, so that they can use the program in a more flexible and versatile manner. The system as has been developed to date is as outlined in the following paragraphs.

3. 2. General setup of SPACE

Figure in parenthesis indicates the literature referenced at the end of this paper.

594
(1) Outline of the system

Subprograms:

At present, our primary efforts are being directed to dividing COSMA subroutines into as minutely classified subprograms as possible and setting up appropriate output controls which precede

output instructions. The number and scope of such programs, therefore, can be surmised by refer- ence to the scope of COSMA described in the section 2 of this paper.

File group:

The files are generally organized as follows:

(i) Common data files - These files contain the data applicable to all kinds of projects.

(ii) Project files - For these files, only the framework of data storage system (the name of file, the sequence of data filing, etc. ) is predetermined, so the designer must compile a file for each individual project by using the applicable phrases.

The major files of each category will be described in Appendix A.

Phrases:

Presently, the COSMA subprograms which have been decomposed are being reorganized into a set of new phrases. The composed phrases will serve the purpose of primary operations. As the next step, the need is felt to develop the phrases which can be used for secondary operations. These

phrases for secondary operations should be capable of modifying a part, not all, of the input data given

out in primary operations, and of reprocessing the phrases which have been modified. For instance,

such a phrase may read "SELECT CHILLERS FOR CHANGED CONDITIONS, "

(2) Relationship between subprograms and phrases

Since it is apparently impossible to describe the computered design process for an entire air

conditioning system within the space allowable for this paper, the functions of subprograms and the subprogram-phrase relationships will be described for some of the phrases used in perimeter system

designs. The function of individual subprograms will be further described in Appendix B. ALC-33 Instructions to read the project titles etc. ALC-34 Instructions to read the design climatic conditions

LAC-44 Instructions to compute heat loads

AAV-44 Air volume computation

AOAV 1 Designation of primary air

AFCO 2 Selection of fan coils

AZON 3 Subprogram for defining the zoning by matrix

APMO 1 Piping design for unit space expressed by matrix

ADMO 1 Duct design for unit spaces expressed by matrix

(a) Some examples of phrase usage

The design can be worked out by a variety of methods by utilizing the foregoing subprograms as shown by the following examples. (The subprograms listed in parentheses are shown for explanation

only, and are necessary only for defining the phrases.) In actual use for a specific project, phrases

and data only need be stated.

On the outset of a project, the heat computation is conducted:

LOAD CALC BY ALC : (ALC-33, ALC-34 & ALC-44)

At the next step, the phrases such as the following may ensue:

595
(1) SELECT FAN COIL (AFCO 2): The instructions that proper fan coil units be selected for each space unit.

(2) SELECT FAN COIL WITH PA (AOAV 1 and AFCO 2): The instructions that proper fan coil units be selected against the load differencial computed by- deducting the cooling capacity of the primary air supplied to each unit space according to the , applicable criterion from the loads on space units.

(3) ZONING BY MATRIX; ZONE (AZON 5) DESIGN FAN COIL SYSTEM (AFCO 2 APMO 1) By these phrases, a computer is instructed to select fan coils and execute piping design and cost estimating on the basis of the given data indicating the proposed space xmit layout and piping sys- tem.

(4) ZONING BY MATRIX; ZONE (AZON 5) DESIGN FAN COIL SYSTEM WITH PA (AOAV 1, AFCO 2, APMO 1 and ADMO 1) After the primary air supply data have been fed and fan coil units have been selected as described

in (2), the piping for fan coil units and the ductwork for primary air are designed and estimated

by the instructions phrased as above. In this example, space unit layout only has been instruted by ZONING phrase, and separate instructions as to how the pipes and ducts sho\ild be laid out must be given by the imput data included in APMO 1 and ADMO 1. Therefore, no trouble will ensue even if the duct layout differs from the piping layout.

For single duct and other systems, the phrases may be combined generally in the same manner

as described above.

4, Conclusion - Versatility of SPACE System

The authors wish to conclude this paper with a brief statement on the development potentiality

of this system.

i. The input data for this system can be further simplified by unifying them with the files for other

engineering disciplines. If the physical data on space xmits are included in the files prepared

by architects, structural engineers or cost estimators, the physical data necessary for heat

load computations can be taken from such files.

ii. The system is adaptable to the future development of equipment. For instance, if it is assumed

that a new type of equipment is developed for air and water system or for water system, and that the equipment is named XUNIT and a new program named XPROG is developed for selecting

this equipment (such a program should be developed without difficiilty because it is to serve a simple purpose of selecting a type of equipment and computing water and air flow rates), the phrases to be used for the design of the system wherein such new equipment is used can be completed simply by replacing the word FANCOIL in the phrases (1) - (4) with the words XUNIT and

by using the word XPROG in lieu of AFCO 2 in the program list.

iii The system has high adaptability to a variety of system combinations.

iv The system has an advantage in that, in developing programs, subprograms may be developed by

an engineer or a programmer, and the phrases can be developed by someone else who systematizes that subprogram.

5. References

(1) IBM, Program language analyzer (Plan), Program description manual, January 1969

596
6. Appendix

Appendix A Structure of files

(1) Common Data Files

a. Foundamental data file consisting of basic data on climatic conditions, physical properties,

etc.

b. Catalogue data file consisting of the data on equipment performance, sizes, cost, etc. which

have been taken for storage from trade literature.

c. Statistic data file (Data to be stored in future)

d. Standard data file (Data to be stored in future)

(2) Project Files

a. Physical data files concerning space units: The data in these files shows the shape, dimensions (length, width and height), and other

physical data on space unit as a shell.

b. Air conditioning system files: These files contains the information relating to the zoning and system designations.

c. Equipment data files:

d. Heat load files: The results of heat load computation and the loads as determined from the required fresh

air volume are filed.

e. Air data files: These contain the data relating to the air volume, primary air volume, pressure loss, etc. for each space unit.

f. Water data files: Water flow rate, head loss, etc. for each space unit are filed.

g. Files of data on selected equipment:

The framework to be determined in future.

Appendix B Description of subprograms

ALC-33

ALC-34

ALC-44

AAV-44

AOAV 1

This subprogram instructs a computer to read the title of project, the names of designers,

the data the design was executed, etc.

This instructs a computer to read such design conditions as the temperature and humidity

of outside and room air, and the shadow factors. ( —> Design conditions and —> shadow

factors files

)

This instructs a computer to read the data on each space unit ( -* Space unit file), to compute the area, volume, etc. ( -» Physical data file for space unit), and to compute heat

loads ( Heat data files). Where the zoning is defined at this stage, the zoning information is also stored in the appropriate file ( -* System file).

The name of zone for which computation is to be made; the computation method((^T^by ADP,

(^T) by the predetermined temperature difference of supply air, by the number of air

changes, ^^by the air volume per unit area, or(^T)by the predetermined air volume per

person in tlie unit space), and the criteria for fresh air volume ( (T^ per area, (^Z^per

person, (^i^per air change, or (^4^ by percentage of the total air supply) are to be instructed.

On the basis of these instructions, a computer will, by reference to Heat data files, calculate air volume ( -» Air data files), fresh air volume ( —» Fresh air data files), the conditions at coil inlets and outlets ( -> Coil data files) for both summer and winter and

will store all these data in the appropriate files.

In accordance with the supply requirements (per area, per person or on the basis of designated value) provided for each unit space within a designated zone, this subprogram

597
instructs a computer; to calc\ilate, making reference to the data on area, number of persons, etc. in architectural file, the primary supply air volume ( Primary air files); to compute the cooling or heating capacity of primary air under the given supply conditions

( -> Coil files, with the design outside air data being filed also in Coil files as the coil inlet conditions); and to compute the coil loads ( Coil files).

AFCO 2 This subprogram instructs a computer to select appropriate fan coil units for each unit space within the zone under consideration, making reference to Heat files, and also to Cooling and Heating capacity files if so instructed (Type, number, water flow rate, pressure loss of the units to be filed in Water files).

AZON 3 This subprogram instructs a computer to transform the simplified space unit arrangement given in the form of a matrix into a perfect arrangement and produce it as output.

( -> Zoning files)

APMO 1 Where unit space arrangements are shown by matrices, this subprogram instructs a computer: to determine the flow rate, diameter and flow velocity for each branch line according

to such input data as the piping layout pattern numbers, the designation as to the loop- reverse, design friction head loss, etc. ; ajid further to obtain the total head loss { Water

files) and the pipe lengths by the diameter. ( Material files)

ADMO 1 This subprogram is basically same as APMO 1.

598
Heat load calculation

Air volume, water flow rate

&: steam flow rate calculation

Equipment selection & cost estimation

Central ref. machine

Absorption ref. machine

Cooling tower

Boiler & pump

Fan

Packaged air conditioner

Air handling unit Air filter Fan coil unit Induction unit

Piping design

and

estimation

Duct design

and

estimation

Fig. 1 The scope of COSMA

599
Read the data showing

the architectural configuration of each space-unit

Compute the load for each

space-tuiit (for summer,

fall and winter) X

Read wall arrangement,

the system to be studied,

and the other necessary data

Fan coil sysbem Single or dual duct systems Induction unit systems

Select fan coil unit and

dtermine required flow

rate of water

Design pipelines

(Compute flow rates in various parts and deter- mine pipe sizes

Compute the required

flow rate of supply air

> Select diffusers and

blending units

1 ' -1

Select induction units and

compute the required flow

rate of water and primary

air

Compute the quantity

of piping materials

Design Ductwork

(Compute air flow rates

in various parts and determine duct sizes)

Compute the quantity

of terminal units

Design piping systems

(Compute the flow rates in various parts and determine

pipe sizes)

Compute the quantity of sheets metal or spiral ducts

by the metal thickness or

the diameter

Design duct systems

(Compute the air flow rates

in various parts and determine duct sizes)

I

Compute the quantity of terminal \inits, the quantity of pipes by the size

and the quantity of sheet

metal thickness or the diameter

Fig. 2 Flow chart for perimeter system program

600
^rri^rnTiij Entire

elevation

li "

i

—

' —

[!

1

1 m 3rlH

South elevation

A Unit number

B Floor-ceiling height C Window glass area ratio Entire D Window orientation

input E Heat transmission coefficient for glass

data F Shadow factor G Grade of heat storage H Shade factor

I Heat transmission coefficient for wall

J Equivalent temperature difference K Area of other walls L Orientation of other walls M Heat transmission coefficient of other walls N Equivalent temperature difference O SH due to causes other than humans

&r Lighting P LH due to causes other than humans

& Lighting Q Load factor for interior loads R No, of occupants in a unit S W per sq. m

Fig. 3 Input data arrangement (for perimeter system

study program)

601
Sheet A

Module combination

(copied from the elevation) Quasi-nodal description is automatically produced.

Sheet B

-fSelection from

duct & pipeline

prototypes Ducts and pipings

computed and estimated

Selection of piping systems

Fig. 4 Schematic chart showing the duct and piping

data processing procedures (for perimeter

system program)

602
Computer selection and evaluation

of Design Weather Data

E.N. van Deventer

Environmental Engineering Division

National Building Research Institute

CSIR Pretoria

The need for hourly design weather data, particularly in

climatic situations typified by large diurnal variations in the

individual elements, is stressed.

For the purpose of determining design data, typically hot

days are first selected on the basis of either computed daily

maximum sol-air temperatures or daily maximum dry-bulb temperature

occurring on 10 per cent, 5 per cent and 2.5 per cent of the

occasions for the period under consideration. Typically cold days,

on the other hand are selected on the basis of daily minimum

temperatures occurring for the same percentages of the time.

The design data are evaluated from coincident values of the

four elements, viz. dry-bulb temperature, humidity, wind and

solar radiation, as they actually occur in practice.

The foregoing is accomplished by the following Fortran IV

computer programmes:

SELECT - This programme computes daily maximum sol-air

temperature, threshold daily maximum sol-air temperatures. It lists the year and day of year on which the daily maximum solair temperature equals or exceeds the threshold values. In

addition it computes hourly values of Linke turbidity factor and

precipitable water vapour content of the atmosphere.

SOLAR - This programme computes hourly values of direct

solar radiation, diffuse solar radiation and atmospheric transmission coefficient for clear sky conditions for places for which

such information is not available, from estimated hourly values

of turbidity coefficient and solar constant.

DWDATA - This programme computes design weather data

selected by programme SELECT, OR, from hot days selected on

the basis of daily maximum dry-bulb temperature, OR, from cold

days selected on the basis of daily minimum dry-bulb temperature.

The solar radiation information is computed for horizontal as well

as vertical surfaces.

Key Words: Weather data, design, computer, computer programmes, FORTRAN, thermal performance, buildings, Sol-air

temperature, Linke turbidity factor.

* Senior Chief Research Officer.

603
1. Introduction

The climate over the major portion of Southern Africa can generally be

described as warm and dry. Such climates are usually typified by large diurnal

variations in air temperature, high solar radiation intensities and an abundance of

sunshine. For instance, the mean annual duration of sunshine for the western interior of South Africa is more than 80 per cent of the maximum possible duration,

whilst over the coastal areas it rarely falls below 60 per cent except along the

west coast where 50 per cent is a more likely value. (l) Under such circumstances

th® outside surface of the exposed elements of a building are alternately heated

strongly during the day and cooled strongly at night so that there is a marked

periodic flow of heat in and out of such elements.

2. Selection of Weather Data

Design weather data for evaluating the thermal performance of buildings

subjected to periodically fluctuating heat flow conditions must be given on at least

an hourly basis. Furthermore any method of selecting weather data from which design

information is to be evaluated should be aimed at describing the weather on typically hot days in summer and typically cold days in winter. Defining a hot or cold day

with respect to the thermal performance of buildings, however, is still a matter of

speculation, although computed daily maximum sol-air temperature seems "co offer the

best possibility.

Winter design data should obviously be based on weather conditions that induce

the maximum cooling of a structure. Under South African conditions, days with the

lowest minimum temperature would represent such conditions in the interior, since,

generally speaking, these low temperatures are due to high rates of radiative cooling during the night. However, in certain areas, such as the South-Western Cape,

maximum cooling rates are usually experienced during the passage of a cold front

with accompanying high winds and low temperatures.

More specifically, the selection of weather data for design purposes is more usefully made in accordance with the probability that similar or worse weather con- ditions will occur on as relatively few occasions during the summer and winter as will justify the specific design criteria; the data should therefore be selected

from coincident values of the pertinent weather elements as they actually occur in

practice and should be expressed in terms of the diurnal variation of the elements.

Runs of successive days of hot or cold weather of different duration must also be

evaluated . ( 2 , 3 , 4

)

Five years of hourly air temperature, relative humidity, wind and solar

radiation data for 15 places in South Africa, South West Africa and Botswana, have

been selected for analysis in this way. It is envisaged that the number of stations

for inclusion in this study will be significantly increased shortly.

The principles outlined above have been used in the preparation of computer

programmes for selecting weather data and evaluating design weather conditions for

the thermal performance assessment of buildings. The programmes are written in

FORTRAN IV for implementation on an IBM S/360 model 65 IH operating under Operating

System Release 18 MVT (Multiprogramming with Variable number of Tasks). The

package consists of three main programmes, viz SELECT, SOLAR and DWDATA and sixteen

subroutine sub-programmes.

3. Description of Computer Programmes

3.1 SELECT

The thermal interaction between a building surface and its immediate micrometeorological environment is a function of the integration, in some way, of the

relevant meteorological parameters . (5 ) The concept of sol-air temperature, introduced by Mackey and Wright (6) provides such an integrated meteorological parameter.

It therefore seems reasonable to select simmer design weather data on the basis of

sol-air temperature. For purposes of comparison, however, days are also selected

purely on the basis of maximum dry bulb temperature.

(l) Figures in brackets indicate the literature references at the end of

this paper.

604
Sol-air temperature may be expressed as follows: (7)

5 = Q + sa oa

s - -^It hnr. (1)

where 9 is the sol-air temperature, Oga "the dry-bulb temperature, oC the

absorptivity of surface for solar radiation, Ig the Intensity of solar radiation,

the long-wave radiation balance of the surface and hoc the coefficient of

convective heat transfer between the surface and the air.

The outside convection coefficient and low-temperature radiation exchange of

the surface and its surroundings are not generally known and the values for both

these factors are therefore derived from, amongst other things, a knowledge of the

outside surface temperature of the surface under consideration. Since this temperature is mostly not known, it has been suggested (7) that eq (l) be written as

otic

(2)

where the values of Ix-^ and

surface coefficient given by

h.QQ are replaced by a so-called combined outside

h

- T oc

where Tp is the film temperature,

surface temperature °C,

4e (T Tp

^ T.

(3)

, Oa the air temperature °C, Or the

Ta the air temperature °K, Ts the surface temperature °K,

the emissivity of the surface and c the Stefan-Boltzman constant.

Roux (7) found that, for South African conditions the combined outside

coefficient was, for practical purposes, constant with a value of 19.873 W/m^ degC

(3.5 Btu/ft^ h degF). Assuming a surface absorptivity for solar radiation of 0.7,

sol-air temperature can be computed from the relationship.

'sa ^oa -0352 I3 (4)

where Iq is the solar radiation in W/m2

In practice in South Africa solar radiation data are summed over hours L.A.T.,

and all other data, with the exception of sunshine, are recorded on the hour, clock

time. Therefore solar radiation data has to be corrected for time, if sol-air

temperature is to be computed.

For computer application the equation of time, employed in determining the

true correction, E, is represented in fourier form as follows :-

E = .005 + .Ol6cos^||^^ - .133sin ^1^^ - .O59cos

4n'n ,169.1n (4TM^ _ (fig) . .OlOsin

where n is the day of year

Programme SELECT computes hourly sol-air temperatures from 08:00 to 16:00

hours for every day from 1 September through 30 April as well as the daily maximum

sol-air temperature. This is followed by a frequency analysis of daily maximum

sol-air temperature. From a cumulative frequency table set up in the computer, the

days on which the daily maximum sol-air temperatures are equal to or higher than the

value that is equalled or exceeded on 10 per cent of the occasions are listed in a table. This table is then sorted into ascending order of sequence on sol-air

temperature. The sorted table is then printed along with the year and day of the

605
year on which each individual value occurred. The 5 per cent and 2.5 per cent

threshold values of daily maximum sol-air temperature are also determined. The

associated sequences of days are, of course, contained in the 10 per cent tabulation.

Unfortunately solar radiation is only measured at 9 of the 15 stations available for analysis, so that sol-air temperature cannot be directly computed in all

cases. Hourly solar radiation data can, however, be computed theoretically for

clear sky conditions. If it can be assumed that hot days are free of clouds, solair temperature can then be computed and hot days selected as before. This assumption is not generally valid, since clouds appear on most afternoons in summer over most of the interior. However, at the time of occurrence of maximum sol-air temperature, around noon, analysis of Pretoria and Maion data indicates that it can be

assumed that on the hottest days the skies are relatively cloudless. Consequently

a programme called SOLAR has been written to compute hourly solar radiation totals

(both global and diffuse radiation) for clear sky conditions for stations for which

recorded information is not available. This programme is discussed in more detail

in subsequent paragraphs. At this stage, it will suffice to state that the

radiation data are computed from estimated mean hourly values of Linke turbidity

factor and extra-terrestrial solar radiation fluxes. One of the functions of programme SELECT is also to compute hourly values of Linke turbidity factor between

08:00 and 16:00 hrs for the same period of the year as above. This is done for the

nine stations for which solar radiation data are available. From these data some idea of the mean hourly turbidity climate of the country can be derived, to make a more reliable estimate of the mean hourly Linke turbidity factor for other places.

The Linke turbidity factor was selected since it is a simple measure of the

haze and water-vapour content of the atmosphere. For total radiation, it gives the

number of clear dry atmospheres that would be necessary to produce the attenuation

of the extra-terrestrial radiation that is produced by the actual atmosphere con- taining water vapour and haze. In fact, this type of turbidity factor was recom- mended for meteorological use by the International Radiation Conference of Davos

1956 in cases where only the total solar radiation is measured, i.e., no filter

measurements . (8)

The extinction by haze and water vapour differs from the extinction by pure

air (molecules), and the deviation of the dependence on wave-length of both these

extinctions gives rise to a diurnal variation in the turbidity factor even when the

water vapour and haze content are constant throughout the day. This variation is

generally referred to as a 'virtual variation' and is different for different

water vapour and haze contents. It is for this reason that hourly values of turbidity factor are computed.

The Linke turbidity factor can be computed from the following relationship :-

I = SIq ^ -^T.Sr (m) . m) (6)

where I is the solar radiation intensity at the earth's surface (measured),

Iq = r Iq;^ dX , representing the extra-terrestrial solar radiation intensity,

T the Linke turbidity factor, a (m) the mean value over all wavelengths of the

extinction coefficient in a clean dry atmosphere (Rayleigh atmosphere), weighted

according to the distribution of the transmitted energy (this complex extinction

coefficient depends on the air mass m because of the shifting of the optical

centre of gravity of the radiation as m changes, S = ^2 where R is the radius

vector of the earth and m the absolute optical air mass.

For computer application the value of S can be approximated by a Fourier

series, such as

S = 0.981 + .037COS (f^) (7)

where n is tne day of year.

(If more accuracy is required additional terms can be added.) The relative air mass is computed from the relationship

606
(8)

where nip is the relative air mass, R the radius of the earth = 6371Km,

p

H the height of a homogeneous atmosphere given by o , where Pq is the atmospheric pressure at sea level = 1.014 x 10-^ Kgm/sec^ ra^ , g the acceleration

due to gravity = 9.80529 m/sec^, "the atmospheric density at sea-level - 1.2923 Kg/m3

Thus H = 8.001 Km ^ = Zenith angle given by cos ^ = sin sin S + cos jzi cos S cost

where ^ is the latitude angle (negative in Southern hemisphere), $ the apparent

IT T solar declination, and t the hour angle of the sun given by , where T is

time of day.

The apparent declination of the sun can be approximated by a Fourier series,

such as

S =: .009 - .401COS (3^^) + .066 sin (fg^)

- .007COS (^) + .001 sin

- .003COS (^) + .001 sin (^) (9)

where n is the day of year.

Traditionally the hour angle is measured from solar noon. For computer

application it is more convenient to increment time from midnight. Thus the

equation for zenith angle becomes

cos sin <l> sin S - cos szi cos % cost (10)

PGR a (m), Puessner and du Bols (9) give an empirical relatlon:-

R

e (m) = 0.907m°-°^® (11)

-aR (m) = - (i*v0.907 + O.Olsinm) (12)

Equation (6) can also be written in the form:

In I = In S + In Iq - THj^ (m) m In e

hence T = P(m) (in Iq + In S - In I) (13)

where P/ \ - (m)

From the above relations it is now possible to compute turbidity factor.

For future reference and in case some alternative method for computing solar

radiation should be attempted, precipitable water vapour content of the atmosphere

is also computed for the same hours and days as turbidity. The Hann formula (10) was used for computing precipitable water vapour content from surface vapour pressure, viz:

Sj^ (m) m

607
w = c (t) (14)

where w is the precipitable water vapour content in cm, c the proportionalityconstant and e^ (t) the vapour pressure at temperature, t. Harm gives a value of 0.25 for e. However, the following values were found

for different centres in South Africa.

Table 1. Mean values of the proportionalityconstant C for January and July

Mean value of constant, C Station

January June

Pretoria (morning) 0 17

Pretoria (afternoon) 0 17 0 13

Durban 0 18 0 12

Windhoek 0 16 0 .13

Bloemfontein 0 18 0 12

Port Elizabeth 0 14 0 11

Cape Town 0 13 0 12

The surface vapour pressures are computed using the well-known Goff-Gratch

formula

3 . 2 SOLAR

Programme SOLAR computes hourly global and diffuse solar radiation fluxes on ; horizontal surface.

Under clear sky conditions for any hour for any place the direct component of

global solar radiation is computed by means of eq (6):

T OT - (T.aR (m) m) , /tc-n I = SlQe ^ K ^ ^ cos^ (15)

The diffuse component of radiation is computed from a relationship given by

Liu and Jordan (11), viz ;

= 0.2710 - 0.2939^1) (16)

where T = Idh/loh and f £> = Ich/Ioh ^oh = extra-terrestrial intensi'

of solar radiation incident on a horizontal surface^ = SI cos , I^j^ tne intensity

direct radiation on a horizontal surface, and 1^^^^ the Intensity of direct radiation

Incident on a horizontal surface.

Alternatively

Dh = 60 (.2710 Iqj^ - .2939 I cos |) (17)

where is the hourly diffuse radiation on a horizontal surface.

608
Spencer (12) has found that the coefficients in eq (16) require some adjustment

for Melbourne. However, Liu and Jordan's coefficients will be used until it has

been possible to verify them for South African conditions.

3 . 3 DWDATA

It was stated above that SELECT produces a list of days in ascending order of

daily maximum sol-air temperatures that are equal to or higher than the 90th

percentile of daily maximum sol-air temperature. The punched cards for the various

elements, i.e. hourly drybulb temperatures, hourly relative humidity, hourly wind

speeds and hourly global and diffuse solar radiation values are then selected

according to this list and form the input for DWDATA.

The programme DWDATA is flexible in the sense that, with the aid of a control

parameter, any one of four methods of evaluating design weather data can be selected; and with the aid of a further control parameter, hourly solar radiation data

can either be read from cards or computed.

Briefly, the four different methods of evaluating design weather data are:-

a. Method 1 According to this method summer design data, selected on the basis of daily

maximum dry-bulb temperature, are evaluated. The first step in this analysis is to

determine the mean dry-bulb temperature for each hour of the day, its standard

deviation and maximum and minimum values for all days selected, as described before.

The next step is to select all the occasions when the hourly_temperature of each

hour of the day taken in succession tj_ is such that (tj - 0.5) ^ ^i,j ^ (tj + 0.5) where i refers to the day and j to the hour under consideration and

tj is the appropriate mean hourly temperature for the days selected for each of the

probability levels taken separately. The other weather elements for these occasions

are then selected and their means , standard deviations and maximum and minimum

values computed. A tabulation of the mean dry-bulb temperature and the associated

relative humidity, wind speed and solar radiation values for the various probability levels, viz maximum, 2.5, 5 and 10 per cent levels, represents the required hot

weather design data. The programme furthermore computes the hourly solar radiation

fluxes on vertical surfaces facing north, south, east and west, and the following

humidity parameters based on the algorithms published by Kusuda (13): wet-bulb

temperature, dew-point temperature, vapour pressure, humidity mixing-ratio, enthalpy

of moist air, entropy of dry air and specific volume of moist air for each hour for

each probability level. This information is tabulated together with the other

hourly information, referred to above.

The method of computing solar radiation fluxes on vertical surfaces consists

of computing the direct component , diffuse component from an unobstructed sky and

diffuse component reflected from a flat, unobstructed surrounding terrain.

The direct component is simply given by:

Gvi _ Dv, = ^ „ cos i (18) V cos 2 ^

'

where, is the direct component of solar radiation normal to given vertical

surface and i the angle of Incidence of direct solar beam on given vertical

surface

For computing the diffuse sky component, clear and cloudy skies have to be

differentiated. Since no hourly cloudiness data have been recorded on punched

cards it was decided to compute the Linke turbidity factor and compare this with

some threshold value of turbidity factor, the latter being for cloudy conditions,

defined as a sky having approximately one-quarter cloud cover. The turbidity factor

is computed as follows:-

log { 1381 S cos^ ") g T = \ - Dh J

0.^3^m (In 0.907-0.018 In m)

609
where T is the Linke turbidity factor, Gh the hourly global solar radiation on a

SI2

9 horizontal surface, w/m , and Dh the hourly diffuse radiation on a horizontal

surface w/m^

Based on an analysis of the data for Pretoria and Maun, a threshold turbidity

of 5.0 seems to be about right.

For computed turbidity < 5.0, the following relationships for computing the

diffuse sky radiation component on a vertical surface have been found for Pretoria

(14):-

for cos i < 0.2:

= Dp^ (0.31 - 0.1 cos i) (20)

for cos i ^ 0.2:

= Dp^e (1-18 cos i - .8) (2i)

For computed turbidity ^ 5.0, the simple relationship (14)

= 0.5 Dj^ (22)

has been found to be valid for Pretoria for average cloudy conditions.

As for the ground reflected solar radiation component, it has been shown (15)

that, for practical purposes, for an unobstructed horizon for Pretoria, this

component can be approximated by

K = ^ (23)

where p = reflectivity of the groimd.

b. Method 2 According to this method summer design data, are evaluated in exactly the same way as a above, except that they are now being determined on the basis of daily

maximum sol-air temperature in stead of on maximum dry bulb temperature.

c. Method 3 In this case hot day design data, selected on the same basis as in b above, are evaluated. However, means, standard deviations, maximum and minimum values are determined for each of the basic and derived elements in the way described for drybulb temperature in a above.

d. Method 4

When the parameter, METHOD, is equal to 4, cold day design data are evaluated.

The basic data are selected on the basis of those daily minimum dry-bulb temperatures that are equal to or less than those daily minimum dry-bulb temperatures

occurring on 2.5, 5 and 10 per cent of the occasions for the period under consideration.

The programme DWDATA also arranges the selected information in ascending order

of sequence on year and day of the year. Runs of days when the daily maximum drybulb temperature or daily maximum sol-air temperature, depending on which of these

elements was employed in defining hot days are equalled or exceeded, can then be

readily determined. In a similar way, runs of cold days can be assessed.

In the case of light-weight elements the effects of heat storage capacity is

relatively unimportant. Therefore, there is no significant cumulative effect due to

610
a succession of hot or cold days. However, in the case of heavy-weight elements,

the cumulative effect is very important. This cumulative effect of sequences of

hot days of varying duration can be computed for such elements and related to the

probability of occurrence of sequences of different duration as they actually occur

in practice.

4. Conclusions

In the field of computer application to environmental engineering problems at

the National Building Research Institute in Pretoria, the stress, up to the present

time, has been on producing design weather data for the thermal performance design

of buildings rather than on the development of sophisticated procedures for computing thermal performance and heating and cooling loads. The philosophy has been

that solutions of such problems can be no better than the physical data on which

they are based, no matter how sophisticated they are. It is believed that the

design data evaluated according to the methods outlined in this paper will, with

perhaps small refinements, provide the basic information required for predicting

thermal performance and evaluating heating and cooling loads with acceptable

accuracy.

5. References

(1) Schulze, B.R. Climate of South

Africa, Part 8, W.B. 28, Pretoria,

Weather Bureau, Department of Transport, (Jan. 1965.)

(2) Van Deventer, E.N. & Van Straaten,

J.F. A rational basis for expressing climatic data for use in building design. In: Proceedings of the

Central African Scientific and Medical Congress, Lusaka, Northern

Rhodesia, 26-30 Aug. 1963, Oxford,

Pergamon Press, (1955.)

(3) Van Straaten, J.F. & Van Deventer,

E.N. The functional aspects of

building design in warm climates

with particular reference to thermal and ventilation considerations.

Int. J. Biochem. Biomet., 8, no. 2,

(Dec. 1964.)

(4) Van Deventer, E.N., Lotz, F.J. &

Boer, P. The assessment of heating

and cooling loads of buildings under

South African climatic conditions.

Fd Inds S. Afr. , XVIII , nos. 10 and

11, (Febr. and March 1966.)

(5) Van Deventer, E.N. Building climatology in Southern Africa. Build

International, 2, no. 7, (Sept.

1969.

)

(6) Mackey, D.O. & Wright, L.T. The

sol-air thermometer - a new instrument. Heat. Pip. Air Condit. , (May

1940.)

(7) Roux, A. J. A., Visser, J. & Minnaar,

P.C. Periodic heat flow through

building components - Heat transfer

through homogeneous wall panels

from the outdoor climatic environment to the indoor air. CSIR Report

no. 71 (formerly DR-9), Pretoria,

CSIR, (1951.)

(8) Instruction Manual, Part VI, Radiation instruments and measurements,

London, Pergamon Press, (1957.)

(9) Fuessner, K. & Dubois, P. Triibungsfaktor, precipitable water, Staub.

Beitr. Geophys., 27, p. 132, (1930.)

(10) Hann, J. v. & Silring, R. Lehrbuch

der Meteorologic, V. Aufl. Bd. 1, S. 133. Leipzig, (1939.)

(11) Liu, B.Y.F. & Jordan, C. The interrelationship and characteristic distribution of direct, diffuse and

total Radiation. Solar Energy, 4, no. 3, (I960.)

(12) Spencer, J.W. Estimation of solar

radiation in Australarian localities

on clear days. Div. of Building

Research Technical Paper no. 15,

Australia, Commonwealth Scientific

and Industrial Research Organization, (1965.)

(13) Kusuda, T. Algorithms for psychrometric calculations. National Bureau

of Standards Report 9818, Washington,

U.S. Department of Commerce, National

Bureau of Standards, (March 1, 1959.)

(14) Van Deventer, E.N., Dold, T.B. &

Wessels, J. Diffuse solar radiation

on vertical surfaces (to be published).

(15) Van Straaten, J.F., Lotz, F.J. &

Van Deventer, E.N. The sun and the

design of buildings for tropical

climates. Presented at the Symposium on Environmental Physics as applied to Buildings in the Tropics,

New Delhi, (Feb. 1959.)

611

Quality Rules for Thermal Performance of Low Cost Dwellings

(Building Climatology for Argentine)

R. Alvarez Forn and I. Lotersztain

INTI - Bouwcentrum Argentina

Maipu 171, Buenos Aires, Argentina

Climatic data from the hourly records of the National Meteorological Service were collected from approximately 22 locations throughout Argentina. These data were then analyzed on the basis of (1) monthly, seasonal and annual averages, (2) typical hot and cold days, (3) probability of occurrence of solar radiation, humidity, and wind for typical hot and cold days and (4) probability of N successive

days "equal" to one intitial typical day. Described in this paper are computer programs for the analysis described above and charts and tables developed for the practical use.

Key Words: Climatic data, probability of occurrence of values, probability of runs of N equal

days, typical days.

1. Preliminary

Since 1967 the INTI (National Institute of Industrial Technology) and Bouwcentrum Argentina

(Center for Building and Housing Research and Information of INTI ' s System of Centers) are at work

in the complex problem of searching for the minimal higro-thermal requirements to be established for

the housing programs of this country. Up to that year only sporadic efforts of isolated researchers were recorded in the Argentine Republic. This is then the first research set up with the necessary

means and with the long-range goal of writing down those requirements for the different climatic region

and socio-economic strata of the country. (Ref. No. 1).

2. Steps of the research

The steps or successive goals of this task were laid down as follows:

2.1. To know the climatic zones of the Argentine Republic, for building purposes.

2.2. To define the convenient levels of thermal comfort for different geographical and socio-economic circumstances.

2.3' To translate those levels into "technical requirements" to be fulfilled by the elements

and/or the whole of the buildings or the urban design.

2.4. To choose experimental controls for the task.

2.5. To put up a theory of thermal comfort and thermal performance of buildings,

useful for the Argentine problems in this area, and based in computer's

capibility.

2.5. To translate the findings into the pertinent legal instruments such as codes, norms,

etc.

oth Civil Engineers

613
5. Chronological developments

This kind of Research is obviously a long-range and long-duration task, with many feed-backs and probably several re-thinking phases about the whole affair. In this moment we deem it possible to make

fair advances in the three years 1969-1970-1971. The work's progress is now following the guilding

lines established at the beginning of the period.

Those guide-lines are the steps before mentioned in paragraph 2. In this paper the first step of the pont 2.1., i.e., deals with the knowledge of the climate of the capital city for building purposes. This task will be eventually expanded to cover the whole of the country.

