Thermal Analysis Research

Program Reference Manual

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Building Physics Division

Washington, DC 20234

March 1983

Sponsored by

National Bureau of Standards

1 and

Building Energy Sciences Branch

Office of Building Energy Research and Development

U.S. Department of Energy

Washington, DC 20545

'
MTP-L -
NATIONAL bureau

OF STANDARDS

library

NBSIR 83-2655

THERMAL ANALYSIS RESEARCH

PROGRAM REFERENCE MANUAL

APR lo 1983

/xxfucc. -eef.

Qc ICO

cCSvo

George N. Walton

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Building Physics Division

Washington, DC 20234

March 1983

Sponsored by

National Bureau of Standards

and

Building Energy Sciences Branch

Office of Building Energy Research and Development

U.S. Department of Energy

Washington, DC 20545

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

ABSTRACT

The Thermal Analysis Research Program (TARP) has been developed as a research

tool for the thermal analysis of buildings. It especially aims to study the

interactions of many complex heat transfer phenomena. TARP uses the detailed

heat balance method for the simultaneous calculation of the energy requirements

of multiple rooms. Interroom conductive and convective processes are simulated

in detail. This program reference manual describes the algorithms, input, output, and program structure of TARP. The program is written to be portable and

modifiable. It is written in FORTRAN 77 and has run on CDC and UNIVAC computers. Future expansions of the program are anticipated, particularly for the

simultaneous simulation of the equipment performance and building thermal

response.

Keywords: building energy analysis; load calculations; computer modeling;

building heat transfer.

iii
PREFACE

This report is one of a series documenting NBS research and analysis efforts in

developing energy and cost data to support the Department of Energy/National

Bureau of Standards Measurements Program. It was prepared by the Thermal

Analysis Group, Building Physics Division, Center for Building Technology,

National Engineering Laboratory, National Bureau of Standards (NBS). This work

was jointly sponsored by NBS and the Department of Energy (DoE). The development of multiroom air flow modeling was supported by DoE/NBS Task Order A008

under Interagency agreement No. EA-77-A-0 1-6010. This report describes a computer program which was written as part of an effort to develop a comprehensive modeling technique for predicting the simultaneous transfer of air, moisture, and heat in and through multiroom buildings.

The author wishes to acknowledge the support and direction given by Dr. T.

Kusuda, Thermal Analysis Group Leader.

The computer program described in this report is intended for research purposes

only. It is furnished by the government and is accepted and used by any recipient with the expressed understanding that the United Stated Government makes no warranty, expressed or implied, concerning the accuracy, completeness, reliability, usability, or suitability for any particular purpose of the information

and data contained in this program or furnished in connection therewith, and

the United States shall be under no liability whatsoever to any person by reason

of any use made thereof.

iv
TABLE OF CONTENTS

Page

I. INTRODUCTION 1 A. BACKGROUND 1 B. OBJECTIVE 1 C. SCOPE 2

II. PROGRAM OVERVIEW 3

A. SIMULATION CAPABILITIES 3

B. PROGRAM STRUCTURE 3

C. EXAMPLE RUN 4

III. ALGORITHMS 13

A. INTRODUCTION 13

1. The Heat Balance Method 13

2. Table of Symbols 13

B. ENVIRONMENT 16

1. Time 16

2. Psychrometrics 18

3. Temperatures 21

4. Wind 22

5. Solar radiation 22

C. TRANSIENT HEAT CONDUCTION 26

1. Use of Conduction Transfer Functions 26

2. Calculation of Conduction Transfer Functions 27

D. WINDOW OPTICS 29

1. Optical Coefficients 29

2. Shading Coefficients 30

3. Uncoated Pane Optics 31

4. Reflective Coatings 33

5. Multi-Pane Windows 36

6. Diffuse Radiation 37

7 . Interior Shading Devices 38

E. SOLAR GAINS AND SHADOWING 46

1. Surface Geometry 46

2. Shadow Projection 47

3 . Homogeneous Coordinates 48

4. Overlapping Shadows 49

5. Solar Gains 31

F. INTERNAL HEAT GAINS 58

1. Sources and Types of Gains 58

2. Distribution of Radiant Gains 59

G. NATURAL AIR MOVEMENTS 63

1 . Wind Forces * 63

2. Thermal Forces 63

3. Flow Equations 64

4. Solution of Flow Equations 65

H. ROOM RADIANT INTERCHANGE 68

1. Detailed Radiant Interchange 68

2. MRT Network Algorithm 68

v
Page

I. SURFACE OUTSIDE HEAT BALANCES 71

1. Simple Surface Conductance 71

2. Detailed Surface Conductance 71

3. Basic Heat Balances 74

4. Heat Balance Cases 75

J. SURFACE INSIDE HEAT BALANCES 79

1. Simple Convection Coefficient 79

2. Detailed Natural Convection Coefficient 79

3. Basic Heat Balance 80

4. Internal Surfaces 80

5. Interzone Surfaces 81

K. ZONE AIR HEAT BALANCE 85

1. System Performance Model 85

2. Simple Infiltration Model 86

3. Zone Ventilation Model 86

4 . Two Zone Mixing Model 86

5. Whole House Fan Model 87

L. HEAT BALANCES ITERATION 92

IV. INPUT 94

A. OVERVIEW 94

B. SYNTAX 94

1. BNF Description 95

2. English Description 95

3. Error Processing 97

C. INPUT DETAILS 98

1. Project Section 98

2. Library Section 102

3. Building Section 108

4. Zone Section Ill

D. INPUT SUMMARY 124

E. ZONE TEMPERATURE CONTROL 127

F. GEOMETRIC DATA 136

1. Surface Coordinate System 136

2. Window and Door Subsurfaces 137

3. Shadowing Subsurfaces 137

4. Zone Coordinate System 138

5. Building Coordinate System 138

6. Detached Shadowing Surfaces 139

G. TABLES 150

1. Shadowing Dates 150

V. OUTPUT 151

A. INPUT REPORTS 151

1. Default Reports 151

2. Run Control Modifications 156

3. Numbered Reports 160

4. Library Reports 170

vi
Page

B. LOADS REPORTS 176

1. Default Reports 176

2. Numbered Reports 179

VI. COMPUTER PROGRAM 197

A. INPUT PROCESSOR 197

B. LOADS CALCULATOR 219

C. VARIABLES 235

D. FILES 277

vii
LIST OF FIGURES

Page

Figure II. 1 Structure of the Thermal Analysis Research Program 7

Figure II. 2 House configuration for examplke problem 8

Figure II. 3 TARP input for example problem 9

Figure II. 4 Calculated loads for example problem 12

Figure III.D.l Variation of solar-optical properties with angle of

incidence 40

Figure III.D.2 Reflection and refraction at an interface 41

Figure III.D.3 Multiple reflections in a pane of glass 42

Figure III. 0.4 Two-pane window system 43

Figure III.D.5 Coordinate system for diffuse radiation 44

Figure III.D.6 Multiple shadow overlaps 45

Figure III.E.l Shadows on an L-shaped building 52

Figure III.E.2 Shadow polygon clipping 53

Figure III.E.3 Shadow casting surfaces 54

Figure III.E.4 Overlapping convex polygons 55

Figure III.E.5 Intercepts of line segments 56

Figure III.E.6 Multiple shadow overlaps 57

Figure III.F.l Sensible heat gains from people 61

Figure III.F.2 Baseboard heat control profile 62

Figure III.G.l Pressure relationships for vertically adjacent zones ... 67

Figure III.G.2 Pressure relationships for horizontally adjacent

zones • 67

Figure III.G.3 Pressure relationships for envelope surfaces 67

Figure III.I.l Thermal network for simple outside surface

coefficients 78

viii
LIST OF FIGURES (cont.)

Page

Figure II I. I. 2 Thermal network for detailed outside surface

coefficient 78

Figure III. I. 3 Thermal network for outside movable Insulation 78

Figure III.J.l Inside surface thermal network 84

Figure III.J.2 Inside movable insulation thermal network 84

Figure III.K.l Zone temperature control profile 89

Figure III.K.2 Ventilation control profile: Ta higher than TV 90

Figure III.K.3 Ventilation control profile: Ta lower than TV 90

Figure III.K.4 Ventilation and heating control profiles 91

Figure III.K.3 Ventilation and cooling control profiles 91

Figure IV.E.l Simple control profile with deadband 131

Figure IV. E. 2 Normalized control profile 132

Figure IV. E. 3 Control profile for three-deck miultizone systems 133

Figure IV. E. 4 Control profile for multizone system 134

Figure IV. E. 5 Control profile for VAV system 135

Figure IV.F.l Rectangle 140

Figure IV. F. 2 Triangle 140

Figure IV.F.3 Quadrilateral 140

Figure IV. F. 4 Window/ door subsurface 140

Figure IV. F. 5 Overhang 141

Figure IV. F. 6 Left fin 141

Figure IV. F. 7 Right fin 141

Figure IV. F. 8 Projection 141

Figure IV. F. 9 Zone coordinate system: tilted surfaces 142

ix
LIST OF FIGURES (cont.)

Page

Figure IV.F.10 Zone coordinate system: flat roof . 143

Figure IV.F.ll Zone coordinate system: floor 144

Figure IV.F.12 Zone coordinate system: four zones 145

Figure IV.F.13 Portion of building with similar zones 146

Figure IV.F.14 Zone 3 described by rotation and translation of zone

2 147

Figure IV.F.15 Zone 4 described by mirror imaging and translation of zone 1 148

Figure IV.F.16 Zone 4 described by mirror imaging, rotation and

translation of zone 1 149

Figure V.l Sample default output 152

Figure V.2 Sample error messages 156

Figure V.3 Double spacing 157

Figure V.4 Cross references 158

Figure V.5 Two reports using metric units 159

Figure V.6 Dump of project control data 160

Figure V.7 Dump of library control data 161

Figure V.8 Dump of weather data 162

Figure V.9 Dump of CTF calculations for massive construct 163

Figure V.10 Dump of optical calculations 164

Figure V.ll Dump of shadowing surface data 165

Figure V.12 Dump of zone data 167

Figure V.13 Dump of cross reference values 169

Figure V.14 Day-schedule reports 170

Figure V.15 Week-schedule reports 171

x
LIST OF FIGURES (cont.)

Page

Figure V.16 Materials report 171

Figure V.17 Constructs report 172

Figure V.18 Construct report for a window 173

Figure V.19 Control profiles reports 174

Figure V.20 Control day-schedule reports 173

Figure V.21 Control week-schedule reports 175

Figure V.22 Default loads calculation output 177

Figure V.23 Dump of SINPFL 181

Figure V.24 Zone description report 186

Figure V.25 Results of shadowing calculations 187

Figure V.26 Shadowing combinations report 188

Figure V.27 Dump of shadowing calculations 190

Figure V.28 Hourly Dump of zone loads 193

Figure V.29 Dump of zone loads calculations 195

Figure VI. A. 1 Tree structure of input processor program 214

Figure VI.B.l Tree structure of the loads calculator program 232

xi

I. INTRODUCTION

I. A BACKGROUND

The effort to encourage the design, construction, and retrofit of energy

conserving buildings will be strengthened by the development of comprehensive

methods for evaluating the thermal effectiveness of those buildings. Since

the development of research programs such as NBSLD [ 1 ]

,

there has been a proliferation of public and private energy analysis computer programs. Computer

assisted analysis is increasingly used in building design. Public domain

research programs have served as sources of validated algorithms and of simulated performance for the testing of the design programs. The majority of

current building thermal simulation computer programs are based upon single

room methods. It was assumed that the conditions in one room were not significantly affected by conditions in another. This was a good assumption because

the low cost of energy made it common practice to keep near constant temperatures in all rooms. Similarly, occupant comfort was not a significant consideration in the early programs because sufficient energy would always be available to achieve comfort. Detailed analysis of moisture migration was unnecesary

because moisture could always be mechanically removed to maintain comfort or prevent condensation. The increasing cost of energy has led to the use of

natural heating and cooling techniques which have gone beyond those assumptions.

Significant variations in room temperatures can be expected as unoccupied

rooms are left unheated and uncooled or as "sun spaces" are built on homes to

help heat them by natural convection. Increased temperature ranges are allowed

in work areas with occupants expected to adjust amounts of clothing to maintain

comfort. Natural ventilation cooling might lead to significant moisture problems. Many other phenomena are poorly understood or inadequately modeled in

existing programs. Simulation of the complex interactions among the many

phenomena in real buildings is especially important.

An improved research-oriented program is needed to allow the detailed study

of simultaneous air, heat, and moisture transfer in and through a building with

complex internal architecture. Such a research program must be easily expandable to test the simulation of new features. This requirement implies that

the program should have a simple structure and be well-documented. The program

should also be able to handle simple or very complex problems efficiently, and

it should be portable so that many researchers can use it.

I.B OBJECTIVES

The objective of this effort is to develop a state-of-the-art researchoriented computer program for the thermal analysis of buildings together with

the documentation necessary for its use.

This computer program is called the Thermal Analysis Research Program

(TARP). The name was chosen to emphasize that this is to be more than an energy/loads predictor. It aims is to study the interactions of many factors

of the thermal performance of buildings. Also, features which would have

enhanced the usability of the program for building designers and engineers

have given way to research features. In its present version it is capable of

1
computing room loads and temperatures by simultaneously considering conduction

and air movements between all rooms in a building. This program provides the

framework for the integration of many more advanced simulation features.

I.C SCOPE

This report is the documentation of the algorithms, user-interface, and

computer code of TARP in its present form. It provides a detailed description

of the structure and mathematical methods of the program. It is not intended

to be a tutorial for persons who are totally unfamiliar with energy analysis

programs and methods.

Chapter II is an introduction to the capabilities, structure, and use of

the program.

Chapter III reviews the algorithms that the program uses to compute the

building energy and air flows.

Chapter IV explains how buildings are described by the input language.

Chapter V describes the various output reports available to the user.

Chapter VI gives the information necessary to understand (and hence modify)

the computer code.

This report uses an outline organization to serve two purposes. It will

allow easier updating of the documentation as the program evolves. It also

allows a simple way to handle the many cross-references within the report. Any

of the chapters may refer to details of the input or algorithms. The form of an input reference is: (3.2.5). It may consist of 1, 2, or 3 numbers separated

by periods. It refers to the detailed input description in chapter IV, sec- tion C. The full reference may be considered (IV. C. 3. 2. 5) with the "IV.

C"

implied. The form of an algorithm reference is: (B.2.4). It consists of a letter and optional numbers and refers to information in chapter III. The full

reference may be considered (III. B.2.4).

References are indicated by brackets and are listed at the end of each

section.

REFERENCES

[1] Kusuda, T., "NBSLD, the Computer Porgram for Heating and Cooling Loads in

Buildings," NBS Building Science Series 69, (July 1976).

2
II PROGRAM OVERVIEW

II. A SIMULATION CAPABILITIES

The Thermal Analysis Research Program uses detailed heat balance

techniques to compute room loads. It may be used to evaluate single "design"

days or it may use up to one year of measured weather data. A large number of

occupant usage features may be scheduled with hourly, daily, and seasonal

variations. The effects of temperature drifts in response to various control

strategies can be accurately evaluated. Input and output may be in English or metric units. Other capabilities can be grouped by the three modes of heat

transfer.

Conduction: Transient conduction effects are modeled by "conduction

transfer functions" which are extensions of response factors. They model the

heat storage effects of walls, furnishings, and partitions between rooms. Movable insulation is closely approximated by a massless insulation model with

appropriate controls which may be applied over windows or walls.

Radiation: The transmittance and absorptance of windows is computed from

the optical properties of the window panes. There may be up to four panes

which may be heat absorbing or have reflective films. Shading coefficients may

be used for windows which cannot be described in terras of their components.

The shadowing and distribution of sunlight on surfaces may be calculated in

several levels of detail up to the amount of light transmitted through windows

onto each surface of the room. The effects of emissivity are modeled for both

interior and exterior surfaces. There is a simple model to account for the

energy savings of daylighting.

Convection: The program uses variable interior and exterior convection

coefficients as functions of temperature difference and system induced flow

velocity when appropriate. It can compute infiltration and the natural flow

of air between rooms caused by wind and thermal forces. There is an alternative simple model for infiltration with options of ventilation cooling, a whole

house fan, and controlled air mixing betwen two rooms.

TARP is an evolutionary development of the BLAST [1,2] computer program.

BLAST is a user, rather than research, oriented program with equipment simulation capabilities not included in TARP. TARP provides more detailed models for

air movement and multiroora analysis. It is also more portable and easier to

modify.

II .B PROGRAM STRUCTURE

The program is written almost entirely in FORTRAN 77. This is a standard

language which has been or is being implemented on most large and medium size

computers. The handling of character data and direct access files help to make

this language machine independent. The TARP should be portable except for some conversions from single to double precision and replacing the use of BLAST

weather tapes. The PARAMETER feature of FORTRAN 77 is used extensively in

modifiable array dimensions so the TARP can handle different size problems.

3
The TARP is divided into two subprograms: the input processor (IP) and

the loads calculator (LC). This structure is illustrated in figure II. 1. The

IP checks the user input, prepares input files for the LC, and reports the

array sizes that the LC will require. The LC performs the building loads

simulation and reports the results. This separation of subprograms allows a reduction in computer core requirements. The IP uses minimal array sizes

because it processes the input one element (surface, schedule, material, etc.)

at a time. The LC uses large arrays which consider these elements simultaneously. The IP and LC may be run as separate jobs when It is necessary to

recompile the LC for correct array sizes, or they may be run as a single job

if the LC is known to have sufficiently large arrays.

The input processor is divided into four major sections. These

correspond to the input language sections (III.C) which they process. This

sectioning allows further reductions in core requirements by the use of overlays (or segments). A small input processor is important to allow the fast job

turn-around necessary to quickly debug the user input deck. Each section contains several subroutines which process the input language "keys” plus others

for special elements of certain keys. The largest of these special routines

are the two groups of subroutines which evaluate the conduction transfer functions and the window optics.

The loads calculator is divided into three sections. The first reads the

input file created by the IP and fills the LC arrays. It checks for sufficient

array space and performs some checks which require that all data for the problem description be present in the arrays. The second section uses the geometric and optical descriptions of the building surfces to compute solar gain

factors for various periods of the year. The third section does the actual

heat balances necessary to compute the multi-room loads. It does this on an hour-by-hour basis.

II.C EXAMPLE RUN

The following example calculation is designed to show how a building can

be simulated with TARP. The building configuration was chosen to emphasize

interzone effects. It is a "passive solar" design as shown in figure 2. The

building is a townhouse configuration with 8 inch thick masonry walls separating

it from identical units to the east and west. The gross floor area is 1584

ft^. The exterior walls and roof are wood frame construction with insulation R

values of 19 and 30 respectively. The house is divided into three major zones:

a north zone for bedrooms, a center zone for the main living area, and a south

zone for the kitchen/utility area. Each zone has a different internal gain

profile consistant with its function. At the top of the center zone is a southfacing 120 ft^ double pane clerestory which is intended to allow sun to shine

directly onto the 8 inch thick masonry wall which separates the north and center

zones. The south exterior walls includes 80 ft^ (23 percent of wall area) of

double pane window where the sun is intended to shine directly on the uncarpeted

slab floor. The north and center zones have carpet on the slab. The partition

between the south and center zones is a nonmassive wood frame and drywall

construction.

4
The TARP input for the example is shown in figure 3. The input begins by

describing project data in the first nine lines between "PROJECT [" and A

project description is given; the location is described; ground temperatures

are given. Then there is a description of the weather between "DDY(" and ")" on the following line. This sets up a mild, late winter condition when the

solar and internal gains nearly offset the infiltration and conduction losses.

The low temperature (LOW) for the day is 30F and the high (HIGH) is 50F. A

clear sky (CLR) for 21 February (DATE) is assumed. A 15 mph (WS=1320 ft/min)

wind blows from the northwest (DIR^IS).

The next section is called the "LIBRARY". It is used to define certain

features which are referred to by the name in later sections of the input. The

first few entries in the library section begin with "DS" which stands for dayschedule. A day-schedule is a list of 24 values, one for each hour of the day.

The third day-schedule is given the name "ON" to indicate that it is being used

to describe the occupancy schedule in the north zone. This day-schedule is

used in the week-schedule (WS) which has the name "OCCN". A week-schedule is a collection of day-schedules, one for each day of the week plus holidays and

other special days. The command WD=ON will assign day-schedule ON to all week

days. The same day-schedule will also apply for other day types by default

since no other day types are specified. Building materials (MATL) are described

in a similar manner. The first material is a gypsum wallboard given the name

"GYP", and having a conductivity (K) of .42 Btu/h»ft»F, a density (D) of 45

lbm/ft^, and a specific heat (CP) of 0.3 Btu/lbf. The wallboard is used in the

first wall construction (CONS) named "WL-I". This lists the thickness and name

of each material layer in the wall listed from outside to inside. There is

0.0521 ft (.625 in) of GYP as the inside surface. The final entries in the

library ("CPFL", "CDS", and "CWS") describe the control of the zone temperatures.

The "BUILDING" section gives commands controlling the heat balance

simulation and descriptions of the roof overhangs.

There are three "ZONE" sections to describe the three zones of the example

building. Each zone is identified by a user supplied name, e.g., "NORTH".

Activities related to the entire zone are the temperature control (CTRL) and

people (PEO), lights (LIT), and equipment (EQP) loads. There are three people

maximum (CAP=3) in the zone. The hourly number of people is determined by that

maximum and the previously defined week-schedule (WS=OCCN). The other activities have similar capacities and schedules. The rest of the zone description

defines the surfaces, both envelope and internal, of the zone. The mass (MASS)

of furnishings is handled by a single surface of appropriate density and area.

"SRF" then describes most of the north wall of the zone as an exterior (EX)

,

opaque (OP), base surface (BS). It is made of the previously defined WL-I

construction. The wall faces north (AZM=0) and is 41 ft long by 8 ft high

(SIZE). It is located relative to the other surfaces of the building by the

origin (ORG) command. The next line of input specifies a window on the wall.

The window is an exterior (EX), transparent (TR) , subsurface (SS) made of the

WDW2 construction. Its size is made to represent all windows on the north

wall. Openings in the wall for identification are combined into a single area

under the "AFS" command. The next surface command describes the remainder of

5
the north wall: the portion at the studs which Is construction WL-S. Four

lines later there is a description of the massive partition described as an interior (IN), opaque (OP), base surface (BS). It is thermally connected to

the center zone by the command "ZONE-CENTER".

Figure 4 shows the computed loads for the sample run. The report is headed

by the project, location, and environment descriptions. Then the following

values are presented for each zone: Total heating and cooling requirements,

peak heat and cooling loads, maximum zone air temperatures, hours at peak

heating capacity (HX), other heating hours (HT), ventilating hours (V), cooling

(below peak capacity) hours (CL), and hours at peak cooling capacity (CX).

Building-wide values are summarized by the line labeled "TOTAL:". These values

include the total heating and cooling requirements for all zones, the peak

coincident heating and cooling loads , and maximum and minimum of all zone temperatures. The hour and day are reported for the occurance of the peak

loads and temperatures.

This example was not intended to provide complete instruction. The user

should read the remainder of the program documentation before attempting to run

TARP.

REFERENCES

[1] Hittle, D. C., "The Building Loads Analysis and System Thermodynamics

(BLAST) Program, Version 2.0: User Manual", CERL Technical Report E-153,

(Construction Engineering Research Laboratory, 1979).

[2] Herron, D. , Walton, G., Lawrie, L., "Building Loads Analysis and System

Thermodynamics (BLAST) Program Users Manual — Volume One Supplement

(Version 3.0), CERL Technical Report E-171, (Construction Engineering

Research Laboratory, 1981).

6
Figure II. 1 Structure of the Thermal Analysis Research Program
Figure II. 2 House configuration for example problem

8
123

45

67

8

910

1112

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

4142

43

44

45

46

47

48

49

50

51

52

1 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/07, 05.38.40. .713

PROJECT C RC(DEM/UIN=ENGLISH/UOUT=ENGLISH/

DESC= ' THERMAL MASS TEST - SIMULTANEOUS ZONES* DIRECT SUN')

RPT ( RNOS = 9)

LOC<DESC=' COLUMBIA* MO. '/LATD=38.?/L0NG«92.3/TZ*6>

GRND(GRT=40*42*48*55*62*67*70*69*63*55*48»42)

DDY < DESC= ' MILD WINTER ' /HI GH=50/L0W=30/UB=40/DATE-21FEB/

CLR=1./M0N/US=1320/DIR=315)

3 L I BR AR Y C DS(NAME=NONE/DESC='ZERO ALL HOURS ' /FFC=24*0

)

DS<NAME=FULL/DESC='ONE ALL H0URS'/FFC=24*1

DS<NAME=ON/DESC=' NORTH OCCUPANCY'/

FFC=6*1, .5* .16*8*0*4*. 16 *2*. 33* .67*1)

DS(NAME=OC/DESC*' CENTER OCCUPANCY'/

FFC=16*0*3*. 17* .67* . 5 * . 67 * . 17 » 0

)

DS(NAME=OS/DESC=' SOUTH OCCUPANCY'/

FFC = 6*0* .5* .5*8*0,2*.33* . 67 * 2* . 16 * 3*0

)

US <NAME=OCCN/DESC=' NORTH OCCUPANCY ' /WD=ON

)

WS(NAME=OCCC/DESC=' CENTER OCCUPANCY ' /WD=OC

)

WS(NAME=OCCS/DESC=' SOUTH OCCUPANCY ' /UD=OS

)

DS(NAME=LN/DESC=' NORTH LIGHTING'/

FFC=6*0* .7* .7*8*0*2*.33,4*.7, .4*0)

DS<NAME=LC/DESC=' CENTER LIGHTING'/

FFC=16*0* .5,5*. 7* .3*0)

DS(NAME=LS/DESC=' SOUTH LIGHTING'/

FFC=6*0, .7* .7* 8*0,5*. 7*3*0)

WS(NAME=LITN/DESC=' NORTH LIGHT ING'/UD=LN)

WS(NAME=L I TC/DESC=' CENTER LIGHTING ' /WD=LC

)

US <NAME=LITS/DESC=' SOUTH LIGHTING'/UD=LS)

DS(NAME=EN/DESC=' NORTH EQUIPMENT'/

FFC=20*0, 3*1,0)

DS<NAME=EC/DESC=' CENTER EQUIPMENT'/

FFC= 16*0 *4*1 ,4*0)

DS(NAME=ES/DESC=' SOUTH EQUIPMENT'/

FFC=6*.3,2*1 *8*. 3 *2*1 *3*. 7, 3*. 3)

WS<NAME = EQF'N/DESC=' NORTH EQUIPMENT ' /UD=EN

)

US (NAME=EQPC/DESC=' CENTER EQUIPMENT ' /UD=EC

)

US <NAME=EQPS/DESC=' SOUTH EQUIPMENT '/WD=ES)

US <NAME=CONST/DESC=' CONSTANT 1 00% ' / ALL=FULL

)

MATL(NAME=GYP/DESC=' GYPSUM UALLBOARD ' /K= . 42/D=45 . /CP= . 3

)

MATL <NAME=UD-S/DESC=' SOFTWOOD '/K=.0675/D=32./CP=. 33)

MATL(NAME=SHTH/DESC=' INTERMEDIATE DENSITY BUILDING BOARD SHEATHING'/

K=.034/D=22./CP=.31

)

MATL (NAME=C-HU/DESC=' HEAVY CONCRETE' /K=1.0/CP“.2/D-140.

)

MATL <NAME=B1/DESC=' AIRSPACE RESISTANCE ' /R= . 9 1/AIR

)

MATL(NAME=R5/DESC='R5 POLYSTYRENE ' /R=5 .

)

MATL(NAME=R19/DESC='R19 INSULATI0N'/R=19.

)

MATL < NAME = R30/DESC= ' R30 INSULATION ' /R=30 .

)

MATL <NAME=SPDS/DESC=' STANDARD GLASS ' /GLASS/R= . 0236/TRNS= . 86

)

MATL (NAME=ASH/DESC=' ASPHALT SHINGLES ' /K=18 . 16/D=70/CP^ . 3

)

MATL<NAME=DIRT/K=.1/D=65./A=.70)

Figure II. 3 TARP input for example problem

9
PAGE 2 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/07. 05. 38. 41. 1.050

53 MATL(NAME=AL/DESC®' ALUMINUM SIDING ' /K- 1 28/D® 171 . /CP® . 2

>

54 MATL(NAME®CPT/DESC*' CARPET t PADVR-2.08)

55 CONS<NAME*WL-I/DESC=' EXTERIOR WALL - INSULATION AREA'/

56 MATL® , 005 2 » AL . .0417.SHTH. 0.R19. .0521.GYP)

57 CONS (NAME=WL-S/DESC=' EXTERIOR WALL- STUD AREA'/

58 MATL= • 0052 . AL . .0417. SHTH. 0.R19. .0521.GYP)

59 CONS (NAME®PTN-A/DESC=' PARTITION - AIR SPACE AREA'/

60 MATL=.0521 .GYP. 0.B1. .0521. GYP)

61 CQNS(NAME=PTN-S/DESC=' PARTITION - STUD AREA'/

62 MATL=. 0521. GYP* .292.WD-S. .0521. GYP)

63 C0NS(NAME=WDW2/DESC='2 PANE WINDOW'/

64 MATL = 0 * SPDS . 0.B1. O.SPDS)

65 CONS <NAME=FRAME/DESC=' WINDOW FRAME ' /MATL=0 . 1354 » WD-S

>

66 CONS(NAME=RF-T/DESC®' CEILING/ROOF - TRUSS AREA'/

67 MATL=. 0104. ASH. ,0417. WD-S. .625. WD-S. .0417. GYP)

68 CONS <NAME=RF- I /DESC*' CEILING/ROOF - INSULATION AREA'/

69 MATL®. 0104. ASH. ,0417. WD-S. 0.R30. .0417. GYP)

70 CONS (NAME=PTN-M/DESC=' MASSIVE PARTIT ION ' /MATL® . 667 . C-HW

)

71 CONS <NAME=SLAB-C/DESC=' SLAB WITH CARPET'/

72 MATL®. 5. DIRT. 0.R5. .333.C-HU. O.CPT)

73 CONS CNAME=SLAB-T/DESC=' SLAB WITH TILE'/

74 MATL®. 5. DIRT. 0.R5. ,333. C-HW)

75 CPFL(NAME®P1 /DESC® 'HEATING SETBACK ' /CAP® 1 . 0/TMP=60 . 62

)

76 CPFL(NAME=P2/DESC=' STANDARD HEATING ' /CAP=1 . 0/TMP=68 . 70

)

77 CDS (NAME = HN/DESC=' NORTH HEATING ' /CPFL=6*P1 . 2*P2 . 8#P1 . 6*P2 . 2*P 1

)

78 CDS (NAME=HC/DESC=' CENTER HEATI NG ' /CPFL® 16*P1 . 6*P2 . 2#P1

)

79 CDS <NAME=HS/DESC=' SOUTH HEATING ' /CPFL=6*P1 . 2*P2 . 8*P1 . 5*P2 . 3*P1

>

SO CWS(NAME=HEATN/DESC=' NORTH HEATING ' /WD=HN

>

81- CUS(NAME=HEATC/DESC=' CENTER HEAT ING ' /WD®HC

)

82 CWS<NAME=HEATS/DESC=' SOUTH HEATING ' /WD®HS

)

83 1 84 BUILDING C 85 SIM(SLDS=3/HTB=0/FL0W/CNVG=.l. .01. .34.12)

86 BSS(AZM=180./TILT=153.4/0RG=0. 12. 16/SIZE=44.2)

87 DSS< AZM=180./TILT=206.6/0RG=0.0.8/SIZE®44.2)

88 DSS< AZM=0./TILT=116.6/0RG=0.36.8/SIZE=44.2)

89 1 90 ZONE C 91 GEOM(NAME=NORTH>

92 CTRL(CWS=HEATN/HEAT=12)

93 PE0<WS=0CCN/CAP=3>

94 LIT <WS = LITN/CAP = 1 ,4)

95 EQP < WS=EBPN/CAP=1 . 0

)

96 MASS(C0NS=PTN-A/AREA=480)

97 SRF(EX/0P/BS/C0NS=WL-I/AZM=0/0RG=44.36.0/SIZE=41.8)

98 SRF(EX/TR/SS/C0NS=WDW2/0RG=12.5.-,25/SIZE=20.2)

99 ‘ AFS(AREA=0. 2/EXP®. 65)

100 SRF(EX/0P/BS/C0NS=WL-S/AZM®0/0RG=3.36.0/SIZE=3.8)

101 SRF(EX/CP/BS/CONS=RF-T/AZM=0/0RG=44.36.8/SIZE=41.8,95/TILT=26.6)

102 AFS(AREA=0. 1/EXP®. 65)

103 SRF(EX/0P/BS/C0NS=RF-I/AZM=0/0R6=3.36»8/SIZE=3.8.95/TILT=26.6)

104 SRF( IN/0P/BS/C0NS=PTN-M/AZM=180/0RG=0.24.0/SIZE=44. 12/Z0NE=CENTER)

Figure II. 3 (continued)

10
PAGE 3 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/07. 05.38.42. 1.467

105 AFS(AREA=0.5/EXP=.50)

106 SRF(IN/0P/BS/C0NS=PTN-M/AZM=270/0RG=0,36,0/VRTS=12,0, 12,12, 0.8)

107 SRF < IN/0P/BS/C0NS=PTN-M/AZM=90/0RG=44 . 24 » 0/VRT8=l2 , 0 . 12.8. 0.12)

108 SRF(EX/0P/BS/CQNS=SLAB-C/AZM=180/0RG=0,36»0/SIZE*44»12/TILT=180)

109 OSC ( TGP=1

)

110 3 111 ZONE C 112 GEOM(NAME=CENTER)

113 CTRL(CWS=HEATC/HEAT=12)

114 PE0(WS=0CCC/CAP=3)

115 LIT(WS=LITC/CAP=1.4)

116 EQPCWS=E0PC/CAP=1.0)

117 MASS(C0NS=PTN-A/AREA=480)

118 SRF(EX/0P/BS/C0NS=FRAME/AZM=180/0RG=0»12»12/SIZE=44,3)

119 SRF<EX/TR/SS/C0NS=WDU2/ORG=2,0»-.25/SIZE=4O,3)

120 AFS(AREA=0.25/EXP=.65)

121 SRF<EX/0P/BS/C0NS=RF-T/AZM=0/0RG=44»24,12/SIZE=41»8. 95/TILT=26 . 6

)

122 AFS(AREA=0. 1/EXP=.65)

123 SRF(EX/0P/BS/C0NS=RF-I/AZM=0/0RG=3»24»12/SIZE=3»8.95/TILT=26.6)

124 SRF(IN/0P/BS/C0NS=PTN-A/AZM=180/0RG=3,12,0/SIZE=41,12/Z0NE=S0UTH>

125 AFS(AREA=0.5/EXP=,50)

126 SRF ( IN/OP /BS/C0NS=PTN-S/AZM=180/0RG=0 .12 »0/SIZE=3.1 2/Z0NE=S0UTH

)

127 SRF<IN/0P/BS/C0NS=PTN-M/AZM=0/0RG=44»24»0/SIZE=44,12/Z0NE=N0RTH>

128 AFS(AREA=0.5/EXP=.50)

129 SRF(IN/0P/BS/C0NS=PTN-M/AZM=270/0RG=0,24.0/VRTS=12.0. 12.16, 0,12)

130 SRF(IN/0P/BS/C0NS=PTN-M/AZM-90/0RG=44»12»0/VRTS=12»0» 12,12, 0,16)

131 SRF(EX/OP/BS/CONS=SLAB-C/AZM=18O/0RG=O»24»O/SIZE=44»12/TILT=18O)

132 OSC < TGP= 1

)

133 3 134 ZONE C 135 GEQM(NAME=SOUTH)

136 CTRL(CUS=HEATS/HEAT=12)

137 PE0(WS=0CCS/CAP=3)

138 LIT (WS=LITS/CAP=1 .4)

139 EQP(WS=EQPS/CAP=9.4/L0ST=,4)

140 MASS(C0NS=PTN-A/AREA=480)

141 SRF ( EX/OP/BS/CONS=WL-I/AZM= 180/0RG=0 ,0»0/SIZE=41»8)

142 SRF ( EX/TR/SS/C0NS = UDW2/0RG=12 » 3

. - . 25/SIZE=20 » 4

)

143 AFS(AREA=0,2/EXP=.65)

144 SRF(EX/0P/BS/C0NS=WL-S/AZM=180/0RG=41,0»0/SIZE=3,8)

145 SRF (EX/0P/BS/C0NS=RF-T/AZM=180/0RG=0,0»8/SIZE=4 1,8. 95/TILT =26, 6)

146 AFS(AREA=0.1/EXP=.65)

147 SRF(EX/0P/BS/C0NS=RF-I/AZM=180/0RG=41 , 0 , 8/SIZE=3 » 8 . 95/TILT=26 . 6

)

148 SRF( IN/0P/BS/C0NS = PTN-A/AZM = 0/0RG = 44,12,0/SIZE = 41,12/Z0NE = CENTER)

149 AFS(AREA=0»5/EXP=.50)

150 SRF< IN/0P/BS/C0NS=PTN-S/AZM=0/0RG=3,12»0/SIZE=3,12/Z0NE=CENTER)

151 SRF(IN/0P/BS/C0NS=PTN-M/AZM=270/0RG=0,12»0/VRTS=12»0» 12,8, 0,12)

152 SRF(IN/0P/BS/C0NS=PTN-M/AZM=90/0RG=44,0,0/VRTS=12,0, 12,12, 0,8)

153 SRF(EX/0P/BS/C0NS=SLAB-T/AZM=180/0RG=0, 12 , 0/SIZE=44 , 12/TILT= 180

)

154 OSC ( TGP=1

)

155 3

Figure II. 3 (concluded)

11
PAGE 6 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/07. 05.39.04. 5.977

BUILDING LOADS FOR

THERMAL MASS TEST - SIMULTANEOUS ZONES* DIRECT SUN

COLUMBIA* MO.

MILD WINTER

TOTAL TOTAL PEAK PEAK MAX MIN

ZONE HEATING COOLING HEATING COOLING TEMP TEMP HX HT V CL CX

< KBTU

)

< KBTU

)

( KBTUH

)

(KBTUH) (F) (F)

NORTH 51.02 0.00 10.166 0.000 69.28 61.90 0 10 0 0 0

CENTER 1.13 0.00 1.126 0.000 73.10 64.10 0 2 0 0 0 SOUTH .31 0.00 .308 0.000 77.86 67.96 0 1 0 0 0 total: 5 . 245E + 01 0. 10.473 0.000 77.86 61.90

MAX HEATING OCCURS AT HOUR 7 ON 21FEB

MAX TEMP OCCURS AT HOUR 18 ON 21FEB

MIN TEMP OCCURS AT HOUR 6 ON 21FEB

Figure II. 4 Calculated loads for example problem

12
Ill ALGORITHMS

I I I. A INTRODUCTION

III. A. 1 THE HEAT BALANCE METHOD

TARP is a large collection of algorithms which perform a simultaneous

evaluation of multi-room temperatures and energy requirements as affected by

dynamic external and internal thermal conditions. The overall simulation

process is best explained in terms of a single room. The calculation of the

room air temperature is based on a heat balance on the room air. The convective gains from the room surfaces and internal sources plus the sensible gain

from incoming air plus the energy added by the air handling system must equal

zero.

CE + E HCi *S i *(Ti - TZ) + E Fj*Cp*(TSj - TZ) + L - 0

where

CE = energy convected from internal sources

Si = area of surface i

HC^ = convection coefficient of surface i

T^ = temperature of surface i

TZ = room air temperature

Fj = mass flow of air through opening j

Cp = specific heat of air

TSj = temperature of the air through opening j

L = energy from the air handling system

(A. 1.1)

The summations apply to all surfaces/openings which are part of the room. The values of the surface temperatures, T^, are obtained by evaluating a heat balance at every surface of the room using an assumed room temperature.

A better estimate of the room temperature is then obtained by solving

equation A. 1.1 for TZ. Repeating this process leads to successively better

approximations of the surface and air temperatures. The process is rapidly

convergent. Multiple rooms can be handled within the iterative scheme given

an appropriate data structure and proper heat balances on the surfaces between

rooms. Multiple rooms are thermally connected by conductive, convective, and

radiative heat transfer. The following sections describe the algorithms for

the various heat transfer mechanisms and thermal driving functions which

culminate in multi-room heat balances.

I I I. A. 2 TABLE OF SYMBOLS

The following symbols are used frequently in the algorithm

descriptions. Symbols which are local to an algorithm are defined as they

occur.

13
Subscripts

Subscripts may be omitted if context is clear.

Symbol Meaning

a ambient air

g ground surface

i surface i

j surface j (usually meaning opposite side of surface i)

k order of conduction transfer functions (CTF) m number of CTF m zone m (usually meaning adjacent to zone n) n zone n

t time

s sky

sg surface to ground

ss surface to sky

Summation limits •

• NC number of temperature CTF

NF number of flux CTF (NF i NC)

NS number of surfaces

NZ number of zones

Parameters:

Symbol Units Meaning

<*i absorptance of surface i for short wave radiation

e i emittance of surface i for long wave radiation

g m/s2 gravitational constant (9.80)

Pi

W/m2K4

reflectance of surface i

0 Stefan-Boltzman constant (5.6688E-8)

Ti transmittance of surface i

0i angle of incidence of sun’s rays on surface i

<t>i surface tilt angle

o surface azimuth angle

A

i area of opening i

cl„

Wh/kgK specific heat (often refers to air - 1004.)

W convective gain from all internal sources in zone n «1 W/m^ convective flux from zone air to (inside of) surface i

CO, W/m* convective flux from environment to surface i

D

1 kg/m3 density

F kg/s mass flow rate

F ij o radiation interchange factor from surface i to surface

HA, W/m;K surface i outside convection film coefficient

HCi W/m2 K surface i inside convection film coefficient

HG^ W/m2 K

r\

surface i radiative conductance

(outside surface to ground radiant temperature)

H0 i W/mzK overall outside surface conductance

HR^ W/m2 K surface i radiative conductance

(inside surface to zone mean radiant temperature)

HSi W/m2K surface i radiative conductance

(outside surface to sky radiant temperature)

14
Ib

xd

*S

J

g

i,k

KIi,t

KIPi,t

KO i,t

K0Pi,t

M

P

PB

PSi

PW± Qli

QLn QLIi

QO.

QSn

W/m2

W/m2

W/m2

W/nr

W/m2 W/m2

W/m2

W/m2

W/K

N/m2

N/m2

N/m2

N/m2

W/mz W

W/m2

W/m2 W

intensity of solar beam (direct) radiation

intensity of solar diffuse radiation

intensity of sky diffuse radiation (sky brightness)

intensity of ground reflected radiation

flux referring CTF

inward conductive flux at inside of surface i at time t

portion of inward conductive flux based on previous

temperature and flux history terms

outward conductive flux at outside of surface i at time 1 portion of outward conductive flux based on previous

temperature and flux history terms

capacitance rate (mass flow times specific heat)

pressure

barometric pressure

pressure difference across surface i due to stack effect

pressure difference across surface i due to wind

total radiant flux absorbed at inside of surface i

total long wave radiation created in zone n long wave radiant flux absorbed at inside of surface i

total radiant flux absorbed at outside of surface i

total diffuse short wave radiation entering

and created in zone n

QSI

± w/m;? short wave radiant flux absorbed at inside of surface i

QSOj W/m2 short wave radiant flux absorbed at outside of surface i

s

i m

2

area of surface i

T C temperature

T K absolute temperature (= T + 273. 15K)

Ta

C temperature of outside (ambient) air

T

g

C ground surface (radiant) temperature

TIi.t C temperature of inside of surface i at time t TM C temperature of movable Insulation

(zone side or outside depending on placement)

T0i>t C temperature of outside of surface i at time t TRn C mean radiant temperature of zone n

Ts C sky radiant temperature

TZn C temperature of zone air

U W/m2K conductance (U-value) of a construct

UM, W/m2 K conductance of movable insulation on surface i va m/ s wind speed (measured value)

^az m/ s wind speed at height z ^az’P m/ s wind speed relative to surface at height z and orientation

X m X-coordinate of a point

Xi o flow exponent

X

i m

W/mz K outside (eXterior) CTF

Y

* m A Y-coordinate of a point

Yi,m W/mzK cross CTF

m Z-coordinate of a point

Z m height (of surface i or zone n)

Zi,m W/m2 K inside (Zone) CTF

15
III.B ENVIRONMENT

III.B . 1 TIME

III.B. 1.1 TIME OF DAY

Currently, TARP uses a one hour time step. The time from midnight to

1:00 AM is hour number 1; from 1:00 to 2:00 AM is hour 2; and from

11:00 PM to midnight is hour 24. The hour number (t 8

) is used as an index in

the program to select array elements. Most driving functions, such as solar

radiation, wind, and scheduled activities, use their average values for the

hour. Temperatures are for the mid-point of the hour. The one hour time

step was chosen because it is the shortest for which weather data is commonly

available, and it is possibly the longest for significant detail in the thermal

analysis. The time step can be changed by slight modification of the program,

primarily in the handling of day (24 hour) schedules.

During some portions of the year, daylight savings time (DST) is in

effect. DST hour numbers (t<j) are given by: t^ = t 8 + 1. TARP responds to

DST by operating scheduled activities according to td hour numbers and the

environmentally controlled activities and parameters according to t

8 hours.

III.B. 1.2 DATES

The TARP includes a package of routines to compute dates in various

forms for different calculational needs. All use integer arithmetic

(remainders of divisions are truncated). The starting values are the year

(YR) , month (MO) and day-of-month (DM). For example the date December 31,

1980 has YR = 1980 (all 4 digits required), MO *= 12, and DM a 31. The leap

year indicator (LY) is determined by the YR. LY » 1 if YR is a leap year,

0 if it is not. A year is not a leap year if it is not evenly divisible by

4, or if it is evenly divisible by 100 but not 400. Otherwise, it is a leap

year. Note that LY(1900) = 0 and LY(2000) = 1. The number of days in each

month (LM) is given by

LM(M0=1) = 31

LM(2) = 28 + LY

LM(3) = 31

LM(4) = 30

etc.

The day-of-year number (DY) is a continuous count of days beginning at 1 January. It can be computed by

MO-1

DY = DM + E LM(m) (B.1.1)

m=0

For M0=1, the sum is zero.

16
The Julian date (JD) is the most powerful date representation. It is

a continuous count of days from 1 January 4713 B.C. Any number of days

added to or subtracted from a JD is a valid JD. The following algorithms

[1] convert between conventional and Julian dates:

L » (MO - 14) / 12

JD - DM - 32075 + 1461 * (YEAR + 4800 + L) / 4

+ 367 * (MO - 2 - 12*L) / 12 - 3 * ((YEAR + 4900 + L) / 100) / 4 (B.1.2)

J 83 JD + 68569

N - 4 * J / 146097

K = J - (146097*N + 3) / 4

YEAR' = 4000 * (K + 1) / 1461001

L - K - 1461 * YEAR’ / 4 + 31

MO’ - 80 * L / 2447

DM = L - 2447 * MO’ / 80

M - MO’ / 11

MO - MO' + 2 - 12 * M

YEAR = 100 * (N - 49) + YEAR 1 + M (B.1.3)

The cyclic date (CD) is used in TARP to represent time periods which

begin and end certain functions. They are given by

CD - 32 * MO + DM • (B.1.4)

The inverse relationships are equally simple.

MO - CD / 32 (B.1.5a)

DM = MOD (CD, 32) (B.1.5b)

where

M0D(A,B) * the remainder of A/B

= A - (A/B)*B (MOD is a FORTRAN intrinsic function)

It is easy to use cyclic dates to determine if CD lies within a period from

CD1 through CD2 , inclusive.

If(CD2 > CD1), then (CD > CD1 and CD < CD2) for CD to be in the period.

If(CDl > CD2), then (CD > CD1 or CD < CD2) for CD to be in the period.

(B.1.6)

A number such as 94 can be a valid cyclic date even though it represents an impossible conventional date - 30 February. This date can be used to end

activities on the last day of February without considering leap year. The

logic of B.1.6 still works because 1 March has cyclic date 97.

Day-of-week numbers (DW) are assigned according to: Sunday = 1, Monday

=2, ..., Saturday =7. DW is given from JD by:

DW = M0D( JD+1 , 7) + 1 (B.1.7)

17
Building activities typically differ on holidays from normal schedules.

The standard U. S. federal holidays are:

I January (New Year's day)

3rd Monday in February (Washington's birthday)

last Monday in May (Memorial day)

4 July (Independence day)

1st Monday in September (Labor day)

2nd Monday in October (Columbus day)

II November (Veteran's day)

4th Thursday in November (Thanksgiving day)

25 December (Christmas)

If any of the four holidays with dates fall on a weekend, the nearest Friday

or Monday becomes a holiday. Five tests can describe the federal holidays

(given that MO is correct).

Mth (DW“N) in the month:

If( DW = N and (DMf6)/7 - M ) , DM is the holiday. (B.1.8a)

Last (DW=N) in the month:

If( DW = N and DM > (LM-7) ), DM is the holiday. (B.1.8b)

Dated holiday (DM=J) on weekday:

If( DM = J and DW ^ 1 and DW t 7 ) , DM is the holiday. (B.1.8c)

Dated holiday on Saturday:

If( DM = J-l and DW = 6 ) , DM is the holiday. (B.1.8d)

Dated holiday on Sunday:

If( DM = J+l and DW = 2 ) , DM is the holiday. (B.1.8e)

A test is also needed for the New Year's holiday on Friday, 31 December.

Daylight savings time is in effect from the last Sunday in April

through the Saturday before the last Sunday in October.

III.B.2 PSYCHROMETRICS

The following algorithms are used to calculate the properties of moist

air. They are presented as a package, but not all are required by TARP.

The psychrometric package gives four ways to compute the humidity ratio

depending on available information. Other values can then be computed from

the humidity ratio, dry-bulb temperature, and barometric presure. The

following nomenclature is used in the psychrometric package.

18
Ta Dry-bulb temperature (C)

Tw

» Wet-bulb temperature (C)

T<j Dewpoint temperature (C)

TS Saturation temperature of water at a given pressure

PB - Barometric pressure (Pa)

PS = Saturation pressure of water at a given temparature

Pw " Partial pressure of water (Pa)

W = Humidity ratio (kg/kg)

H “ Enthalpy (kJ/kg)

RH = Relative humidity

V Specific volume (nrVkg)

TS and PS are computed from polynomial expressions obtained by fits to

the detailed correlation [2]. These expressions are of the form

Y(X) = Aq + AX *X + A2 *X2 + ... + An

*XN

(B.2.1)

The coefficients for computing PS(T) (+0.02 %) are:

Range of T A0 A1 a2 A3

-70. to -60. 187.72756 9.7388459 .19227592 .0017092958 5.7638449E-6

-60. to -50. 304.327455 17.544515 .38850839 .0039049250 1.4989099E-5

-50. to -35. 456.91552 30.071980 .77543816 .0092327737 4.2579887E-5

-35. to -20. 578.24965 43.849126 1.3678040 .020662996 .00012607288

0 . •U o o . 1CM 611.12442 50.242069 1.8540594 .037851608 .00036358829

0. to 20. 617.57030 44.857183 1.4599520 .024895806 .00041888641

20. to 40. 674.80450 34.735044 2.1525746 .0029183585 .00069389647

40. to 70. 1882.1549 -75.905764 6.0054813 -.057650288 .0010572251

70. to 100. 10003.937 -537.34244 15.931817 -.15349268 .0014076596

The coefficients for computing TS(P) (+0.005 C) are:

Range of P A0 A1 a2 a3

a4 a5 a6

0.2617 to -80.481222 60.488509 -104.02603 116.27016

1.08 -70.240148 17 .403927

1.08 to -71.907528 17.059641 -7.6219223 2.2337690

3.94 -.35643002 .023469826

3.94 to -62.643477 4.8931575 -.58140203 .047441082

22.35 -.0023302718 6. 2036235E-5 -6. 8559241E-7

22.35 to -50.166219 1.0796773 -.025433803 .00041771901

103.26 4. 1788472E-6 2. 2878800E-8 -5. 2415828E-1

1

103.26 to -36.261166 .23970771 -.0010835426 3.3697165E-6

617.56 -6.2986874E-9 6. 3667218E-12 -2 .6646050E-15

617.56 to -21.4716785 .052658152 -3.8998869E-5 1.9227789E-8

2364.9 -5.1661347E-12 5 .7225294E-16

2364.9 to -6.2548222 .017442339 -3.7406571E-6 5.4267058E-10

7471.5 -4.3379212E-14 1. 4427502E-18

7471.5 to 9.3624054 .0065309333 -4.6769042E-7 2.4048849E-11

31605.7 -7.6034040E-16 1 .3232127E-20 -9 .6773935E-26

31605.7 to 33.328934 .0017898571 -2 .7520024E-8 2 .8970085E-13

102862. -1.6828604E-18 4.0679479E-24

19
The polynomials are faster than the ASHRAE detailed algorithm which

involves a logarithm and an exponential. The other relationships are based on

the ideal gas law and are generally accurate to better than 0.7 percent. The

humidity ratio may be obtained from one of the following algorithms [3].

W (Td , PB)

Pw = PS(Td )

W - 0.62198 * Pw / (PB - Pw) (B.2.2)

W (Ta , Tw , PB)

P* = PS(TW )

W' = 0.62198 * P' / (PB - P')

W = [(2501. - 2.381*Tw)*W' - (T a - Tw)

]

/ (2501. + 1.805*T a - 4.18*Tw)

W (Ta , RH, PB)

Pw = RH * PS(Ta )

W = 0.62198 * Pw / (PB - Pw)

W (T a , H)

W = (H - Ta ) / (2501. + 1.805*Ta )

The following values may be computed when

Td (W, PB)

Pw = PB * W / (0.62198 + W)

Td

= TS(PW)

RH (Ta , Td )

RH = PS(Td ) / PS(Ta )

V (Ta , W, PB)

V = 287.055 * (1. + 1.6078*W) * Ta /

H (T a , W)

H = Ta + W * (2501. + 1.805*Ta )

Tw (T a , W, PB)

Tw is computed by iterating (B.2.3).

(B.2.3)

(B.2.4)

(B.2.5)

the humidity ratio is known.

(B.2.6)

(B.2.7)

PB (B.2.8)

(B.2.9)

20
III.B.3 TEMPERATURES

III. B. 3.1 AIR TEMPERATURES

All temperatures occur on the half-hour. Dry bulb temperature and

barometric pressure are read from the weather tape. The wet bulb temperature,

dew point, or relative humidity are also read to allow computation of the

humidity ratio and the wet bulb temperature. For design days a temperature

profile is generated between the maximum (Ta+

) and minimum (T “) temperatures

for the day according to

T

at

- T

a+ - ft * (Ta+ ' Ta*> <B - 3a >

where f t is given by

t: 1 2 3 4 5 6 7 8 9 10 11 12

f.85 .90 .94 .98 1.0 .99 .95 .89 .78 .64 .48 .31

t: 13 14 15 16 17 18 19 20 21 22 23 24

f: .17 .06 .00 .01 .07 .16 .23 .41 .53 .63 .72 .79

These values were obtain by interpolating between the hourly temperatures

given by ASHRAE [4]. This profile is for summer days. For design days the

user also gives PB and T

w

corresponding to T

a+

. A humidity ratio is computed

from these and used with Ta and PB to compute Tw for every hour.

III.B.3. 2 SKY TEMPERATURE

The net thermal radiative flux between a horizontal surface and the sky

(Qss ) is given by

°ss = H * (a * T0i

4 - es * a * T

a

4

) (B.3.2)

with e s , the sky emmisivity, given by the correlation [5]

e

s where

[0.787 + .764*ln(Tj/273) ] *( 1 + ,0224*N - .0035*N2 + .00028*N3

) (B.3.3)

N = tenths cloud cover

TARP uses a slightly different formula for computing Qss .

Qss = H * a * (T0l

4 - T

s 4

)

so that

(B.3.4)

(B.3.5)

21
III. B. 3.

GROUND TEMPERATURES

The user specifies monthly ground temperatures. Useful advice for the

selection of ground temperatures is a subject of ongoing research.

III.B.4 WIND

Wind speed increases with height according to the formula

V = V

Q

* 3 * ( Z / Z

Q ) a (B.4.1)

where

VQ

= wind speed at standard conditions

Z = height being considered

Z0 = standard height of wind measurements (10m)

a, 3 terrain dependent coefficients given below.

Terrain Parameters for Standard Terrain Classes [6]

Class Description a 8

1 ocean or other body of water with at

least 5km of unrestricted expanse

0.10 1.30

2 flat terrain with some isolated obstacles (buildings or trees well

separated from each other)

0.15 1.00

3 rural areas with low buildings,

trees, etc.

0.20 0.85

4 urban, industrial, or forest area 0.25 0.67

5 center of large city (Manhattan) 0.35 0.47

Wind speeds are usually measured at class 2 sites (airports). Therefore, the

reported velocity is VQ

. Eq (B.4.1) can be rearranged to compute VQ for V

measured at non-standard sites.

III.B.5 SOLAR RADIATION

The general factors in determining solar position and solar radiation

intensity are described by ASHRAE [ 7 ]

Most of that information is not

repeated in the following discussion.

III. B. 5.1 SOLAR POSITION

The solar position is described in terms of three direction cosines

which are convenient for determining the angle of incidence of the sun's

rays on a building surface (E.2.2). The following procedure is used to

determine the direction cosines. The values of the solar declination angle,

6, the equation of time, e, and the distance form the earth to the sun, R

(in AU: 1 AU = 149,504,000 km) are determined by a U.S. Naval Observatory

algorithm [8].

22
For a given JD, compute the number of centuries since 1900.

T - (JD - 2415020.5) / 36525. (B.5.1)

Then compute the following fundamental angles (in degrees).

Mean anomaly of the sun:

G = 385.475833 + 35999. 049750T - 0.000150T2 (B.5.2a)

Mean longitude of the sun:

L = 279.696678 + 36000. 768920T + 0.000303T2 (B.5.2b)

Mean longitude of the moon:

C = 270.434164 + 481267. 883144T - 0.001133T2 (B.5.2c)

Longitude of the ascending node of the moon's orbit:

N = 259.183275 - 1934.142008T + 0.002078T2 (B.5.2d)

Mean anomaly of Venus:

V = 212.603219 + 58517 .803875T + 0.0001286T2 (B.5.2e)

Mean anomaly of Mars:

M = 319.529425 + 19139. 858500T + 0.000181T2 (B.5.2f)

Mean anomaly of Jupiter:

J = 225.444651 + 3034.906654T (B.5.2g)

Then compute the following values.

0 « 0.397930 sin(L) + 0.009999 sin(G-L) + 0.003334 sin(G+L)

- 0.000208 T sin(L) + 0.000042 sin(2G+L) - 0.000040 cos(L)

- 0.000039 sin(N-L) - 0.000030 T sin(G-L) - 0.000014 sin(2G-L)

- 0.000010 cos(G-L-J) - 0.000010 T sin(G+L) (B.5.3a)

p = 1.000421 - 0.033503 cos(G) - 0.000140 cos(2G)

+ 0.000084 T cos(G) - 0.000033 sin(G-J) + 0.000027 sin(2G-2V)

(B.5.3b)

<)) = -0.041295 sin(2L) + 0.032116 sin(G) - 0.001038 sin(G-2L)

- 0.000346 sin(G+2L) - 0.000095 - 0.000080 T sin(G)

- 0.000079 sin(N) + 0.000068 sin(2G) + 0.000046 T sin(2L)

+ 0.000030 sin(C-L) - 0.000025 cos(G-J) + 0.000024 sin(4G-8tft-3J) - 0.000019 sin(G-V) - 0.000017 cos(2G-2V) (B.5.3c)

The maximum error in 0 or <}> is .0001 AU and the maximum error in p is .0001

AU2 for the years 1800 through 2100. This is more accurate than is needed

for building thermal analysis. Equations (B.5.3a-c) can be truncated with

some loss in accuracy. That loss can be estimated by the sum of the

magnitudes of the truncated coefficients. TARP uses the first 4, 4, and 5 terms of these equations, respectively. With the shortened equations, only

G and L are evaluated.

Then compute the solar declination angle, equation of time, and the

earth-sun distance.

6 = arcsin( 0 / /p”)

e -arcsin( <f> / /p-0 2

) / 15

23

[hours

]

(B.5.4a)

(B.5.4b)
R - /p (B.5.4c)

The hour angle, H, is the number of hours from solar noon.

H - 15 (12 - t 8 - e - TZ) + LONG (B.5.5)

where

t

s » standard time (hours) at midpoint of the timestep

TZ = time zone number (1.3.4)

LONG = longitude (1.3.3)

The solar direction cosines can be determined from these values plus the

latitude, X (north positive, south negative), of the site.

CSp = cos 6 sinH (B.5.6a)

CS 2 = sin5 cosX - cos 6 sinX cosH (B.5.6b)

CS 3 = sin6 sinX + cos 6 cosX cosH (B.5.6c)

CS3 is the cosine of the solar zenith angle which also equals the sine of

the solar altitude angle. The solar azimuth angle, t|j (relative to north),

can be determined from

These angle calculations apply for the northern and southern hemispheres.

The calculation of direct normal solar intensity, Ib , and diffuse solar

intensity, I s , for clear design days is exactly as described in [7],

The values of A, B, and C are calculated by a truncated Fourier series fit

to the data in Table 1 of [7], Seasonal effects implicit in that table

would not apply to the southern hemisphere. When the clearness number is

less than 0.75, it is assumed to represent the ratio k-p defined as

(B.5.7a)

(B.5.7b)

III. B. 5.

2

SOLAR INTENSITY

I b

= Ae“B/CS3

Is = C * Ib

(B .5

,

8 a)

(B.5.8b)

kT

= I / I 0 (B.5.9)

where

I = the total solar radiation on a horizontal surface

( - I b

* CS 3 + I8

)

24
Iq the solar radiation on a horizontal surface above the earth's

atmosphere [ - (

sc /R2 )*CSo

]

I - the solar constant (1353 w/m2

) 9 C On such cloudy design days the following correlation [9] is used.

1.0 - 0.249 kT kT < 0.35

I 8 /I = 1.557 - 1.84 kx 0.35 < kT < 0.75 (B.5.10)

0.177 kT > 0.75

Weather tape data is used by means of the BLAST program weather file

processor. For transportability, a version of this processor should be

incorporated into TARP. This version should include the most current solar

radiation correlations.

REFERENCES

[1] Fliegel, H. and Van Flandern, T., "A Machine Algorithm for Processing

Calender Dates," Communications of the ACM , Vol. 11, No. 10

(October 1968), p. 657.

[2] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 5.2.

[3] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), pp 5. 3-5. 5.

[4] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 26.6, table 3.

[5] Clark, G. and Allen, C., "The Estimation of Atmospheric Radiation for

Clear and Cloudy Skies," Proceedings of the 2nd National Passive Solar

Conference (AS/ISES, 1978), pp. 675-678.

[6] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 22.15, table 7.

[7] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), pp 27.2-9.

[8] Doggett, L. E. , Kaplan, G. H. , and Seidelmann, P. K. , Almanac for

Computers for the year 1978 , (United States Naval Observatory, 1978)

pp All-17.

[9] Orgill, J. F. , and Hollands, K. G. T., "Correlation Equation for

Hourly Diffuse Radiation on a Horizontal Surface", Solar Energy 19

(Pergamon Press, 1977), p 358.

25
III.C TRANSIENT HEAT CONDUCTION

III.C.l USE OF CONDUCTION TRANSFER FUNCTIONS

The conventional equation for calculating steady state heat flux from the

inside to the outside of a wall is

KO - U * (TI - TO) (C.1.1)

This equation is valid only when the wall is non-massive or when the inside or outside temperatures are constant in time. In the more common and complex

situation where transient effects cannot be safely ignored, heat conduction

calculations which properly account for the dynamic effects must be utilized.

The methodology implemented in TARP is based on the standard response factor

technique [1] developed by Stephenson and Mitalas [2] and Kusuda [3] modified

for efficiency according to a suggestion by Peavy [4]. The modified response

factors are called "conduction transfer functions" (CTF). The heat conduction

at (and toward) the inside surface at time t is given by:

NT NT NF

KI t - E Ym*TOt_m - E Zm*TI t -m + Z Jk*KIt-k (C.1.2)

m=0 m°0 k*l

The heat conduction flux at (and toward) the outside surface is

NT NT NF

K0 t - E Ym*TI t _m - E Xm*TO t _m + E Jk*KO t_k (C.1.3)

m=0 m=0 k=l

TARP uses the convention that the X CTF refer to outside (or exterior) surface

temperatures, and that the Z CTF refer to inside (or Zone side) temperatures as in [1]. The opposite convention is often used in other programs.

The current inside and outside conductive fluxes are functions of the

current inside and outside temperatures plus a factor containing the previous

temperatures and fluxes. TARP initializes the temperature and flux histories

by starting from a steady state and repeatedly calculating the building thermal

performance for the first day of the simulation period until essentially equal

results are achieved. Equation (C.1.2) can be rewritten to emphasize the

unknown values at time t.

KI t = Y0 *TOt - Zo*TI t + KIPt (C.1.4)

where

NT NT NF

KIP t = E Ym

*TOt _m - E Zm

*TI t _m + E Ji*KI t _U(C.1.5)

m=l m=l k=l

Equation (C.1.3) may be similarly rewritten.

K0 t = Y0*TI t - X0*TO t + KOP t (C.1.6)
where

NT NT NF

KOP t

Z Y^TI^- Z Xjn*TOt _m + Z Jk

*KOt_k(C.1.7)

m*l m«l k"l

For lightweight surfaces, such as sheet metal or thin glass, there are no CTF

terms for m > 1 or k > 0. In that case Xq Yq “ Zq U, and equations (C.1.4)

and (C.1.6) both reduce to equation (C.1.1). Air cavities are handled by

massless 'slabs' which have only thermal resistance. This resistance cannot

be described as temperature dependent. The conductive properties of a multipane window are described in this manner and appropriate conduction transfer

functions are computed.

III.C.2 CALCULATION OF CONDUCTION TRANSFER FUNCTIONS

The CTF method is based upon the exact solution of a triangular

temperature pulse on either side of the wall. A series of triangular temperature pulses can be superposed to produce a good approximation of a continuous

temperature function. The triangular pulse is solved by a Laplace transform.

TARP follows the calculation technique used in BLAST [5] and described in detail

by Hittle [6]. That description is quite lengthy and is not repeated here.

One useful property of the CTF is that the steady state conductance of

the wall is related to the CTF by

NT NF

U - Z Xm / (1 - Z Jk) m=0 k=l

NT NF

- Z Ym / (1 - Z Jk) m=0 k=l

NT NF

- E Zm / (1 - Z Jk) (C.2.1

)

m=0 j=l

This provides the method for determining the number of CTF terms to produce

the desired accuracy.

REFERENCES

[1] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), pp 23.09-23.10.

[2] Stephenson, D. G. and Mitalas, G. P., "Cooling Load Calculation by Thermal

Response Factor Method", ASHRAE Transactions , Vol 73 (ASHRAE, 1967).

[3] Kusuda, T., "Thermal Response Factors for Multilayer Structures of Various

Heat Conduction Systems", ASHRAE Transactions , Vol 75 (ASHRAE, 1969), p 246

[4] B. A. Peavy, "A Note on Response Factors and Conduction Transfer Functions"

ASHRAE Transactions, Vol 84 (ASHRAE, 1978), pp 688-690.

27
[5] Hittle, D. C., "The Building Load Analysis and System Thermodynamics

(BLAST) Program, Version 2.0: Users Manual", CERL Technical Report E-153.

(Construction Engineering Research Laboratory, 1979).

[6] Hittle, D. C., "Calculating Building Heating and Cooling Loads Using the

Frequency Response of Multilayered Slabs", CERL Technical Manuscript E-169

(Construction Engineering Research Laboratory, 1981), pp 20-70.

28
Ill .D WINDOW OPTICS

Windows are thermally critical elements of the building envelope. They

are difficult to insulate and produce much greater conductive gains and losses

than corresponding wall areas. Most can be opened to provide ventilation, but

then they are significant sources of infiltration. The unique characteristic

of windows is the transmission of light (short wavelength thermal radiation)

directly into the building. This transmitted light is usually a desirable

heat gain in the winter and an undesirable gain in the summer. It also provides natural lighting inside the building. The following sections describe

the TARP optical algorithms.

III.D.l OPTICAL COEFFICIENTS

Figure D.l shows how the solar-optical properties of typical uncoated

glazing materials vary with the incident angle of the light [1]. As the incident angle increases from 0=0 degrees (normal incidence), the transmittance

decreases, reflectance increases, and absorptance first increases due to the

lengthened optical path through the glass and then decreases as more incident

radiation is reflected away. These properties also vary with the wavelength

of the incident radiation. The total solar radiation incident on a window (Q)

is composed of beam and diffuse components,

Q

= I b*cos0 + I d (D.1.1)

The beam component (Ib ) comes directly fom the sun and is incident at angle 0.

The diffuse component (I d ) comes uniformly from all directions. Some of the

incident radiation is transmitted according to

QT = T b

* I b* cos 0 + Td* I d (D.l. 2)

where

Tb

is the beam transmittance at 0 and

T d is the transmittance for diffuse radiation.

Some is absorbed according to

QA = Ab

* I b* cos0 + Ad

* I d (D.l. 3)

where Ab and Ad are the beam and diffuse absorptances . If an internal shade

is present, it also absorbs radiation with absorptances ASb and ASd

.

QS = AS b* I b* cos 0 + AS d

* I d (D.l. 4)

The energy absorbed in the shade is convected directly to the room air. The

energy absorbed in the glass is convected both into the room and to the outside

according to proportions (neglecting the thermal resistance of the glass which

is small compared to HI and HO) defined by

29
QAin - QA * HI / (HI + HO) (D.1.5a)

and

QAout “ QA * HO / (HI + HO) (D. 1 .5b)

where

HI = inside surface heat transfer coefficient and

HO = outside surface heat transfer coefficient.

The expressions become more complicated for a two pane window.

QAin - QAI * (U/HO + U/HS) + QAO * U/HO (D.1.6a)

and

QAout = QAI * U/H! + QAO * (U/HI + U/HS) (D.1.6b)

where

U = 1 / (1/HO + 1/HS + 1/HI),

HS = heat transfer coefficient of the air gap,

QAI = energy absorbed in the outer pane and

QAO = energy absorbed in the outer pane.

In TARP a consistant description of absorption in single and multi pane windows

is achieved by separating QA into equal components, QAI and QAO, for the single

pane window. HS is then the U-value of the glass. The actual distribution of

the QAI qnd QAO is handled by the more general surface heat balance equations

(1.3.2) and (J.3.2).

The angle dependent properties of T^, AO^, AI^, and AS(j are represented

by polynomial equations in terms of cos0. Two ranges of cos9 are used for

greater accuracy, so each property (X) has two equations

X = cq + c^cos9 + C

2 (cos 0 )^ + ... + c^(cos9)^ [cos0 > 0.5) (D.1.7a)

and

X = d^cos9 + d

2 (cos 0 )^ + ... + c^(cos0)^ [cos9 < 0.5] (D.1.7b)

The coefficients c-^ and d^ are determined by curve fits to optical values

computed by methods described in the following sections. TARP also computes

transmittance and absorptances for diffuse radiation.

III.D.2 SHADING COEFFICIENTS

The solar optical properties of windows are often described by a shading

coefficient, SC, [2] which is defined as

SC = Solar Heat Gain of Window /

Solar Heat Gain of Reference Glass (D.2.1)

30
For single glazing this is

SC - [QT + QA* ( HO+HI ) /HO ] /

[QTdsa + QAdsa*(HO+HI)/HO] (D.2.2)

where

QT » radiation transmitted

QTdS a

= QT of DSA glass

QA = radiation absorbed

QAdsa " QA of DSA glass

HO “ outside surface heat transfer coefficient ( 22.7 W/m^k)

HI » inside surface heat transfer coefficient ( 8.3 W/m^K)

The reference glazing material is double-strength sheet glass (DSA) with 0.86

transmittance, 0.08 reflectance, and 0.06 absorptance at normal incidence.

A shading coefficient is implemented in TARP by multiplying SC times the

c^ and d^ of (D.1.7) computed for the reference glass. This gives correct

steady state solar gains, but does not give correct proportions of transmitted

and absorbed radiation (esecially for heat absorbing glasses). Correct proportions are necessary in dynamic simulation because the absorbed component produces an instantaneous convective gain to the space while the transmitted

component is first absorbed by the surfaces of the space and produces a delayed

gain. Therefore, the shading coefficient method is not recommended unless data

for the following detailed method is unavailable.

III.D.3 UNCOATED PANE OPTICS

When a ray of light reaches a smooth interface between two non-conducting

media, part of the ray is reflected and part is refracted as in figure D.2.

The angle of reflection equals the angle of incidence (0^). The angle of

refraction ( 82 ) is given by Snell's law:

nj * sinQ^ = n2 * sin02 (D.3.1)

where n^ and n2 are the indexes of refraction of the two media. The refractive

index of air is effectively equal to unity. The refractive index of glass is

dependent on both the composition of the glass and the wavelength of the light.

The variation is small for typical wavelengths between 0.3 and 3.0 microns,

but it is enough for a glass prism to separate a ray of white light into the

spectrum of colors.

Reflectance is the ratio of the energy reflected from the interface to the

energy incident upon it. The electromagnetic description of light shows that

reflectance depends on the polarization of the incident light. The two components of polarization are perpendicular to the plane of incidence (also called

transverse electric or TE) and parallel to the plane of incidence (called trans- verse magnetic or TM) . A simple formula [3] for reflectance at the interface

shown in figure D.2 is

P = KPi “ P2 )/ (Pi + P2)]

2 (D.3.2)

31
Pi = cos0i * ni for TE light (D.3.2a)

and

Pi ** cos0i / ni for TM light (D.3.2b)

Unpolarized light may be considered to consist of one half TE and one half TM

polarized light. (D.3.2) is a computationally simpler form of the more familiar

Fresnel equations.

The fraction of light transmitted through the interface is given by

t = (p 2 /Pi )* [ 2*p i / ( p i + p 2

)] 2 (D.3.3)

with the same polarization dependent values for p as above. It is easier to

calculate transmittance from the simple energy balance: t = 1 - p.

Glass absorbs light passing through it in proportion to the intensity of

the light. The fraction of light (xg) transmitted through a given distance

(x) of glass is given by the exponential decay formula

where k is the extinction coefficient of the glass. The value of k is

wavelength dependent but independent of polarization. The fraction of light

absorbed is ag = 1 - tg. For a glass plate of thickness L, the distance the

light travels in passing from one side to the other is x = L / cos02

. Therefore

i

g

= e"kL/cos0 2 (D.3.5)

A ray of light incident on a sheet of glass will be both reflected and

refracted at the front surface. Part of the refracted component will be

absorbed in the glass before reaching the back surface where it is again

reflected and refracted. This continues until all the light is either absorbed

or escapes from the front or back surfaces of the glass. Figure D.3 shows the

first several reflections of the incident light ray. Summation of the transmitted, reflected, and absorbed components of the incident ray give the total

transmittance (t), reflectance (r), and absorptance (a) of the sheet of glass.

These values must be determined separately for both polarization components,

p, x (= 1 - p), ig, and cig (= 1 - Tg) are functions of the angle of incidence

and wavelength of the light. They are identical at both sides of the glass.

Single pane transmittance:

t = (l-p) 2 T g + (l-p) 2 p

2 Tg 3 + (l-p) 2 p ^Tg 5 + ...

= (

-

p

2 Tg O- + p2 Tg

2 + p ^

Tg^ + **• ^

= t

2 Tg / (1 - p2 Tg 2

) (D.3. 6)

32
Single pane reflectance:

r p + (l-p) 2 pT

g

2 + (l-p) 2

p

3

Tg

^ + ...

» p + (l-p)2pr

g

2 (1 + p2

Tg

2 + ^Tg + ••• )

“ p + t 2

p Tg

2

/ (1 - p

2

Tg

2

) (D.3.7)

Single pane absorptance:

a » [

(

1—P )—

(

1—P

)

Tg ] + [ (l-p)pTg-(l-p)pTg2

] + [(l-p)p 2 Tg

2 -(l-p)p 2 Tg3

] + ...

(l-p)(l-Tg)(l + P Tg + p

2

Tg

2 + ... )

B t ag / (1 - p Tg) (D.3.8)

The energy balance (t+r+a=l) allows any one of the three components to

be computed from the other two, or it allows a check for the consistency of

all three.

The extinction coefficient of a pane of glass can be computed from the

thickness, normal incidence transmittance, and index of refraction. At normal

incidence

p = [(nj - n

2 )/(n1 + n

2

)]

2 (D.3.9a)

= [(n- l)/(n+l)]2 for air and glass

and

t - [(1 - p)

2

Tg

]/[1 - p

2

Tg

2

] (D.3.9b)

which combine to give a quadratic equation for Tg. The solution of that

equation is

t » ( -B + / B

2 + 4C ) / 2 (D.3.10)

o where B = (l-p)^/(p^ t) and C = 1/p^. Finally, from (D.3.5)

k = - ln(

g

) / L (D.3.11)

This provides a means of describing the glass pane in terms of simply measurable

optical properties and makes it unnecessary to use the less exact shading

coefficients when those properties are known.

III.D.4 REFLECTIVE COATINGS

A metallic film will be treated as a thin, smooth coating on one side of

the pane of glass. Let medium 1 be the air, medium 2 the film, and medium 3

the glass substrate. The mathematical treatment of the optics of a metallic

film [4, 5] is based on the index of refraction of the metal being a complex

number (complex numbers indicated by ~)

33
n [ i = m (D.4.1)

2 = n2 " lk2 where n£ is the (real) index of refraction and k 2 is the extinction coefficient.

Snell's law still applies, but it leads to a complex value of cos^ = x + iy. Let

and

Then

and

c = [ (nj*sin0 ^*n2 )/(n

2

^ +

d = [ (n^sinG^k^)/^ 2 + k

2

2

)] 2

x = / 1 - c + d + /(1-c+d)^ + 4*c*d T~1

y

= c * k2 / (x * n2

)

(D.4 . 2a)

(D.4.2b)

(D.4. 2c)

(D.4. 2d)

The amplitude (not energy) reflectance at the interface between media i and j

for light incident from medium i is given by

Pil

= (Pi “ P-j)/(Pi + P-i) (D.4. 3a)

where

jk = cos * n^ [TE polarization] (D.4. 3b)

p i = n^ / cos ^ [TM polarization] (D.4. 3c)

The amplitude transmittance at an interface is given by

Tij = 2 * p i

/ (p^ + pj) (D.4. 3d)

Note that Pj^ = “Pjj and = 1 - Pjj^*

Amplitude transmittance (x^) within the metallic film is based on its

phase thickness defined as

a = 2*TT*D*n2 * cos$

2

/ X (D.4. 4a)

where

D = thickness of the film and

\ = wavelength of the light

so that~ _ -id

t

£ - e [i = /"=

1

] (D.4 ,4b)

Considerations of multiple reflections within the film leads to expressions

for the total amplitude reflectance and transmittance. For light incident

from medium 1 the expressions are

P n (P 12 23

T f

2

) / (1 12 23

?

2

) (D.4. 6a)

and

34
t (D.4.6b) 13 t 12 / (1 + p 12 * p 23

*

)

Reverse the subscripts for light incident from medium 3.

The energy reflectance and transmittance are given by

(D.4.7a)

(D.4.7b)

, p 13 " Pl3 * Pl3

and

I •" » A/ I A/ t 13 = t 13 t 13 P3 ' Pi

where p and t are the complex conjugates of p and ?. Energy is absorbed in

the metallic film (p ^

+ T 13 < 1 ).

Host of the above expression are complex. Rather than expanding them to

get solutions in terms of real numbers, it is easier to let the computer

evaluate the expressions by using complex arithmetic.

Coated glass has the same multiple reflection property as uncoated glass.

Derivation of the total reflectance, transmittance, and absorptance is complicated by the fact that reflectances at the coatings depend on the direction of

incidence. Again consider a light ray incident from the left (as was done in

figure D.3). Properties (p, t) for both the left and right surfaces of the

glass are dependent on whether the light is incident from the left or right.

Consider the left side to be the "front" and the right side to be the "back"

of the glass. The following subscripts specify these conditions:

1: light incident on the left side from the left

2: light incident on the left side from the right

3: light incident on right side from the right (none)

4: light incident on right side from the left

so that for light incident from the front (superscript f)

r

f =

pj + p^ t

1 t 2

Tg

2

/ (1 - p 2 p^ rg

2

) (D.4.8a)

and

t f = t

1 t 4

Tg

/ (1 - p 2 p^ Tg

2

) (D.4.8b)

A simple exchange of subscripts (1:3 and 2:4) will give the expressions for

light incident from the back (superscript b).

r b

= p 3 + p 2

t 3t 4Tg

2

/ ( 1 - p 4 p 2 Tg

2

) (D.4.9a)

and

t b = t

3

t

2 Tg / (1 - p4 p 2 Tg 2

) (D.4.9b)

Since light is absorbed in the glass and in the coatings on either side, it is

easiest to compute absorptance from the energy balance: a=l-r-t. If

both sides of the glass are uncoated, Pi = P2 = P3 = P4> an<* T 1 = T2 = T3 = T4

and equations (D.4.8a and b and D.4.9a and b) reduce to (D.3. 7) and (D.3. 6).

35
III.D.5 MULTI-PANE WINDOWS

The optical properties of a combination of two panes of glass can be

determined from the properties of the component single panes. The values for

the TE and TM polarization components must be determined separately and then

added according to the relative proportions of each component [6].

Figure D.4 shows two panes of glass with fluxes of light going to both the

right (I) and to the left (J). The radiation fluxes are made up of all transmitted and inter-reflected components. Let

t n transmittance of pane n (as an individual pane)

n absorptance of pane n for flux from left (front)

an

° = absorptance of pane n for flux from right (back)

rn^

= re flectance °f pane n for light from the left (front)

r b = reflectance of pane n for light from the right (back)

then

I, * r 0 r + Jo * tJ

0 = x0

* r

l + J

1 * Z

l h

-

II * t

2 + J

2

* r

2

b

I

x - I„L * t, + J, * r

o 1

'1 1

(D.5 . la)

(D. 5. lb)

(D.5. lc)

(D.5. Id)

The optical properties for light incident only from the front are given by

setting J 2 “ 0, and substituting (D.5.1a-d) into the following definitions.

T

f - I

2

/ I 0

R

= B * t2

£ - j

0 / 10

= r/ + B * r

2 f * t

1

l l f .= (3^ * I n + ai

D

L * J,) / I, o

= a, f

L 1 +~ OB * r^1 2

, f = a 0 f * I

1 / I 0 = B * a

2

f

(D.5. 2a)

(D.5. 2b)

(D.5. 2c)

(D.5. 2d)

where

36
B » t (D.5.2e)

x / (1 - r

x b * r

2

f

)

For light incident from the back, set Iq * 0, to obtain

T

b = J

0 / J

2 = C * tl

R

b = I

2

/ J

2 = r2 b + C * rjb * t2 A2 b = (a

2 b * J2 + a2 ^ * 1^) / J2 = a2 b + C * r^ b * a2 ^

Al ba

l b * J1 / J2 * C * ai

b

(D.5.3a)

(D.5.3b)

(D.5.3c)

(D.5.3d)

where

C = t

2

/ (1 - r

2 ^ * r^ b

) (D.5.3e)

Note that = T

b . All other front and back coefficients may be different.

Similar heat balances can be set up for triple glazing. They lead to the

following equations for front radiation.

T

f - e * D * t

3 (D.5 .4a)

R

f - r

x f + E * t

l * (r 2

f + D * r^ f * t

2

) (D.5. 4b)

A

l f = al f + a: b * E * (r2

f + D * r

3

f * t

2

) (D.5. 4c)

A

2

^ = E * (a

2

^ + a

2 b * D * r^) (D.5.4d)

Ao f » a,

f * E * D (D.5 .4e)

where

D - t

? / (1 - r? b * r 3 ) (D.5.4f)

and

E - t

x / (1 - r^ * r

2

f - D * r^ * r 3

* C 2> (D.5.4g)

There is a similar set of equations for radiation incident from the back. TARP

also uses expressions for quadruple glazing, which are not repeated here.

III.D.6 DIFFUSE RADIATION

Diffuse radiation is considered to be of uniform intensity from all

directions and to be unpolarized (equal amounts of TE and Til polarizations).

Consider a small area, dAj , under a hemisphere of uniform brightness I (fig- ure D.5). The energy received is given by [7]

dQ = I dA^ cos0 dfi (D.6.1)

where

37
dQ / dAj ° energy per unit area

dQ the differential solid angle » dA2

/ r

= 2 tt (r 8in0) r d0 / r2

Let X( 0) be the transmittance, reflectance, or absorptance for beam radiation

of a system of glass panes. Then the diffuse property, X^, is given by

tt/2 tt/2

Xd = / X(0)2 tt I sin0 cos 0 d0 / /

2 ir I sin0 cos0 d0 (D.6.2)

0 0

The integral is evaluated by Simpson's method using beam values of X(0) at

appropriate 0.

III.D.7 INTERIOR SHADING DEVICES

Windows commonly have drapes or blinds in addition to the panes of glass

discussed so far. In TARP such interior shading devices are modeled as diffusely transmitting (ts), reflecting (rs) and absorbing (as) surfaces. When

an interior shading device is added to the glazing system, a new set of interreflected components is created (figure D.6). The total forward flux on the

shade is I

g (=lQ*T f + Note that we are interested in the diffuse

back reflectance of the panes of glass. The total (diffusely) transmited flux

through the shade is I

t = Is * t8

. The total leftward flux is Jg = I

g * r

g

. Therefore, I

g * Iq * T^ / (1 - r

g * R^*5 ) t and the total transmitted flux is

T

t - l0

* T

f

* C

s

1 (1 - r

s * Rd”> <D- 7 -l>

The total shade absorptance is

A

s - 1s * a

s

' *0 - lf * c s * a

s

I - r

s * R

d

b

> < D - 7 - 2 >

The total forward absorptance of each pane of glass is modified by

= AJ + J* * , b n n s nd

- An

L + And‘ * Tf * r / (1 - r e * Rjb

) (D.7.3)

Thus in the evaluation of the optical properties of a pane/shade system, it is

first necessary to compute the diffuse back absorptance of each pane in the

glass system by integrating beam An

b over 0. Then the pane/shade beam transmittance and absorptances are computed at the angles to be used in the optical

properties curve fits. Finally the pane/shade diffuse properties can be

computed.

REFERENCES

[1] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 27.14.

[2] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), pp 27.14-17.

38
[3] Born, M, , and Wolf, E., Principles of Optics, 4th ed, (Pergamon Press,

1970), pp 36-42.

[4] Heavens, 0. S., Optical Properties of Thin Solid Films , (Academic Press,

1955), pp 51-58.

[5] Born, M. , and Wolf, E., Principles of Optics, 4th ed, (Pergamon Press,

1970), pp 627-632.

[6] Hottel, H. C., and Sarofim, A. F., Radiative Transfer, (McGraw-Hill,

1967), p 197, fig 5-12.

[7] Kreith, F., Principles of Heat Transfer , 3rd ed. (Intext Educational

Publishers, 1973), pp 230-231.

39
TRANSMITTANCE

1.0

0.8

0.6

0.4

0.2

A = DSA glass

B = 6mm (0.25 in) clear glass

C = 6mm (0.25 in) heat absorbing glass

Figure III. 0.1 Variation of solar-optical properties

with angle of incidence

40
Figure III.D.2 Reflection and refraction at an interface

41
(1-p) 2 r

f

l

|1-p) 2 P

2 r

3|l

(1-p) 2p

4r*l

Figure III.D.3 Multiple reflections in a pane of glass

42
Figure III.D.4 Two-pane window system

43
Intensity

in

Figure III.D.5 Coordinate system for diffuse radiation

44
Figure III.D.6 Window system with interior shade

45

shade
Ill .E SOLAR GAINS AND SHADOWING

When assessing heat gains in buildings due to solar radiation, it is

necessary to know how much of each part of the building is shaded and how

much is in direct sunlight. As an example, figure E.l shows a flat roofed,

L-shaped structure with a window in each of the visible sides. The sun is

to the right so that walls 1 and 3 and windows a and c are completely

shaded, and wall 4 and window d are completely sunlit. Wall 2 and window b are partially shaded. The sunlit area of each surface changes as the

position of the sun changes during the day. The purpose of the TARP shadow

algorithm is to compute such sunlit areas.

The shadow algorithm is based on coordinate transformation methods

similar to Groth and Lokmanhekim [1] and the shadow overlap method of Walton

[ 21 .

1 1 1 . E . 1 SURFACE GEOMETRY

Shadow calculations first require that the building surfaces be

described geometrically. Surfaces are described by the coordinates of their

vertices in a three dimensional Cartesian coordinate system. This "global"

coordinate system has the X-axis pointing east, the Y-axis pointing north,

and the Z-axis pointing up. The azimuth angle ( xp) of a surface is the angle

from the north axis to the projection onto the X-Y plane of a normal to the

surface (clockwise positive). The surface tilt angle (<j>) is the angle

between the Z-axis and the normal to the surface. The vertices are recorded

in counter-clockwise sequence (as the surface is viewed from outside its

zone)

.

TARP input allows the user to specify a rotation of degrees of the

"building" coordinate system from the global coordinate system. The global

coordinates of zone origins are related to the building relative coordinates

by

xzo

= xbr * cos ^b “ Ybr * sin^b

Y zo

= xbr * sln^b + Ybr * cos ^b

zzo

= zbr

(E.l. la)

(E.l. lb)

(E.l.lc)

The user is also permitted to rotate a zone i\> z degrees relative to the

building coordinate system. Origins of zone surfaces are then given

realtive to the zone coordinate system. The global coordinates of the

surface origins are given by

so xzo + XA * zr cosi|>z - v * L zv sinij;.

so Yzo + x zr

* sini|>z +T yI * zr cos4> ;

so z zo + Zzr

(E.l. 2a)

(E.l. 2b)

(E.l. 2c)

46
A surface azimuth angle relative to the zone coordinate system ( ) is

converted to a global azimuth by

^

=

'I's + ^z + ’J'b (E.1.3)

The surface tilt angle ( <f>) is not changed by these rotations about the

Z-axis

.

The coordinates of the surface vertices are given in a coordinate

system in the plane of the surface relative to the second vertex as shown

for four surfaces in figure E.2. The X-axis of the surface coordinate

system is a horizontal line through the second vertex. The global

coordinates of the surface vertices are given by

X = Xgo - Xgr * cos^ - Ysr * sinij> * cos<f> (E.1.4a)

Y = Yso + Xsr * sinij/ - Ysr * cosi|> * cos<J> (E.1.4b)

Z = Z so + Ysr * sin<{> (E.1.4c)

Vertices in the global coordinate system can be transformed to the

coordinate system relative to a given surface by

X* = X - Xso (E. 1 .5a)

Y’ = Y - Yso (E. 1 .5b)

Z' = Z - Zso (E . 1 .5c)

X sr = -X’ * cost + Y' * sint (E.1.5d)

Y sr = -X* * sint * cost - Y' * cost * cost + Z* * sint (E.1.5e)

Zsr = X* * sint * sint + Y' * cost * sint + Z' * cost (E.1.6f)

III.E.2 SHADOW PROJECTION

All architectural forms are represented by plane polygons. This can

give good accuracy even for curved surfaces: a sphere can be approximated

by the 20 nodes of an icosohedron with only 3 percent error in the shadow

area cast by the sphere. Consider how a solid object, which is composed of

a set of enclosing plane polygons, casts a shadow. Figure E.3 shows a box

shaped structure on a horizontal surface. The structure consists of a top

(surface 1) and four vertical surfaces (2 and 3 visible to the observer and

4 and 5 not visible). The sun is positioned behind and to the right of the

structure and a shadow is cast onto the horizontal surface (the ground).

Surfaces 1, 4, and 5 are in sunlight; 2 and 3 are in shade. It is possible

to think of the structure's shadow as the combination of shadows cast by

surfaces 1, 2, 3, 4 and 5 or by 1 , 4 and 5, or by surfaces 2 and 3. This

last combination of shadow casting surfaces is the simplest. In the TARP

shadow algorithm every surface is considered to be one of the surfaces which

47
enclose a solid, and only those surfaces which are not sunlit at a given

hour are considered shadowing surfaces.

The expressions in eq (E.1.6f) are the direction cosines of the

surface:

CWi = sim{> * sin<(>

CW2 = cos^ * sin<J>

CW3 = cos<{>

(E.2.1a)

(E

.

2 . lb)

(E 2 . lc)

The cosine of the angle of incidence of the sun's rays on the surface are given by the dot product of surface and sun (B.3.3) direction cosines.

cos 9 = CSj * CWi + CS 2 * CW2 + CS 3 * CW3

If cos9 is less than zero, the sun is behind the surface.

(E.2.2)

A shadow is projected from the vertices of the shadowing surface (SS)

along the direction of the sun's rays to the plane of the shadow receiving

surface (RS). If any vertices of the SS are below the plane of the RS

(z < 0), a false shadow is cast as in figure E.3. The "submerged" portion of

the SS must be clipped off before projection. This is done by finding, through

linear interpolation, the points on the perimeter of the SS which intersect

the plane of the RS. These points become new vertices of the SS, which

together with the other positive vertices define a clipped SS which casts

only a real shadow.

A vertex located at (x, y, z) relative to the RS coordinate system

casts a shadow to a point in the plane of the RS given by

where

and

x' = x - z * a / cos

9

y' = y- z * b / cos

9

a = sinij> * CS^ - cos\|> * CS 2

(E.2.3a)

(E.2.3b)

b = -cosij^ * costjj * CSi - simj) * cost}) * CS 2 + sin<j) * CS 3

III.E.3 HOMOGENEOUS COORDINATES

Two-dimensional homogeneous coordinate techniques are used to determine

the vertices of shadow overlaps. In homogeneous coordinates, points and lines

are represented by a single form which allows simple vector operations between

those forms [3]. A point (X, Y) is represented by a three element vector

(x, y, w) where x = w*X, y

= w*Y, and w is any real number except zero. A

line is also represented by a three element vector (a, b, c). The directed

line (a, b, c) from point (x^, y^ , wj ) to point (x2 , y2 , w2

) is given by

(a, b, c) = (xj_, yi , wj) cross (x2 , y2 , w2

) (E.3.1)

48
The sequence in the cross product is a convention to determine sign. The

condition that a point (x, y, w) lie on a line (a, b, c) is that

(a, b, c) dot (x, y, w) = 0 (E.3.2)

Normalize the representation of a point by dividing by w. Then if

(a, b, c) dot (x/w, y/w, 1) > 0 (E.3.3)

the point is to the left of the line, and if it is less than zero, the point

is to the right of the line. The intercept (x, y, w) of line (a^ , b^ , c^)

and line (a2 , b2 , 02 ) is given by

Note that the use of homogeneous coordinates as outlined above provides

a consistant method and notation for defining points and lines, for

determining intercepts, and for determining whether a point lies to the

left, to the right, or on a line. Normalization provides the means for

transforming to and from homogeneous notation and Cartesian coordinates.

Thus, if (X, Y) is a Cartesian coordinate pair, its homogeneous coordinates

are (X, Y, 1). Similarly, the homogeneous coordinates (x, y, w) can be

transformed to the Cartesian point with coordinates (x/w, y/w).

III.E.4 OVERLAPPING SHADOWS

After transforming the shadows onto the plane of the receiving surface,

the basic job of the shadow algorithm is to determine the area of the

overlap between the polygons representing the shadows and the polygon

representing the receiving surface.

There is considerable simplification if only convex (no interior angle

> 180 ) polygons are considered. The overlap between two convex polygons is

another convex polygon. Coordinate and projection transformations of a convex polygon produce another convex polygon. Any non-convex polygon can

be constructed as a sum of convex ones.

The vertices which define the overlap between two convex polygons, A

and B, consist of:

1) the vertices of A enclosed by B,

2) the vertices of B enclosed by A,

3) and the intercepts of the sides of A with the sides of B.

In figure E.4a point a is the result of rule 1, point c is the result of

rule 2, and points b and d result from rule 3. The overlap of A and B is the

polygon a-b-c-d. Figure E.4b shows an overlap where all of the vertices of

A are enclosed by B. Figure E.4c shows an overlap defined only by the

intercepts of A and B. Figure E.4d shows a more complex overlap.

(x, y, w) = (aj, bi, c^) cross (a2 , b2 , C 2 > (E.3.4)

49
Coordinate transformation retains the order of the vertices of a polygon, while a projection reverses the order. The sequence of vertices of

the receiving polygons should be reversed so it and all shadow polygons will

have the same sequence.

A point is enclosed by a clockwise, convex polygon if it lies to the

right of all sides (or does not lie to the left of any side) of the polygon.

The intercept of two sides may not lie beyond the ends of either side.

These are "line segments" rather than "lines". It is possible to tell if

line segments A and B intercept within their end points by noting that the

ends of A must lie on both sides of B, and the ends of B must lie on both

sides of A as shown in figure E.5. This should be done before the intercept

is calculated.

Once the vertices are determined, they must be sorted into clockwise

order for the area to be computed. Given a plane polygon of n sequential

vertices (xls y^, (x2 , y2 ), •••, (*n , yn ), its area is given by [4]

A = ( Xl y2 + x2 y3 + ... +y^-iyn + V! - y^2 - y2 x3 - ... - y^)^

(E.4.1)

The area is positive if the vertices are counter-clockwise and negative if

they are clockwise.

If two shadows overlap the receiving surface, they may also overlap

each other as in figure E.6. The vertices of this overlap can be computed.

The areas of all overlaps can be computed. The total sunlit area can be

expressed as the sum of all polygon areas given a proper sign on each of the areas. The following convention was adopted:

receiving surface positive (A)

overlap between shadow and receiving negative (B & C)

overlap between two shadows positive (D)

and so on through multiple overlaps where the sign of the overlap area is

the product of the signs of the overlapping areas.

Partially transparent shadowing surfaces can also be modeled by giving

a transparency (x) to every shadowing polygon. Let x of the receiving polygon

be one. Then the x of every overlap of polygons i and j is the product of x^

and x j . The shaded area is then computed by summing A-^* (1 - Xj[) for all

overlap polygons.

It is easy to determine the sunlit area of a window once all the shadow

and overlap vertices on the wall have been computed. Consider wall 2 of

figure E.l. First the wall is considered a simple rectangle and the window

on it is ignored. The shadow overlapping is performed and the sunlit portion

of the gross wall area is computed. Then the window rectangle is overlapped

with the shadow to determine its sunlit area. The sunlit area of the window

is subtracted from the gross wall sunlit area to determine the net wall sunlit

50
area. During this calculation it is not necessary to recompute the shadows,

because they were precisely determined on the wall.

III.E.5 SOLAR GAINS

The total solar gain on any exterior surface is a combination of the

absorption of direct and diffuse solar radiation given by

QSO = a * (Ib* cos0 * S s / S + I 8 * F ss + I g

* Fsg ) (E.5.1)

where

a = solar absorptance of the surface

9 = angle of incidence of the sun's rays

S = area of the surface

S s = sunlit area

I b

= intensity of beam (direct) radiation

I s = intensity of sky diffuse radiation

Ig = intensity of ground reflected diffuse radiation

F S g = angle factor between the surface and the sky

Fgg = angle factor between the surface and the ground

For the surface of a building located on a featureless plain

F ss = (1 + cos<j>) / 2 (E.5.2a)

and

F sg “O'” cos<t>) / 2 (E.5.2b)

These values can be modified by the user.

For a window the absorptance, a, is divided into components ab (for beam

radiation) and aj (for diffuse radiation) as described in section D. A similar

expression describes the transmittance of solar radiation into the zone. In

its default mode, TARP assumes that all transmitted beam radiation is incident

on the floor. The floor absorbs a fraction of that radiation equal to the

floor inside solar absorptance. The unabsorbed portion of the beam radiation

is combined with the diffuse radiation and then evenly distributed over all

surfaces as described in section F.2. In the detailed mode, TARP computes the

beam radiation distribution on all surfaces.

REFERENCES

[1] Groth, C. C. , and Lokmanhekim, M. , "Shadow - A New Technique for the

Calculation of Shadow Shapes and Areas by Digital Computer," Second

Hawaii International Conference on System Sciences, (Honolulu, HI,

January 22-24, 1969).

[2] Walton, G. N., "The Application of Homogeneous Coordinates to Shadowing

Calculations", ASHRAE Transactions , Vol 84 (ASHRAE, 1978), Part I.

[3] Newman, M. W. , and Sproul, R. F., Principles of Interactive Computer

Graphics , (McGraw-Hill, 1973).

[4] Selby, S. M. , ed. , Standard Mathematical Tables , 22nd Edition,

(CRC Press, 1974) p 369.