4. Source of raw data and processing equipment

Source of raw data is the National Meteorological Service. We have an arrangement made with this

official agency for the access and use of the climatic data recorded in punched IBM cards.

The National Meteorological Service, founded in 1872 (by suggestion of the North-American astronomer

Gould) by President D. F. Sarmiento, has now up to 8 million IBM cards with data from many parts of the country. This data covers the last 15 years.

The cards are the international type used in 700 stations over the world (350 in the U. S.) (Fig. 1)

The type "A" card is prepared for hourly data. In practice it is used with 24 observations/day

and also with 8 to 5 observations/day.

Unfortunately such different type of records are made often at the same place in different periods

or runs of years.

The type "B" card is prepared for daily data or parameters and as such as it records only one or two values in each 24 hour period.

The type "77" card is used with monthly parameters.

In this research we used only the "A" and "B" types of cards.

For instance, in the first city studied (Buenos Aires) we used a record of 5 years with hourly data

and another, also of 5 years, with data at the hours 2 and 8 a.m., and 2 and 8 p.m. These data come from

the station "Central observatory" placed near the geographical center of the city. We have only two othe stations in the city and it outskirts with data in punched-cards . One is by the River Plate and the other about 25 km inland. We hope to check those stations' data with the former, in a later phase of our task.

The IBM 1130 machine works with disks (each capable of 248.000 words).

This computer is in the CITMADE (INTI's computer center) and our research has a part-time arrange- ment for its use.

Climatic parameters for building purposes in typical hot or cold days

1. Goals of the Work

This research aims at the statistic specification of all the relevatn climatic parameters of a "typical hot day" and a "typical cold day".

Those days are to be selected following statistical criteria with 2 different levels of complexity.

We deem this work suitable for calculations and specifications in the following fields.

(a) -Design of buildings and/or its parts for suitable thermal insulation, good natural ventilation, efficient vapour barriers, convenient sun exposures, etc.

(b) -Urban design of new communities and housing schemes, etc.

(c) -Design of heating, ventilating and air conditioning installations or appliances, from

the following points of view:

i. Outdoor design basis for the project,

il. Outdoor conditions for testing purposes.

614
2. Summary of the first task

The first task was then to get acquainted with the climatic parameters of different zones and/or

cities of this country.

As the climatic parameters as [jrocessed by the standard methods of our National Meteorlogical

Services for other ends were inadequate for building purposes, it was decided, then, to process the raw data (in the form of IBM cards provided by the NMS) in the CITMADE's computer, following several new

programs written down especially for this goal. The plan is to record the data in up to a million cards

of the NMS in about 12 disks, according to those programs. These data are from about 20 cities or re- gions of the country. It is expected to develop such work in a span of about 3 years.

The hypothesis laid down for the task were these:

(h-i) The design conditions must take into account all the pertinent climatic parameters:

(a) air temperature

(b) humidity (by one or more of the several variable used for measuring it)

(c) speed and direction of the mind

(d) sun radiation

(h-ii) The study of the parameters one by one was deemed not satisfactory in this problem,

so we stated that the statistical probability of concurrence of typical values of those variables had to be worked out.

(h-iii) A "typical hot day" and a "typical cold day" had in turn to be analyzed hour by

hour and the results submitted to a statistical probability analysis in order to fulfill the item (h-ii).

(h-iiii) The probability of occurrence of successive runs of 2, 3, N typical hot-days and typical cold-days had to be worked out.

3. Main features of the Argentine climate

This country stretches from 22° to 55° south latitude, and besides has several territories further

to the South, on islands and a segment of the polar continent. On the mainland we have the following

broad climatic zones: (each zone is subdivided in two, as shown in the map , fig. 2).

i. Hot: 1 - humid; 2 - dry

ii. Temperate: 1 - humid; 2 - dry

iii. Dry: 1 - semi-arid; 2 - "patagonic"

iiii. Cold: 1 - dry; 2 - "humid"

Nevertheless, the geographic and seasonal climatic variations are not so marked as in the N. W. or central U. S. or central and east Europe. This is because South America is really a tongue of land between two huge masses of water, the South Atlantic and the South Pacific Oceans; and the Polar Cape

is more than 1.000 km. South of Cape Horn, the tip of the Continental Block and adjacent islands. But

the long Cordillera de los Andes forming the West limit of the country (about 2.500 km) is really a great "climatic dam" and a decisive factor of our climatic patterns; it produces marked alterations in

the overall atmospheric circulation, and superimposes an West-East influence over the normal NorthSouth axis of climatic levels.

The most remarkable climatic factors are: hot summers in NE , NW and W zones; mild conditions in both seasons in the Center; cool and very windy in the lower half (Patagonia). Snow is a problem only

in high motintain and plateaux zones. The East half of the country has abundant rains, but the rest is under the level of 500 mm (20 inches) in the average year and so, under the minimum rain level for agricultural purposes (except zone in the N.W. and other in the southern cordillera and the island of Tierra del Fuego, both cold and rainy).

2 2 The first region occupies about 1.700.000 km and the second 1.000.000 km . More than 3/^ of the total population of 22 million inhabitants live in the humid region.

615
4. Fundamental criteria for choosing and describing the typical or design day (hot or cold)

One climatic parameter was to be chosen as the fundamental, and the probability of concurrence of values of the other three (excepting precipitation) to be studied.

The first one had to be the most important for the higro-thermal state. A review of the climatic

zones of our country showed that not always the temperature of the air - the best known and more often

used parameter - seems to be the best choice. Maybe the solar radiation in the hot zones or the wind

in the Patagonia would be better. But for the sake of uniformity and also because the temperature of

air has always the best record in each locality, this was our choice for the role of "leading parameter".

As mentioned before, the work was begun with Buenos Aires and we used type "A" (hourly) and type "B" (daily) IBM cards. For the 5 years 1959 to 1963 we had hourly data and for the next 5 years 1964 to 1968 we had only data from 2 and 8 a.m. and 2 and 8 p.m. In both runs we had also the daily card of the

"B" type. (Fig. 2 shows the two cards and the relevant items of the punching-code used by the NMS)

The first computing task was to get the usual average, maximum and minimum values of the relevant

variables. This was checked with other period's results, giving in general a good agreement (of course,

up to this point the work was rather of the usual climatic type). (Fig. 3)

The second task was different and implied an entirely new approach - at least for our country - aimed at the determination of the design days, for building purposes.

This was done as follows:

4-1 The ogive of the average daily temperatures of the 3^50 days (10 years, without the 29th

of February for the sake of simplicity) was worked out in absolute and relative frequencies

by the computer. Let's call "p" the cumulated relative frequencies.

4-2 For each of the levels of p = 2,5%, 5%, 10%, 90%, 95%, 97 ,,5%, and 99%, we worked out the steps that follow.

Here we give the general explanation for the p = 2,5% level, because we take p = 2,5%

for the typical cold day, but in the graphs and comments we give also the results for

the p = 97,5% level for the typcial hot day.

4-3 The machine was ordered:

(a) to find the p = 2,5% day and pick up its card;

(b) to pick up the cards of the "next" ten days over that day; and the "next" ten days below that day. "next" means here the days whose cards showed average daily temperature numerically

(not chronologically) in the neighborhood of the p = 2,5% day.

4-4 For this set of similar 21 days the machine then did the following:

(a) worked out the relative frequencies of average values of temperature,

humidity and insulation (Fig. 5)

(b) worked out the average hourly temperature, i.e., the average 1 h, 2 h, 3 h, 24 h temperature; with those values we traced

the curve (Fig. 4)

(c) the same calculations were made for the relative humidity, hour by

hour and also the curve was traced (Fig. 4)

(d) worked out the frequency of the wind in 8 directions and one "no-wind" state, also hour by hour. The machine also got the average

speed for each direction. (Fig. 5 bottom)

(e) in the drawing (Fig. 5, lower) for the solar radiation we used "heliophany" or relative insulation parameter (the ratio of the real sunny time of a day to the astronomical one) and with such basis we made the calculation of the average direct sun radiation

on 8 vertical planes and the horizontal plane. (Fig. 6).

For the typical hot days see Figs. 7, 8 and 9.

The radiation values were worked out using the tabulated

616
results of a sun thermal radiation program prepared

by Architect Victor Olgyay, and generously given to us during his 1969 stay in Bouwcentrum. (Ref. 14)

The program was processed in the IBM machine and gave

for each degree of latitude and for the mid-month day

the before-mentioned radiation values, for a theoretically cloud free and clean air day. Those values are then the maximum possible ones. For Buenos Aires we

used the latitude 34° 1/2 South.

In order to get the real magnitudes, these theoretical

values were affected by a "F" factor, less than the unit established for Montevideo (a city only 200 km

from Buenos Aires and almost in the same latitude) in a statistical calculation summarized in appendix "A".

As the two cities have very similar climates, we felt

that we could use values of the insulation factor "F"

of Montevideo for our work about Buenos Aires (Ref. No. 2).

4- 5 Another useful statistical criterium was used: the machine worked out the probabilities of chronological runs of 2, 5 N successive typical cold

days, following this sequence (Figs. 10 and 11):

(1) we had established before the average temperature of

the "first" cold day and chosen the respective card (paragraph 3, item (a).

(ii) the machine then worked out the probability of having the next day with an average temperature equal or less than the value of this parameter in the "first" cold day (item (i); and also the probability of having 3; ^ 10 successive

"cold days" so defined. Of course, in the case of the typical hot day, in the item (ii) we read "equal or more"

instead of "equal or less".

(iii) then it did the same with an allowance of + 1°C and

+ 2°C for the typical cold day's average; and I'C and 2°C for the typical hot day's average.

5. Comments and remarks

Several comments and remarks could be made on the method just explained. We state here

a few of them:

5- 1 of course, the "desing days" obtained with such processes are a kind of statistically representative or meaningful days, for the hot or cold condition

studied.

The various parameters will evolve, during such a day, in a typical manner, represented by our tables and graphs.

5-2 In the typical cold day it is observed that:

(a) the lowest temperature is above the freezing point

(+ a.y'c)

(b) the wind blows from the W or SW at the coldest hours

(c) the sun shines bright, it is a clear day

617
(d) the daily span of the temperature is significant

(9.3°C)

(e) the humidity has also a marked oscillation being very high at the coldest hours, and rather low at the hottest hours

(f) the probability of chronological runs of such days goes down very fast and is negligible after a few days

5-3 In the typical hot day it is observed that;

(a) the maximum temperature is moderately high (+ JS'C)

(b) the wind blows from the N, NE and E in the hottest

hours

(c) the sun shines brightly - it is a clear day

(d) the daily span of temperature is significant (9°C)

(e) the relative humidity has a marked oscillation, being

low at the hottest hours (457i,)

(f) the probability of chronological runs of such days goes down very fast and is negligible after a few days

5-4 The findings are of interest from several points of view:

(a) from the standpoint of the thermal lag of buildings

(b) from the standpoint of the heating or conditioning system,

their thermal lag and the control systems to be used

(c) from the standpoint of the possible use of analogue computers

for simulating the conditions (electronic or hydraulic)

(d) from the standpoint of the possible use of digital computers

for the same end (i.e., for resolving the electrical circuit)

(e) from the standpoint of the different levels of probability

likely to be used in different problems

On the points (a) and (b) it can be said that in this city

it is important to have a heating or winter conditioning

system with great "time flexibility" and with zonification

according to the rose, i.e., "spatial flexibility".

This is because of the important daily oscillations of temper- ature and the high solar radiation at the NE; N and NW exposures .

The summer service of air conditioning in buildings with

great exposure requires also, both flexibilities, as the typical hot day shows.

The prevailing winds blowing from the N, NE and E in those hot days can be used for natural ventilation of dwellings,

schools, industrial buildings, etc., not equipped with air conditioning.

618
It is also possible to see that light buildings can be brought in "resonance" with the exterior conditions

(transient period 1 to 3 days, for instance), but heavy

structures cannot attain such condition (transient periods

from 4 days up). This problem is very important for low- cost dwellings in summer, because it is not economically

possible to furnish such houses with air-conditioning

appliances and therefore, it is necessary to study the spontaneous evolution of the internal conditions as a function of the external ones, (a very difficult problem

from a physico-mathematical point of view)

About the points (c) and (d) , it is obviously necessary

to know the chronological recurrences of such days in order to simulate the real situation in the computers.

(f) This study shows only the results for the "2,5% day" as

a typical cold day and the "97,5% day" as the typical

hot day. Hovjever, we worked out, as stated before, the levels Ps 17o, 5%, lOX, 907„, 95%, and 99% because we felt that for idfferent problems it may be necessary to use such different levels.

Of course, with the levels 5%, 10%, 90%, and 95% the "character" of the typical cold or hot day is not so well marked and it is a matter open to discussion as to the meaning of such days.

We want to state here our thanks to the authorities of

the following instiuttions for their decisive support

to this research:

INTI (National Institute of Industrial Technology)

CIBA (Bouwcentrum Argentina, Center for the Research

and Documentation in the Building Industry); CITMADE (Center of Mathematical and Computer's Techniques);

SMN (National Meteorological Service).

Appendix "A:

Factor (f) of conversion of the sun thermal directo radiation for clear sky in the value

for mean sky (R2) taking into account the insulation and the nubosity (Ref. No. 2).

These auxiliary symbols are used: Rl direct radiation for clear sky.

Insolation; (%) I = Real time with bright sun/Astronomical length of the day

NOTE: Insolation is called "heliophany" in the figures.

N = Geometrical area of the sky

Clarity: (%) C = 100 - N

The paper (Ref. No. 2) shows that with an error not in excess of 4% for Montevideo it is correct to write:

619
F (%)

This factor is to be applied to any hour in the day if that day has insolation I (?„) and nubosity N (7o) = 100 - C (%) , and gives for those conditions.

The day in question can be a single one or a statistical

average day.

Further, the paper shows that the coefficient M = I/C has in Montevideo a maximum value of 1.461 and a minimum of 1.327. This means that it exists in fact a correlation between the values of I and C as can be expected, and this justifies the use of F.

Appendix "B"

Prehistory of this paper

The choice of the statistical criteria for this study was the result of a rathe?' long process. Maybe it is interesting to outline its principal steps. It must be remembered

that we started with a totally new approach in our country, and we had only foreign bibliography on the subject; then we made the following remarks in the course of the studies:

First: We were at a loss when we tried to understand clearly the reasons that several

researchers had in mind when they stipulated their climatic parameters for building purposes. Such reasons were not explained, or maybe were not good

between-lines readers (Refs. 3, 4, 5, 6 and 7).

Second: We felt that in order to adapt, modify or reject some of this pre-existent

work, it was necessary to gain knowledge about such a background.

Third: We deemed necessary to find a way to state not only the parameters as if its influences over the building and the human comfort were independent of the others, but also in their mixed or complex effects. As an example, the Sol-Air theory (Ref. 8) showed a good advance towards such an "upper level"

of complexity, fusing the sun radiation and the heat of the air in one parameter.

Fourth: We saw that, for obvious reasons, in each country the parameters and criteria

related to the outstanding characteristics of their climate were those more

studied. This showed that for our purposes it would be necessary to study

with special dedication the technical documentation produced by countries with

climates not very dissimilar from ours. And between these, the papers about

the problems in temperate, hot-arid and hot-humid regions were the most useful because the thermal comfort is more difficult to attain in those circumstances than in the moderate cold prevailing in our winters (Ref. 9, 10, and 11).

All this boiled down to the following "obvious" remark; The building

climatology is a science "in the making" and as such shows plenty of disagreement between authorities, not only about the answers, but also - and maybe in the first place - about which are the problems.

An illunimating paper came then in our hands (Ref. 12). Here the two authors

stated clearly what we had been searching for: the basis for new criteria in the "upper level" in question.

620
It is an act of justice to mention here that one of us was in England during

6 months of 1968, working with Professor A. Pratt (Ref. I3) , and that during

three months of 1969, we had the technical assistance of Professor Victor

Olgyay (Ref. 14). Working and discussing with those authorities was a very

useful experience for our background.

We decided then, to try our hand at the problem, reduced for the first effort,

to the definition of the typical hot and typical cold days working in such

an "upper level" of complexity, and using Buenos Aires climatic data.

For this we made, as a first step, a classification of all the parameters

used for the others researchers following several criteria:

i. extensive, specific and intensive variables

ii. types of periodic functions approached by these

iii. possible useful combinations of variables in

the "upper level" of complexity

iiii. miscellaneous.

And finally, with all this background, we asked ourselves: what is a hot day in Buenos

Aires like? - A cold day? How would such a day affect the thermal comfort of a person? And

the thermal performance of buildings? - And with those "simple" questions in mind we write

down the criteria to be used by the programmer of the IBM machine and we passed the question

and the answers over and over again through this filter. Up to now, the results are des- cribed in the present paper. . . . and this is the little story about the making of such research.

References

(1) R. Quintela C. Vasino, "Bases de. la clima^ tizacion artificial en Buenos Aires", Meteo

ros (octubre-diciembre 1955)

(2) R. Rivero,. "Calculo de la energia termica de

la radiacion solar directa y difusa en varies pianos. Para Montevideo", Montevideo

(Uruguay), Facultad de Arquitectura , Montevideo, octubre 1965.

(3) A. Fournol, "Climats et habitation, cahiers

du centre Scientifique et Technique du Bati

ment", Paris, France, Livraison 25, Cahier

223.

(4) J. Borel, "Notice technique pour 1' application du reglement de la construction en Al- gerie" idem, Livraison 57, cahier 456.

(5) Reef 58 Vol. II, Paris, 1961. Recueil. Sec- tion D5, Hygrothermique et ventilation.

(6) H. Reiher y D. van Zuilen, "Report on the symposium regarding the problem of the effect of climate upon building", GIB Bulletin

No. 3 (1966).

(7) American Institute of Architects. House Beautiful, Climate Control Project, Re- gional Climate Analyses and Design Data, for 15 cities and regions of the USA

(AIA Journal 1950-1951 passim).

(8) Sol-air theory applied to the orientation

of Buildings, (pgs. 54-62 of book Ref. 10 below)

(9) A. van Straaten, E. van Deventer, "Thermal Performance of Buildings", Amsterdam, 1967. Elsevier Publishing Company.

(10) V. Olgyay, "Design with Climate", Princeton

(USA), 1953. Princeton University Press.

(11) Directives communes pour I'agrement des Procedes de Construction par Grands Panneaux Lourds Prefabriques , (UEATG) , Cahiers du Gen

tre Scientifique et Technique du Batiment,

Paris, France. Livraison 80, cahier 696.

(12) E.N. van Deventer and J. F. van Straaten, "A rational basis for assessing Climatic Data

for use in Building design", National Building Research Institute. Pretoria (South Afri

ca), 1967.

(13) Prof. A. W. Pratt, Head of Department of Building, Aston University in Birmingham;

directs research in thermal problems of building.

(14) Prof. Victor Olgyay (1910-1970). Worked

with his brother Aladar Olygyay (1910-

1950) at the Princeton School of Architecture, in the field of architecture and climate.

621
622
623
TEMPIP»TURA t-.tn'Mlk MEDIA Y M'NIM* MFNSUAl IC I

BUENOS AIRES

GRADOS OIAS

(base y ba»e ]8rCD>

_[=JL

PRECIPITACION MAXIMA.

MEDIA V MINIMA

MENSUAL ImmJ

//VT-/ - c/ ooc/yvcavmM'f

Figure 3. Standard climatic data of Buenos Aires

624
625
DIA T/nCO A/W

NivcL tsy.

TCMTCKATUKA

«.# :» «.7 c* <.v

-Tm'''///, m

m r.'

' ' ' "/ m

o a no IS ao as 30 3S 40 *e ao mas ao m. IB ao mi

f cm • 2 6 m /s<5

Figure 5. Average values of temperature, humidity and wind frequency for typical cold days

626
627
628
629
DIA TinCO CAUDO

9 x> rs so OB ^ <is

C^^^' <^><L^aOG 7>-XXK 'HCCKPG OC

Figure 9. Average values of temperature, humidity and wind frequency for typical hot days

630
631
dt

632
Fortran IV Program to Calculate z-Transfer

Functions for the Calculation of Transient Heat Transfer through Walls and Roofs

G. P. Mitalas and J. G. Arseneault

Division of Building Research

National Research Council of Canada

Ottawa

The heat transmission matrix for a wall or roof has elements

A, B, C and D; i.e.,

e o A B e.

1 Q

o C D Q.

1

where 9 = Laplace transform of surface temperature, and

Q = Laplace transform of surface flux

The elements A, B, C and D are functions of the thermal properties,

thickness and position of materials in the wall. When the boundaryconditions are of the first kind (i.e. when 9 and 9. are given), the fluxes are given by

Q

o 1 D , -1 9 o Q.

1 B

1 , -A 9.

1

and when boundary conditions are of the second kind, the equations

invert to

9

1C

A , -1 Q

o

9. 1 , -D

o Q . X 1

The program presented in this paper evaluates the coefficients of a set of z-transfer functions that are equivalent to the Laplace transfer functions D/B, 1/B, A/B, A/C, l/C and D/C.

These z-transfer functions relate to the z-transforms of the surface

temperatures and heat fluxes in the same way as their counterpart

Laplace transfer functions relate to the expressions above.

Research Officer and Computer Systems Programmer, respectively.

633
The program will evaluate z-transfer functions that are exact for either a unit step input, a ramp type input or a periodic

input with specified harmonic components. The user can choose,

therefore, the option that best suits a particular problem.

Key Words: Frequency response, roofs, transient heat

conduction, walls, z-transforms.

The heat transmission matrix for a wall or roof has elements A,B,C and D, i.e. ,

e o A B e

1 Q

o C D Q.

1

where 9 = Laplace transform of surface temperature

Q = Laplace transform of surface flux

The elements A, B, C and D are functions of the Laplace parameter, s, and of the thermal properties

thickness and position of materials in the wall. When the boundary conditions are of the first kind

(i.e. when 9 and 9. are given), the fluxes are given by

Q 1 D , -1 9 o o

Q.

B

1 , -A 9.

1 1

and when boundary conditions are of the second kind, the equations invert to

e o 1 A , -1 Q

o

9.

1

~ C

1 , -D Q.

1

The program presented in this paper evaluates the coefficients of a set of z-transfer functions

that are equivalent to the Laplace transfer functions D/B, 1/B, A/B, A/C, l/C and D/C. These

z-transfer functions relate to the z-transforms of the surface temperatures and heat fluxes in the same way as their counterpart Laplace transfer functions relate to the expressions above.

The program will evaluate z-transfer functions that are exact for either a unit step input, a ramp type input or a periodic input with specified harmonic components. The user can choose,

therefore, the option that best suits a particular problem.

2

1. Calculations of z-Transfer Functions [Ref. 1]

The z-transfer functions for a multilayer wall can be calculated in two ways:

Method 1 consists of choosing either a step or a ramp input function, I(z), and evaluating the output, 0(z), that corresponds to l/ s or 1/ s^ times one

of the Laplace transfer functions. The related z-transfer function is determined from 0(z)/l(z).

The literature reference is at the end of the main text of this paper.

634
Method 2 involves solving a set of simultaneous linear algebraic equations

to obtain the coefficients of a z-transfer function whose frequency response

matches the exact frequency response of the multilayer slab at certain selected frequencies.

The z-transfer function corresponding to any one of the Laplace transfer functions can be ex- pressed as the ratio of two finite polynomials, N(z)/D(z). The denominator, D(z), is the ssime for all the transfer functions that have a common denominator in their Laplace transfer function equivalents,

and is the same for Method 1 and Method 2. The procedure for finding the coefficients of the denominator polynomial involves two steps.

(1) Determination of the poles of the associated Laplace transfer function: .

i.e., find 3 , the roots of B = 0; n

or Y > the roots of C = 0; n The elements of the transmission matrix for a wall have an infinite set of roots, which lie along the negative real axis in the s -plane. The position of the roots depends on the dimensions and thermal properties of all the layers, and cannot be expressed in any simple

way. The necessary poles can be found numerically, however, by evaluating the functions

B or C for a sequence of negative real values of s. This program evaluates the roots of B

between zero and -30/A , and the roots of C between zero and -450/A , where A is the specified sampling interval of the z-transform.

(2) The evaluation of the product:

-& A D(z) = n (1 - e " z' )

when the parent Laplace transfer function has the element B in the denominator, or

-Y A D(z) = n (1 - e " z' )

when Laplace transfer function has C in the denominator.

Methods 1 and 2 differ only in the way the numerator polynomial is determined. Method 1 requires the evaluation of the time function that corresponds to l/ s (step input) or to l/ s^ (ramp input)

times the appropriate Laplace transfer function, for t = A, 2A, 3A, The coefficients of 0(z) are evaluated by finding the residues of the Laplace transfer function at the previously determined

poles.

The numerator (N(z) is then evaluated using the expression

N(z) = D(z) . 0(z)

I(z)

where I(z) = — for a step input

1 - z

I(z) = j—^ for a ramp input.

z(l - z

)'

635
Method 2 requires the evaluation of the Laplace transfer function of the wall at s = io) , and the calculation of the denominator D(z) at z = where lUj^ is the angular velocity at which the z-transfer function is to match the exact frequency response. This gives a pair of equations for each

value of uUj^ (i.e. real and imaginary parts are equated separately) except at - 0-0 (i.e. steady

state) where only the real part of the equation exists. The resulting set of equations for a series of values of can be expressed in matrix form, viz. :

11 11

1 1L ^0 A(0)

1 Cosuu^A Cos2uUj A CosJuu^A ^1 X(a^)

0 SinuUjA Sin2(U^A SinJuo^A ^2 Y(a)j)

1 CosUJ^A

2 Cos2uu,A2 CosJou^A2

^ 2'

0 SinOJ^A Sin Ziu^^ SinJuu^A

where the a's are the unknown coefficients of the N(z) polynomial and X(a)^) and Y((JUj^) are real and

imaginary parts of the product of the Laplace transfer function and denominator D(z) evaluated at

ia)„ A

s = iuUj^ and z = e respectively. The solution of this matrix equation gives the unknown coeffi- 2n

cients. It should be noted that in setting up this matrix, uu^ > should not be used since higher

frequencies than this tend to give poorer results.

2. General Description of the Program

This Fortran IV program is designed for an IBM -360 computer with line printer. Appendix A

consists of the coding sheets (A-1 to A-20), a sample of output (A-21 to A-25), and the flow diagrams

(A-26 to A-31) for this program.

The program can handle slabs that are comprised of no more than 20 layers of homogeneous

material and no more than 100 significant poles. The poles are evaluated to 10"-'^'^ precision, and

the limit for the numerator and denominator series of the z-transform is set at 10"'^. At least one of the layers of the composite slab must have significant heat-storage capacity.

The program is designed to operate continuously; i.e. , after the z-transforms for one wall

have been completed, the program automatically reads the data for the following calculation. The

program terminates when A = 0. 0 is read.

2. 1 Input

Card 1 Sampling time interval A Format: (F 10.3)

Card 2 and 3 Description of the slab for title purpose only.

Format: (80 Al)

Cards 4 to I Groups of cards giving thermal properties, thickness, and description of the layers. Whenever applicable, the first card of the group contains values of thickness of layer,

thermal conductivity,

density,

636
specific heat, and

resistance of radiation path.

Otherwise, the first card contains the thermal resistance of a layer that has

negligible heat storage capacity.

Format: (5F 10.4)

The second, third ... or more cards of the group can be used for the description of the layer if an integer is inserted in Column One.

Format: (30 Al)

Card I + 1 Blank card to terminate the above input of thermal properties and their descriptions.

Card 1+2 Code number, ICASE, and the number of frequencies, NW, to be fitted when

Method 2 is to be used (see Table 1). Format: (II, II)

Card 1+3 This card is read only when ICASE = 2 or 5. It specifies the periods of the harmonics to be used in frequency response calculations.

Table 1. Code Number ICASE

Input

Function

Boundary

Condition

Method 1 Method 2

Square

Pulse

Triangle

Pulse

Group of Harmonics

First

Kind

Invalid

Combination 1 2

Second

Kind 3 4 5

3. Reference

[1] Stephenson, D.G. and Mitalas, G.P., Calculation of heat conduction transfer functions for multilayer slabs. Submitted to ASHRAE for presentation January 1971.

4. Acknowledgement

The authors gratefully acknowledge the many helpful suggestions made by Dr. D.G. Stephenson.

This paper is a contribution of the Division of Building Research, National Research Council of Canada, and is published with the approval of the Director of the Division.

637
START

\ INPUT —\ FROM

\ CARDS,

INPUT

/ DT

CARDS

EVALUATE

INVERSE LAPLACE

TRANSFORMS

AT t = A,2A...

CALCULATE

THE COEFFICIENTS

OF N (Z)

->-

CALCULATE

THE COEFFICIENTS

OF D (Z)

= 2 OR 5 ICASE > >

METHOD I

CALCULATE

RESIDUES AT THE POLES

CALCULATE

RESIDUES AT THE ORIGIN

1,3 OR 4

/subroutinen

\ origin

-<- METHOD 2

SET UP THE SQUARE

MATRIX

'SUBROUTINE^

, FREQRE /

CALCULATE RHS

OF MATRIX EQUATION

i.e X(W),Y(W)

OUTPUT

ON

^PRINTER/

SOLVE MATRIX

EQUATION FOR COEFF OF

N (Z) * DETAILED ON FOLLOWING PAGES

MAIN -PROGRAM

Figure A-1. Flow diagram for z-transfer function calculation program.

638
LAST= 0

I ROOT = 1 SET Rl AND R3

YES

store : roots functions

and derivatives

in its proper ORDER

REPLACE EITHER

Rl OR R2 BY RTEMP SUCH

THAT Rl AND R2 ARE OPPOSITE

IN SIGN

SUBROUTINE

MATRIX

Rl> Fl -FPI

LAST = LAST + I

^ I .LAST

( RETURN )

Rl =ROOT (LAST-i; R3 = R00T (LAST)

I = I R2 = Rl +

(R3-RI) 20.0 * I

SUBROUTINE \ -^—{ MATRIX j >-

R2-* F2-FP2/

I -21

CHECK FOR TWO CHANGES

IN SIGN

FPI * FP2

CHECK FOR CHANGE IN SIGN FROM

F I ^ F2

^0 NO

1 = 1 + 1

«* NOTE

Rl = O.OOOI/DT

R3 = R00T (LAST)

IR00T=IR00T+l

CHECK FOR CHANGE IN SIGN FROM

F 1 * F2

>

<

/SUBROUTINE MATRIX R2^F2

I ROOT = I ROOT-I

LAST = LAST-I

R2 = Rl +

J * (R3-RI)

I = I NN= 10 * I J = I

J-NN

<0

>0

' > 1 = 1 + 1 > <

DETAILED ON FOLLOWING PAGES ABNORMAL

TERMINATION WITH MESSAGE

** NOTE

DUE TO ORIGINAL SETTING OF Rl AND R3 THIS PATH

WILL NEVER BE TAKEN THE FIRST TIME THROUGH,

i.e. WHEN CHECKING FOR THE FIRST ROOT.

SUBROUTINE - POLES

Figure A-2. Flow diagram for determination of poles of Laplace transfer function and calculation

of the values of A, B, C, D, and their derivatives at these poles.

639
START ^

>

F =0.0

F = F + F3(J-i) * F3(J)

F3 (J) = F

FF=FF+F

J = J+ I

F3(J)= F2(J)

1 = 1+1

FF = 0.0 —

YES/ ARE

-< —<DERIVATIVES)

^WANTED,

F = Fl(l) FF = F2(l)

c

RETURN

I = 2 F =0.0

>0 I-M >—

1=1+1 Fl(i)=F

F=F + FI (l-i) * Fl (1)

SUBROUTINE - MATRIX

Figure A-3. Flow diagram for the evaluation of A, B, C, D, and their derivatives for any real

negative value of s.

640
START yMP = 0.0 MPP = 0.0

ELEMENTS OF

- TRANSMISSION - MATRIX A(II

DERIVATIVE Of

- TRANSMISSION

MATRIX B(II

SECOND

DERIVATIVE OF

" TRANSMISSION

" MATRIX Cm

I-l

1=0

<— E=e(ii

TEMP = D»F

TEMPI = E«G

MPP=MPP

+TEMPI

K= I

1-M

>0

MP=Bli)

MPP=C(il

RETURN^

SUBRROUTINE - ORIGIN

Figure A-4. Flow diagram for the evaluation of first and second derivative of A, B, C and D at

s = o.

641
CALCULATE

TRANSMISSION

MATRIX ELEMENTS

FOR W(j) AND LAYER I

( RETURN )

>0

J-LW

^0

J = J + I A(J) = MMM

MMM=MM

M M M M ~ MMMM + MM^MMM

MMM=MMMM

>0

1=1+1

SUBROUTINE - FREQUE

Figure A-5. Flow diagraxn for the evaluation of A, B, C and D for pure imaginary arguments.

642
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668
Application of Multilayer Periodic Heat Flow Theory

To the Design and Optimization of Roofing Systems

C. P. Smolenski and E. K. Halteman

Pittsburgh Corning Corporation

Pittsburgh, Pennsylvania 15239

and

E. M. Krokosky

Ca rneg i e

Pi ttsburgh

Mel Ion I nst i tute Pennsylvania 15213

Techniques for studying the periodic heat fluxes through multilayered roof systems subject to equivalent sol air input driving functions have been coupled with

a multi-functional optimization procedure for the selection of material components,

which, when combined into a roof section, will satisfy certain object functions.

The object functions can be any or all of the following type: maximum thermal lag,

minimum total integrated flux, minimum peak flux, minimum temperature variation of the most temperature susceptible material, minimum cost, minimum weight, and others

related to purely structural consideration such as deflection, stresses, etc.

A computer program has been designed such that a search is made through a directory of roofing materials in order to select the right combination of materials,

both from a dimensional and property standpoint as well as actual position within the roofing section. The basis of the optimization procedure is a generalized multivariable optimization criteria that essentially compromises the design objectives

and is capable of handling any number of additional inequality constraints.

The multi-layer boundary value problem for temperature and flux at any position

within the layers was solved by use of the Lapace transform which converts the partial

differential equation of linear heat flow into an ordinary differential equation which

is then solved in matrix form. When incorporated into the optimal design procedure

the multi-layer heat flow theory gives the designer or analyst a powerful tool for studying roofing design.

Specific design examples are presented to show the importance of material

selection and sequence of material layers on the most critical components of the roofing system. The multitude of choices possible in terms of combinations of materials, thicknesses and sequence of layers precludes solution other than by

computer.

Key Words: Built-up roofing, optimization, periodic heat flow theory,

roof design, sol-air temperature.

Research Engineer and Research Physicist, respectively.

Associate Professor.

669
./ , 1.1 ntroduct ion

Over the last twenty years, there has developed an awareness of, and a concern for premature failures of built-up roofing systems. Various sources have estimated that annually ten to fifteen percent

of the installed new roof systems will ultimately fail prematurely; i.e., within one to five years after initial installation [1].^

There are a large number of different types of failures and associated factors causing the failures[l]. Many failures can be directly attributed to poor design, poor workmanship, poor installation, or simply attributed to the hostile environment in which the built-up roofing must function.

Cullen [2] [3], Handegord [^] and Joy [5] have singled out thermal cycling and solar radiation exposure

as two of the most important factors influencing roofing membrane durability and integrity. Specif icall/ thermal cycling can be related to thermal shock and thermal expansion-contraction movements, while the solar radiation can be related to photo-oxidation of the asphaltic materials.

Some knowledgeable researchers [I] in the field of roofing design have suggested that roofs should

be designed so as to provide a more favorable environment for the waterproof membrane. To quote Baker,

"Either improve membranes to withstand the harsh real world environment, or protect the membranes from

the environment." The economics of conventional built-up roofing being what they are, it is unlikely

that they will be replaced in the near future. Therefore, the protected membrane system is the more

likely to offer immediate solutions to the problem.

In order to protect the membranes, it is necessary to determine the thermal fluctuations of the felts. In order to do this, it is necessary to have an analytical technique for handling multilayer

periodic heat transfer. However, the choice, location and thickness of the insulating material to protect the felts is governed by certain performance characteristics for the roofing system as a whole.

The former aspect of this problem requires a thermal model for multilayer heat transfer while the later aspect of the model requires a multi-object function optimization scheme. The purpose of this paper is to present a combination of an analytical model for heat transfer and an optimization scheme which will

be used to design a roofing system to protect the roofing felts from thermal fluctuations but at the same time provide a suitable thermal barrier at a reasonable cost.

2. Roof Model

For purposes of illustration and comparison, a relatively simple roofing model was chosen, see figure 1. The three major components of the roof system are the structural deck, in this case a concrete

slab, the insulation, arbitrary, and the built-up membranes, i.e., four ply hot asphalt-asphalt saturated

organic felts. The roof system ideally must perform two main functions: (1) insulate the building;

(2) provide a weather barrier. The roof model is bounded by an internal space of constant air temperature and an external exposed surface upon which is imposed a sol-air temperature input.

3- Sol-Air Temperature Equivalent

The heat flow into a roof is due to the outdoor temperature 6 (t) and the incident solar flux l(t). The rate of heat transfer q^ will be given by

q^(t) = h^(e^(t) - 6(0, t)) + al(t) (1)

where h is the surface conductance of the roof surface, 6(0, t) is the surface temperature at distance

of X = 8 and time t, and a is the solar absorptivity of the roof surface. This may be also expressed as

q^(t) = h^(eit) - 6(0, t)) (2) o Ob

where 6^ is a fictitious temperature, the sol-air temperature and may be written as

9p(t) ho= 6 (t) + al(t)/h^ (3) O Since the surface absorptivity and outside surface heat transfer coefficient is contained in this ex- pression, the relation is only good for a particular surface. A rather complex computer subroutine was developed to automatically determine the sol-air temperature for any specified location, time of the year, and for any given surface condition and orientation.

Figures in brackets indicate the literature references at the end of this paper.

670
h. Multilayer Periodic Heat Flow

Periodic heat flow through composite roof systems have been studied by a number of investigators,

Mackey and Wright [7] and more recently, Hoglund, Mitalas and Stephenson [6]. The present study employs

a computer program especially developed for determining temperatures and fluxes at any position within

a layered system and is a modification of an earlier program developed for making thermal diffusivity

measurements [8]. A Laplace transform was employed to convert the partial differential equation of

linear heat flow into an ordinary differential equation which was then solved in matrix notation form. The input driving function at the exposed outer roof surface boundary consisted of the sol-air temperature expressed as a Fourier Series.

The tempera turCj^d i s t r i but i on , e^(x,t) within a given layer m of a multi-layer infinite slab of

total thickness L = composed of M layers of thickness L ,is given by the solution of the one dimensional equation of linear heat flow with specified boundary condition,

a 6 (x,t) = e (x,t). ik) m moo mt The distance x is measured from the input face of the first layer. The thermal diffusivity, a of

each layer is defined as ammmmm = A /d C with A being the thermal conductivity: d , the density; and c"^, m m

the specific heat. It is assumed that each diffusivity is independent of position, time, and temperature. The subscripts, 6 and t, denote differentiation with respect to distance and time.

The boundary condition at the input face, x = 0 will be the sol-air temperature, e^(t) expressed

as a Fourier Series,

e^(t) = + I sin (27rnt + 6^) (5)

and

e (x,t)= 0 t 0 (6) m for all M layers. The temperature at the output face will be maintained constant at T^ for all time,

e(L,t) = T^ t > 0 (7)

In a multi-layer slab of M layers, an additional pair of boundary conditions is required at each

interface; namely, the flux and temperature must be continuous. At the interface between the m'th and m'th + 1 layer, the boundary condition may be expressed as m m

~ e ( iL ,t) = e ^, ( ,t) (8) m y m m+ 1 | m

m m

X e AJl ,t) = A _^,e ^.Ah ,t) (9) m m6 'j' m m+1 m+16 j m ^

'

This multi-layer boundary value problem can be solved by the use of the Laplace transformation

which converts the partial differential equation in G(x,t) to the ordinary differential equation in u(x,p). The transformed equation for the m'th layer becomes

_ m- 1 m

u ..(x,p) - q'^u (x,p) =0 y L < X < Tl (4') m66 '^^mm '^ ^m jm ^

'

2 , q = p/a

m m

The interface boundary conditions at the input face of the m'th layer transform to the form

m- 1 m

I

1 Vl( K'P^ = ^m( ^m'P) (8')

m mS

I m-1 m-1

f ,( ,p) = f ( [L ,p).

where f is the transformed flux.

( IL ,p) = XuA lL,p) (9')

m-,

,

671
The boundary condition at the final output face will be

u^(L,p) = 0 (7')

while the transform of the input boundary condition at x = 0 will depend upon the time dependence of the input function.

The general solution for the m'th layer can be written in matrix form [8]

umo ^11 ^12 u . m 1 u . m 1 f mo ^21 ^22 f . mi Tm f . m 1 (10)

where the subscripts o and i designate the value of the transformed temperature or flux in the plane of

the output or input face of the m'th layer. The terms in the square matrix are given by

T] 1 = T._ = cosh (q L ) 11 22 mm

12

s i nh (q L ) ^m m

\ mmq

21

A q s i nh (q L ) mm m m

(11)

and T is the matrix for the m'th layer.

m

If layers from 1 to M are placed in series so that the output of the m'th layer becomes the input

of the m'th + 1 layer, the matrix equation becomes

"li

f , .

m=l

TT T m=M

m

(12)

1 i

For a general position, x > measured from the input face of the m'th layer, the matrix equation is

(13)

m-1 where the arquments of the hyperbolic functions in the matrix T wi 1 1 be q x or q (x - Tl ) as x i

mx m m m y m measured from the input face of the first layer. The values of the input functions of the m'th layer are given in terms of the output functions by

u u . mx

T

m 1

f mx f . mx mi

•1

f .

(I't)

where T is the inverse of T . m m Thus, the value of the function at x the m'th layer is given in terms of the output

mx

mx

mx

or in shortened form

mx

mx

mx

m=M

^Mo

^Mo

'^Mo

T-'m ^Mo

T-'m

^Mo

^Mo

(15)

(16)

672
Solving equation 12 for the input functions gives

^li m=M

= TT T-'

'^Mo

^li

ni=l m

''mo

Mo

""mo (17)

The ratio of the temperature at x to the temperature at the input face, x = 0, for a constant tem- perature at the output face, x = L is given by solving eq 16 for u^ and eq 17 for Uj. and dividing to obtain the desired ratio; i.e., '"^

u N,_ mx = _L2

^li ^12

Mo

''mo

u(x,p)/u(0,p) = N|2/D,2 = Z (18)

The value of Z, the ratio of the transformed temperature at x to the transformed temperature at

X = 0, ^\2^^]2' ^ complex quantity dependent upon q, the thickness of the layers and their physical

properties. The expressions for e(x,t) and 8(0, t) are obtained from u(x,p) and u(0,t) by use of the Inversion Theorem by which the residues at the poles of the integrand are evaluated. For the case of

the steady periodic state, only the residues at the poles which occur along the imaginary axis need to

be evaluated. For an input function containing a single frequency, w, these poles will be at -iu. Thus,

for a sine wave input function, Z is obtained by evaluating '^]2^'^12 ^'^^ factor q in each argument

given by q^ = ( i oi/a^) '•^^

. The vector Z gives the attenuation and phase lag of an input sine wave of temperature when measured as a temperature at a position x in a multi-layer infinite slab.

For periodic input functions expressed as a Fourier Series, the application of the Inversion Theorem

on the transform of the temperature requires the evaluation of the residues at pairs of poles at ±inaj where the values of n depends upon the harmonic content of the input function. The residues will be

^ given by A Z where Z is the value of Z with the factor of q of each argument given by q = (inoj/a )

•'• ^'nn f

n ^^ ^m m and A is the coefficient of the n ' th harmonic of the Fourier Series expansion of the input function

6(0, t^

The matrices N and D become unwieldy when used to obtain an explicit expression for Z of a slab containing more than two or three layers. The matrices can, however, be evaluated by purely numerical

methods using complex-mode computer programs. When this method of calculation is used, each term in the matrices N and D is determined with equal ease. It is thus possible to find a vector Z giving the amplitude and phase lag of the temperature or flux at a point x with respect to a temperature or flux wave

incident on the input face of a multi-layer slab with the output face held in an isothermal or adiabatic

condi tion.

5. Design Objectives

As indicated earlier, a roof is to perform the major objectives, i.e., provide thermal insulation

for the control of the internal environment and act as a waterproof weather barrier. It should accomplish these objectives within certain economic design limitations. The total roofing system also has to carry its own dead weight plus any live loading from wind, snow, rain or normal maintenance traffic.

The latter objective is generally the sole responsibility of the structural deck system. Certain types

of application may also require a fire rating for the roof system. In total, there may be as many as five or six functions to be performed by a given roof system, and in most cases, there will be conflicts

between certain design objectives which will require some form of compromise in terms of the final design.

Determining the amounts and type of insulation to be employed within the confines of a particular system

can involve a number of considerations ranging from economic to thermal performance. A procedure for performing mu 1 t i va r i ab 1 e optimization has been developed previously and is described in the following

section.

6. Basis of Optimization

The basis of the optimizing procedure is a generalized mu 1 t i va r i ab 1 e optimization criteria that attempts to compromise design objectives and any inequality constraints. The procedure was originally presented as a structural design aid by Gall and Krokosky [9]. Since every design is a compromise

673
between conflicting goals, each design reflects the designer's ability to perform some trade-off among various goals. The present design program still requires the judgment and selectivity of the designer to determine realistic perfor,mance indices. The determination of performance indices is by far the most difficult part of the entire procedure. Variations of the procedure are limited only by the imagination

and resourcefulness of the designer. However, for the untrained designer, the determination of perfor- mance indices can be developed heuristical ly

7. Present Optimization Scheme

The current program specifically designs a three-layered composite roof system by selecting the materials from a data bank of discrete material properties. The final design represents a compromise

between thermal performance variables and cost. The importance of each design objective is determined

by the designer in setting up the various performance indices into a so-called ranking matrix consisting

of levels of desirability.

8. Ranking Matrix

The heart of the present procedure utilizes a ranking matrix of system functions which reflects the designer's ability to recognize and to assess the relevance and desirability of each design function.

Table I shows such an array for a typical roof design considered herein.

TABLE I

Design Ranking Matrix for Roof Section

Cost of Insulation

Total Integrated Flux Maximum Peak

Thermal Flux

Max i mum Fe 1

Temperature Differential

($/ft^) (BTU/ft^24-hr . pe r i od (BTU/hr/ft^) (°F)

0.00 0.00 0.00 0 .00

0.25 50.00 10.00 25 .00

0.35 75.00 10.00 25 .00

0.45 100.00 20.00 25 .00

0.55 125.00 30.00 25 .00

50.00 150.00 300.00 300 .00

Limi ts

Thickness (ft) 0.0833 tl 0 500; t^ = 0.0208; tj = 0.333

Density (#/ft^) 1 . 9 .< p

, .< 27. 0; ^2

= 70.0; = ]k0.0

The matrix ranks system attributes against an absolute scale of performance. The first row, J = 1, represents the most optimistic desires for the performance of the system as well as the upper bounds for each system attribute. Row two, J = 2, gives the designer's appraisal of excellent performance and so

on down the following rows with each succeeding row having less desirable characteristics than the pre- vious row. The designer can use as many rows as needed. In each case the last row is known as the funnel row and its function is to funnel the performance characteristic within ranking considerations.

The only restrictions on the construction of such an array are that each row must contain values of system attributes of equal desirability and each column in the array must be montonically increasing

or decreasing.

9. Search Procedure

The optimization search procedure relies on a pseudorandom or adaptive search techniques in which the search probability is not fixed but shifts around as the search progresses. A purely random search pro- cedure would use a probability density that is uniform over the whole search procedure. The search

relies on a probability density that is a maximum at the current best value of the design parameters.

In the present program, these parameters are the density of the insulation, conductivity and the corres- ponding thicknesses of the insulation.

674
On each side of the current best value the probability density decays with some exponential value

of [odd integer - l)/odd integer]. A new choice of parameters is determined by

K0[I] = KB[I] + [ |uB[l] - LB[I] | R^] (19)

in which KO = the newly chosen search parameter; KB = current best value; LB and UB = the upper and lov/- er search parameter bounds; R = a uniform probability density between -I and I; and 9 is the odd integer

describing the probability density decay. Every time a better point is found that results in a lower value of J , its corresponding variables are stored in KB. The maximum value of all the desirability

ratings is given by J^, i.e.

J = maximum [RA[N]] (20) m

in which N = the number of system variables and RA = the desirability of each system variable which is obtained by linear interpolation of the calculated value and the design values from the ranking matrix.

Thus, figure 2 shows the flow chart for the ranking optimization program. In this particular variation

of the program, the density variable is used to select the materials for insulation. The random value

of the density is used in conjunction with the discrete material file. An interpolation is carried out

and the discrete material having the density closest to the pseudorandoml y generated value is then chosen along with its properties for a given ranking. The program can be run for any given period of time until the desirability of each system variable is approximately equal or until there is no appreciable change in the J value.

^ m

10. Inequality Constraints

The ranking array can be set up to act as an inequality constraint so that underdes i gned quantities

are the ones that are immediately reduced, see Table II. Underdes i gned quantities are fixed so that

they have a high J , therefore a low desirability, while the overdesigned have a low index and are not usually reduced further.

Table II

Typical Ranking Array Showing Implications of Underdesign and Ove rdes i gn

Des i rab i 1 i ty Maximum Temperature Des i rab i 1 i ty Equivalent To

1 ndex Gradient Across 1 ndex

Felts, °F J[l] Most desirable 0 J[l] Overdes igned

J[2] 25 J[2]

J[3] 25 J[3] A 1 1 owa b 1

25 J[4]

J [5] Funne 1 Row 300 JL5J Underdes i gned

II. Illustrated Example Application

Possibly the best method of showing the usefulness of the previously described analytical techniques

is to consider a specific example. The thesis previously expressed was that conventional roofing design

employing the built-up roofing waterproof membranes exposed to the weather was, in fact, somehow poor

des i gn

The aforementioned thermal analysis and optimization procedure were applied to this particular problem in an effort to search out more desirable designs. Specifically the present design considers the implications of placing the built-up membranes under the insulation.

Initially only four major parameters were considered in the ranking matrix as shown in Table I. These were the cost, total integrated flux, maximum temperature differential of the membrane layer, and maximum thermal flux transmitted through the roof section. TJne inclusion of cost as a comparative parameter is obvious, whereas the other parameters may not be as obvious. The temperature differential of

the felt membrane layer was considered for protection against thermal shock and excessive thermal cycling.

Finally, the peak thermal flux was considered to give some indication of the overall thermal design of

the roof as far as the interior environment was concerned.

675
Initially the search was also limited to six specific insulations as shown in Table III. Other insulations or variations of insulation properties with density could have been included as well, but the present study was purposely kept simple so that the overall approach could be emphasized.

The object of the present search was to select the most economical insulation, and thickness of in- sulation, from the possible insulations listed in Table III which would also satisfy the criteria of the ranking matrix, Table I. Allowable insulation thicknesses are also shown in Table I.

Table III

Material Properties

Material Density Thermal Conductivity Specific Heat Cost #/ft^ BTU-ft/hr.°F-ft^ BTU/lb/°F $/Board ft. Urethane 1.9 0.012 0.21^0 0.17

FOAMGLAS 9-0 0.033 0.185 0.15

Aspha 1 t-coated

lightweight 15-0 O.O38 0.200 0.08 aggregate

Fiberboard 15-1 0.030 O.5OO O.O7

Lightweight

aggregate insul- 25-0 O.O58 O.I69 0.08 ating concrete

Cone rete-coa ted lightweight 27.0 O.O65 0 . 1 80 0.10

agg rega te

Built-Up Roof 70.0 0.093 0.370 0.22

Concrete 140.0 1.000 0.210 0.05

The specific climatic conditions considered in this paper correspond to a site just east of Pittsburgh, Pennsylvania"". Both a representative summer and winter day was evaluated. Specific information

concerning dry bulb air temperatures, cloud cover, wind velocity, etc. was chosen to be representative.

In the present program, any region of the United States could just as easily have been considered.

11. Results

Summer, Case I - (Concrete structural deck) + 4 ply membrane + Insulation. The first example con- sists of conventional k ply built-up roofing membranes placed over four inches of structural concrete

deck and subjected to a typical summer sol-air temperature driving function as shown in figure 3. To begin the search, a guess is made as to the yet unknown insulation and its thickness. Initial values of system object functions are then calculated and compared to the allowable limits. If the values are all within the limits, each function is then ranked according to the ranking matrix shown previously. The next cycle of the search then attempts to improve the rank of the worst ranked parameter by either a change of insulation thickness or insulation material.

Shown in Table I V-A are actual ranking output generated by the program for which several improved

ranks were found. It can be quickly seen that the initial estimate was unsatisfactory in terms of the total heat gain, (i.e., rank k-2'ik). It should be remembered that the more desirable the function, the lower the rank value will be. After only slight improvement was achieved by an increase in thickness,

the search procedure shifted to a lighter and more efficient insulation. In so doing, the cost then became the critical parameter and further searching ultimately produced a design where the cost and total flux were of approximately equal rank and the search was terminated.

..................................

J

676
Table I V-A

Optimization Search Output

A. Summer Condition - Concrete Decl<.

Design Parameters and Rank Current Insulation Choice Max i mum Fe 1

Den s i ty #/ft^

1 11 1 \v l\l 1 C O 3

Ft.

Cost $/ft^

Tota 1 F 1 ux BTU/ft^/2'4 hr.

Peak Flux BTU/ft^/hr.

Temp . Differentisl

°F

25.0 0.210 0 202 105.85 7 75

8.888

(1 806) [ ^.23k] (1 775) (1 .355)

25.0 0.217 0 208 103.61 7 559 8.6^49

(1 833) [ ^.l^t^t] (1 756) (1 . 3^*6)

9.0 0.217 0 390 68.30 k 859 5.397

[3 ^402] ( 2.732) (1 it86) (1.216)

9.0 0. 1970 0 355 73.58 5 266 5.899

[3.046] ( 2.9^*3) (1 527) (1.236)

Table IV-B

Optimization Search Output

Winter Condition - Concrete Deck.

Current Insulation Choice

Design Parameters and Rank

Max i mum Fe I

Dens i ty

ff/ft^

Th i ckness

Ft.

Cost S/ft^

Tota 1 F 1 ux BTU/ft^/24 hr.Peak Flux BTU/f t^/hr.Temp. Differe

°F

9.0 0.210 0 378 145.37 7 863 5 .560

(3 28) [ 5. 815] (1 786) (1 .222)

1 .92 0. 172 0 3509 102.29 4 578 1 .21

(3 009) [ 4.092] (1 458) (1 .049)

1 .92 0. 179 0 3647 y8.82 4 421 1 .169

13 147) [ 3.953] (1 442) (1 .047)

1 .92 0.213 0 4347 84.36 3 772 0 .983

[3 846] ( 3.374) (1 3/7) (1 .039)

All system attributes were not equally ranked because the original ranking matrix tended to overdesign the peak flux and maximum temperature differential for the present input function.

Winter, Case I - (Concrete structural deck) + 4 ply membrane + Insulation. Since most of the northern latitudes of the United States experience a great difference in ambient outdoor temperature from

Summer to winter seasons and any insulation system must function year round; real designs would have to consider more than just one input sol-air condition. Although more elaborate design criteria would un- doubtedly be considered in an actual design, for the sake of demonstration and comparison, a typical

winter sol-air temperature was developed for the same roof and location as in the summer case just discussed. This sol-air temperature shown in figure 4 was used as input to the optimization program and a new search was made for the optimal insulation to function under winter conditions for the same design

criteria as given in the ranking matrix of Table I.

677
Table IV-B shows the actual ranked designs for the winter input. It is seen immediately that what

was the best choice of insulations for the summer sol-air conditions no longer was acceptable because of

the large heat loss shown as total flux, i.e. Rank, (5.815) • The next ranked design shows the effect of

a lighter and more efficient insulation, but again a more costly insulation. This is reflected in a shift of the critical parameter from total flux to cost. Further searching produced a slight reduction

in the cost rank by reducing the thickness.

It is interesting to note that the optimized designs for summer and winter conditions do not suggest

the same insulation in each case. The summer design uses 2.36 inches of 9-0 pcf density insulation and

the winter case selects 2.56 inches of 1.92 pcf density insulation. In a real case an additional criteria such as the cost of heating and cooling could be included to aid in the decision. The addition of such

a criteria in the present program would present no serious problems.

Figures 3 and h show computer-generated data for both the sol-air equivalent driving functions and

the responses of both the protected and conventional membrane roofing systems when insulated with the designed winter insulation. It is at once obvious that the protected membrane system effectively damps out the large thermal fluctuations of the driving input sol-air temperature and provides a relatively

stable thermal environment. The conventional designed membrane on the other hand very closely tracks

the input sol-air temperature. The conventional membrane curves and sol-air temperature are shown as

a single line because the membrane temperature is so close to the input.

Since the initial example consisted of a rather massive structural deck, i.e., 4.0 inches of con- crete which provides the potential for a large amount of heat storage, it was decided to test a second example with a vastly different deck construction. The second case consists of a corrugated metal deck

and a 0.5 inch layer of fiberboard adhered there unto as a base for the built-up roofing membranes.

Once again the task was to determine the type and thickness of insulation to protect the membranes and

to provide the major insulation for the building for both the summer and winter conditions.

Summer, Case II - (Corrugated metal and fiberboard deck) + k ply membrane + Insulation. Table V-A

shows the resulting ranks for both the initial tion, and succeeding generated values. estimate, i 2.52 inches of 25.0 pcf density insulaTable V-A

Opt i mi za t i on Sea rch Output

S umme r Condition - Steel Deck + Fi berboard

Current nsulation Choice Des i gn Parameters and Rank

Cost Total Flux Peak Flux Maximum Felt

Dens i ty #/ft^Th i ckness

Ft. $/ft^ BTU/ft ^/2k hr. BTU/ft^/hr.

Temp. Differential

°F

25.0 0.210 0.202 84. 51 1 1 273 29.711

(1 .806) ( 3. 380) ( 3 127) [ 5.017]

9.0 0.217 0.390 57. 83 7 806 20.587

[3.'t02] ( 2. 313) (1 781) ( 1.824)

9.0 0.197 0.355 61

73 8 376 22.098

[3.046] ( 2. 469) (

1 838) ( 1.884)

15.0 0. 197 0. 189 67. 52 9 032 23.809

(1 .756) [ 2. 701] (

1 903) ( 1.952)

Initially, it is seen that the membrane temperature differential was the critical, or worst, ranked parameter. Attempting to correct this, the cost then became the decisive parameter. Finally the search procedure settled on a compromise insulation where total flux transmission was the critical variable.

At this point time terminated the search procedure and it can be seen that three of the four ranked parameters are approximately of equal ranked value. Had time not terminated the run, it is most likely

that the thickness of insulation would have been increased, increasing cost slightly, while lowering

total flux, peak flux and maximum felt temperature differential. The cost and total flux would then have been of approximately equal ranking magnitude. It is somewhat interesting to note that with this

678
lightweight metal deck system there is an increase in the maximum felt temperature differential over over that observed with the more massive concrete deck system. The mass of the concrete tends to pro- vide inertia which resists the rapid input fluctuations.

Winter, Case II - (Corrugated metal and fiberboard deck) + h ply membrane + Insulation. Once again

the second part of the procedure was to evaluate the search for the winter sol-air temperature input. Table V-B shows the results from the optimization search. Initially the total flux, i.e., heat loss, was the critical parameter with a rank of [5.261]. The search procedure improved on this rank by

switching to a more efficient insulation which also increased the cost. Further searching reduced the cost somewhat but not enough to remove the cost as the critical parameter. As in the former case, a different optimum design is suggested for the winter case as compared to the summer condition.

The input sol-air temperature and system thermal response are shown for both summer and winter con- ditions in Figure 5 and 6. As with the previous example, the insulated or protected membrane remains

essentially isolated from the large input temperature fluctuations although as noted earlier, the present case does show somewhat larger fluctuations than the concrete deck system.

Table V-B

Optimization Search Output

Wi nter Condition - Steel Deck + Fiberboard.

Des i gn Parameters and Rank Current

Dens i ty Insulation ChoiceTh i ckness Cost Total Flux Peak Flux Maximum Felt

Temp. Differential

#/ft^ Ft. $/ft2 BTU/ft^/2i( hr. BTU/ft^/hr. °F

9.0 0.210 0.378 131 .52 8.739 21 .085

(3.28) [ 5.261] (1 .87^*) { 1.843)

1 .92 0.210 0.it28l 81 .i)7 4.033 4.695

[3.781] ( 3.259) U .403) ( 1.1878)

1 .92 0.207 0.4225 82.39 4.078 4.749

[3.725] ( 3.29b) (1 .408) ( 1.190)

12. Conclusions

Although we have not had enough experience with the present program to be able to state generalizations regarding the design of protected membrane roofing systems, we feel the present approach will be extremely useful toward that eventual end. We believe it is significant that seasonal demands caused by

different sol-air temperature driving functions dictate different insulation requirements for summer as compared to winter conditions. The present example has shown the benefits to be derived in terms of a stabilized thermal environment for the membrane in a protected membrane roof insulation system independent of seasonal conditions.

The present multifunctional optimization program offers the design engineer an efficient means of assessing the effects of variations in specific design parameters on the overall design of a building

material system.

We feel that it is especially useful in discovering and resolving the conflicts between the various

design criteria which do arise in multifunctional systems. The designer can then easily determine the degree of interplay and the limitations of design variables. The need for rational compromise is then made more apparent.

Since the most difficult part of the design process appears to be the specification of equivalent

desirable performance criteria for the many variables involved, it is also possible to use the present

program as a heuristic design learning process for the actual establishment of said performance

cr i ter i a

679
680
DES IGNATE

UB, LB [l];

KB

J MAX 10--'-- RANNO ^- K0[I] ^- KB[l] + ((UB[l] - LB[l]) * (RANDOM4 9))

K0[I]

K0[I]

LB[I]

UB[I]

NO _1

YES

RELATIONSHIPS BETWEEN

SYSTEM VARIABLES & DESIGN PARAMETERS

XO[C] ^ - K0[I]

RANNO:

PSEUDO:

RANK XO [C ] XO[C] > J0[5,C]

COST, ETC.

1 4 F

DETERMINES DESIRABILITY INDEX

RA[C] XO[C]

JMAX < RA[C])>-

ALL SYSTEM VARIABLES

RANK XO[C] FLUX

XO [C] > J0[5,C] T^

DETERMINE DESIRABILITY INDEX

J[C] <- X0[C]

equal number of system

pa rame te rs initially any va 1 ue will

time limiterwill end

p rog ram

JMAX <RA[C]'^

FOR ABOVE RA[C] JMAX *- MAX RA[C]

KB [1 ] K0[I]

do

GO TO PSEUDO

Figure 2. Flow Diagram for Optimization Program

681
160 r

120

100

SOL AIR TEMPERATURE AND CONVENTIONAL ROOF MEMBRANE

PROTECTED MEMBRANE

60

i*0

20

Location: Pittsburgh, Pennsylvania

Latitude: kO° 27' h6" N Longitude: 79° 'tO ' 35" W Summer: July 9, 1970

CI earness : 1.0 Wind Velocity - 5 knots 2.0" Urethane Insulation

k.Q" Concrete Structural Deck

2 k 10 12 1^ 16 18 20 22 2k

TIME, HOURS

Figure J. Periodic Temperature Variations for Conventional and Insulated Membrane Roof Systems Summer Conditions

682
160

140

120

Location: Pittsburgh, Pennsylvania

Latitude: 40° 27' 46" N Longitude: 79° 40' 35" W Winter: January 9, 1970

C 1 ea rness : 1.0 Wind Velocity - 10 knots 2.0" Urethane Insulation

4.0" Concrete Structural Deck

100

80

60

PROTECTED MEMBRANE

40

20 .

SOL AIR TEMPERATURE AND CONVENTIONAL ROOF MEMBRANE

10 12 14 16 18 20 22 24

TIME, HOURS

Figure 4. Periodic Temperature Variations for Conventional and Insulated Membrane Roof Systems - Winter Conditions

683
160

120 _

100 -

80

60 _

ho -

20 _

SOL AIR TEMPERATURE AND CONVENTIONAL ROOF MEMBRANE

PROTECTED MEMBRANE

Location: Pittsburgh, Pennsylvania

Lati tude: 40° 27' 46" N Longi tude: 79° 40' 35" W

Summer: July 9, 1970

C 1 ea mess : 1.0 Wind Velocity - 5 knots 2.4" Porous Bonded Aggregate Insulation

15.0 pcf

1/2" Fiberboard

Corrugated Metal Deck

0 I I I '

I

I I I I I I- I

0 2 4 6 8 10 12 14 16 18 20 22 24

TIME, HOURS

Figure 5. Periodic Temperature Variations for Conventional and Insulated Membrane Roof Systems Summer Conditions

684
160

Location: Pittsburgh,

Lati tude: 40° 27' '6" Longitude: 79" ^0' 35" Winter: January 9, Clearness : i .0 Wind Velocity - 10 knots 2.5" URETHANE Insulation

1/2" Fiberboard

Corrugated Metal Deck

Pennsy 1 van i a

NW

1970

140

120

100

PROTECTED MEMBRANE

60

ho

20 SOL AIR TEMPERATURE AND CONVENTIONAL ROOF MEMBRANE

0 2 4 6 8 10 12 14 16 18

TIME, HOURS

20 22 24

Figure 6. Periodic Temperature Variations for Conventional and Insulated Membrane Roof Systems - Winter Conditions

685
1

1

I

I

I

i
Pulse Transfer Function & Its Application Related to Buildings

H. Yamazaki

Kyushu Institute of Design

Fukuoke-City , Japan

Abstract

For the digital calculation of a linear system, it is more convenient to use the Z-transform than

the S-transform (Laplace transform). The transformation of the product of the system input and transfer function on the S-domain into the Z-domain is very complicated.

This difficulty is overcome, however, if we assume that the output varies very slowly in response

to a sudden input change

Discussed in this paper is the general technique of obtaining the Z-transform transfer function

and the application of the technique to calculate room temperature of air-conditioned rooms under an automatic control system.

Keywords: Linear systems, transfer function, Z-transform

1. Introduction

Need exists to calculate dynamic changes of room temperature and heating/cooling loads. The method

of these calculations are either frequency response method or the pulse response method. The frequency

response method requires the solution of simultaneous equations with complex coefficients. With a careful plan the computer time for the complicated system can be decreased considerably. On the other hand,

the pulse transfer function method requires polynominal expression of time series data in power of Z"l. Although the pulse transfer method is convenient for dealing with sampled data, there is no superiority

or inferiority over the frequency response method.

It is possible to obtain the pulse transfer function in three ways:

1. transfer function

2. frequency response

3. Weighting function

Reference (1) describes the method to derive the pulse transfer function from the frequency response.

This paper is based on a method of obtaining approximate pulse transfer function from transfer function.

2. Input, Output and Components

The inputs may be the time changes of solar radiation, outdoor air temperature, internal heat gen- eration in the room heat due to lighting and equipment or due to the occupants. The outputs may be the room temperature and heating /coo ling load. These inputs and outputs are related by the thermal system

components, which may be the structural characteristics of walls.

3. Principles of the Method

First, a method of obtaining the approximate pulse transfer function from the transfer function in

a continuous system will be described. It is assumed that:

1. The system considered herein is linear

2. The change of the output is gradual even when the input is abrupt

These assumptions are not too far off in the real thermal systems. Denoting the input by F(S), the output by H(S) and the transfer function by G(S), it can be shown that

H(S) = G(S) • F(S) (1)

687
With the assumptions given above, this equation can be modified to

Ipf(S) • Gh(S) = G(S) • F(S) (2),

where ff'(S) is the modified output to suit the sampling width. If Gh(S) is to represent the triangular

pulse function

Gh(S) = d-e"^^)^ • e^^/(TS^) (3)

Equation (2) now may be represented in the Z-domain by

H(Z) = Ga(Z) . F(Z) (4)

Here Ga(Z) is the pulse transfer function and

Ga(Z) = l/C(Gh(S)/G(S)) (5)

Thus it can be shown that the product of the linear system input and the transfer function can be ob- tained by multiplying the sampled input by the pulse transfer function.

4. Pulse Transfer Function

4.1 Heat Flow, Imaginary Function of a Slab

In a linear heat conduction system, for a slab of constant thermal resistance r, diffusivity

and thickness I, when subjected to the unit surface temperature excitation at one side and zero at another, the Laplace transform of the heat flux at the excitation side is

X = V'J'a cot h ihi (6)

The heat flux at the zero temperature side is

Y = l, cosec iln (7) a a

when s is the complex parameter. The solution for the multi-layer wall will be treated in the next section as a function of X and Y.

4.2 Surface Temperature Transfer Function For Mult i- layer Wall as Temperature Input

Multi- layer wall temperature WqCS) responding to the unit surface temperature and zero at another

will be (figure (2)),

.W (S) = Bw/Aw (8)

1 o

where i is an index for the side of input and o is for the output, and Aw is expressed as follows.

Aw = a* . a* • a* a* , (9)

i Z J n-1

•'k '^k a, = X, + x^^]^ (k=l,2 ... ,n-l

688
and if we let input i as 01 and output o as 12, Bw is

Bw = b* . b* . b* b* , (10)

L z i n-i

\^ \ ^

^k+1 = 2, 3, ... . n-1)

b* = Y

1 I

and if we let input i as nn+1 and output o as 12 , Bw is

B = b* . b* . b* b* , (11) w 1 2 3 n-1

b* = Y

k k+1

and if i is 01 and o is n-ln, Bw is

Bw = b* . b* . b* b* , (12)

1 / J n-i

4.3 Transfer Function of Single Room Temperature as Heat Supply

Further if we make some assumptions as

(3) Heat supplied into the room diffuses instantly into the room air

(4) Number of air changes in the room is constant

(5) Heat radiation is considered as a part of the overall heat convection coefficient

The transfer function of the single room temperature for the supply heat Rh(S) is

Rh(S) = l/(Qa . S-tQa . N + D (A./Ri.) . (I'mWi, -(S)) (13)

where Qa is air capacity of the room, N is number of air changes, Aj is area of the wall of number j,

1/Ri is overall thermal coefficient corresponding to wall j and 01^12, j^^^ '^ transfer function of wall

surface temperature on the side of excitation (outside surface) and S is complex parameter. In this

case, we let X, and Y. as 1/Ri, and X and Y as 1/R . ' 11 ' n n o Now from eq. (13), room temperature 6r(S) as supply heat Ht(S) will be in linear system,

er(S) = Rh(S) . Ht(S) (14)

Ht(S) includes heat exchange with outdoor air heat conduction through wall while the room temperature

assumed to be 0. If we want to obtain frequency response of room temperature as heat supply, i .w would

replace S in eq . (13). Where i is an Imaginary number index and w is an angular frequency of heat supply.