51
52

Figure

I

II

,15.1

Shadows

on

an

L~

shaped

building
Sun’s rays Sun’s rays

Figure III.E.2 Shadow polygon clipping

53
I

Figure III.E.3 Shadow casting surfaces

54
55

Figure

III.E.4

Overlapping

convex

polygons
56

Figure

III.E.5

Intercepts

of

line

segments
Figure III.E.6 Multiple shadow overlaps

57
Ill .F INTERNAL HEAT GAINS

III.F.l SOURCES AND TYPES OF GAINS

Internal heat gains from lights, people, and equipment of various types

are usually significant elements in the zone thermal balance. TARP allows

the user to specify heat gains from equipment of various types, lights,

occupants, and baseboard heat controlled by outdoor temperature. The total

heat gain is made up of convective, radiant, and latent gains in various

proportions from each of these sources. Convective gains are instantaneous

additions of heat to the zone air. Radiant gains are distributed on the

surfaces of the zone, where they are first absorbed and then released back

into the room (and some fraction conducted through the surface) according to

the surface heat balances (section I). Latent gains must be handled by ventilation or air conditioning equipment. Recommended heat gains for many items

of equipment are given by ASHRAE [1]. These recommendations include the sen- sible (convective plus radiative) and latent proportions. Sensible gains from

equipment are predominately radiant. The user can specify the heat gains and

proportions appropriate for any type of equipment. The gains from lights,

people, and baseboard heat are slightly more complicated.

III. F. 1.1 LIGHTS

Radiant gains from lights must be handled differently from other

radiant gains for reasons described in F.2. It is necessary to divide the

total radiant gains into visible and thermal portions. The total electric

input to typical incandescent lights is converted into 10 percent visible

radiation, 80 percent thermal radiation and 10 pecent convective gain. The

electric input to typical flourescent lights is converted into 20 percent

visible radiation, 20 percent thermal radiation, and 60 percent convective

gain [2].

III.F.l. 2 PEOPLE

Heat is generated in the human body by oxidation at a rate called the

metabolic rate. This heat is dissipated from the body surface and

respiratory tract by a combination of radiation, convection, and

evaporation. The relative portions of sensible (radiation plus convection)

and latent (evaporation) heat from people is a complex function of the

metabolic rate and environmental conditions. TARP uses a polynomial

function to divide the total metabolic heat gain into sensible and latent

portions. That function is based upon a fit to data [3] at average adjusted

metabolic rates of 350, 400, 450, 500, 750, 850, 1000, and 1450 Btu/h each

at temperatures of 70, 75, 78, 80, and 82 F. Sensible gains of 0 at 96 F

and sensible gains equal to the metabolic rate at 30 F were assumed in order

to give reasonable values beyond the reported temperature range. The

original data for the polynomial was in English units, but the following

correlation is in metric units.

58
S “ 6.461927 + .946892*M + .0000255737*112

+ 7 . 139322*T - .0627909*T*M +.0000589172*T*M2

- . 198550*T2 + . 0009400 18*T 2*M - .00000149532*T2 *M2 (F.1.1)

where

M « metabolic rate (W)

T = air temperature (C)

S = sensible gain (W)

L = latent heat gain (W) [ = M - S ]

This function is compared to the original data points in figure F.l. The

radiant fraction of the sensible gain is determined by the user.

I I I. F.l. 3 BASEBOARD HEAT

Outdoor temperature controlled baseboard heat adds energy to the zone according a control profile as in figure F.2. At T a

= T£, the baseboard

heat gain is Q 2

. For T a > T 2 , there is no heat gain. For T a < Tj_, a maximum amount of energy, Q]_, is added to the zone. There is proportional

control between those temperatures:

Q = Q2 - (Q2 - Qi)*(T2 - Ta )/(T2 - T X ) (F.l. 2)

III.F.2 DISTRIBUTION OF RADIANT GAINS

It is useful to consider the distribution of short wavelength

(including visible) radiant energy separate from long wavelength (thermal)

radiant energy because many materials have different optical porperties at

the different wavelenghts. An extreme example is glass which is opaque to

the long wavelengths and transparent to the short. Properties of materials

vary across the entire spectrum of wavelengths. In TARP, all radiant

interactions are represented in terms of only two wavelengths: "short" and

"long". Short wavelength refers to the distribution given by a ~6000K black

body source such as the sun. Long wavelengths refer to radiation from ~300K

sources such as walls or people, there is negligible overlap between these

two distributions. Some sources, such as lights, must be considered as emitting both long and short wavelength radiation in proportions which

approximate their actual effects on room surfaces.

Long wavelength radiation from all internal sources, such as people,

lights, and equipment, is combined and then uniformly distributed over all

surfaces according to (H.2.5).

Some fraction of the beam solar radiation transmitted into the zone is

directly absorbed by the interior surfaces according to the solar distribution

algorithm (3.1.5) selected by the user. The beam radiation not directly

absorbed, plus the diffuse sky and ground-reflected radiation, plus the short

wavelength radiation from lights are combined and distributed over the surfaces

of the zone according to:

59
(F.2.1)

NS

OSIi - QS n

* ot / E S ± * (1 - Pi)

i=l

If all surfaces of the room are opaque, the radiation is distributed in

proportion to the area*absorptance product of each surface. For surfaces

which are transparent, = 1 - aj.- x^. That fraction of radiation

represented by ii is lost from the zone.

The transmittance and absorptance of transparent surfaces (windows) are calculated as in section D based on optical properties of the window

material layers. The total absorptance of the window is computed for the

interior shading device, the inside surface, and the outside surface for

diffuse solar radiation incident from outside the zone. Those absorptances

are used for short wavelength radiation incident from inside the zone. In

most cases, this should not cause significant error. When movable

insulation covers the window, the radiation which would have been

transmitted is absorbed at the outer surface of the window (thermally equal

to the inside surface of the insulation).

REFERENCES

[1] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), pp 26.26-26.28.

[2] Handbook of Air Conditioning System Design (Carrier Air Conditioning

Company, McGraw Hill, 1965), pp 1-99 to 1-100.

[3] Handbook of Air Conditioning System Design (Carrier Air Conditioning

Company, McGraw Hill, 1965), p 1-100, Table 48.

60
Published

data

at

61

Figure

III.F.l

Sensible

heat

gains

from

people
OUTDOOR TEMPERATURE

Figure III.F.2 Baseboard heat control profile

62
Ill .G NATURAL AIR MOVEMENTS

Most building surfaces contain openings, either large or small, which

permit the movement of air through them whenever there is a pressure

difference across the surface. Pressure differences arise from naturally

occurring wind and thermal forces. The following discussion of air

movements emphasizes the relationships to basic principles of fluid

mechanics.

Ill .G. 1 WIND FORCES

Wind pressures on surfaces are proportional to the velocity head of the

undisturbed air stream [1]. The wind pressure is thus calculated from

Bernoulli’s equation as

PW1

’ = 0.5 * D

a

* V

2 (G. 1.1)

The density of air is given by

Da

= 0.0034838*PB/Ta (G.1.2)

The wind speed is evaluated at the highest point of the surface using the

wind speed to height correlation (B.3.1).

Wind direction effects are dependent on the building's configuration

and its relationship to surrounding structures. No single correlation can truly model directional effects on all buildings or even the effects on a single building in different environments. The following correlation is a compromise derived by averaging several published correlations [2, 3]. It

accounts for the trends observed in wind pressure measurements.

Let Y = angle of incidence of wind on the surface (0<=Y<=180.)

If (Y<=90 . ) PWi = ( .75-1 .05*Y/90. ) * FWj.'

If (Y>=90. ) PWt = (0. 15*Y/90.-.45) * PW-j/ (G.1.3)

III.G.2 THERMAL FORCES

Temperature differences cause air density differences which cause bouyancy (or "stack”) effects. The magnitude of the force on a submerged

surface (all surfaces are submerged in air) is equal to the area times the

pressure at the centroid of the area. It is therefore necessary to know the

pressure at the centroids and the locations of those centroids. The effect

of air density on the pressure on any surface can be considered by a single

simple formula. The pressure at height Z1 is equal to the pressure at height

Z2 plus fluid density times the graviational constant (9.80 m/s^)tiraes ( Z2 - Zl). Figure G.l shows a surface separating two vertically adjacent zones.

The pressure difference (AP) across the surface is Pj - Pi. It is more useful

to know this AP in terms of zone pressures Pm and Pn:

63
Pj = pm + Dm * g

* (Zm - Zj )

Pi = Pn + °n * g

* (Zn " zi>

(G.2.1a)

(G.2. lb)

The sane formulae apply to a vertical surface as in figure G.2. They also

apply to an envelope surface where Pj is the pressure of the outside air

(figure G.3). Ambient air variables are substituted for the zone ra variables

Pj = Pa + Da * g

* (Za - Zj) (G.2.2)

Za is the reference height for air pressure measurements. Its location is

arbitrary. The zone reference heights, 7^ and Z^ are also arbitrary. All

are chosen for convenient or physically meaningful representation.

The pressure difference across surface i is

AP = Pj - Pi

- Pm - Pn + ’ Dn*g*(Zn-Zi)

= Pm

- Pn + PSi (G.2.3)

where

PSi - Dm*g*(Zm-Zj) - Dn*g*(zn-z1 )

is the "stack pressure" on surface i.

The height of the centroid of a triangle or rectangle is the average of

the heights of the vertices. Since the stack effect also occurs within the

thickness of a horizontal surface and since it is necessary to leave no building internal height unaccounted, Zi and Zj in figure G.l should both be

replaced by their average.

III. G.3 FLOW EQUATIONS

The flow through small openings in a surface is based on the orifice

equation

F=C*A*D*/2*AP/D (G.3. 1)

where A is the observed opening area and where the flow coefficient, C, is

a function of the Reynolds number and the ratio of the opening size to the

entire surface. When the opening is small, C equals 0.6 for a wide range of

Reynolds numbers [4]. TARP assumes this value of C. The user may modify C

by using an effective flow area (FA) which differs from the actual proportional

opening area. Experimental results indicate that flow through real surfaces

is a combination of orifice flow (Fa /AP ) and capillary flow ( F a AP ) with an exponent of about 0.65 [5]. In order to retain the concept of opening

area and provide a simple grouping of all other terras in (G.3.1), C is multiplied by /2 and D divided by /D to give:

64
F

± « 0.848 * FA£ * /d * (AP) Xi (G.3.2)

where FA-^ is the effective flow area of the openings in the surface, D is

the density of incoming air, and is the flow exponent. The pressure

difference for envelope surfaces is

AP = PWi + PSj_ - P n (G.3.3a)

and the AP for interzone surfaces is

AP - PSi + Pm

" Pn The surface flow equation becomes

F

a - 0.848 * FAa * /Dm

* (AP) X1 (AP > 0) or

F

i = -.848 * FA

t * /Dn

* (~AP) Xi (AP < 0)

For each zone there must be a mass balance

F s + I Fi = 0 (G.3.5)

where Fg is the net mass flow into the zone from the air handling system and

the F-i are the flows through openings in the zone envelope surfaces. These

mass balances form a system of non-linear algebraic equations which can be

solved for the zone pressures.

III.G.4 SOLUTION OF THE FLOW EQUATIONS

In some schemes for the evaluation of these simultaneous equations it

is important to know the following partial derivatives:

(G.3.3b)

(G.3.4a)

(G.3.4b)

3F, —i = -X, * F, / AP

3Pn

1 1 (G.4.1a)

3F

—i = Xj * Fj / AP

3Pm 1 1 (interzone surface) (G.4 . lb)

or

3F

3F

1 = 0

m

(envelope surface) (G.4. lc)

Note that it is not necessary to evaluate (AP)^ X^~^^ to compute these

derivatives. Note also that as AP approaches zero these derivatives cannot be

evaluated. This condition applies for large openings which cannot support a large pressure difference (except with very high flow rates). This is a potential source of trouble which must be considered.

65
These equations have been successfully solved by a modified Newton’s

method in all cases tested. A standard Newton's method was found to sometimes

give very slow convergence because of overcorrections during the iteration.

The modification reduces the Newton correction when this problem appears to occur.

REFERENCES

[1] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 22.3.

[2] Shaw, C. Y. and Tamura, G. T., "The Calculation of Air Infiltration

Rates Caused by Wind and Stack Action for Tall Buildings", ASHRAE

Transactions , Vol 83 (ASHRAE, 1977), part 2.

[3] Shaw, C. Y. , "A Method for Predicting Infiltration Rates for a Tall

Building Surrounded by Lower Structures of Uniform Height", ASHRAE

Transactions , Vol. 85 (ASHRAE, 1979), part 1.

[4] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 4.13, Fig 18.

[5] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 22.8.

66
F

1 = 0.848 * FAt * /D * (AP) Xi (G.3.2)

where FA-^ is the effective flow area of the openings in the surface, D is

the density of incoming air, and is the flow exponent. The pressure

difference for envelope surfaces is

AP = PWi + ?S ± - P n (G.3.3a)

and the AP for interzone surfaces is

AP = PSi + Pm- Pn The surface flow equation becomes

F

t = 0.848 * FA

t * /Dm

* (AP) Xi (AP > 0) or

= -.848 * FA

±

* /Dn

* (-AP) Xi (AP < 0)

For each zone there must be a mass balance

F s + Z Fi = 0 (G.3.5)

where Fs is the net mass flow into the zone from the air handling system and

the F-^ are the flows through openings in the zone envelope surfaces. These

mass balances form a system of non-linear algebraic equations which can be

solved for the zone pressures.

III.G.4 SOLUTION OF THE FLOW EQUATIONS

In some schemes for the evaluation of these simultaneous equations it

is important to know the following partial derivatives:

(G.3 ,3b)

(G.3 .4a)

(G.3. 4b)

3F, —1 = -Xj * F, / AP

8Pn

1 (G.4. la)

3F • —i = Xj * Fj / AP 1 1 (interzone surface) (G.4 . lb)

or

3F —1 = 0

3 pm

(envelope surface) (G.4. lc)

Note that it is not necessary to evaluate (AP)^-*-""^ to compute these

derivatives. Note also that as AP approaches zero these derivatives cannot be

evaluated. This condition applies for large openings which cannot support a large pressure difference (except with very high flow rates). This is a potential source of trouble which must be considered.

65
These equations have been successfully solved by a modified Newton's

method in all cases tested. A standard Newton's method was found to sometimes

give very slow convergence because of overcorrections during the iteration.

The modification reduces the Newton correction when this problem appears to occur.

REFERENCES

[1] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 22.3.

[2] Shaw, C. Y. and Tamura, G. T., "The Calculation of Air Infiltration

Rates Caused by Wind and Stack Action for Tall Buildings", ASHRAE

Transactions , Vol 83 (ASHRAE, 1977), part 2.

[3] Shaw, C. Y. , "A Method for Predicting Infiltration Rates for a Tall

Building Surrounded by Lower Structures of Uniform Height", ASHRAE

Transactions , Vol. 85 (ASHRAE, 1979), part 1.

[4] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 4.13, Fig 18.

[5] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 22.8.

66
ROOMm

Zm

zzzzzzzZzzzzzzzz

Pi

ROOM n

*Pn

Zj

Z|

z„

Figure III.G.l Pressure relationships for vertically adjacent zones

ROOM n

•Pn

I

I

Pm

IROOMm

Zm

Z|,Zj

Z„

Figure III.G.2 Pressure relationships for horizontally adjacent zones

ROOM n

Pi*^*pj

1

AMBIENT

P.

Zi,Z,

Z,

Figure III.G.3 Pressure relationships for envelope surfaces

67
Ill .H ROOM RADIANT INTERCHANGE

III.H.l DETAILED RADIANT INTERCHANGE

The surfaces of a room form an enclosure where they exchange energy

with the room air by convection and directly with each other by radiation.

The net radiant flux absorbed by surface i is given by

QI i = E F

ii *(T.j 4 - T^) + QLI

± + QS^ (H.1.1)

j

This expression is not usually substituted into the surface heat balance

equations since the T

4 terms would make the equations nonlinear and difficult

to solve. The radiation interchange factor, F-jj (which includes geometry and

radiocity factors) is difficult to calculate for rooms with arbitrary geometry.

Since each surface interacts with all other surfaces of the room (total of N

surfaces) there are N^ interactions to be considered. This requires a time

consuming solution technique. Quicker solutions are possible by linearizing

and assuming constant radiative and convective coefficients for all surfaces

[1]. Alternate methods are available which use mean radiant temperature

instead of the detailed radiant interchange. These methods allow efficient

treatment of the problem without assuming constant coefficients. They so significantly affect the solution time for problems with many surfaces that

they make simultaneous heat balances for many rooms feasible [2].

III.H.2 MRT NETWORK ALGORITHM

In the TARP radiant interchange between room surfaces is based on the mean radiant temperature network (MRTN) method of Joseph A. Carroll [3],

Surfaces radiatively interact with an MRT instead of directly with each

other.

QIi = HRi * (TRn

- T± ) (H.2.1)

o where HR^ is a radiative conductance. This gives N instead of N

interactions. The time required to solve the inside surface heat balances

is reduced from order N^ to order N. The effects of QLI^ and QSI^ are discussed below.

Since the MRT includes the effect of all surfaces, coupling the surface

to the MRT couples it to itself. The MRT network method includes a factor

F^, the "MRT view factor", which compensates for the self weight of surface

i in the MRT.

F ± = 1 / [1 - S^Fi / ( E Sj*Fj ) ] (H.2.2)

j

This expression can be solved iteratively.

The effects of surface eraittance are modeled by a surface resistance in

the radiative conductance.

68
HR (H.2.3) t = A*a*T3 /[l/F1 + ( l-e

± )/e±

]

Near room temperature the radiative couplings between surfaces vary by

about 1 percent per degree C variation in the mean radiant temperature. The

TARP allows a quick mode of calculating the radiant interchange which uses a constant T (= 296K = 23C) for evaluating HR^. A more accurate model uses

the following algorithm to account for the non-linearity of the detailed

equation.

1. Initialize all the HRi for a temperature of 27C:

HRi = 6.13 / [ 1/F ± + (l-e i )/e 1 ] (H.2.4a)

2. At each iteration first adjust all

HRi = (0.865 + 0.005*Ti> * HRi (H.2.4b)

3. Then evaluate

TRLn

= £ HRi*Ai*Ti / E HR^Ai (H.2.4c)

where the sura applies to all surfaces of room n

4. Then again adjust all

HRi = (0.865 + 0.005*TRLn ) * HRi (H.2.4d)

This method scales each HR^ by two factors nearly proportional to T** 3

, and

estimates the radiant fluxes to within about 1 percent for surfaces between 0C

and 50C.

In addition to the radiation from other surfaces, there is longwave

radiation from various energy sources in the room. The effect of these

radiant sources can be factored into the MRT and the radiant flux

automatically distributed over the room surfaces.

TRn = (£ HRi*Si*Ti + QLn ) / £ HR^Si (H.2.5)

Shortwave radiation, such as from the sun and lights, should not be handled

by this modification of the MRT because the room surfaces can have entirely

different emissivites for short and long wavelength radiation. Therefore,

H.2.1 should be written:

Qli = HRi *(TRn

- Ti> + QSIi (H.2.6)

The MRTN method of Carroll is slightly more accurate than the "balanced

mean radiant temperature" (MRTB) method of Walton. In addition it can easily handle multiple reflections and air emittance effects. However, when

MRTN is used in the TARP iterative heat balance, it is slower than MRTB . A

single MRTN iteration is slightly faster than MRTB, but more are required.

This is because MRTN updates TRn once per heat balance iteration of all

69
surfaces while MRTB updates TRn for each surface during the heat balance

iteration. The effect is the same as Jacobi versus Gauss-Seidel iteration [4]

.

The MRTN method was chosen over MRTB because of its accuracy and potential for

future expansion. It thus became important to find a method to reduce the

number of iterations to regain speed similar to MRTB. This method is described

in section L.

REFERENCES

[1] Sowell, E.F., and Walton, G.N. , "Efficient Computation of Zone Loads",

ASHRAE Transactions Vol 86 (1980), Part I. [2] Walton, G. N. , "A New Algorithm for Radiant Interchange in Room Loads

Calculations", ASHRAE Transactions Vol 86 (1980), Part II.

[3] Carroll, J. A., "An 'MRT Method' of Computing Radiant Energy Exchange

in Rooms", Proceedings of the 2nd Systems Simulation and Economics

Analysis Conference (1980).

[4] Conte, S. D., and de Boor, C., Elementary Numerical Analysis: An

Algorithmic Approach, (McGraw-Hill, 1972), pp 166-167.

70
III.

I

SURFACE OUTSIDE HEAT BALANCES

III.I.l SIMPLE SURFACE CONDUCTANCE

The convective plus radiative heat flux from a surface to the environment

may be represented by:

. CO + QO = HO * (TO - Ta ) + QSO (1. 1.1)

The surface coefficient, HO, accounts for both convection and longwave radiant

interchange. QSO is the absorbed shortwave radiant flux. A simple correlation for HO uses a polynomial expression [1] based on an ASHRAE relationship

[2] which relates the surface coefficient (W/m^K) to wind speed (m/s) and

surface roughness.

H

0 - *0 + Al*Va + Vva

2 0.1.2)

The values of the coefficients are determined by the surface roughness:

Roughness

Index

A0 Al a2 Example Material

1 11.58 5.894 0.0 Stucco

2 12.49 4.065 0.028 Brick, rough plaster

3 10.79 4.192 0.0 Concrete

4 8.23 4.00 -0.057 Clear pine

5 10.22 3.10 0.0 Smooth plaster

6 8.23 3.33 -0.036 Glass, paint on pine

Va is the reported wind speed unmodified for surface height or orientation.

This is reasonable for estimating design loads, but it needs improvement for

detailed simulations.

Rain causes the surface temperature to rapidly approach the water

temperature. TARP models this by setting HO to 1000. W/m^K and replacing Ta

in (1.1.1) by the wet bulb temperature.

III. I. 2 DETAILED SURFACE CONDUCTANCE

A detailed description of the outside surface coefficient must include

components of forced convection (Hf), natural convection (Hn ), and radiant

interchange (Hr

). These are affected by surface size, shape, location, orientation, and many features in the surrounding environment. All of these effects

are open to further study [3]. The following algorithms have been combined

(perhaps not justifiably) to allow the user to study the effects of certain

details in the outside conductance algorithm on relative zone conditions.

They show the kind of details that can be considered in TARP. They will be

progressively enhanced as better algorithms are developed.

71
III. I. 2.1 FORCED CONVECTION

Wind velocity tends to increase at increasing heights above the ground.

The relationship for this increase is described in B.3.

V

aZ = va

* b

* < z/zo> a 0.2.1)

Studies of the effect of surface shape on Hf give the following

correlation [4]

.

st * Pr2/3 = 0.86 * Re-1/2

Hf - 0.86*D *C*P "2 / 3 *(.25*V *C*v/A)!/ 2

I a p L cLZ where

St = Stanton number (Hf/DaCpVz ) Pr = Prandtl number (CpV /k)

R.e = Reynolds number ( ^V azA/Cv)

A = surface area

C = surface circumference

D a

= density of air

Cp = specific heat of air

V az = free stream wind velocity (at height of surface)

v = kinematic viscosity

For air Pr~2/3 = 1.245, C

p - 1004 J/Kg K , and D

a iTv 5 0.00472 Kg/s m

5/2

which combine to give

Hf = 2.537 * f~C]k * /~V^T (1.2.4)

The local value of Hf was found to be greatest near the edges of the surface

where the thermal boundary layer is thinnest. Therefore, to avoid computing

too large a value for small subsurfaces (windows and doors), TARP uses the same C/A for the subsurfaces as for the wall they are on.

There is as yet no definitive study giving an algorithm for wind direction

effects. Therefore, it was decided to follow the suggestion of Cole [5] and

multiply Hf by a wind direction modifier, Wf, of one half for the leeward

surfaces. Wf equals one for windward surfaces. In TARP leeward is defined

as greater than 100 degrees from normal incidence.

A simple surace roughness multiplier, Rf, was developed from the ASHRAE

graph of surface conductances [6]. At 0 mph all lines on this graph intercept

at about 1.9 Btu/hrft2 F. The correlations for the six roughnesses are nearly

linear. Therefore, a simple roughness multiplier was constructed by subtracting 1.9 from all values of H (at 25 mph) and dividing by the quantity [ H

(of roughness 6 at 25 mph) - 1.9 ] as summarized below.

( 1 . 2 . 2 )

(1.2.3)

72
Roughness H (at 25 mph) Rf

1 13.6 2.1

2 10.8 1.67

3 10.1 1.52

4 8.0 1.13

5 7.9 1.11

6 7.3 1.00

1 1 1. 1. 2. 2 NATURAL CONVECTION

There must be a natural convection component in the overall surface

coefficient to account for the convection which exists at zero wind velocity.

The same expressions are used for outside natural convection as for inside

convection (J.2).

Heat flow up: H

n

- 9.482* 3

>/| TO-Ta| /(7 .238- | cos 4> |

)

Heat flow down: H

n

= 1 ,810* 3 /|TO-Ta| / (1 .381+ 1 cos<j> | )

This component is assumed to be present at all wind speeds.

111. 1. 2. 3 RADIANT INTERCHANGE

There is radiant interchange between the surface and the sky, and between

the surface and the ground surface or adjacent structures. The effective

temperature of the ground surface is assumed to be equal to Ta (pending further

algorithm development). The effective temperature of any point in the sky

depends on the optical path length through the atmosphere. Section B.3 describes the algorithm which computes the effective sky temperature which would

be seen by a horizontal surface. For tilted surfaces the radiant interchange

coefficient (Hr ) must be divided into three parts: one (HS) to sky temperature,

one (HG) to ground surface temperature, and one (Ha) to air temperature.

Ha = a * e * F

gg * (1 - cos( <t>/2) )*(T0 4 - 1^

4 )/|T0 - Tj (1. 2. 6a)

HS = a * e * F * cos(<j>/2)* (TO 4 - T o 4 )/|TO - T | (1. 2. 6b)

HG = a * e * F * (TO4 - T

4

)/ | TO - T | (I. 2. 6c)

^ o o o Pending further research, TARP assumes the ground surface temperature, Tg,

equals the air temperature, T a

. This three component split of Hr must still

be validated or modified by experimental data. It produces proper results

for horizontal surfaces. It causes a vertical surface to radiate to an effective temperature of (.35 T s + .65 T a

) . TARP allows for radiant exchange

to surfaces of buidings to be represented by the user-specified values of R ss and F S g. Other building surfaces can be expected to have about the same temperature as the surface in question. Therefore, there is no net radiant transfer to it, and the view factor to all other building surfaces is represented

by 1 - Fgs - FS g.

(I. 2. 5a)

(I. 2. 5b)

73
III. I. 2.

4

COMBINED FACTORS

Since the expressions for Hn and Hr are used to evaluate TO, the most

recent value of TO is used in their calculation. The three factors combine

to give the following expression for combined convective and radiative flux.

CO + QO = (H f *Wf*Rf + Hn + HA)*(Ta-TO) + HS*(Tg-T0) + HG*(T„-T0) + QSO

(1.2.7)

I II. I. 3 BASIC HEAT BALANCES

A heat balance must exist at the outside surface-air interface. The

incoming conductive, convective, and radiative fluxes must sum to zero:

KO + CO + QO = 0 (1.3.1)

In contrast to the internal surface heat balance which treats all surfaces

simultaneously, the external thermal balance for each surface is performed

independent of all other surfaces. This implies that there is no direct

interaction between the individual surfaces.

The TARP includes four possible representations for the basic outside

surface heat balance. The first two depend on which of the optional surface

conductance algorithms the user selects. The simple outside surface conductance (1.1) which includes both the convective and thermal interchange between

the surface and the environment in a single coefficient, is represented by

the thermal network in figure 1.1. (1.3.1) can be expressed in terras of

(C.1.6) and (1.1.1) as

KOP t + Y0 *TI t - X0 *TOt + HO*(Ta - T0t ) + QSO = 0 (1.3.2)

This can be solved for the outside surface temperature.

T0 t = (KOP t + QSO + Y0*TI t + HO*Ta ) / (X0 + HO) (1.3.3)

The detailed outside surface conductance model (1.2) considers convection

and radiant interchange with the sky and with the ground as separate factors.

Its use in the outside thermal balance is shown in figure 1.2. In this case

(1.3.1) can be expanded according to (C.1.6) and (1.2.7) to give

KOP t + Y0 *TI t - X0*TO t + HA*(Ta - T0 t

)

+ HS*(T s - T0 t

) + HG*(T

g

- T0 t

) + QSO = 0 (1.3.4)

This can be solved for the outside surface temperature:

T0t = (KOP t + QSO + Y0*TIt + HA*Ta + HS*Ts + HG*T

g

)

/ (Xq + HA + HS + HG) (1.3.5)

74
The third and fourth representations occur when the outside surface has

been covered with a movable insulation. The insulation has a conductance of

UM. This case is represented by the thermal network in figure 1.3. The

insulation must be massless because it is not generally possible to perform a correct thermal balance at the juncture of two surfaces each modeled by CTF.

The equation for the thermal balance betwen the surface and the insulation is

KOPt + Y0 *TI t - X0 *TOt + UM*(TM-TOt ) + QSO = 0 (1.3.6)

which can be rewritten to solve for TO:

T0t = (KOP t + QSO +Y0*TI t + UM*TM) / (X0 + UM) (1.3.7)

Depending on whether or not the detailed or simple algorithm for surface

conductance is being used, there are two expresions for TM, the outside

temperature of the insulation. For the simple conductance:

TM = (QSM + UM*TOt + HO*Ta ) / (UM + HO) (1.3.8)

For the detailed conductance:

TM = (QSM + UM*TOt + HA*Ta + HS*Ts + HG*T

g

) / (UM + HA + HS + HG) (1.3.9)

In this case the values of HA, HS, and HG must be found by using an estimated

value of TM in place of TO in (1.2).

I I I. I. 4 HEAT BALANCE CASES

T0 t and TIt are related through the Yq CTF. However, TI t is also unknown.

While it is possible to combine the outside and inside surface heat balances

to compute T0 t and TI t simultaneously, the TARP uses a simpler procedure

where T0t is based on a previous value of TI. When Yq is small, as occurs in

well insulated or very massive surfaces, TIt can be replaced by TI t _i (which

is known from the previous hour's heat balance) without significantly effecting

the value of T0t

. When Yq is large, TO and TI can be so strongly coupled

that separate outside and inside heat balances do not work because the environment and zone temperatures have negligible influence on the heat balances.

The TARP uses the inside surface heat balance to couple T0t with TZ and TR,

These two temperatures are less strongly influenced by TO and allow a reasonable heat balance. On the first heat balance iteration, TZ and TR are the

values at time t-1. The user may optionally require that T0 t be recomputed

with every iteration of Tlf In this case TZ and TR have the values from the

previous iteration, and a true simultaneous solution is achieved. In most

conventional construction, recomputing T0 t does not significantly change the

computed zone loads and temperatures. The inside surface heat balance is

given by (J.3.3) which is repeated here.

TI t = (KIP t + QSI + HC*T Z + HR*TR + Y 0*TO)

/ (Zq + HC + HR) (1.4.1)

75
The surface heat balances can be combined in eight ways according to

conditions for calculation of the outside surface temperature. Compute

Fj_ = Y0 / (Zq + HI + HR)

F2 = UM / (UM + HO)

F 3 = UM / (UM + HA + HS + HG)

(I. 4. 2a)

(I. 4. 2b)

(I .4 .2c)

as needed for the following cases.

CASE 1: Yq small, simple conductance, no movable insulation. From equation

(1.3.3):

T0t = (KOP t + QSO + Yo^TIj--! + HO*Ta ) / (Xq + HO) (1.4.3)

CASE 2: Yq not small, simple conductance, no movable insulation. From (1.3.3)

and (1.4.1):

T0t = [KOPt + QSO + HO*Ta + F 1 *(KIPt + QSI + HI*TZ + HR*TR)

]

/ (Xq + HO - F!*Y0 ) (1.4.4)

CASE 3: YO small, detailed conductance, no movable insulation. From (1.3.4):

T0 t = (KOP t + QSO + Y Q*TI t _ 1 + HA*Ta + HS*Ts + HG*T

g

)

/ (X0 + HA + HS + HG) (1.4.5)

CASE 4: Yq not small, detailed conductance, no movable insulation. From

(1.3.4) and (1.4.1):

TOt = [KOP t + QSO + HA*Ta + HS*Ts + HG*T

g

+ F 1 *(KIPt + QSI + HI*TZ + HR*TR)

]

/ (Xq + HA + HS + HG - F 1 *Yq) (1.4.6)

CASE 5: Yq small, simple conductance, with movable insulation. From (1.3.7)

and (1.3.8):

T0 t = [KOP t + QSO + YQ*TI t _i + F 2 *(QSM + HO*TM)

]

/ (Xq + UM - F2 *UM) (1.4.7)

CASE 6: Yq not small, simple conductance, with movable insulation. From

(1.3.7), (1.3.8), and (1.4.1):

T0t = [KOPt + QSO + F2 *(QSM + HO*Ta ) + F 1 *(KIPt + QSI + HI*TZ + HR*TR)

]

/ (Xq + UM - F2 *UM - Fj_*Yq) (1.4.8)

76
CASE 7: Yq small, detailed conductance, with movable insulation. From (1.3.7)

and (1.3.9):

T0t - [KOP t + QSO + Yo*TIt_! + F3 *(QSM + HA*Ta + HS*Ts + HG*T

g

)]

/ (Xq + UM - F3 *UM) (I. A. 9)

CASE 8: Yq not small, detailed conductance, with movable insulation. From

(1.3.7), (1.3.9), and (1.4.1):

T0t = [KOPt + QSO + F 1 *(KIPt + QSI + HI*TZ + HR*TR)

+ F3 *(QSM + HA*Ta + HS*Tg + HG*T

g

)]

/ (Xq + UM - F3 *UM - F X *Y0 ) (1.4.10)

REFERENCES

[1] T. Kusuda, "NBSLD, the Computer Program for Heating and Cooling Loads in

Buildings," NBS Building Science Series 69, (July 1967), p 66a.

[2] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 23.2, Figure 1.

[3] R. J. Cole and N. S. Sturrock, "The Convective Heat Exhcange at the

External Surface of Buildings", Building and Environment, Vol 12 (1977)

pp 207-214.

[4] E. M. Sparrow, J. W. Ramsey, and E. A. Mass, "Effect of Finite Width

on Heat Transfer and Fluid Flow about an Inclined Rectangular Plate,"

Journal of Heat Transfer , Vol 101 (May 1979), p 204.

[5] R. J. Cole and N. S. Sturrock, "The Convective Heat Exchange at the

External Surface of Buildings", Building and Environment, Vol 12

(1977), p 212.

[6] ASHRAE Handbook - 1981 Fundamentals, (ASHRAE, 1981), p 23.2, Figure 1.

77
Figure III.I.l Thermal network for simple outside surface coefficient

Tl

Figure III. 1. 2 Thermal network for detailed outside surface coefficient

Figure III. I. 3 Thermal network for outside movable insulation

78
III.J SURFACE INSIDE HEAT BALANCES

III.J.l SIMPLE CONVECTION COEFFICIENT

The convective heat flux from the zone air to a surface is given by:

Cl = HC * (TI - TZ) (J.1.1)

The coefficient for natural convection heat transfer is based on data from

ASHRAE [1], The ASHRAE values are for combined convection and radiation, so

a radiative component of (1.02 times emissivity of 0.9) is subtracted from

the tabulated values which are then converted to metric. When warm air is

below a cool horizontal surface (or cool air above a warm surface), there is

more convective mixing than for air next to a veritcal surface. Conversely,

when cool air is below a warm surface (or warm air above a cool surface)

there is reduced convection.

HC (W/m2 K)

4.043

3.873

3.078

2.283

0.920

Type of

Heat Flow

enhanced

enhanced

normal

reduced

reduced

Surface Tilt

157.5 to 180 or 0 to 22.5 degrees

112.5 to 157.5 or 22.5 to 67.5 degrees

67.5 to 112.5 degrees (vertical surface)

22.5 to 67.5 or 112.5 to 157.5 degrees

0 to 22.5 or 157.5 to 180 degrees

When the air handling system is moving air through the zone, a single value

of 6.14 W/m2 K (= 2.0 - 1.02 * 0.90 Btu/h*ft2 *F) should be used for HI.

III.J. 2 DETAILED NATURAL CONVECTION COEFFICIENT

ASHRAE has the following expressions for natural convection from large

surfaces [2].

HC (W/m2 K)

1.52* 3 /|TZ-TI

1.31* 3 /| TZ-TI | 0.76* 3 /| TZ-TI

Direction of Heat Flow

Upward

Horizontal

Downward

(J.2. la)

(J.2. lb)

( J.2 . lc)

It may be noted that these expressions are inconsistant with the values

given for the simple algorithm.

To account for all surface tilts, the following expressions are used.

Heat flow horizontal or upward:

HC = 9.482 * 3 /| TZ-TI | / (7.238- | cos<|) | ) (J.2. 2a)

79
Heat flow horizontal or downward:

HC = 1.810 * 3 /| TZ-TI | / (1.382+|cos<|)|) (J.2.2b)

III.J.3 BASIC HEAT BALANCE

A heat balance must exist at the inside surface-air interface. The

incoming convective, radiative, and conductive fluxes must sum to zero:

Cli + QIj_ + KIt = 0.0 (J.3.1)

This equation can be expanded according to the descriptions of convection

(J.l and J.2), radiation (F.2.6), and conduction (C.1.4) and as shown in

figure J.l to give

HCj^CTZn-TIi) + HR^CTRn-TIi) + QSIi + KIPi + Y0> i*TOi - Zo^TIi = 0.0 (J.3.2)

Interior surface temperatures of envelope surfaces are computed by

rearranging (J.3.2):

TI± « (HC i *TZn + HRi^TRn + OSIi + KIPt + Y0> i*TOi)

/ (HCi + HRi + Z0ji ) (J.3.3)

The value of TO^ must have been previously calculated by the methods in

section 1.4.

The following two partial derivatives are useful in improving the rate

of convergence of the heat balance iterations.

3TI

t 3TZn

= HCi / (HCi + HRi + Zo.l) (J.3.4a)

3TIi

3TRn

= HRi / (HCi + HRi + Z0,i) (J.3.4b)

III.J.4 INTERNAL SURFACES

Internal masses and partitions separating identically conditioned zones can be treated as surfaces with equal inside and outside temperatures. In

that case Equation (J.3.2) may be rearranged to give:

TI ± = (HC i*TZn + HRi *TRn + QSIi + KIP i)

/ (HC± + HRt + Z0>1 - Y0 ,i>

The partial derivatives are

3TIi

3T Zn HCi / (HCi + HRi + Z

0j i Y0 ,i)

(J.4.1)

( J . 4 . 2 a

)

80
and

(J.4.2b) 3TX “ = HRi

1 (HC1 + HR1 + ZQ.i " Y0,i)

III.J.5 INTERZONE SURFACES

In the TARP interzone surfaces are permitted to have movable

insulation. This creates another set of basic heat balances at the

air-insulation and the insulation-surface interfaces (figure J.2). The

inside heat balances (with movable insulation) are

HCi *(TZn-TM1

) + HRi *(TRn-TM1 ) + UM1 *(TI1 ~TMi

) + QS!^ = 0.0 (J.5.1)

KIPt + Y0 ji *T0i - Zq + UMi *(TM1-TIi ) + QSIj. = 0.0 (J.5.2)

A similar set of equations exist for the far side of the surface (described

as surface j adjacent to zone m) . The far side heat balance (without

movable insulation) is

HCj *(TZm-TIj ) + HRj*(TRtn-TIj ) + OSIj + KIPj + Y0 j*TOj - ZQ

} j*TIj =0.0

(J.5.3)

The far side heat balances (with movable insulation) are

HCj * ( T Zjjf-TMj ) + HRj*(TRm-TMj) + UMj*(TIj-TMj ) + QSMj = 0.0 (J.5.4)

KIPj + Y

0) j*TOj - Zq

^ j *TIj + UMj *(TMj-TIj ) + QSIj =0.0 (J.5.5)

The following relationships apply because i and j refer to opposite sides of

the same surface:

TIi = TOj ; TOi = TIj ; KIPi = KOPj ; KOPi = KIPj ;

Zo.j - X0>1 (= X0 ); Y

0>j - Y0>1 (= Y0 ).

The placement of insulation on either side leads to four basic cases. Compute

F x = Y0

/ (Xq + HCj + HRj

)

F2 = UMi / (UMjl + HCj: + HRi)

F3 = UMj / (UMj + HCj + HRi)

F4 = Yq / (Xq + UMj - F3 *UMj

)

as needed for the cases below.

( J.5 .6a)

(J.5.6b)

(J.5.6c)

(J.5.6d)

CASE 1: No movable insulation on either side. From equations (J.3.2) and

(J.5.3):

81
Tit = [HCi^Zn + HRi*TRn + QSIi + KIPi +

F1 *(HCj*TZm + HRj^TR^j + QSIj + KIP-j ) ]

/ (Zq + HCi + HRt - F 1 *Y0 ) (J.5.7)

The partial derivatives are:

3TI, , , )Yf

- HCj / <HCi + HRi + ZO - W

and

(J. 5 .8a)

3TL ^

= HRjL / (HCi + HRi + Z0 Fi*Y0 ) (J.5.8b)

CASE 2: Movable insulation on near side only. From equations (J.5.1),

(J.5.2), and (J.5.3):

TIi = [KIPi + QSIi + F 1 *(HCj*TZm + HRj *TRm + QSIj + KIPj

)

+ F2 *(HC1 *TZn + HRi *TRn + QSMi) ]

/ (Zq + UMi- F^Yq - F 2 *UMi) (J.5.9a)

TMi = F 2 *[TIi + (HCi*!^ + HRi *TRn + QSM1 )/UMi ] (J.5.9b)

Since UMi should be small, the partial derivatives are:

3TX —i = HCi / (HCi + HRi + UMi)

n and

(J.5 . 10a)

3TI —i - HRi / (HCi + HRi + UMi)

9TR

n CASE 3: Movable insulation on far side only. From equations

(J.5.4), and (J.5. 5):

TIi = (HCi*TZn + HRi*TRn + KIPi + Q SI i

+ F 4*[KIPj + QSIj + F 3 *(HCj*TZm + HRj *TRm + QSMj ) ]

/ (Zq + HC± + HRi " F4*Y0)

(J.5. 10b)

(J.3.2)

,

}

(J.5. 11)

The partial derivatives are given by (J.5. 8a) and (J.5. 8b).

CASE 4: Movable insulation on both sides. QSIi and QSIj are both zero because the insulation is assumed opaque. From equations (J.5.1), (J.5.2),

(J.5.4) and (J.5. 5):

82
TIi - {KIPi + F4

* [KIPj + F 3 *(HCj*TZm + HRj*TRm + QSllj ) ] + F 2*(HC i*TZn + HR1*TRn + QSM^)

}

/ (Z0 + UMj - F 4*Y0 - F 2*UMi

) ( J.5 . 12a)

TMj. = F2 *[TI1 + (HC^TZn + HRi *TRn + QSMjO/UMjJ (J.5. 12b)

The partial derivatives are given by (J.5. 10a) and (J.5. 10b).

REFERENCES

[1] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 23.12, Table 1.

[2] ASHRAE Handbook - 1981 Fundamentals (ASHRAE, 1981), p 2.12, Table 5.

83
TZ

Figure III.J.l Inside surface thermal network

Figure III.J.2 Inside movable insulation thermal network

84
Ill .K ZONE AIR HEAT BALANCE

The calculation of the zone air temperature is based on a heat balance

on the zone air. The convective gains from the room surfaces and internal

sources plus the sensible gain from incoming air plus the energy added by

the air handling system must equal zero.

CE + Z HC i *S i *(T 1 - TZ) + I Fj*C

p*(TSj - TZ) + L = 0 (K.0.1)

The summations apply to all surfaces which are part of the zone.

The system performance model (III.K.l) may be used with the detailed

natural air movement model (III.G) if the supply and exhaust air flows of

every zone are equal (that is, Fs in equation (G.3.5) must be zero). The

simple air movement models (III.K.2 through III.K.5) may not be used

siraulatneously with the detailed air movement model.

III.K.l SYSTEM PERFORMANCE MODEL

The energy from the system is based on the user defined control profile

which approximates the performance of the actual system. The control

profile consists of a set of control points which define the heating or cooling capacity of the system as a function of the control temperature as in figure K.l. Control range p is between temperatures T

p

and Tp+j . The

control profile is linear between the control points. Simple

proportionality gives

L - Lp + (T - T

p

)*(Lp+1 - L

p

)/(Tp+1 - T

p

) (K.1.1)

This can be rearranged to

L = LT * T + LC (K.l. 2a)

where

LT = (Lp+1 - L

p

)/(Tp+1 - T

p

) and LC = L

p - LT*Tp

(K.l. 2b)

The control temperature consists of both the air and the mean radiant

temperatures according to the formula

T = 0 * TR + (1 - 0) * TZ (K.l. 3)

where 0 is the user defined radiant fraction. When this expression is

substituted into the zone air heat balance, it gives the following

expression for computing the zone air temperature

TZ = [ CE + SUM HC i *S 1 *T i + SUM Fj*C

p

*TS-j + g*LT*TR + LC]

/ [ SUM HC i *S i + SUM Fj *C

p

- (1 - f?)*LT ] (K.l. 4)

85
III.K.2 SIMPLE INFILTRATION MODEL

An equation for the mass flow of infiltration air can be developed from

measured values in similar structures [1]. The TARP assumes a correlation

of the form

FI - (A0 + Al *|TZ - T

a | + A2 *V + A3 *V2

) * D

a (K.2.1)

This correlation accounts for stack effects in the temperature difference

terra and wind effects in the two velocity terms. Equation (K.1.4)

simplifies to

TZ = [ CE + I + FI*C

p

*Ta + f?*LT*TR + LC]

/ I HC-^Sjl + FI*C

p - (1 - 0)*LT] (K.2.2)

III.K.3 ZONE VENTILATION MODEL

The heating effect of ventilation air is given by

LV = FV * C

p

* (T a - TZ) (K.3.1)

TARP ventilation operates by creation of a ventilation profile similar to

the zone temperature control profile. A new ventilation profile is created

every hour as the ambient temperature changes. No point on the ventilation

profile is permitted to overlap the heating or cooling portions of the

control profile. This assumes the same fan is used for ventilation and

heating or at least that two separate fans are managed by the same controller.

Several types of ventilation profile are possible. Figure K.2 shows a profile when the ambient temperature (T a ) is higher than the desired temperature (TV). No cooling occurs until the zone air temperature exceeds TA.

When Ta is less than TV, there is a cooling capacity at TV. A small

ramp between TV and TV+0.01 is created for stability of the heat balance

iterations as in figure K.3.

When there is a heating control profile and the desired ventilation

temperature is below the point which initiates heating, the TARP revises TV

to above that point as in figure K.4.

When there is a cooling control profile, the ventilation profile is not

permitted to extend upward into the cooling temperature range (figure K.5).

III.K.4 TWO ZONE MIXING MODEL

A simple model can be developed to describe the forced mixing of air

between two zones with simple controls. A mass flow of up to FM will exist

from zone ra to zone n when TZm

- TZn > TD. It is assumed that an equal

return flow exists from zone n to m. Since the two zone air temperatures

86
are intimately coupled, it is best to seek an exact simultaneous solution.

The description of that solution is simplified by rearranging equation

(K.2.2) to

Bn

* TZn - ^ (K.4.1)

where

An

- CE n + E HCi^TIi + FI n*Cpn

*Ta + 3*LTn*TRn + LCn

B n

= E HCi + FI n*C pn - (1 - B)*LT n

A similar equation exists for zone m. The effect of an interzone air flow

is given by the two equations

(Bn + MM)*TZn

« An + MM*TZm (K.4 . 2a)

(Bm + MM)*TZm

= Am + MM*TZn

where MM = FM * C

p

.

(K.4.2b)

There are three possible conditions for the interzone air flow. First

is that TZjh - TZn < TD and therefore MM = 0. Second

flow rate still leaves T - TZn > TD. Simultaneous

(K.4. 2a) and (K.4. 2b) gives

is that the maximum

solution of equations

TZn

= (An + F^Ajjj) / (Bn + MM - F^MM) (K.4. 3a)

TZpj = (Apj + MM*TZn ) / (Bm + MM)

where Fj = MM / (Bm + MM)

(K.4. 3b)

The third case occurs when no flow gives TZq - TZn > TD and full flow would

cause TZm- TZn < TD. It is then necessary to solve for the partial flow

during the hour which will cause TZtn - TZn = TD. This gives

MM = [Am- Bm

* ( TD + An

/Bn )l / [TD*Bm/Bn + TD] (K.4. 4a)

TZn = (An + MM*TD) / Bn

(K.4. 4b)

TZm

= TZn + TD

III.K.5 WHOLE HOUSE FAN MODEL

(K. 4 ,4c)

A model similar to the zone mixing model (III. K.4) can be developed

which describes the effects of a fan moving air only from zone n to zone m with movement of air to and from ambient completing the mass balance. Such

a case is the exhaust of house air into its attic. A simple control scheme

allows a mass flow of up to FF whenever TZn > TD > Ta

. The effect of the

air flow on the zone energy balances is given by

87
(Bn + MF)*TZn - An + MF*TA (K.5.1a)

and

(Bm + MF)*TZn = ^ + MF*TZn (K.5.1b)

where

MF = FF * C

p

similar to equations (K.4.2).

There are three possible conditions for the interzone air flow. First

is that TD < T a or TZn < TD which gives MF=0. Second is that the maximum

flow leaves TZjB > TD. Direct solution of equations la and lb gives

T^ = < An + MF*TA) / (Bn + MF) (K.5.2a)

TZn, = + MF*TZn) / (Bm + MF) (K.5.2b)

The third case occurs when no flow gives TZn ^ TD anc^ full flow would cause TZn < TD. It is then necessary to solve for the partial flow during the

hour which causes TZn = TD.

MF = (An" Bn*TD) / (TD-Ta ) (K.5.3a)

TZn

= TD (K. 5.3b)

TZm = (An + MF*TZn ) / (Bm + MF) (K.5.3c)

REFERENCES

[1] Coblenz, C. W. and Achenbach, P. R. , "Field Measurements of Ten

Electrically-Heated Houses", ASHRAE Transactions (ASHRAE, 1963),

pp 358-365.

88
Figure III.K.l Zone temperature control profile

89
Figure III.K.2 Ventilation control profile: Ta higher than TV

Figure III.K.3 Ventilation control profile: Ta higher than TV

90
Figure III.K.5 Ventilation and cooling control profiles

91
Ill .L HEAT BALANCE CONVERGENCE

In any zone the air temperature, mean radiant temperature, and the

surface temperatures are intimately related. A change in any one will cause changes in all of the others. Those secondary changes should be predictable.

It was observed that, with the zone air temperature held nearly

constant by a large heating capacity, there was a regular pattern in

successive radiant temperature values during the heat balance iterations for

a given hour.

(TR^+2 ~ TR^+i) / (TR^+j - TR^) = constant (L.1.1)

where

k is the iteration number.

The value of that constant is

E (HRi * S

i * mi ) / E (HRi * S

±

) (L.1.2)

9TRn with i for all surfaces of the zone. The partial derivatives are described

in section J.

The following logic led to a method for improved convergence for fixed

or floating zone air temperature.

(1) Do the first iteration in the normal manner.

(2) During the second iteration a new TR is computed (H.2.5). It is ATRO

greater (negative value means less) than the first iteration TR.