In this system 9r(S) is output, therefore we can transform room temperature 9r(S) in accordance

with assumption (2) and eq. (2) as follows,

er(S) = er*(S) . Gh(S) (15)

689
where 9r*(S) is the sampled temperature of the room. Equation (14) is now modified to

er*(S) . Gh(S)/G(S) = Ht(S) (16)

Equation (16) is then transformed to Z-domain as follows,

er(Z) . ^(Gh(S)/G(S)) = Ht(Z) (17)

In this case Ht (Z ) corresponds to input in eq. (4). And if we consider eq . (17) as pulse transfer

function of single room for heat supply,

Rh(Z) = l/g(Gh(S)/G(S)) (18)

where Rh(Z) corresponds to Ra(Z) in eq . (5), then eq . (17) becomes,

er(Z) = Rh(Z) . Ht(Z) (19)

Now, from eq . (3), eq . (13) and eq . (18), we can get Rh(Z) in the following,

Rh(Z) = l/(Qa . (Z-l)/T-(Qa , N+ Z (l-^Wio ) • A./Ri.)) (20)

01 12, J J J

where . (Z ) is calculated by assumptions (2), (3), (4), and (5) and eqs. (3), (4), (5), (6), (7),

(8), (91, (10), as follows

0l"l2,j^^^ = Bw/Aw (21)

when Aw and Bw are given in eq . (9) and eq. (10), respectively. However, we denote X as x(Z) and Y as y(Z) in this case to represent

x(Z) = (l+(2/t) . S (Z/(Z-1) + Z/(Z-dj^))/ck)rl (22)

y(Z) = (H-(2/t) . S (-1)'' . (Z/(Z-1) + Z/(Z-d^))/cj^)/rl

cj^ = . rr^/(l^/a^)

d^ = EXP(-C;^ . T)

T: sampled width

In these equations, slab number of multi-layer wall are omitted. x(Z) and y(Z) may also be expressed

as

x(Z) = (l+(2/T) (S (l-d,)/c, +S (S (1-d, )^ . d!""^)Z/c "'°)rl k=l M=l K=l

(23)

y(Z) = (l+(2/T) (S (-l)^(l-d^)/Cj^ + S (-l)''(l-d^)^d^'bz/cj^"'")rl

5. Pulse Transfer Function of Multi-connected Rooms Temperature

Now, if we let the input as heat supply Hj^(S), in which i is the room number and let output as room temperature ©^(S), and if the transfer function of this room is Rh^(S)

e^(S) = Rhj^(S) . H^(S) (24)

690
and if we let the transfer function of a multiply-connected rooms as Rhj£(S), where j is the room number

of input and i is the room number of output, Q^^CS) becomes

e. (S) = E Rh. . (S) . H. (S)

1 J3- J

where Rhjj^(S) equals Drj^^/Dr. Dr and Dcji are as follows,

(25)

Dr =

§21

=nl

'In

Dr.. = g 11

•21 0

0 Rh. . . JJ- 0

=nl

g. . = -(A/R. ) . .W. (S) . Rh. (S)

'In

(room of number i adjacent to room of number j)

= 0 (non-adjacent)

= 1 (i = j)

Therefore, pulse transfer function of this system Rhj^(Z) will be,

Rhj.(Z) = l/C(Gh(S)/S Rh..(S))

We can obtain the solution of eq . (27) by using assumption (2).

(27)

6. Temperature of an Automatically Air-conditioned Rooms

It is assumed that an office room is automatically air-conditioned during the office hours by a feed back controlled system. Temperature of the rooms during the off office hours will vary naturally

in accordance with eq . (14).

Now, the heat supplied into the room during the air-conditioned period is Hm(S). Heat supplied

during the off-hours is Ho(S). The programmed temperature profile is Op(S), then equations will be,

er(S) = Rh(S) . Ho(S)/(H-Rh(S) . Tf(S)) +Rh(S)-. Tf(S) . Gp (S )/ (1+Rh (S ) . Tf(S)) (28)

Hm(S) = Tf(S) . (ep(S) - er(S)) (29)

and if we want to express eq. (28) by the Z-expression,

691
er(Z) = Rh(Z) . Ho(Z)/(l-tilh(Z) . Tf(Z)) +Rh(Z) . Tf(Z) . Gp (Z )/ (l-Wh (Z ) . Tf(Z)) (30)

when Rh(Z) is shown in eq. (18) and Tf(Z) is 1/ (Gh (S )/Tf (S ) ) . If we let Tf(S) as p.(l+I/S), Gh(S) as eq . (3 ) , then

Tf(Z) = (1-q- Z (l-q)^qj"^z"j)/(p.I.T) (31)

q = E2CP(-I.T)

And the programmed temperature will be expressed in Z-expression as follows,

e ep(z) = z er.z'J + s ep.z"^ + s er.z'^ (32)

b then, if Sp^ and T are given, Qr^ can be solved from eqs. (30), (31) and (32).

7. References

[1] H. Yamazaki, Method of Time-varying Load-calculation of Air Conditionied Room by Use of Frequency

Response, Extra Summaries of Technical Papers of Annual Meeting of A. I. J., 1969.

[2] H. Yamazaki, Frequency Response of Wall and Room Temperature, E. S. T. A. I. J., 1966.

[3] H. Yamazaki, Approximation of Double-Layer Wall Transfer Function, E. S. T. A. I. J., 1968.

[4] H. Yamazaki, Approximate Formula on Transfer Function of Single Wall Surface Temperature on the Side of Excitation as Room Temperature Input, E. S. T. A. I. J., 1967.

[5] H. Yamazaki, Pulse Transfer Function on Analysis of Room Temperature Variation, Technical Papers

of Annual Meeting of A. I. J., Kantoh-District , 1969.

[6] D. G. Stephenson and G. P. Mitalas, Cooling Load Calculation by Thermal Response Method, ASHRAE

Trans., Vol. 73, 1967.

[7] E. I. Jury, Sampled-Data Control Systems, John Wiley & Sons, Inc.

imagery

. X

face temperature

0

1 surPig(l) Heat flow imagery function of a slab

imagery

inside outside

Fig(2) System ol transfer function

of multi- layer wall

692
A Calculating Method for Heating Loads of Buildin,

Yasuaki Nakazavra

Department of Architecture

Kyoto Technical Univercity

Kyoto

Japan

A method of calculation for heating loads of buildings, which are heated ( or cooled ) intermittently, is presented.

This method depends on the Fourier analysis. Then the thermal

properties of the walls are described as the frequency transfer

function, and the outdoor temperatures and the room temperatures are approximately expressed by the Fourier series.

To calculate the room air temperature is not so difficult when the

supplied heat quantity is known, hut it is comparatively difficult

to determine the heating loads of the building which is heated

intermittently

This method is applicable for the above two cases and also for the

next cases.

1. A building is consist of both heated and unheated rooms.

2. Ventilation rates in the rooms vary periodically.

This method is expressed by matrix equations. Namely, rooms of a building are divided into some blocks and the system is expressed

by the tri-diagonal matrices whose elements are consist of the

minor matrices.

If the rooms are laid in the grid type, the system is expressed

by the transition matrices.

Since matrix calculation is used in this method, it is suitable for

computer programming.

Finally, by using this method the heating loads H, which are to be

supplied in the rooms to form the appointed temperatures B , are determined, then the room temperatures 6 are determined for the

obtained H. By comparing e and e ,the usefulness of this method

is considered.

Key Words: Heating loads, intermittent heating, temperature,

Fourier analysis, frequency transfer function, Fourier series,

ventilation, matrix, grid plan, tri-diagonal matrix,

transition matrix.

1 . Introduction

The calculation methods for the thermal environment of buildings can be classified

roughly into the follov;ing tvro kinds of methods. The one is for the problems that the room temperatures are to be determined under the known supplied heats. The other is

for the contrary cases in which the room temperatures are known and the heat to be

supplied are unknown during some time.

Phenomena which we must calculate are generally unsteady. For the phenomena we

have some calculation methods of the v;eighting function ( or inditial response ) which is gained on each v/all. [n,C2] ,C5},C4) , , [7] ,C8)

693
For the periodic states we have also sorae calculation methods of the frequencytransfer functions gained on each wall. (9), (lo) , (l l) , (12)'

As mentioned before, strictly speaking, the thermal phenomena surrounding the

buildings are unsteady, therefore the periodic changes are only approximations of the

phenomena. However, if v;e want the data for the purpose of the thermal planning of the

building or the decision of the "zoning", it seems that the results calculated by the

approximated periodic state meet our needs sufficiently. Moreover, in comparison with

the vreighting function and the frequency transfer function it is more diffcult to

obtain the weighting function for multi-layer wall than the other function. Further

the latter has a big advantage such as we can obtain it exactly.

This paper presents calculation methods for the periodic states in the multi-room

building. The calculation methods are carried in terras of matrices as much as possible.

Namely, at first, the properties of the each layer of the composite v:all are expressed in the "four terminal matrix" . Then the four terminal matrix for the multilayer wall is obtained by connecting the matrices of the all layers of the multi-layer

wall, and from this matrix the "admittance matrix" is obtained.

Next the system is expressed in the three kinds of the matrix expressions by using

the elements of these four terminal matrices and admittance matrices of the vralls.

The first expression is sho\m in general matrix form of the simultaneous equation

whose coefficients are complex numbers. Secondly, the system is divided into some blocks and it is expressed in the tri-diagonal matrix whose elements are consist of the

minor matrices. The third, the system is expressed in the transition matrices.

The second expression needs less amounts of memory of computer than the general

matrix expression. The third expression by the transition matrix is especially

applicable for such problem that we want to know the relations between some two blocks

in a building.

Nov; a method of analysis for intermittent heating ( or cooling ) is proposed.

This method depends on the least squares method. Namely, the time during which

the heat h is to be supplied is divided into n, then let h^ (k=1, ,n+l) be the

heat quantities at the time k. At first the unknovm heat h is approximately

expressed in arbitrary function by using those unknovm h,J, and then the function is

expanded in the Fourier series as following.

h=2(xat.t, h^)cosu;it+x(rbi.^,hJ^)sinaj^t

Then the unknown hj^ (k= 1

, . . . ,n+ 1 ) are obtained by solving the following

simultaneous equation.

where 6 is the given room temperature from time ti to t^ , and is the room temperature which depends on the unknovm heat hj, , However, the number of unknov/ns in the simultaneous equation which is expressed

for a multi-room building generally becomes too large, then it is not advisable to

calculate the equation directly. Then an iterative method is presented as a practical

procedure

Finally the usefulness of the calculation method for intermittent heating is

considered by using the numerical results of an example.

i'

I Figures in brackets indicates the literature references at the end of this paper.

694
2. Notation

j=^/-l symbol of imaginary number

CO angular frequency (hr'')

X thermal conductivity ( W deg"'m' ) c specific heat ( W deg''Kg~') t specific gravity (Kg m"^) a=Vcir thermal diffusivity (m^hr ) 1 depth of wall ( m ) o< transfer coefficient ( W deg"'m'^) r transfer resistance ( deg mfW"')

t time ( hr ) D temperature ( deg ) q, h heat quantity ( W ) Co. , heat capacity ( W hr deg"') c®= @ exp ( ju)t ) complex temperature ( deg ) cQ= Q exp( jiut ) complex heat quantity ( W )

5. Thermal Properties of Wall

3.1. Multi-layer Wall

Relation between complex number heat flows cQo, cQi and complex number temperatures

So, c0i at the surfaces of a wall is expressed as following. (_]'^~)

where the matrix is named four terminal matrix ( or foundaraental matrix), and its

elements are as followings.

A=c oshjg-lc osJgl+ jsinhjglsinjgl ^ 72X^[(^i"^S^ ^°^/Sl+°°shiSl sinjgl)+j(-sinhgl cos^l+cosh/glsiijgU

C=xgj(sinh^l cos^l-cosh/f^l sinjf^l kKsinhJf^l cosjf^l+cosh^l sinigl)}

D = A

(2)

If there is contact resistance r between the walls or at the surface, they are expressed as following. fiB^

A=l , B=r , C=0 , D=l (3)

For multi-layer wall, we have

695
r<e„i =rAn Bk] .... ta, b,"i rso]

(4)

Equation (4) can be written in the follov;ing form.

c9n 'a C0O C D [cQJ

(5)

where 'A B 'An Enl .. ta, Br

D > LC, D,J (6)

If there are heat sources cHt^=H(,exp( jwt ) (k=2,,..n) at the each boundary, eq (5)

bee omes

Q

A B

+ 21 .-^ A, B, Bk

(7)

v?hich nTT

•n TT Ate Bk

A„ B„

1 0

0 1

(8)

However, I will explain for the case, H=0. Each four terminal matrix of v/all

has the next property. (^i?}

A B

C D

= AD-CD =1 (9)

From the property on the product of determinants,

An B A, B,

C, D,

An Bn

Cn Dn

|A, B, ICi D, (10)

Substituting eq(9) into eq (10), we have also the follov/ing property for the

multi-layer wall.

A B

C D

An. Bn Cn Dn

A, B

C, D| = 1 (11)

As an another form of the matrix, we can obtain the following equation by using

eq (5).

696
c9n

Ji^ii Y^v (12)

where Y --^

^" " B '

y AD - CB

Ya, =—= Y.

B ' (15)

and the matrix in eq (12) is named admittance matrix in electric engineering.

It must be noticed that the direction of the heat flov; v;hich flows from the

surface n (or the surface 1 ) to the surface () is determined as the plus direction

for eqs (1),(4),(5) and(7). On the other hand for the eq.(12) direction of heat flow

which flows into the inside of the wall from tt^e surfaces is determined as the plus.

5.2 I'lulti-layer Wall + Semi-infinite Wall

Relation between c&, and cQs which are the temperature and the heat flow at the

surface of the semi-infinite wall is expressed as

(14)

Where

Z = (1-j) (15)

'When a multi-layer wall, vrhose elements of the four terminal matrix are A, B, C

and D, is adjacent to a semi-infinite wall, the relation between cBn, c&s and Jin, cQs > which are the complex tem.peratures and heat flov;s of the surfaces of the multi-layer

wall, are expressed as follov^ing by using eq (6).

tQr. A B

C D

(16)

Substituting eq (14) into eq (16), v;e obtain

= A + B ,q

(17)

697
so that

1 A + 2

TtT^-^'^ ^^^^ Z A + B •

Frora eq (16), we have

d3n= C ces+ D cQs

= ( C+-|-).0, . (19)

Substituting eq (18) into eq (19), we have

ZA + B Z

- ZC + D o ZA + B

= Ym c8,v, (20)

where Y„- ^2,

ZA + B

(21)

4. Heat Balance Equations for A Multi-room Building

Now we obtained the thermal properties of the v/all in the four terminal matrix and

the admittance matrix. By using these matrices the system is expressed also in the

matrix equations.

4.1. Heat Balance Equations for Each Room

Let ki be the room which is adjacent to the room i. When we express the elements

of the admittance matrix of the wall, which exists between the room i ani the room k^,

by Ytei^inYk;-i2.»Yte.~2i and Yr;~xx , the heat flow cQm^tei , which flows into the room i through the wall v/hen the temperature of the room i, ^8; , is zero and the temperature

of the room k; is cQk,, is expressed as follovang.

On the other hand, when Sk; equals zero and c®i is not zero, the heat flow which

flows out from the room i is obtained by

698
And the heat quantity cQ^-l v/hich is stored in the heat capacity of the room i,

Cm-i , depending on the temperature fluctuation is expressed as follows.

cQc~i — Ca-i dt

(24)

Expressing the heat quantity by sign cHi which is supplied into the room i, and

another knovm heat quantity in the room i by the sign cQ; , then v/e have the heat balance

equation for any co , as following.

(25)

By expanding the temperature and the heat into the Fourier series, which have m

terms, eq (25) can be vrritten as following.

m.

If there are ventilations G^(.t) from the room kc to the room i and Gj^.(t; from i to

k;, eq (26) becomes eq (27).

f

[^Hc^i + cQ,.j] =fl(^Jc^,^,o~i +^G;^ (t) + jw^C^.. )cer.i + 2:(Y(,,,.,,).^+6r,,(t))^6j^_J (27)

4.2. Heat Balance Equation of Multi-room Building (1)

( General ^^at^ix Expression )

For the room 1, eq (27) becomes

for the room 2,

for the room n.

Vie can write eq (28) as follov;ing matrix form.

699
(29)

where Aj^ is the complex number matrix which is determined by admittances, heat capacity

of the room air, and where G(t) is time variant matrix determined by the ventilations,

and , ^©.^ are the supplied heat and kno^/m heat respectively.

4.5. Heat Balance Equation of Multi-room Building (2)

( Tri-diagonal Matrix Expression )

When we divide the system into three blocks as shown in figure 1 , for the block

1 the heat balance equations are expressed as follows.

lAii c0i, + ,A,i c0,x + ,Rm cBzi = cHi, + cQii

1A21 c©,, +,A«c®ii + lAj, ,6,3 + |Ri, c0!.i + .R>^ cSii = cHu + cQ,z V

.An c0,a + .A53 c0,3 + iRncOjj = cH,3+eQ,3 J

(50)

Equation (50) is expressed in the following matrix equation.

',A„ ,A,x 0

^

' .©„

~ iR(i 0

^

,A„ ,Aix 1A23 + ,Rz,

. 0 lAjz 1A33, .0 ,Rji,

(51)

In the same vray, for the block 2 the matrix equation is

2.L11 iLi2. 0

^ 0 2L21 iLij

, <0r3 /

'lA,, zAu^rA, iRu zRij 0

0 ^Ri. .R^5, 1032

C033

(52)

and for the block 5,

'?L„ 0

. 0 jLjz.

C0J.I 3A,, jA,. 0

jAii jAzz jAij

0 sAsi 3A33j

' C031

, t033/ . CH33

(55)

Getting together these three equations, we obtain the following matrix equation.

700
'lAii lAii

I All 1A22

1 0 .A„

[2X111 zXlll

,A:

i:

0

0

0

0

1 ,R2I 0 (R32, An zAii r jAj, lAai I

3LII 0

'

0 3L?2j

3A.I 0

0

tl0

.R.

jAiJ

00

00

0 1 jAii jAj3 jAji jAj3

til II f ' n

~1 cyii tQii

fcHail + (34)

vrhere L, A, R are complex coefficients which are determined by the admittances of

the walls and by the heat capacities of all rooms, and Sii is the temperature of the room (i,j), cHJ is the supplied heat, and cQii is the known heat in the room (i,j).

By using the minor matrices A, L, R, 0 and the vector expression, eq (34) can be

described as following.

A, R, L. A.

N +

/ [ 003 J (35)

If there are air flov/s between rooms, eq (35) becomes eq (36).

fA, R, 0 N Az R:. lo L, A3

G„ Gil 0

Gil Gi

Gji G3

f'®0 'cHi^ fcQi>

£ Hi

.C0B . 'HiJ

(36)

Equation (55) and eq (36) are tri-diagonal matrix equations,

be obtained for the general multi-room building.

Same expression can

4.4. Heat Balance Equation of Multi-room Building (5)

( Transition Matrix Expression )

Though it is possible for the general multi-room building to obtain the transition

matrix expression by using eq (56), here I will explain the case of the one-story house

which is built in the grid type. Assume that there are j rooms (j=1,.,,nx) in the

direction x and i rooms (i=l , . . . ,ng-) in the direction y in the house.

The following signs are adopted here.

wall between a room(i,j-l) and a room(i,j)

vrall between a room(i-l,j) and a room(i,j)

floor of a room(i,j)

roof of a room(i , j

)

room temperature of a room(i,j)

thermal capacity of the air in a room(i,j)

supplied heat in a room(i,j)

knovm heat in a room(i,j)

heat flow into a room(i,j) from another room(k,j) when

c@ii.O and c&^^O

heat flow from a room(i,j) towards another room(k,j) when

=0 and c®,^ kO

heat flow into a room(i,j) through wall jXi+i depending on

the room temperatures, tOij. and c&ii.*-\ heat flow from a room(i,j) through wall ^x; depending on

ce.-^ and t^ii-^ t^ii^\2 jYii-^iz elements of the admittance matrix of wall

701
(1) Heat Balance Equation of the Wall x

For each v;all iX^^ the follov;ing equation exists.

Q' (i=l,...,nM) (57)

Expressing as follov/s,

f40

"

0 1

(c

s

0

0 k

7

H- =

0 B

0

Dn

>

(38)

By using eq (58), eq (57) becoms eq (59)

(59)

(2) Heat Balance Equation in the Room(i,j)

The total heat flow c% v/hich flov;s into the room(i,j) is given by the following

equation.

On the room(i,j) the follo\\'ing heat balance equation is obtained.

(40)

X,Hr^. +,Q,, +,H„ +,H?^ = 2:,Q^ +.Qe,.-;

Rearrangeing the eq (41), we obtain the following.

(41)

Hi =2,q;^+.Q4 +.Q..i, -.Q., -cH., -2cH,,

, (42)

in which cQii^ and cH^ are expressed as follovra by using admittances of the wall y,

702
and

cH,^ = Yi^^a c% ( l=i,i+l; k=i-l,i+1) , (43)

(44)

Substituting eqs (43) and (44) into eq (42), v:e obtain the follov.dng equations,

for i= 1

,

for i=2.

cHJ^ =cQ.'^ + (Y.^.„ +Y5,.,, +>Co..,^) c0.; -Y,;.,2C05i -Y.^.^,c0.i - C0., - cH.; V(45)

for i=nj

,

Equation (45) can be ivritten as the following matrix equation.

J

Tj;,jj 0 (46)

where '-i-kk =Yfej-.ii +Yte+,^.ij^ +j'"Ca^|,_^ (k=2, . , , ,n^ -1 )^

(k=2,...,n^) ^

(k=l,...,n3-1).

y (47)

Equation (46) is simplified as following.

(48)

Where

Tj:-i2 ^^*i3

'

Tj'-.i4 Tj^22 T;»2j (49)

703
(3) Transition Matrix Expression

Substituting eq (48) into eq (59), we obtain the follovrings.

_ r(A. +B^T^-, ) c0,-, +B, cQi-, 1 _ [Bi ( cH,.,+ .Q,., ) -

L(C^ +Di T,_, ) ,0,-.. +D, .Q'_, J

I^D, ( .H^.,+ ,Q,., )j

_rA, +Bj Tj_, B,| r 0.-,] +rBj) (-cH^.,

(50)

(51)

By using the eq (51), eq (50) can be v?ritten as,

(52)

Connecting the eq (52), v/e obtain the followings.

For j=T A. B,[(c®»

c, dJUq;

(53)

for j=2 B^ D.J

c n 1 (54)

finally for j=

D

' (55)

In which, let

]V I Ai' Bjl _ fA„ B«7 (56)

704
and

1 0 0 1 (57)

Equation (55) is the same expression as eq (7) for the multi-layer wall which has

the heat sources at all boundaries.

Transition matrix can be v/ritten as follov;s.

{M '4 -

[

ki +BiT/-, B,

Cj +D, Tj-, Dj

_ rk, B^rn 1 00] (58)

If there are no ventilations between the rooms which are laid in the x direction

( direction of heat flov; Q' ), the follov.dng result is obtained.

Aj Bj A, 0 A. . 0

0

IfB,

D, 0 ^

[aXd] - tcJfBj

[a d) - [C B]]

(a D - C b]|

A,D, - Ci B, A,D.- C.B.

0

o

In the same way v/e obtain

So that

= 1 (59)

1 0

= 1 (60)

Aj B, - 1 B,|| 1 0 1

1 dJITj-, 1 1 = 1 (61)

705
The property given by eq (61) is the same of the four terminal matrix of the wall.

By this property it becomes very easy to obtain the inversion of the transition matrix.

Even if there is no x vrall, v;e can treat the system as if there is x wall by

considering an imaginary v/all, v;hose elements of the four terminal matrix is as follows

A=D=1, B=C=0

5. A Calculation Method for the Intermittent Heating

By using eq (29), ^'hich is the general expression for the m.ulti-room building, I will explain the calculation method. Let G(t) be zero. The calculation method for

G(t)=^() is presented in the next chapter.

Since G(t)=0, eq (29) can be written as follov;s.

x[Aji:0j=xj[.H,}4.QOj (62)

Let t the time during v;hich the heat flow h is supplied in the room, dividing t

into m and I express the heat quantity at the time k by h^ ( k=1,...,m+l ).

Nov/ the unknovm heat h is approximately expressed in arbitrary function by using

these unknovm h^ ,and then the function is expanded in the Fourier series as follovring.

h=r(£'a^^j^ )cosu;(,t+ z;(2.'b^^^^ h|, )sinujjt (65)

From eq (63), v;e obtain

cH=2:x(a^.^j -jb^^) h'^ exp(jaj£t). (64)

For each uj^ v/e can v/rite in the matrix form as follows.

[cHj] =z[a^^^ -jb^^i^J h^exp(jtu^t) (65)

Considering cQc =Qeexp( iioet ) and substituting eq (65) into eq (62) we have eq (66),

then by multiplying the eq (66) by the inverse matrix TA,;] ', v/e have eq (67).

e [Aj3[,0e) =:sz[a5^(, -jbi.^,3 h;,exp(ju;jt)+2:[Q^]exp(jw;j^t) (66)

U^l] =f^^l^l h;jexp(jaJit)+r[Ae][Qjexp(ju;gt)

= hw)^xp(ju;^t)+2:[Q']exp(ja;,t) , (67)

706
where

(68)

Let

then, from eq (67) the real function 6j can be written as follows.

9^=n(t,Re^^ cosLOjt-hliL^i, sincojt )h|^+ ^jcos oogt- sinoogt (69)

Let 6 be the given temperature from time ti to tz, then the unknovm heat

quantities h^ are obtained by solving the simultaneous equation which is gained by the

following equation.

9 -J(©-|

e/dt= ^|l.®"ft^'^ kRj-f^'COS wjt- i;[j^^'Sinu;jt)h>^R5Cos«jjt-<^I^sinu;^t|dt

=

j |^^|e-s:Cz(^Rj^^-cosu;jt- J^^i^.sinujjt )h'^'+ ^R^cosu^^t- .^Ij sinu>jt)| Jdt

"t| ^ ^ = 2 jp-z 2(tiR5^^. cosujjt- i^IiL~te'Si^'^4*)'^te'+'^f^?°°S"^e*~|I(i sinu^^tj

x[ i:(KRt.^„ coscojt-i^I^^^^ sinu5^t )jdt

= 0 ( k=l, • • - ,m+l ) (70)

6. An Expression for an Iterative Method

The number of unknovms of eq(70) which is expressed for a multi-room building

generally becomes too large, then it is not advisable to solve the equation directly.

Moreover for the case G(t)#0, it is very difficult to obtain the analytical

solution for eq (70). Then, here, as a practical procedure an iterative method is

explained.

We write again eq(29),

^{[aO +(G(t)]j j;,ej= ^{(cH,} + isi,]] (71)

Divide the matrix (A^] into the two matrices as follows.

707
' -^l-ii ^l^a • ^t-ll ^t-li h-ii ^s-ji ^t~i3

Ao,

L

:

'. 0

(72)

The first terra at the right side of eq (72) is a diagonal matrix and the all

diagonal elements of the second matrix are zeros. Substituting eq (72) into eq (71), v/e obtain

2: 0 Ae.iz G„(t)

= z (75)

The iterative procedures are carried as follows by using eq (75).

Procedure 1. Let the mean ventilation rates be the approximate rates, and then

assume that the room temperature to be determined is equal to the adjacent rooms. By these approximations eq(75) becomes the follov/ing.

''Aj^i +G,

= Z. + z.

{ a (74)

in which

and T is the time of one period.

Gi =

(i=1,...,n) ,

^Jj-^]G,-^(t) dtj (i=l,...,n) ,

(75)

(76)

Thus the coefficient matrix of eq(71) results in the diagonal matrix, then we can

obtain the each room temperature and heat to be vSurpclied in each room independently

by eq(74).

After the procedure 1 , the follov/ing procedure is repeated untill v/e obtain the

satisfactory results.

Procedure 2, Let the temperatures ©• obtained already be the temperatures of the

adjacent rooms and assume that the matrix G(t) is multiplied by the temperatures 0'.

By this procedure eq (75) becomes eq (77).

0

A«^n + +

)

I -G(t) (77)

708
In eq (77), the^ vector c&' is knovm, then we obtain the follov/ing.

0 = H +

0"

Q"

= 11 +

1

(78)

where

and

Qir

Ac.

r a' ^

0"

-G(t)

.Qa.i = cQiM + cQt.c + ^Q^l; (i=l,...,n)

(79)

(80)

Equation (78) is also the diagonal matrix, so that we can determine the unknown

heats to be supplied and the room temperaturs of the each room independently. We repeat

the procedure 2 untill 0' becomes nearly equal to @.

7. An Example

An one-story concrete house vras taken as an example ( figure 2), and the following

quantities were calculated.

1. The room temperatures 9n, which are formed when the outdoor temperature (i=1,

...,6) are those as shown in figure 3 and there are no supplied heats in the house.

2. The heat quantities H,v7hich are to be taken off from the rooms to form the room temperatures excepting corridor in 25°C from 9 am. to 5 pm.

5. The room temperatures 6c, which are formed when the heat quantities H are taken

off from the rooms excepting corridor.

For numerical calculation temperatures and heat quantities were expanded in the

fifteen terms Fourier series ( w, , co^, u?,, . . . ju;,^)

Unknown heat quantities H v/ere divided into five parts and approximated as the

broken lines respectively.

The sol-air temperatures 0j-£(i=1 , . . . ,6 ) in the figure 3 act against the east, the

west , the south, the north walls, the roof and the floors respectively.

The results of calculation are shown in figure 4.

It needed four times calculations for each room to obtain the satisfactory result.

709
8. Conclu'5ion

By using the frequency tran??fer function, three kinds of matrix equations whose

elements are complex v/ere expressed for the multi-room building.

The first one is expressed in the general matrix form of the simultaneous equation,

the second is the tri-diagonal matrix equation v;hose elements are consist of the minor

matrices, and the third is the transition matrix equation.

The tri-diagonal matrix expression reqires the less amounts of the memory of the

computer than the general matrix expression. The transition matrix expression for the

building is similar to the four terminal matrix expression for the wall. Therefore we can say that the four terminal matrix is only a special form in the transition matrices.

This expression is especially usefull when we vrant to know the relations between

some tv;o blocks in a building.

It was introduced that the determinant of the transition matrix is unity as same as the determinant of four terminal matrix. By this property that the determinant is unity

it becomes very easy to obtain the inversion of the transition matrix.

A calculation method for the intermittent heating, depending on the Fourier

analysis, vras presented.

As the practical procedure, an iterative method vras proposed. For an example

at first the heat quantities, v;hich are to be taken off from the each room to form the

predetermined room temperatures, v;ere determined, and then the room temperatures were calculated for the obtained heat quantities.

As shoTM in figure 4 arround 9 and 17 o'clock there are comparatively large

differences between the predetermined and the determined temperatures, but at the most

of the time they are in good agreement.

Of course more detailed research is necessary for the method proposed in this paper,

but from these results it seems to be quite all right to consider that this method is

useful for the some problems such as the thermal planning or dicision of zoning.

9. References

( 1] Maeda,T. Theory on the room temperature variations. Trans, of Architectural

Institute of Japan (A.I.J) April 1941 (in Japanese)

L 2j Maeda,T. Theory on formation of the predetermined room temperature variations,

Trans. A.I.J. Sept. 1956 (in Japanese)

[ 3] Fujii,S. Temperature variation in the concrete buildings, Trans. A.I.J. No. 65

Oct. 1959 (in Japanese)

[ 4) Hasegawa,F. Analysis of room temperature. Trans. A.I.J. No. 64 Feb. 1960

(in Japanese)

[ 5] Akioka,M. The theory of transient room temperature for intermittent heating,

ventilating and air conditioning, Journal of the S.H.A.S.E. Vol.41

1967 (in Japanese)

[ 6J Ochifuji,K. Analytical method of transient room temperature in multiple rooms. Technical Report of Hokkaido Univ. Vol.46 1968 (in Japanese)

[_ 7j Aratani , Sasaki and Enai, Successive integration method for the analysis of room air temperature or thermal load variations, Technical Report of

Hokkaido Univ. Vol.51 1968 (in Japanese)

[ 8^ Nakazavra,Y. A calculation method for room temperature, Trans. A.I.J. , Extra, Oct.

1969 (in Japanese)

C 9] Maeda,T. A calculation method for periodic room temperature variations in the

grid type building. Trans. A.I.J. NO. 49 Oct. 1954 (in Japanese)

[10} Eguchi,K. Theory on the room temperature variations and heating loads. Trans.

A . I .J . ,Extra , Aug, 1969 (in Japanese)

[1 1} Yamazaki,H. A calculation method for heating loads, Trans. A .I.J. , Extra, Aug, 1969

(in Japanese)

(12} Nakazav;a,Y. Theory on the room temperature for intermittent heating, Trans, A.I.J.

Extra, Aug, 1969 (in Japanese)

(15) Carslaw and Jaeger , Conduction of heat in solids, Oxford, 1959

710
(1.1) ROOM (3.1)

(1.2) (3.2)

(2.2)

(1.3) (3.3)

BLOCK1.BLOCK2.BLOCK3.

Fig 1 Block Plan of a Building

N

5M 5M ' 5M

1

1

ROOM

2 3

(

CORRIDOR

6M

3M

2.5M

Fig 2 Plan and Section of a Model Building

711

713
1
An Bxample of Heating and Cooling Load Calculation Method

for Air-conditioning of Building by Digital Computer

Shoichi Kuramochi

Taiaei Construction Co., Ltd., Tokyo, Japan

Today, many air conditioning engineers recognize that the actual load for air

conditioning system can hardly be achieved by the conventional heating and cooling

load CEdculation method. In 1966, the author worked out a load calculation system,

in which the numerical ceilculation method was adopted to solve the problem on heat

transmission, and has finally perfected this calculation system for actual use

quite recently. The characteristics of this calculation method can be summarized as follows: The air conditioning system in Japan is in majority operated intermittently in a day and quite particular phenomena appear during the early hours after

the commencement of operation and right after the termination of operation. These

phenomena are caused by the transition of heat retained by the building and air

conditioning system as heat capacity. The calculation method worked out hais advantages over the others in representing the phenomina mentioned. To be more

specific, while any physicail system doesn't particularly need to be conditioned

linear or invariable for calculating heat transmission, the storage heat load can be accurately ccQculated by use of this calculation method. Moreover, this calculation system is marked by its reliability in securing an accuracy within the allowable degree for load calculation. It also permits easy understanding for the practice engineers in general, hence it will be widely useful for the professional

engineers. Improvement and modification to this calculation system can be also

made without much difficulties. This calculation system is mainly composed of two

parts, namely,

1, the calculation for obtaining the outputs of the heat source equipment

of air conditioning system, and the heat transfer rate of thenml medium

transportation syston and the changes of room temperatures, and

2* the calculation for the heating and cooling load changes in the airconditioned rooms.

In the text of this report, the equations adopted for this calculation are

firstly illustrated, then the formation of the calculation system is explained in

detail and lastly the results of the calculation made for the model building in ex- istence are checked and assured by carrying out the actuail meeisurements and by com- paring the measured values with the values obtained by the cetlciilation syst^.

Key Words: Computer, air conditioning, heating load, cooling load,

numerical method, room temperature, medium temperature, simulation,

radiation, meeisurement, intermittent operation, evetluation.

1. Introduction

The heating and cooling load of air conditioning is a heat that changes temperature and humidity

in the room being air-conditioned, other than produced by an air-conditioning syst^. It occurs in the

form of an external heat invading the room or an internal heat produced in the room. The heat from the

air-conditioner absorbs this heating and cooling load, thereby maintaining the temperature and htunidity

of the air in the room at a required level.

13ie calculation system that will be referred to in this paper is composed of the following two

principal parts:

1 Mechanical Ikigijieer

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(l) Calculation of heat transfer and change in room air temperature relative to heat source equip- ment output and heat medium transportation system.

(2) Calculation of change in the heating and cooling load in the room being air-conditioned.

This paper will deal with the subject, starting will the details of the calculation system. Then, the result obtained from the calculation upon application to an existing building will be compared with

the actual measurement data to confirm the exactness of the calculation. First of all, the features of

the calculation system will be explained:

(1) The system gives a relation between cooling and heating load Q(^) and output of air-conditioning heat source Qjj3(^)t therewith enabling calculation of the room air temperature ^j(^) under an es- tablished condition.

Despite the fact that air-conditioning systems are operated intermittently in many cases in Japan,

thermal changes at the early stage of operation and after the operation have not been much regarded. By

the said calculation system, such changes can be clairified.

(2) A relation between the time tj^ required for room air temperature d-. to reach a predetermined

level after the air-conditioning system starts operation and the capacity of the air-conditioning heat source Qg^^j can be obtained, thereby permitting reasonable design of heat medium transportation systems,

(3) The calculation system deals with heat transfer by a numerical method. Cl»2) This elimi- nates the need for any linearity or invariability of the thermal system and permits calculation independent of such changes in heat flow and temperature. Also, the calculation system is easy for practiced

designers to understand, and caji be applied and improved without difficulty, thus offering wide use by

professional designers.

(k) In making up the calculation system, approximation methods of new concept have been introduced; (a) Simulation of the heat medium transportation system in the air-conditioning system, (b) simulation of radiant heat trainsportation in the room, and (c) simulation of heat exchanging in the airconditioning system.

The heating and cooling load in the room being air-conditioned is defined as a heat in a give-andtake relation with the room air, where the heat causing the room air temperature to increase is expres- sed as "positive" and that responsible for the decrease as "negative". Other definitions necessary in the calciilation will be given as required.

2. Principal Equations Adopted in Calculation System

2.1 Ebccitations

Excitations are used as ain input factor to achieve the calculation, which can be obtained by means of necessary relative formulae available from the design condition data. These formulae are prepared as subrutine. While the design condition involves solar radiation, sky radiation, other effective radiations, atmosphere, humanbody, animals, lights and heaters, their relation with the excitations directly

related thereto has been well known.

2.2 Numerical method of heat tremsfer

(1) Fundamentail equation of steady state heat transfer (2-dimensional)

K = . \ ...(1)'

d

where, Q. .: Rate of heat flow from point j to adjacent point i, d: Divided dimensions (see

figure 1), (^j^"'^.: Temperatures at points i and j. As Thermal conductivity. Assuming &2*"'

to be the temperatures at points 1, 2,... and to be the rate of a heat flow to point 1, we nave.

1 Figures in brackets indicate the literature reference at the end of this paper.

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...(2)

For the steady-state heat transfer, the left member of the eq (2) is zero.

(2) Fundamental equation of unsteady state heat transfer (2-dimensional)

C = c.r.d^ ...(3)

a. At P-—5- ...(6)

d*^

d.o< N = ...(7) X

where 6-^ : Temperature at point 1 after time interval of dt, a: Thermal diffusivity, C: Heat capacity of element volume, c: Specific heat, f: Specific weight. At: Time interval, o(: Heat

conductivity.

The various equations of heat transfer to be produced by the above fundamental equation and the

traditionsQ. equations will be illustrated in appendix.

(3) Temperature variation in thermal medium transportation system ( 5)

With a tube as shown in a figure 2 (1) considered to be a model of the thermal medium trainsportation tube, it is assumed that the surface of the tube is insulated, and the temperatures of the tube and

thermal medium are equal at auiy contacting point and time. Next, chainges in temperature with time at respective points as shown in figure 2 (2) where the medium temperature is changed in step order as much

as aO"^ in the transportation system maintained at a constant temperature are replaced by lineair changes

as shown in figure 2 (3)1 and it is assumed that Q'^ changes at a uniform rate during the period of 2m1.<3t to reach a final level, 0'^ corresponding to &^ that freely changes can be obtained by the following

equation.

2m1 2m1-m+1

'^2(n.dt) = '^I(n.4t-2m1./lt) ^ ^^1 f(n-2m1-«i-l)<lt} '"^^^

m=l Eral ^

c.r.v.at

•••(*})

where, ^-i/j^ 4t)' Temperature of medium fluid at inlet of system at time n.At, Q-^/ ^At)' Temperature or medium fluid at outlet of system at time n,At, AQ'.f Temperature dltrerence at

inlet during At at time n.At, n, m: Number showing time by multiple of dt, f: Total heat capacity of

transportation system, p, v: Flow rate of medium fluid, c: Specific heat of medium fluid, IT

Specific weight of medium liquid.

When ml is under a relation of 0,5<m1 <1, it is regarded as 1, and if under a relation of ml^l,

an. integer closet to the actual value is employed. Especisilly when m1<0.5j 6'^ is always considered

equal to 0- t This means that the effect of the heat capacity of the system is to be taken into account

when it isT.arge, and such effect may be ignored when small.

3. Change in Room Air Temperature and Heat Medium Transportation System

The calculation system dealt with in this Section takes the heating and cooling load Q as the input

data, thereby computing the output of heat source equipment Qjgg and the change of room air temperature

ftj^. Calculation system concerning Q will be explained in Section 'f. Between the two calculation

systems for S'.^ and Q, input and output must be exchanged to carry out the calculation. The heat produced

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by the heat soiorce equipment is carried into the air-conditioning room by the transportation system, and

the heating or cooling load is carried into the heat soiirce equipment by the same system. These heat

transportation phenomena are under the influence of: (l) Heat capacity of the transportation system

plus heat medium, (2) Thermal load caused by trainsportation equipment power, and (3) Heat from outside

of the transportation system, whereby the thermal characteristics of the transportation system will be

formed. In addition, the air-conditioning system is provided with automatic control unit. With these

factors, an air-conditioning process system will be made up under restrictions by the design requirements.

In this Section, assuming a simple basic model as shown in figure 3 further explanation will be

made.

3.1 Conditions for design calculation

Principal control values for the air-conditioning system include (a) room temperatvire (b) chilled or hot water temperature &»vlmand (c) conditioning air temperature ^fim* As restrictive conditions,

there are (a) capacity of heat source QRBm» (b) flow rate of chillied or hot water p, (c) flow rate of

air-conditioning air v^, (d) volume of outdoor air induced Vq, (e) time required for room air temperature to reach a stable level at early stage of operation t^, (f) time required for heat source output to reach a stable level at early stage of operation t-| and (g) time required till complete elimination of

heat source output after operation stop t^.

Figure k shows the changes in Q andS-^^ at early stage of operation, and figure 5 indicates

their trend of subsquent changes after operation is over. The control values and restrictive conditions

are applied as design requirements together with outdoor and indoor conditions.

The changes in at early stage of operation and after the operation is over which are given as the characteristic of the heat source equipment, can be regarded as linear cheinges in the case of

ordinary refrigerators and boilers, and thus are treated as a certain restrictive factor. Assuming

n-| = t-|/4t, and ^jsm = maxioua heat source output, we have /3Qgg = ORBn/n^ = constant at early stage of

operation. If n is between 0 and n-|, this equation can be rewritten as

n.Qi•RBm

^EBCn.iflt) ...do)

Also, assuming that the time to stop operation is t = 0, and n^ = t^/4t, the following relation can

be obtained if n is between 0 and n^

^^5

In addition ^ variables necessary for the calculation, such as; W-|: Total heat capacity of supply

system of cooling or heating water, Total heat capacity of return system of cooling or heating

water, f^: Total heat capacity of supply air duct system, V: Volume of room, c.T. V(l+(5): Total ef- fective heat capacity of room air, Bi Additional coefficient of heat capacity of room air must be as- sumed for calciilation.

Initial conditions are related to the thermal state of the air-conditioning system at the time of commencement of the calculation, and may be assumed through engineering judgements guided by location of

building, data, time, thermal characteristics of building and system, and statistical data.

Now, assuming that O'q is outdoor air temperatiu:"e , $-"^ is return air temperature at the inlet of

heat exchanger, and 0-^^ is mixed air temperature on the side of the heat exchanger, $'^2 ^® obtained

from the following equation.

(V - V ) S-". + V (9- /I - 1 O 1 0 0 V Jowg asj

Slight errors in assumed values for the initial condition are negligible as^subsequent input data

are correct, because the calculation system itself has convergence and if the time to start calculation

is advaince.

3»2 Variation in room temperature

Variation in room temperature is obtainable by the following eqxiation.

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e-iCn.dt+zlt)- ^i(n.4t) -^^^Kn.^t) = '^Kn.^t) c.r.V(l+p) "

where, QfiBCn.^t)' Rate of heat transported from air conditioning system to room at time n.4t,

^(n./lt)* Heating or cooling load in room at time n.4t,4%(n,dt) • Difference in room temperature

between dt at time n.dt. And if the supply air temperature at diffuser at time n.^t is 6^"fi(n.4t),

Wdt) = '=-^-^t^'fl(n.4t) - «^i(n./lt)^

According to the equation (l'+), it is noted that the room temperature at time (n.^t + i^t) is ob- tainable from respective values at time n.4t. This fact is of great significance for the subsequent

calculation. Apparent variation in retained heat of room air relative to changes in room temperature

at the early period operation from 0 to tl^ is given as, % = o.rM^.^)l\^^^^^^^ - 0-.^^} ...(15)

where ni^ = ti^/At» The decisive factor for the change in room temperatiire where the absolute value

of Qy. is smaller than that of j^'Qj^dt is a balsincing relation between Q and Q"'hb. With relative

increase in Q^., however, its effect on t/^ can no longer be ignored, and must be given due consideration

in selecting the value of Qggp.* At the early stage of usual intermittent air-conditioning operation,

the maximum output of the heat source equipment is required, aind Qjjan '-^ often determined by setting t^

at a required value. The relationship between ti^ and Qrb,^ ^® obtained. Today, there is no better

way than a trial and error method to find the relationship between t^^ and Qrbdi*

3«3 Heat exchanger

Air must be used as final thermal mediijra when heat produced by the air-conditioning system is transmitted into the room. Heat exchangers of the air-conditioning system in general use today employ

water as primary thermal medium and air as secondary thermal medium, excepting heat exchanger for heat

source equipment. The capacity and service condition of the heat exchanger are subject to the related

design specifications. In order to quantitatively find the cheiracteristics of the heat exchanger under

other service conditions, it is necessEiry to incorporate complicated characteristic relationship as it

is into the calculation system. This, however, is so intricate to deal with that a practical simple

method will be employed here.

General usage and performance of the heat exchanger most used recently are as follows, with the flow rate of air v-| passing through the heat exchanger considered invariable, chilled or hot water at an

almost constant inlet temperature fi'''^-]ni is supplied by controlling its flow rate p by means of a two-way

or three-way valve. Assuming the return water temperature to be l^'^2» rate of exchanged heat is ex- pressed as p (^'^^ - &\2)* This formula is equal, whether two-way or three-way valve is involved.

If the air temperatures at the inlet and outlet of the heat exchanger are

'^fl' ^^^pectively,

the corresponding enthalpies are and i^, and the latent heat load to be eliminated is'Qj^, the rate of

exchanged heat is had as follows,

While the values of ^'^g ^f? established spontaneously during the air-conditioning operation,

(9''^-juj stnd

©f-ijjj sei^e as control values. Design values p and v^, therefore, must be adjusted so that these control values may not be exceeded even under the maximum air-conditioning load.

Taking for example a cooling operation to simulate the action of this heat exchanger, the mutual

relation with temperatures is shown in figure 6. In figure 6 a relationship under maximum load is

given, where the value of c/a is assumed to be invariable under medium load shown in figure 6 (2).

Under this relation, a = &^2 ~ l^'wl' ^ = *^'w2 " ^'w1» ^' = C ^'w2) " "S^'wl and c = ~ (P-fi. The difference between G-'^2

'-^'w2'' *° correspond to the latent heat load Ql. The relation between c and b

is at given by the equation (l6). The value of a becomes maximum when the load comes to the maximum, at which point, it is necessary not to overestimate the value ofQ-j^.

The values of ^'-^-^ and ^'^2 ohtained from this simulation are not equal to those actually measxired. But what is actimlly needed is the difference in temperature (&'^2 ~ ^'w1^' thus if near actual

values are desired, they can be obtained by comparing the value of with and adjusting (9-^2 as

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much as the resultant difference.

Simulation of the automatic control performance at the early stage of operation is achieved as fol- lows: The value is changed toward the predetermined veilue of 6'f-iq,t ^'^Q^g increased till 9-^ reaches its predetermined value. WithQgj^ reaching Q jj3[j , this state is maintained. After the room temperature reaches the pre-determined level, the difference in &--^ corresponding to the load variation is feed back to the heat source side with the medium temperature and (9''^2» thereby controlling the out- put Ogg.

The thermal relations in the heating operation C£in also be established merely by reversing the symbols for temperatures and heat given above.

3.^ Calc\U.ation of thermal relation in air conditioning system

Figure 7 shows a thermal relation in the air conditioning system based on a simulation model shown

in figure 3» and the calculation procedure to obtain various values. To simplify and smoothly eccomplish

the cailculation, some assumptions are set as follows:

(a) Time required to transport heat medium is ignored.

(b) External heat load invading the heat medium transportation system is proportional to the heating or cooling load (this is obtainable by calculation as required).

(c) This calculation system includes no exact calculation method for relative humidities. Thus,

the relative humidity of the air in the room is considered always maintained at 50^.

(d) Room air temperatures within one calculation unit (will be referred to later) at same time are all equal.

(e) Calculation is carried out at each step of time interval ^It. The calculation at t = n./dt + ^t

subsequent to the completion of the cycle of calculation at desired time t = n.dt is started with room air temperature

^ ^^y

(f) As shown in figure 7, calculation is csirried out in the order of room temperature, return air

duct system, return water pipe system, supply water pipe system and supply air duct system, followed by

calculation of room air temperature with time advanced as much as ^t.

(g) Although the heat flow of the cooling or heating load is reversible, the flow of heat trans- ported by the heat medium transportation system is inreversible.

(h) The temperattires at various points of the air-conditioning system are calculated by the use of

known related temperatures obtained when time is most advanced, sib a general rule.

Today, these assumptions are within the permissible range of the overall calculation accuracy.

The following will outline the transfer of heat in the air conditioning system step by step.

(l) Return air system

The return air temperature changes with changing room air temperature. Assuming change in return

air temperature between times n.4t and n.^t + 4t to be 4&'^(n.4t), it can be expressed as follows:

^'i(n.At H-Zlt) = ^'tinU^t) ''^'^'i(n.dt) ...(17)

Suppose that the return air inlet temperatiu^-e (9-*i(ii,^t +4t) changed to &"i(n,^t + 4t)

outlet* This temperature chauige can be caused to occur by external heat q^^ invading the system and the heat capacity of the return air system, A relation between and (9"^ can be obtained by the following

equation, using the equations (8) and (9), with qj^ token into account.

2m1 2m^-m^^ ^f2 ©-"Kn.dt+dt) = ^'i(n.^t-Hlt-2m1.At) * ari* ^'^'i{(n-2m1-Hn)4t} * ^TTtIT^

'"^'^^^ m\ = i^/ dC^.^Z-df) •'•(19)

The temperature of a mixture of this return air and outdoor air is obtainable from the equation(l2).

(2) Return water system

According to the given order of calculation in this paper, the calculation now comes to the return

720
water system at time (n.^t +4t). As shown in figure 3, the system contains a water pump, where the

flow rate of water is p, water temperature at the outlet of the heat exchajiger is water temper- ature at the inlet of heat source equipment is ^,,2* also assumed that all the thermal changes

caused by the air at the inlet of the heat exchanger will be taken over by the return water system, which

will join the effects dependent on the rate of invading heat q^, power load of the pump %i|fp and heat

capacity of the system in the return water system.

The effects of the mixed air will be taken over by the equation (l6), and by applying equations (8)

and (9) to the above changes, the water temperature at the inlet of the heat source equipment

frw2(n.4t + 6t) ^® obtained as follows:

n' J. 2m2-m+1 / "^2^ ^*^lt4- Con") ^w2(n.4t+dt) =^w2(n.At+4t-2m2.4t) 2in2 '^'^w2{(n-2m2-Hn)4t} 5

...^^u^

m2 = —r ...(21) p.4t

where ®'w2' ^w1 l9'|-| used in equation (I6) are values expressed at times (n.4t +4t)

and n.&t, respectively.

(3) Supply water system

Thermal chsuiges in the return waters system are carried over into the supply water system. The

heat source equipment is located between the two systems sind is subjected to the change in temperatxire

depending on the output Qjjb* Assuming that the water temperatures at the inlet and outlet of the heat

source equipment are & ^ and the relation ofQjjgwith them isQog = P^^„i ~ '^'=2^* ^^^^ ^Vil assumed to be the water ?emperature at the inlet of heat exchanger and temperature chauige caused by heat

invading the system q^-| taken into consideration, 0'\-\ can be expressed by the following equation in the same meinner as above.

^wl(n.4t+4t) ='^wl(n.4t+4t-2m3.4t) * ^£3 ^^wl(n-2m3-Hti)^]t ^"T"^^*

...(22)

m3 = ...(23) p.4t

(4) Supply air system

Thermal changes in the supply air system are taken over by the supply air system via heat exchanger.

Values for

(5^f2» ^\'] ^' 2 ^® ^'^^ measured at time (n.4t +zlt), as well as In the supply air

system is provided a fan. JLssuming that the air temperature at the outlet of the heat exchauiger is &f^i

average temparature of the diffused air is power load from the fan isQj^mjp, and heat invading the system is qj.j i we can obtain 9"^^ by the following equation in the same manner as above.

Ai. XI. ^ 2m't-m+1 , ... ^ fl(n.4t+/lt)= ^fl(n.At+4t-2m4,At) ^. 2mk ^^fl{(n-2mif-Hn)Zlt} ^ c.r.v,

•••^^f;

ra=1 ' ' 1

f1 c.Jf.Vj.At

m'^ = " ...(25)

The four systems mentioned above are connected by (a) air-conditioning room, (b) the heat ejcchanger for air-conditioning and (c) heat source equipment. The performance of these connected systems and heat

medium transportation system will serve as various basic components of an air-conditioning system. Also,

the air-conditioning system is available in other types using boost heater, dual duct system, three or

four piping system, etc. These cases can be handled in the theoretically same manner asQrvg ^^^vmt

where subrutine is prepared for the calculation. By the combination of VEirious basic models and subroutine as required, various types of air-conditioning systems and associated heat medium transportation

systems can be made up.

't. Heating and Cooling Load in Room

When the material of wall surrounding the room, dimensions, position and service condition of the

room, atmospheric condition and initial condition are given, and room temperature and humidity are

designated, the heating and cooling load tends to be determined. In this Section, the calculation

721
systftm whereby the trsuismitting course and thermal rate of the heating and cooling load can be obtained

will be explained.

4,1 Preparation for calculation system

(1) Calculation unit and area element

Unline the conventional method to calculate the load per each room, the calculation system being

referred to in this Section is such that a plurality of rooms that little differ in temperature and are considered equal in temperatiu?e variation during the calculation are dealt with in one calculation unit*

In case one room has two or more typical temperatvires, as many calculation units as the number of typical

temperatures are provided in the building. Thus, while the calculation unit has something related to the concept of zoning, it still depends on the typicsG. room twnperatures. Practically, rooms where the temperature difference is always within + 1.3°C may be regarded as one calculation unit.

Heating or cooling load in the room is obtained by the calculation of transient heat transfer phenomena, except convection heat transfer, draft and latent heat that are directly obtainable. When the room air absorbs the heating or cooling load, its temperature changes at a rate dependent on its heat capacity. As the heat capacity of this room air, an apparent heat capacity c.r.V(l+^) is used. Walls, floor

and ceiling forming a room play a leading role in the transfer of heat, radiant heat that has invaded the room cannot become a load without having been absorbed by the solid objects in the room.

The transmission course of the heating or cooling lead is formed as a thermal system chiefly by the

siorrounding structural objects, and its thermal characteristics depend largely upon the construction and

composition of the structual siu-roundings , the load phenomenon occurs in largely different manner depending on whether the glass window is wide or narrow, or whether a cvirtain wall or concrete wall is used.

A calculation of heat transfer does not necessarily require simulation exactly to the thermal con- position of the room, in this calculation system, the areas of structural objects equal in heat transfer

phenoemonea are totalled for ceG-culation and the results are proportionally divided per area. These area are called area elements for calcxilation.

(2) Thick wall and thin wall

Oistufbances with large changes are caused by the external atmospheric condition, and response depends on the properies of the outer wall. To estimate the rate of heat transfer ftom the wall body,

thermal transmittance or thermal conductivity is used. The rate of temperature changes inside the solid

can be determined according to the thermetl diffusivity. The wall bodies are available in many types,

such as concrete wall having a heat capacity with property of heat insulation, metal panels having a low

heat capacity with poor heat insulating power, a combination of metal panels with heat retaining materi-

£l1 that is low in heat capacity yet has proper heat insulation, and glsiss plates that let radiant heat

penetrate through.

These wall bodies are classified by hsat capacity per unit area, according to which those high in heat capacity are ceLLled a thick wall and those low in heat capacity are called a thin wall. The relation expressed by equation (6) is referred to for practical classification, irtiereby the divided measure- ment "d" relative to divided time^^t is determined. Accordingly, the wall whose thickness is divided

into two or less portions is called a thin wall, and that with three or more divisions of its thickness

is Cfdled a thick wall. For the calculation on the thin wall, equation (1) or CfS) is applied combined

with such an expedient as including part of the heat capacity of the wall body in that of room air.

k,2 Course of heating or cooling load

The calculation of heating or cooling load in the room is aimed at clarification of the quantity of

heat transfer through the analysis of the transfer course of the heating or cooling load. The flow rate and direction of heat always involves the temperature gradient on the course according to Fourier's low. With a temperature change of the heat medium on the course, the rate of its retained heat increases or

decreases, and this behavior of the heat has an important bearing on the load. Kink of disturbance and

intensity of the heat flow are given as the design considerations, and various eqviations shown in the

ftJsJseTvdiX ^® applied for the calculation of heat transfer inside the building. The application of

these equations is very simple, and will be outlined below in connection with the points particularly

considered in this calciilation method.

(l) Heat transfer on interior structural bodies

The room has many pillars and beams in addition to the walls. While these structural bodies do not serve very much as the course of the external heat, they release or absorb the retained heat with changes

in room temperatiire. Also the surrounding wall has a rugged surface, which has a similar thermal action. To compensate for these thermal actions, subrutines by the application of equations (5) and (36) throu^

722
(38) are prepared.

(2) Badiant heat transfer in the room

Let us aBsiune a film at the boundary dividing the exterior and interior structurEil bodies. This

assimied film represents a surface condition of the interior structual body, smd its surface temperature

(MET) is S'jj^ = § Aln^ ^In/§ *In* effective radiant heat transfer between the external surface and

the film can be obtained by equation ik2). If there is no marked temperature difference over the entire

exterior structure, its average temperature (MET) is = §

A^^X ^qx/^ f^n* radiant heat transferred to the assumed film from the exterior can safely be considered to be received evenly by the whole

surface of the interior structitre.

(3) Radiation from interior heating bodies

Interior heating bodies are available locally and in the objects evenly scattered on the floor,

such as human bodies and lifting equipment. In the latter caise, radiant heat is emitted evenly to the ceiling and floor.

k,^ How to set up load variation calculation system

To achieve calculation by cc»nputer, the design conditions and area element per room are applied as

input data. Of the results from the calculation, necessary data are taken as output, and expressed with

a proper time inteirval. The calculation system must be ready to tsike all kinds of possible input date

conditions. If any special conditions occur, and the system is not prepared to permit their application

thereto, an approximation method is emplyed in a form close to the existing method. If the effect of

the approximation is not permissible, then the calculation system itself must be improved for higher accuracy. Such instances often occur in respect to multi-layer wall, or when the air-conditioning room is

adjacent to a room under special condition.

3. Example of Calculation

The calculation system being dealt with in this paper is based on the simulation of a air-conditioning system, and is a computer program intended to obtain design data. The details of the setup, however,

are the questions directly related to the programming, and thus are omitted in this paper. Already, this

calculation method has provide to be able to provide permissible calculation data upon application to several existing buildings and comparison with actual values. The following is an example of the practical application.

3*1 Application of calculation method

(1) Preparation for calculation

Prior to calculation, the air-conditioning system is determined. Then, input data are prepared

from the related materials. Since the capacities of the associated equipment are unknown prior to the designing, they are estimated from the actual statistic values. The capacity of heat source equipment

for intermittent air conditioning <^ian ^® obtainable from its relation with the time required to stabilize the room air temperature ti,,, and accordingly values for p and v^ can also be determined. For the operation of the calculation system, engineering decisions, such as initial conditions, are required.

Various values estimated at first are corrected to proper values upon investigation of the calculation

results, and are recsilculated if necessary. For example, the temperatiire change in room air temperatiire

in the adjacent part that will not be calculated is assumed and if this aissumption is found far different

from the calculation result obtained later, the calculation is repeated from the beginning.

(2) Application to building ( 6)

Location: Tokyo. Name: 0 Building. Purpose of use: to provide office spaces. Construction:

SRC (curtain walls used as outer walls at the south and east sides). Scale: Nine storied, 3 basement

floors and 3 penthouses. Total area: 7,260m2. Air-conditioning area: 3,400m2, Operation: Intermittent (8:30 to 17:30).

The application of this calculation method to the air conditioning of this building was attempted.

In this application, actual values were emplyed, instead of exterior and interior design conditions.

For the air-conditioning system, the model shown in figure 3 could be applied as it is, and the calculation was carried out in one calculation unit.

723
(3) Results of calculation

By this calculation method, the temperatures and heat flows in the building and at the respective

components of the air-conditioning system, could be calculated in detail over the given calculation

perior. However, recording of all the data on the tonperature and heat flow is tremendous and practically meaningless. Thus, what was considered necessary for the design was selected from among these data as the output, from which values for 6"^ and only were picked up and diagrammed as given in figure

8 (2) with full lines and brocken line. The changes of the heat medium temperatures O'fy, &f2i ^"flt

(^•'wl ^'w2 "s^® as shown in figure 9 with full lines. From these calculation results, the following were found out.

(a) To bring the room air temperature at the early stage of operation to a predetermined level,

the heat source equipment is to be operated with full output for a time. According to the conventional

design method, however, the flow rate of air in the supply air system becomes short. Thus, the output

declines prior to arrival at the predetermined room air temperature level. As a result of a trial calculation with increased supply air rate to avoid the shortage, it was found that full output operation

has to be continued till the room air temperature reaches the predetermined level, as shown in figure

10.

(b) The part indicated with A in figure 8 (2) at the initial stage of operation represents what is spent for the increase in the retained heat of the equipnent (negative heat in the cooling operation). In contrast, the part B appearing after the operation is finished results from the discharge of this

heat. Both rates of heat are not always equal, however.

(c) By the application of this CEtlculation method to the air conditioning design, adequ&te value

for QsBa ^® discovered. "Qiere are other advantages that rational heat medium transportation syston

stiited to ^® designed and that a proper air-conditioning plan can be set up.

In this example, calculation was made vising known veuLues for QK£kn> P "^^ sjet&n set up

by the conventional design method, thus given other results than those for rational equipment.

5.2 Comparison with measured values and evaluation

Changes of and 1$'^^ obtained from the actual air conditioning meEisurement in this building are given in figure 8 (2) with dotted lines together with exterior conditions as figure 8 Changes of

heat medium temperatures are shown in figure 9 with dotted lines. The corresi)onding calculation results are as given in figure 8 (2) and 9 with full lines and brocken line. A comparison between both results

snows that the change of Qijq, Q and 9^ with time shows similar vailues and trends. Although the heat

medium temperatures themselves are a little different because of difference in control method, the necessary t^nperature difference are in near agreement.

What calls for specific attention here is the fact that the existing air-conditioning system is the product of the conventional design method and not of a rational method. Also, when it comes to the actual construction, there were unexpectedly many causes of heating £tnd cooling load, such as that from

the heat medium transportation system exposed on the roof. With these points taken into consideration, a difference by 10% or so between the calculated and actual values for ^ggj is unavoidable.

For reference, the time and labor required for this calculation method are such that IBM 3^0 com- puter took 20 to 130 seconds with 4t at 3OO to 60 seconds per one calculation day, and a little more labor than for conventional method was required for input data preparation.

Judging from the above, we believe the practical value of this calculation method by degital com- puter is very high.

6. Conclusions

In the future, calculations of the type mentioned above will have to depend on computers by all means. As the calcxilation methods for solid heat transfer, there are weight function method, response

factor method and analog method, in addition to the numerical method employed in our system. All these methods, however, pertain to the problem on less than 30% of the heating and cooling load, and ets to remaining part of the load, they have little to differ. Uie gist of the heating and cooling load calculation should lie, not in the methodology of the solid heat transfer caJ-culation, but in the systenatization of the calculation method altogether.

Our calculation method introduced in this paper has been systematized since several years ago, independently of the progress in other methods. With the numerical method, too, it is possible to reduce

the calculation time and memory capacity if proper consideration is given, and satisfactory results

724
could be obtfdjied in respect to acctiracy*

Improvement of this ceilculation method itself and interchange with other methods are the problems

ronaining to be solved.

This paper limited clarification to the design problems ahead of the heat source equipment output,

and has not dealt with the air conditioning energy. It, however, can be easily obtained using, the handling of the heat medium transportation system as a guide, provided the performance of the system

components is already known.

While it is still premature to draw a conclusion because of insufficient data, the physical veilue for the wall body, a ( = jjfy ) is considered different between cooling and heating period. For such

phenomenon, this calculation method is more advantageously applicable than other methods as in the case of intermittent air conditioning operation.

To conclude this report, the author expresses his profound appreciation to Dr. Kenichi Hiraga under

whom he works for the opportunity of compiling this paper and very helpful advices and guidance.

7* Appendix

7*1 Various equations related to unsteady state heat transfer

Temperature in one dimensional object, see figure 11 (l)

^I.Zlt = ^^^^2 + <^3 + - 2)<^i) ...(26)

One dimensional, surface temperature of object in contact with fluid with temperatiire of, see

figure 11 (2)

•^l.^t " ^^^2 * ^'^t * - - ''^^1'' ...(27)

N. (9-x + 20- or, = ^—1 ^ figure 11 (3) ...(28)

One dimensional, surface temperature of object subjected to heat flux q, see figure 11 Cf)

®l.At=2P(<^2*^i-''^^1 -^29)

Heat produced at uniform rate inside object Q, see figure 11 (5)

KAt = <^ - ^3 ^ - 2)ft, ^ Q ^) ...(30)

One dimensional, surface temperature of object with heat produced at uniform rate inside Q, see

figure 11 (6)

2 ^^,it ' ^^^2 + N<^f + - N - 1X9-^ + Q|-j ...(31)

One dimensional, heat conduction between two objects, see figure 11 (7)

^1.At = ^(^2 - ^3 ^ -

- -^^l)

^11 = -.^ 1 ^2

725
where, Aj: Thermal conductivity of object with point 1, Ajj: Thermal conductivity of object

without point 1.

Two dimensional, irregular shape surface temperature of object

In case of figure 11 (8):

•^l.^t = 2P[^-^ + + N.^^ + - N - 2)6-^) ...(33)

In case of figure 11 (9):

^1.4t = *^3* 2 * ^'^f 5^ V '"^^^

In case of figure 11 (10):

^1.4t = ^^^-^ + N.^^ + (^ - N - D^J ...(35)

Value for K used in equations (33) to (55) is a corrected heat transfer coefficient inversely pro- portionate to increase or decrease in area of the object surface.

7.2 Values of P and N

Because of the condition where multiplying coeffecient for in the right member of the equations

for &-)>At will not become minus, At has a permissible maximum limit. For example, tram equations (26)

and (27) given in the latter paragraphs, we have

P < 1/2 inside object ...(36)

P <

2('\^ti) object surface ...(37)

Also, the permissible range of P relative to any value of N is as follows: P £;l/3 ••.(38)

7,3 Surface heat transfer ( 3)

Q = a(& - (9-.) ...(39)

B 1

0( = C< +(X ...CtO)

c r

where, Q: Hate of heat transfer at surface, CX : Total heat transfer coefficient, 0^^: Convection

heat transfer coefficient, CXj.: Radiation heat transfer coefficient.

7.^ Badiation (solar) temperature O'g

& = ^ I + ...(41)

where, I: intensity of radiation, a: absorption rate.

7.5 Radiation ( 3)

%Z = *2^fl2S2 ^^105> - <10§> 3

•••<'*2)

726
Q-,2 - - S21 .^.ikk)

C .C

b

= ^2 ^ ^2 same wave length) ,..('f6)

where, Qi2^ ^^''^ rate of radiation from surface A-j to A2t A-j, A2: Areas of surfaces exchanging

heat by radiation opposite to each other, ^la* Total shape factor between A^ and Ag, T^, T2: Surface

temperatxires of A^ and A2, dA^, dA2: Small element areas in surfaces A^ and A2, <^^, f^' Angles be- tween normals on oA^ and dA2 and line connecting dA^ and dA2, a^, a^' Absorption factors of A^ and A2»

e^, Snissitivities of A^ and A2.

7«6 Equivalent out door temperatiu-e &^ and equivalent temperatxire difference ( '*)

^e = ^sm*^C^,(T)-^em:i -^'^7)

4&e=<^sm*<'^s(t)-0-^i

where, Hoom air temperature, f: Decrement factor, T: Time lag, ^BiX)' Value of O'g as much as before time being calculated*

8. References

( 1) H, S. Carelow and J. J. Jarger, Conduction ( 5) S. Kuramochi, An Calculation Method of

of heat in Solid, P.467~'t78. Air-Conditioning Heating and Cooling Load,

( 2) T. Kudo, Dennetsu Gairon, P.394~in6,

SHASHJ, Vol.43, No. 12, Vol.Vt, N0.I

( 6) S. Kuramochi, Investigation and Measxire-

( 3) K, Watanabe, others, Kenchiku Keikaku ments of Air-Conditioning on Buildings

Genron, P.29, 60. (I) (3), AHASBJ, Vol.44, No.2, N0.3.

( 4) H. Uchida, Kuuki Chyosei no Kihon

Keikaku, P.90 , 91

727
y

r —d —

" T

1

~1

\ r- L

1 1

1 -H ^

>2 ! 1

1 i U -

i

1 _ J_

1

1

1 1

1

i_

i

1

1

1

1

. _J

-X

Fig-1 Heat Conduction in Solid, Two-Dimension

728
(D -X

Fig-2(1)~(3) Simulation of Thermal Medium Transportation

System

729
F fan

P pump

Pi control Panel.