(3) By itself, this would cause an increase of cx*ATRq in the value of TR in

the next iteration, a is the constant given by (L.1.2).

(4) It also causes an increase in the zone air temperature due to increased

convective gain. Assuming that the average change in surface temperatures

equals the change in radiant temperature

AT Zq = ATR0

* E HC i *S i

/

[E HC-j^Si + E Fj *Cp - (1-3)*LT ] (L.1.3)

(5) Increasing TZ will then increase the TI because of convective gain.

Again assuming the change in surface temperatures is about equal to the

change in radiant temperature

ATR

X = ATZq * E HC

i *S i * 9TI

i / E HC^S1 8TZn

92
= ATRq * E IIC i *S i * aTI i / 8TZn

[Z HCi^Si + E Fj*Cp - (l-e)LT ]

= Y

* A TR0 (L.1.4)

(6) Combine the changes in radiant temperature in (3) and (5) to give the

total change in TR for one iteration.

ATR2 = (ot + y) * ATRq (L.1.5)

The total change in TR over several iterations is

ATR = ATRq * [ 1 + (oc+y) + (cx+y)^ + (o+y)^ + ••• ]

= ATRq / (1 - a - y) (L.1.6)

(7) Similarly, the total change in zone air temperature is

given by

ATZ = [ATRq * E HCi *Si

) * [ (crHy) + (cc+y)

2 + ... ] /

[E HCi*S1 + E Fj *C

p - (1-S)*LT ] (L.1.7)

(8) The current estimates of TR and TZ are therefore increased by ATR and

ATZ, respectively. Then the surface temperatures and resulting new zone air

temperature are calculated in the normal manner. For the convergence test

the new TZ is compared to the predicted value of TZ instead of the previous

iteration value. If the two temperatures (or associated heating/cooling

load) are sufficiently close, the solution has converged.

On the first iteration of a given hour, many parameters may have

changed from the previous hour. These parameters include the delayed

conductive gains and radiant and scheduled loads. These are additional

factors which must be included in the convergence algorithm. So far that

has only been partially successful.

Sample results of the convergence improvement algorithm for a single

zone showed a reduction from an average of 7.6 to 2.3 iterations per hour

in the floating temperature mode and from 5.4 to 2.1 iterations per hour

in the fixed temperature mode.

93
IV. INPUT

IV. A OVERVIEW

It is intended that the TARP input deck be an on-line file which is

created and modified by a text editing system. It can also be a deck of

punched cards. There is a simple, consistant input structure. The input is

based on a keyword system (keyword = value) to produce a free-format,

self-descriptive input. In some ways it is similar to NAMELIST input which

is a feature of some versions of FORTRAN. The keywords have been kept short

(usually less than 5 letters) to reduce the amount of typing that must be

done. The keyword system is organized in a logical hierarchy which groups

related concepts and data. Defaulting is used extensively. This applies to

individual values and to groups of values representing entire elements of

building operation or description. Some groups of often used data can be

named and then used many times by referring to the name.

This input method was chosen from the following four basic

alternatives.

1. Columns or lines of numbers for simple fixed or free format FORTRAN

reading.

2. A free-format, self-descriptive language such as used by BLAST or DOE.

3. A prompting, fully interactive system.

4. A graphic, interactive system.

Method 4 could not be used because of its equipment and programming

time requirements. The complexity of describing building geometry may make

it the logical choice of input for a user-oriented loads program. Simple

FORTRAN reads (method 1) are easy to program and produce a small, fast

computer program. However, it is difficult to incorporate simple defaulting

and optional input. It is also difficult to understand and correct the

input without running it through the input processor. Self-descriptive

input (method 2) can be criticised as taking too long to prepare and

presenting more opportunites for error because of the additional words used

to describe the numbers. But defaulting is easy to incorporate, and the user can understand the input deck directly after only a little practice.

Prompting, interactive input (method 3) can be of great help to the

beginning user. The large number of values involved in a complete building

description can make full prompting tedious. The prompting system must

allow for changing the input after it has been used for a loads calculation.

This method may be worth the programming time it would take to implement.

IV .B INPUT LANGUAGE SYNTAX

Several goals were assisted by the development of a simple, consistant

input structure. That input structure may be considered a language and the

relationships of the components of a language are called "syntax". The

following pages describe the input syntax in two ways. First is the

Backus-Naur Form (BNF) which is traditional to computer science. Second is

94
an English description of the same features for those who are unfamiliar

with BNF.

IV.B.l BNF DESCRIPTION

1. < INPUT DECK> <SECTION> {<SECTION>}

2. <SECTION> <SECTION NAME> [ <KEY> {<KEY>} ]

3. <KEY> ::= <KEY NAME> ( <SUBKEY> {<SUBKEY>})

4. <SUBKEY> < SUBKEY NAME> / | < SUBKEY NAME> = <DATA> {, <DATA> } /

5. <DATA> ::= <NAME> | <INTEGER> | <REAL> | <DATE> | <DESCRIPTION>

6. <NAME> <CHAR> {<CHAR> | <NULL>}

7. <UNS INTEGER> : := <DIGIT> {<DIGIT> | <NULL>}

8. <INTEGER> ::= <UNS INTEGER> | - <UNS INTEGER>

9. <REAL> <INTEGER> | <INTEGER> . | . <UNS INTEGER> | <INTEGER> . <UNS INTEGER> | <INTEGER> . <UNS INTEGER> E <INTEGER>

10. <DATE> ::= <M0NTH> <UNS INTEGER> | <UNS INTEGER> <M0NTH>

11. <DESCRIPTION> ’ {<CHAR> | <SYMB0L> | <NULL>> *

12. <CHAR> ::= <LETTER> | <DIGIT> | - | .

13. <SYMB0L> :;- / | - | , | ( | ) | $ | * | [ | ]

14. <NULL> <BLANK> | +

15. <LETTER> : A | B | ... | Y | Z

16. <DIGIT> ::= 0 | 1 | ... | 8 | 9

17. <M0NTH> ::= JAN | FEB | ... | NOV | DEC

18. <C0MMENT> : := $ | ) | ] {<CHAR> | <SYMB0L> | <NULL>} END-OF-LINE

IV. B. 2 ENGLISH DESCRIPTION

1. The TARP input deck consists of several sections. There are presently

four sections: PROJECT, LIBRARY, BUILDING, and ZONE.

2. Each section consists of a section name and one or more keys enclosed in

brackets

.

95
3. A key is a key name and one or more subkeys enclosed in parentheses.

4. A subkey consists of a subkey name or a subkey name, an equals sign, one

or more data values, and a terminating slash. When only a subkey name is

called for, entry of that name enables some option. Most subkeys introduce

one or more elements of data. Multiple data values are separated by commas.

5. There are five different data types. Only descriptions may be longer

than 10 non-null characters.

6. A name consists of characters.

7. An unsigned integer consists of digits.

8. An integer is an unsigned integer for positive values or an unsigned

integer preceeded by a minus sign for negative values.

9. There are five distinct representations for real numbers. Note that a decimal point is not necessary and that exponential notation is possible.

10. Dates consist of a month name and a day number.

11. A description is a string of characters and other symbols enclosed in

apostrophes. It may be up to 100 characters long, including nulls and

symbols. An apostrophe may not occur within the string.

12. "Characters" are letters, digits, hyphen (minus), and period.

13. There are several generally recognized symbols in FORTRAN 77. These

symbols are used as punctuation in the input language. Most systems also

provide other symbols which may be used in those language elements which use "symbols" such as ", %, @, etc.

14. The blank and plus sign are nulls. They are ignored by the input

reader. Therefore, elements of the language may be separated by blanks to

improve readability. The plus sign does not affect the value or character

count of a number.

15. Letters are the 26 letters of the alphabet.

16. Digits are the 10 numerals.

17. Months are first three letter abbreviations of the 12 months.

18. Comments begin with a dollar sign or at the end of a key or end of a section and continue to the end of the line. They may be included on lines

with input or on separate lines.

96
Other features:

Successive identical subkey values " . . .

, <DATA> , <DATA> , <DATA> , . .

. " may

be replaced by " . . . ,<UNSIGNED INTEGER>*<DATA> , . .

. " .

A line of input may be up to 80 characters long. Input features may be

continued on succeeding lines. Punctuation determines the end of all input

features except comments, which terminate at the end of the line.

The final subkey slash before ending a section may be dropped. That

is, "/ )" may be replaced by ")" . The slash may be considered a separator

rather than a terminator.

IV. B .3 ERROR PROCESSING

The TARP handles incorrect input by reporting the error and then

skipping to the next readable input. It makes no attempt to correct the

input error. It is more important for the user to correctly type

punctuation than names or values. The approximate order of importance of

punctuation is: '$[]()/=,. Similarly, section names are more

important than key names which are more important than subkey names which

are more important than data. For example, an incorrect data value would

cause the program to not process only that value, but an incorrect subkey

name causes the program to skip all values following it (because the program

cannot know to which subkey they apply) and go to the next subkey, which

will be after the next "/"• Similarly, an incorrect key name causes the

program to skip the entire key including all its subkeys. The key name will

have to be corrected and another run made to find any errors in the subkeys.

The punctuation is critical because it determines where the input skipping

stops. The program must then find a recognizable name or another skip will

occur. Thus the brackets and parentheses are more important than slashes

because an error in them causes more skipped input. The apostrophe and

dollar sign are most critical because descriptions and comments can include

punctuation symbols which could totally confuse the input reader. Although

this process sounds complex, the consistancy of the syntax makes it very

easy for the user to check punctuation before submitting the input to the

computer. The input deck can be debugged in a small number of runs because

the entire deck will be processed during every run instead of quitting at

the first error.

97
IV.

INPUT DETAILS

The input must be made meaningful by defining the "vocabulary" of names

and data which fill in the syntax. Every section, key, and subkey is

discussed below. Each subkey description is headed by a line containing six

elements

1. The section, key, and subkey numbers (e.g. 2.4.1). These serve in

cross-referencing to other input. Several related subkeys may be grouped

under one subkey number.

2. The subkey name, "", data types. The data types mean: n * name, r = real, i = integer, d = date, desc ° description.

3. The default. Dimensional values are in metric units. Immediately below

is the value in English units.

4. The units. means dimensionless. English units are given below the

metric units.

5. The status, "reqd" means a value must be given, "opt" means a value is

optional; otherwise the default will be used, "cond" means conditional.

One of several values must be chosen or a value must be chosen if some other

input has been set.

6. The permitted range of the data value.

IV.C.l PROJECT SECTION

1. PROJECT [ Project Section.

This section is required. It also must be first. It creates the data

that relates to the entire project: weather data and various

input/output controls.

1.1 RC ( Run control parameters.

This key is optional, but if it is used it must be first.

1.1.1 DESC = 'desc' blank - opt

This description will appear on the loads reports.

1.1.2 SYNTAX no - opt

This subkey causes the input processor to do only a "syntax check".

Syntax and typing errors are listed. This avoids many of the calculations that are normally done, so that the processor can run quicker

and with less core, but it does not produce a simulation input file

(SINPFL) for the loads program.

1.1.3 DEM no - opt - This subkey will enable the printing of more detailed error messages.

It may be useful in the early debug phase or for the inexperienced

user.

98
1.1.4 2SPC no - opt

This will cause double spacing. A blank line will be inserted between

each user input line which is echoed in the input processor report.

This enhances readability.

1.1.5 XREF no - opt

The input processor will report the sequence number of every major

input element. This will aid in locating the input that may be causing

errors in the loads calculation. See V.A.2.3 for further details. 1.1.6

OLDW no - opt

This subkey may be used if a environment file (ENVTFL) has been prepared

and saved in a previous run. It causes keys 1.3, 1.4, 1.5, and 1.6 to

be skipped, saving the time that would be spent preparing a new

identical environment file.

1.1.7

ENGLISH yes - opt

METRIC

UIN = n UOUT « n These subkeys provide different ways of specifying the units used for

the input and output of numbers. See the Table of Units. ENGLISH

means the input and output are in English units. METRIC means they are

in metric units. Alternatively, the input units can can be either

UIN=ENGLISH or UIN=METRIC and the outputs either UOUT=ENGLISH or UOUT=METRIC.

1.2 RPT ( Set reports flags.

1.2

1

RNOS = i,i,... 9 - opt

1 = dump PROJECT and LIBRARY data

2 = dump DDY and WTAP data

3 = dump CTF calculations

4 = dump glass calculations

5 = dump DSS data

6 = dump ZONE data

7 = dump cross reference values

8 = dump SINPFL as read by loads program

9 = report description of zone

13 = report sunlit areas

14 = report shadowing combinations

15 = dump shadow calculation controls

16 = dump shadow calculations

20 = dumps 21-24 during warm-up period

21 = dump primary zone data

22 = dump constant load components

23 = dump variables

24 = dump temperature and flux histories

25 = dumps 21-24 on WED nearest 21st of month

99
1.3 LOC ( Location.

1.3.1 DESC - 'desc' blank opt —

1.3.2 LATD - r 40 . degrees opt -90.<»r<»90.

The latitude of the site. Degrees north is positive.

1.3.3 LONG - r 90 . degrees opt -180.<-r<-180.

The longitude of the site. Degrees west is positive.

1.3.4 TZ » r 6. — cond O.Or<“24.

The time zone number of the site. The United States eastern time zone

is 5 and the Pacific time zone is 8.

1.3.5 ALT = r 0 . - opt - The altitude of the site. Not used by the program.

1.3.6 TER = i 2 - opt l<-i<-3

Type of terrain is used only with HO » 2 (3.1.6).

Type numbers are as described in III.B.4.

1.4 GRND ( Ground parameters.

1.4.1 GRT = r,r,...<12> 12*12.78 C opt

12*55. F

Ground temperatures for the 12 months starting with January. They are used only with other side coefficients (4.3).

1.4.2 MWT = r,r,...<12> 12*12.78 C opt

12*55. F

Make-up water temperatures for the 12 months starting with January.

Not yet used by the program.

1.5 WTAP ( Weather tape parameters.

1.5.1 DESC = 'desc* blank - opt

1.5.2 SKIP = i 0 - opt 0<=i<=365

Skip this number of days on the weather tape before starting to process

days for the environment file (ENVTFL).

1.5.3 DAYS = i 365 opt l<-i

Process this number of days from the weather tape (WTHRTP) to the

environment file (ENVTFL).

1.6 DDY ( Design day description.

1.6.1 DESC = ’desc' blank - opt

100
1 . 6.2 HIGH = r 35.0

95.0

High temperature for the design day

1.6.3 LOW = r 22.78

73.0

Low temperature for the day.

1.6.4 WB = r

opt

opt

opt

L0W<=HIGH

25.56 C

78.0 F

Wet bulb temperature at the time of the day's high temperature. This

temperature must be psychrometrically possible.

1.6.5

DATE = d 21JUL - opt

The date determines the solar position and length of daylight,

1.6.6 PRES = r 100000. Pa opt

401.5 in H20

The absolute barometric pressure at the site is used in the

psychrometric calculations.

1.6.7 WS = r 3.353 m/s opt - 660. ft/min

The default wind speed is 7.5 miles per hour. (1 mph = 88 ft/min)

1.6.8 DIR = r 270. degrees opt -360.<=r<=360.

Wind direction: north = 0 degrees, clockwise is positive. The default

wind is from the west.

1.6.9 CLR = r 1.0 - opt 0.<=r

The total solar radiation on a horizontal surface is the ASHRAE clear

sky amount times this clearness number. The proportion of beam and

diffuse radiation changes according to a correlation function.

1.6.10 RAIN no - opt - RAIN causes the outside temperatures of surfaces exposed to ambient to

be set to the wet bulb temperature. This models the cooling effect of

rain on the building.

1.6.11

SNOW no - opt - SNOW causes the ground reflectance to be increased from its default of

0.2 to 0.7. This gives a much higher diffuse solar gain to the zones.

1.6.12

SUN ... MON - opt

The day of the week determines which day-schedules (2.2) and control

day-schedules (2.6) are used. Allowable day names are: SUN, MON, TUE,

WED, THU, FRI, SAT, HOL, SP1 , SP2 , SP3 , SP4

.

101
IV. C.

LIBRARY SECTION

2. LIBRARY [ Library Section.

The library simplifies input by grouping relatively large amounts of

data by name. That name can be referenced later in the input process

instead of again specifying all the data. This produces economies when

items are used several times. There are seven types of library data:

day-schedules (DS), week-schedules (WS) , materials (MATL) , constructs

(CONS), control profiles (CPFL), control day-schedules (CDS), and

control week-schedules (CWS).

LIB ( Library control parameters.

NAME = n blank - opt — Not yet used.

NDS = i 16 - opt - NWS = i 16 - opt - NMATL = i 16 - opt - NCONS « i 16 - opt - NCPFL = i 16 - opt - NCDS = i 16 - opt - NCWS i 16 - opt - These subkeys control the number of library elements which can be

defined. Library names are stored in an array which is 256 elements

long. The total number of named library elements cannot exceed 256.

The sum of these subkeys (including those left to default) cannot

exceed 256.

i ALL no - opt - DS no — opt - WS no - opt - MATL no - opt - CONS no - opt - CPFL no - opt - CDS no - opt - CWS no - opt - These eight subkeys control the printing of library data. The eight

individual names will each produce reports for that class of library

data. ALL will cause all eight classes to be reported.

2.2 DS ( A day-schedule is

variation in some

Day-schedules

a set of 24 numbers used to provide an hourly

building parameter.

2.2.1 NAME = n blank - reqd - Each day-schedule name must be different from all other day-schedule

names

102
2.2.2 DESC * desc’ blank - opt

A description will more fully describe the purpose of the schedule. It

will appear in the day-schedule report.

2.2.3 FFC =* r,r,...<24> 24*1.0 - opt 0.<“ROl.

Fraction of full capacity. 24 values are required: one for each hour

of the day. They may range from zero to one. A zero value can be

replaced by OFF and ON can be used in place of one. This may be more

intuitive for day-schedules which are controlling the on/off operation

of something.

2.3 WS ( Week-schedules.

A week-schedule is a set of 12 day-schedules: one for each day of the

week, one for holidays, and one for each of 4 special day types (SP1,

SP2 , SP3, and SP4). It is referenced by name in subsequent building

input

2.3.1 NAME = n blank - reqd - Each week-schedule must have a name different from all other

week-schedule names.

2.3.2

DESC = 'desc' blank - opt - A description is useful in more fully describing the schedule, but its use is optional.

2.3.3

WD = n blank - cond

Set weekday (Monday through Friday) pointers to the named day-schedule.

That day-schedule must have been previously defined (2.2). Other

options are:

WE = n Set weekend (SAT & SUN) pointers.

ALL = n Set all 12 pointers.

SUN = n Set Sunday pointer only

MON = n Set Monday pointer only,

and similarly for TUE = n, WED = n, THU = n, FRI = n, SAT = n, SPl = n,

SP2 = n, SP3 = n, and SP4 = n. At least one day must be defined (other

pointers will be set by default rules).

2.4 MATL ( Materials.

These describe the materials used in the walls, windows, floors, etc.,

of the building. Conductive, optical and surface properties can be

described. The user must define the conductive properties (K, CP,

and D) or R.

2.4.1 NAME = n Each material must

blank

have a unique name. reqd

2.4.2 DESC = 'desc’

2.4.3 K = r

Conductivity.

blank opt

0 . W/m*K cond

0 . Btu/hr*f t*F

0.<r

103
2.4.4 CP - r .8368 kJ/kg*K cond 0.<r

0.2 Btu/lbm*F

Specific heat.

2.4.5 D “ r 0 . kg/ra3 cond 0.<r

0 . lbm/ft 3

Density.

2.4.6 R - r 0 . ra^*K/W cond 0.<r

0 . hr*ft^*F/Btu

Thermal resistance (R-value).

2.4.7 A " r .75 opt 0.<«r<'

Absorptance (and emittance) for solar radiation.

2.4.8 E = r .90 - opt 0.<r<l

Emittance (and absorptance) for thermal wavelength radiation

2.4.9 TRNS = r 0 . opt 0.<r<l

Transmittance of GLASS (2.4.17) and SHADE (2.4.16) materials

2.4.10 IR = r 1.52 - opt 1 .<r<2

Index of refraction of GLASS (2,.4.17) materials.

2.4.11 FTRN - r 0 . opt 0.<r<l

This is the transmittance of a sheet of GLASS (2.4.17) with a thin metallic film on the inside surface.

It must be used in conjunction with TRNS (2.4.9) which is the

transmittance of the glass without the film.

FTRN must be less than TRNS.

The thickness of the film is computed from those values and IR

(2.4.10) with optical properties of aluminum assumed for the film.

2.4.12 REF = r 0. - opt 0.<r<l.

Reflectance of a SHADE (2.4.16)

2.4.13 SC ® r 0. - opt 0.<r<1.14

The ASHRAE defined shading coefficient of a window. This must be used

with GLASS (2.4.17). All other optical properties are ignored.

2.4.14 RGH = i 2 - opt l<=i<=6

The roughness index interacts with the wind speed to determine the

outside convection coefficient. Index values:

1 very rough - stucco, built-up roof with stone, wood shingles

2 rough - brick, plaster, concrete block

3 medium rough - concrete, asphalt, shingles

4 medium smooth - clear pine

5 smooth - smooth plaster or metal

6 very smooth - glass, smooth painted surfaces

104
2.4.15 AIR - - cond

This subkey must be used if the material is to used as an air layer in

any transparent construct. The optical algorithms assume that the

glass panes are separated by air layers. Those air layers

automatically have TRNS=1 and IR=1.

2.4.16 SHADE - - cond

This indicates that the material is an interior shade in transparent

constructs. It must have information on TRNS (2.4.9) and REF (2.4.12).

Conductive properties need not be defined because they will not be

used. 2.4.17

GLASS - - cond

This subkey indicates the glass panes in a transparent construct. A

GLASS material must have conductive properties and optical properties

chosen from: (TRNS, IR) or (TRNS, IR, FTRN) or (SC). The program

assumes that multiple panes are separated by air layers for the optical

calculations

.

2.5 CONS Constructs.

Constructs are the wall and window sections, described in terms of

their constituent layers, that make up the building.

2.5.1 NAME = n blank - reqd - Every construct must have a name different from all other constructs.

2.5.2

DESC = ’desc' blank - opt - A description will appear in the construct report to more fully

describe the construct.

2.5.3

MATL = r,n,r,n,... 0, blank m, - reqd

ft, -

This subkey describes the material layers which form the construct.

The values are pairs of (thickness, name of material) from the outside

to the inside layer. Layers which are described by R-value (2.4.6)

must be given a thickness to maintain the proper sequence of values.

The value of that thickness is not used in the conductivity

calculations, so even a zero is adequate.

2.5.4 OA = r

- - opt 0.<=r<=l.

Outside absorptance (and emittance) for solar radiation. If no value

is given, the default is the absorptance (2.4.7) of the outside (first)

layer.

2.5.5 OE = r - - opt 0.<=r<=l.

Outside emittance (and absorptance) for thermal radiation. If no value

is given, the default is the emittance (2.4.8) of the outside (first)

layer.

105
2.5.6 ORGH - i - - opt l<-i<-6

This describes the roughness of the outside surface. It has the values

of subkey 2.4.14. If no value is given, the default is the roughness

of the outer layer.

2.5.7 IA « r - - opt O.Or<"l.

Inside absorptance (and emittance) for solar radiation. If no value is

given, the default is the absorptance (2.4.7) of the inside (last)

layer.

2.5.8 IE = r - - opt 0.<-rOl.

Inside emittance (and absorptance) for thermal radiation. If no value

is given, the default is the emittance (2.4.8) of the inside (last)

layer.

2.6 CPFL ( Control profiles.

Control profiles relate the capacity of the air handling system to the zone temperature.

2.6.1 NAME *» n blank - reqd - Every control profile must have a unique name.

2.6.2 DESC =* 'desc' blank - opt

The description more fully describes the control profile.

2.6.3 TMP = r,r,... - C reqd

F

This subkey is a list of the control point temperatures which make up

the control profile. See IV. E on control profiles.

2.6.4 CAP = r,r,... - - reqd -l.<=r<=l.

This subkey is a list of the control point capacities which make

up the control profile.

Each capacity is matched to the control temperature (2.6.3).

There may be no more than eight capacities in the profile.

See IV. E on control profiles.

2.7 CDS ( Control day-schedules.

A control day-schedule is a set of 24 control profiles.

2.7.1 NAME = n blank - reqd - Each control day-schedule name must be different from all other control

day-schedule names.

2.7.2 DESC = 'desc' blank - opt

A description will more fully describe the purpose of the control

day-schedule. It will appear in the day-schedule report.

2.7.3 CPFL = n,n,... blank - reqd

24 profile names are required: one for each hour of the day. They

must have been previously defined (2.6).

106
2.8 CWS ( Control week-schedules.

A control week-schedule is a set of 12 control day-schedules: one for

each day of the week, one for holidays, and one for each of 4 special

day types (SP1, SP2, SP3, and SP4). It is referenced by name in

subsequent building input.

2.8.1 NAME = n blank - reqd

Each control week-schedule must have a name different from all other

control week-schedule names.

2.8.2 DESC = 'desc' blank - opt - A description is useful in more fully describing the schedule, but its use is optional.

2.8.3

WD = n blank - cond - Set weekday (Monday through Friday) pointers to the named control

day-schedule. That control day-schedule must have been previously

Other options are:

Set weekend (SAT & SUN) pointers.

Set all 12 pointers.

Set Sunday pointer only

Set Monday pointer only.

and similarly for TUE = n, WED = n, THU = n, FRI = n, SAT = n, SP1 = n,

SP2 = n, SP3 = n, and SP4 = n. At least one day must be defined (other

pointers will be set by default rules).

defined (2.7).

WE = n ALL = n SUN = n MON = n

107
IV. C.

3

BUILDING SECTION

3. BUILDING [ Building Section.

This section describes features referring to all zones of the building.

The entire section is optional. If used, it must occur before any zone (section 4.) descriptions.

3.1 SIM ( Simulation control parameters.

If this key is used, it must occur before any detached shadowing

surfaces (3.2). It may not be used more than once.

3.1.1 N = r 0.0 degrees opt -360 .<-r<**360

.

Degrees from true north to the north axis of building coordinate system

(IV. F. 5).

Clockwise is positive.

3.1.2 SLDS = i 0 - opt 0<=i<=3

Solar distribution algorithm:

0 = shading from ' SHD f surfaces only;

1 = shading from ' SHD' and ’DSS 1 surfaces;

2 = shading from all surfaces including other zones;

3=2+ distribution of beam radiation on interior surfaces.

The surfaces of each zone must form a simple convex envelope.

3.1.3 CNVG = r,r,r,i .056 , .01 , . 1 ,6 C,-,W,- opt

.1,. 01, .34,6 F,-,Btu/hr,-

Heat balance iteration convergence limits:

First variable = temperature convergence: when there is no heating or cooling load successive iterations of zone air temperature must be

within r degrees.

Second variable = loads convergence: when there is a load, successive

iterations of loads must be (1 - load(n)/(load(n-l)) < r. Third number = minimum load: when load(n) < r, the next iteration

would cause division by a small number. Therefore convergence is

assumed. Convergence is also assumed if |load(n) - load(n-l)| < r. Fourth number = maximum number of iterations. Then record occurance of

non-convergence and go to next time step.

It is not necesary to give all 4 numbers, but to set the third number

the first two must also be given.

3.1.4 FLOW = i 12 - opt 0<i

This subkey indicates that the loads processor will use the detailed

air flow algorithm (III.G). It may be used without the value. The

value specifies the maximum number of iterations: Run terminates if

this number is exceeded because the heat balance is not valid if the

flows are not balanced. Two other air flow convergence parameters

are set as functions of the heat balance parameters (3.1.3).

Relative flow convergence = realtive loads convergence.

Absolute flow convergence = .00005 * minimum load.

108
3.1.5 HTB = i 0 - opt i - 0, 1, or 2 Solve surface heat balances using only a single calculation of the

outside surface temperature (0 or 1) or by iterating the outside

temperatures simultaneously with the inside surface temperatures to

convergence (2). The simpler mean radiant temperature (H.2.3) is used

with HTB = 0 and the more detailed MRT (H.2.H) is used with 1 or 2.

3.1.6 HO = i 0 - opt i = 0 or 2

Compute exterior convection coefficient using simple (0) or detailed

(1) algoritrah (1.1 and 1.2).

3.1.7 HI = i 0 - opt i = 0 or 1 Compute interior convection coefficient using simple (0) or detailed

(2) algorithm (J.l and J.2).

3.2 DSS ( Detached shadowing surfaces.

Shadows from these surfaces are not used unless SLDS > 0 (3.1.2).

3.2.1 AZM = r 0 degrees opt -360.<=r<=360

.

Azimuth (facing) angle of surface relative to building coordinate

system. For example, north = 0, east = 90, south = 180, west = 270 or -90.

3.2.2 TILT = r 90 degrees opt 0.<=r<=180.

Tilt of surface (0 = facing upward like flat roof; 90 = vertical; 180

= facing downward like floor).

X = r 0 . m opt -

0 . ft

Y = r 0 . m opt -

0 . ft

Z = r 0 . m opt

'' -

0 . ft

ORG = r,r,r

Coordinates of lower left corner of surface relative to building

coordinate system. ORG provides a simpler way of describing all

coordinates at once (ORG = X, Y, Z) . See IV. F on geometric data

3.2.4 W = r 0. m

0. ft

reqd -

H = r 0. ra 0. ft

reqd -

SIZE = r,r

or VRTS = r,r,r,r or r,r,r,r,r,r

The first two forms specify the width and height of a rectangular

surface (SIZE = W, H). The last form is for triangles or quadrilaterals. The first pair of numbers are the surface relative x-y

coordinates of the first vertex counter-clockwise from the lower

left vertex. The subsequent pairs of numbers are the coordinates

3

109
of the remaining vertices in counterclockwise sequence. See IV.

F

on geometric data.

3.2.5 TRNS - r 0. - opt

Transmittance of the shadowing surface.

3.2.6 FROM - d 1JAN - opt

THRO - d 31DEC

The surface may apply for only part of the year,

used, but for greatest efficiency dates should be

shadowing surface dates table.

0.<rOl

.

Any dates may be

chosen from the

110
IV. C.

ZONE SECTION

4. ZONE [ Zone Section.

A zone is a space under the control of one thermostat (or uncontrolled)

where the air can be considered well mixed. The zone is composed of

surfaces which connect it to the environment or to other zones,

scheduled internal loads, and air temperature control strategy. There

may be multiple zone sections. They must appear after the PROJECT,

LIBRARY, and BUILDING sections.

4.1 GEOM ( Zone geometry.

This key is required and must be the first key in the zone section. It

may not be used more than once.

4.1.1

NAME = n blank - reqd

Each zone must have a unique name.

N = r 0.0 degrees opt -360.<=r<i=360.

Degrees from building north axis to north axis of zone coordinate

system. Clockwise is positive.

X = r 0 . m opt

0 . ft

Y = r 0 . m opt

0 . ft

Z = r 0 . m opt -

0 . ft

ORG = r,r,r

Coordinates of the lower left corner of the zone relative to the

building coordinate system. ORG provides a simpler way of describing

all 3 coordinates at once (ORG = X, Y, Z) . See IV. F on geometric data.

Zone origin is necessary only for the more detailed shadowing

calculations (SLDS > 0; sec 3.1.2).

4.1.4

CLHT = r 3.0 m opt

9.84 ft

Height of ceiling is used only in computing the zone height for

detailed air flow calculations (3.1.4 and G.2).

4.1.5

MIRX no - opt

This key causes all surface x-vertices to be mirrored about the y-axis

(north-south axis).

4.1.6

MIRY no - opt - This key causes all surface y-vertices to be mirrored about the x-axis

(east-west axis).

4.2 PEO ( Occupant heat gains.

4.2.1 WS=n - - reqd

The occupancy schedule is selected from the library of week-schedules

(2.3). The hours refer to clock time.

Ill
4.2.2 CAP - r 0 - cond 0.<r

Enter the number of occupants.

4.2.3 ACT - r 0.1318 kW opt . 102<-r<-.425

.450 kBtu/hr .350r<»1.45

Enter the activity level. The program will divide this number into

latent and sensible portions based on room air temperature.

4.2.4 RAD = r .5 - opt 0.<-r<«l.

This is the fraction of the sensible heat gain which is radiated to the room surfaces. The rest is convected to the room air.

4.2.5 FROM = d 1JAN - opt

THRU - d 31DEC - opt

The occupancy week-schedule may apply for only part of the year. The

schedule used by another PEO key may not overlap.

4.3 LIT ( Heat gains from lights.

The total heat gain from lights is divided into several fractions and

each is handled differently. The convective fraction is 1 .-RA-RAD-VIS

.

It may not be less than zero.

4.3.1 WS=n - - reqd

The total lighting energy is modified by the week-schedule element

(2.3) for the appropriate day and hour (clock time).

4.3.2 CAP = r 0. kW reqd 0.<r

0. kBtu/hr

CAP is the peak power consumption (capacity) of the zone lights.

4.3.3 RA = r 0. - opt 0.<“rOl.

This is the fraction of the total lighting energy which goes directly

into the return air instead of into the zone. This can occur with

vented light fixtures.

4.3.4 RAD = r .20 - opt O.Or<=l.

This is the fraction which can be considered long-wave radiant energy.

It interacts with zone surfaces according to their inside emittance

(2.5.8). The default fraction is typical of flourescent lights. A

value of 0.80 is appropriate for incandescent lights.

4.3.5 VIS - r .20 - opt 0.<-r<-l.

This is the fraction which can be considered short-wave (or visible)

radiant energy. It interacts with the room surfaces according to their

inside absorptance (2.5.7). It can leave the zone through transparent

surfaces without creating a load. The default is typical of flourescent lights. For incandescent lights 0.10 is an appropriate value.

4.3.6 REP = r 0. - opt - This is the fraction of lighting energy which can be replaced by

daylight (4.10).

112
4.3.7 FROM » d 1JAN - opt

THRU = d 31DEC - opt

The lighting week-schedule may be applied to only part of the year.

The schedules used by other LIT keys may overlap. This allows a simple

way to combine lighting from different sources as might be necessary to

describe area and task lighting.

4.4 EQP ( Heat gains from equipment.

EQP describes the heat gains from various types of equipment. The

convective fraction of that gain is 1 .-LAT-RAD-LOST. It may not be

less than zero.

4.4.1 WS = n

- - reqd - The equipment is selected from the library of week-schedules (2.3).

The schedule refers to clock time.

4.4.2 CAP = r 0. kW reqd 0.<r

0. kBTU/hr

CAP is the peak power consumption of the equipment. A negative

capacity is permitted. It can describe a process which cools the zone. A zero capacity is meaningless.

4.4.3

LAT = r 0. - opt 0.<=r<=l

This is the latent fraction, i.e., the fraction of energy used to add

water vapor to the zone air.

4.4.4 RAD = r .3 - opt 0.<=r<=l.

This is the radiant fraction which is treated as long-wave radiation.

4.4.5 LOST = r 0. - opt 0.<=r<=l.

The fraction lost allows the user to add energy to the total zone and

building consumption without effecting the zone loads. For example, it

might be used to account for outside lighting.

4.4.6 FROM = d 1 JAN - opt

THRU = d 31 DEC - opt

Time periods for multiple EQP keys may overlap.

EL

electricity

cond

GS gas cond

ST steam cond

HW hot water cond

OTHR other cond

These simple subkeys identify the energy source of the equipment. They

allow summing of the building energy requirements by energy type. One

of them must be given. OTHR allows a load to occur in the zone without

adding to the energy requirements.

4.5 INF ( Simple infiltration - Algorithm K.2.

INF allows scheduling of infiltration with simple temperature and wind

113
speed dependencies. It may not be used with the detailed air flow

option (3.1.4).

4.5.1 WS = n

- - reqd

The infiltration schedule is selected from the library of

week-schedules (2.3). The schedule refers to clock time.

4.5.2 CAP = r 0. m

2 /s reqd 0.<r

0. ft^/min

Enter the peak infiltration volume flow rate. The user must convert

"air changes" to volume flow rate.

C = r .606 - opt -

T = r .03636 1/C opt - .0202 1/F

V = r .1177 s/m opt - .000598 min/ ft

j-i ii >> 0. (s/m) 2 opt -

0. (min/f t) 2 The scheduled infiltration is modified by the factor:

(C + T*|TZ - TA| + V*SPD + VV*SPD2

) where TZ = zone air temperature

TA = ambient air temperature

SPD = wind speed

The default values are for a 7.5 mph wind and 0 temperature difference

Users who wish to have a constant infiltration should set C to 1 and

the other coefficients to 0.

4.5.4 FROM = d 1JAN - opt

THRU = d 31 DEC - opt

Time periods from multiple INF keys may not overlap.

4.6 VENT ( Ventilation - Algorithm K.3.

Ventilation describes the use of unconditioned outside air to cool the

zone. It may also be used to precool the zone during unoccupied hours

It may not be used with the detailed air flow option (3.1.4).

4.6.1 WS=n - - reqd

The ventilation schedule is chosen from the library of week-schedules

(2.3). The schedule refers to clock time.

4.6.2 CAP = r 0. m^/s reqd 0.<r

0. ft^/min

Enter the peak volumetric flow rate.

4.6.3 MIN = r 20. C opt

This causes ventilation to seek to bring the zone air temperature down

to the value given. If this subkey is used, do not use MAX (4.6.4).

114
4.6.4 MAX = r 90. C opt

This causes ventilation to occur whenever the zone air temperature is

greater than this value. If this subkey is used, do not use MIN

(4.6.3).

4.6.5 TD = r 2. K opt 0.<=r

3.6 F

This requires that the outside air be TD degrees cooler than the inside

air before ventilation can occur.

4.6.6 FROM = d 1 JAN - opt

THRU = d 31DEC - opt

Time periods of multiple VENT keys may not overlap.

4.7 MIX ( Two zone mixing - Algorithm K.4.

MIX simulates the controlled mixing of two zones such as occurs in

attached sunspace designs. It may not be used with the detailed air

flow option (3.1.4).

4.7.1 WS = n

- - reqd

The mixing schedule is chosen from the library of week-schedules (2.3).

The schedule refers to clock time.

4.7.2 CAP = r 0. m-Vs reqd 0.<r

0. ft^/min

Enter the peak volumetric flow rate. The mass flow will be based on standard (1.2kg/m3) air.

4.7.3 TD = r 0. K opt 0.<=r

0. F

There is mixing with the adjacent zone whenever the zone air

temperature is TD greater than the adjacent zone. When TD is zero,

there is always mixing (as controlled by the schedule).

4.7.4 ZONE = n

- - reqd - Give the name of the adjacent zone.

4.7.5 FROM = d 1 JAN - opt

THRU = d 31DEC - opt

Time periods of multiple MIX subkeys may not overlap.

4.8 FAN ( Whole house fan - Algorithm K.5.

Fan simulates a whole house fan which exhausts house air into the

attic. It may not be used with the detailed air flow option (3.1.4).

4.8.1 WS = n

- - reqd

The fan schedule is chosen from the library of week-schedules (2.3).

The schedule refers to clock time.

115
4.8.2 CAP “ r 0. m^/s reqd 0.<r

0. ftVmin

Enter the peak volumetric flow rate. The mass flow will be based on standard (1.2kg/m3) air.

4.8.3 T = r 0. C reqd 0.<=r

0. F

The FAN will seek to cool the zone air temperature to T.

4.8.4 ZONE ** n

- - reqd

Give the name of the adjacent (attic) zone.

4.8.5 FROM - d 1JAN - opt

THRU - d 31DEC - opt

Time periods of multiple FAN subkeys may not overlap.

4.9 CTRL ( Zone control - Algorithm K.l.

Details of zone temperature control are described in IV. E.

4.9.1 CWS = n

- - reqd

The control schedule is sectected from the library of control

week-schedules (2.8). The control profile is referenced by clock time.

4.9.2 HEAT = r 1.E6 kW opt O.C-r

Enter the peak heating capacity.

4.9.3 COOL = r 1.E6 kW opt O.Or

Enter the peak cooling capacity.

4.9.4 RAD = r 0 . - opt O.Or<l

.

The control profile refers to a control temperature which is defined as (1-RAD)*TZ + RAD*TR where TZ is the zone air temperature and TR is the zone mean radiant temperature.

4.9.5 FROM = d 1 JAN — opt - THRU = d 31 DEC - opt - It is common to operate with different control profiles during

different seasons as heating or cooling capacities are shut off. The

time periods from multiple CTRL keys may not overlap.

4.10 DLT( Daylighting.

The program uses a very simple model to estimate the savings in

lighting energy by using daylighting. All DLT keys should appear in

the zone description before any LIT keys.

4.10.1 WS - n

- - reqd - The fraction of beam sunlight which is usable for lighting is modified

by the week-schedule (2.3) element for the hour (standard time).

116
4.10.2 BEAM “ r 0 opt O.Or<“l

This is the fraction of beam sunlight entering the zone which can be

used to offset the visible energy from the lights.

4.10.3 DIFF ° r 0. - opt 0.<-rOl.

This is the fraction of diffuse sunlight entering the zone which can be

used to offset the visible energy from lights.

4.10.4 FROM = n 1 JAN opt

THRU = d 31DEC - opt

Time periods from multiple DLT keys may not overlap.

4.11 BBH ( Baseboard heat.

This key describes a system which adds heat to the zone based on the

outside air temperature.

4.11.1 WS = n

- - reqd

The peak heating capacity avalable at any hour (clock time) is modified

by the baseboard heating schedule selected from the week-schedule

library (2.3).

4.11.2 CAP = r,r 0.,0. kW reqd O.Or

The first value is the peak heating capacity. The second value is the

minimum heating capacity at the shut-off temperature. Two values are required.

4.11.3 TMP = r,r 0.,0. C reqd - The first value is the highest temperature at which the system gives

full heating capacity. The second value is the maximum temperature for

which the system produces any heat (the shut-off temperature). Both

values are required.

4.11.4 RAD = r .3 - opt 0 . <=r<=l

This is the radiant fraction which is treated as long-wave radiation.

4.11.5 FROM = d 1 JAN - opt

THRU = d 31DEC - opt

Time periods from multiple BBH keys may not overlap.

4.11.6 ST

HW

These refer to the source of heating energy: steam or hot water. One

or the other must be given.

4.12 MASS ( Internal mass. Internal masses are modeled by the internal surface algorithms. The

only difference from the treatment of a partition is that the internal

mass is not given a location in the zone and, therefore, beam sunlight

cannot fall directly on it.

cond

cond

117
4.12

4.12

4.13

4.13

4.13

4.13

4.13

1 CONS = n

- - reqd

Select the composition of the mass from the constructs library (2.5)

(2.5).

2 AREA = r 0. m

2 reqd 0.<r

0. ft 2 The mass must be given an area.

SRF ( Heat transfer surfaces.

All zone surfaces which conduct or store heat (except internal mass;

4.12) are described by this key.

1 CONS = n

- - reqd

Select the composition of the surface from the constructs library

(2.5).

EX - - cond -

IN - - cond - OP - - cond - TR - - cond - BS - - cond -

SS - - cond - The user must specify the following three factors: Is this an EXterior

or INterior surface? Is the surface OPaque or TRansparent? Are its

coordinates defined as a Base Surface or a Subsurface? (The

coordinates of a subsurface are defined relative to the most recently

described base surface.) There are eight combinations of these

factors. Three of those are not permitted because of various

algorithmic restrictions in the program. The following table explains

the three factors in terras of the common English names for such

surfaces (at three basic tilt angles).

EX/ IN OP/TR BS/SS 90 deg 0 deg 180 deg

EX OP BS wall roof - EX OP SS door - - EX TR BS *** not permitted *** EX TR SS window skylight - IN OP BS partition ceiling floor

IN OP SS *** not permitted *** IN TR BS - - - IN TR SS *** not permitted kick

AZM = r 180. degrees! Opt -360.<=r<=360.

Azimuth (facing) angle of the surface relative to the zone coordinate

system. North = 0; clockwise positive. This is used fo base surfaces

only. Subsurfaces face the same direction as their base surface.

4 TILT = r 90. degrees opt 0.<=r<=180.

Tilt of surface ( 0 = facing upward like flat roof; 90 = vertical;

180 = facing downward like floor). This is used for base surfaces

only. Subsurfaces have the same tilt as their base surface.

118
4.13.5 W » r reqd 0.<r

H « r

0. m

0. ft

0. ra 0. ft

reqd 0.<r

SIZE ® r,r

VRTS *= r,r,r,r or VRTS r,r,r,r,r,r

The first two forms specify the width and height of a rectangular

surface (SIZE = W, H). The last form is for triangles or quadrilaterals. The first pair of numbers are the surface relative x-y

coordinates of the first vertex counter-clockwise from the lower left

vertex. The subsequent pairs of numbers are the coordinates of the

remaining vertices in counter-clockwise sequence. See IV. F on geometric data.

X - r 0 . m opt -

0 . ft

Y - r 0 . m opt -

0 . ft

Z - r 0 . m opt -

0 . ft

ORG = r,r,r

For base surfaces (BS - 4.13.2) these are the coordinates of the lower

left corner of the surface relative to the zone coordinate system. The

base surface origin is not used in the simple shadow calculation mode

(3.1.2). For subsurfaces (SS - 4.13.2) these are the coordinates

relative to the lower left corner of the base surface. The Z

coordinate is the amount of the setback. ORG provides a simpler way of

describing all three coordinates at once (ORG = X, Y, Z) . See IV. F on geometric data.

4.13.7 FSS = r .5 - opt 0.<=r<=l.

FSS is the angle factor between the surface and the sky. It is used in

determining the intensity of diffuse sky radiation incident on the

surface. If FSS is not specified, it is computed from the TILT

(4.13.4) angle: FSS =* (1 + cos(tilt))/2.

4.13.8 FSG = r .5 - opt 0.<=r<=l.

FSG is the angle factor between the surface and the ground. It is used

in determining the intensity of diffuse ground reflected radiation on the surface. If FSG is not specified, it is computed from the tilt

(4.13.4) angle: FSG = (1 - cos(tilt) )/2.

4.13.9 ZONE = n blank - opt

This is the name of the zone on the other side of the surface from the

current zone. The program will check for that zone to have a surface

which refers to this zone. That is, a single partition (or ceiling or floor) which is between two zones, must must be described in each zone. The program checks that these two surfaces have the same area and

U-value. It makes a partial check on the conduction transfer

functions. Remember that constructs are defined from the outer to the

inner layer and, therefore, asymmetric interzone partitions will have

to be defined twice to be referenced from the different zones.

119
4.14 AFS ( Air flow surface - Algorithm G

AFS describes the crack area and other openings in the base surface

which are used in the detailed air movement simulation. FLOW (3.1.4)

must have been specified. The base surface must be either an exterior

surface or an interzone surface (4.13.2 and 4.13.9). The AFS assumes

the azimuth of the base surface for computing wind direction effects.

When the AFS applies to an interzone surface, there must be an identical AFS specified for the appropriate base surface in the

adjacent zone.

4.14.1 AREA = r 0. m^ reqd 0.<r

0. f t^

This is the effective area of the opening.

4.14.2 EXP = r .65 opt .5<-r<-l.

EXP is the flow expontent. It is typically .65 for exterior walls and

.50 for interzone openings.

4.14.3 ZS = r - m opt

ft

This is the height of the centroid of the surface or opening relative

to the zone origin (G.2). The default value is the average of the

heights of the vertices of the base surface.

4.14.4 ZT = r - m opt

ft

This is the height at which the wind speed is evaluated for the opening

(G.l). The default value is the highest vertex of the base surface.

4.15 SHD ( Shadowing subsurfaces.

SHD describe simple shadowing surfaces which apply to the most recently

defined base surface (BS - 4.13.2) and all of its subsurfaces. The

base surface must be an exterior (EX) surface unmodified by OSC (4.16).

4.15.1 OHNG - - cond - LFIN - - cond - RFIN - - cond - PROJ - - cond - There are four configurations for these features

overhang

right fin, and projection. See IV. F for details.

4.15.2 W = r 0 . m reqd 0 ,<=r

0 . ft

H = r 0 . m reqd 0.<=r

0 . ft

SIZE = r,r

These subkeys specify the width and height of the rectangular shadowing

surface. SIZE is a shorter description (SIZE = W, H) . See IV. F on geometric data.

120
4.15

4.15

4.15

4.16

4.16

4.16

4.16

3 X = r 0. m opt ~

0. ft

it >* 0. m opt

0. ft

II N 0. m opt 0 ,<=r

0. ft

ORG = r,r,r

The positioning of the shadowing subsurface is given relative

base surface coordinate system. See IV. F on geometric data.

4 TRNS = r 0. — opt 0.<=r<l

Transmittance of the shadowing surface.

5 FROM = d 1 JAN — opt

THRU = d 31 DEC - opt

The surface may apply for only part of the year. Any dates may be

used, but for greatest efficiency dates should be chosen from the

shadowing surface dates table (IV.G.l).

OSC ( Other side coefficients.

OSC provides a means of approximating conditions on the outside of a surface where it is not desirable (or possible) to simulate those

conditions. The OSC key applies to the most recently described

surface. That surface should be EX / OP / BS (4.13.2). It should also

have no shadowing or heat transfer subsurfaces. Other side

coefficients establish an outside temperature which is a function of

several factors. The temperature is computed from the formula:

T = (TZP*TZ + TAP*TA + CTP*CT + TGP*GRT + WSP*SPD*TA)

/ (TZP + TAP + TGP + WSP*SPD)

where TZ = most recent value of zone air temperature

TA = ambient air temperature

GRT = ground temperature (1.4.1)

SPD = wind speed

and the other factors are user defined as described below. At least

one of the factors in the divisor of the equation must be defined

nonzero.

1 HO = r 0. W/m^K opt 0.<=r

0. Btu/hr*ft^F

This is the value of the outside surface convection coefficient. If it

is zero, the OSC temperature is the surface outside temperature. If it

is not zero. The OSC temperature is an air temperature which is used

with the convection coefficient to compute the outside surface

temperature.

2 TZP = r 0. - opt

Zone temperature part.

3 TAP = r 0. - opt

Ambient air temperature part.

121
4.16.4 CT = r 0. opt

0.

Constant temperature.

4.16.5 CTP = r 0.

Constant temperature part.

4.16.6 TGP - r 0.

Ground temperature part.

4.16.7 WSP - r 0.

0.

Wind speed part.

4.17 EMI ( Exterior movable insulation.

Exterior movable insulation is applied to the most recently defined

surface. That surface must have been defined as exterior (EX; 4.13.2)

and not modified by subsequent OSC (4.16). EMI may apply to either

massless or massive surfaces. EMI is opaque and can prevent solar

gains through windows.

4.17.1 CONS = n

- - reqd

The movable insulation is chosen from the constructs library. The

movable insulation algorithm handles only massless insulation. It uses

the U-value, outer solar and thermal absorptances and roughness of the

construct

.

4.17.2 DS = n

- - cond

SNUP - - cond - SNDN - - cond

One of three methods must be chosen for control of the EMI. The first

is reference to a day-schedule (2.2). A value of zero means no EMI for

that hour (standard time) and a one means the EMI is in effect.

Fractional values in the day-schedule modify the R-value. Any schedule

value greater than zero causes sunlight to be absorbed on the EMI

rather than on the surface. Second is SNUP which means the EMI is in

effect whenever the sun is above the horizon. SNDN means the EMI is in

effect when the sun is below the horizon.

4.17.3 FROM = d 1JAN - opt

THRU = d 31 DEC - opt

The EMI may apply for only part of the year. It may be desirable to use different controls during different seasons. Any dates may be

used, but since the EMI effects the solar gain calculations, dates

should be chosen from the table of shadowing surface dates (IV.G.l) for

greatest efficiency. Time periods from multiple EMI subkeys may not

overlap.

C

F

opt

opt

s/m opt

min/ft

122
4,18 IMI ( Interior movable insulation.

Interior movable insulation applies to interzone surfaces only. That

is, the most recently defined surface should be interior (IN; 4.13.2)

and have an other side zone name (4.13.9).

4.18.1 CONS = n

- - reqd

The movable insulation is chosen from the constructs library. The

movable insulation algorithm handles only massless insulation.

4.18.2 DS = n

- - cond

GAIN - - cond

LOSS - - cond

One of three methods must be chosen for control of the IMI. First is

reference to a day-schedule (2.2). A value of zero means no IMI for

that hour (clock time) and a one means the IMI is in effect. Fraction

values in the day-schedule modify the R-value. The second method is

GAIN which causes the IMI to be in effect whenever the surface

temperature is greater than the zone control temperature (4.9.4). LOSS

is the inverse of the GAIN operation.

4.18.3 FROM = d 1JAN - opt

THRU = d 31 DEC - opt

Since IMI does not effect the zone’s solar gain, the dates need not

refer to the shadowing surface dates. Time periods from multiple IMI

subkeys may not overlap.

123
IV. D INPUT SUMMARY

This summary of the input language is intended to serve as a reminder of the

syntax and all the keywords. As the user becomes more familiar with the

input, he will use this summary more and the detailed input description

(IV. C) less. It may be desirable to copy these pages and place them near

the computer terminal.

Data types: n = name, r » real, i » integer, d date, desc description

1 . PROJECT [

1.1 RC ( DESC - 'desc' / SYNTAX / DEM / 2SPC / XREF / OLDW /

ENGLISH / METRIC / UIN - n / UOUT - n )

1.2 RPT ( RNOS » i,... )

1.3 LOC ( DESC = ’desc* / LATD - r / LONG =r/TZ“r/ ALT " r /

TER - i )

1.4 GRND ( GRT - r,...<12> / MWT = r,...<12> )

1.5 WTAP ( DESC - ’desc’ / SKIP - i / DAYS « i )

1.6 DDY ( DESC = ’desc’ / HIGH - r / LOW - r / WB - r / DATE - d /

PRES = r / WS = r / DIR r / CLR r / RAIN / SNOW /

SUN / MON / TUE / WED / THU / FRI / SAT /

HOL / SP1 / SP2 / SP3 / SP4 )

]

2 . LIBRARY [

2.1 LIB ( NAME =n/NDS=i/NWS=i/ NMATL - i / NCONS = i /

NCPFL - i / NCDS = i / NCWS = i / ALL / DS /

WS / MATL / CONS / CPFL / CDS / CWS )

2.2 DS ( NAME = n / DESC = ’desc' / FFC - r,...<24> )

2.3 WS ( NAME = n / DESC = ’desc' /WD=n/WE=n/ ALL = n /

SUN = n / MON = n / TUE = n / WED = n / THU = n / FRI = n /

SAT = n / HOL - n / SP1 = n / SP2 = n / SP3 = n / SP4 = n )

2.4 MATL ( NAME - n / DESC = 'desc' /K=r/CP=r/D=r/ R=r/A=r/E=r/ TRNS - r / IR - r / FTRN = r /

REF = r / SC = r / RGH - i / AIR / SHADE / GLASS )

2.5 CONS ( NAME - n / DESC = ’desc’ / MATL = r ,n,r ,n, . . .<10> /

OA = r / OE = r / ORGH -i/IA-r/IE-r)

124
2.6 CPFL ( NAME - n / DESC - 'desc' / TMP = r,...<8> / CAP - r,...<8> )

2.7 CDS ( NAME = n / DESC - 'desc' / CPFL - n,...<24> )

2.8 CWS ( NAME - n / DESC - 'desc' /UD=n/WE=n/ ALL = n /

SUN = n / MON = n / TUE = n / WED = n / THU » n / FRI » n /

SAT = n / HOL = n / SP1 = n / SP2 = n / SP3 = n / SP4 «= n )

]

3 . BUILDING [

3.1 SIM ( N = r / SLDS - i / CNVG » r,r,r,i / FLOW - i /

HTB - i / HO - i / HI = i )

3.2 DSS ( AZM = r / TILT =r/X=r/Y=r/Z=r/ORG« r,r,r /

W = r / H = r / SIZE = r,r / VRTS = r,...<4 or 6> /

TRNS = r / FROM = d / THRU = d )

]

4 . ZONE [

4.1 GEOM ( NAME =n/N=r/X=r/Y=r/Z=r/ORG= r,r,r /

CLHT = r / MIRX / MIRY )

4.2 PEO ( WS = n / CAP = r / ACT - r / RAD - r / FROM = d / THRU = d )

4.3 LIT ( WS = n / CAP = r / RA = r / RAD = r / VIS = r / REP = r /

FROM - d / THRU = d )

4.4 EQP ( WS = n / CAP = r / LAT = r / RAD = r / LOST = r /

FROM = d / THRU = d / EL / GS / ST / HW / OTHR )

4.5 INF ( WS = n / CAP =r/ C=r/T=r/V=r/VV=r/

FROM = d / THRU = d )

4.6 VENT ( WS » n / CAP » r / MIN = r / MAX = r / TD = r /

FROM = d / THRU = d )

4.7 MIX ( WS = n / CAP = r / TD = r / ZONE - n / FROM = d / THRU = d )

4.8 FAN ( WS = n / CAP = r / T = r / ZONE = n / FROM = d / THRU = d )

4.9 CTRL ( CWS = n / HEAT = r / COOL = r / RAD = r / FROM = d /

THRU = d )

4.10 DLT ( WS = n / BEAM = r / DIFF = r / FROM = d / THRU = d )

4.11 BBH ( WS = n / CAP = r,r / TMP = r,r / RAD = r / FROM = d /

THRU = d / ST / HW )

125
4.12 MASS ( CONS - n / AREA - r )

4.13 SRF ( CONS « n / EX / IN / OP / TR / BS / SS / AZM - r / TILT - r / W-r/H-r/ SIZE - r,r / VRTS - r,...<4 or 6> / X r /

Y - r / Z - r / ORG - r,r,r / FS - r / FSG - r / ZONE - n )

4.14 AFS ( AREA -r/EXP-r/ZS-r/ZT-r)

4.15 SHD ( OHNG / LFIN / RFIN / PROJ /W-r/H-r/

SIZE -r,r/X-r/Y-r/Z-r/ORG- r,r,r /

TRNS “ r / FROM - d / THRU - d )

4.16 OSC ( HO - r / TZP - r / TAP - r / CT - r / CTP - r / TGP - r /

WSP - r )

4.17 EMI ( CONS - n / DS - n / SNUP / SNDN / FROM - d / THRU - d )

4.18 I MI ( CONS » n / DS » n / GAIN / LOSS / FROM - d / THRU - d )

]

126
IV.

E

ZONE TEMPERATURE CONTROL

The zone air temperature is determined by the interaction of the energy

flows in the zone and the operation of the air conditioning system. The

present version of the TARP does not include detailed system models. The

operation of the system is modeled by control profiles like those in the

loads section of the BLAST program [1] from which much of the following

discussion is taken. A control profile relates the zone air temperature to

the capability of the system to add or remove heat from the zone. The use

of the control profile in the zone air heat balance is described in III.K.l.

Figure E.l shows a simple control profile which can either heat or cool the

zone.

Point 1 might occur on a winter day. At that point, the room is at 68

F (20.0 C) and the heat loss from the room air exactly equals the room

heating capacity available at 68 F. In this example, the room heating load

(= heat delivered to the room air) is 40.0 kBtu/hr (11.7 kW).

Point 2 might occur on a mild day in the spring or fall. At this point

(73 F [22.8 C]), no room heating or cooling is accomplished by the building

fan system (although heating or cooling energy may be consumed to condition

ventilation air). For the heat balance to occur at point 2, convective heat

gains caused by such factors as lights or occupancy must be balanced by

convective heat losses to room surfaces or by infiltration. The load at

point 2 is zero.

Point 3 shows a cooling condition. Here heat gains to the room air are balanced by cooling capacity available at the balance point temperature.

The control profile can be described in terms of the temperatures and

heating/cooling capacities at control points A, B, C, and D. Simple linear

proportionality is assumed between the control points. At temperatures

below point A, the heating capacity is constant. The cooling capacity is

constant above point D. The control profile is described in two phases in

TARP. The full heating and cooling capacities are given for each zone (4.9.2 and 4.9.3). The shape of the profile is described in the library

section by normalizing the control point capacities (divide heating

capacities by the full heating capacity; divide cooling capacities by the

full cooling capacity, the result being set negative). This allows the same profile to be used in many zones which have identical control temperatures

but different full capacities. Full heating and cooling capacities can then

be adjusted independently of each other. The control profile in figure E.l

normalizes to that in figure E.2 which could be described by the input

language (2.6) as:

CPFL ( NAME=C1 / TMP=67 , 69 ,77 , 79 / CAP=1,0,0,-1 )

The tempertures and capacities of the control points must be given in the

sequence shown. Very steep profiles are possible. The user may set two

successive control temperatures equal to each other to hold the room temperature constant. TARP will make the second 0.01 C greater than the

first to permit the air heat balance calculations.

127
System type can subtly affect room temperature control profiles. For

example, assume that a package DX (direct expansion) condensing unit with

electric heat has been selected to serve the zone whose control strategy

is shown in figure E.l. Futher assume that the unit delivers 3850 cfm

(1.82 m^/s) to the space, that the cooling coil was selected to allow 55 F

(12.8 C) air to be delivered at the design sensible load of 100 kBtu/hr

(29.3 kW), and that the heating coil was selected to deliver 86.2 F (30.1 C)

air at the design heating load of 80 kBtu/hr (23.4 kW). In this case,

figure E.l closely approximates the achieved room temperature control. The room thermostat will modulate the condensing unit from "off" to "full" capacity through as many capacity control steps as are available on the unit.

This modulation will occur in a roughly linear fashion as the balance point room temperature varies from 77 to 79 F (25 to 26.1 C). The heating will be

similarly modulated between 69 and 67 F (20.6 and 19.4 C) , and both heating

and cooling will be "off" between 69 and 77 F (20.6 and 25 C). Since the

condensing unit's maximum heating and cooling capacity are approximately

constant, the unit adds or removes fixed quantities of heat whenever the room temperature is below 67 F (19.4 C) or above 79 F (26.1 C).

If a single-zone drawthrough unit served by hot and chilled water is

selected, the control strategy of figure E.l may require a slight revision.

When room temperature remains between 67 and 79 F (19.4 and 26.1 C), figure

E.l is correct. However, as long as the boiler and chiller serving the

coils in the fan unit can deliver constant temperature hot and chilled

water, the maximum capacity of the heating and cooling coils is not

independent of room temperature. For example, as the room temperature rises

toward 79 F (26.1 C), the room thermostat opens the cooling coil's chilled

water valve until the valve is fully opened at 79 F (26.1 C). If room heat

gains are sufficient, the room air temperature will continue to rise; but as it rises, the temperature of the air entering the coil also rises.

Therefore, the cooling capacity of the coil gradually increases. The

capacities below point A and above point D of figure E.l are not constant,

but are slowly increasing. Coil catalog data can be used to determine the

change in coil capacity.

Figure E.3 shows the equivalent control profile that should be used if

a three-deck multizone unit is selected to serve several zones with the same thermostat throttling ranges and deadband. The rationale for selecting this

profile is:

1. Range C-D is the thermostat deadband in which air delivered to the zone passes through the bypass deck and is neither heated nor cooled.

2. In range B-C, air from the hot deck and the bypass deck of the fan

system are mixed to meet zone heating requirements. This is the heating

throttling range for the thermostat. At its lower end (67 F [19.4 C]), all

air to the zone comes through the hot deck and is delivered to the zone at

the hot deck terapeature (86.2 F [30.1 C]

,

for example).

128
3. If heat losses are severe, the room temperature may fall into range

A-B. In this range, air entering the room comes from the hot deck only. As

long as the fan system heating coil is not overloaded, the air is supplied

to the zone at constant temperature. However, the amount of heat added to

the room air continues to increase as the room air temperature falls. The

amount of heat added per hour can be calculated from the following formula:

L = F * Cp * (Ts - TZ)

where

F » mass flow rate of air supplied by the fan system to the room

Cp “ specific heat of air

Ts supply air temperature to the room (the hot deck temperature)

TZ =* air temperature in the room

For this system, F and Cp are constant and Ts is constant for range A-B.

Therefore, as room temperature (TZ) falls, the heat added to the room increases linearly as shown in figure E.3.

4. Ranges D-E and E-F are analogous to ranges B-C and A-B, but are for

cooling.

The TARP description of the profile in figure E.3 is:

CPFL ( NAME-C2 / TMP=60 ,67 ,69 ,77 ,79 ,85 / CAP“1 , .73 ,0 ,-0 ,-.8 ,-l )

When defining a control profile like the one shown in figure E.3, users

should select arbitrary low and high room temperatures to establish the full

heating and cooling (+1 and -1) points on the profile. In the example

above, 60 and 85 F (15.6 and 29.4 C) were selected. When specifying

corresponding heating and cooling capacities for each zone, the "design"

capacity generally should not be used. Capacity should correspond with the

selected low and high temperatures.

In the DX condensing unit, single-zone drawthrough, and three-deck

multizone examples, load calculations will yield identical results when the

control profiles shown in figures E.l or E.3 are used, provided that the

temperature in the space stays between 67 and 79 F (19.4 and 26.1 C) during

the hours when the conrtol profile is in effect. Fortunately, most systems

are designed with sufficient capacity to maintain comfort conditions, and users need be concerned about room temperature control characteristics which

are outside the range of the thermostat only when the heating or cooling

system has been indavertantly or deliberately undersized.

The same reasoning used for the three-deck multizone system can be used

to construct control profiles for spaces served by conventional multi-zone,

dual duct, or reheat systems (see figure E.4). Ranges A-B and C-D

correspond to ranges A-B and E-F of figure E.3, respectively. Range B-C

covers the temperature range where the mixing box, zone dampers, or reheat

coils are modulated by the room thermostat. The TARP description of such a profile is:

129
CPFL ( NAME=C3 / TMP = 60,73,77,85 / CAP = 1 , .58 ,-.74 ,-l )

No deadband is possible with these profiles so they cannot be approximated

by profiles of the type shown in figures E.l and E.3.

Figure E.5 shows a typical control profile for a VAV (variable air

volume) system with reheat. It was constructed based on the assumption that

3850 cfm (1.82 m-Vs) of 55 F (12.8 C) delivery air is to be supplied to the zone with the VAV dampers fully open at 79 F (26.1 C). The dampers close to

20 percent of full flow at 77 F (25 C). Reheat is to operate between 69 and

67 F (20.6 to 19.4 C), and the reheat coil will deliver air at 140 F (60 C)

when fully energized. The following temperatures and capacities define the

control profile:

Temperature Capacity Normalized

F ( C) kBtu/hr(kW) Capacity

60.0 (15.6) 66 (19.3) 1.0

67.0 (19.4) 61 (17.9) .91

69.0 (20.6) -12 (-3.5) -.09

77.0 (25.0) -18 (-5.3) -.15

79.0 (26.1) -100(-29 .3) -.80

85.0 (29.4) -125(-36.6) -1.0

The TARP input for this profile is:

CPFL ( NAME=C4 / TMP=60,67 ,69 ,77 ,79 ,85 / CAP=1 , .91 .-.09 ,-.15 ,-.8 ,-l )

REFERENCES

[1] Hittle, D. C., BLAST, Version 2.0: Users Manual, Vol 1, U. S. Army

Construction Engineering Research Laboratory, Technical Report E-153

(Champaign IL, 1979), pp 41-46.

130
SYSTEM

CAPACITY

Figure IV.E.l Simple control profile with deadband

131
NORMALIZED

SYSTEM

CAPACITY

+1.0

Figure IV. E. 2 Normalized control profile

132
NORMALIZED

SYSTEM

CAPACITY

Figure IV. E. 3 Control profile for three-deck multizone system

133
Figure IV. E. 4 Control profile for multizone system

134
Figure IV. E. 5 Control profile for VAV system

135
IV.

F

GEOMETRIC DATA

To accurately account for shading, solar gains, and the effects of wind

on exterior walls, windows, and roofs, a fairly detailed description of the

building's geometry is required. Every building surface is represented by

a plane polygon of three or four sides. Within the program, each polygon is

represented by the locations if its vertices in a simple Cartesian coordinate

system. In that system, the X axis points due east, the Y-axis points north,

and the Z-axis points upward. The orientation of each surface is maintained

by two conventions. First, the vertices are stored in counter-clockwise

sequence as the surface is viewed from outside the zone it encloses. (Looking

at the surface from the opposite side would give a clockwise sequence.)

Second, the orientation is described in terms of the "azimuth" and "tilt"

angles.

The simplest level (0) of shadowing detail (3.1.2) requires that only

the azimuth and tilt angles be specified. Detailed air flow analysis (3.1.4)

and the detailed exterior surface coefficient algorithm (3.1.6) require

correct heights for every surface. The first and second levels of shadowing

detail require that all surfaces of the building envelope be correctly positioned in the building coordinate system. The third level of shadowing

detail requires that internal surfaces also be correctly positioned and that

the zone is completely enclosed.

A heirarchy of coordinates systems exists to simplify the positioning of

surfaces. The building coordinate system is a simple rotation from the true

coordinate system which allows major building features to be aligned along

the X-Y axes. There is a coordinate system for every zone which is located

relative to the building system for simplifying the description of the zone geometry. Finally, each surface of the zone has a coordinate system for

defining the size and shape of the surface and the location of subfeatures

which apply only to that surface.

IV.F.l SURFACE COORDINATE SYSTEM

Every wall, roof, or floor of a building is represented by a plane

surface of three or four sides. The origin of the surface coordinate system

is located at one of the surface vertices. The X-axis is a horizontal (relative to the global coordinate system) line in the plane of the surface. The

Y-axis is perpendicular to the X-axis and also in the plane of the surface.

The Z-axis is perpendicular to the surface. It is used in the descriptions

of subsurfaces. The coordinates of the vertices of the surface are described

in the surface coordinate system as the surface is viewed from outside its zone.

Input (4.13.5) allows a simple description of rectangular surfaces. For

example a rectangular wall 12 feet wide by 8 feet high ( W=12 / H=8 or equivalently SIZE=12,8 ) would be described by figure F.l. This representation of rectangles places the origin at the lower left corner so that all

vertices are positive numbers.

136
Non-rectangular surfaces can also be described by giving the

coordinates of the vertices. For example, VRTS“10,0,5,30 describes the

triangle in figure F.2. Negative coordinates like VRTS=12 ,-3 ,7 ,7 ,-5 , 10 are also possible (figure F.3). In the description of non-rectangular surfaces,

a vertex at the origin (0,0) is assumed. The remaining vertices are given

by their X-Y coordinates going counter-clockwise around the surface. Only

convex surfaces (no interior angle greater than 180 degrees) with 3 or 4

vertices are permitted. Other surfaces should be divided into two or more

convex surfaces. The reasons for this are discussed in III.E.4.

IV.F.2 WINDOW AND DOOR SUBSURFACES

The location and size of these features are described in the coordinate

system of the base surface (wall, roof, etc.) on which they lie. The size

of each window or door is given by its width and height (for example, W=4 /

H=6 or equivalently SIZE“4,6 ). The subsurface is located on the base

surface by giving the coordinates of its lower left corner relative to the

origin of the base surface (for example Xes 4 / Y“1.5 or 0RG“4, 1.5,0 ).

Coordinates are given relativve to the base surface coordinate system.

Figure F.4 shows the window thus described placed on the wall from figure

F.l. The subsurface must lie completely within the base surface. Nonrectangular subsurfaces must be described as equivalent rectangles.

It is common for windows and doors to be set back slightly behind the

plane of the base surface. This causes shadowing of the subsurface,

especially as the sun's rays become nearly parallel to the surface. The

setback is described by the Z coordinate ( Z=-.5 ) of the location of the

subsurface. (A "set forward" is not permitted.)

IV. F.3 SHADOWING SUBSURFACES

TARP input (4.15) provides a simple way to describe rectangular

shadowing features which are parallel to the major axes of the base surface

coordinate system. There are four configurations:

1. An overhang (OHNG) lies parallel to the X-Z plane and can cast shadows

downward onto the surface (figure F.5).

2. A left fin (LFIN) lies parallel to the Y-Z plane and is to the left of

its shadow (figure F.6).

3. A right fin (RFIN) also lies parallel to the Y-Z plane but lies to to

the right of its shadow (figure F.7). Section III.E.2 explains why TARP

surfaces cast shadows to one side but not the other. It is necessary to use an LFIN and an RFIN to describe a feature which can shade both directions . 4. A projection (PROJ) lies parallel to the X-Y plane in front of the

surface which it shadows (figure F.8).

Figures F.5 through F.8 show how the size and position of these

shadowing features are described in terras of W, H (or SIZE) and X, Y, Z (or

ORG).

A shadowing subsurface will shade the base surface and all its window

or door subsurfaces. It will not shade any other base surface.

137
IV. F.

4

ZONE COORDINATE SYSTEM

The surfaces of a zone are located relative to each other in the zone coordinate system. It is a Cartesian coordinate system with a vertical

Z-axis and the X and Y axes oriented parallel to major zone features to

simplify placement of surfaces. A surface is located in the zone coordinate

system by giving the coordinates of the surface origin relative to the zone origin ( X=r / Y-r / Z-r or ORG»r,r,r [4.13.6]) and the azimuth ( AZM - r [4.13.3]) and tilt ( TILT-r [4.13.4]

)

angles of the surface.

The tilt angle is the angle from the Z-axis to the normal to the

surface. A vertical surface has a tilt of 90 degrees. A horizontal roof

has a tilt of 0. A floor has a tilt of 180 (the outward normal points

down)

.

Azimuth is the clockwise angle between the Y-azis and the horizontal

projection of the outward normal of the surface. For vertical surfaces this

is simply the direction the wall faces. Figure F.9 shows the locations,

azimuths and tilts of three vertical and three tilted surfaces. For

horizontal surfaces the true azimuth angle is undefined, but one must be

given to properly locate the surface vertices in the zone coordinate system.

This is most easily done by imagining the horizontal surface rotated about

an edge until it is vertical to allow identification of origin, width, and

height as in figure F.10 for a flat roof and figure F.ll for a floor.

IV.F.5 BUILDING COORDINATE SYSTEM

The building coordinate system is chosen to simplify the placement of zones relative to each other. The X- and Y-axes are usually chosen to lie

along the axes of most of the zones. Each zone is located in the building

coordinate system by giving the coordinates of the zone origin relative to

the building origin ( X=r / Y=r / Z=r or ORG°r,r,r [4.1.3]) and the angle

from the building Y-axis to the zone Y-axis ( N«*n [4.1.2]). Figure F.12

shows the location of three zones in a building coordinate system.

Because of the general orientation of the building, the Y-axis may not

line up with true north. The angle from true north to the Y-axis of the

building coordinate system ( N«r [3.1.1]) must be given to allow TARP to

compute the true coordinates of the surface vertices.

It is common for buildings to have two or more zones which are geometrically identical except for their location and orientation as shown

by the four zone examples in figure F.13. TARP allows two ways to describe

zones in terms of others already defined. First is rotation and translation. The description of zone 3 can be produced by duplicating the description of zone 2 and adding a rotation of 180 degrees about the zone origin

and shifting the origin to ORG=24 .5 ,55 ,0. This process is illustrated in

figure F.14. Use the text editor to duplicate the geometric features of zone 2, and do the rotation and origin translation of the origin in the

GEOM (4.1) key. This reduces the number of new lines that must be typed to

describe a similar zone.

138
Zone 4 in figure F.13 is very similar to zone 1, but its geometric

description cannot be obtained by any combination of rotations and translations. It is a mirror image of zone 1. Its description must use one of

the mirror image commands ( MIRX [4.1.5] or MIRY [4.1.6]). Figure F.15

shows how zone 1 is first mirrored in the Y direction (Y coordinates in the

zone system are replaced by their negatives) and then translated to a new origin to produce the description of zone 4. Figure F.16 shows that the same results could have been obtained by mirroring in the X direction,

rotating 180 degrees, and translating the origin. Mirror imaging works for

all surfaces and subsurfaces except those cases where a subsurface is on a non-rectangular base surface which was described with the first vertex not

lying on the X-axis (such as the base surface in figure F.3).

IV. F. 6 DETACHED SHADOWING SURFACES

The georaerty described thus far will allow calculation of shadowing

from subsurfaces like fins and overhangs, and from other zone surfaces. In

addition the user may wish to describe adjacent buildings or other significant shadow casting features which are not part of a particular zone and

which can shade more than one zone or surface. This is done with the

"detached shadowing surface" (DSS [3.2]). The description of such a surface invloves defining its size and shape ( W=r / H=r or SIZE=r,r or VRTS=r,r ,r ,r,r ,r [3.2.4]) as described above for a zone surface and then

locating ( X=r / Y=r / Z=r or ORG^rjrjr [3.2.3]) and orienting ( AZM=r

[3.2.1] and TILT=r [3.2.2]) the surface in the building coordinate system.

The critical consideration in locating and orienting the surface is that

it casts a shadow only into the hemisphere which it faces.

139
Y

Y

Figure IV.F.l Rectangle Figure IV. F. 2 Triangle

Y

Figure IV. F. 3 Quadrilateral Figure IV. F. 4 Window/door subsurface

140
Figure IV. F. 5 Overhang Figure IV. F. 6 Left fin

• Subsurface origin • Base surface origin

Figure IV. F. 7 Right fin Figure IV. F. 8 Projection

141
1: ORG = 0, 18.2, 0 / SIZE = 10.7, 8 / AZM = 270 / TILT = 90

2: ORG = 0, 7.5, 0 / SIZE = 10.7, 8 / AZM = 225 / TILT = 90

3: ORG = 7.5, 0, 0 / SIZE = 10.7, 8 / AZM = 180 / TILT = 90

4: ORG = 0, 18.2, 8 / SIZE = 10.7,8 / AZM = 270/ TILT = 20

5: ORG = 0, 7.5, 8 / VRTS = 10.7, 0, 5.3, 4/ AZM = 225/ TILT = 20

6: ORG = 7.5, 0, 8 / SIZE = 10.7, 8 / AZM = 180 / TILT = 20

Figure IV. F. 9 Zone coordinate system: tilted surfaces

142
ORG = 0, 0, 8 / SIZE = 12, 12 / AZM = 180 / TILT = 0

Figure IV.F.10 Zone coordinate system: flat roof

143
ORG = 0, 12, 0 / SIZE = 12, 12/ AZM = 180/TILT = 180

Figure IV.F.ll Zone coordinate system: floor

144
3: ORG = 0,0, 10

4: ORG = 15, 0, 10

Figure IV.F.12 Building coordinate system: four zones

145
Figure IV.F.13 Portion of building with similar zones

146
Figure IV.F.14 Zone 3 described by rotation and translation of zone 2

147
GEOM (MIRY/ORG = 0, 55, 0/

Figure IV.F.15 Zone 4 described by mirror imaging and

translation of zone 1

148
Figure IV.F.16 Zone 4 described by mirror imaging, rotation and

translation of zone 1

149
IV. G TABLES

IV.G.l SHADOWING DATES

Shadow patterns are normally computed for the 14 time periods listed

below. These periods were chosen so that the error in the solar position

would be less than 2 degrees on any day in the period. This causes the

periods to be shorter around March 21 and Sept 21 when the solar declination

angle changes rapidly. Shading features which do not use these dates will

increase the number of time periods and therefore the amount of time

necessary to calculate shadowing. Most shading features will occur over several time periods, e.g. FROM - 16MAY / THRU = 30SEP.

PERIOD FROM THRU

1 1 JAN 31 JAN

2 1 FEB 20 FEB

3 21 FEB 12 MAR

4 13 MAR 31 MAR

5 1 APR 20 APR

6 21 APR 15 MAY

7 16 MAY 31 JUL

8 1 AUG 24 AUG

9 25 AUG 12 SEP

10 13 SEP 30 SEP

11 1 OCT 20 OCT

12 21 OCT 15 NOV

13 16 NOV 15 DEC

14 16 DEC 31 DEC

150
V OUTPUT

The Thermal Analysis Research Program produces output in various levels

of detail as directed by the user. Output reports generally consist of

tables of numbers suitable for printing or display at a terminal. Development of more elegant graphic output has not been pursued because of the TARP

emphasis on the fundamental heat transfer algorithms and computational

methods. Almost every intermediate result that TARP calculates can be

printed. Most of these intermediate results are available through "dumps"

which have minimal descriptive information with the numbers and are in

metric units — the internal data representation. Several "reports" are also available. Reports present summary data and can be in either English

or metric units. The following sections discuss the various output options.

V.A INPUT REPORTS

V.A.l Default Reports

The input processor produces an "echo" of the user input. This echo is

organized by numbered lines on numbered pages as shown in the report for the

sample problem from II. C shown in figure 1 on the following pages. Each page

heading includes a page number, title, date, time of day, and central processor execution time. This last number is based on a non-ANSI function and may

not be available on all computers. The input lines are numbered primarily to

aid in editing the user input file. If user lines are not over about 72 characters long, the output will appear on most terminals without "wrap-around".

The last page of the input processor report tells the unused library

elements and the required array dimensions (parameters) for the load calculator. The report of unused library names can help to identify typing errors which cause library elements to not be found when they are referenced later

in the input. The report also identifies elements which can be removed from

the input deck (possibly by commenting - $) to use less array space. The

array dimensions report tells the minimum parameter sizes (see VI. C for a complete list of parameters) necessary to run the simulation.

151
12

3

45

678

9

10

1

1

12

13

14

15

16

17

18

19

20

2122

23

24

25

26

27

28

29

30

31

32

33

3 4 35

36

37

38

39

40

4142

43

44

45

46

47

48

49

50

51

52

1 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/17. 06.07.55. .715

PROJECT t RC<DEM/UIN=ENGLISH/UOUT=ENGLISH/

DESC* ' THERMAL MASS TEST - SIMULTANEOUS ZONES » DIRECT SUN')

RPT < RNOS = 9 . 21)

LQC<DESC='COLUMBIA» MO. '/LATD=38. 9/LONG =92. 3/TZ*6)

GRND(GRT=40.42.48.55.62.67.70.69.63. 55.48.42)

DDY<DESC= 'MILD W I NTER ' /H I GH=50/L0W=30/WB=40/DATE=2 1 FEB/

CLR= 1 ./M0N/WS=1320/DIR=315)

3 LIBRARY C DS(NAME=NONE/DESC='ZERO ALL HOURS ' /FFC=24*0

)

DS(NAME=FULL/DESC='ONE ALL HOURS ' /FFC=24* 1

)

DS<NAME=ON/DESC=' NORTH OCCUPANCY'/

FFC = 6*1 . . 5 » . 16.8*0.4* . 16. 2*. 33. ,67.1)

DS<NAME=OC/DESC=' CENTER OCCUPANCY'/

FFC = 1 6*0 . 3* . 1 7 . ,67. .5. .67. , 17.0)

DS(NAME=OS/DESC= 'SOUTH OCCUPANCY'/

FFC=6*0. ,5. .5. 8*0. 2*. 33. . 67 . 2* . 1 6 . 3*0

)

WS(NAME=OCCN/DESC= 'NORTH OCCUPANCY ' /WD=ON

)

WS(NAME=OCCC/DESC=' CENTER OCCUR ANCY ' /UD=OC

)

WS(NAME=OCCS/DESC=' SOUTH OCCUPANCY ' /WD=OS

)

DS(NAME=LN/DESC=' NORTH LIGHTING'/

FFC=6*0 . ,7. .7. 8*0. 2*. 33. 4*. 7. .4.0)

DS<NAME=LC/DESC=' CENTER LIGHTING'/

FFC=16*0» ,5. 5*. 7. .3.0)

DS<NAME=LS/DESC='SOUTH LIGHTING'/

FFC = o*0 . .7. .7. 8*0. 5*. 7. 3*0)

US<NAME = I.ITN/DESC='NORTH L I GHT I NG ' /WD = LN

)

WS(NAME=L I TC/DESC=' CENTER LIGHTING ' /WD=LC

)

US<NAME = LITS/DESC='SOUTH L I GHT I NG ' /WD = LS

)

DS<-NAME = EN/DESC=' NORTH EQUIPMENT'/

FFC-=20*0.3*1 .0)

DS(NAME=EC/DESC=' CENTER EQUIPMENT'/

FFC=16*0.4*1»4*0)

DS(NAME=ES/DESC=' SOUTH EQUIPMENT'/

FFC = 6*. 3.2*1 .8*. 3. 2*1 »3*,7.3*,3)

US <NAME=EQPN/DESC=' NORTH EQUIPMENT' /WD=EN

)

US <NAME=EQPC/DESC=' CENTER EQU I PMENT ' /UD=EC

)

US(NAME=EQPS/DESC=' SOUTH EQU I PMENT ' /UD=ES

)

US <NAME=CONST/DESC=' CONSTANT 1 OOX ' /ALL=FULL

)

MATL(NAME=GYP/DESC=' GYPSUM WALL BOARD ' /K= . 42/D=45 . /CP= . 3

)

M ATL(NAME=WD-S/DESC=' SOFTWOOD '/K=.0675/D=32./CP=. 33)

MATL<NAME=SHTH/DESC=' INTERMEDIATE DENSITY BUILDING BOARD SHEATHING'/

K=,034/D=22,/CP=,31)

MATL(NAME=C-HW/DESC=' HEAVY CONCRETE ' /K= 1 . 0/CP= . 2/D= 1 40 .

)

MATL<NAME = B1/DESC=' AIRSPACE RES I ST ANCE ' /R= . 9 1 /A I R

)

MATL<NAME=R5/DESC='R5 POLYSTYRENE '/R=5.

)

MATL<NAME = R19/DESC='R19 I NSUL AT I ON ' /R= 1 9 .

)

MATL<NAME=R30/DESC='R30 INSULATION ' /R=30 .

)

MATL ( NAME=SPDS/DESC=' STANDARD GLASS '/GLASS/R=.0236/TRNS=. 86)

MATL<NAME=ASH/DESC=' ASPHALT SH I NGLES ' /K= 1 8 . 1 6/D=70/CP= . 3

)

MATL(NAME=DIRT/K=.1/D=65./A=,70)

Figure V.l Sample default output

152
PAGE 2 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/17. 06.07.56. 1.048

53 MATL<NAME=AL/DESC=' ALUMINUM S I D I NG ' /K = 1 28/D= 1 7 1 . /CP= . 2

54 MATL<NAME=CPT/DESC=' CARPET 8 PAD'/R=2.08)

55 CONS<NAME=WL-I/DESC='EXTERIOR WALL - INSULATION AREA'/

56 MATL= . 0052 » AL , .0417, SHTH, 0.R19, .0521, GYP)

57 CONS <NAME=WL-S/DESC=' EXTERIOR WALL- STUD AREA'/

58 MATL= . 0052 » AL » ,0417. SHTH, .292, WD-S, .0521, GYP)

59 CONS(NAME=PTN-A/DESC=' PARTITION - AIR SPACE AREA'/

60 MATL=. 0521 .GYP. 0.81. .0521. GYP)

61 CONS<NAME=PTN-S/DESC=' PARTITION - STUD AREA'/

62 MATL=. 0521, GYP. .292.WD-S. .0521. GYP)

63 C0NS(NAME=WDW2/DESC='2 PANE WINDOW'/

64 MATL=O.SPDS» 0.81. O.SPDS)

65 CONS (NAME=FRAME/DESC =/ WINDOW FRAME ' /MATL=0 . 1 354 » WD-S

66 CONS <NAME=RF-T/DESC=' CEILING/ROOF - TRUSS AREA'/

67 MATL.= , 0104. ASH. .0417. WD-S. ,625. WD-S. .0417. GYP)

68 CONS(NAME=RF-I/DESC= 'CEILING/ROOF - INSULATION AREA'/

69 MATL=. 0104. ASH. .0417. WD-S, 0.R30, .0417, GYP)

70 CONS<NAME=PTN-M/DESC='MASSIYE PART I T I ON ' /MATL= . 667 , C-HW

71 CONS(NAME r-SLAB-C/OESC='SLAB WITH CARPET'/

72 MATL= . 5 » DIRT , 0.R5, .333, C-HW, O.CPT)

73 CONS (NAME=SLAB-T/DESC=' SLAB WITH TILE'/

74 MATL= , 5 » D IRT » 0.R5, .333.C-HW)

75 CPFL<NAME=P1/DESC='HEATING SETBACK ' /CAP=1 , 0/TMP=60 , 62

76 C P FL < NAME- P 2/ DESC =/ STANDARD HE AT I NG ' /CAP= 1 , 0/TMP=68 , 70

77 CDS <NAME=HN/DESC=' NORTH HEATING'/CPFL=6*P1,2#P2,8#P1,6#P2,2*P1)

78 CDS <NAME=HC/DESC=' CENTER HE AT I NG ' /CPFL= 1 6 *P 1 , 6*P2 , 2*P1

79 CDS ( NAME = HS/DESC= 'SOUTH HE AT I NG ' /CPFL = 6*P 1 , 2*P2 , 8*P 1 , 5*P2 , 3*P 1

80 CWS(NAME=HEATN/DESC=' NORTH HEAT ING ' /WD=HN

81 CWS<NAME = HEATC/DESC=' CENTER HE AT I NG ' /WD = HC

82 CWS<NAME=HEATS/DESC=' SOUTH HEAT ING ' /WD=HS

83 3 84 BUILDING C 85 SIM(SLDS=3/HTB=0/FLOW/CNVG=,1» .01, ,34.12)

86 DSS< AZM=180./TILT=153.4/0RG=0, 12, 1 6/SI ZE=44 , 2

87 DSS(AZM=180,/TILT=206,6/0RG=0»0»8/SIZE=44»2)

88 DSS( AZM = 0./TILT = U6.6/ORG= 0,36»8/SIZE = 44,2)

8? 3 90 ZONE C 91 GEOM( NAME-NORTH)

92 CTRL(CWS=HEATN/HEAT=12)

93 PE0(WS=0CCN/CAP=3)

94 LIT <WS = LITN/CAP=1 ,4)

95 EQP (WS=EQPN/CAP=1 ,0)

96 MASS(C0NS=PTN-A/AREA=480)

97 SRF(EX/0P/BS/C0NS=WL-I/AZM=0/0R6=44»36»0/SIZE=41»8)

98 SRF(EX/TR/SS/C0NS=WDW2/0RG=12,5,-.25/SIZE=20,2)

99 AFS(AREA=0.2/EXP=,65)

100 SRF ( EX/0P/BS/C0NS=WL-S/AZM=0/0RG=3,36,0/SIZE=3,8)

101 SRF(EX/0P/BS/C0NS=RF-T/AZM=0/0RG=44,36»8/SIZE=41,8.95/TILT=26.6)

102 AFS ( AREA-0 . 1/EXP= .65)

103 SRF ( EX/0P/BS/C0NS=RF-I/AZM=0/0RG=3»36»8/SIZE=3»8.95/TILT=26,6)

104 SRF < IN/0P/BS/C0NS=PTN-M/AZM=180/0RG=0,24»0/SIZE = 44» 12/Z0NE=CENTER)

Figure V.l (continued)

153
105

106

107

108

109

no

1 1

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

3 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/17. 06.07.58. 1.491

AFS(AREA=0. 5/EXP*. 50)

SRF ( IN/OP /BS/C0NS=PTN-M/AZM=270/0RG=0»36.0/VRTS=12»0» 12. 12. 0.8)

SRF ( IN/0P/BS/C0NS=PTN-M/AZM=90/0RG=44.24»0/VRTS=12»0» 12.8. 0.12)

SRF(EX/0P/BS/C0NS=SLAB-C/AZM=180/0RG=0.36»0/SIZE=44»12/TILT*180)

OSC < TGP= 1

3 ZONE C GEOM<NAME=CENTER)

CTRL(CWS=HEATC/HEAT=12)

PE0(WS=0CCC/CAP=3)

LIT (WS=LITC/CAP=1 .4)

EGP(US=EQPC/CAP=1 .0)

MASS(C0NS=PTN-A/AREA=480)

SRF (EX/O P/BS/C0NS=FRAME/AZM*180/0RG=0» 12. 12/SIZE=44»3)

SRF(EX/TR/SS/C0NS=UnU2/0RG=2.0.-.25/SIZE=40.3)

AFS( ARE A=0. 25/EXP*. 65)

SRF <EX/0P/BS/C0NS = RF-T/AZM = 0/0RG = 44»24» 12/SIZE = 41 »8.95/TILT = 26.6)

AFS(AREA=0. 1/EXP*. 65)

SRF(EX/0P/BS/C0NS=RF-I/AZM=0/0RG=3.24.12/SIZE*3.8,95/TILT*26.6)

SRF(IN/0P/BS/C0NS=PTN-A/AZM=180/0RG=3»12»0/SIZE=41.12/Z0NE=S0UTH)

AFS(AREA=0. 5/EXP*. 50)

SRF ( IN/0P/BS/C0NS=PTN-S/AZM=180/0RG=0. 12»0/SIZE=3» 12/Z0NE=S0UTH)

SRF ( IN/0P/BS/C0NS = PTN-M/AZM = 0/0RG = 44»24.0/SIZE = 44. 1 2/ZONE = NORTH)

AFS ( ARE A=0. 5/EXP*. 50)

SRF ( IN/0P/BS/C0NS=PTN-M/AZM=270/0RG=0.24»0/VRTS=12»0» 12.16. 0.12)

SRF < IN/0P/BS/C0NS = PTN-M/AZM = 90/0RG = 44. 1 2 » O/VRTS* 1 2 . 0 . 12.12. 0.16)

SRF ( EX/OP/BS/CONS=SLAB-C/ AZM* 1 80/0RG=0 . 24. 0/S I ZE=44» 12/TILT* 180)

0SC(TGP=1)

1 ZONE C GEOM(NAME=SOUTH)

CTRL(CWS=HEATS/HEAT=12)

PE0(WS=0CCS/CAP=3)

LIT <WS=LITS/CAP=1 *4)

EQP(US=EQPS/CAP=9. 4/LOST*. 4)

MASS(C0NS=PTN-A/AREA=480)

SRF(EX/0P/BS/C0NS=WL-I/AZM=180/0RG=0.0»0/SIZE=41»8)

SRF(EX/TR/SS/C0NS=WDU2/0RG=12.3.-.25/SIZE=20»4)

AFS< ARE A=0. 2/EXP*. 65)

SRF(EX/DP/BS/C0NS=WL-S/AZM=180/0RG=41»0»0/SIZE=3»8)

SRF(EX/0P/BS/C0NS = RF-T/AZM=180/0RG = 0.0.8/SIZE = 41 » 8 . 95/T I L.T = 26 . 6

AFS< AREA=0. 1/EXP*. 65)

SRF<EX/0F'/BS/C0NS=RF-I/AZM=180/0RG=41.0»8/SIZE=3»8.95/TILT=26,6)

SRF ( IN/0P/BS/C0NS=PTN-A/AZM=0/0RG=44»12»O/SIZE=41.12/ZONE=CENTER)

AFS(AR‘EA = 0,5/EXP=,50)

SRF ( IN/0P/BS/C0NS=PTN-S/AZM=0/0RG=3. 12»0/SIZE=3» 12/Z0NE=CENTER)

SRF < IN/0P/BS/C0N3 = PTN-M/AZM = 270/0RG = 0.12.0/VRTS=12.0. 12.8. 0.12)

SRF< IN/0P/BS/C0NS=PTN-M/AZM=90/0RG=44.0.0/VRTS=12»0. 12.12. 0.8)

SRF <EX/OP/BS/CONS=SLAB-T/ AZM* 180/0RG=0. 12. O/SI ZE*44. 12/TILT* 180)

0SC<TGP=1)

1

Figure V.l (continued)

154
PAGE 4 MBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/17 06.07.59 1.884

UNUSED LIBRARY NAMES (IF ANY):

day-schedule: none week-schedule: const

MRLP MINIMUM ARRAY DIMENSIONS:

zon: 3 srf: 32

hts : 32

afs : 10 cos: 12

gtp: 1 tfh : 283

ctf: 140

gsc: 3 dsh: 11 wsh: 10 con: 11 pfl: 2 cds: 3 cws: 3

Figure V. 1 (concluded)

155
V.A.2 RUN CONTROL MODIFICATIONS

The run control statement (1.1) includes four optional modifications

of the output.

V.A.2. 1 DEM and error messages.

TARP does extensive input checking. Incorrect or questionable input is

reported to the user by error messages which begin with two stars and a severity descriptor. Figure 2 shows how error messages appear in the

output. NAME has been misspelled as NAEM in line 15 of the input. This is

immediately reported. Since DEM (1.1.3) was specified in the run control

statement, a list of valid key words is also printed. Errors that might

occur due to bad punctuation, causing the input processor to believe it is

in a different input section, can be quickly spotted from the SECTION: and

KEY: entries. At the end of the day-schedule description (line 16) it is

noted that the user did not give this schedule a name (since the required

NAME subkey was never recognized). The error in line 15 propagates through

the program causing some other errors to be noted. At line 20, the

week-schedule is not created because the day schedule named OC could not be

found. The final error message at the end of the output indicates that a loads input file (the SINPFL) was not created. All input which produces

SEVERE errors must be corrected before the SINPFL is created.

IDEM AND ERROR MESSAGES

15 DS(NAEM=0C/DESC=' CENTER OCCUPANCY'/

** SEVERE INVALID SUBKEY*. NAEM

section: library key: ds valid subkeys are: NAME DESC FFC

16 FFC=16*0,3*. 17, .67, ,5. .67, ,17.0)

** SEVERE LIBRARY ELEMENT MUST HAVE NAME

17 DS<NAME=0S/DESC='S0UTH OCCUPANCY'/

18 FFC=6*0, .5, .5, 8*0, 2 *.33, . 67 , 2* . 1 6 , 3*0

1? WS<NAME=OCCN/DESC=' NORTH OCCUPANCY ' /UD=0N

20 WS<NAME=OCCC/DESC='CENTER OCCUP ANC Y' /WD=0C

** SEVERE OC NOT IN LIBRARY

** SEVERE WEEKDAY-SCHEDULE NOT DEFINED

** FATAL INPUT FILE NOT CREATED BECAUSE OF 'SEVERE' ERRORS

Figure V.2 Sample error messages
V.A.2.2 Double spacing

The 2SPC command (1.1.4) causes a blank line to be printed before every

input line echo as shown in figure 3. Note that double spacing does not

begin until the command has been recognized, so there is no skip between

lines 1 and 2.

PAGE 1 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/07. 07.07.18. .707

1 PROJECT C 2 RC(DEM/2SPC/UIN=ENGLISH/U0UT=ENGLISH/

3 DESC= ' THERMAL MASS TEST - SIMULTANEOUS ZONES . DIRECT SUN')

4 RPTCRNOS = 9)

5 LOC(DESC='COLUMBIA» MO .

' /LATD=38 . 9/L0NG=92 , 3/TZ=6

)

6 GRND<GRT=40»42»48>55»62»67»70»69»63»55»48»42)

7 DDY ( DESC= 'MILD WINTER ' /HIGH=50/L0W=30/WB=40/DATE=21FEB/

8 CLR=1 ./M0N/WS=1320/DIR=315)

9 I

10 LIBRARY C

11 DS<NAME=N0NE/DESC='ZER0 ALL HOURS ' /FFC=24*0

)

12 D3<NAME=FULL/DESC='0NE ALL HOURS ' /FFC=24*1

)

Figure V.3 Double spacing

V.A.2.3 Cross referencing

The XREF command (1.1.5) allows the user to match the data in the

reports and, especially, the dumps to his input. In general, the input is

read and organized into various arrays. The XREF reports the array

locations. In figure 4, line 87 describes a detached shadowing surface

(3.2). Information about this surface will be stored as element 2 in arrays

having a MAXSRF parameter dimension. The next DSS (line 88) is stored as element 3 in those arrays. Zone controls and scheduled loads (lines 92-95)

are stored in arrays with MAXCGS dimensions. The MASS is the first heat

transfer surface, so its data goes into the MAXHTS dimensioned arrays at

location 1. The surface description (line 97) has two cross references

because both geometric data (in MAXSRF dimensioned arrays) and heat transfer

data (in MAXHTS arrays) must be stored. The zone number appears after the zone description is completed (line 110).

157
87 DSS<AZM=180./TILT X 206.6/0RG=0»0»8/SIZE*44»2)

SRF = 2 88 HSS<AZM = 0./TILT = U4.6/0RG = 0>36»8/SIZE = 44*2)

SRF = 3 89 3 90 ZONE C 91 6E0M<NAME=N0RTH)

92 CTRL<CWS=HEATN/HEAT=12)

CGS = 1 93 PE0<US=0CCN/CAP=3>

CGS = 2 94 LIT<US=LITN/CAP=1 .4)

CGS = 3 95 EGP<WS=EGPN/CAP=1 *0)

CGS = 4 96 MASS<C0NS=PTN-A/AREA=480)

HTS = 1 97 SRF < EX/0F‘/BS/C0NS = UL-I/AZM = 0/0RG = 44>36>0/SIZE = 41 » 8)

SRF = 4 H j S — 2 98 SRF<EX/TR/SS/C0NS=UDW2/0RG=12>5>-.25/SIZE=20»2)

SRF = 5 HTS = 3 99 AFS<AREA=0,2/EXP=,65>

AFS = 1

107 SRF<IN/0P/BS/C0NS=F'TN-M/AZM=90/0RG=44»24>0/VRTS=12>0» 12>8» 0»12)

SRF = 11 HTS =9

108 SRF < EX/0P/BS/C0NS = SLAB-C/AZH=180/0RG = 0>36»0/SIZE = 44 »12/TILT = 180)

SRF = 12

HTS = 10

109 03C < TGP= 1

)

SSC = 1 110 ] ZON = 1 111 ZONE C 112 GEOM(NAME=CENTER)

113 CTRL(CWS=HEATC/HEAT=12)

CGS = 5 114 F'E0<WS = 0CCC/CAP = 3)

CGS = 6

Figure V.4 Cross references

V.A.2.4 Metric units

TARP processes input and writes reports in English units by default.