P2 pump

Ti thermostat

Vi valve for heating

V3

V5 three way Valve

for cooling

Fig-3 A Model of Air-conditioning System

730
operation start

Fig-^- Change of Thermal Medium Temp. Just after

Operation Start

Fig-5 Change of Value of Qj^g, Q"pg and Q just after

Operation Stop

731
732
733
734
735
736
CIS

8 9 10 Uptime

Fig-lO Results of Calculation in case of enough Air

supply

737
(1)

Variation of Heat Transfer to be

738
739
f

(5)

Fig-U Cont. (4 and 5) Variation of Heat Transfer to be adopted

7A0
(7)

Fig-11 Cont. (6 and 7) Variation of Heat Transfer to be adopted

741
742
743

Heating and by Means of Cooling Load Calculations

Periodic Window Function

Kazuo Eguchi

Building Research Institute

Ministry of Construction,

Japanese Government

One of the computer calculation procedures for the determination of heating and cooling loads, is presented in this paper. This method uses time series on assumption of linearity and s ta tioneri ty . The concept of "window function" is introduced as combining function of time and time-series. The "triangular wave function" is considered as one of the periodic window functions that are practically easy to handle. The problem of heating and cooling load on building is assumed to be a periodic phenomenon, and this justifies the use of periodic window function.

The calculation procedure is first to determine the "heat flow matrix", of which elements consist

of rate of heat flow emanated from each room for a given time, and this rate of heat flow assumed to be proportional to the room temperature. In the case of intermittent heating and cooling, the room temperature and rate of heat supply are alternately unknown. Then, both unknown temperature and heat supply

rate is collected, and heat flow matrix is transformed into "thermal matrix". To determine the thermal

matrix is to obtain the heating and cooling load and the fluctuation of temperature in each room at each

time. In its principle, this method is readily understood and computer programing is also easy. In addition multi-room problem and completed time schedule of the indoor design condition can be easily

handled.

Included in this report are an example of heating load evaluations for dwelling with five rooms and

for building of which the whole space above the ceiling consists of a plenum chamber. Keywords: Heating and cooling load calculation, window function, time-series, triangular wave

function, response factor method, heat flow matrix, thermal matrix, warming-up period, duct-type

room, multiple rooms. Gauss elimination, Gauss-Seidel method.

1. Introduction

Recently computer has come to be widely used in the field of architectural engineering. With respect to the calculation of thermal load of buildings, for example, ASHRAE's Task Group on Energy Requirements has developed a calculation procedure [l] based on the Response Factor Method [2], [3]

From the stand point of engineering usage, load calculation using computer will have to take account

of the following points.

(1) Accuracy from engineering point of view.

(2) Applicability of commonly used computers.

0) Short computation time.

(4) Simplicity in the preparation of input data and in the operation of partial modification of the data.

(5) Wide range of application.

Research Officer, Building Physics Section, B.R.I,

figures in brackets indicates the literature references at the end of paper.

745
It would be difficult .to satisfy all these points. It is therefore desirable to prepare several cal- culation procedures having their respective characteristics features, so that designer may be able to choose a most efficient procedure according to his objective.

In this paper, a calculation procedure for periodical heat flow problem is prevented. The method

of solution is based on the principle of superposition, which assumes linearity and stationerity

2.1 Time-Series and Window-Function

"A time-series is just a series of numbers or quantities representing the values of a function at successive equal intervals of time." [3]

The time-series is assumed to be an approximation, using a finite number of information, of a timefumction which varies with time. Thus, a concept of "window function" is introduced to relates arbitrary

time-function to its time-series.

There are two types window function wf(t), i.e. transient type and periodic type which have the following properties

wf(0) = l Transient type J wf(N./)= 0 ;N±{1,2, ) (1)

[ (t)dt = J

Periodic type Jwf (t)= wf(tf;j.T) ;N±(1,2, ) wf (0)= 1 wf(N"Zl)=0 ; N'=l,2, , T/A-1 (2)

jjf(t)dt = zl

where J is the time interval of time-series and T is the period.

If a time-function f(t) represents a periodic phenomenon, it is convenient to use a window function

of periodic type, and if f(t) represents a transient phenomenon it is necessary to use a window function

of transient type.

If F(N) ; N=0,l,2, is the time-series of f(t), then the approximate time-function f ' (t) represented by this time-series is given by the following equation,

f(t)=lF(N).wf(t-N.J) (3)

where Z stands for 21 J.f wf (t) is transient type and forjr if it is periodic type. The terra of the timeseries is a time-function obtained by the product of the window function having time origin at that point and the value of the time-series.

From eq(3)

f (N.Zl)= f (N'J) ; N=0,l,2,

f(t)^f(t) ; t=N-J

746
In general, f'(t) is identically equal to f(t) in the limit as time interval /I approaches infinitely

aoall. IfJis a finite time interval, f'(t) is an approximation to f(t) at • 3) .

If J has a fixed finite value, the degree of approximation depends on the property of the window

function as well as that of f(t).

In response factor method [l] , [2] , [31 , the triangular pulse is used for window function.

There exists infinitely many window function satisfying eq(l) or eq(2). However, it is desirable

to choose one on practical consideration such as precision and ease of handling depending on the case. Figure 1 illustrates some examples of window function of transient type and periodic type.

2,2 Triangular Wave Function

Triangular wave function is a window function of periodic type which is represented in the form of

Fourier series. Such functions are infinite in number, and the following is a relatively simple one

r (mnN/2)-1 ( f^-] 1 twfrM(+)-('/^'^ l+-C2/M)-EC0S(J-x) l+Z(2i/M)-C0S(J-^-(M-i))

J = l i=i '

+ (Ml)-C0S(M-NN-X/2) 1 (5) where X =(2TT/T)-t

NN =T/A (even number)

M =1 ,2, — (in the following, M is referred as "order")

C ^ = 0 ; M = even

[0 ^]/^ ; M = odd

The degree of eq(5) as a polynomial in trigonometric function is (M«NN/2). The lowest degree

of the triangular wave function is NN/2, which corresponds only to eq(5) with M=l, that is.

Ml , > (NN/2 ^ iwV^u^v =[1/NN)- ly-cos(j-x)

lj=0 J (6)

where if = 1 ; J = 0 and J =lMKl/2

J =2 ; J = 1.2,-'--,NN/2-l

Substitution of the windo-v function twfjj^ of eq(6) in eq(3) gives

= Yfm-tvj\^^{t-u-A) (7)

X)j (8)

or HN/2 , f'(t) =Z 8- a(K>COS(K-X)+b(K)-SlN(K

K=0 I where nn a(K) = (t/NN)-Z FCL)-COS(K-L-J)

u-1 b(W=(l/NN)-Z: F(L) SIN(K-L-J)

747
Equation (8) represents the result of harmonic analysis of NN time-series, and is the lowest degree

Fourier series pa^ssing through NN points. Expressions in eq(8) are called Fourier coefficients. Hence, when we use twffjfjfor window function, representation of periodic function f (t) by the time-series F(N) and representation by Fourier coefficients a (k), b(|<) (k= 1,2, , NN/2) are identical. Method of

analysis using Fourier coefficients a(|<), b(|^) or using amplitude and phase constant obtained from them

is called the frequency response method. Characteristic feature of the Jjroblem of heating and cooling

load calculation which is different from the general engineering problem is that i) in the ordinary

intermittent heating and cooling, the unknown time period for temperature and heat flow rate appear

alternatingly, and ii) that the problem is not determination of response to a particular frequency but determination of the resultant temperatures and heating loads superposed over the whole frequency range.

In this respect, the method of time-series which can treat the temperature and thermal load at each time

period directly as unknown variable is more convenient that the frequency response method.

Oi the other hand, as for approximation of uniformly continuous curve, use of twf^' for window

function is generally better than the broken line approximation (use of triangular pulse for window

function) or the step function approximation (use of rectangular pulse for window function). However,

in the thermal problem of buildings where discontinuity points appear in cases of beginning and termination of heating and cooling or on and off of illumination, approximation using the window function twfNW

is not sufficiently good because of the appearance of overshoot immediately before and after the time

period. Equation (5) is made up, considering these points and the overshoots are reduced by increasing

the order M. The relation between M and overshoot is shown in (fig, 2), where M values in even number

are superior to those in odd numbers. With the order M gradually increased, eq(5) approaches a periodical

Triangular pulse.

2.3 Response of Sjstem Elements

Thermal system of a building or a room is the set of basic elementary system such as heat conduction

system of wall and floor and heat transfer system of ventilation. It is therefore required to determine

the response of these basic system elements in the first place. The response time-series of the system

corresponding to the window function input is denoted to be R(N).

The output time-series G(N) of the system corresponding to the input time-series F(N) is given by

G(N)=ZF(M),R(N-M) (9)

where I stands for^2.^if the window f'onction is transient type and for E if it is periodic type. Thermal

response of wall and floor corresponding to artificial function such as triangular pulse and rectangular

pulse is generally an infinite exponential function. Thus in practical computation, it is necessary to produce approximation by cut-off or rounding, and the error produced by such approximation will be referred to as "internal error" in this paper. In contrast with this, approximation error in representing

a time-function by time-series as previously described and the hypothertical error regarding input will

be referrd to as "external error". When artificial function is applied to window function, the final

estimation of errors are very difficult, as both of the internal and external errors are included in the result of calculations. While, the thermal response of walls and floors corresponding to the trian.gular wave function expressed by Fourier series being easily and accurately calciilated, therefore, only external errors are considered.

3. Construction of Calculation F^cedure

3,1 Heat Balance Equation of Room Air

and Heat Flow Matrix

The following description in this paper adopts an approximation neglecting the energy interchange

by radiation from enclosing wall surfaces. In other words, it is aussumed that the heat transfer between

the surface of waJJLs and floors and air is propotional to overall surface conductance and that overall

surface conductance is invariant with respect to time. The problem is dealt with the multi-rooms problem

and totaline; number of the rooms is denoted by JJ, Heat flow matrix denoted by[THlis a matrix whose

element in row (^) and column {j^) is the coefficient of the rate of heat flow flowing out of room J at time M.*z) with respect to the room temperature T(n ) of room I at time N*zl. Heat flow matrix is a square matrix whose dimension is given by the following equation

NXJ=JJ.NN (10)

748
where

NN= T/4 T = period

J and 1= Integer denoting room number

M and N= Integer denoting time ( in the later description, U.A and N.J . are replaced by M and N respectively for simplification)

Heating or cooling load H (J,) and the room temperature 'V(li) are presented in the column matrix (Hj and [TJ respectively. Heat supply into room air caused by atmospheric temperature, solar radiation,

illumination and heat generation of the rcom occupants, which can be calculated independently of room

temperature T(5) and thermal load H(m), is denoted HO(S), of which column matrix is symbolized [H|.

Now, heat balance of room air is expressed in matrix form as

(TH). [T]l-[Hj=tHO]l (11)

Heat flow matrix [TH] represents the characteristics of thermal response of building with room

temperature as input and heat quantity as output, if interchange of air by ventilation between the adjoining rooms, the heat flow matrix is a symmetric matrix. The inverse matrix tTH)"^ of heat flow matrix

[TH] will be named temperature matrix and shown as [HT) . The temperature matrix IHTI represents the characteristics of thermal response of building with heat quantity as input and room temperature as output.

3.2 Elements of Heat Flow Matrix

The element of heat flow matrix TH(M'N)is given by

TH = -W1+ WO-?I+VO+HFA+HAA (12 ) The terms are defined as follows.

1) Heat gain by conduction from walls and floors (WI),

Wl(^'L)i^j =2WS(I,J,K)-Y(K,M-N) (13)

2) Heat loss by conduction into walls and floors (WO).

WO(S';^)i=j=?ZwS(l,J,K)-X orZ(K,M-N) (14)

1=1 K

where

WS(I,J,K)= area of wall No. K, that facing to both room I and J, JT= J J -I- numbers of atmospheric temperatures (room temperatures known

at each time are considered as atmospheric temperature).

X(K,M)

] Y(K,M) = response time-series value of wall No.K at time M. Z(K,M)

Representation of X, Y,Z,are in accoi<dance with response

factor method [ 1), [2), (3).

3) Heat gain by ventilation (VI).

Vl(S'MjM=N= C-V(I,J,M) (15)

1 h) Heat loss by ventilation (VO).

749
vo(S'n)S;h = ?c-v(j,i,M)

i.i ^ J J ' (10

where

C=heat storage capacity of air per unit volume,

V(I,J,M)= rate of air flow from room I into room J at time M,

5) Heat storage by indoor objects such as furniture (HFA),

HFA(?.'vi)i=j = ZSF(J,K)'XF(K.M-N) (17)

where

SF( J ,K) = surface area of No.K heat storage object in room J, XF(K,M) = time-series of heat storage response of object K.

Wall and floor dividing two rooms having identical temperature fluctuation, is treated as heat storage object ; in which case,

XF= (X+ Z - 2Y)/2 (18)

6) Heat storage by room air (HAA)

HAA(?^'^,) = C-RV(J)-HA(M-N) (19)

where

RV(J) = air volume of room J, HA(M) = time-series of differential coefficient of window function Wf (t)

In case a triangular wave function is applied to window function, it is easy to determine HA(M).

However, in case an artificial function such as triangular pulse is applied, an appropriate approximation

is adopted 12).

3-3 Thermal Matrix

Heating and cooling of buildings are generally conducted intermittently. Thus, during the period

when room temperature is specified, thermal load is the unknown variable, and during the period when

the operation of heating and cooling system is stopped, room temperature is the unknoAin variable. , Let (5') denote the time and the room for which^room temperature is specified in eq(lL). Since T( Sj') is known, the product of each element of column (J/) of the heat flow matrix [TH) and the value of T(iE,') is added to the right side of eq(lO). Then, assuming T( 5, ) replaced by unknown H(J, ), column (Jj ) of

the heat flow matrix (TH] is 1 in row (^a) and 0 elsewhere, If(M'-) is the room and the time for which

heat supply from the heating and cooling system is specified (generally zero is specified), then H( J--) is added to the right side of eq(ll) and T( j^-,) is left as unknown variable. The matrix obtained by

transforming the heat flow matrix [THj by the above operation is referred to as "thermal matrix" and

is denoted by["H']. The column matrix which is composed of unknown temperature and supply heat quantity

is denoted by[|];j]|. Furthemore, the column aatrix on right hand side which is composed only of known

valiables is denoted by[*^^°j. Then the eq(ll) is transformed as follows

rHH^]=p (20)

Solving the said matrix eq(20) the unknown temperature and supplied heat value (nJare obtained.

3'h Problem During Warming-Up Period in

Intermittent Heating and Cooling

750
In intennittent heating and cooling operation, maximum load usually takes place in warming-up period

and the capacity of equif^ent of heating and cooling system is determined by this peak load. During the warming-up period, both room temperature T and thermal load H being unknown, the equations corresponding

for unknown values ctm not be completed by heat flow matrix (TH) only. However, this problem is solved,

in this paper, by approximation as follows.

Namely, the thermal load during warming-up period can be considered to be equal to the one at the starting time of the specified room temperature (i.e., at the time°^termination of the warming-up period).

According to this approximation, the number of unknown variables of thermal load H can be reduced so as to determine the thermal matrix l"^]. Assuming U" to be the marginal time between warming-up period and specified temperature period, the column (5 ) of thermal matrix (J indicating room number while time M

is within the warming-up period) is simplified by the following subtraction converting into (^ )'. (cf.

table 1, 2, 3 )

converted column ( m )| = ( ^ ) ~ jcolumn ( J, ) - column (?i")| (21 )

As a matter of course, similar subtraction must be conducted simultaneously as for column matrix['w']l« By this transformation, the thermal matrix in the case including warming-up period takes the same form

as in the case not including warming-up period, (cf. table 2, 3 )

3.5 Problem on Duct-l^pe Room

In case the whole space above the ceiling is occupied by plenum chamber, i,e, conditioned air is

indirectly supplied Ju to room under the ceiling, not directly but through the space above the ceiling, this

space above the ceiling is referred to as "duct-type room" and the room under the ceiling (the room to

be air conditioned) is referred to as "main room". In this case, the duct-type room is also considered

a room to be calculated. In this duct-type room, both room temperature and thermal load are unknown

during the period when specified temperature is maintained in the main room. However, in case heat is

not directly supplied to the main room, there being no unknown variables in the main room during the

period, the thermal matrix can be determined.

In case heat is supplied to both main room and duct-type room, this problem is indeterminate.

However, even in this case, the thermal matrix (XV) can be determined by either oneof the following two

methods, i) the time-series of the temperature difference between the air temperature in main room and that in duct-type room are preliminarily provided (i,e, consequently the temperature in the duct type room is

preliminarily specified so as to decrease the unknown quantities of temperature by one), or ii) the time-series of rate of heating quantity directly supplied to the duct type room and the main room plus

duct-type room (i,e, consequently, the unknown quantities of thennal load are decreased by one).

3-6 Solution of The Thermal Matrix

From the viewpoint of practical application, it is required to solve the thermal matrix accurately

and rapidly. Dimension of the thermal matrix is NXJ same as that of the heat flow matrix and as shown

in the eq(9), it is determined by period T, time subdivisioni and total number of rooms JJ. Thermal

matrix is introduced for convenience sake to explain the relation between unknown variables and equations

The number of unknown variable is NXJ, but this does not necessarily mean that the dimension of the simultaneous equations to be solved is always NXJ.

In other words, assuming the period when room temperature Is specified to be N', this period can be eliminated from the calculation of simultaneous equations and the dimension of the substantial simultaneous equations to be actually calculated are (NXJ-N')- (cf. table 2, 3)

Thus, all the unknown variables of the room temperatures can be detennined by calculating the simultaneous equations of dimension (NXJ-N')> and using these quantities, thermal loads can be obtained

by simple multiplications and additions. In case the dimension of the simultaneous equations (NXJ-W)

is not too large, they can be accurately calculated by well known "Gaussian elimination".

In Case the dimension is large, the "method of succesive displacement" (Gauss-Seidel method) is appropriate. In case of applying the method of succesive displacement, unknown variables are successively

determined along the time elapsing, calculating the small matrix of dimension equal to the number JJ

at each time. (cf. table 16)

751
During the warniing-up period, the small matrix expanded up to the terminating time of warming-up

period (dimension of matrix is an integer multiples of JJ). (cf. table 17) In case duct type room is

care must be taken in calculation, as principal diagonal of the matrix sometimes contains ^ero.

In addition, response factor method can be considered to solve a matrix of infinite dimension by successive

displacement. That is, since the transient response to the pulse input of wall and floor becomes almost

zero, after a long time, calculation steps of the successive displacement method after this time period

yield almost exact solution successively, if we proceed by arbitrarily setting up an initial condition.

Generally speaking, decision as to the choice between Gauss elimination and successive displacement

method depends on the capacity of the computer and the dimension of the matrix to be solved.

k. Example Problem

Two examples are shown in the following.

Both have their principal objective to seek the peak load and the daily total heating load when the designeted time schedules of intermittent heating are changed. Periodic triangular pulse is used for win- dow function and calculated with^=l hour and period=24 hour. Solar radiation, mutual radiation change

between surfaces and heat storage of furnitures in room are neglected. Latent heat load is not included.

Thermal matrix [^] was solved by Gauss elimination and the computer used was TOSBAC-3400 (core memory

16 m, magnetic disc 2400 KW)

4.1 Example Problem (I),

Heating Load of Dwelling

Heating load for a dwelling unit of an apartment house as shown in (fig, 3) is calculated.

Adjacent units up, down, right and left of the unit were assumed to be in the same thermal condition as

the objective unit. The dwelling was divided into four rooms and one stair room (commonly used by

dwellers in other houses). Arrangement of walls and floors, their composition and area, thermal constant

of materials and air volume of the rooms are respectively shown (fig, 4) table 4, 5, 6. Assuming the life pattern of four family members as shown in (fig. 5), the heat quantities to be generated by lighting,

electric appliance, cooking and human bodies roughly estimated by the said assumption are shown in table

7 (cooking heat is over estimated). The natural ventilation between rooms is classified by night time

and day time and shown in (fig. 6), Assumption on five patterns concerning design temperatures in each

room and their time schedule is shown in table 8. Designed outside air temperature adopted for calculation is shown in (fig. 7).

Plesults of calculation concerning the heating patterns A, B, C,D and E are respectively shown in (fig.

7-11). Total sum of the heating load for rooms [I] - [4] at each time is shown in (fig, 12) by heating

patterns. The relation between peak load and daily totil heating load is shown in table 9« Results of

calculation indicates the big differences between heating patterns.

Since the temperature environment in room itself varies with the heating pattern, comparison by

peak load and daily total load alone is difficult, Ptoughly speaking, however, programmed control (E

type) is considered to be superior.

4.2 Example Problem (II),

Office Building with Duct Type Room

Heating load and fluctuation of room temperature of an intermediate story in an office building with center core as shown in (fig. 13) are to be calculated. Upper and lower storey of this storey are assumed

to be in the same thermal conditions as this storey. Heats generated from human bodies and lighting

devices are neglected. Various values for calculation such as composition and area of walls and floors,

thermal constant of materials, and air volume of rooms are^ respectively shown in table 10,11 and 12. Two kinds of warming-up period (2 hours and 3 hours) for calculation are shown in table 13, Three kinds J of assumed ventilating patterns A,B and C are shown in table 14. Explanation of RHS patterns 0, 1, 3

' for calculation is shown in table. 15,

752
Here RHS is the ratio of "ratio of heat supply to duct type room" and "sum of heat supply ratio to duct type room and to main room" during warming-up and specified temperature period in main room. Combination of warming-up period, ventilation pattern and RHS pattern for calculation is represented as shown in the following example.

( 1 , A , 1 )

I

T ^

. n warming-up period ventilation pattern FHS pattern

Calculations are conducted for nine combinations such as (1, A, 0), (1, A, 1), (1, B, 0), (1, B, 1),

(2, A, 0), (2, A, 1), (2, B, 0), (2, B, 1), (2, C, 3). Result of calculation are shown in (fig. lA-22).

The relation between peek load and daily total load of each calculation are shown in (fig. 23).

Although this is only one example of calculation, referring to the results of such caluculation,

designers may be able to choose the rational and economic equipment and air conditioning system of

building.

5. Conclusion

Solution by means of time-series is cleared by the concept of "window function". Window function

can be chosen at liberty according to the problem, and when treating periodically fluctuating phenomenon

use of "triangular wave function" is appropriate. In the problem to predict room temperature fluctuation

and thermal load of a building, "heat flow matrix " plays a fundamental role. Unknown quantities such

as room temperature and thermal load can be determined by solving "thermal matrix" which is obtained by

a transformation of the heat flow matrix on the basis of indoor design condition (time schedules of intermittent heating or cooling and existence of duct type room) and outside condition (solar radiation,

atmospheric temperature etc.), TWo method for solving thermal matrix, i.e. Gauss elimination and method

of succesive displacement are selectively applied in compliance with the nature of problems and the capacity of computer to be applied.

With the method of calculation described in this paper adopted, the problem of intermittent heating

of multipls rooms can be treated as ordinaly one and the problem for single room only becomes rather

special one. The periodical phenomenon is treated in the present paper, however, by extending the period T to infinity, the response factor method may also be considered to be included in the calculation

method described here.

The effects in case time schedules of intermittent heating are changed, are mainly explained in the

said examples of calculation. Ease of such calculation will be a great help to the designers and will

facilitate them in their more accurate overall decision making.

6. Fteferences

1 Proposed procedure for determining heating 3 and cooling load for energy calculations,

The task group on energy requirements for heating and cooling, ASHRAE. ,1968.

D.G. Stephenson, and G.P. Mitalas, Cooling load calculations by thermal response factor method,

trans. ASHRA3., vol.73, part I, 1967,

2 G. P. Mitalas, and D. G. Stephenson, Room

thermal response factors, trans. ASHRA3., vol.

73, part I, I967.

4 K. Eguchi, A method of space temperature and and heating and cooling load calculations by

window function and time series, trans. AIJ. Summaries of Tech. Papers of AIJ. , AUG. 1669.

753
7. Appendix

Solution of Thermal Matrix by

Method of Successive Displacement

(1) The case in which all unknown variables are room temperature (problem of room temperature fluctuation)

(2) In case room temperature is specified (without warming-up period)

As shown in table 2, dimension of the simultaneous equations to be solved at that time decrease

comparing with the case of 7X1) (cf. table 16), however, the method is basically the same as above

(cf. table 2, 3, table 17).

(3) In case warming-up period is provided

In a simple example shown in the table 17, small matrix expanded until the time when warming- up is finished must be solved, (cf. table 17)

Considering the case when warming-up periods in different rooms and specified temperature period

are overlapped, the said expression must be corrected as follows for making the expression more

strict, i.e. "snail matrix expanded from the time when v*araiing-up period is started in any room

to the time when warming-up periods are finished in all rooms". However, same as the case shown

in table 3, dimension of the simultaneous equation decrease less than appearance.

754
Function of iime by time-sen'es

(A ) Transient typed window -function and windoi^/ -function

Notes : T ; Periodic time , A ; Time sejment of time-series.

Fig. 1, Example of window function and function of time as represented through superposition

of the former.

755
Fig. 2, Example of trianguler wave function (twf kjij ) and relation between its order (m) and

overshoot.

Plan @

Room No. Descn pt .on m Living rm. (a), Bedrm.Cb), Kitchen Cc) Bed rm. and study rm.4or chi Id ( I ) Bed rm. and study rm. -for child ( E ) s Entrance hall, bath rm., lavatory ^

Stair-case Ccommon use ) @ Out side air ("South Side) 1 ^ 0 ditto (North Side) i

^ ; PoomCa),(b)andCc')ar€ gathered and computed as room IT] . *»; AsSumif^g that: temperature of B is ecj^ual to that ot [zl

Fig. 3, Example problem (l), Heating load of dwelling. Sketch of dwelling used for calculation.

756
. 12 13 12 13 12 13 0

0

f7) (8)

N5Z2ZZZ7

5

5

5 5

4 S

1

( 13

(6)

(3

J,

H]

(9)

E

(7)

0

(8) (7)

:$4

13 13 13 0

Notes j Figures in D show each room Mo..

Fiaures in ( ) show No. of each floor. ) , ^ K'SeeTable4 3 Others show No. of each wall

Fig-. 4, Example problem (l). Heating load of dwelling. Arrangement of wall and floor.

757
Hour 0 12 15 18 21 24

Husband m E m

(b) (b)

Wife m m |l.2,3,4| m m m , m m

(b) (C )

Child (I) m m H H

ta) fa:) T-"^^

Child (I) (D CD m @

Note : Dotted lines indicate sleeping hour and figures in D indicate

the number of room.

Fig. 5. Example problem (l), Heating load of dwelling. Assumed living pattern of an occupant.

(Number of family members : 4)

Night ti me

Time (l7, 18, ,24, 1 ,- - 8) 84 42 48

o'clock

63 51

Daytime

Time ( 5. 10, -•-

, 16)

f68

150

El

,

.

, „ .30

m

(44 48

16

Fig. 6, Example problem (l). Heating load of dwelling. Natural ventilation betvreen rooms.

758
II 234 I Tetnp.

20

01Q_e

0) 10

Remarks:

Real- line ; Room air temperd"ture BroKen- line; Heating toad Figures in indicate the No. of room.

>! X—< X—><—X—-V [UTemp. /

y.—><—y—y—X

X—X—

Outside air temperature

1 d / g] \ T / T>

\ if

4000

oA

3000

2000

«3U

o

COc 1000 t^X

1/

0

12 (6 24 hour

Fig. 7, Example problem (l), Heating load of dwelling. ( Heating pattern A )

759
20 uo

\ I

<D3 -P

i-

<D£-P

10

£

o

o

DC

II 2 341

I • • • • • •

Te m p . \

EK 1

( the same remarKs

as that of F;^ - 7 )

X.— <—K—X x-^—'^"~\ V-x—

X—X—X—

f

1

1

1

1

\ 1

r"^ 1

II

11

h2.3.4l 1

° ^

\

1u

1 1

4000

3000

2000 r

1000

o

12 18 24 hour

Fig. 8, Example problem (l), Heating load of dwelling. ( Heating pattern B )

760
20

o

E

rt3 E8

(0

4000

( the same rem&rks

as that o-f Fig.7 )

[5] Temp. X—X—X-X—S-^X—XA

1y

\3

A—

1

\ I

12 18

3000

2000

^5

O

c

-p

01

1000

24 hou r

Fig. 9, Example problem (l), Heating load of dwelling. ( Heating pattern C )

761
762
3

QJQ_

E

dJ

^ 10

eo

K—/—X— ><—X'—X—X—K

Temp.

Temp.

4000

( the same remat-Ks as that of F;g.7 )

-43 A-A

12 18

3000

2000 5

O

1000

24 Hour

Fig. 11, Example problem (l), Heating load of dwelling. ( Heating pattern E )

763
764
Plan

(6)

(5).

(6)'

(2)/3)

(7),(8)' of centei--core

Section 'I

j HI ' Office roomCMam room)

[2] ; Space over cdling ( Duci-type room)

[E : Corridor and center- Core

SJ: Ouiside air

Mote: Figures in ( ) desijnd"te the number of I

and -floor indicating fhe'ir COnnposit ion .

( See Table 10 ) .

Pig. 13, Example problem (ll). Office building with duct-type room. Sketch of office building used for calculation.

765
30

u

Warming up

Ventilation patte

2 hour

rn •. A

: 0 (non- duct- type room^

10

/

Out Side air temperature

200'xio'

(supplied to H]

o

o

-©—e—e—e—e—i—e- o o o—o o o 6 0

12 hour 24

Fig. 14, Example problem (ll). Office building with duct-type room. Combination of design condition : ( 2,A,0 )

766
767
Warminn up : 2 hour ^ I Ventilation pattern '. B

RHS pattern : 0 (non- duct-type room)

200

X10'

. Heating load (supplied to 0 ) V\

100

13

o

-o—e—e—e—e- 12 18 hour 24

Fig. 16, Example problem (ll), Office building with duct-type room. Combination of design condition : ( 2,B,0 )

768
30

IVarmln^ up '. 2 hour

Ventilation pattern '• B

Fig. 17, Example problem (ll), Office building with duct-type room. Combination of design condition : ( 2,B,1 )

769
30

Warming up : 3

Ventilation pattern

RHS pattern : 0

hour

: A

C non-duct-type room)

200

x10"

Heatinj load (supplied to 0

100

KJ

o

-4-)

6—o—Q—G—e—e- <!) o o o o o—i 0

12 18 hour 24

Fig. 18, Example problem (ll). Office building with duct-type room. Combination of design condition : ( 3,A,0 )

770
30

Warming up : 3 hour

Ventilation pattern : A

RHS pattern : 1

Heating (oad (supplied to H] )

12 hou I 24

Fig. 19, Example problem (ll), Office building with duct-type room. Combination of design condition : ( 3.A,1 )

771
Fig. 20, Example problem (ll), Office building with duct-type room. Combination of design condition : ( 3,B,0 )

772
Fig. 21, Example problem (ll), Office building with duct-type room. Combination of design condition : ( 3tB,l )

773
30

20

10

Warmiri'^ up : 3 hour

Ventilation pattern : C

^RHS pattern : 3

^Dltemp.

Total heahn

Heating load /

(supplied to [D )\ /

^ load (supplied to Hand [H )

Heating load / (supplied to S )

• \

' V

.A/

I

1

\

\

1

1

\

\

\

\

200

xlO"

100 -2

I -C

<<3 o

12 18 hour 24

Fig. 22, Example problem (ll). Office building with duct-type room. Combination of design condition ; ( 3>C,3 )

774
RemirKs

Warming up hou r

No. of RHS

pattern OdAl)

•(?• ( 1 B 1)

(lAO) •

@ (2A 1

)

0 1 |h • o ® ©

show the vent; lation pattern B

(IBO) •••

(2B0)-®

•6-(2BI)

®

(2A0)

(g) (2C3)

q 10 11 12

Dally -total load [Kcal • day"' ]

Fig.23> Example problem (ll), Office building with duct-type room. Peak load and daily total load.

775
Table 1. An example of heat flow matrix [TH]

~T;me -Room NN = 4 J J = 2

MX J = 6

t ^Room

Time

Symbols used +o show the composifion of ma+riX element

A/alland Floor Ven+ilation Furnitui-e Room air Desctlp^:ion Symbol WI WO VI VO HFA HAA Derailed term ofrnotrix element

I = J N=M • • • • A matrix element sho*/n in the symbol column left side

l-epresents summation morked

terms on the righthand.

N¥ M 0 o O O

N = M m • • B O

Notes • : Vdlue of response to window -function input when time is zero. o: Values of response tro window function input when time is not zero.

IN

1 2 3 4

M \I J\ A B A B A B A B A X

/ //

1 B X / / —

2 A / X

// / —

B / X /

3 A / m

B / X /

4 A / /

B /

W/

Table 2. Thermal matrix [""iV] in which warming-up period is not included.

Time schedule

Period of desi^riated temperature (|S5 Room A time 2,3

Poom B 3,4

unKnown ->- - - T - - > -- H

-

1 2 3 4 1 2 4 2 3 3 4

A B A B A B A B B B A A A B B

1 A 0 0 0 0 1 A m /

1 B 0 0 0 0 ) B y i /

2 A 1 0 0 0

Exchange

of rows

2 B u

2 B 0 0 0 0 4 /

3 A 0 1 0 0 2 A / X X 1

3 B 0 0 1 0

and of Columns 3 A / X 1 4 A 0 0 0 0 3 B / 0

1

4 B 0 0 0 1 4 B X X I

-Time Room

(Empty space is 5ame aslTH] matrix element ) / Por"l:ion enclosed with bold line is coefficient matrix of simultaneous linear

\ e^j^ua-tion to solved.

776
Table 3- Thermal matrix [TV] in which warming-up period is included.

Time Schedule

Warming up U) Des:3nal:ed('/3)

Room A Time 1 2, 3

Room B 2 4

<nown L-T —/- - H

V]

1 2 3 4 •Time

"'' ime 1 / 1 4 2 3 3 4

A B A B A B A B -Room ^/ B A A B B

1 A 1 0 0 0 l' A' 1 B 0 0 0 0 I B X /

2 A 1 0 0 0

2' B'

1

1 0

2 B 0 0 1 0 4 A / m

(^^ 3 A 0 0 0 Exchange

0+ rows and 2 A / X /

(,3) 3 B 0 0 1 0

of columns 3 A / / 1 4 A 0 0 0 0 3 B / /

0

1

^|3) 4 B 0 0 0 1 4 B / X 1

fEmpty space is same as[TH] matrix element ) Por"(:ion enclosed with bold line i5^

coefficient matrix of simultaneous

linear eijuation to Solved. /

777
Table 4. Example problem (l), Heating load of dwelling.

Composition and area of walls and floors (continued).

Mo.

Bui Iding

element

Composition of material and

its layered

01

o

x: (min ]

Heat transfer Coefficient

(Kcal.h-I m\'C' ]

Facing rooms Area

L ]

1 Outside wall

/iir (outside surtace ) 15 5.9 4 4

Concrete 210

Insu 1 ation 15

Ply- wood 4

Air (inside surface)

2 ditto. dltto.(exCept insulation thicKness 30 ) n, 9 8.2

1 1 ditto. ditto(except insulation thickness 50 ) m^m

5. 1 6.8

13 Window

AirCOufs.de surface) 15 m-E 6.4

1. 3

f 9

3.4-

1,6 ^

1.4 0.1

G 1 a ss 4

Air space 5 Glass 4-

/^IrCinSide surface)

4 Partition

( Heavy

Construction )

Air (surfaced & 14.4

11. 2 13.5 M. 6

11.9 20.6 5.8

Cone re"te 1 80

Air (surtace^ G

5 Partition,

(Li^ht- weight

Construction ) Door,

Japanese

sliding screen

Air (surface

)

[T]« m

9.6

(2, 0

(. 6

(. & 23.8

I 2. 2

Ply- wood 4

Air space 5

Ply - wood 4

A,r Tsurface ) 6

778
Table 4. Example problem (l), Heating load of dwelling.

Composition and area of walls and floors (concluded).