The user can request that the input or output or both be in metric units

(1.1.7). Two samples of metric reports are shown in figure 5. The first is

the final loads summary described in V.B.l. Second is a wall and conduction

transfer function report described in V.A.4.4.

158
BUILDING LOADS FOR

THERMAL MASS TEST - SIMULTANEOUS ZONES * DIRECT SUN

COLUMBIA* MO,

MILD WINTER

TOTAL TOTAL PEAK PEAK MAX MIN

ZONE HEATING COOLING HEATING COOLING TEMP TEMP HX HT V CL CX

(KWH) (KWH) (KU) < KW<C> <C>

NORTH 14.94 0.00 2.977 0,000 20.71 16,61 0 10 0 0 0 CENTER .33 0,00 .330 0.000 22.84 17.83 0 2 0 0 0

SOUTH ,09 0.00 ,090 0.000 25.48 19.98 0 1 0 0 0 total: 1 .536E+01 0. 3.067 0.000 25.48 16.61

MAX HEATING OCCURS AT HOUR 7 ON 2 1 FEB

MAX TEMP OCCURS AT HOUR 18 ON 2 1 FEB

MIN TEMP OCCURS AT HOUR 6 ON 21FEB

PTN-S 5 PARTITION - STUD AREA

4 : DESCRIPTION OF CONSTRUCTION

LAYER THICKNESS CONDUCTIVITY DENSITY SPECIFIC HEAT RESISTANCE

METERS W/(M*K> KG/M**3 KJ/<KG*K) M**2*K/W

GYP

WD-S

GYP

.0159

.0890

.0159

726 720.831 1.255 0.000

117 512.591 1.381 0.000

726 720.831 1.255 0.000

5 CONDUCTION TRANSFER FUNCTIONS OF ORDER 2 TIME INTERNAL CROSS EXTERNAL FLUX

1 8.68390584 .01854220 8,68390584 .58886750

2 -11.49423688

3 3.53278776

4 -.16599941

.30212722

.22263065

.01302198

1 .49423688

3.53278776

-.16599941

-1 -.03735637

- .00006837 .00006688 -.00006837

THERMAL CONDUCTANCE = 1.241 W/<M**2*K)

OUTER THERMAL ABSORPTANCE = .90

INNER THERMAL ABSORPTANCE = .90

OUTER SOLAR ABSORPTANCE = .75

INNER SOLAR ABSORPTANCE - .75

OUTER SURFACE ROUGHNESS =ROUGH

Figure V.5 Two reports using metric units

159
V.A.3 NUMBERED REPORTS

Seven data dumps can be requested by specifying report numbers (1.2.1)

V. A.3.1 RNOS = 1; dump PROJECT and LIBRARY data

This provides summaries at the end of the PROJECT and LIBRARY sections

The DUMP OF PROJECT CONTROL DATA shown below lists the values associated

with different variables which can be set in the PROJECT section. Refer to

VI. C for a description of the individual variables.

DUMP OF PROJECT CONTROL DATA

COMMON /TITLES/?

F'TITLE = THERMAL MASS TEST - SIMULTANEOUS ZONES * DIRECT SUN

LTITLE = COLUMBIA* MO.

ETITLE = MILD WINTER

COMMON /RUNCTL/J

EMU I = 2 SYNTAX = F CALCS = T DEM = T OLDW = F

COMMON /EFLHDR/:

l.ATD 38.900

LONG 92.300

it NR 6.000

ALTD 0.000

TRRAIN = 3 SINL .628

CQSL .778

MERID = 2.300

TGRND = 4.4 5.6

TMKUP = 12.8 12.8

NRENVS = 1 NRDAYS 1 WSTATN = 0

8.9 12.8 1 A . 7 19.4 21.1 20.6 17.2 12.8 8.9 5.6

12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8 12.8

COMMON /REPORT/*.

EMUO

RFLAGS = T T

F F F F

T T T T

F F F F

F F F F

TF

F

F F F

F F F

F F F

Figure V.6 Dump of project control data

160
The DUMP OF LIBRARY CONTROL DATA shown below gives the number and

names of all library entries. First, summary data is given for each of

the seven libraries. This data is taken from common block LIBCTL. It

begins with the day-schedule (DS) by giving the 0 location (DSO) , the

number of schedules defined (NDS), and the maximum number of schedules

permitted (MXDS). This last number can be set by the user (2.1.2).

Similar data is presented for the other six libraries. Next comes a list

of all library element names (LNAMES) presented in eight names per row in

sequence. The list of numbers can be used to determine to which library

the names belong. For example, the first 16 names are day-schedules. DS

names occupy the first two rows including the five undefined (blank) names in the second row. Week-schedules (WS) names occupy the net two rows with ten names defined and six left undefined, etc.

DUMP OF LIBRARY CONTROL DATA

LIBRARY NAME =

DS — 0 11 16

WS = 16 10 16

MATL = 32 13 16

CONS 48 11 16

CPFL = 64 2 16

CDS 80 3 16

CWS = 96 3 16

ELEMENT names:

NONE FULL ON OC OS LN LC LS

EN EC ES

OCCN OCCC OCCS LITN LITC LITS EQPN EGF'C

EQF'S CONST

R30 GYP WD-S SHTH C-HW B

R5 R 1

SF'DS ASH DIRT AL CPT

WL-I WL-S PTN-A PTN-S WDW2 FRAME RF-T RF-I

F'TN-M SLAB-C SLAB-T

PI P2

HN HC HS

HEATN HEATC HEATS

Figure V . 7 Dump of library control data

.3.2 RNOS = 2 ; dump of DDY and WTAP data

This is a dump of all weather data for every day described in the DDY

(1.6) and WTAP (1.5) keys. It is a dump of data in the EVDAT common block.

The data names are summarized as follows:

161
NAME VARIABLE DESCRIPTION

YEAR YEAR year

MO MONTH month number

DY DYOFM day of month

DW DAYOFW day of week number

HOL HOLIND holiday and special days indicator

DST DSTIND daylight saving time indicator

SSDECL SSDECL sine of the solar declination angle

CSDESL CSDECL cosine of the solar declination angle

EQTIME EQTIME equation of time (h)

TD ODB dry bulb temperature (C)

TW OWB wet bulb temperature (C)

BP OBP barometric pressure (Pa)

H OHR humidity ratio

WS SPD wind speed (m/s)

WD DIR wind direction (deg)

TS SKY sky radiative temperature (C)

QB SRADBM direct normal (beam) solar flux (W/m**2)

QD SRADDF sky brightness (W/m**2)

QR SRADGR ground brightness (W/m**2)

RN RAIN rain indicator

SN SNOW snow indicator

7 ODY ( DESC = 'MILD WINTER'/HIGH=5O/L0W=30/WB*40/DATE=21FEB/

8 CLR= 1 ,/M0N/WS=1320/DIR=315)

YEAR MO DY DW HOL DST SSDECL CSDECL EQTIME

1958 2 21 2 0 0 -.184 .983 -.229

TD TU BP H US UD TS QB QD QR RN SN

.33 -.87 100000. .0031 6.7 315. -16.16 0.0 0.0 0.0 0 0

- .22 -1.19 100000. .0031 6.7 315. -16.69 0.0 0.0 0.0 0 0

- ,67 -1.45 100000. .0031 6.7 315. -17.10 0.0 0.0 0.0 0 0 -1.00 -1.64 100000. .0031 6.7 315. -17.42 0.0 0.0 0.0 0 0 -1.11 -1.71 100000. .0031 6.7 315. -17.52 0.0 0.0 0.0 0 0 -.89 -1 .58 100000. .0031 6.7 315. -17.31 0.0 0.0 0.0 0 0 -.33 -1.25 100000. .0031 6.7 315. -16.79 0,0 0.0 0.0 0 0 .67 -.67 100000. .0031 6.7 315. -15.85 307.4 18.6 10.2 0 0 2.11 . 09 100000 . .0031 6.7 315. -14,49 734.5 44.5 51 .

1

0 0 3.78 1.05 100000. .0031 6.7 315. -12.93 875.8 53.1 88.0 0 0 5.67 2.12 100000, .0031 6.7 315. -11.15 937.7 56.8 116.1 0 0

7 . 44 3.09 100000. .0031 6.7 315 . -9.48 965.4 58.5 133.2 0 0 8,78 3.80 100000

.

.0031 6.7 315. -8.23 972.2 58.9 138.0 0 0

9 . 67 4.27 100000. .0031 6.7 315. -7.39 961.0 58.2 130.2 0 0 10.00 4.44 100000 . .0031 6.7 315. -7.08 927.0 56.2 110.4 0 0 9.67 4.27 100000. .0031 6.7 315. -7.39 852.7 51 .7 80.0 0 0 8.89 3.86 100000. .0031 6.7 315. -8.12 675.5 40.9 41.5 0 0 7.67 3.21 100000. ,0031 6.7 315. -9.27 107.0 6.5 2.6 0 0

6.22 2.43 100000. .0031 6.7 315. -10.63 0.0 0.0 0.0 0 0 4.78 1 . 62 100000. .0031 6.7 315. -11.99 0,0 0.0 0.0 0 0 3.56 .93 100000. .0031 6.7 315. -13.14 0.0 0.0 0.0 0 0 2.44 .28 100000

.

.0031 6.7 315. -14.18 0.0* 0.0 0.0 0 0

1 .56 -.17 100000

.

.0031 6.7 315. -15.02 0.0 0.0 0.0 0 0 .89 - . 55 100000. .0031 6.7 315. -15.64 0.0 0.0 0.0 0 0

Figure V.8 Dump of weather data

162
V.A.3.3 RNOS “ 3; dump of conduction transfer function calculations

Details of the CTF calculations are presented beginning with a list

of the layers and their thermal properties (L thickness, K conductivity,

CP " specific heat, D density, R 05 thermal resistance value). SUMB,

CND, RR, and CC are variable names (see VI. C). The RR value is calculated

only for single layer constructions. The number of roots (NRT) found and

the search increment (SINC) are reported as well as the values of the

ROOTs and the variable RATIO. From the ROOTs and RATIOS the CTF are com- puted for orders zero (0 0) through (0 5) until the convergence criteria

have been met. The X, Y, Z, and J CTF are reported for all orders. This

report is simplified for massless constructs since no CTF (only the U

value) are calculated.

DUMP OF CONDUCTION CALCULATIONS FORI

PARTITION - STUD AREA

LAYER L K CP D R GYP .016 .726 1.255 720.831 0.000

WD-S .089 .117 1.381 512.591 0.000

GYP .016 .726 1.255 720.831 0.000

SUMB = 254.58173 CND = 1 . 24059 RR S -I CC = 14368.09

NUMBER OF ROOTS = 9i SEARCH INCREMENT * .007856

N ROOT RATIO

1 .013546079 .516548286

2 .027011651 ,072319215

3 ,040288196 .002899261

4 ,053198718 .000037605

5 065446912 ,000000201

6 .076662966 .000000001

7 .036835154 .000000000

B .096795305 .000000000

9 ,107590765 ,000000000

NUMBER OF RESPONSE FACTORS = 55 ORDER = 2

N 0 0 0 1 0 2 0 3 4 0 5

1 3.683909 8.683909 8.683906 8.683909 8.683909 8 .683909

2 -6.380569 -10.866227 - 11 ,494237 -11 .519418 -11.519744 -11 .519746

3 - .548920 2.746952 3.532788 3.566114 3,566547 3 .566549

4 -.250886 .032658 -.165999 -.176242 -.176376 - .176377

5 -.127301 ,002293 -.000068 0.000000 0.000000 0 .000000

1 .013542 .018542 ,018542 .018542 .018542 .013542

2 .313046 .303468 .302127 .302073 .302073 . 302073

3 .406281 .244577 .222631 .221755 .221743 .221743

4 .240573 .030710 .013022 .012377 .012368 .012368

5 .126555 .002288 ,000067 0.000000 0.000000 0 .000000

1 8.683909 8.683909 8.683906 8.683909 8.683909 8 .683909

2 -6.380569 -10.866227 - 11.494237 -11.519418 -11.519744 -11 ,519746

3 - .548920 2.746952 3.532788 3.566114 3.566547 3 .566549

4 -.250886 .032658 -.165999 -.176242 -.176376 - .176377

5 -.127301 .002293 -.000068 0.000000 0.000000 0 .000000

.588868 -.037356 0,000000 0.000000 0.000000

Figure V.9 Dump of CTF calculations for massive construct

163
V.A.3.4 RNOS = 4; dump of glass calculations

Details of the optical calculations are presented beginning with the

DESCription of the construction and a list of the normal transmittance,

index of refraction, film transmittance, and reflectance of the GLASS or SHADE layers (AIR layers are assumed between each optical layer). The

optical properties for the individual panes are:

EXTC = k*L from (D.3.5)

GN = index of refraction

FN = film index or refraction (D.4.1)

FK = film extinction coefficient (D.4.1)

FD = film thickness.

Then the computed reflectances and transmittances of the panes are reported at various angles of incidence:

T1 = transmittance for TE light

Rll = reflectance for TE light incident from outside

R12 = reflectance for TE light incident from inside

T2 = transmittance for TM light

R21 = reflectance for TM light incident from outside

R22 = reflectance for TM light incident from inside

The polynomial coefficients are the least squares fit values for

(D.1.7b) and (D.1.7a). T refers to transmittance, A to absorptance, 0 to

outside, I to inside, and S to shade.

DUMP OF OPTICAL CALCULATIONS FOR: 2 PANE WINDOW

LAYER TRNS IR FTRN REF

SF'DS .860 1.52 0 0.000 0.000

B 1 0,000 1.520 0.000 0.000

SF'DS .860 1.520 0.000 0.000

OFT I CAL PROPERTIES AT WAVELENGTH = ,725

PANE* 1 EXTC= .065 GN= 1 ,520 FN=0 .000 FK=0 . 000 FD=0 . 000

F'ANE= 2 EXTC= .065 GN = 1 . 520 FN=0 , 000 FK=0 .000 FD=0 , 000

OPTICAL VALUES AT COS ( THETA ) = ,991

PANE= 1 T 1 = .858 Rll* .079 R 12= .079 T2= .861 R2 1 = ,075 R22* .075

PANE* 2 T 1 = .858 R 1

1 = .079

• R 1 2= .079 T2= .861 R2 1 = ,075 R22* ,075

OPTICAL VALUES AT COS < THET A ) = .875

PANE* 1 T 1 = .828 R 1 1 = .106 R12= .106 T2= .882 R21* .051 R22= .051 PANE* 2 T 1 = .828 Rll* ,106 R 1 2= .106 T2= .882 R21* .051 R22* .051

OPTICAL VALUES AT COS < THET A ) = .938

F'ANE= 1 T 1 = .845 Rll* .090 R 1 2= .090 T2= .871 R21= .064 R22= .064 PANE* 2 T 1 = .845 Rll* .090 R12= .090 T2= .871 R21* .064 R22* .064

OPTICAL VALUES AT COS < THET A ) = 1.000

FANE* 1 T 1 = .860 Rll* ,077 R 1 2= .077 T2= .860 R21* .077 R22* .077

PANE* 2 Tl= ,860 Rll* .077 R 1 2= .077 T2= .860 R21= .077 R22= .077

Figure V.10 Dump of optical calculations

164
POLYNOMIAL COEFFICIENTS

I T2 A02 AI2 AS2

1 3.8544537E-01 2 » 427646 1 E + 00 5 , 75769 1 2E-0

-I

2 1 .0308017E+01 -2 , 2363210E+01 -3.6428286E+00 -I

3 -3.3949733E+01 1 .0021852E+02 1 .4986929E+01 -I

4 5.0154231E+01 -2.3554957E+02 -3.4400820E+01 -I

5 --3.9590559E+01 2 7725274E+02 3 » 984 1 064E + 0

-I

6 1 .4092558E+01 -1 . 2867078E+02 -1 .8204343E+01 -I

I T

A0All AS 1 1 -3.8380648E-01 1 .2150528E-01 1 .2238673E-02 -I

2 4.402 1 943E+00 -1 .3248196E-01 2 , 4052260E-0-I

3 -6.7817725E+00 1 .6526246E-01 -4 . 1181869E-01 -I

4 4 » 835 1 028E + 00 -1 .2219971E-01 2 . 9334734E-0-I

5 -1.3277812E+00 3 . 52326 1 9E-02 -7.9688593E-02 -I

Figure V.10 (continued)

V.A.3.5 RNOS = 5; dump of DSS data

This dump begins with the surface number (same as SRF number in

V.A.2.3). Then the coordinates of the vertices of the surface are presented

as X, Y, and Z values (in meters) arranged in the same order as the surface

is viewed. For example, (-.000 3.113 5.150) are the X, Y, and Z coordinates

respectively of the upper left vertex. (13.411 3.658 4.877) refers to

the lower corner. Several individual values are then presented:

CA = cosine of the axirauth (global coordinate system) angle

SA = sine of the aximuth angle

CT = cosine of the tilt angle

ST = sine of the tilt angle

TRNS = surface transmittance

ON = start date in cyclic date (B.1.4) form

OFF = end date

SI ,S2 = variables SHDSRF(I,1) and SHDSRF(I,2). See VI. C.

85 BUILDING C 86 SIM(SLDS=3/HTB=0/FL0U/CNVG=.1» .01 » .34.12)

87 D S S ( A Z M = 180, /TILT = 153 » 4/0RG = 0 » 1

» 16/SIZE=44»2)

surface: 1 VERTICES : - ,000 3.113 5.150 13.411 3.113 5.150

0,000 ro >0 in CO 4.877 13.411 3.658 4.877

CA SA CT ST TRNS ON OFF SI S2

-1 ,000 -.000 -.894 448 0.000 33 415 0 0

88 DSS<AZM= 180. /TILT = 206 . 6/0R6=0 i0i 8/SIZE = 44 , 2 ) SURFACE

2 VERTICES

- . 000 -.545 2.165 13.411 -.545 2.165

0.000 0.000 2.438 13.411 -.000 2.438

CA SA CT ST TRNS ON OFF SI S2

-1 .000 -.000 -.894 -. 448 0.000 33 415 0 0

Figure V.ll Dump of shadowing surface data

165
V.A.3.6 RNOS “ 6; dump of ZONE data

The zone data dump produces output as shown in figure 12. There are different data formats corresponding to the many different elements of zone

data. Controls and scheduled loads produce similar output as shown for

lines 92 through 95. First the schedule number (corresponding to CGS in

V.A.2.3) is given. Then the contents of CGSZON (zone number), type of

load), GGSON (on date), CGSOFF (stop date), CGSDX (week-schedule pointer),

and elements 1 to 5 of RCGS (see VI. c) are given order.

Lines 96 and 101 produce dumps of heat transfer surface data. They

begin with the heat transfer surface number (corresponding to HTS in

V.A.2.3). On the next two lines the following values are given:

NAME VARIABLE DESCRIPTION

AREA AREA Area of surface (m2)

INV ISENV Zone number

ONV OSENV Outside environment / far side zone number

FSS FSS View factor to sky

FSG FSG View factor to ground

K KPTR Pointer to construct data

AZM SFAZIM Azimuth angle (degrees)

CTILT CTILT Cosine of tilt angle

HOC HOC Factor for detailed outside convection

THE TMPHPR Pointer to external temperature histories

THI TMPHPI Pointer to internal temprature histories

QHE FLXHPE Pointer to external flux histories

QHI FLXHPI Pointer to internal flux histories

The surface described in line 101 is part of the envelope of the zone. Therefore, it also has shadowing surface data identical to that described in

V.A.3.5.

The air flow opening at line 102 produces another dump beginning with

the XREF number (corresponding to AFS). Then following variables are dumped

in order:

NAME VARIABLE DESCRIPTION

AREA FAREA Effective flow area

EXP FEXP Flow exponent

ZS ZS Height of opening

ZT ZT Height of top of base surface

C0S1 FC0S1 Direction cosine

C0S2 FCOS2 Direction cosine

PTR AFSPTR Number of adjacent zone (0 = ambient)

ZONE ZNMOUT Name of adjacent zone

Other side coefficients (line 109) also produce a data dump beginning with

the XREFF number (corresponding to OSC). Then the following variables are dumped in order:

166
90 ZONE C 91 GEOM<NAME=NORTH)

92 CTRL<CWS=HEATN/HEAT=12)

schedule: i ZON TYP ON OFF DX R1 R2 R3

1 12 33 415 1 3514 *501###*###### 0.000

93 PE0(WS=0CCN/CAP=3)

schedule: 2 ZON TYP ON OFF DX R1 R2

1 1 33 415 1 3.000 131.800

94 LIT (WS=LITN/CAP=1 ,4)

schedule: 3 ZON TYP ON OFF DX R1 R2

1 2 33 415 4 410.025 0.000

95 EGP<WS=EGPN/CAP=1 .0)

schedule: 4 ZON TYP ON OFF DX R1 R2

1 3 33 415 7 292.875 0.000

R3

.500

R3

.200

R3

.300

96 MASS(C0NS=PTN-A/AREA=480)

HEAT TRANSFER SURFACE: 1 AREA INV

44.59 1 AZM CTILT

0. 0.000

ONV FSS FS6

-1 0.000 0.000

HOC THE THI

0.000 0 0

K

3QHE

1 GHI

1

R4 R5

0.000 0.000

R4 R5

0.000 0.000

R4 R5

.200 0.000

R4 R5

0.000 .700

101 SRF<EX/0F/BS/C0NS=RF-T/AZM=0/0RG=44»36»8/SIZE=41>8.95/TILT=26.6)

HEAT TRANSFER SURFACE: 5 AREA INV ONV FSS FSG

34.09 1 -3 .947 .053

AZM CTILT HOC THE THI

0. .894 3.339 20 26

K

7 GHE

32

GHI

37

surface:

VERTICES . 7

13 .411 8.534 3.660

13 .411 10.973 2,438

CA SA CT ST TRNS

1 ,000 0 .000 894 .448 0.000

102 AFS( AREA =0,1/EXP=. 65)

AIR FLOW SURFACE: 2 AREA EXP ZS ZT ,009 .650 3,049

.914 8.534 3.660

.914 10.973 2.438

DN OFF SI S2

33 415 5 5

C0S1 C0S2 F'TR ZONE

5 .448 0.000 0

109 0SC(TGF'=1)

OTHER SIDE COEFFICIENTS’, 1 HO TZP TAP CT CTP TGP WSP HTS

0,000 0.000 0,000 0,00 0.000 1,000 0,000 10

110

Figure V.12 Dump of zone data

167
NAME VARIABLE DESCRIPTION

HO RSSC(2 ,1) Convection coefficient

TZP RSSC(3 ,1) Zone air temperature part

TAP RSSC(4 ,1) Ambient air temperature part

HO RSSC(5 ,1) Constant temperature

TZP RSSC(6 ,1) Constant temperature part

TAP RSSC(7 ,1) Ground temperature part

WSP RSSC(8 I) Wind speed factor

HTS ISSC(9,I) HTS number of the base surface

Movable insulation also produces a data dump from the RSSC/ISSC

NAME VARIABLE DESCRIPTION

R RSSC(l.I) Thermal resistance of insulation

A RSSC(3 ,1) Outside solar absorptance

E RSSC(4 ,1) Outside thermal emittance

RGH ISSC(5 ,1) Outside roughned number

ON ISSC(6 ,1) Start date for movable insulation

OFF ISSC(7 ,1) Stop date

CTL ISSC(8 I) Control type or pointer to day-schedule

HTS ISSC(9 ,1) HTS number of the base surface

V.A.3 .7 RNOS = 7; dump of cross reference values

The matching of interzone partitions and openings can become difficult,

so the following dump has been provided (figure V.13). As the input

processor encounters interzone partitions (IZP) and openings (AFO) it checks

data in two match-up lists. If the IZP/AFO does not match one of the

entries in the list, it is added to the list. Otherwise, if it does match,

the matched element in the list is removed. This dump monitors that

process

.

The first interzone partition is defined at line 104. No match for

this IZP is found, so the number of unmatched IZP's is now 1. The far side

and near side zone names are CENTER and NORTH, respectively. The surface

area is 449.053 m^; the U-value is 8.5074 W/m^K; the number of temperature

CTF terms is 3; and the number of flux CTF terms is 2. These numbers and names will be used to find the matching description of the IZP from the

adjacent zone.

The air flow opening at line 105 also created an entry in the AFO

table. The count and zone names are similar to those used for the IZP. The

number are the opening area, flow exponent, and opening height, respectively.

The input processor continues to not find matches (lines 124, 125, 126,

148, and 149) or to match IZP and AFO (lines 127, 128, and 150). When a match is found, the reduced number of items IZP or AFO tables is reported as well as the HTS or AFS of the match. In this particular example, there is

a typing error in the name of the adjacent zone at line 148. This error prevents a match of both IZP and AFO. At the conclusion of input processing

168
this failure to match is reported as SEVERE errors. The data accompanying the error messages (produced by default) should be sufficient to determine the

incorrect or missing surfaces and openings.

104

105

SRF< IN/0P/BS/C0NS=PTN-M/AZM=180/0RG=0»24f 0/SIZE=44, 12/Z0NE=CENTER)

IZP - NO MATCH t 1 CENTER NORTH 49.053 8.5074 3 2 AFS< AREA=0.5/EXP=.50)

IZF - NO MATCH! 1 CENTER NORTH .04645 .500 1.829

124

125

126

127

128

SRF(IN/0P/BS/C0NS=F'TN-A/AZM=180/0RG=3»12>0/SIZE=41*12/Z0NE=S0UTH)

IZP - NO MATCH*. 2 SOUTH CENTER 45.708 4.8998 1 1 AFS(AREA=0.5/EXP=.50)

IZF - NO MATCH: 2 SOUTH CENTER .04645 .500 1.829

SRF< IN/0P/BS/C0NS=PTN-S/AZM=180/0RG=0> 1 2 > 0/S I ZE = 3 , 1 2/Z0NE = S0UTH

IZP - NO MATCH? 3 SOUTH CENTER 3.345 1.2406 4 2 SRF(IN/0P/BS/CON5=PTN-M/AZM-O/0RG=44»24.0/SIZE=44>12/Z0NE=N0RTH)

IZP - MATCH: NIZP = 2» HTS = 7 AFS(AREA = 0.5/EXF’=.50)

izf - match: nuafs = u afs = 3

148

149

150

» SRF ( IN/0F'/BS/C0NS = PTN-A/AZM = 0/0RG = 44» 12»0/SIZE=41 > 1 2/Z0NE=CETNER

IZP - NO MATCH: 3 CETNER SOUTH 45.708 4.8998 1 1 AFS< AREA=0.5/EXP=.50>

IZF - NO MATCH*. 2 CETNER SOUTH .04645 .500 1.829

SRF( IN/DP/BS/C0NS=PTN-S/AZM=0/0RG=35 12 > 0/SIZE=3, 1 2/Z0NE=CENTER

IZP - MATCH: NIZP = 2 i HTS = 17

PAGE 4 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/14. 06.33.00. 1.733

** SEVERE UNMATCHED INTER-ZONE SURFACES’.

ZONE FAR SIDE HTS AREA CONSTRUCT

CENTER SOUTH 16 45.708 PTN-A

SOUTH CETNER 28 45.708 F'TN-A

: SEVERE UNMATCHED INTER -zone openings:

ZONE FAR SIDE AFS AREA EXP zs CENTER SOUTH 6 .04645 .500 1 .8 SOUTH CETNER 10 .04645 .500 1 .

UNUSED LIBRARY NAMES (IF ANY):

DAY-SCHEDULE: NONE

DAY-SCHEDULE

week-schedule: const

** FATAL INPUT FILE NOT CREATED BECAUSE OF 'SEVERE' ERRORS

Figure V.13 Dump of cross reference values

169
V.A.4 LIBRARY REPORTS

The library data can be reported by library commands (2.1.3).

V.A.4.1 Day-schedules (DS)

Figure 14 shows typical reports for two day-schedules. A simple graph is

provided with the data. The first line of the DS report is the user defined

name (ON) and description (NORTH OCCUPANCY). The next line gives the schedule

number / array index (3). Then comes a list of hour numbers. Below these the

hourly fractions of full capacity are presented by a simple bar graph. Each

hour is three X's wide. The final line of a DS report is the hourly fractions

as a percent of full capacity.

ON l NORTH OCCUPANCY

3 5 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 19 20 21 22 23 24

1.0 +XXXXXXXXXXXXXXXXXX XXX+

+XXXXXXXXXXXXXXXXXX XXX+

.8 +XXXXXXXXXXXXXXXXXX XXX+

+XXXXXXXXXXXXXXXXXX XXXXXX+

6

.4

0

+XXXXXXXXXXXXXXXXXX

+XXXXXXXXXXXXXXXXXXXXX

+XXXXXXXXXXXXXXXXXXXXX

XXXXXX+

XXXXXX+

XXXXXX+

+XXXXXXXXXXXXXXXXXXXXX

+XXXXXXXXXXXXXXXXXXXXXXXX

+XXXXXXXXXXXXXXXXXXXXXXXX

XXXXXXXXXXXX+

XXXXXXXXXXXXXXXXXXXXXXXX+

XXXXXXXXXXXXXXXXXXXXXXXX+

+XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX+

100100100100100100 50 16 0 0 0 0 0 0 0 0 16 16 16 16 33 33 67100

0C : CENTER OCCUPANCY

4 » 1 23456789 10 11 1.0 ++

.8 ++ .6 ++ .4 ++

.2 ++

12 13 14 15 16 17 18 19 20 21 22 23 24

+

+

+ XXX XXX + XXX XXX + xxxxxxxxx + xxxxxxxxx + xxxxxxxxx + xxxxxxxxxxxxxxxxxxxxx + xxxxxxxxxxxxxxxxxxxxx + 0 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX+

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 17 17 67 50 67 17 0

Figure V.14 Day-schedule reports

V.A.4. 2 Week-schedules (WS)

The first two lines of the week-schedule report give the user defined

name, description, and the schedule number. These are followed by a list of

12 days: SUN through FRI on one line and SAT through SP4 lines below. Below

each day name is the name of the day-schedule in effect on that day. Below

that is the day-schedule number. Figure 15 shows three week-schedules.

170
0CCN *, NORTH OCCUPANCY

i

SUN MON TUE WED THU FRI

ON ON ON ON ON ON

3 3 3 3 3 3

SAT HOL SP1 SP2 SP3 SP4

ON ON ON ON ON ON

3 3 3 3 3 3 occc J CENTER OCCUPANCY

21

SUN MON TUE WED THU FRI

OC OC OC OC OC OC

4 4 4 4 4 4

SAT HOL SP1 SP2 SP3 SP4

OC OC OC OC OC OC

4 4 4 4 4 4 OCCS J SOUTH OCCUPANCY

3*. SUN MON TUE WED THU FRI

OS OS OS OS OS OS

5 5 5 5 5 5

SAT HOL SP1 SP2 SP3 SP4

OS OS OS OS OS OS

5 5 5 5 5 5

Figure V.15 Week-schedule reports

4.3 Materials (MATL)

The first two lines of the materials report give the user defined name,

description, and the schedule number. The thermal properties of the material

are given below the names (using the input subkey names) of those properties.

Optical properties are also reported when they apply.

MATERIALS S

GYP

1 :

J GYPSUM WALLBOARD

K.420

CP

.300

OTHER

D 45.000

R0.000 .7!

E.90

RGH

WD-S : SOFTWOOD

K,068

OTHER

CP D R .330 32.000 0,000

A.75

E.90

RGH

Figure V.16 Materials report

171
V.A.4.4 Constructs (CONS)

The first two lines of the construct report give the user defined name,

description, and the schedule number. The name and thermal properties of

each layer are given. The number and values of the conduction transfer

functions are reported. "Internal" refers to the Z functions, "cross" to

the Y functions, "external" to the X functions, and "flux" to the J functions. The thermal conductance and surface properties are reported as shown

below in figure 17.

Considerably more data is reported for transparent constructs. Figure

V.18 shows a sample report for a double pane window. It begins with a report

of the conductive properties. There is only one CTF because the layers have

no thermal mass. Then the optical properties are reported. The transmittance

reflectance, and absorptances of the window are reported for 16 evenly spaced

values of the cosine of the angle of incidence and for diffuse radiation. The

program computes polynomial coefficients to approximate the angular dependence

of these properties. These fitted values are reported for the window transmit

tance and absorptances at the outer and inner surfaces of the window.

PTN-S *. PARTITION - STUD AREA

4!

DESCRIPTION OF CONSTRUCTION

LAYER THICKNESS CONDUCTIVITY DENSITY SPECIFIC HEAT RESISTANCE

FEET BTU/<HR*FT*F> LB/FT**3 BTU/(LB*F> HR*FT**2*F/BTU

GYP .0521 .420 45.000 .300 0.000

WD-S .2920 .068 32.000 .330 0.000

GYP .0521 .420 45.000 .300 0.000

5 CONDUCTION TRANSFER FUNCTIONS OF ORDER 2

TIME INTERNAL CROSS EXTERNAL FLUX

1 1 .53034770 ,00326766 1.53034770 .58886750

2 -2.02560683 .05324329 -2.02560683 - .03735637

3 .62257626 ,03923376 ,62257626

4 -.02925375 .00229484 -.02925375

5 - ,00001205 ,00001179 - .00001205

THERMAL CONDUCTANCE = ,219 BTU/<HR*FT**2*F)

OUTER THERMAL ABSORPTANCE = .90

INNER THERMAL ABSORPTANCE = .90

OUTER SOLAR ABSORPTANCE = .75

INNER SOLAR ABSORPTANCE = .75

OUTER SURFACE ROUGHNESS =R0UGH

Figure V.17 Constructs report

172
WDU2 : 2 PANE WINDOU

5 * DESCRIPTION OF CONSTRUCTION

LAYER THICKNESS CONDUCTIVITY DENSITY SPECIFIC HEAT RESISTANCE

FEET BTU/<HR*FT*F) LB/FT**3 BTU/<LB*F) HR*FT**2*F/BTU

SF'DS 0.0000 0.000 0.000 .200 .024

B0.0000 0.000 0.000 .200 ,910

SPDS 0.0000 0.000 0.000 .200 .024

1 CONDUCTION TRANSFER FUNCTIONS OF ORDER 0 TIME INTERNAL CROSS EXTERNAL FLUX

1 1.04471375 1.04471375 1.04471375

THERMAL CONDUCTANCE = 1.045 BTU/<HR*FT#Kc2*F)

OUTER THERMAL ABSORPTANCE = .90

INNER THERMAL ABSORPTANCE = .90

OUTER SOLAR ABSORPTANCE = .75

INNER SOLAR ABSORPTANCE = .75

OUTER SURFACE ROUGHNESS =ROUGH

OPTICAL VALUES

LAYER TRNS IR FTRN TRNS

SPDS .860 1.520 0.000

SPDS .860 1.520 0.000

REF

ANGULAR DEPENDENCE OF VALUES:

COS< THETA)

.0625 .1250 .1875

transmittance:

REFLECTANCE

ABSORPTANCE:

ABSORPTANCE*.

.0563

.8314

.0872

.0251

,1548

.7109

.0975

,0368

.2639

.5932

.0982

.0447

FITTED VALUES FOR LOADS CALCULATIONS*.

transmittance:

OUTER ABSORPTANCE*.

INNER ABSORPTANCE:

.0568

.0355

.0249

.1540

.1002

.0371

.2643

.0971

.0446

ANGULAR DEPENDENCE OF values:

COS ( THET A ).5625 .6250 .6875

transmittance:

reflectance:

ABSORPTANCE:

ABSORPTANCE:

.6743

.1832

,0811

,0615

,6962

.1639

.0788

.0611

.7117

.1511

.0767

.0605

FITTED VALUES FOR LOADS CALCUL AT

ons: transmittance:

OUTER ABSORPTANCE?

INNER ABSORPTANCE?

.6742

.0811

.0615

.6963

.0788

.0612

.7118

.0767

.0605

2500 .3125 .3750 .4375 .5000

3705 .4647 .5415 .6003 .6434

4830 .3875 .3109 ,2532 .2119

0959 .0926 ,0893 .0862 .0835

0507 .0552 .0584 .0603 .0612

3708 .4645 ,5412 .6004 ,6436

0944 .0932 .0906 .0859 .0822

0505 .0553 .0585 .0603 .0611

7500 .8125 .8750 .9375 H o o DIFFUSE

7228 .7308 .7366 .7409 .7440 .6554

1429 .1380 .1352 .1341 .1341 .2089

0747 .0728 .0709 .0691 .0673 .0782

0595 .0584 .0572 .0559 .0546 .0575

7228 .7307 .7366 .7410 .7439 .6554

0747 ,0728 .0709 ,0691 ,0673 .0782

0595 .0584 ,0572 .0559 .0546 .0575

Figure V.18 Construct report for a window

173
V.A.4.5 Control profiles (CPFL)

The first two lines of the control profile report give the user defined

name, description, and the schedule number. The next line is a list of the user defined control temperatures followed by a line of matching fractions

of full capacity. The number of control points is determined by the user subject to array dimension constraints. Figure 19 shows this report for two

control profiles.

CONTROL profiles:

PI

tmp:

cap:

: HEATING SETBACK

60.000 62.000

1.000 0.000

tnp:

cap:

: STANDARD HEATING

68.000 70.000

1.000 0,000

Figure V.19 Control profiles reports

V.A.4.6 Control day-schedules (CDS)

After the two line of standard heading information the CDS report gives a list of 24 hours (on four lines) with the profile name and index reported below

each hour. Figure 20 shows a CDS report for two control day-schedules.

V.A.4.7 Control week-schedules (CWS)

The first lines of the control week-schedule report give the user defined

name, description, and the schedule number. These are followed by a list of

12 days: SUN through FRI on one line and SAT through SP4 four lines below.

Below each day name is the name of the control day-schedule in effect on that

day. Below that is the control day schedule number. Figure 21 shows two

control week-schedules.

174
CONTROL day-schedules:

HN : NORTH HEATING

i

i: 2 3 4 5 6

PI PI Pi Pi Pi PI

1 1 1 l l 1

7 8 9 10 li 12

P2 P2 PI PI Pi PI

2 2 1 1 1 1

13 14 15 16 17 18

PI PI PI PI P2 P 2

1 1 1 1 2 2

19 20 21 22 23 24

P2 P2 P2 P2 PI PI

2 2 2 2 1 1

HC J CENTER HEATING

2

1 2 3 4 5 6 PI PI PI PI PI PI

1 1 1 1 1 1

7 8 9 10 11 12

PI PI PI PI PI PI

1 1 1 1 1 1

13 14 15 16 17 18 PI PI PI PI P2 P2

1 1 1 1 2 2

19 20 21 22 23 24

P2 P2 P2 P2 PI PI

2 2 2 2 1 1

Figure V.20 Control day-schedule reports

CONTROL UEEK-SCHEDULES:

HEATN J NORTH HEATING

1 : SUN MON TUE WED THU PRI

HN HN HN HN HN HN

1 1 l 1 1 l SAT HOL SPl SP2 SP3 SP4

HN HN HN HN HN HN

1 1 1 1 1 1

HEATC J CENTER HEATING

n SUN MON TUE NED THU FRI

HC HC HC HC HC HC

2 2 2 2 2 2

SAT HOL SPl SP2 SP3 SP4

HC HC HC HC HC HC

2 2 2 2 2 2

Figure 21. Control week- schedule reports

175
V.B LOADS REPORTS

V.B.l DEFAULT REPORTS

Sample default output of the loads calculator program is shown in figure

22. The loads calculator is designed to be recompiled to match the specific

problem being simulated. The user may decide to store different compilations

on tape. Therefore, the first action of the loads calculator program is not

to print the maximum available array space so the user can determine the

capabilities of the program by executing it, even without a simulation input

file (SINPFL). The names for the array sizes match those reported by the input

processor as described in V.A.l and VI. C. If the user has attached a SINPFL,

the program prints the array space required to solve the current simulation.

If insufficient space is available, a warning is given, and execution is

terminated. Otherwise, simulation begins. If the available array space is

much too large, it may be desirable to compile so that just sufficient space is

available and charges for program size during execution are minimized. During

the calculation of the solar gain multipliers, two other array requirements are reported: the shadowing combinations (CMB) and homogeneous coordinate space

(HCS). These sizes depend on the number of surfaces, the shadowing algorithm

(3.1.2)

, and the specific arrangement of surfaces and so they cannot be known

before program execution.

The next default report is shown as page 2 in figure 22. It describes the

calculational effort used to determine the building loads. First, the temperature and flux history initialization period is reported. The execution time

for initialization can be determined by comparing the completion time with the

start time (which was given with the page 2 header). Initialization proceeds

until load and temperature extreme values for two successive days are within

the convergence limits. In this example that required seven days. There were

635 surface and air heat balances, or about 3.78 iterations per hour. This

number can be reduced by widening the convergence limits. That will also

result in fewer days for initialization. Wider convergence limits tend to

change peak values more than they change the total loads. There were 2181

Newton's method iterations to compute air flows. That is about 3.43 iterations

per heat balance iteration. There were no heat balance iterations which failed

to converge. Failure to converge may be due to an inadequate iteration limit

(3.1.3) or to cycling between points on two different segments of a control

profile. The loads for that hour may or may not be reasonable. Check the

peak loads (below) for impossible values. Similar information on time, days,

and iterations is given for the simulation period.

The final summary of building loads is presented as page 3 of the example.

The report is headed by three descriptions: project (1.1.1), location (1.3.1),

and weather (1.5.1 or 1.6.1). Then the following values are presented for each

zone: Total heating and cooling requirements, peak heat and cooling loads,

maximum and minimum zone air temperatures, hours at peak heating capacity (HX)

,

other heating hours (HT), ventilating hours (V), cooling (below peak capacity)

hours (CL), and hours at peak cooling capacity (CX). Building-wide values are summarized by the line labeled "TOTAL:" These values include the total heating

and cooling requirements for all zones, the peak coincident heating and cooling

176
loads, and the maximum and minimum of all zone temperatures. The hour and day

are reported for the occurrence of the peak loads and temperatures. In the

example, there Is no time reported for peak cooling since there was no cooling

load.

PAGE 1 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/17. 05.38.06. 3.004

MRLP MAXIMUM ARRAY DIMENSIONS!

zqn: 4 SRF

!

36

HTS J 36

AFS 5 24

cgs: 16

GTP 5 4 TFH * 512

CTF! 192 ssc: 16

dsh: 16

wsh: 16 con: 16

pfl: 8 cds: 8 ows: 8

MRLP ARRAY SPACE USED!

zon: 3 srf: 32

hts : 32

afs: 10

cgs: 12

gtp: 1 tfh: 283

ctf: 140 ssc: 3

dsh: 11 wsh: 10 con: 11 pfl : 2 cds: 3 cws: 3

REQUIRED CMB = 82

REQUIRED HCS = 10

Figure V.22 Default loads calculation output

177
PAGE 2 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/OP/ 1 7 • 05.38.09 3.469

BEGIN TEMPERATURE AND FLUX HISTORIES INITIALIZATION

INITIALIZATION COMPLETE AT TIME 5.576

7 DAYS SIMULATED

635 HEAT BALANCE ITERATIONS

2181 AIR FLOW ITERATIONS

0 ITERATIONS DID NOT CONVERGE

SIMULATION COMPLETE AT TIME 7.867

1 DAYS SIMULATED

100 HEAT BALANCE ITERATIONS

335 AIR FLOW ITERATIONS

0 ITERATIONS DID NOT CONVERGE

PAGE 3 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/17. 05.38.17. 7.868

BUILDING LOADS FOR

THERMAL MASS TEST - SIMULTANEOUS ZONES* DIRECT SUN

COLUMBIA* MO.

MILD WINTER

TOTAL TOTAL PEAK PEAK MAX MIN

ZONE HEATING COOLING HEATING COOLING TEMP TEMP HX HT V CL CX

( NBTU

)

< N B T U ) < KBTUH

)

(KBTUH) ( F

)

(F)

NORTH 52.29 0.00 10.300 0.000 69,26 61.89 0 11 0 0 0 CENTER 1.45 0.00 1.292 0.000 73.00 64,01 0 2 0 0 0 SOUTH .56 0.00 .563 0.000 77.64 67.78 0 1 0 0 0

total: 5.430E+01 0, 10.863 0.000 77.64 61.89

MAX HEATING OCCURS AT HOUR 7 ON 2 1 FEB

MAX TEMP OCCURS AT HOUR 18 ON 21FEB

MIN TEMP OCCURS AT HOUR 6 ON 21FEB

Figure V.22 (continued)

178
V.B.2 NUMBERED REPORTS

Several reports and data dumps can be requested by specifying report

numbers (1.2.1).

V.B.2. 1 RNOS =» 8; Dump of SINPFL as read by loads program

This is a dump of every value transferred from the input processor to the

loads calculator by the simulation input file (SINPFL). It includes all project

data except the weather and can, therefore, be rather long. Figure 23 for a SINPFL dump of the sample problem data is four pages long.

The SINPFL dump begins with a dump of variables which can be described as run control data. Refer to VI. C for a description of the individual variables.

Next comes a dump of library data beginning with the day-schedules. The data

for each day-schedule consists of the array index, the schedule name, and 24

hours of capacity fractions expressed as percents. The week-schedules are dumped in a similar manner. Each line describes one schedule and consists of an array index, the schedule name, and 12 pointers to day-schedule array

indices

.

There is no data for materials. All materials have been used in constructs.

The headings for the constructs data are:

NAME VARIABLE DESCRIPTION

NT NTRTFC

PE TRTFPE

PC TRTFPC

PI TRTFPI

NF NFRTFC

PF FLRTFP

XO CTFXO

Y0 CTFYO

ZO CTFZO

AO OSABS

E0 OTABS

AI ISABS

El ITABS

VF IVABSF

U UVAL

R 0R0UGH

W WTYPE

Number of temperature CTF terms

Pointer to external (X) CTF terms

Pointer to cross (Y) CTF terms

Pointer to internal (Z) CTF terms

Number of flux CTF terms

Pointer to flux CTF terms

X CTF for time=0

Y CTF for time=0

Z CTF for time=0

Outside solar absorptance

Outside thermal emittance

Inside solar absorptance

Inside thermal absorptance

Multiplier for diffuse solar absorptance

Thermal conductance of construct

Outside roughness number

Pointerr to window array index

The conduction transfer functions are listed directly from the CTF array

at ten numbers per line. The construct pointer values (PE, PC, and PI) point

to the location immediately before CTF location. For example, the X(l) value

of WL-S is -6.3074297 (PE = 7; therefore CTF index = 8). The X(0), Y(0), and

Z(0) values are stored separately. The window pointer, WTYPE , points to the

array index of the window coefficients. In this example, there is only one window type, but each type has four line of data: one each for transmittance

179
and outside, inside, and shade absorptance. Each line of data consists of

the window type index, data abbreviation, value for diffuse radiation, and

polynomial coefficients for angular properties.

Control profile data consists of the array index, profile name, number of

control points, and control temperatures and capacity fractions. In the

example, the capacities for PI are 1.0 at 1=15.56 and 0.0 at T-16.67. The

control day-schedule data consists of the array index, schedule name, and 24

pointers to control profile array indices. The control week-schedule data

consists of the array index, schedule name, and 12 pointers to control dayschedule array indices.

Inputs (4.2) through (4.11) create scheduled loads and activities. Each

line of the scheduled loads dump consists of the array index, zone number

(CGSZON), type (CGSTYP), start and stop dates (CGSON and CGSOFF), schedule

pointer (CGSDF), all 5 values of RCGS, and zone names (CGSZON). See VI. C for

descriptions of these variables.

Next the surfaces involved in shadowing and solar gains (SRF) are described.

This consists first of the array index, number of vertices, and X, Y, and Z coordinates of the vertices for each surface. Then comes the subsurface data

previously described in V.A.3.5.

are:

The heading for the columns of data for the heat transfer surfaces (HTS)

NAME VARIABLE DESCRIPTION

AREA AREA Area of surface

Z ISENV Zone number

ONV OSENV Outside environment / far side zone number

FSS FSS View factor to sky

FSG FSG View factor to ground

SSC SSCPTR Pointer to special coefficients

K KPTR Pointer to construct data

THE TMPHPE Pointer to external temperature histories

THI TMPHPI Pointer to internal temperature histories

FHE FLXHPE Pointer to external flux histories

FHI FLXHPI Pointer to internal flux histories

AZM SFAZIM Azimuth angle (degrees)

CTILT CTILT Cosine of tilt angle

HOC HOC Factor for detailed outside convection

The special coefficient data consists of the array index and nine values

from ISSC or RSSC (see VI. C) depending on the type of data being described

(see also V.A.3.6). Special surface coefficients are stored at the bottom of

the array and movable insulation data are stored at the top.

180
PAGE

3

NBS

THERMAL

ANALYSIS

RESEARCH

PROGRAM

62/05/17.

05.38.07.