M A InO.

Buildin_5 element

Composition of mater i a 1 and

its layered

V)in

dJc

(m.mj

Heat transfer Coefficient

(KMi.h-'.m-^.°c-'J

Facmj rooms A rea

C m2 ]

Air (surface) G

Closet Cone rete (50 4.35

Air (surface) 5

Air space ( closet

)

r 1 Sliding screen of closet

[ Air (surface) J

/Issurrin^ — 5

6, 5

3. 5

g' C loset (11/ II . ) dittoleyceptturn mside out ) [AJ^ 1 ' 1 4.35

Air (above Surface} 8 28.0

1

i 1 00 r Tata mi' (-flooring) 50 23.2

and Ply - wood 4- 32. 8

ceil in^ Air space 5

(Tatarri ~) Concre-te 120

Air space 4

ply - wood (ceiling

)

4

Airfunder surface) 8 AirCabove Surface) 8 46.4

8 Floor and Asphalt file (flooring) 3 34.4

ceilln3 ply- wood 4

Msphalt Air space 5

tile ) Cor\c rete 120

Air space 4

Ply - WOO d(cei ling) 4

Air ( under Surface) 8

F loor

Air (above Surface) 8 6.7

9 Concre-te. 180

Air (under surface) 8

^; The thermal response of entrance door

the Sdme as that of wall No. 13 .

is assumed as

779
Table 5. Example problem (l), Heating load of dwelling. Thermal constant of materials.

Materials

Thermal conductivity

[Kcal.h-'.m-'-»C-' ]

Thermal d'lffusivity

Cm^. h-' ] ^10^

Concre'te 1,4 25.0 Insu lalion 0.04 8.0

Ply - wood 0, 1 4- 4.0

Ta-ta m i 0. 1 3 7. 0 Asphalt -tile 0, 28 5.8 G 1 a ss 0.7 l4. 0

Table 6. Example problem (l). Heating load of dwelling.

A.ir volmeof each room.

Room Wo. Air volume [r

i 84.8

2 23. &

3 30.6

4 4 1. ( 5 1 7. 1

Table 7. Example problem (l), Heating load of dwelling. Time series of heat generation from

lights, electric equipments, cooking and human bodies.

Time

Room

Q] m,m m [5] 133 6 0 13 0 7 922 0 13 0 8 248 0 0 0 3 - n 45 1 6 0 0

12 320 0 0 0 13 50 0 0 0

14 93 0 0 0

1 5 1 14 0 0 0

1 6 287 0 43 0

1 7 274 132 43 0 18 (250 0 56 0

1 9 565 0 56 0 20-21 435 132 43 0 22 242 60 1 3 0

Unit : C Kcal - h"' ]

780
Table 8. Example problem (l), Heating load of dv/elling. Daily heating pattern ( Designated

temperature and its time schedule )

S'l^n of heating

pattei-n

Room

hlo.

Designated

temperature

Period in which temperature is Kept as dlsi^nated

Descri ption

A

1 23

0-24

(Continuously )

Every room is Kept continuously

at 23 °C .

23

4

B

12 23 7-2)

Every room is periodically heated to Keep temperature at 23°C during

7-21 O'clocK.

3

4

C

1 23 7-21 Room 111, m and lU are periodically heated

during 7- 21 O'clock, while the ternperature

in El and H] is specitied (^o'c) lower than

that -.n H] (ssoG :>

Room 111 is kept at I7°C continuously.

2 j 20 7-21

3

4- 1 7 24

D

1 23 7-2 1 Room D] is same as above.

Room IHand IE are heated at 20°C

only when children use them.

Room [4] Is not heated.

2

1 20 14-2!

34 not heated

E

1 [ 23 7-21 ] Aufomatic -temperalrure conhrol for varying temperatures in different

time zones is assumed.

2 U 1 8 Other hours '

3

r 20 7-21 )

1 18 Other hours J 4 1 7 0-24

No-te ; Room H] is not hea-ted any heatin^^ pa-tterns.

Table 9. Ezample problem (l), Heating load of dwelling. Peak load and daily total load in each heating pattern.

Heating

pattern

PeaK load

CKcal - h-' ^

Daily total toad [Kcal-day"']^ 10^ 4 100

6 590

5 510

5 560

4 600

83.5

77.8

71. 5

61.7

72.2

781
Table 10. Example problem (ll), Office building with duct-type room. Composition and area of walls and floors.

Mo.

Building elemeirt

LompoSiXion or

ma'beriSil and

'liiS Idyered

IS) iDC

:^

ct ^h- [m.ml

Heat tranSTer

out: 11 1 L t c_ r 1 0

LKcal.n .m c j

Facing rooms Area

[ m ^

)

1 Cei ling

Airfiibove surface) 8 Rock wool 18 m-[2] 28 5 5

Air (under 5ur-face ) 8

2 Floor

Air ( above surface

)

8 (048

4T4 L',_ght-wei5h-t- Concrefe 155

AirCunder surface) 8

3 Floor

ditto (except ffiicKness of Light- wei^ght

concrete 80

)

180 7

8 1 G

4 Door

Air (5urf ace ) 6

Steel plafe (nej 1 Ig 1 ble ) 29

Air space 10 Steel plate (negligible)

Ai r ( Surface ) G

6 Window

Airfoatside surface) 15 Glass ( n 65 1 i q i b 1 e ) 3 2 0

Air Cinside surface

)

G

6

wall

Airfoutside surface) 1 5 3 24

34 0

Metal sKm (negligible)

Air space 1 5

1 nsu 1 atlon 30

Air space 10 In su lation 30

Ply - wood 5

Airfinside 5urface

)

6

7 Pariihon

Air (^urface^

Plaster 15 403

Air space 5 Plaster 15 A i r C6urface ) G

8 Pdr-ti-t-.on

Air (surface ) G [0-0 1 3 5 1279

Li^ht- weight -concrete 120

Air (surface) G

782
Table 11. Example problem (ll), Office building with duct-type room. Thermal constant of materials.

Md-terial Thermal conductivity

[Kcal-h-'- m-'.^C-' ]

Thermal di-ff usivity

[m2-h-' ) * 10"^ Rock wool O.O 64 4.9

Ligh-t - weight conchete 0.5 8 14. 0 Insu 1 1 o n 0.1 3 11.3

Ply - wood 0. 1 3.6

Plaster Q. 5 5 2.0

Table 12. Example problem (ll). Office building with duct-type room. Air volume of each room.

Room Mo. Room Air volume Cm

m 0"ffice room 7310

Space a^bove

eel 1 i ng 3654

Corridor and

center- core 2477

783
Table 13. Example problem (ll), Office building with duct-type room. Daily heating pattern ( Designated temperature and its time schedule )

Room LU

Period of non- designated "tern pera-ture

f Temperafure change)

?er\oi of Wdrming-up

(Constant load)

feriod of designated

temperatuf-edoid change) 2 hour

warming-up Time 18, 11 — ,0,1,- ,6, 7 8

1

9, 10, ---JV

Pesignated temperature is 20*c 3 hour wdrming-up

I8jq,- - ,0, 1. ,6 7, 8

If should be noted that the term warming-up hour is meant as 3uch

sinown in the following charts, on account of the periodical triangular

pulse bein^ used as window function.

Hedtinj load

2 hour Wdrming up

Heatirig load 3 hour warming up

T 8 9 Time €.769

d) Deiigndted

j temperature

period

* Ti me

Room [2j dnd [1] are conf;'i nuously non - designated temperature.

Table 14. Example problem (ll), Office building with duct-type room. Daily pattern of ventilation between room.

Symbol of ventilation pattern

Period of non- designated

temperafiure

period of

Warmi ng-up

period of desijna-fced tern peratrure

A o/ r

B o(

C

9000

1 m

m

IU58200^ 1'

1 f—^

067200^

' 3000

[ ^ 58200 E 9000_|

Nion- venti lated Only 5lr circiila-tion between D] and S

(without -flesh air supply) Unit :Cm^h-']

784
Table 15. Example problem (ll), Office building with duct-type room. Daily pattern of RHS.

_ Ratio of heat supply to room \z\ (Duct- iype rmQ

Ratio cf heat supply (to room [1] + to room iT]( Ma m rm.))

No. of RHS

pattern Descri pfion

0

Necessai-y heat dmount is directly supplied to CD (fnain rm. ).

f There's not duct-type room)

015 main room and [2 is duct- type room.

Necessary heat is directly supplied to [1] (duct-type rm-^

E i5 main room and H] is duct-type room.

Necessary heat is directly supplied to Hi during warmlnj-up p€r,od of |j] During the designated temperature period of [D , the necessary hea.t is supplied to both U] and \2i according to following assumed R 1-1 S values m var hour.5.

Time q 1 0 1

12 13 - 17 RHS 0.1 0.2 0.4 0.8 1.0

785
Table 16. A case where all unknown is room temperature.

A B 4ABA

-Time

- Room

Table 17- A case where warming-up period is included.

Time 5chedu le

T; me 1 2 3 4

A rm. Men- designated VVdrrnin_g - up Coi) desig nated C/B ) C B rm. Nion- desijneted

\N 1 2 3 4 *-Ti me M H A B A B A B A B - - Room

1 A W/ X t \ -(u nl^nown iS hea-ting load ) B W/m

2 A W) i X 1 0 B X 1 0 0

3 A X 1 X

B X 0 1

4

A fa) \ X <— (A case of Appendix

B 0

786
BANQUET ADDRESS

Computers and the Building Industry

S . Daryanani

Syska and Hennessy, Inc.

Computer technology has made amazing advances within a short period of the last two decades. The

computers are being utilized in many phases of business and industry--from guidance of missiles to op- eration of meat packing plants for optimization of meat mix for hot dogs. Considering the popular ac- ceptance of the computer in today's technological society, one would expect to find extensive utilization of the computer throughout the building industry. Surprisingly, the degree to which computers

are actually used in the building industry is very slight. Even the design disciplines do not make any

significant use of it.

Compared to other industries, the building industry is just starting to utilize the computers.

Several engineers have developed impressive problem-solving programs. Most of you are already familiar

with programs developed by APEC. Some large-scale computer systems have been developed and implemented

for structural analysis and construction project management. However, all the computer utilization at the moment does not replace even 5 percent of the total design manpower involved in the building industry, and therefore is insignificant and somewhat discouraging.

Why the building industry is not using computers at the moment

There are several reasons for lack of utilization of computers in the building industry.

We are proud of our building industry here. People all over the world are fascinated by our highrise buildings which are ever leaping skyward. Visitors are always anxious to see the latest projects

of our architects and engineers.

While we are proud, we should also be realistic.

If the building industry is compared with any other automated industry, such as the manufacture of

automobiles or television, the problems will be evident. The construction industry has scarcely reached

the level of mass production. Strangled by lack of organized research, outdated building codes and con- servative trade unions, it has remained, in a large measure, a pre-industrialized craft. The industry's

rate of technological advance is far below that of other industries. We know the more advanced the technology, the easier it is to automate.

The building Industry is large but consists of several forces pulling in different directions and therefore lacks a sense of direction. The professional talents required in financing, design and con- struction of a large building are amazingly diverse. For the sake of explanation, these can be clas- sified into one of four general sectors: Management, Design, Construction and finally. Operation and Maintenance.

Let us consider the problems associated with the design disciplines, though extensive computer usage could also be made in the other three sectors.

787
The Architect has been the leader of the design team—and safeguards the owner's interests during

design and construction. Due to the widely divergent and highly technical nature of many aspects of building design, the architect has to depend on professional consultants in the engineering areas, such

as the structural engineer, the foundation engineer, the mechanical engineer, the electrical engineer.

The design team may also have the cost estimator, the interior designer and the specialists in acoustics, illumination and landscaping.

This diversity of intellectual disciplines involved in the building design generally fragments

the building team in several ways, the most important being the intellectual fragmentation. The architect does not appreciate the mechanical engineer's goal. The mechanical engineer does not care about

the electrical engineer's objectives; and so on. The design profession is like a universe with several

planets, each merrily surviving in its own orbit.

The most damaging consequence of this fragmentation is the problem of communication. As we know,

communication is the binding force of any social unit, be it design or construction of buildings.

Various disciplines cannot be integrated without communication and professional interaction.

The lack of communication always results in suboptimization of design. Conceived without communication, the best structural design can force a suboptimal mechanical design. A solution based on initial cost may be viable on the basis of the operating cost. The optimized building design is more

a matter of communication than of linear programming.

The last consequence of lack of communication is expensive duplication of effort. The same information is handled over and over again by different persons involved in the process of design.

Another reason for lack of use of computers in the building industry is due to the rais-match in the requirement of the building industry and the present applications of the computer. While the major problem in the building industry, in design and construction, is that of communication, the present computer

applications are geared mainly to engineering problem solving. In addition to problem solving, what we

need is a system which will consolidate all the information about the project in a central file of data

where it will be available to all the members of the design team at the same time. The availability of data to all designers will allow for analyzing the impact of design decisions made in one design area on

the other aspects of the overall design. Thus, engineers could develop integrated designs in terms of overall project goals instead of being limited to their own discipline.

Most of the computer efforts in engineering to date have been aimed at problem solving capabilities.

As you know, the major effort of engineering is not problem solving but integration of the solutions to form a project. Therefore, concentration on the problem solving capabilities has fragmented the work

that can be done on a project with the computer, and has slowed down application of computers to solution of communication problems.

The problem solving approach to engineering has resulted in two handicaps which have again affected

utilization of the computer.

First of all, there is duplication of effort since each problem solving program contains repititions

or large parts of some other programs. Secondly, data from problem to problem, even within the same discipline, has to be transferred manually. The situation is similar to having a road system without

intersections for transferring from one road to the other road. When you reach an intersection you walk off from one vehicle and take the other vehicle on the other road.

The manual transfer of data combined with extensive initial data gathering and input preparation

involve much mundane work on the part of the engineer. This tends to discourage the engineer from application of the existing programs unless the problem is complex or sufficiently large. Several

problems require more than one run of the program to enable the engineer to zero-In on the solution.

Repeated effort in data transfer, data gathering and input preparation adds to the cost of the program utilization and often the result is more expensive than the old fashioned slide rule solution.

This brings us to the problem of economics as related to the cost of computers.

In spite of all the progress in programming, it is still time-consuming and expensive. Actually

at present programming has not advanced at the same rate as developments in hardware. We are unable

to estimate the magnitude of effort involved in coding and algorithms for all the building disciplines.

As a point of reference, the structural design and analysis system in ICES called STRUDL comprises al- most ten million characters of coding and data. As you know, the structural component is just a frac- tion of the entire building design. We do not know how many characters of data would be required to describe completely a building design if it were stored in a computer. When we consider a complete

computer-aided design system, no one is prepared to answer questions such as:

"What is the cost of suitable hardware?" "How many man years will it cost to take to develop suitable software?" "How much will it cost?"

788
The reason for 'no' or vague answers is that based on the present capabilities, the cost of such a computer-aided design system will be out of this world; beyond the economical reach of most of the design

organizations

Why should we be using computers in the building industry?

"The computers are not economical at the moment". "Programming is difficult and time consuming".

"The building industry is too disorganized to be automated".

Having said all that, the question is "why should we be using computers in the building industry?".

The answer to this question involves awareness of the challenges of the future rather than the handicaps of the present.

The key factor of the challenge of the future is the expected growth of population. Next to food,

shelter is a necessity for human survival. The building industry has to plan to meet the critical demands of the future.

The world population is expected to almost double by the year 2000 and have a 30% increase by the year 1985. The following figures for increase in population are based on conservative estimates:

(Figures in millions)

1970 1985 2 000

World 3,700 4,600 6,900

U.S.A. 210 240 310

Developed Countries 1,060 1,350 1,570

Less Developed Countries 2,640 3,250 5,530

(Developed countries include: North America, Soviet Union, Australia, New Zealand, Europe and Japan. Less developed countries include: East Asia (excluding Japan), South Asia, Africa, Latin America and

others .

)

Now you can translate this population growth in the demand for housing, schools, areas of business,

hospitals and recreation facilities. All of this adds up to a heavy demand or may be critical shortage

for building construction facilities.

One can look at this problem from a different perspective. In 1850 only four cities had a population of one million or more. By 1900, the number had increased to nineteen cities. By 1960, 141 cities

had a population of more than one million people. The past trend has shown that the population expansion has taken place around the cities. If this trend continues and if population doubles by the year

2000, by that time we will have to double the existing cities. We will have to build one more London,

one more Rome, one more Tokyo, one more New York, one more Chicago, one more Los Angeles and so on.

It is expected that by the year 2 000 the United States will probably have three megapolises, one

on the East Coast which will extend from Boston to Washington; maybe from Portland, Maine to Portsmouth,

Virginia and might contain almost 25% of the United States population, that Is about 80 million people.

The second megapolis will be concentrated around the Great Lakes area which may stretch from

Chicago to Pittsburg and possibly also north to the Toronto region of Canada--thereby including Detroit,

Toledo, Cleveland, Akron, Buffalo and Rochester. This megapolis seems likely to contain more than oneeighth of the United States population, about 40 million people.

The third megapolis on the Pacific Coast would probably stretch from San Diego to Santa Barbara,

ultimately from San Francisco to Santa Barbara and would contain one-sixth or about 20 million people.

789
Let us continue to look at this problem from a different perspective. In the last 70 years in this country, the consumption and therefore production of goods and services has almost doubled every

15 years. If this rate of increase continues, we will see one more doubling by the year 1985 and another doubling by the year 2000. As you well know, both production as well as consumption of goods

and services will require additional construct ion--that is factories, stores, warehouses and offices.

With progress in technology, we can automate production of goods, introduce efficiencies in production

and services, but up to now we have no plans for automating the consumption.

Let us continue to look again from a different perspective, this time the growth in educational

facilities

In spite of extensive educational facilities here, there are estimated to be about 25 million

adults, 18 years of age or over, in the United States with less than eighth grade education. This has created the problem of unemployable unskilled labor. 15% of the unemployed in the three major ghetto

areas in New York City have never had a white collar job at any time. On the other hand, 507e, of job

vacancies in the New York City area are for white collar workers. It is estimated that in 10 years only

47o of the employment market will be open to the unskilled. We will need more schools, colleges and universities to educate people, not for the sake of education alone, but to enable them to hold jobs

and provide services for the future.

In some of the less developed countries, the educational system is either non-existent or minimal.

We have educational problems here, but our problems are similar to a shot from a toy pistol as compared

to the educational explosion which is going on in countries such as Africa, Asia, Arabia, and Latin

America. These nations feel that it is crucial to their development to have a basic educational system.

Well over half a billion people must be taught to read, write and master simple computational skills.

Hundreds of millions of people must be brought to accept new practices in agriculture, health and home management

The occupational skills of millions must be brought up to the requirements of new Industries,

public works and service occupations which are waiting to be created. These educational facilities

will again require buildings and more buildings.

Medical facilities are being improved constantly, which have increased the life span for people

throughout the world. We will need more hospitals, not only because of increased population, but also

for more people, as, hopefully, people will be living longer.

In the Colonial times, the buildings were planned for a life of no less than 100 years. The recent construction, it is hoped, will last at least 30 years. In other words, a building completed

today, will have to be replaced by the year 2 000 if not sooner.

Finally, in this respect we know that as societies become more industrialized, people work less and less on their job, and we tend to have a leisure-oriented society. It is expected that by the year 2000, working hours will be reduced from the present, about 1900 hours per year, to 1100 per year. In such a leisure-oriented society, one could spend kO°L of one's day on vocation, 407=, on avocation and 20% on neither, just relaxing. The increased availability of time for leisure, avocation and relaxation will require increase in buildings for recreation and travel.

At present, apart from lack of money, the second critical shortage is of design and construction

personnel for the building industry. If we are planning to meet the critical needs of the future, we have to utilize efficiently all the available resources. Our plans will have to include the potential

of computers to solve the communication problems of the building industry.

What should be done to plan for the future?

In order to plan for the future and avoid making mistakes, we must begin to anticipate earlier

than we have in the past the problems of the future. Some of them already are becoming quite clear, and their impact can be expected to be so enormous as to require a long lead time for assessment and preparation.

A look at the history of scientific and technological change will help us understand that in- adequately perceived goals may be of greater significance than any possibilities we can foresee. We

must alter our standard approach to the future in a way that will enable us to cope with what cannot be anticipated. At the same time, however, we must also try to anticipate as much as possible in order to provide a rational framework for our expectations.

First of all, we do not have to be discouraged by the present cost and capabilities of the com- puter.

790
In the past, computer performance has increased by a factor of 10 in every two or three years, and

this is considered a consfervative estimate. If computer capabilities were to continue to increase by

a factor of 10 every , two or three years until the end of the century, then all current concepts about

computer limitations will have to be reconsidered. Even if the trend continues for only the next decade

or two, the improvements over current computers will be factors of thousands to millions. If we add the likely enormous improvements in input /output devices, programming and problem formulation and better

understanding of the basic design process, the estimates of improvement will be conservative. Even if the rate of change slows down by several factors, there will still be room in the next thirty years for overall improvement of some 5 to 10 orders of magnitude. Therefore, it is necessary to ignore often

meaningless or non-rigorous statements such as "we are at present limited by the computer".

The computer costs will continue to decrease while the manpower cost will increase rapidly. What

might seem uneconomical today, will be economical tomorrow, and a necessity for survival day-aftertomorrow.

With improvement in the computer hardware and reduction in cost, one can foresee that the computer

utility industry will become as fundamental as the power industry. A large central processor will

handle information at a low unit cost just as a large central generator produces electricity at a low unit cost. It will be cheaper to make use of this central utility than it is for each individual to have his own generator.

With the development of telecommunication for computers whereby engineers can use low cost terminals in their offices, it will be possible to help in the matter of locational fragmentation existing

at the moment

We have already established the critical needs of the building industry. We hope that the com- puter technology will progress fast enough to enable us to satisfy our requirements. While suitable

hardware is being developed, we will have to work on development of a Computer-Aided Design System to solve problems of communication. Such a system will have several subsystems, but all of these will

share a common data file for the entire project stored on a secondary storage.

It is now up to us to develop such a system based on our imagination, expectations and capabilities. From the stage of problem solving we have to progress to the concept of communication as a key to com- puterized building design system.

We also have to recognize the necessary components or requirements of such a system.

The most important component of the system is people: People or designers. Because of present

inadequate understanding of the design process the computer-aided building system must allow the de- signers to make all the critical decisions involved in the use of the system. The real danger in

developing a computer-aided design system is not that it will produce poor design, but that it may

fail to consider the human element of the system and force the user into rigid procedure in its use, thereby either discouraging use of the system or stifling any creative aspects of design.

Most important, we have to analyze and increase our understanding of the basic design process in order to utilize full potential of the computer-aided design system.

When computers first became available, the tendency was to program all of the approximate methods

of analysis that have been designed for hijman users. It was only when reformulating the process that engineers realized that the appropriate way to attack the problem of computerized analysis was to use

all the abilities of the computer and program rigorous method of analysis.

As you can appreciate, development of a computer-aided design system will be an expensive and time

consuming task. We cannot afford any duplication since we have limited resources and are racing against

time. It is therefore necessary that all of you who are interested in the building industry should pool your resources and join in a common effort in developing such a computer-aided design system.

The sheer intensity of the future demand makes it ridiculous to compete in this task on a pro- fessional, regional, or national basis. We can utilize our resources more efficiently by establishing

international cooperation on what appears to be a common. goal. You can achieve this objective by

joining, supporting and leading existing cooperative efforts.

How much progress will be made to meet the problems of tomorrow will depend on you.

791

Candid Views of the Participants at the Symposium Banquet

F. H. Bridges, Pr esi dent of ASHRAE

,

Master of Cermonies of the banquet.

Banquet head table from left to right: A. T. Boggs, ASHRAE; Mrs. P. R.Achenbach;

F. H. Bridgers, ASHRAE; S. Daryanani, APEC;P. R. Achenbach, NBS ; J. M. Ayres,

President, APEC;Mrs. F. J. Powell; and T. Kusuda, NBS. (Not shown at the left end

of the table are Mrs. T. Kusuda and F. J. Powell, NBS . )

Japanese delegation with Dr . T. Kusuda, Chairman

of the Program Committee and Mrs. Kusuda.

K. Kimura, Head of delegation, is shown at the center of front row.

793

I
G. L. Gupta, Building R esearch Institute,

India; Mrs. G. L. Gupta; T. Y. Sun,

J. M. Ayres, and K. Parks of Ayres,

Cohen & Hayakawa and Julia Szabo, ASHRAE

(left to right).

I. Hogland, Royal Institute of Technology, Sweden;

A. T. Boggs, ASHRAE; P. G. Down, Oscar Faber

and Partners, England; C. W. Phillips, NBS;

J. B. Chaddock, Duke University; and E. N. Van

Deventer, National Building R esearch Institute,

South Africa (left to right).

J. J. Anquez and L. G. Bertolo, CSTB, France;

K. Fitzner, LTG Lufttechnis che Gmbh, West

Germany; W. K. Thomas, Thomas -Young Associates

R. F. Mehnert, B. H. Silber stein As sociates ; and

J. L. Norris, Long Island Lighting Company (left to right).

F. J. Powell, NBS, Vice Chairman, Symposium;

Mrs. F. J. Powell; R. H. Tull, ASHRAE; P. R. Achenbach, NBS; and Mrs. P. R. Achenbach

(left to right).

794
Mrs. G. L. Gupta; N. Gulati, D. C. Government;

G. L. Gupta, Buildiog R esearch Institute, India;

Mrs. N. Gulati; Mrs. A. Chawla;A. Chawla, D. C. Government; Valerie Butler, Nash Love Associates;

and N. K. Khosla, Enviro-Management & Research

(left to right).

C. W. Phillips, NBS, Chairman of Arrangements

Committee, (left), and F. Clain, COSTIC, France.

A

PR

E. N. VanDeventer, National Building R esearch

Institute, South Africa; Sarah Torrence, NBS; and

E. Christopher son, Danish Building R es ear ch

Institute (left to right).

E. M. Barber, NBS; A. R. Paradis, Dynamic

Graphics Inc. ; Mrs. A. R. Paradis; N. La

Courte, ASHRAE; B. W. Ward, Britt Alderman,

Jr. ; L. G. Spielvogel, Inc. ; andH. K. Varma,

North Carolina A h T State University (left to right).

LIST OF REGISTERED ATTENDEES

J. T. Adams

Union Carbide Corp. - Nuclear Division

Post Office P - Building K-lOOl

Mail Stop 157 Oak Ridge, Tennessee 37830

S. Agerbek

The Ralph M. Parsons Co., Los Angeles, Cal. 16428 Santa Bianca Drive

Hacienda Heights, California 91745

J. R. Akerman

University of Michigan

1213 Van Dusen Drive Ann Arbor, Michigan 48103

W. R. Anderson

Bureau of Reclamation

Department of Interior

Denver, Colorado 80201

C. A. Alders

Texas Electric Service Company

P. 0. Box 970 Fort Worth, Texas 76101

J. M. Alvord

Alvord and Swift, Incorporated

60 East 42nd Street New York, New York 10 017

D. F. Anderson

DeLeuw-Cather Company

955 L' Enfant Plaza, S.W. Washington, D. C. 20024

J. J. Anquez

C. S. T. B. Avenue du Recteur POINCARE

Paris , France

N. Aratani

Architectural Department

Faculty of Engineering of Hokkaido

University

North-12, West-8

Sapporo, Japan

A. E. Arledge

Carrier Overseas Corporation

Carrier Parkway

Syracuse, New York 13201

R. S. Arnold

Carrier Air Conditioning Company

Carrier Parkway

Syracuse, New York 13201

E. G. Arntzen

Los Alamos Scientific Laboratory

P. 0. Box 1663 Los Alamos, New Mexico 87544

R. G. Attridge, Jr. Ranco Controls Division

601 West Fifth Avenue

Columbus, Ohio 43201

L. R. Axelrod

Powers Regulator Company, Systems Division

2942 MacArthur Boulevard

Northbrook, Illinois 60062

J. M. Ayres

Ayres , Cohen & Hayakawa

1180 South Beverly Drive

Los Angeles, California 90035

D. Bahnfleth

Heating, Piping, and Air Conditioning

10 South La Salle Street

Chicago, Illinois 60515

C. H. Barcus Professor of Architecture

Miami University

5176 Westgate Drive

Oxford, Ohio 45056

B. H. Barksdale

Hayes, Seay , Mattern & Mattern

P. 0. Box 1490

Roanoke, Virginia 24007

W. B. Barnard

Honeywell, Incorporated

Commercial Division

North Austin Avenue Morton Grove, Illinois 60053

C. Barton

Smith, Hinckman 6. Grylls Associates, Inc. 3107 West Grand Boulevard

Detroit, Michigan 48202

J. R. Beckum, P.E. Vincent G. Kling & Associates

1401 Arch Street Philadelphia, Pennsylvania 19102

G. Bees ley DP&L Company

1506 Commerce

Dallas, Texas 75201

797
H. F. Behls

Sargent & Lundy

140 South Dearborn Street Chicago, Illinois

W. F. Beiderman

American Telephone & Telegraph Company

32 Avenue of the Americas , Room 2112 New York, New York 10013

E. L. Bell Hawkins & Anderson, Consulting Engineers

2117 North Hamilton Street Richmond, Virginia 23230

A. G. Bendelius

Parsons, Brinckerhof f , Quade & Douglas, Inc 111 John Street New York, New York 10038

H. Benjamin

Surveyor, Nenniger & Chenevert , Inc. 1550 de Maisonneuve Boulevard, West Montreal 107, Quebec, Canada

L. M. Bent Department of Public Works

301 Elgin Street Ottawa, Ontario, Canada

L. G. Bertolo

C. S. T. B. 4 Recteur Poincare

Paris, France

J. J. Sevan Philadelphia Electric Company

211 South Broad Street, 9th Floor

Philadelphia, Pennsylvania 19105

L. D. Beverage

The Potomac Edison Company

Downsville Pike

Hagerstown, Maryland 21740

A. Bijl

Architecture Research Unit

University of Edinburgh

55 George Square

Edinburgh, Scotland, UK EH 8 9JU

B. E. Birdsall

Ziel-Blossom & Associates, Incorporated

700 Valnut Street Cincinnati, Ohio 45202

W. P. Bishop

Joseph P. Wohlpart Associates

155 East 42nd Street New York, New York 10017

G. H. Blair

Honeywell, Incorporated

24-30 Skillman Avenue Long Island City, New York 11101

H. G. Blasdel

Department of Architecture

University of California

Berkeley, California 94720

A. W. Boeke

Technische Hogeschool, Leerstoel

Klimaatregeling

Mekelweg 2, Delft

The Netherlands

A. T. Boggs ASHRAE

345 East 47th Street New York, New York 10017

A. Boysen

National Swedish Institute for Building

Research

Box 27163, S-102 Stockholm 27, Sweden

A. P. Brazzale

Post Office Department

Bureau of Facilities

Washington, D. C. 20260

P. J. Breman Union Carbide Corporation

P. 0. Box Y Building 9733-1

Oak Ridge, Tennessee 37830

F. H. Bridgers ASHRAE

213 Truman Street, N.E. Albuquerque, New Mexico 87108

R. E. Brigham

Department of Defense DIASA-3B

Pentagon

Washington, D. C. 20301

C. Broder

Port of New York Authority

111 8th Avenue

New York, New York 10011

G. Brown

Royal Institute of Technology

10044 Stockholm 70, Sweden

R. S. Buchanan ASHRAE

345 East 47th Street New York, New York 10017

798
S. R. Buchanan

Johnson Service Company

507 East Michigan Street Milwaukee, Wisconsin 53201

R. S. Bycraft

Department of Public Works of Canada

Design Branch, Mechanical Engineering

Division

Sir Charles Tupper Building Ottawa 8, Ontario, Canada

J. H. Cansdale ASHRAE

345 East 47th Street New York, New York 10017

J. D. Carson

Leo A. Daly Company

1025 Connecticut Avenue, N.W. Suite 712 Washington, D. C. 20036

J. B. Chaddock

Duke University

Department of Mechanical Engineering

Durham, North Carolina 27706

A. C. Chawala

D. C. Government

Department of General Services

Washington, D. C. 20406

J. Y. Chini

IBM 18100 Frederick Pike

Gaithersburg, Maryland 20760

E. Christophersen

Danish Building Research Institute

Postgird 2786

1300 Copenhaven, Denmark

I. C. S. Chou

Mechanical Engineering Department

University of Hawaii

Honolulu, Hawaii 96822

B. 0. Cingilli Tennessee Valley Authority

Knoxville, Tennessee

F. Clain

Co. S. T. I. C. 9, Rue La Perouse

75 - Paris 16, France

J. T. Cleckley

Georgia Power Company

P. 0. Box 4545 Atlanta, Georgia 30302

L. B. eleven

State of Wisconsin

Bureau of Capitol Development

1 West Wilson Street Madison, Wisconsin 53702

I. L. Clunie

Nicholas Fodor and Associates, Ltd.

38 Charles Street, East Toronto 5, Ontario, Canada

R. F. Cook

Westinghouse Electric Corporation

700 Braddock Avenue 7L27 East Pittsburgh, Pennsylvania 15112

Z. Cumali

Consultants Computation Bureau

594 Howard Street

San Francisco, California 94105

A. Curl

Space, Incorporated

1015 Elm Street

Dallas, Texas 75202

D. M. Curtis Oscar Faber & Partners

18 Upper Marlborough Road

St. Albums, Herts, England

M. Dagenais

LaLonde Valois Lamarre Valois & Associates

615, rue Belmont

Montreal 101, P. Q. Canada

B. Davis Deere & Company

Manufacturing Engineering Department

Moline, Illinois 61265

T. Davis

McGaughy , Marshal and McMillan

220 West Freemason Street

Norfolk, Virginia 23510

L. 0. Degelman

Associate Professor of Architecture Engin.

Pennsylvania State University

101 Eng "A" Building

University Park, Pennsylvania 16802

J. DeGuise

P. DeGuise & Associates

10127 St. Laurent

Montreal, Quebec, Canada

P. DeGuise

P. DeGuise & Associates

10127 St. Laurent

Montreal, Quebec, Canada

799
E. I. Diab

Letendre, Monti, Lavoie, Nadon

1253 McGill College, Suite 530 Montreal, P. Q. , Canada

H. B. Dickenson

Hayes, Seay, Mattern & Mattern

P. 0. Box 1490 Roanoke, Virginia 24007

C. Dorgan

Wright-Patterson Air Force Base Ohio

G. Dombusch

Columbia Gas of Maryland

1 South Potomac Street

Hagerstown, Maryland 21740

P. G. Down

Oscar Faber & Partners

18 Upper Marlborough Road

St. Albans

Herts, England

G. R. Dunham

Corps of Engineers - Sacramento District

650 Capital Mall - Room 5122 Sacramento, California 95814

M. R. Edwards

Washington Gas Light Company

1100 H Street, N.W. Washington, D. C.

G. Engholm

GARD/GATX

7449 North Natchez Avenue

Niles, Illinois 60648

P. Euser Technisch Physische Dienst TNO-TH

Stieltjesweg 1 P.O.B. 155

Delft, Netherlands

H. E. Faller

Harold E. Faller & Associates

1600 South Salcedo Street New Orleans, Louisiana 70125

K. H. Faller

Harold E. Faller & Associates

1600 S. Salcedo Street New Orleans, Louisiana 70125

T. Fehrenbacher

McDonnell Douglas Automation Corporation

Building 105, Level 4, Post D2

St. Louis, Missouri

D. Fitzgerald

Heating & Ventilating Research Association

Old Bracknell Lane Bracknell Berks RG12 4AH, U. K.