3.085

ooooooooooo o o ro ©orsps©©©©©©©

© < ** <r ro o ro oowisooooooo o ro >o n n o ro OOWO'OOOOO oo ©Min^NNNO rs H H O O>0 N-OO ©CO ©© O H «c H N N N © fs ^ H

©O'CNNCOCOO© © ^ h N N N c N ©©«CNWrt©COO© O h h M M N N C©

00'CNWK0©©©0 Ch H«n in N o©

©©c©oo©o© ©o © ro ©0©©©0©0©©0 © K ©©©©©©©COCO e ro ©O©©©©©©©©© © rO ©©©©©©©©©©© © ro ©©©©©CO©©©© © ro ©OOCOO©©©©© © ro ©©©©©©©©©©©

©©>c©©©©©©©© © ^ lo rs rs © ©©©©©©©©©©© © in in iv rs © ©©©©©©©©©©© © © ro

ro <r in >o n co o ©

ro^ifi'Orscoo'© ^ cn

L*)'Orvooos©^CN

M^-ll'OfVOOOsO^M

M^LI'ONOOO'OhCN

ro^jiTsorsCOOsO-iCNj

ro <r in>0 NCD 0'©-.(\

30©0©-«00 © © o o KNNNNNN f^NNfj

0'©©^aoo‘ 0‘ m rs rs O'

rs o o » ruj >o co © in ^

©CNOOCNO'COIf) in -r in ~ U*) CN QO oo©o*oo©ooo©

u.if)ininmroinminininin ©rsrsrsrx^rsrs rs rs rs rs

©©©©©©© ©©©© •-•©©©©©©©©©©© Lkl O' D« »> &> O' &. > (h O' O' O'

©©O©©©© ©©©© •-•inininintninin m inn \n ©rsrsrsrsrsrsrsrsfsrsrs

©©o©©©© ©©©© o©©©©©©© UO'OO'O'O'OO' O' O' O' O'

©©©©©©©©©©© oinmifiininmin in in © ©

©rsrsfsrsrsrsrs rs rs rs rs

co<r<r<rco^ij,)0'^nro <* co O' co cn a, "Q >o cd if) ^

©(N>o«r>oO'«r©rocoinin

<raococoinincDroro(Nro

ro ro c in ro o cc o © in lo © ©

r. o c h rv c in «* o © © CN © in © O' (f)© h«o ©

^ L*) 'OrO^’TCDHMM^CO ©OOCLCsiCDO-rsCCOO

©CDlf)'T«COo-'C CD CC ro ro (N<raicoif)if)'Orororsrs

ro L.'COTNO'inTiniiT-'O

Cl. ~«(\roro«r'Ofscc-<ro

U. CN — CN © ^ ID ©©©©©©©©oo© © © ro ©©©©©©©©©©© © © ro ©o©©©©©©©©© © © ro ©©©©©©©©©©© o o ro

ro^if)sOrsCDOs©s-<CN

ro«rmorscoo'©»-<(N

ro o* in >o rs co o o ** cn

ro <r in o rs coo*© cn

M^bTronoocc ro cn ro O' u. csi ro ro «r n is co © rj

(j (\l ^ CN O' 0s ^ (N fH O' ^ fx

1 a. ^(Mr'jro^WNNO'N

ujosHioo>0"CO"ONin

U_ CNCNfOrO^ <0 N CC -•

>0 ©

in ©

UD ^

© ©

Os©

• CN © <

© © ©

© O ©

^ © ©

© © ©

©©©©©©©©©©© © © ro ro<r ut 'O rs co O' o cm rj«r»-'«TOCN'CcNrocDrs

ii ii h u h n ii n ii u ii n ii 2

o o

u 32

cn ^ WOO Cl © ©

-J 2 2

O U U

cn i— i

CN

CD H- _J © »-H ©

2 X CCi o <r i-

-J 2 X

CD CD 3

-I -I O

© © -J II Ii a r-< ©

cn ro O CD CD © © © 2 2 2

u u cj © © ©

III UJ J

I 2 -J cJoz> 2 ucn:zucn 2 ucn

CO ZliOQOjJjlilUlil

20 CO 2 O CO Z O COCO UUL)l-KWiiIu.2 oo u -• -« *“• © © ©o OO O —I _J -J UJ UJ liJ u

© CO UJ 2 I

I h jo i i rj r r- h i x a

I l 2 2 3 © I

| 2 © © Jjr*wwiiiU,wjj 33iiu.3iiCIilOw

>-»Hf'iro<rij,)'ONCDt)'Ow uj»-«CNroo‘in'OfscDO'© 2 ~«cNro^in'0rsa)0'©«-<

Figure V.23 Dump of SINPFL

181
TRANSFER

FUNCTIONS:

1

-2.5278906

.0007745

.0585821

.0000064

-3.9713113

.0023383

.0005898

-6.3074297

2.1913321

-.1701522

mcNi'OtNOrvCNo cm *i rs nNOo^in’OCD o^fS'Oin

ian oo« ro Nw © © * ro ro m h f inin o on hoomn rsjM'O^oaoin'O o ogo 10 ooorso'O'O&oO'O o © m oo cm NrtNOIO'OODOD 000^00

(N K M H

I ««* I ^

I

I Ps I GO

I

o- o- v (h o cd < n in n *o ifi <

'ooo -o rg co oo in © O' © © rs

«o < in O' in rs 9-« a, n w >o o do 'Oo ro in rs o* o- O' o- o *-« © rg oo Nin >o o o t: © © © © in oo m^ino'Oc oo'Oocn 00 O (N CD O H f O © *h © PO

1 I I

ro ~ i ^ H

I I

< o 1 O*

1 CM

1 CM

po rg O' <r H O' PM PO Ps o- -4 4T O' T- O

PO PO rg rv rg ro ro o- o O' H O' o O' ~

o o CM O' © © © rv

cc o CM po m © © 00

PO o © ro © © © rs

in 1 rs rg 1 'C CM

i

i

o- <r in O' © 00

O' O' CD CO 94 rs O PO o- o- ro 00 oo in

00 O' O' ^ © 94 O' rg o o m © O' o CM -4

9^ © rs © rH o o ^

00 o rg O © © Tl CO

*o *0 | rl

1 PO

1

rg O' ro rv O' •o © *H

oo ro rg © CD 'O o' in

rg po rg © ro © fs N

o o O' ^ 00 © O' r* in © 4T © rg ©

PO © in O O' © ro «-> © © © T © Ps O'

CO

i 1 *4

1

O' — © rv so ro rg rv © in ro O O' © fS ^

<, O' o- rg 9i © O' ^

O' ro (M ro tr © in o'

PO O' 00 o © © > U") ro © c © rs \n © o 00 © 9H © ro ©

94 1 1 in i

o rg 94 Pv O' IM 00 "C © rs in ro 9-f rg CD O' © o- <r © (M © <1

*r O' co CD 9i © 94 CO

'O rg 94 O' O' © O' ©

rs © © co ro © in ro

IM © © 9-« ro © ro o

rg

i PO fv

1

1 'O

i

CM *h © «r rH rg ©

co «r 00 © oo co © ro

*T O' *T o «r CD © oro © rs © 9H in © rg

O' © rg o o © o ro © © o o © © © ^

o © ** © © © ©

i 'O i rg

ro

1

i

in CM rg ui O' o- po

co o* o < © O' o rg

ro < in fM 91 'C © o

>o rg rs O' sO rv © pm

O' *h T—

1

O' CO ui © O'

O' © O' rg cm rg o ro rl © o- o © © oPO 9* 9*

•0 CD ^ h

in N M I (\ o ^

O'N O

O o CM

O' 00 GO

-4 CM ^ ^ I

I *C O < **

in n o i O (N H

O' U*5 O^

in CM GO 0^ rv os K N I")

I CM

PO fM CM Hi

CM in ffl I ^ O' o

in o- ©

hino* 0 in o- inn w

CM I

I M (N M h

Nin o* i O' oo 0

^ H 00 O' rg O' MOT no h

1

CM H M H

OCJ CD I OC PO CM C *0 *

ro ro •

o

I

in in n w

T'fl N I m pm in

oo CM PM

ro <r in

CM

co m* O' ^

n pg *o i pv in O'

CM P'5 N woo

*H I

o o m *-• hn n i in rg ro

PO CM O'

00 *h CM

<r i

im < cg w N rg oo i r4 m 4H

oo -c h

Pv Hi <T O I

O' 00 CM hi h t m i cm rg o O M T

t h rg

o* i

co rg th WHO

o o

o o

o o

o c

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

o o

in o

CC 0C CC CC XX XXLj Id Id Id X X X X

p- >- »-->- p— »— »— p— I— >— »— Ctcrz Z Z Z X =5 X D co oou uiiducoao Z2 Z Z (J (J (J (J 05 05 05 05 oo ooo ooooooo oo ooooooo OO ONO © © rs © © © PO ooo ooo ooo

oo ooo ooooooo oo ooooooo oo (moo o rg o o o cn t oo ooo ooo

oo OOO ooooooo oo ooo ooooooo om cm ro © m cm ro © w cm po

4+0 004+ 0004+000 4+0 + 4+00 + 00004+0000

4+ • . • 4+ •••*••• 4+^4 004+ *4 O O 4+ *h O O

4+ P'5 4+ PO 4+ PO

4+ 4+ 94 4+94

•h o in in o in 1(5 h o in o oo cm rs © o rg n o o eg rg ino o com oooomooo

<r ro o cm t n o rg t n o n

o ^ 0' 9-4 in m o- cm in t rg in <r rs PO P'5 PO CM

i '-t rs cm rg in co ro po *o O'

u.mm ininm in in m in in in in o o' o* o* o- <r o- <r o <r o'

z po po po po po popopopoporopo O po PO ro ro ro ro ro ro ro ro ro ro

o O' O' O' © >0 m O' © m O' Hi in GO rs © Ui X U 05 Cu rg rg po cm rg po rg © © 00 ro rg ro IS CD © O' o U in PS in o -J u 05 HI >- 94 94 94 ro -0 O' o rs co o © © 'O rg Hi o © © © Hi 05 1 <1 P-

'O O' '0 © *h co © © © rg >0 U. • * • L. 1 z o

rg ro rg © o © O' © © © rg u. © O > Ld -J rg ro Ps fs © o ro © © © O' Id CC <x Id

rg © o n © rg ro © © © CO O Cu © 3 Z U 05 a pg 9H TH 9 rg rg rg fg PO

i oo H CM c w cn 3 p- <r <t <t o

a

z irgfOTin'ONoooHrgro h h h h h

_j _J J « <t «

O 94 CM OZCJ05 Q Ld Id Id

CC Cu ul iZXXX ccxxx

P— — P" z r-4 rg z h cm m z n cm ro o o o

u u o

i HCMMTingJNODCpOHrg

Figure V.23 (continued)

182
SURFACES

in is 05 o* cd o- >0 md m3 >0 o* o rs ® CD CO >0 '

0

>0 CD >0 © O’ CO 'O '

0

O o- •o o

o* © o* >0 >0 MD o’ o m o co GO nO 'O 'O CO © o- © O’ >0 *o •o <i o- -0 o

in CM CM CM 1 (N ro to ro ro CM 1 i o- o- ro ro

3. 4, 3.

1 CM 1 CM ro ro ro PO CM 10 1

HP in m IS rO is ro po CM CM N CM S3 -h GO 00 '0 M> CM M3 CM 'O © ro o «r o- M3 -0 © «o ©

** in cm pH o* in m ro ro O' PO >0 O' 00 00 >0 >0 PO >0 PO 'O o ^ © o- ^ >0 <0 © * o

PO 1 pH

pH ono rH pH

GO 00 rs rs 10, 7,

PO o- <r po ro

7.

3i

7. PO | CM I CM CM PO PO ro i

pH pH ,H ^ in © »H © pH © r-i pH ph © pH © r*» pH © © noin pH O 4H -MO© -4 —4

O' O’ O' O' rv © O' © O’ © O’ O’ o- CO O' © O’ O' © © O’ o- m rs O' in o* O' © © O' T

ro ro ro O' © © ro 1 ro ro ro CM © ro © i ro ro cm O' PO rs ro © 1 ro ro

pH -4 pH pH ^4 rH pH *H *•4 4-1 4H pH *-1 pH —4 -4

I

00 O' 4P © 00 © o- O’ O © © © 'C CD >0 M3 © © © © © © © 00 © O' o* © © © © ©

CD O' o- © © © O’ O’ O © © © <1 © 'C M3 © © © © © © © © © o- o- © © © © ©

O' CM CM © i © CM CM © ©

0, 0, PO 1 PO ro

0. 0, © © © © © t © CM CM

0. 0. 0, 0. 0.

MD © rs rs cm rs rs rs CM CM rs rs M3 © CM CM M3 M3 CM *C CM CM © ^4 © © © 'C <1 © M3 M3

M3 © O' O' in O' O' O' ro ro O' O' M3 © PO ro '0 M) ro ms ro ro © O' © © © 'O '0 © M3 'O

PO 10, 10, 1

,

10, 10, 10, rs rs 10. 10, PO

0, 7.

rs ro ro

7, 3, 7.

rs i i i i 3. 3. 0, 3. 3.

ph —4 rH rH in o rH © rH © rH rH rH © pH © rH rH © © r4 rH O VO ,H © rH rH © © rH rH

<r O' O' O' rs © O' © *T © <r «r o- 00 O' © O' O' © o p- C in rs O' in o’ O' © © O’ O*

ro PO PO O' © © ro i ro ro ro CM © ro © i ro ro CM O' ro cm ro © 1 ro t*l

1 ** tH rH ** ** r4 rH -4 rH rH 4*4 H

CD © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © Z © © © © o © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © o © © © © © © © © © © © © © © © © © © © © © © © © © © ©

© o* <t © co © o- o* © © © © M3 CD O M3 © © © © © © © 00 © <r t © © © © o cc

00 O* «r © © © o- O' © © © © O © 'O >0 © © © © © © © © © «r nr © © © © © r— © © © © © © © © © © © © © © © © © © © © o © © © © © © © © © © ©

O* CM CM © i © CM CM © © © © P0 1 ro 3, 0. 0, 0, 0, 0, © © 1 © CM CM

0, 0, 0, © ©

u. in in in © © © © © © © © © © © © © © © © © © © © © © © o © © © © ©

L. rH rH o o- O' O'

M3 © rs rs cm rs rs N CM IS cm rs M3 © CM CM S3 M3 rs CM 'C CM © rH © © © M3 •O M3 © M3

M3 © O' O' m O' O' O' PO O' ro O' *0 © ro ro '0 M3 ro ro S3 P0 © O' © © © M3 S3 M3 © M3

ro P0 ro © © © © © © © © © o © © © © © © © © © o © © © © © © © © ©

PO © © © rH © © © rs © is © PO © is is ro ro 7 7 3 rs © © © © ro ro ro © ro o ro ro ro

rH —4 H rH rH rH rH

© o © rH O rH rH © © ^4 © © tH rH -4 rH © pH © ^4 © © >0 © © © rH pH © rH © CM © 0 0 CM rs O' in 6 7 CD O' o CM rs o- m md is CD o* © pH in s> rs CD O' © pH rs © © © o- O O' O' O' © © O' © © M3 o* O' O' © >r o p © © M3 in © in o* O' © o © cn i pH pH pH ^ pH pH rH rs CM rs CM rs rs rs rs rs ro ro ro © 0

0.

P0 ro ro © © ro © © ro © MOM o © ro CM © CM ro © ro ©

1

*“c rH rH H *4 rH rH rH pH © 0 0 CM ro O' in S3 rs CO O' © rs ro o' in md rs CO O' © pH ro «r in o is CD CK © «H ri CD pH pH —4 pH -4 rH pH rs rs CM CM rs rs rs rs rs ro ro ro

in IS 03 O' CD O' MD M3 MD o- 'O © rs CD CD CO S3 MD S3 M3 CO © O' 00 O' M3 >0 M3 S3 M3 O' ©

rH rH O' O' © O' M3 MD M3 O' <1 © in © 00 CO S3 M3 S3 M3 CO © O' © O' M3 M3 M3 S) M3 O' ©

I— CO 00 O' © © © 03 CO © © o © © O CO CO © © © © o o © © © CO CD © o o © ©

in CM CM CM 1 rs ro ro ro rs ro 1 O' 1 O' 4 3 3 3 3 4 i CM 1 rs 3 3 3 3 3 CM i 03 O' <r Ch © © © O' O' © © © © © © O- O' © © © © © © © © © O' O- © © © © ©

O' O' oo © © © O' O' © © o © © © O' TOO © © © © © © © O' O' © © © © ©

i r H r pH *4 1 rH - rH rH r i - r - 1

in in rs ro is ro ro rs rs CM rs M3 •h CD 03 S3 M3 cm rs *o M3 © ro © o* O' 'O S3 M3 © ©

rH in cn O' rH O' m in ro O' ro ro 'O O' CO 00 S) M3 ro ro >o >0 © ~4 © O' 4T MD S3 M3 © © o* «r oo © © © O' O' © © © © © © O' O' © © © © © © © © © O' O' © © © © © U O' O' O' © © © O' O' © © © © © o o O' © © © © © © © © © O' O' © © © © ©

ro 1 -pH © CM © co 8 7 © 7 7 ro o- 4 3 3 7 7 3 ro i rs i 2 2 ro 3 3 1 © 00 CD o' © © © CD 00 © © © © © © 00 00 © © © © © o © © © CD CD © o © © ©

rH rH

1 1 1 1 1 1 1 1

1 pH 1 1 1 1 1 1 1

1

1 1 • 1

i i •

i © © © 4H S3 rH © © © © -4 rH -4 rH © pH © © © MD © © o rH © © <x © © © © © © © © © © © © © © © © © © © © o © © © © © © © © © © ©

o © © O' S3 O' O' O' © © O' © © M3 O' O' O' © O' © O' © © MD in © in O' O' © O' © 03 © © © © © © © o © o © © © © © © © © © o © © © © © © © © © © © ©

© © © © © © © © © © © © © © © © © © © © o © © o © © © © © © © ©

i • © ro ro ro ii ro i i ro 1 ro i ro i i ro rs CM ro 1 ro 1 rH SP pH pH ** 1 1 o © © © © © 1

1 ^ 1

1 1 © © 1 1 ©

1

1 1 1 i 1

1 ©

i

i

<E © © © o © o © © © © © © © © © © © © © © © © © © o © © o © o © ©

o o © © o © o © o © © © © © © © © © © © o © © © o © © o © © © © © © © © o © © © © © © © o o © © o © © © o o © © © © o © © o © o

O' O' O- O' O' O* O' O' O' O' O' O' o- o* O' O- o* O' «r O' O' o- O' O' O' O' *T O' O' O' O' O’

1 pH pH - - - - -

1

1 r 1 1 1 1 - 1

1 1 1 1 1 1 - - ii

r-4 cm ro "T in sd 00 O' o rs ro o' in M3 rs 00 rH rs ro O' in M3 IS GO O' © CM rs ro O' in S3 is 03 O' o pH rs ro 4T in S3 is CD O' © rs ro «r in s> rs 00 O' © pH rs rH rH rH 4 rH 4 pH rs rs rs rs rs rs rs rs rs rs ro ro ro *4 pH pH rH pH rH rH pH tH rs rs CM rs rs rs rs rs rs

Figure V.23 (continued)

183
HEAT

TRANSFER

SURFACES?

AREA

Z

ONV

FSS

FSG

SSC

K

THE

THI

FHE

FHI

AZM

CTLT

HOC O -O'OOO^^-OOOOOtNM V^OOOOOOO •0'000*, «

, ©0©0© onnconoooonoiflintPJOooooMOMncDMOoooort

owrojnM'OOoo^oininw'Oooooo^owwinw'Ooooo^

OOOOO'O'OOOOOOO^O'OOOOOOOOOOO-^'OOOOO O OOOCOGDOOOOOOO GOGOOOOOOOO 000000300000

O I I

I I I I ^ O I I I I I I I O I I I I I I 1 ~

I I I o o o o o

rs

CNI o o

O GO o o o ooo rs o

^ rg o o

00 o00 o o

00 00 o o o

00 oo o o o

rs O' o

00

»h rs oo oo rs rs

*h ro «r

00 ^ to

in >o oo 03 O' cs (^JC^l*•0'^0'<r'O^^Isooa^^srsO'*o•«^*, *h rg rg n m ^ ^ 'Ors isrsoco^^rgrsjroin

^ CM rg ro

^ -o co o rg o «r Oho co ro in rs *h O' *r -h O' ^rg»H -ooo'Org'O^-O'O'O-© ^m^min'Orscoo'O' ©rg~rgmro«-'OrsrsiscD©~<<Nrgrgroin h h M rg hh^cnnhhmmcvi

o co rg 0 <r co ro co -h rs *h in h to m in *h >o ^ <r o o-cocN'0 <rcoO'0 ^ro

THCN^r-cininrscDO'O' o ^ rg rg ro ro m rs rsrsaoo'HHTHrgrgro*- ~ r-« ^ *h *h *h h h h rg rj rg rg rg rg

o rgcoco o mh m ©m rs O' in inrsoo o © h >oo iNcoooorgroin'O^'O

rg o- ro in in 'O oo co O' O' *h ^ rg « ro <r <r rs is rs rs o» *h rg rg m ro ro

•“* »h rg rg HHHHHHHHtNHnrgrgrg

ro th in rg rs co O' O' O' o ro in is oo ro <r cs cs o © ro **mrgrscoroo, 0' 0'»H

ooooooooo'oooooooooooinoooooooooo^-

o ooo id inr- o oo © © © m in fr- om in in o o ininoomin©© l-OOO© OOOlfllilhl-OOO minooinininoo mm©

CL CL

UJ z z UJ o o o UJ H L- L- —

o o o 2 2 3 CL 2

o o o <c UJ O O UJ

• • • 2 CJ 03 2 o

o o o

CL o o rg o o fO - o o rg

I- o o o CL o o ©

o o o o o o ooo © © o o

• • • rg o o o o o © O © o ©

tH HH W CI3 o o o o o O o © o o o

O ooo 1 o o © i i ©

li. o o o o o o

o o o

• * • o CO o O CD © © © 00 o

o o o tH o «r o © *T © © © <r ©

03 o «r o © «* © © © o* o

O

CJ —

«

o tH O o tH 1 ©

o o o li. 1 I o o o o o o

o o o O' o o ro o* © © «r © ©

'O rs rs n rs rs rs 'O rs rs © OOO N OOO ooo

ooooinmoooooooominoo o m in in O'O'^inmo o in in O' O' rg

£>» rs o o o o ooomin'orsooo

rg ininooininino'&'HHiny3o

o o o o o o HMnMWMrgrgMg, HMMMnnMH(NN i i i i i i i i i i i i i i i i rorororororgrgrgrg

i i i ii ill

ooo rg i/in h s ro ro rg in ro rgoco^rgoDOorgoco

ooo cn HMH«r^HHHrOH

isl

• • • ooo

-« h h h ^ ,h th th ^ rg rg rg rg (N rg rg eg rg rg rg ro rororororororororo ro

O' rs rg ro ck o in m in in O' o in O' o- c m h H NMrochO'HViniDin ii3<rNNOvOHHOiDNHO’rNroo'0'OOin^g, rgo^, NroHHo

o ro rg «r n O' h h o c rg h «r rg in ro o w in O' ^ osM^rgyironHo.

o- ro ro ^ HH«r <thh « <r «r h H <r <r ro ro <r *h

03k o o o

2 0 0 0

u ooo

u o o o

Li. U.

uj ro ro ro ou

O o o o o o

cl. in in © m m ©

x 'O >o in -o o in

•• uj *••••*

03 U.

UJu

<tu.

cl g >o ro in rg ro i

n

3 uj C0O''<3ro0''O

03 CL H o t rg O <T <L O o O O o O

3

O

ooo o in in

in 'O >o

in <o ro O go O'

<r o ooo

o

o

in

in

'O

«ro

h rg ro v m >0 IS ^Hrgro<rb*3'0fsco0'0’-‘rg hhh h h h n h h rg rg rg rOg*b3>ON©0'OH

rg rg rg rg rg rg rg ro ro rgro u

u o in <r

0. HHH

03

CL

HH

<x

rg ro ^ Li >o rs ao O'

Figure V.23 (continued)

184

ZONE

RELATED

VALUES?

NAME

FSRF

LSRF

FHTS

LHTS

FAFS

LAFS

ZZ

VMULT

VCONV

1

NORTH

A

12

1

10

1

3

1.500

.0056

0.0000

2

CENTER

13

22

11

21

A

7

1.500

.0047

0.0000

3

SOUTH

23

32

22

32

8

10

1.500

.0055

0.0000
The headings for the air flow opening data are:

NAME VARIABLE DESCRIPTION

FAREA FAREA Effective flow area FEXP FEXP Flow exponent

ZS ZS Height of opening

ZV ZVMOD Factor for wind pressure calculation

FC0S1 FC0S2 Direction cosine

FC0S2 FC0S2 Direction cosine

PTR AFSPTR Number of adjacent zone (0=ambient)

NAME AFSNAM Name of adjacent zone

The zone related values consist of the array index, the zone name, the

indices of the first and last surfaces which are part of the zone, the first

and last heat transfer surface numbers, the first and last air flow surface

numbers, the height of the zone for pressure calculations, and multipliers for

visible and convective gains.

V.B.2.2 RNOS = 9; Zone description report

This report gives a description of each zone (one zone per page). It

begins with the zone name, for example, NORTH in figure V.24. Next is a listing of the scheduled loads and controls. The data is presented using

the input variable names. The surfaces of the zone are described next. The

first zone includes a description of the detached shadowing surfaces. The

reported U-values do not include surface coefficients. Finally, the air

flow openings are described. ZONE is the name of the zone on the other

side of the opening.
PAGE 4 NBS THERMAL ANALYSIS RESEARCH PROGRAM

DESCRIPTION OF ZONE NORTH

82/05/17. 05.38.07. 3.234

SCHEDULED LOADS AND CONTROLS

TYPE SCHEDULE

CTRL HEATN

PEO OCCN

LIT LITN

EQP/EL EQPN

SURFACES

FROM THRU

1 J AN 31DEC

1 JAN 31DEC

1 JAN 31DEC

1 JAN 31DEC

DATA

HEAT= 1.20E+04 COOL= 3.41E+09 RAD=0.00

CAP= 3.00E+00 ACT= 4.50E+02 R AD= .50

CAP= 1.40E + 03 RA = 0 . 00 RAD* .20 VIS* .20

REP=0 . 00

CAP= 1.00E+03 L AT=0 . 00 RAD* .30 L0ST=0.00

TYPE AZM TILT AREA U CONSTRUCT ZONE

DET. SHADE 180. 153.

DET. SHADE 180. 153.

DET. SHADE 0. 117.

ENVELOPE 0 . 90. 328.00 .049 WL-I

WINDOW 0 . 90. 40.00 1.045 WDU2

ENVELOPE 0 . 90. 24.00 .176 WL-S

ENVELOPE 0. 27. 366.95 .100 RF-T

ENVELOPE 0. 27. 26.85 .033 RF-I

INTERZONE 180. 90. 528.00 1.499 PTN-M CENTER

PARTITION 270. 90. 120.00 1.499 PTN-M

PARTITION 90. 90. 120.00 1 . 499 PTN-M

USER DEFND 180. 180. 528.00 .081 SLAB-C

AIR FLOW OPENINGS

AREA EXP ZS ZONE

.0186 .65 1.22 AMBIENT

.0093 .65 3.05 AMBIENT

.0465 .50 1.83 CENTER

FROM THRU TRNS

1 J AN 31 DEC .000

1 JAN 31 DEC .000

1 J AN 31 DEC .000

Figure V.24 Zone description report

V.B.2.3 RNOS = 13; Report of sunlit fractions

This report gives the fraction sunlit area for all heat transfer surfaces.

It begins with the date and solar declination and equation of time values used

in computing the solar position. The values of the cosine of the angle of

incidence on each surface and the sunlit fraction are presented for 24 hours on

the half hour. Nine values from ISSC or RSSC (see VI. C) depending on the They

are in the HTS number sequence. The sunlit fractions apply only to the outside

of envelope surfaces, so partitions and such cannot have sunlit fractions but are reported to maintain the sequence of surfaces.

186
V V N N V V N V

o o © © o © © O © © 'O © o © © © © © © © © O' © © © © © © O >0 © © © m © 0 0 © © © © © © © ©

» » at *• a. »

t-i >—

in 0^ O' >0 m sd >0 S3

1 1

1

1 ss oo CD in CN «r cn

<r o S3 in cn rs IN o

1

•

i i 1 \ V V V v \ V N V

© © © © © © \n © © © (N ©

© © © © © © «r © © © ©

© © © © © © in © © © m © 0 0 0 0 © ^ © © -* ©

» * •> » *• *

NH •—

t-t O' CD O' in '0 o >o in

| 1 1 1 CD CD a >0 <r cn <r cn

S3 -s >0 «r rs cn IN CN

* * • • • • • • n s X \ \ V \ \ \ N s \

© © h< © © © © © © ^ ©

© © 1 © © © i © © © 1 ©

© © © © © © © © ©

• • • • o © © © a-4 «-* © «-4 ©

o a. a. » •> a. a. •t at at CN t-i M t-i CD CD OH in O >0 * in

CN 1 1 1 1 CD 00 | >0 CN CN 1 CN

• aH *H <r CN CN CN

1

II * *

l * * *

LJ V s N V \ \ \ \ N N

z

*-* © © © © © O' © © © CD © ©

© © © © © CN © © © rc O ©

© © © © O O' © © © O' © ©

C © © © © © © a-t © ©

a. •» Z H *-« 00 O' S3 O' S3 S3 S3 >

c 1 1 1 1 00 CD in CD c\ cn u «-• o \n S3 cn rs S3 IN

• *

i 1 • *

1 1 \ \ N N \ Nt \ \ \ N \ N

ro

CN

COo \ \ \ \ \ N \ \ N N \ © © © © © © © © ** © ©

II © © © © o O' © O O O' © O

z © © © © © © © © © © © ©

o

-1 *+ 0 0 0 0 © © © © © ©

(J b- * •* Ul (J h-< >-< *-* O' O' in O' S3 S3 m 'O Cl <X 1 1 1 1 CD CD >0 00 - cn <r

>-• ce *0 *0 «r S3 rs in CN N

cn Li. • • • • • * • * o 1 1 i i u 1-H \ \ \ \ \ \ \ \ s \ N N

-1z © •“« © © © *-« © © © « © ©

3 © 1 © © © 1 © © © i © ©

cn © © © © © © © © ©

in •

rv * © © © © © i-i © ©

CD UJ . * at •» «-« CJ HH M Ok »-• in lO S3 in «r • z 1

1 1 1 CD 1 S3 © <T 1 CJ O'

cn i UJ *o «T CD IN CN CD z n Ci • • • . • • o 1 1 1 1 HH CJ

b~ -j z s \ \ N \ N N % N N N N

<x o M

-J LJ © © © © © © © © © © © o

3 a U- © © © © © © © © © © © ©

U w o © © © © © © O © © © © © z • <X HH UJ © © © © © © © *« 0 0 ©

u cn z * at . «t at * •t •t at at at at H o © O' >0 O' W © S3 S) >o o cn ro 1 1 1 1 n co ot CD © M <T CN «T O' z o •• •• in O CD •• IN S3 IN CD

»-H u o © • • • • —

• • a • 3 i i 1 aH 1

1 1 o a \

Ot UJ II \ \ \ N II \ \ N N 11 N N \ N

<z u. I H •• Ui •-* © o © UJ -« © © S3 UJ HH o © IN

cn CN <x z 1 © © © z i © © O z 1 © O CN

b- >—© o © M © © FN 1—© © IN

U- II <r b- • • * b~ o 3 o © © o © © ©

LJ a at at at at a *

cn b- U. ct 1—1 >-< DC m in O' O' cn hh m S3 C

- <T o 11

1 1 <X 1 'O CD CD <z 1 c-t <r Q Ci a <r S3 o a CN (N IN 3 z z z * . * z • • cn lC <x <i <i Lu o b- i— -

iZ u. cn \ \ \ \ cn N \ \ \ cn N \ N N

Figure V.25 Results of shadowing calculations

187

REQUIRED

HC
V.B.2.4 RNOS = 14; Report of shadowing combinations

Some surfaces of the building can never be shaded by others because of

various geometric constraints. TARP does a one-time determination of which

surfaces can possibly be shaded by others and stores the results to save

time in long term or multiple environment runs. The shadowing combinations

report for the example problem is shown in figure 26. Information is

presented for each General shadow Receiving Surface (GRS), that is, each

EXterior, Base Surface (4.13.2) of the building. Surfaces are referred to by

their SRF numbers. The first such surface is GRSNR = 4. For this surface

there is one possible shadowing surface (NGSS = 1), seven interior surfaces

which may receive direct sun through the window (NBKS = 7), and one subsurface

(NSBS “ 1) (4.13.2). A general shadowing surface (GSS) is either a GRS or a detached shadowing surface (3.2). The one GRS which might shade GRS #4 is SRF

#3. The detailed solar distribution within the zone must refer to the EXterior

of INterior (4.13.2) surfaces which are called back surfaces (BKS) during

shadowing calculations. The seven back surfaces which might receive beam

sunlight through the window are SRFs #6, 7, 8, 9, 10, 11, and 12. The only

subsurface of the GRS is SRF #5. Note that GRS #6 has no (transparent) SBS

and therefore no BKS need be computed.

PAGE 4 NBS THERMAL ANALYSIS RESEARCH PROGRAM 82/05/11, 14,04.45. 3.182

SHADOWING COMBINATIONS

GRSNR = 4 NGSS = 1 NBKS = 7 NSBS = 1 GSSNR = BKSNR = SBSNR =

3

6 7

5 8 9 10 11 12

GRSNR = 6 GSSNR = NGSS = 3

1 NBKS = 0 NSBS = 0

GRSNR = 7 NGSS = 0 NBKS * 0 NSBS = 0 GRSNR = 8 NGSS = 0 NBKS = 0 NSBS = 0 GRSNR = 13

GSSNR = NGSS =

1 26

3 27

NBKS = 8 NSBS = 1 BKSNR = SBSNR = 15 16

14

17 18 19 20 21 22

GRSNR = 15 NGSS = 0 NBKS = 0 NSBS = 0 GRSNR = 16 NGSS = 0 NBKS = 0 NSBS = 0 GRSNR = 23

GSSNR = NGSS = 2

1 NBKS = 8 NSBS = 1 BKSNR = SBSNR = 25 26

24

27 28 29 30 31 32

GRSNR = 25

GSSNR = NGSS =

2

1 NBKS = 0 NSBS = 0

GRSNR = 26

GSSNR = NGSS =

1 13

2 NBKS * 0 NSBS = 0

GRSNR = 27

GSSNR = NGSS =

1 13

2 NBKS = 0 NSBS = 0

REQUIRED CMB = 82

Figure V.26 Shadowing combinations report

188
V.B.2.5 RNOS ** 15, 16; Dump of shadowing calculations

The shadowing calculation dumps are intended for checking the shadow

calculation process. They produce a large amount of output. Figure V.27

shows part of the output for only one hour. Report 15 provides summary

results such as a record of which subroutines where called and the net

results of the calculations. Report 16 gives the details of the homogeneous

coordinate calculations. The output from 16 is printed as the calculations

occur, and so it is intermingled with report 15. The output consists of

subroutine names (see VI. B) and variable names (see VI. C) with values. To use this report, follow the calculations through the program listing and

simultaneously through the report.

189
\ \ N \

o o o ©

O o -h o

0 0-00

o o o

in O' O' 'O

S3 CO CO in O >0 ©

I I \ \ \ s

o o in o

o o <r o

o o in ©

O'

\

GO©

'O

PO

I O ^ O

O' 00 O' 10

QC CO CD -O -o h so^r

• a • * H © O' ro rN © © ©

II CM CN a H © \ Ns Ns Ns II A II II II II II X CJ X X X X h* o o Hh © CJ o o u CJ o o 1 o © © © © ©

o o © CJ O u CJ CJ L) © • • • o © o o o o

T-i aH © -I a —J -J -1 -J

at at at a» © a © © *—

1

in II Ns CM © © 1 S3 1-4 © © © s-4 © © 1 rH «r A m • • • II <X II II II II ©

1 © © © © ©

A A A A A

Ns \ X © in © © © © II z rs z z z z

o O' o © • UJ o cj o © CC o O' © © N II © © © ©

• • • • o

tH © © II A II II II II ©

•> a at at © © © © © 'O © O' S3 O' 2 2 2 2 2 II © © in © A © A A A A i ©

aH S3 i

n

S3 Z © Z Z z Z © • • • * cj © i frH

1 1 S3 a O' X

CN H s-H © vH © © M ©

S X s Ns S3 11 © a II X II II II II ©

© A © © © © II © II 1- © © © © Ns \ m

'O CD © © © © © © ©

Ns Ns \ Ns «r Z M z z z Z II ro z

IN Z © © ©

© T-i © © a © © H <• O O' © © 1 <1 © II © -0 © >c O' S3 O' o ©

o o © © <T A U © © CN © cn <r <r cn II • • • • in rs X * fN a CN * CN • fN © CN o © © CN a -J © • © * ^ a CN '* m z

a. * •> a CN 1 © © 1 m a © H-t O' O' in O' a II t-H CD •1 II II II © z

m © S3 © <*h, CnI Z **. ^s /-t a so S3 <r S3 CD a CD CD CD CD T-i © fN

• • • II Z tH z Z Z Z II T-i II ©

i 1 A © © II © II © II © II © © - CN II H CD CD ~ CD ~ CD ~ CD n ro \ N \ Ns «s* CD II © © © © © © © © S3 H Z M- © *w II CJ 1- ~ h- h- ~ h- © CN © w O' o hh © © o <t X X « X « X <r x <l \n CJ O Z ©

o 1 © © CJ h~ M © w — w 1- ^ h- ^ H- CN a a © © © z UJ Z A <Z Id <1 Ul «I Ul <1 UJ a 1 *

• • a X X w © Ul X Ul X Id X UJ X CM II CN CM II o © © H- © Z CD CD 1- CD »- CD h- *-t 1 ««t

a. •• •> a u A <E U <1 CJ <t CJ <Z CJ \ © \ II ©

O' HH in m © © © © z O' m 2

© 1 S3 © CN © T-i © T-i © © NWS

o o o o

o o o o

o o o o

o o o ** O O' -o O' in

PO CD © CD O

•• *o in -o co

U1 w O o 'O x i © o s: h o o rs

h- ...

o o

cd >-< in O' O'

<r i o co oo a o o Z * • • <XhIfl \ \ S\

o o o o o

II II II II CJ o o u XIII cn co © co 2 2 2 2

a a a a

z z z z

o

M O «h © • a*

CN \ H \

00 «* ** 00 I in O'

1

it «

UJcc

<x

<T »-H

!l ** © m

hhz

ii u

I

;i cn m v 2

Z hZ

O'

o

© © m

• o

ooo

o \ H \

oo 1 <r

in ^

Ns aH

00 «T

00 I in

1

h CM CM

II II U CJ 1

1

cn cn

<r ncc H ZZ

O'

i cn

cn

<r h-i

o o

O O CM O

• o O II cn

CM

** ii II <L cn uj

H- cc I <x

O' cn0 II ~ <z

<r uj

I- 2

UJ ^

1

U

0 I

cn

II 2

u a 1 li- en

cn

<r © S3

O' z cm

00 CM

II 00 II ~ in ~ 2 CJ 2

Z . z

cn cm cn

CO h z

© A

CM CN CM CM CM

II II II II II U CJ U CJ XXX -

cn cn cn 2 2 2 AAA

U U. U

CN

<

;i Ns K> © :> © z

m

i

N, P0 © => © Z

CJ CM

CN fN fN

II II II

X © X © HI X X © H-4 © © z © © z © © © z 2 a 2 a 2 2 • A © * K> A © ro O A A © m

U II T-4 CJ © u II O CJ U U. II © ©

H* © II s-H — rH II — T-i II «r tH *H at

S3 v-f Z © z © >0 z

»* rj fN H^ CM CN CJ H

fN z CM © z CN S3 rs z ©

I •

II O'

I N»

II UJ UJ II UJ

CJ x x ~ x

© II © ©z

©

II X o X fN X © X ro K © 1- K © «“V a-l <r u <r Z CJ U l- © «r S3 fN © II II X

© II II II ii :> ^ z> •w K © © © © z «T T-t Z rs <r X II Z II Z II z || z ro W CN CN UJ w CD © CD © 2 © 2 © H II 2

« Z © Z © Z © Z © ^ II CN ^ II ii <C

Ul © © © © © © © © 2 © 2 2 ©

© © © © © II Z II Z 2 z

<1 © © © © © © © © ©

© © © © z z z z O' © © © © so 2 2 2 2 o A A A A II ©

~ w ~ <X

<1 •! <1 <1 UJ K H- |- h- ©

UJ UJ UJ liJ <x x x x x

CN II

II V ©

© © z©

z ©

<r ©

i Ns II O' ©

S3 ©

© Z

II ©

<x

Id ©

V © ©

© z z

© ©

^ 2 A A

t-i <r

<r

I Ns II © ©

in ©

S3 z ©

i- o u u cj u <r

ii ii II II CM

it ©

© © Z

w ^ <r i <x <t “ PUl UJ X X

h- H- CJ u

II CN© CN

© © © ©

Z z 2 Z II © © © © ©

* * * 2 z

A A A A

© A •• © © © © © CD © © .. aa A •• X © 2 A 2 A 2 A 2 A © •• a. © aa X © © A © X © X © X © X 2 O © © CJ © A © A © A © A © A © © X © CD X © A X X X X CJ © CJ Z A Z A © z © z © z © z x A X

X Ul Z HH HH HH HH X

© © Ul A CD A © A © A © w

Id Z Ul 2 UJ 2 Ul z Ul A UJ A Ul A Ul A UJ A

Z©

© •* 2

«* CD CO © A

© ©

<1 o

-J •• A © •* 2©©!©©©©©2CJ © © ©©2 2 222AX OO© A ill A A A CJ AAAAAAAAX xxzxxxxx © ©UJ©©©©©

aH || © ©

z z

©

II II © ©

z z

© ©

2 2

A A

© U ©

=> x z

O A

© •• -I 2 CJ © AX© CJ O

CJ © ©

X © ©

A A

A A

X X

© ©

© •• - 2 0© AX© O C X

Figure V.27 Dump of shadowing calculations

190
NWS

w v u

O O O O o o no

o o ©

in 'O >o >o cn * <N cn in rs >o

s S w

© O (N| © © © «r © © © in ©

©

© ro

• ©

o*

O' 'S

'O

o

© M

* ©

© © ©

©© © ©

© © ©

© © © © ©

© © © © © ©

© © ©

© © ©

© © ©

© © ©

© «* © © ©

>o <o >o in t cn eg N rg in eg

© © ^ O © © I © © © ©

*a -o h in

cn eg I CN CN CN CN

II CC cn <x

II <cUJ

CL

<Z

eg

«T ©

II A

cn eg

cn *h

ii ro \

=> <r 2 H

O'

eg ro © * co © CN

cn 2

cn a

H- 2

\ X

<T^ © eg O UJ

u: ii © u

cn i

cn

th eg 2 H

cn ’-i 2 o

x <r ii

ii eg ii cn a

© © *4 © o x in

O' 2 A 2 00 -I

II

<r ©

ii ^

cn *h

© <r 2 *h

eg ii tH o

x in

eg © ii tm ecu 2 x

cn cn

•* 2

cn

cn cn 2 2

2 ©

<r ro u ^

o X

n <r ^ u ii © tH o ©

u ii _j o

X X • cj cn u i 02 •* o :

ii o

A

© M

in eg S3 rs

O II H OUhX . —i tH

ro ©

in cc N3 2

ii cn

II CJ i- ~ x x n cn v

2 A ©

^ cn uj

cn 2 iX A ©

cn

ck ro eg

ro * ^

• ©

II ii x

© ii ^

i u ^ cn ro

i in cn h

• CJ 2 h- O ~

-J A

X II

a cn

cn u

a x

— -i _j u © ©

I cccc A CJ X X

cn

A _J <C 0-1

•• X H- O -I •* X O

cj cn z i- cc o i- X t-i —J O X A —

A A O O 2 0

2 X X UJ X

u cn

OHO?

1-2

Cl. J h •*

<L O A ** a?

-i — x x cn cc cc u cn A CD © x a cn A O 2 A X

UJ 2 A cn UJ 2

UJ A

2

Ul

© © ©

© © © © ©

© © ©

© rv © © o

O' © *H S3 C IN TH © >0

O' O' rv

'O N3 ©

o O' ro © N3 ro © -TH ©

o eg ro © on ©

© © ro

© cn ©

© A ©

© © ©

© © ©

©

© © ©

© © ©

© © © © © ©

© © ©

© ©

© © ©

© © ©

© © rv © eg © © ©

© *h © o- © ©

S S \ N

© A © © © eg © © © O' © ©

'C 'C 'O 'C eg «r eg «r eg rs >o is

I i \ s \ \

NSW

© »H © ©

© O' © © © © © ©

<1 M3 bn <

«r <r eg <r

in in eg in NWS

© >H © © © I © © © © ©

© fN o O

© O' ro ro o un <r o*

H bn «r

i eg O'

eg a

©ho ©©©©in© «r ro ro ©bn© © o o ©ro© CNunbO ©©©©©©©©©rO'O'O

© © © © ©

© © © o © © © o © © cn a ©©©©©©©©©©-H^H ©oo©©©©©©©egeg OOCOQOOOOOhh

NSW

© © o ©

© © © © © © © © O O © tH

•> k •> » © S3 ~0 -C *3

“ ro «r eg <r o- ••IN 'O in a

» \ \ S N

UJH O ON

x i © © eg H © © fN

bn VD *0 eg «r o- eg n s

Figure V.27 (continued)

191
V.B.2.6 RNOS = 21; Hourly dump of primary zone loads data

This report provides hourly loads data. It consists of a line of time

data, a line of weather data, and a line of loads data for each zone (see

figure V.28). All data are in metric units. The time data consists of:

STDTIM standard time; ts in (III. B. 1.1)

CLKTIM clock time.; td in (III. B. 1.1)

DAYOFS number of days simulated (including current day)

DAYOFY day of year; DY in (B.1.2)

MONTH month number

DAYOFM day of month

DAYOFW day of week; DW in (B.1.7)

DAYTYP day type; pointer to schedules

CDATE cyclic date; CD in (B.1.4)

The weather data consists of:

DB dry-bulb temperature

WB wet-bulb temperature

BP barometric pressure

SPD wind speed

DIR wind direction

TS sky temperature

HB direct normal solar flux

HD sky brightness

HR ground brightness

TG ground temperature

The zone loads data consists of:

TZ zone air temperature

TR zone radiant temperature

SN sensible load (+ = heating, - = cooling

LA latent gain from internal sources

EE energy for lights and electric equipment

GE energy for steam equipment

ST energy for gas equipment

HW energy for hot water equipment

OT energy for other equipment

RA energy direct to return air

BB baseboard load

OAMFL mass flow rate of outside air into zone
CN ro CN ro CN ro

-1 o © -J © © © © ©

Cl 1 1 u 1 i U. 1 i Z LU Ui z © UJ Z © ©

<r © 0- <1 O' © <L CN © O ID © o \n TH O CN CN

'

rx >0 ID O’ o >0 ©

ID • ID • • ID « • * © o • <c 0 8 • © O' ID ID ID

II II II O © O K iXi t- A t- A A A A

«»

ID O id in ID >0 © © • • • © . o o © © © 0 0 CN 0 0 ©

II © ii <r II Ui LJ UJ H II i- ii »- II <t cl <c cl <X CL a X « A X «t A I

u cl o a U

«»

<•> rx O' •* ©

CN • • » • CN • • • • cn • • • • O © © © © 0 0 'C 0 0 o

II ID ii «r Ii 0. Cl a. > II > II >- ii K a H* A 1- A

>- Z h- >- Z K >- z 1-

<C o © O <L O

O A A

«•> *•> IS ID ©

CN CN O 0

, 0

, CN ID O © © cn rx 0

. Oi ©

II ID ii rx ii ©

3 © 3 ND 3 ~4

u. II U. II U II o A O A O A

> Z 3 >- Z 3 > Z 3

<x Z © Z <X Z a a A

O' CN rx H * o © © t-4 * © 0 0 tH • 0 0 ©

CN IS CN © CN O'

II 1 II 1 II 1 r Z z

Li. II U II u II O © H» O © 1- o © r-

>- K © >- h- © >- h- ©

<c © <1 A A A

«» (»

• « • * • • ID O © © *•* ID © 0 0 «* ID 0 0 ©

cn CN *-i CN ^

ro ro ro

ii ii ii ii ii ii x CL Z CL Z CL

H- - UJ r- hh uj 1- >H ©

Z a © ZAO Z A O

CJ c O

Z z z

rx • • • rx • • • IS • * •

«•> • o © © «K . © 0 0 «•* • 0 0 ©

CN o CN O CN <t

ID ID ID

ii CN II CN cn ro II CN CN ro

11 a © II A © © © II A © © ©

>- Cl Ui -1- >- u_ UI 4- 4- 4- >- a. ©4-4- 4- Ll © Ui UI u cn ui U UI Ld u © © © © ©

O cs o ro O' © o rO O' ©

>- ID >- \n is <r >- © O' <r

<1 «* CN <z «•* ro O' © <t ro IS ©

A • * • * A • • * • A • • - * o o © © © T-i t ro © Ti LD ro o © ©

«•» o ... o « o

T-» o TH © H ^ © T-i © © © © © © © © ©

*-4 <r T-t © -4- 4- <14-4- 4-

11 ii -i II II -J UI UJ UJ II II © © © ©

© ll © Cl © *4 in © Cl O' © SD u A U. A © © Ll A ro O' T-i o O SD rx o O t-i rx o

>- >- • >- © © © © «- t-i CN ID <r CN CN o a IS A -0 A r-* (N © CN

* • ro • ro

<•. <r ro © «•* ro ©

o z is z 4- © Z 4-

T-i © i © Ui cn uj

II ii ii n © ii ii CN x A Z A <r Z A CN 4 3 4 3 © 4 3 rx

h- h- I- © © © Z CN © © Z T-I © ©

-J «•« _j .» -J «•* U IS U O' u rx o © ID CN m «T is rx >0 O' ro CN

+ CL* in © • CL <T rx • cl rx © rx

• «•* © i- « • . ** is H- - • •

'O CO CN ro rx O' CN <T © O' 4 T

T-i tH CN CN •rH T-i CN CN tH CN CN

II II II 11 11 ll x CO Z A Z A

t—

CO N CN rx O' w u N rx © o *“1 A N rx <r 'O

»- 1— 'O ro rx 1- t- o* IS CN 1— »- ID CN ro A • • • A • * * A • - • 1— •* rx CN ro 1— — o CN If) 1- .. O CN ©

CO cc ^ CN CN © CfC cn CN CN © iZ CN CN CN

LU — UI -* © •* Z © X © I ©

H- A ^ CN ro cn ro •• h- A t-i CN ro © <T <Z LU © © © <r <t z UI o X LU O z © O

HH 3 _J *—< 3 —

*-• 3 ©

1- 1— 1—

Figure V.28 Hourly dump of zone loads

193
V.B.2.7 RNOS “ 21, 22, 23, 24; Dump of zone loads calculations

Reports 22, 23, and 24 give details of the loads calculation process. All

are in metric units. These dumps can be quite lengthly. Figure 29 shows part

of the output generated for one hour. Report 21 should be specified to report

times for the other reports.

Report 22 describes the control profiles and solar gains for the hour.

The report of control values describes the control profile (IV. E) for each

zone. It consists first of the zone number, the number of control temperature

ranges (NRCTR) , and the temperature range which will be used for the first air

heat balance (EFSTR) . The second line is a list of control point temperatures.

It is followed by the QFSTDC and QFSTIF variables for the control ranges between

the indicated temperatures. The solar gains data consists first of the total

short wavelength (including from lights) flux (W/m^) absorbed by each heat

transfer surface on the outside (QSO), the inside (QSI), and on any movable

insulation (QSM). Then the radiant gains converted directly to convection

(QC), the total diffuse solar gain (QD), the total diffuse shortwave radiant

gain (QS), the total beam sunlight into the zone (QBV), and the total diffuse

sunlight into the zone (QDV).

The following dumps (23) describe the heat balance calculations. They

begin with the airflow calculations. The following data is presented for each

airflow opening (I).