K. Fitzner

LTG Luf ttechnische Gmbh

D-7 Stuttgart 40, Werner Str. 1191129 Postfach 39, West Germany

D. Fletcher

Detroit Edison Company

2000 Second Avenue

556 Service Building

Detroit, Michigan 48226

S. R. Fogleman

Sam R. Fogleman Associates, Consulting

Engineers

1225 Ponce de Leon Avenue

Rio Piedras, Puerto Rico 00926

C. T. Fox Gas-Fired Products, Incorporated

305 Doggett Street, P. 0. Box 3485 Charlotte, North Carolina

E. T. Fredricks, Jr. Gritschke & Cloke, Incorporated

221 North LaSalle Street Chicago, Illinois 60601

D. Freeling

Post Office Department

12th NW & Pennsylvania

Washington, D. C. 20260

J. E. Fromm

K07/025

IBM Research Laboratory

Monterey and Cottle Roads San Jose, California 95114

C. A. Fry, P.E. Chief Mechanical-Industrial Engineer

Buchart-Horn (Consulting Engineers & Planners)

40 South Richland Avenue

York, Pennsylvania 17405

Y. Fukushima

Shin Nippon Air Conditioning Company, Ltd. 4-2, Hongoku-cho , Nihombashi, Chuo-ku

Tokyo, Japan

D. W. Galehouse

Automated Construction Technology, Inc.

P. 0. Box 103 Dayton View Station

Dayton, Ohio 45406

800
J. p. Galloin

Carrier Overseas Corporation

Carrier Parkway

Syracuse, New York 13201

V. M. Garcia

School of Architecture

University of Puerto Rico

P. 0. Box 21909 UPR Station

Puerto Rico 00931

J. J. Gat to Westinghouse Tele-Computer Systems Corp. 2040 Ardmore Boulevard

Forest Hills, Pennsylvania 15221

P. G. Lavoie

Lorrain & Gerin-Lavoie Consulting Engineers

4070 0. Jean Talon

Montreal 308

P. Quebec, Canada

D. S. Gill

DeLeuw-Cather & Company

955 L'Enfant Plaza, S.W. Washington, D. C. 20024

L. Gill

Mountain Fuel Supply Company

Salt Lake City, Utah 84111

T. Gooch

Benham-Blair & Affiliates

6323 North Grand Boulevard

Oklahoma City, Oklahoma 73118

M. D. Good

Los Angeles Department of Water & Power

111 Hope Street, North

Los Angeles, California 90054

H. D. Goodman

Joseph R. Loring & Associates

Two Pennsylvania Plaza

New York, New York 10001

R. A. Gordon

Cornell, Howland, Hayes & Merryfield

1600 Western Boulevard

Corvallis, Oregon 97330

K. M. Graham

Southern California Gas Company

P. 0. Box 3249 Terminal Annex

Los Angeles, California 90054

0. Granlund

Ingenjorbyra Olof Granlund Antti Oksanen

Elisabetsgatan 19 A 5 Helsingfors 17, England

M. H. Gray, III Whirlpool Corporation

Higliway 41 North

Evansville, Indiana 47727

K. J. Guion

Smith, Hinchman & Grylls Associates, Inc. 3107 West Grand Boulevard

Detroit, Michigan 48202

N. K. Gulati

Sanitary Engineering Department

D. C. Government

B29 E Street, N.W., Room 945 Washington, D. C. 20004

C. L. Gupta

CSIRO Division of Building Research, Hyhelt

P. 0. Box 56 Australia VIC 3190

E. F. Gurka, Jr.

U. S. Postal Service

12th & Pennsylvania Avenue, N.W. Washington, D. C. 20260

K. Hagimoto

Mitsubishi Heavy Industries, Ltd.

No. 1, Takamichi, Iwatsuka-cho , Nakamura-ku

Nagoya, Japan

H. J. Haebler , Jr. , P.E. Luther M. McLeod and Associates

200 East Joppa Road Towson, Maryland 21204

N. E. Hager, Jr. R 6i D Center, Armstrong Cork Company

2500 Columbia Avenue

Lancaster, Pennsylvania 17604

R. W. Haines

Collins Radio Company

Dallas, Texas 75207

A. Handshy

Bank Building Corporation

1130 Hampton Avenue

St. Louis, Missouri 63139

J . J . Harmon

Carrier Air Conditioning Company

8508 Bentridge Lane

Richmond, Virginia 23229

G. N. Hashmi

Ellerbe Architects

333 Sibley Street

St. Paul, Minnesota 55101

801
R. J. Hatwell

U. S. Coast Guard Headquarters

400 7th Street, S.W. Washington, D. C. 20591

T. Haw, III Chrysler Corporation

P. 0. Box 1919 Detroit, Michigan 48231

J. E. Hays

Naval Facilities Engineering Command

Electronic Facilities Support Division,

Code 044 Washington, D. C. 20390

K. J. Hazell

J. L. Richards 6i Associates , Ltd. 864 Lady Ellen Place

Ottawa, Ontario, Canada

J. B. Headrick

Dallas Power and Light Company

1506 Commerce Street Dallas, Texas 75201

M. A. Hertzberg, P.E.

M. A. Hertzberg, Consulting Engineers

Sugarbush Village

Warren, Vermont 05674

J. B. Hoaglund

ITT 320 Park Avenue

New York, New York 10022

I. Hoglund

The Royal Institute of Technology

Division of Building Technology

S-100 44 Stockholm 70, Sweden

G. M. Hollander _

; Veterans Administration

810 Vermont Avenue, N.W. Washington, D. C. 20420

R. F. Hughes

Earl Walls Associate

7460 La Jolla Boulevard

La Jolla, California 92057

R. L. Hughes, Jr. ENTCO

5 East 23rd Street Baltimore, Maryland 21218

E. Isfalt The Royal Institute of Technology

Stockholm 70, Sweden

H. Ishino

Waseda University (Graduate School)

4-170, Nisi-Ogikubo , Shinjuku-ku

Tokyo, Japan

J. H. Jacobs, Jr._ Chas. T. Main, Incorporated

441 Stuart Street

Boston, Massachusetts 02116

G. F. Jacobson

Headquarters PACAF

1414 Aalapapa Drive

Kailua, Hawaii 96734

J. S. Jarolim

Army and Air Force Exchange Service

ATTN: CSXPT-2 Dallas, Texas 75222

F. Jennings

Walter Kidde Constructors, Incorporated

19 Rector Street New York, New York 10006

J. W. Jones

Ohio State University

206 West 18th Avenue

Columbus, Ohio 43219

J. E. Kampmeyer, P.E. Robert E. Lamb, Incorporated

Valley Forge Industrial Park

Valley Forge, Pennsylvania 19481

J. Y. Kao National Institutes of Health

Room 2905, Building 13 Bethesda, Maryland 20014

M. B. Kassay

Sahara, Incorporated

29-28 41 Avenue

Long Island City, New York 11101

E. R. Kaufman

U. S. Postal Service - San Francisco

Regional Office

631 Howard Street

San Francisco, California 94105

H. W. Keil

Alvord and Swift

60 East 42nd Street

New York, New York 10017

N. K. Khosla

Enviro-Management & Research, Incorporated

901, 8th Street, N.W. Washington, D. C. 20008

802
C. Kimball. Carrier Corporation

Carrier Parkway

Syracuse, New York 13201

T. Kimoto

Oversears Industry Research Center

4-4, Kojimachi, Chiyoda-ku

Tokyo, Japan

K. Kimura

Waseda University (Associate Professor)

4-170, Nishiokubo, Shinjuku-ku

Tokyo, Japan

G. R. Kinzer

Johns-Manville Products Corporation

Research & Engineering Center Manville, New Jersey 08835

M. B. Kispert

Ellerbe Architects

333 Sibley Street

St. Paul, Minnesota 55101

W. J. Kissell

Mountain Fuel Supply Company

180 East First South Street

Salt Lake City, Utah 84111

S. H. Klein

Department of National Defense, Canada

C. F. H. Q. - DCEDE - Ottawa 4 Ontario , Canada

J. L. Kmetzo, P.E. Syska U Hennessy, Incorporated

144 East 39 Street New York, New York 10016

R. Kobrick

Seelye, Stevenson, Valve, & Knecht

99 Park Avenue New York, New York 10017

G. Koch

IBM

Real Estate & Construction Division

1000 Westchester Avenue

White Plains, New York 10604

A. Kokalari

American-Standard, Incorporated

P. 0. Box 2003 New Brunswick, New Jersey 08903

Y. Konishi

The Shimizu Construction Co., Ltd. Research Laboratory

2-1, Takara-Chou, Chou-Ku

Tokyo , Japan

A. Konoike

Kantogakuin University

4834 Mutsuura-cho

Kanazawa-Ku, Yokohama, Japan

C. L. Koppenhaver

Gilbert Associates, Incorporated

P. 0. Box 1448 Reading, Pennsylvania 19603

R. Kramer Honeywell, Incorporated

8330 North Austin Avenue Morton Grove, Illinois 60053

S. F. Krogstad

AEDC Arnold A. F. Station Tennessee 37389

D. A. Krot Carnegie Mellon University

Schenley Park

Pittsburgh, Pennsylvania 15213

S. Kuramochi

Taisei Construction Company, Ltd.

No. 2-1, Kyobashi, Chuo-ku

Tokyo , Japan

F. Kurihara

P. T. Morimura & Associates

Consulting Mechanical & Electrical

Engineers

1-2-9, Yoyogi, Shibuya-ku

Tokyo, Japan

C. F. Kwok

Veterans Administration

810 Vermont Avenue, N.W. Washington, D. C. 20420

C. LaBrecoue

P. DeGuise & Associates

10127 St. Laurent

Montreal, Quebec

Canada

N. A. LaCourte

ASHRAE

345 East 47th Street New York, New York 10017

R. Lahmon

Eastman Kodak

Kodak Park

Rochester, New York 14650

J. T. H, Lammers University of Technology, Building Dept.

Building Wen S, Room 9938 Eindhoven

The Netherlands

803
L. L. Lampert

Buerkel & Company, Incorporated

129 Maiden Street Boston, Massachusetts 02118

S . Larm

AB Svenska Flaktfabrlken

S-104 60 Stockholm

Sweden

T. A. Lawand

Brace Research Institute

MacDonald College

Ste. Anne de Behlevue

Quebec, Canada

K. G. Lawrence Philadelphia Electric Company

211 South Broad Street - 9th Floor

Philadelphia, Pennsylvania 19105

J. DeBaut Electricite de France

Les Renavudieres Eludes et Recherches

77 Ecuelles, France

H. S. Lewis

Jaros , Baum & Bolles

345 Park Avenue New York, New York 10022

B. G. Liebtag

Duquesne Light Company

435 Sixth Avenue

Pittsburgh, Pennsylvania 15219

T. D. Lin

Portland Cement Association

5420 Old Orchard Road

Skokie, Illinois 600 76

E. J. Leon National Research Council of Canada

Montreal Road Laboratories

Ottawa 7, Ontario

Canada

M. Lokmanhekim

General American Research Division of GATX

7449 North Natchez Avenue

Niles, Illinois 60648

J. L. Loomis Human Performance Research Laboratory

Pennsylvania State University

University Park, Pennsylvania 16802

T. Looney

McFall and Konkel Consulting Engineers, Inc. 2160 South Clermont Street Denver, Colorado 80222

R. P. Lortie

Associated Engineers, Incorporated

670 West Sixth Street Winston-Salem, North Carolina 27101

I. Lotersztain

Bouwcentrum Argentina

Cangallo 700 esq. Maipu

Buesnos Aires, Argentina

N. M. Love Nash M. Love Associates

901 8th Street, N.W. Washington, D. C. 20001

W. H. Loyd

Bender Burrell Associates

P. 0. Box 13 Camp Hill, Pennsylvania 17011

F. F. Lusby, Jr. Lusby & Company, Consulting Engineers

300 North Potomac Street Hagerstown, Maryland 21740

E. L. MacFerran Tennessee Valley Authority

Knoxville, Tennessee

H, D. MacPhee

Department of Public Works of Canada

P. 0. Box 3010, Halifax South Postal

Station

Halifax, Nova Scotia, Canada

C. J. R. McClure

Charles J. R. McClure & Associates, Inc 10427 Old Olive St. Rd.

St. Louis, Missouri 63141

A. F. McCrea Robertshaw Controls Company

1701 Byrd Avenue

Richmond, Virginia 23226

D. McCurdy

Ontario Hydro

5760 Yonge Street Willowdale, Ontario, Canada

R. W. McDonald

Carolina Power & Light Company

Box 1551 Raleigh, North Carolina 27602

R. W. McKinley

PPG Industries

1 Gateway Center

Pittsburgh, Pennsylvania 15243

804
W. C. McMurry

American Gas Association

1515 Wilson Boulevard

Arlington, Virginia 22209

D. McNamara

Ministry of Public Buildings & Works

Cleland House, Page Street London SWl , England

W. L. McNamara

ADI Limited

P. 0. Box 4A, Fredericton New Brunswick, Canada

J. C. Magnussen

Honeywell , Inco rpo rated

2701 Fourth Avenue South Minneapolis, Minnesota 55408

Jeet Mahal

Vosbeck, Vosbeck, Kendrick and Redinger

720 North St. Asaph Street Alexandria, Virginia 22314

Fiji Maki

Nikken Sekkei Ltd. Planners /Architects /Engineers

2-38, Yokobori, Higashi-ku

Osaka, Japan

J. F. Malarky

PPG Corporation

One Gateway Center Pittsburgh, Pennsylvania 15222

Stanley Mankowski

The Austin Company

450 West First Avenue

Roselle, New Jersey 07203

Seprl Marcq et Roba Consulting Engineers

Boulevard Leopold II 1080 Brussels, Belgium

John W. Markert

General Services Administration

18th and F Streets, N.W. Room 5325 Washington, D. C. 20405

H. J. Martin, Jr. Public Service Electric and Gas Company

80 Park Place, Room 3174 Newark, New Jersey 07101

Robert L. Mason

Texas Technical University

Mechanical Engineering Department

P. 0. Box 4289 Lubbock, Texas 79409

S. Mass on Perkins and Will Service Company, Inc. Washington, D. C. 20036

Koichi Matsuda

Hitachi Plant Engineering & Construction

Company, Ltd. 1-13-2, Kita-Otsuka, Toshima-ku

Tokyo , Japan

T. Mazuchowski

Smith, Hinchman & Grylls Association, Inc. 3107 West Grand Boulevard

Detroit, Michigan 48202

Robert W. McKinley

PPG Industries

One Gateway Center Pittsburgh, Pennsylvania 15222

Ralf F. Mehnert

Benjamin H. Silberstein Associates

21 Hanover Place Hicksville, New York 11801

Laheri Mehta

S&H Information Systems, Incorporated

144 East 39th Street New York, New York 10016

H. T. Mei

Lamar State College of Technology

Box 10028, Lamar Station

Beaumont, Texas 77705

R. F. Meriwether

Ross F. Meriwether & Associates, Inc. 1600 N. E. Loop 410

San Antonio, Texas 78209

S. R. Michaelis

Perkins & Will Service Company, Inc. Washington, D. C. 20036

S. Miletta

Walter Kidde Constructors, Incorporated

19 Rector Street New York, New York 10006

James R. Miller

Westinghouse Tele-Computer Systems Corp. 2040 Ardmore Boulevard

Pittsburgh, Pennsylvania 15221

E. C. Mills

Philadelphia Electric Company

211 South Broad Street Philadelphia, Pennsylvania 19105

805
Wayne A. Mills

Director of Government Sales Washington Gas Light Company

1100 H Street, N.W. Washington, D. C. 20005

Dale R. Missler

Hellmuth, Obata & Kassabaum

315 North 9th Street

St. Louis, Missouri 63101

G. P. Mitalas

National Research Council

Building Research Division

Ottawa, Ontario, Canada

H. G. Mitchell

The Electricity Council

Trafalgar Buildings, 1 Charing Cross

London, S.W.I, England

Eiji Miyaji

The Shimizu Construction Company, Ltd.

2-1, Takara-cho, Chuo-ku,

Tokyo , Japan

Raymond J. Moss

IBM-Real Estate Division

1000 Westchester Avenue White Plains, New York 10604

D. J. Mosshart

Limbach Company

Four Gateway Center Pittsburgh, Pennsylvania 15222

W. H. Mueller

Indianapolis Power & Light Company

25 Monument Circle

Indianapolis, Indiana 46206

Jim Mullen

Lennox Industries, Incorporated

1600 E. Linn

Marshalltown , Iowa 50158

G. Mullins

Brown, Davis, & Mullins, Associates

Champaign, Illinois 61820

J. Manzo Vollmer Associates

P. 0. Box 407 Alexandria, Virginia 22313

R. Muralidharan

General Electric Research & Development

Center Building 37, Room 615, P. 0. Box 43 Schenectady, New York 12301

Mr. Jerry Myers

Oklahoma Natural Gas Company

Post Office Box 871 Tulsa, Oklahoma 74102

Kermit B. Myers

Mechanical Engineering Department

Iowa State University

Ames, Iowa 50010

Yasuaki Nakazawa

Kyoto Technical University

Matsugasaki, Sakyo-ku, Kyoto, Japan

L. W. Nelson

Honeywell, Incorporated

2701 4th Avenue, South

Minneapolis, Minnesota 55408

G. Newton

Huf sev-Nicolaides Associates, Incorporated

215 Malaga Avenue Coral Gables

Miami, Florida 33134

Y. Nishi

John B. Pierce Foundation Laboratory

290 Congress Avenue

New Haven, Connecticut 06519

Soren F. Normann

DERAC Consultants, Incorporated

8822 South East 56th Mercer Island, Washington 98040

J. T. Norris

Long Island Lighting Company

250 Old Country Road

Mineola, New York 11501

0. J. Nussbaum

Halstead & Mitchell

Division of Halstead Industries, Inc. Zelienople, Pennsylvania 16053

Garfield A. Nuttall

Lakehead University

240 Van Horne Street Thunder Bay, Ontario, Canada

U Tin Nyo

Berger Association Incorporated

3920 Market Street Camp Hill, Pennsylvania 17011

Willard Oberdick

Smith, Hinchman & Grylls

University of Michigan

1503 Ottawa Ann Arbor, Michigan 48105

806
R. H. O'Brien

C-K Engineering Company, Incorporated

1061 Paulison Avenue

Clifton, New Jersey 07011

Kiyoshi Ichifuji

The Faculty of Engineering

Hokkaido University

Sapporo, Japan

Tim 0' Connor

Inatome & Associates, Incorporated

8980 West Nine Mile Road

Oak Park, Michigan 48237

Ferenc Oezvegyi

Sulzer Brothers Limited

8401 Winterthur, Switherland

Shogo Ogasawara

Sanki Engineering Company, Ltd. 1-10, Yuraku-cho, Chiyoda-ku

Tokyo, Japan

Toshio Okajima

A.C. Martin & Associates

1900 Union Bank Square Los Angeles, California 90017

Yasukazu Okuda

Nikken Sekkei Ltd. 1-4-27, Koraku, Bunkyo-ku

Tokyo, Japan

Lowell B. Orange

Sacramento , Municipal Utility District

P. 0. Box 15830 Sacramento, California 95813

J. M. Owendoff

U. S. Air Force Headquarters Aerospace Defense Command

(DEEEN) ENT Air Force Base, Colorado 80912

D. F. Owens John Graham & Company

2826 Mt. St. Helens Place, South

Seattle, Washington 98144

Ferenc Ozvegyi

Sulzer Brothers Ltd. 8401 Switzerland/Winterhur

W. P. Palmer

Peter F. Loftus Corporation

900 Chamber of Commerce Building

Pittsburgh, Pennsylvania 15219

T. E. Pannkoke

Northern Illinois Gas Company

P. 0. Box 190 Aurora, Illinois 60507

A. R. Paradis

Dynamic Graphics Incorporated

3434 Dwight Way

Berkeley, California 94704

T. V. Paranilam

Albert Kahn Associates, Incorporated

345 New Center Building

Detroit, Michigan 48202

Kyoung Park

Ayres, Cohen £i Hayakawa

1180 South Beverly Drive

Los Angeles, California 90035

Gul Paryani

Reynolds , Smith and Hills

4019 Boulevard Center Drive

P. 0. Box 4850 Jacksonville, Florida 32201

J. M. Patton

Sales Engineer

Mississippi Power Company

P. 0. Box 4079 Gulfport, Mississippi 39501

F. W. Paul

Carnegie-Mellon U. Pittsburgh, Pennsylvania 15213

Ifan Payne

University of Maryland

College Park, Maryland 20742

C. 0. Pedersen

University of Illinois

130 Mechanical Engineering Building

Urbana, Illinois 61801

R. E. Ferryman

Sandia Corporation

P. 0. Box 5800 Albuquergue, New Mexico 87115

J. A. Pettineo

Philadelphia Electric Company

900 Sansom Street Philadelphia, Pennsylvania 19105

H. M. Philippi

Atomic Energy of Canada Ltd. Chalk River, Ontario, Canada

807
H. Harry Phipps

Energy Systfems Consultants

6803 Sea Gull Drive South

St. Petersburg, Florida 33707

E. D. Plociennik

Robertshaw Controls Company

Box 178 King of Prussia, Pennsylvania 19406

F. E. Polk

Naval Facilities Engineering Command

Electronic Support Division

Code 044C Washington, D. C. 20390

Leo Pop

Ontario Hydro, Sales Division

620 University Avenue

Toronto, Ontario, Canada

G. W. Pozeck

General Services Administration

Public Buildings Service

Region 5 219 South Dearborn Street

Chicago, Illinois 60604

H. E. Puttbach

Log Etronics Incorporated

Dryomatic Division

6628 Electronic Drive

Springfield, Virginia 22151

W. J. Radle

Airtemp Division

Chrysler Corporation

P. 0. Box 1205 Dayton, Ohio 45401

F. M. Ramsay

Post Office Department

Bureau of Facilities

Washington, D. C. 20260

David Ramsey Herman Blum Consulting Engineers, Inc. 1015 Elm Street Dallas, Texas 75202

A. S. Ratra Washington Gas Light Company

1100 H Street, N.W. Washington, D. C. 20005

J. A. Reese The Trane Company

3600 Pammel Creek Road LaCrosse, Wisconsin 54601

George Reeves

Edison Electric Institute

750 30 N.E. New York, New York 10017

S. W. Reid

Gilbert Associates, Incorporated

P. 0. Box 1498 Reading, Pennsylvania 19603

D. L. Richardson

Arthur D. Little, Incorporated

20 Acorn Park

Cambridge, Massachusetts 02140

C. P. Robart, Jr. Electric Heating Association, Inc. 437 Madison Avenue

New York, New York 10022

J. B. Roberson

Southern California Edison Company

P. 0. Box 351 Los Angeles, California 90053

Charles Robertson

Architecture Research Unit

University of Edinburgh

55 George Square

Edinburgh, Scotland, UK EH89JU

R. J. Rodde

Godwin C. Rogerson

General Services Administration

7th and D Streets, S.W. Washington, D. C. 20407

Richard J. Rodde

Associated Engineers, Incorporated

505 West Nebraska Avenue

Peoria, Illinois 61604

B. T. Rogers

Los Alamos Scientific Laboratory

P. 0. Box 1663 Los Alamos, New Mexico 87544

Robert Romancheck

Pennsylvania Power & Light Company

901 Hamilton Street Allentown, Pennsylvania 18101

T. B. Romine

Romine and Slaughter, Incorporated

3224 Collinsworth

Fort Worth, Texas 76107

Roy Rose

Reynolds, Smith and Hills

Architects, Engineers and Planners, Inc. 4019 Blvd. Center Drive, P. 0. Box 4850 Jacksonville, Florida 32201

808
Harvey Rosenhouse

American Standard Research Center

P. 0. Box 2003 New Brunswick, New Jersey 08903

Teddy Rosenthal

Wahlings Installationsutveckling AB Mysingsvagen 5, Box 1 Danderyd 1. Sweden 18211

R. V. Ross Bucher Meyers and Association

8777 First Avenue

Silver Spring, Maryland 20910

Harold E. Rucks Architects Hansen Lind Meyer

116 South Linn Street

Iowa City, Iowa 52240

James E. Rucks Architects Hansen Lind Meyer

116 South Linn Street

Iowa City, Iowa 52240

Sam Sachs Skidmore, Owings & Merrill

30 West Monroe

Chicago, Illinois 60603

J. L. Salinsky

Sargent -Webster-Crinshaw & Folley

2112 Erie Boulevard East Syracuse, New York 13224

R. Sandy

W. Hardy Craig & Associates Ltd. Consulting Engineers

2175 Victoria Park Avenue, Scarborough

Ontario, Canada

J. R. Sarver Westinghouse Electric Corporation

Box 1077 Chatham Center Office Building

Pittsburgh, Pennsylvania 15230

William A. Schmidt Veterans Administration 08H

810 Vermont Avenue, N.W. Washington, D. C. 20420

G. R. Schmieding

Northern Natural Gas Company

2223 Dodge

Omaha, Nebraska 68102

J. R. Schneider

Sverdrup & Parcel and Associates, Inc. 800 North 12th Street

St. Louis, Missouri 63101

Judith Schurek

Bell Canada

100 Wynford Drive, Room 415 Don Mills, Ontario

E. C. Schuster

Michigan Wisconsin Pipe Line Company

P. 0. Box 149 615 W. Moreland Boulevard

Waukesha, Wisconsin 53186

Bob Scott

Bob Scott, Architect & Engineer

Cambridge Road Marietta, Ohio 45750

Gert K. A. Siggelin

American SF Products, Inc. 701 Palisade Avenue

Englewood Cliffs, New Jersey 07632

Hector R. Seiglie, P.E. Connell Associates, Incorporated

Post Office Box 677 Miami, Florida 33135

Jashwant Shah

Roy C. Ingersoll Research Center Borg-Warner Corporation

Wolf and Algonquin Roads DesPlaines, Illinois 60018

H. C. Shaner Kling-Leopold , Incorporated

Consulting Engineers

121 North Broad Street Philadelphia, Pennsylvania 19107

C. L. Shearburn

Human Performance, Research Laboratory

The Pennsylvania State University

103 Human Performance Building

University Park, Pennsylvania 16802

D. G. Scheatzle

Wright-Patterson Air Force Base

Ohio 45433

S. M. Shefferman

Shefferman & Bigelson Company

1111 Spring Street

Silver Spring, Maryland 20910

J. Y. Shih Powers Regulator Company

Systems Division

2942 Mac Arthur Boulevard

Northbrook, Illinois 60062

Tatsuo Shimizu

Suga Company, Ltd. 17-19 Shimbashi 6 Chome Minato-Ku

Tokyo, Japan

809
Jorge E. Sierra

Smith, Korach, Hayet, Lippack, Haynie & Associates

721 N.W. 21st Court

Miami, Florida 33125

Edward Simons

Consulting Engineer

P. 0. Box 945 Tiburon, California 94920

Michael Skrzywan

Systems Simulation, Inc. 207 East 37th Street New York, New York 10016

C. C. Smith

Johnson Service Company

507 East Michigan Street Milwaukee, Wisconsin 53201

J. H. Smith

National Institutes of Health

Room 2905, Building 13 Bethesda, Maryland 20014

R. B. Smith

Jersey Central Power & Light Company

Madison Avenue at Punch Bowl Road Morristown, New Jersey 07960

H. V. Snively

Robertshaw Controls Company

1701 Byrd Avenue

Richmond, Virginia 23226

Clyde Somerset Jr. Sherlock, Smith & Adams, Incorporated

P. 0. Drawer 11006 Montgomery, Alabama 36111

J. K. Sonsteby

Pennsylvania Power & Light Company

901 Hamilton Street Allentown, Pennsylvania 18101

L. G. Spielvogel

L. G. Spielvogel, Incorporated

Consulting Engineer

Wyncote House Wyncote, Pennsylvania 1909 5

J. H. Sporidis

Benbassat & Sporidis Company

8121 Georgia Avenue

Silver Spring, Maryland 20910

Eugene Stamper

Newark Coll. of Engineering

323 High Street Newark, New Jersey 07102

James L. Stephens Brown and Root Incorporated

P. 0. Box 3 Houston, Texas 7 7001

D. G. Stephenson

National Research Council

Building Research Division

Ottawa, Ontario, Canada

R. G. Stinson

John Graham & Company

1426 5th Avenue

Seattle, Washington 98101

W. F. Stoecker

University of Illinois

Urbana, Illinois

Takeshi Sugama

Takasago Thermal Engineering Co. Ltd. 1575 St. Rd. Apartment A-13

Warminster, Pennsylvania 18974

Tseng-Yao Sun Ayres, Cohen & Hayakawa

1180 South Beverly Drive

Los Angeles, California 90035

P. L. Sundberg

Consolidated Engineers, Incorporated

2400 South 72nd Avenue

Omaha, Nebraska 68124

G. C. Rocerson

General Services Administration

7th and D Streets, S.W. Washington, D. C. 20407

Sazuku Tanaka

Kajima Corporation

2-19-1 Tobstakyu

Chofu, Tokyo, Japan

B. Taylor

Minneapolis Gas Company

733 Marquette Avenue

Minneapolis, Minnesota 55402

Leonard H. Taylor

Southern Technical Institute

1556 Huntington Drive, N.W. Marietta, Georgia 30060

Hideo Teraguchi

Ayres , Cohen & Hayakawa

1180 South Beverly Drive

Los Angeles, California 90035

John C. Thies

Southern Services, Incorporated

Box 2641 Birmingham, Alabama 35202

810
Paul E. Thoman

General Services Administration - Region 3 7th & D Streets Washington, D. C. 20407

William K. Thomas

Thomas-Young Associates, Incorporated

525 Mill Street Marion, Massachusetts 02738

Donald H. Tingley

Tingley Engineering Company

314 West Lee Street Charleston, West Virginia 25302

Norio Tohda

Kajima Corporation

1-2-7, Moto-Akasaka, Minato-ku

Tokyo, Japan

J. M. Trews dale University of Nottingham

Building Science Laboratory

Nottingham, England

Robert H. Tull

Private Consultant

Deer Hill Road, RD 3, Box 163 Lebanon, New Jersey 08833

L. Bowman Turner

United McGi-1 Corporation

200 East Broadway

Westerville, Ohio 43081

William E. Utt

U. S. Air Force Washington, D. C.

E. N. Van Deventer National Building Research Institute

P. 0. Box 395 Pretoria

Republic of South Africa

J. F. Van Straaten National Building Research Institute

P. 0. Box 395 Pretoria

South Africa

Hari K. Varma

5005A Brompton Drive

Greensboro, North Carolina 27407

(N. C. AT&T State University

Mechanical Engineering Department

Greensboro, North Carolina 27411)

Tom A. Vernor , Jr. P.E. Engineering Consultant

Central Power and Light Company

P. 0. Box 2121 Corpus Christi, Texas 78403

Iran Van Vi Brace Research Institute of McGill University

MacDonald College

P. 0. Box 400

Ste. Anne De Bellevue

P. Quebec, Canada

J. C. Vorbeck

Charles J. R. McClure & Associates, Inc. 10427 Old Olive Street Rd.

St. Louis, Missouri 63141

Hiroshi WADA

Shinryo Air Conditioning Company, Ltd.

4, 2chome , Yotsuya

Shinjuku-ky

Tokyo , Japan

Milan W. Walker

National Institutes of Health

9000 Rockville Pike

Bethesda, Maryland

Robert Walker (084) Veterans Administration

810 Vermont Avenue, N.W. Washington, D. C.

Dr. Gerald T. Ward

Brace Research Institute of McGill University

MacDonald College, P. 0. Box 400

Ste. Anne De Bellevue

P. Quebec, Canada

B. W. Ward, Jr. Britt Alderman, Jr., Consulting Engineer

410 Bona Allen Building

Atlanta, Georgia 30303

A. W. Ware

Abbott Laboratories

14th & Sheridan Road North Chicago, Illinois 60064

Jay Weening

T.S.W. International, Incorporated

1900 Exchange Building

Memphis, Tennessee 38103

W. T. White

General Services Administration

Building 41, Denver Federal Center

Denver, Colorado 80225

John E. Williams

University of Michigan

School of Architecture

University of Michigan Ann Arbor, Michigan

811
Thomas H. Williams

The Trane Company

12320 Parklawn Drive

Rockville, Maryland 20852

C. B. Wilson

Department of Architecture

University of Edinburgh

16-18 George Square

Edinburgh, Scotland

Foster C. Wilson

Owens-Corning Fiberglas Corporation

P. 0. Box 415, Technical Center Granville, Ohio 43023

J. J. Wisnewski

Perkins & Will Service Company, Inc. Washington, D. C. 20036

Donald R. Witt

Pennsylvania State University

Department of Architectural Engineering

101 Engineering "A" University Park, Pennsylvania 16802

L. D. Wood, Jr. Sam R. Fogleman Associates

Consulting Engineers

1225 Ponce De Leon Avenue

Rio Piedras, Puerto Rico 009 26

F. J. Wooldridge

W. Boyce Blanchard Consulting Engineer

355 Warrington Circle

Hampton, Virginia 23369

M. J. Wooldridge

Commonwealth Scientific & Industrial

Research Organization

P. 0. Box 26 Highett, Victoria 3190 Australia

Hitoshi Yamazaki

Kyusyu Institute of Design

226 Shiobara, Fukuoka, Japan

Koichi Yokoyama

Shin Nippon Air-Conditioning Co. , Ltd. 4-2, Hongoku-cho, Nihombaski

Chuo-ku, Tokyo

Japan

H. C. Yu Hankins and Anderson, Consulting Engineers

2117 North Hamilton Street Richmond, Virginia 23230

Dsvid J. Zabner

D. J. Zabner & Company

10232 West McNichols Road Detroit, Michigan 48221

Willard R. Zahn

York Division, Borg-Warner Corporation

Richland Avenue

York, Pennsylvania 17405

812
FORM NBS-1I4A 11-71) •

1 U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession BIBLIOGRAPHIC DATA jjgg ggg 39 No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Use of Computers for Environmental Engineering Related to Buildings, Proceedings of the First Symposium

5. Publication Date

'-'CHJUGIT J. 7 / J- 6. Performing Organization Code

7. AUTHOR(S) 8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE

10. Project/Task/Work Unit No.

11. Contract/Grant No,

12, Sponsoring Organization Name and Address National Bureau of Standards, Washington, D. C. 20234

American Society of Heating, Refrigerating and Air Conditioning

Engineers, Inc., United Engineering Center, New York, NY 10017 Automated Procedures for Engineering Consultants, Inc., Dayton. Ohio 45406 '

, y

,

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) This proceedings of the First Symposium on the Use of Computers for Environmental

Engineering Related to Buildings contains all of the technical papers and invited

addresses presented at the symposium, which was held November 30 - December 2, 1970, at the National Bureau of Standards.

The fifty-nine papers deal with the application of the computer to such environmental

engineering problems as building heat transfer calculations, heating and cooling load calculations, system simulations, energy usage analyses, computer graphics, air and smoke movement inside buildings, and weather data analyses for load and energy usage calculations.

17. KEY WORDS (Alphabetical order, separated by semicolons) Building heat transfer analysis, energy usage, environmental engineering, heating

and air conditioning, use of computers

18. AVAILABILITY STATEMENT

fxl UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES 826

22. Price

$7. 75

USCOMM-DC 66244-P71

<r U. S. GOVERNMENT PRINTING OFFICE : 1971 O - 447-985




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