N (inside) zone number

M (far side) zone number (0 = ambient)

PS stack pressure (G.2.3)

PW wind pressure (G.1.3)

PZ zone pressure

DP pressure difference across opening

FLOW mass flow rate through opening (+ = in, - = out)

Then the partial outside (KOP) and partial inside (KIP) conductive fluxes

(C.1.7 and C.1.5) are presented for each heat transfer surface. These values

are constant for the hour. The convection coefficients (HC) are also presented

for each surface followed by the outside surface temperatures (TO) and then the

inside surface temperatures (TI). The results of the zone air heat balances

are summarized under ZON:

TZ zone air temperature

TR zone mean radiant temperature

ET effective temperature

CT control temperature range

VT ventilation control range

SL sensible load (+ = heat, - = cool)

LL latent load

SUMC sum of direct convective loads

QL total longwave radiant gains

PZ zone air pressure

194
The FLOW, TI and ZON values are dumped for each heat balance iteration.

HC and TO may also be dumped if new values are computed.

Report 24 is a dump of the contents of the temperature and flux histories

array. It occurs after heat balances have converged. The hourly shift of the

histories is accomplished by the TSHIFT variable until it equals zero and the

histories are moved. NTFH is the number of temperature and flux histories.

The histories are matched to their respective heat transfer surfaces by the

TMPHPE, TMPHPI, FLXHPE , and FLXHPI pointers which can be obtained by reports 6 or 8. Report 21 then summarizes the zone loads for the hour.

TIME! STDT I M= 1 7 f CLKTIM=17f D A YOFS= If BAYOFY= 52f HONTH= 2f PAY0FM=21I

WEATHER: DB = 8.89J WB = 3,86. BP=100000.J SP0 = A. 7 > DIR=315.f TS= -8.12f

control: zone= n nrctr=3* efstr=i

contem: -98.000 20. 000 21 .111 98.000

qfstdc: 0. -3,1 63E+03 0. qfstif: 3.515E+03 6 . 678E + 04 0. control: zone= 21 NRCTR=3I FFSTR=3

contem: -98.000 • 20. 000 21 .111 98.000

ofs tdc : 0. -3.163E+03 0. qfstif: 3.515E+03 6 . 678E+04 0. control: zone= 31 NRCTR=3I EFSTR=3

contem: -90,000 20. 000 21 .111 98.000

qfstdc: 0. -3 . 1 63E+03 0. qfstif: 3.515E+03 6. 678E+04 0. qso: 0.000 30.890 3.278 30.890 41.927 41.927 0.000 0.000

0.000 0.000 0.000 51.047 27.444 41.927 41.927 0.000

0.000 0.000 0.000 0.000 0.000 0.000 160.489 21.825

200.228 240.603 240.514 0.000 0.000 0.000 0.000 0.000

qs i

.535 .535 2.463 .535 .535 .535 .535 .535

. 535 .535 2.851 2.851 19.673 2,851 2.851 2.851

2.851 16.057 2.851 51.005 2.851 2.053 2.053 15.643

2.053 2.053 2.053 2.053 2.053 2.053 15.217 13.679

qsm: 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

QC QD QS QBV QDO

i 0 . 1 , 274E+02 7.130E-01 0. 1 . 003E+02

2 0. 8 . 084E+02 3.801E+00 2.053E+03 3 , 009E+02

3 0 . 4.971E+02 2 . 737E+00 1.05 2E+03 2 .006E+02

flow: I N M PS PW PZ DP FLOW

1 l 0 18.06 2.57 19.75 4.25820 161 .67

2 1 0 18.72 -1.14 19.75 -.11059 -7.42

3 1 2 .06 0.00 19.75 -.98394 -153.97

4 2 0 19.60 -3.30 20.79 - 2.10995 -125.08

5 2 0 19.69 -1.27 20.79 -.16838 -9.67

6 2 3 .02 0.00 20.79 -.01496 -18.83

7 2 1 -.06 0.00 20.79 .98394 153.97

8 3 0 17.99 -2.57 20.83 .27151 27.01

9 3 0 19. 10 -3.61 20.83 - 1 .88684 -46.41

10 3 2 -.02 0.00 20.83 .01496 18.83

kop: 91,796 28.722 .000 54.964 81 .925 46.633 771.327 771.327

771 .327 46.261 91.796 59.301 ,000 82 . 829 46.871 91 .796 199.303 771.327 771 .327 771.327 46.923 91 .796 41 .915 .000 85.136 133.525 76.771 91 .796 199.303 771 .327 771 .327 49.593

kip: 71 .786 71.192 -.000 138.661 131.319 57 . 395 698.483 603.115

603.115 39.761 91 .968 70.383 -.000 162.679 73.416 93.171

197.591 760.825 747.766 765.739 44.098 96.059 95.667 -.000

192.235 174.818 77 . 400 94.865 202.337 765.428 761 .470 794.945

DAY0FW = 2 f DAYT YP= 2f HB = 675 . 5 1 HD= 40,9

Figure V.29 Dump of zone loads calculations

ci

t i

195
140

6.140

6.140

6.140

6.140

6.140

6.140

6.140

CO GO

rv rv o* © o o

co © m o co rv >0 CO O' LI 43 CD

CN *0 *0 LI CM o

<r rg rv ro N MN <T O CN o u. rv rv oo roro<rrvroouiivrg

-4 cn *h rg

O' © ©

CN IN

i i i

rococo o- o 0^ <r rv T-< »-4 xrvfvcNrsuix-^rvrox O'NOO

rg © © O' -« © rg ro iv in _j 'OO'O' a*.*

rgrororg©roro&.rgroro © co co

CM •* ih rg CN C4 cm li -• *H O' K GO CD rv rv

co © ©

ro ro ro

GO © GO

rv cm rv © O' ©

ro ro

rv oo O'

in -o O' H HO> © © ro »-«** (N

O' o o

«r li in

rg rv li © © in

CM «r rg

'O cm ro © rv <r

ro in CM *h C4

o ro <

43 «r 43 >0 <3 GO

cm in co (M *“< »-4

O' CM

O' 43

O' © U

• • £

ro ro z) cm cm co

O' oo ro <

CM 'O ^ ro _i

CM CM

rg cm oo

co ^ rv

o- co ro © ^ ro

ro ©

©Hfi

© © -« o rv O' ^ cm m

CD CD OD co 'O -4 IV LI O' ©

rv fM rv rv rv —4 co ro cm i-4 CD © © © oo CO O' O' in O' O' <3 © © ©

ro ro ro O' © ro CN m O' ro ro -J in © ©

eg CN 44 44 CN CM CD * • •

«r © © m

co CD ro ro «r ro <r *T «T ro rv ro

rv rv CD o <3 «T rv 43 43 <r *4 o © CN rv •o ro CN <T 43 ro O'

ro ro CM O' CM CM m ro cm CN ro r- ^4 CM CN *4 CM CM CM ©

h- v4 ro ro u

© CD ro O' « <r —4 © © <r in

fv 43 li -4 © in O' CN ro >0 ro 44

•* © CD IV li ro 0*5 iv eg O' O' h- rv «r CD

43 ro ro O' li O' m in in CM CN CO rg <T 44 *4 *4 CN CM ** rg CM O 43 >0 ©good <r co co «r «r x o o cz li rg rv <rvvo>-o-oiiiO"0'Oirw • • • 44 © © go cm 4> cn co cm 43 © li rg ro CM CM

-O -<3 ro ro ui rv ro «r in N N ro H ^ ^ ^ ^ (>j eg o ro ^

N V CCD

h* * • •

co rg

•• ^ rg cm

cj o

x h- o

M ^4 cm ro

© © © © © © © © © © © © © © © © © © © o © © © © © ©

4- 4- b b b b i b 4* 4* 4- b 4* 4- 4- b b b 4- b + 4* 4- Id Id Id id Id Id Ld Id Id Id Ld Ld Id Id Ld Ld Ld Id Ld Ld Id Id Ld Id Ld

co rv rg rv 44 44 <3 00 CM <r rv CN m O' >0 © <T in 44 rv CN X >0 O (N rv © © rg *o in m O' 44 ro cm in •4 rg m 44 rg O' >0 CN ro iv in >0 co © rv © co in «o in <r ro rg CM rg in -• CN cn rg rg V CM m rg

O' CM

i - CD CN - in ^ - m - CN CM in rg

1 - CN 7

CM CN in CN © o 44 O © ^ © © © ^ © 4- o

© © © © © © © o o © © © © © © © © © © © © © © © © © b 4- +- b i b b 4- 4- 4- 4- b 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- id Id Id UJ Id Ld Id Ld Id Id Ld Id Ld Ld Ld Ld id Id Id Id id Id Ld Id U. Id

<r rv *0 *r in © >o rv ro <r CM 00 O' <3 <3 <3 O' <r in iv 44 4T 43 X O' © O' 44 © O' <r in o O' O' <3 44 rv ro m rv CM © CN X X O' m - X

vO © rv cd m rg m rv CN ro © CN CN m 43 O' CN in «r r. LI ro in

00 in

1 - 44 ^

i i +i in 44 CN - 44 - CN CN in CN

1 m

i X CN

i ro rg

i in rg ro

i © o 44 44 © ^ © 44 o 44 1-4 © © © © © © © © © © © © © © o © © © o © © © © © © © ©

4- 4- b -b 4- 4- b 4- 4- 4- 4- 4- 4- b 4» 4- 4- 4- 4- 4- 4- b 4- 4- id Id id Id u Ld Ld Ld Id Id Id Ld Id Ld Ld Ld Id Ld Id Ld Id Id Id Id Id Id

rv o CM 44 «r >0 ro © O CO CM 4“ rg < <r 44 rv X O' CN © <3 *0 LI

in ao in cn ro 'O in O' <r <r o rg X <r m X 'O 43 iv m rv <r ro LI >o rg m >o co O' © rv in 'O CM CN O 00 CN CN m © © O' ro *0 -• ro LI ro 44 m O' -

i i in ^ *

1 44 CN 7

CN CN m CN

1 ** 44 CN ro

i CM CN in rg ro

•4 44 44 .4 © -• o H 44 © 44 44 44 44 o

© © © © o o © © © © © © © © © © © © © © © © © © © ©

4- 4- -b 4- -» 4- 4- b 4- 4- 4- b b 4- b 4- 4- 4- 4* 4- 4- 4- b 4- b

Id Id U Id Ld Ld Ld Id Ld Ld Id Ld Id Ld Ld Id Ld Ld id Id Id Id Ld LU Id Ld co ro ro 4 4 rv •o rg 44 rv o 44 >0 ro 44 rg <r rv 44 X © — O' X 44 43 rv ro © in O' O' in O' rg go m X CM X <3 O' X © rg rg 44 o rg © ro rv >o CN ro rv rv m rv 'O o © rv CN O' O' ro ro rg ro <r >0 ro

«4 H -

i d m <r

i - CN 7

CN CN

1 o1

2. 6. rg (N rg CM

1 CN *1 7

cm rg

i

44 44 © 44 © -h © © © -1 44 © 44 O — -4 © © © © © © © © © © © © © © © © © © © © © o © © © o

4- b b b b b b 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- Id UJ id Id Ld U Id Ld Ld Id Id Id Id Id Ld Ld Ld Id Id Id Ld Ld Ld Id Id Id O' © IV O' <, O' >0 O' ro ro ro <r rv X «r <r O' rg X X m •4 rg <T V 44 CM <3 <3 rv «r O' in rg CN in ro IV © co X «r rv in li ro rv rv iv rg — ro O' 'C ro ro O' rv in rv O' ro m in X ** ro <r cn in O' «r rv rv <r ©

44 *4 - m 44

i <4 in ^ <r

1 CN CN

1 o- 441 ro

i CN rg CN CN rv

i rg rv

i rg

i rg rg

i

44 -« © 44 © ^ © 44 44 © © 44 44 44 44 - © © © © © © © © © © © © © © © © © © © © © © © © c o ©

4- 4- b b + b 4- 4- 4- 4- 4- 4- 4- 4- 4" 4- 4- 4- 4- 4- 4- 4- b 4* b b

Id Id Id Id Ld Id Id Id Id Ld Id Id Ld Id Ld Id Ld Ld Ld Id Id Id (d LU LU Id

li o- ro rv o 44 rg «r CM rg <3 m X <3 X ro rg < in rg x — CN

O' CO ro iv m 111 in o- <r m <3 O' ro © ro in >0 © O' <3 43 O' 43 ro rv © *o 'O rg 00 u*) rv ro © ** cm ro <r CN in ro >0 rg in © rg CN <r > -- - «r 44 ** in 44 O'

i ro rg

i rg CM CN in >0 - rg cn - rg rg rg rg x

O' © *4 44 44 44 44 © 44 © *4 © © 44 44 44 44 © ©

li © © © c © O o © © © © © © © © © © © © © © © © © o ©

CM 4- 4- b 1 b b b 4- 4- 4- 4- 4- 4- b 4- 4- 4- b 4- 4- 4- 4- 4*

ii Id Id u Ld U Id Ld Ld Id Id Ld Id Id Id Id Ld Id Ld Id Id Id Ld Ld id Ld LU X O' O' ro <r >0 IV © CM O' o ro 44 O' ro rv >C Hi 4? ro t in rv cc ro >0 «r Id 43 rg O' CD 44 44 <r in CM in -0 © X >0 ro in 43 © < © in rg ro X Li 43 H- rv cd ro ro © O' rg rv rv © CM in ro ro in ro ro ro © li ro rg LI O'

O' 44 - -- 4* <r 44 in rg rg

1 i rg CN m >0 - rg cn ro 44 rg rg LI X

CO © ^ —1 © © 44 44 © 44 © 44 © 44 44 44 44 © ©

<3 © © © © © © o © © © © © © © © © © © © © © c © © O ©

-b -b 4- b 4. b 4“ 4- b 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- 4- b 4- b 4- 4- 4-

Id Ld Id Id id Id Id Ld Ld Ld Ld Ld Id Ld Ld Id Ld U Ld Ld Ld LU Id LU lu Id

II rv c- *r IV © <r <T O’ rg rv >0 44 IV rg O' <3 rg O' X iM © 44 rg >0 LI

1- «r ro <3 O' © o rg rg 44 43 rv O' © O' in rg in CN Li ro O' >0 LI Li X

u. © ^ CM o ro rv O' rv © co © ro ro m O' O' © o -r ro ro LI O' X

ID

«0 44

1 - ^ rv

i i in rg rg

i - CM rg m - rg

i rg cn rg 44 rgi rg LI ©

1-

i4 *4 44 © 44 © © © © © 44 *4 44 44 © © © © © © © © © © © © o © o © © © © © © © © © © © © ©

•• b 4- 4- b 4- 4- 4- 4- b 4- 4- 4- b 4- 4* b 4- 4- 4- b 4- 4- 4- CD Id Id Id Ld Ld Ld Id Ld Id Id Id Ld Id Ld Id Ld Ld Id Id Ld Id Ld Ld LU Id Id Id © o* in ro 44 © IV >0 ro © <T © <r <T rg <3 T 44 CO © «r 44 <r <3 •O Li

uo in rg rv ro rv O' in 44 ro © © O' CN >0 m © X LI LI X O' CN ro li ro O -4 © <3 rg O' rv m rv rg rg ro CM <3 >0 m © «T O' Li o- <r © LI o

»-

CD

44 44 - 44 oo

i 44 in m - - 44

1 CN 44

1 in

i in CN rg w- rg 44 rg

i I LI O' X 4 44 44 © 44 © © o © © 44 ~ © o -

1 © © © © o © © © © © o © © © © © © © © © © o o © © X + •+ b 4- 4- 4- b 4- 4- 4- 4- 1 b 4- 4- 4- 4- 4- 4- 4- -+- 4- 4- 4- 3 Id Ld Ld Ld Id Id id Id Id Ld Id Id Ld Id lu Ld Id Id Id Id LU d4 LU Id Id -J O' 0“ O <3 ro O' < ro CO CD © ro O' 44 <3 O' © *r O <T 44 LI >0 Id O' © CO O' © O' in o co <3 rg rv rg CN in rv rg Li ro ro © ro O' Li © a

© © «o in o rv in rv © ro CD rg © CM m o CN IV © CM O- o LI Li rg z »4 h o pg ri iii in h h c mn c ui n -< t-i -* rg ^ iv *-4 in rg

<£ II III (III!

IdX

X

Figure V.29 (continued)

196

LOAHS!

TZ

TR

SN

LA

EE

GE

ST

HW

0T

RA

BB

OAHFL

1

20.47

19.44

2.040EL03

1.600E+01

1.353E102

0.

0,

0.

0.

0.

0.

4.559E-02

2

22.78

22.47

0.

2.701E101

4.979E+02

0.

0.

0.

0.

0.

0.

0.

3

25.20

24.77

o.

S.915ET01

3.040E+03

0.

0.

0.

0.

0.

O.

8.418E-03
VI COMPUTER PROGRAM

The general structure of the Thermal Analysis Research Program was described in chapter II. B and figure II. 1. This chapter expands upon that

introduction by describing the program subroutines, variables, and files.

VI. A INPUT PROCESSOR

The input processor (IP) is the first of the two TARP subprograms. It

checks and interprets the user input, creates the input files for the loads

calculator (LC), and writes various reports. This processing involves all

of chapter IV and primarily sections B, C, and D of chapter III. Data about

the location and weather goes to the LC in the ENVTFL (environment file).

The description of the building, including library data, goes in the SINPFL

(simulation input file).

The IP is divided into four major sections corresponding to the input

language sections. These sections may be used to reduce core requirements

by overlay (or segmentation). A small input processor will help to give

fast job turn-around necessary to quickly debug the user input deck. Each

section is headed by a subroutine that is called when a section name and "["

is encountered in the input. The name of that routine is similar to the

section name. The section processor subroutines all have similar

structures, especially for how they handle incorrect input.

Each section contains several subroutines which process the input

language keys. The names of these routines are the same as the key names. Most of the key processing routines also have similar structures consisting

of: initialization, decoding the subkeys, error checking, calculation of

derived data, output to SINPFL, reports and dumps. The output to SINPFL

consists of an identifier record containing two integers and one or (sometimes) more data records. The data records usually have values for a single surface, schedule, etc., which is read by the LC into arrays for all

surfaces, schedules, etc.

Some key processing subroutines call other groups of subroutines for

complex calculations. The largest of these groups are those that compute

the conduction transfer functions and the window optical coefficients.

A short description of each of the 130 input processor subroutines is

given below. After the descriptions is a diagram (figure VI. A. 1) showing

the general relationship of the IP routines and the segment structure.

AFS subroutine

Evaluate the subkeys of AFS (4.14). The AFSDAT common block contains

data to match interzone openings. Data is output in the AFSIL common

block.

197
BBH subroutine

Evaluate the subkeys of BBH (4.11). Data is output in the SSCISL

common block.

BDLIB block data

Set initial values for library processing.

BDPROJ block data

Set initial values for project processing.

BDSLR block data

Set initial values for processing user input.

BEAM subroutine

Evaluate window optical properties for beam sunlight at 16 angles of

incidence.

BLANK(ARRAY ,LEN) subroutine

Blank (set to ' ' ) an ARRAY of character strings of length LEN.

BUILDG subroutine

Evaluate the keys of BUILDING (section 3). This is the root subroutine

of the building segment.

CDS subroutine

Evaluate the subkeys of CDS (2.7). Convert control profile names to

pointers

.

CHKCP subroutine

Check description of control profile: number, range, and order of

temperatures and normalized capacities.

COMPMS subroutine

Compute the optical properties for the pane-shade system for both

polarizations of light incident from the outside. Compute overall

transmittance and reflectance and individual absorptances

.

198
CONS subroutine

Evaluate the subkeys of CONS (2.5). Evaluate the thickness of each

layer, and convert its material name to a pointer to retrieve materail

data from unit 4. Compute conduction transfer functions. Compute

optical coefficients for constructs having no opaque layers. Data is

written to the constucts file (unit 5) for reference by zone surfaces.

Data is output to the SINPFL in common blocks CONDAT, GLAS, and GLASO.

CPFL subroutine

Evaluate the subkeys of CPFL (2.6). Call CHKCP to check the control

profile. Data is output in the CNTPFL common block.

CREPT (SCRFL) subroutine

Transfer constructs reports (2.1.3) from unit SCRFL to the output file.

CTRL subroutine

Evaluate the subkeys of CTRL (4.9). Data is output in the CGSIL common

block.

CTF(I,CONVG) subroutine

Calculate the higher order conduction transfer functions from the

response factors (order 0 CTF) and the RATIO’S. Check convergence by

(C.2.1).

CWS subroutine

Evaluate the subkeys of CWS (2.8). Convert control day-schedule names

to pointers.

DCHXYZ subroutine

Compute conduction transfer functions of a single layered slab

using the algorithm of D. C. Hittle.

DDY subroutine

Evaluate the subkeys of DDY (1.6). Data is output as a single day in

the ENVTFL

DER subroutine

Calculate the total construct and total derivative matrices for a single value of the Laplace parameter.

199
DIFFUS subroutine

This subroutine operates in one of two modes. It may compute the

optical properties of a combination of glass panes for both polarizations

of diffuse light of a given wavelength incident from both sides (D.6.2).

Or it may compute the optical properties af a pane-shade system for both

polarizations of diffuse of a given wavelength incident from the outside

only. A Simpson's rule integration is used.

DIFSHD subroutine

Compute the reflectance of an interior shading device for both

polarizations of diffuse light.

DLT subroutine

Evaluate the subkeys of DLT (4.10). Data is output in the CGSIL common

block.

DMPAFS subroutine

Dump air flow opening data in the AFSIL common block. Dump initiated by

RN0S=6 (1.2.1).

DMPCGS. subroutine

Dump zone control and general schedule data in the CGSIL common block.

Dump initiated by RN0S=6 (1.2.1).

DMPHTS subroutine

Dump heat transfer surface data in the HTSIL, HTSIS, and HTSISL common

blocks. Dump initiated by RN0S=6 (1.2.1).

DMPSRF subroutine

Dump surface geometry data in the SRFIS common block. Dump initiated by

RN0S=6 (1.2.1).

DMPSSC subroutine

Dump special surface data in the SSCISL common block. Dump initiated by

RNOS=6 (1.2.1).

DS subroutine

Evaluate the subkeys of DS (2.2). Check number and range of profile

values

.

200
DSS subroutine

Evaluate the subkeys of DSS (3.2). Coordinates are converted from the

building to the global coordinate system by (E.1.1) and (E.1.4). Data

is output in the SRFIS common block.

DUMPGL(MODE) subroutine

Dump optical calculations according to MODE.

M0DE=1: describe optical layers.

M0DE=2: report optical properties.

M0DE=3: report optical values (T, R, A) for each layer.

M0DE=4: print polynomial coefficients.

Initiated by RN0S=4 (1.2.1).

DUMPLB subroutine

Dump library control data initiated by RN0S=1 (1.2.1).

DUMPNV subroutine

Dump one day of weather data. Initiated by RN0S=2 (1.2.1).

DUMPPJ subroutine

Dump project data: common blocks TITLES, RUNCTL, EFLHDR, and REPORT.

Initiated by RN0S=1 (1.2.1).

DUMPRF(MODE) subroutine

Dump conduction transfer calculations according to MODE.

M0DE=1: describe conductive layers.

M0DE=2: print roots and ratios.

M0DE=3: Print all orders of conduction transfer functions.

Initiated by RN0S=3 (1.2.1).

DUPLIB(LO,LEN) subroutine

Check for duplicate name in library.

DYS( JFLAG ,DY ,M0 ,DM,LY) subroutine

If JFLAG = 1, compute day-of-year (DY) from month number (MO),

day-of-month (DM), and leap year indicator (LY) (B.1.1). Otherwise,

compute MO and DM from DY and LY.

EMI subroutine

Evaluate the subkeys of EMI (4.17). Data is output in the SSCISL

common block.

201
EQP subroutine

Evaluate the subkeys of EQP (4.4). Data is output in the CGSIL common

block.

E RROR( MSG , ETYPE) subroutine

Print error message (character string MSG). Process according to error

type (ETYPE).

ETYPE=0: informative message.

'warning' — unusual, but not fatal, input.

'severe' — input error which will prevent running LC.

COUNT of type 2 errors may not exceed 30.

'fatal' — immediate run termination,

set ETYPE to the highest ETYPE number with which ERROR

was ever called.

ETYPE- 1: ETYPE-2

ETYPE-3

ETYPE<0

EXTCF(T0,N) real function

Compute k*L (extinction coefficient times thickness) of glass pane N

with normal incidence transmittance TO (D.3.11).

FAN subroutine

Evaluate the subkeys of FAN (4.8).

block.

F ILM( J , N , LAMBDA , CTHETA , STHETA , CPHI

)

Compute the optical properties

(l=outside, 2=inside) of glass

FINDFD( N , TPLAIN , TFILM)

Data is output in the CGSIL common

subroutine

of a thin reflective film on side J

pane N.

subroutine

Determine the thickness of a thin reflective film on pane N by its

normal transmittance with (TFILM) and without (TPLAIN) the film.

FINISH subroutine

Finish input processing. Check for and report unmatched interzone

surfaces and openings. Check for and report unused library names. Terminate run if there were any 'severe' errors. Report minimum LC

array sizes (PARAMETERS). Write the last SINPFL record - common block

RUNCTL.

GEOM subroutine

Evaluate the subkeys of GEOM (4.1). Values are set for the subsequent

geometric processing of zone surfaces.

202
GETB3W(NSKIP ,NDAYS) subroutine

Skip NSKIP days of weather data from the BLAST 3.0 weather file

(WTHRTP, unit 3). Transfer the following NDAYS of data to the ENVTFL.

GETLIN subroutine

Get the next line on user input from the INPUT file. Echo the line in

the output file. Print error message if data is being skipped.

GLASSX subroutine

Compute the total transmittance and reflectance of a system of up to

four panes of glass and the absorptance of each pane for both

polarizations of light and both directions of incidence (at a given

wavelength and angle of incidence).

GRND subroutine

Evaluate the subkeys of GRND (1.4). Data goes into ENVTFL header

record.

ICTF subroutine

Initialize arrays for conduction transfer function calculations

.

IDSTF(MO,DM,DW) integer function

IDSTF = 1 when daylight savings time is in effect, and it equals 0

otherwise. IDSTF is based on the month number (MO), the day-of-month

(DM), and the day-of-week (DW). Daylight savings time begins on the

last Sunday in April, and it continues until standard time resumes on

the last Sunday of October.

ILL INI ( A, B,T0L,RT, REPEAT) subroutine

Use modified false position method to compute root (RT) in the interval

bounded by A and B. Convergent solution is found the upper bound - lower bound < TOL. If solution is not found, set REPEAT to true.

IMI subroutine

Evaluate the subkeys of IMI (4.18). Data is output in the SSCISL

common block.

INF subroutine

Evaluate the subkeys of INF (4.5). Data is output in the CGSIL common

block.

203
INITCF subroutine

Compute the units conversion factors. Most factors are derived from

CFL(2)“.3048 , CFM(2)=. 45359237 , and CFC(2)«4 . 184 to give a consistant

set of conversion factors.

INITGL subroutine

Direct the calculation of window optical coefficients. Set up

properties of optical layers (no air layers). Set coefficients of

shading coefficients window directly. Otherwise, evalaute optical

properties (SPCTRM) and compute polynomial coefficients (WDWPOL).

Print dumps and reports as required. This is the root subroutine of

the optical calculations segment.

INITRF subroutine

Direct calculation of conduction transfer functions. Compute

properties of conductive layers (no interior shades). Evaluate CTF for

multi-layer (EESPNS) or single layer (DCHXYZ) constructs and report

results. This is the root subroutine of the conduction calculations

segment.

INTCON(ANUM,EFLAG) integer function

Evaluate character string ANUM as an integer (syntax rule [IV.B.l] 8).

If ANUM is a proper integer, return EFLAG set to 0. Otherwise, set

INTCON to 0, set EFLAG to 1, and print error message.

I SHADE subroutine

Add the effect of an interior shade to optical properties of the glass

panes in the window (D.7).

I ZERO ( ARRAY, LEN) subroutine

Set ARRAY (length LEN) of integers to 0.

JDS( JFLAG, JD ,YR,MO ,DM) subroutine

If JFLAG = 1, compute the Julian date (JD) from the year (YR), month

(MO), and day-of-month (DM) (B.1.2). Otherwise, compute YR, MO, and DM

from YR (B. 1 .3)

.

LIB subroutine

Evaluate the subkeys of LIB (2.1). Data is used to control the

processing of library input. Open the library report scratch files.

204
LIBRRY subroutine

Evaluate keys of LIBRARY (section 2.). Insure sequence of key input.

This is the root subroutine of the library segment.

LIT subroutine

Evaluate the subkeys of LIT (4.3). Data is output in the CGSIL common

block.

LOC subroutine

Evaluate the subkeys of LOC (1.3). Data is stored in the weather file

header (common block EFLHDR)

LOCLIB( ITEM, LO, LEN, LOC) subroutine

Determine location (LOC) of ITEM in the library relative to LO. The

library consists of seven groups of named elements. All names in the seven groups are stored in the LNAMES array beginning at various

locations. LO is the array location before the first entry in the

group of interest. LEN is the number of elements of that group. LOC

records the sequence in which the library entries were defined and in

which they exist on scratch files or will exist in the loads calculator

arrays. If ITEM is not found, set LOC to zero.

LOCORD(LIST, LEN, ITEM) integer function

Determine the location of ITEM in a LEN long array (LIST) of

alphabetically ordered words. If ITEM is not found, return the value

zero. A bisection search is used.

LOCRAN(LIST ,LEN , ITEM) integer function

Determine the location of ITEM in a LEN long array (LIST) or unordered

words. If ITEM is not found, return the value zero. A linear search

is used.

LREPT ( SCRFL , NLINES , TITLE ) subroutine

Transfer library reports (2.1.3) from unit SCRFL to the output file.

Each report element is NLINES long and is given a TITLE. Close the

SCRFL when finished.

LSQFIT ( ITYPE ,N,N1 ,N2) subroutine

Compute the polynomial coefficients of the optical properties equations

(D.1.7a and b). A standard least squares fit is used.

ITYPE = 1 does the polynomial which is evaluated by P0LY1F.

ITYPE = 2 does the polynomial which is evaluated by P0LY2F.

N is the order of the polynomial.

Nl is the location in X and Q of the first data value.

N2 is the location in X and Q of the last data value.

205
LYF(YR) integer function

Compute the leap year indicator from the four digit year number (YR)

If YR is a leap year, set LYF to 1. Otherwise set LYF to 0.

MASS subroutine

Evaluate the subkeys of MASS (4.12). Thermal properties are read from

UNIT 5. Data are output in common blocks HTSIL and HTSISL.

MATL subroutine

Evaluate the subkeys of MATL (2.4). The input data are checked against

appropriate ranges. The material properties are written to UNIT 4 for

reference by the CONS subroutine. The materials report (MATL - 2.1.3)

is written to UNIT 23.

MATRIX(W) subroutine

Evaluate the conduction matrix for a multi-layered slab.

MIX subroutine

Evaluate the subkeys of MIX (4.7). Data is output in the CGSIL common

block.

MODY( DATE , EFLAG ) integer function

Evaluate character string DATE as a date (syntax rule [IV.b.l] 10).

Compute MODY in the cyclic date form (B.1.4). If DATE is a valid date,

return EFLAG set to 0. Otherwise, set MODY to 0, set EFLAG to 1, and

print error message. Note that day-of-month numbers from 1 through 31 are considered valid for all months.

OSC subroutine

Evaluate the subkeys of OSC (4.16). Data is output in the SSCISL

common block. Error checking includes (1) OSC not permitted with

interior surface, (2) OSC not permitted with EMI on same surface, and

(3) multiple definitions of OSC for the same surface not permitted.

206
PAGE (IACT, NEED) subroutine

Write output report page headings. This routine can be used to count

the number of lines being printed on issue page eject commands at

appropriate intervals according to the use of IACT and NEED.

IACT“0: Initialize page routine. Set page length to NEED.

IACT=1: NEED lines are to be printed. If there is insufficient space

remaining on the page, eject page and print heading.

IACT=2: Return page number in NEED.

IACT=3: Return number of lines left on page in NEED.

IACT=4: Eject page and print heading if NEED lines not left on page.

Do not increment line count.

The page heading includes a report of cumulative program execution time

determined from the non-ANSI function SECOND. This function can be

removed without otherwise affecting the program.

PANE(N) subroutine

Compute the transmittance, reflectance and absorptance of pane number

N (counted from the outside). This routine uses the optical algorithms

of III.D.3.

PEO subroutine

Evaluate the subkeys of PEO (4.2). Data is output in the CGSIL common

block.

P0LY1F(X,A,N) real function

Evaluate simple polynomial expression (D„1.7a):

P = A( 1 ) + A(2)*X + A(3)*X2 + ... + A(N)*XN_1

P0LY2F (X ,A,N) real function

Evaluate simple polynomial expression (D.1.7b):

P = A(1)*X + A(2)*X2 + ... + A(N)*Xn

PROJCT subroutine

Open the simulation input (SINPFL) and environment (ENVTFL) files.

Evaluate the keys of PROJECT (section 1.). Write the weather file

header record and close the weather file. Write the first records on

the simulation input file. Initiate dump of "project" data (RN0S=1 - 1.2.1). This is the root subroutine of the project segment.

PSYCH subroutine

This routine may be used to test the psychroraetric package. It is not

called by TARP.

207
PSYDPW(W,PB) real function

Compute the dew point temperature (TD) from the humidity ratio (W) and

the barometric pressure (PB) (B.2.6).

PSYHTW(TA,W) real function

Compute the enthalpy (H) from the dry bulb temperature (TA) and

humidity ratio (W) (B.2.9).

PSYRHT(TA,TD) real function

Compute the relative humidity (RH) from the dry bulb (TA) and dew point

(TD) temperatures (B.2.7). Check for 0 < RH < 1.

PSYTWD(TA,W,PB) real function

Compute the wet bulb temperature (TW) from the dry bulb temperature

(TA) , humidity ratio (W) , and the barometric pressure (PB). TW is

computed by iteration of function PSYWTP to a convergent solution. The

first set is to check for saturated air which means TW * TA. Failing

that, an initial guess for TW is made at TA-1. This initial guess is

increased if it produces an impossibly low humidity ratio. The initial

guess is used in a secant iteration. If the secant iteration should

fail, a slower but more reliable bisection iteration is available.

PSYVTW(TA,W,PB) real function

Compute the specific volume (V) of moist air from the dry bulb

temperature (TA) , humidity ratio (W) , and barometric pressure (PB)

(B.2.8). Check for reasonable range: 0.58 < V < 3.

PSYWDP(TD ,PB) real function

Compute humidity ratio (W) from dew point temperature (TD) and

barometric pressure (PB) (B.2.2). Check for W > 1.61E-6 (W for TD = -70C).

PSYWTH(TA,H) real function

Compute humidity ratio (W) from dry bulb temperature (TA) and enthalpy

(H) (B.2.5) . Check for W > 1.61E-6 (W for TD = -70C).

PSYWrP(TA,TW,PB) real function

Compute humidity ratio (W) from dry bulb (TA) and wet bulb (TW)

temperatures and barometric pressure (PB) (B.2.3). Check for W > 1.61E-6 (W for TD = -70C).

208
PSYWTR(TA,RH,PB) real function

Compute humidity ratio (W) from dry bulb temperature (TA) , relative

humidity (RH), and barometric pressure (PB) (B.2.4). Check for W > 1.61E-6 (W for TD = -70C)«

QTF subroutine

Compute flux conduction transfer coefficients from RATIO values.

RC subroutine

Evaluate the subkeys of RC (1.1). Data are stored in the RUNCTL common

block and used in subsequent processing of user input.

READER subroutine

Decode the user input (in UINREC) according to input syntax rules

(IV.B.1). Output is current status (UISTAT) and individual words in

the AWORD array. The longest element of input processed in one call to

this routine is a subkey with data.

RELCON( ANUM , EFLAG) real function

Evaluate character string ANUM as a real number (syntax rule [IV.B.l]

9). If ANUM is a valid number, return EFLAG set to 0. Otherwise, set

RELCON to 0.0, set EFLAG to 1, and print error message.

REPTGL(LSC) subroutine

Report on the calculation of window optical coefficients. This report

is initiated by CONS (2.1.3). The report is in two formats: one for

detailed optical calculations and the other if a shading coefficient

was used (LSC true)

.

REPTRF subroutine

Report on the calculation of conduction transfer functions. This

report is initiated by CONS (2.1.3). Also report surface properties.

RESPNS subroutine

I Direct the calculation of conduction transfer functions for

multi-layered slabs.

! RFCOMP subroutine

Compute conduction transfer functions for multi-layered slab from the

roots and residues.

209
RPT subroutine

Evaluate the subkeys of RPT (1.2). Data is stored in the RFLAGS array.

RSBF(I ,COSINC ,WL) real function

Compute reflectance of an interior shading device. This returns the

value of RSO which was computed from user input REF (2.4.12). This

routine is a program stub to allow computation of reflectance from

polarization (I), angle (COSINC), and wavelength (WL) when data for

such a calculation exists.

SATPTX(T) real function

Compute the saturation pressure of water at temperature (T) by the

detailed ASHRAE correlation (B.2). This subroutine is not called by

TARP. It is used with PSYCH to test the psychrometric package.

SATUPT(T) real function

Compute the saturation pressure of water at temperature (T) (B.2.1).

Check for -70 < T < 100.

SATUTP(P) real function

Compute the saturation temperature of water at pressure (P) (B.2.1).

Check for P in the range corresponding to -70 < T < 100.

SEARCH subroutine

Determine upper and lower bounds within which a root must exist. Call

ILLINI to converge to root. Trigonometric identities are used (with

APPROX) to evaluate AS and BS as PT is incremented. The search for

roots of BS is helped by the fact that roots of BS must lie between

roots of AS.

SETUPV subroutine

Compute vertices of polygon. Vertices of rectangular and

non-rectangular base surfaces are evaluated in the global coordinate

system by equations (E.1.4). Rectangular subsurfaces have vertices

computed in the base surface coordinate system. Subsurface azimuth and

tilt angles are computed from the base surface angles.

SHD subroutine

Evaluate the subkeys of SHD (4.15). Data is output in the SRFIS common

block.

210
SIM subroutine

Evaluate the subkeys of SIM (3.1). Data is stored in the RUNCTL common

block and output as one of the last steps of input processor operation.

SLR program

SLR stands for "simplified language reader". This is the root program

of the input processor. It initializes program variables and opens

files, directs the processing of input sections, prints final reports

and closes files. The variable SEQ is used to insure that sections are

not used out of sequence.

SKYTF(TA,TD,N) real function

Compute sky temperature from dry bulb (TA) and dew point (TD)

temperatures and tenths cloud cover (N - integer) (B.3.1 through B.3.4)

SPCTRM subroutine

Use the detailed optical algorithms to compute the window optical

properties. This routine includes a loop to integrate the optical

properties over wavelength. The loop is executed for only one average

wavelength. This was found to give sitisfactory results for typical

window materials.

SRF subroutine

Evaluate the subkeys of SRF (4.13). Data is output in the SRFIS,

HTSIL, and HTSISL common blocks. The subkey names (in KEYS) are sequenced according to frequency of occurrance to speed the INDEX

operation in SUBKEY. The large number of options in the SRF

description make this the most complex input subroutine. There are several error messages relating to syntax requirements. Then the sky

and ground view factors are computed by (E.5.2a) and (E.5.2b), unless

the user chose to provide his own values by (4.13.7) and (4.13.8). The

surface area (gross area for base surfaces) is computed from (E.4.1).

The conductive and radiative properties of the surfaces are read from

unit 5. If the surface is an interzone partition (IZP), and attempt is

made to match it to previously defined IZP’s. An IZP must be described

in two zones. RN0S=7 (1.2.1) reports on this matching process. The

surface geometric data (primarily coordinates of vertices) is computed.

Values are stored in the BASES common block for the geometric

description of subsurfaces.

211
SUBKEY (KEYS , LKEYS ,NKEYS ,LOC) subroutine

This subroutine evaluates the subkey name (syntax element [IV>B>1] 4).

The subkey name is always the first word in ALIST. KEYS is a single

string of all subkey names, each no more than LKEYS characters long.

The number of names in KEYS is NKEYS. LOC is the word number location

of the subkey name in KEYS. The INDEX function is used in determining

LOC. If the name is not found, an error message is printed. All valid

subkey names are optionally (DEM- 1.1.3) printed.

SUDDEN subroutine

This routine fills a single day of weather data in common block ENVDAT

from the user's dedign day description (DDY - 1.6). Calendar values

are computed. A dew point temperature (TD) for the day is computed.

It is used in computing the hourly wet bulb temperatures, humidity

ratios, and sky temperatures. Solar intensities are computed.

SUN2(DAYYR,A,B,C,AVSC) subroutine

Compute the ASHRAE A, B, and C values from the day-of-year (DAYYR).

These are computed from truncated Fourier series computed from data in

ASHRAE 1981 Fundamentals, page 27.2.

SUN5(H0UR) subroutine

Compute the solar direction cosines at standard time HOUR.

SURFIN( ZAVG , ZTOP) subroutine

Compute coordinates of surface vertices. Determine avarage and maximum

height of surface from ground.

TSBF(I ,COSINC ,WL) real function

Compute transmittance of an interior shading device. This returns the

value of TSO which was computed from user input TRNS (2.4.9) and REF

(2.4.12). This routine is a program stub to allow computation of

transmittance from polarization (I), angle (COSINC), and wavelength

(WL) when data for such a calculation exists.

VALID(KEYS , LKEYS , NKEYS , LEVEL) subroutine

List valid input names. LEVEL (equals 1, 2, or 3) determines whether

section, key, or subkey names are being listed. The names are all in

the single string KEYS. The number of names is NKEYS. Each is LKEYS

characters long.

VENT subroutine

Evaluate the subkeys of VENT (4.6). Data is output in the CGSIL common

block.

212
WDWPOL subroutine

This routine directs the calculation of the polynomial coefficients

(D.1.7a and b) describing the optical properties of the window.

WS subroutine

Evaluate the subkeys of WS (2.3). Data is output in the local array

PTR and the optional report is on unit 22. The day schedule pointers

can be filled from a single weekday pointer.

WTAP subroutine

Evaluate the subkeys of WTAP (1.5). Get weather from the BLAST weather

file unless SYNTAX (1.1.2) or OLDW (1.1.6) are in effect.

WXREF(A,I) subroutine

Write cross reference data consisting of the array name (A) and the

location (I) in that array. WXREF is initiated by XREF (1.1.5). It

relates the input keys to the arrays reported by DUMPIN in the loads

calculator. DUMPIN is caused by RN0S=8 (1.2.1).

ZERO ( ARRAY, LEN) subroutine

Set ARRAY (length LEN) of real numbers to 0.

ZERORE subroutine

ZERORE calculates the residues related to the double pole at zero.

ZONE subroutine

Evaluate keys of ZONE (section 4.). Insure sequence of KEY input.

Data is output in the ZONISL common block. Key names (in KEYS) are approximately in the order of frequency of occurrence to speed

execution of the INDEX function. This is the root subroutine of the zone segment.

213
This diagram (continued over several pages) shows the general relationship

of the input processor subroutines to each other. A subroutine calls other

subroutines which are to the right and below it on the diagram. Multiple calls

to the same subroutine are not shown, only the first. Circled letters are con- tinuation points for often used groups of subroutines and for large groups of

subroutines. Not all subroutines and functions are included. The intrinsic

FORTRAN 77 routines have been left out. Several simple utility routines which

are called from many places are not always shown. These include: ERROR,

INTCON, I ZERO, LOCLIB, MODY, PAGE, RELCON, WXREF , and ZERO.

BDSLR

BDPROJ

BDLIB

SLR —

INITCF

PAGE

READER

-VALID —PROJCT

-BLANK

-GETLIN

PAGE

ERROR

-ERROR

-INTCON

-READER

-VALID

-RC

(B).

-RPT

-LOC —GRND —WTAP

-SUBKEY (B)

•SUBKEY (B)

-SUBKEY -—(B)

~k

—DDY 1

l—F

-READER

-VALID

-ERROR

SUBKEY —(B)

ETB3W

DUMPNV

ERROR

SUBKEY —(B)

SUDDEN (C)

DUMPNV

•(A)

l

I

I PAGE

jI J

l-DUMPPJ

Figure VI. A. 1 Tree structure of input processor program

214
-LIBRRY—

-READER-

-VALID

-LIB.

-DS.

-WS

—MATL-

-CONS.

—CPFL-

-CDS.

-CWS.

1-DUMPLB

•(A)

-SUBKEY

SUBKEY.

DUPLIB

-SUBKEY-

-DUPLIB

SUBKEY-

-DUPLIB

-SUBKEYDUPLIB

•INITRF-

•INITGL-

•SUBKEY - DUPLIB

CHKCP

•SUBKEY-

•DUPLIB

SUBKEY-

•DUPLIB

—BUILDG

-ZONE

-READER

-VALID

-SIM

*—DSS

I—READER

VALID

AFS

—BBH

•CTRL

•(A)

SUBKEYSUBKEYDMPSRF

(A)

SUBKEYDMPAFS

SUBKEYDMPCGS

SUBKEY - DMPCGS

Figure VI. A.

(B)

(B)

(B)

(B)

(B)

(D)

(E)

(B)

(B)

(B)

—(B) —(B)

(B) —(B)

(B)

( continued)

215
216
DYS

JDS

IDSTF

SUN2

PSYWTP

PSYDPW

PSYTWD

t

t

SATUPT

PSYWTR

SATUPT

SATUTP

PSYDPW

PSYWTP1

SATUPT

SATUPT

PSYWTRPSYWPD

•SKYTF

SUN5

“LSATUPT

SATUPT

•RESPNS —

•REPTRF —DUMPRF

-ZERORE

-SEARCH 1MATRIX

ILLINI

DUMPRF

-DER

-RFCOMP

ERROR

•DCHXYZ—

|

1

DUMPRF

ICTF

CTF

QTF

“L,MATRIX

1

ZERO

ICTF

CTF

QTF

Figure VI. A. 1 (continued)

217
•EXTCF

.FINDFD—

UpaneLerror

-FILM

•SPCTRM—

i

V—DUMPGL

DIFFUS

COMPMS—

»

r

-DIFSHD—

U*TSBF

Lrsbf

Lbeam-

-WDWPOL

•DUMPGL

-REPTGL

LSQFIT

1P0LY2F

POLY IF

PANEFILM

Uglassx

LisHADEt-TSBF

RSBF

.COMPMS —

»

UpaneL

•FILM

•GLASSX

Lishade tRSBF

TSBF

Figure VI. A. 1 (concluded)
VI.

LOADS CALCULATOR

The loads calculator (LC) subprogram of TARP computes the zone loads

based on the algorithms in chapter III, primarily sections E through L. It

is divided into three sections. The first reads the SINPFL created by the

IP and fills the LC arrays. It checks for sufficient array space and

performs some checks and calculations which require that the entire building

description be present in the arrays. The second section section uses the

geometric and optical descriptions of the building surfaces to compute solar

gain factors for various periods of the year. The third section computes

the zone loads by simultaneous, hour-by-hour heat balances.

The three segment structure of the LC is used to name many of the

common blocks. For example, common block HTSISL is composed of variables

dimensioned MAXHTS and is used in the Input, Shadowing, and Loads segments.

Common block ZONL has variables dimensioned MAXZON and is used in only the

Loads segment.

A short description of each of the 90 loads calculator subroutines is

given below. After the descriptions is a diagram (figure VI.B.l) showing

the general relationship of the LC routines and the segment structure.

AIRMVO subroutine

Compute air movements for the simple algorithms: infiltration (INF - 4.5 - K.2), two zone mixing (MIX - 4.7 - K.3), and whole house fan (FAN

- 4.8 - K.4). The mixing and fan models may not be used when other

ventilation (VENT - 4.6) is possible.

AIRMV1 subroutine

Compute infiltration and interzone air flows using the detailed air

movement algorithms in III.G.

BDMRL block data

Set initial values for loads calculator program.

BDSIM block data

Set initial values for loads simulation.

BTWEEN(N1 ,N0,N2) logical function

Determine if cyclic date Nl lies between dates NO and N2 (B.1.6).

CALOAD subroutine

Calculate values for the building loads report including system status

hours, zone loads, zone peaks, building loads, and building peak

values

219
CHACS subroutine

Set up the control points and coeficients of the system performance

(K.l) and ventilation models (K.3).

CHKBKS ( NRS , NB S ) subroutine

Check that a convex zone has been defined. No vertex of surface number

NBS may lie in front of surface number NRS.

CHKGSS( NRS, NSS, ZMIN, NOSHAD) subroutine

Determine if surface number NSS can possibly shade surface NRS. If it

can, set NOSHAD false. NSS cannot shade NRS if any of the following

conditions are true:

(1) No point of NSS is above the lowest point (height ZMIN) of NRS.

(2) NSS is horizontal and faces up.

(3) NSS is entirely behind NRS.

(4) NRS is entirely behind NSS.

CHKSBS subroutine

Check that a subsurface is completely enclosed by its base surface.

This routine uses the shadow overlap technique.

CISAF subroutine

Compute the fraction absorbed by each surface of the total beam solar

energy transmitted into the zone. This is for the simple solar

distribution which assumes all beam solar gains are incident on the

floors of the zone. The fraction absorbed is proportional to the solar

absorptance of each floor.

CIVAF subroutine

Compute the distribution of diffuse short wavelength radiation on all

surfaces. Each surface absorbs a fraction of the total diffuse energy

in the zone in proportion to its area and solar absorptance with an allowance for loss through transparent surfaces (F.2.1).

CLIP subroutine

’Clip* the shadowing surface polygon so that none of it lies below the

plane of the shadow receiving surface (E.2). This prevents the casting

of false shadows.

CROSS(A,B,C) subroutine

Compute C as the cross product of A and B. All are three element

vectors

.

220
CTRANS(NS,NR) subroutine

Transform the coordinates of the vertices of surface NS from the global

coordinate system to the surface coordinate system relative to surface

NR (E.1.5).

DAILY subroutine

Perform all operations which can be done once per day. Read the weather

data and set date values. Set the solar gains file group number. Check

external movable insulation and set pointers if the date is in effect.

Set the schedule and control pointers according to the date. Set the

monthly report flags.

DOT(A,B) real function

Compute the dot product of A and B which are each vectors of 3

elements

DUMPAF subroutine

Dump air flow values (RNOS=23 - 1.2.1).

DUMPEH subroutine

Dump values in the environment file header (RN0S=8 - 1.2.1).

DUMPHW subroutine

Dump weather values for the hour (RN0S=21 - 1.2.1).

DUMPIN subroutine

Dump all values read from the simulation input file (RN0S=8 - 1.2.1).

DUMPQB subroutine

Dump results of the zone loads calculations (RNOS=23 - 1.2.1).

DUMPSC subroutine

Report shadowing combinations (RN0S=14 - 1.2.1).

DUMPSG subroutine

Dump solar gain values (RNOS=22 - 1.2.1).

DUMPST subroutine

Dump Surface temperatures and other surface related values (RNOS=23 -

1 . 2 . 1 ).

221
DUMPSl(I) subroutine

Print the solar incidence angles and sunlit fractions for all heat

transfer surfaces for hour number I (RN0Sa 13 - 1.2.1).

DUMPS2(M0DE) subroutine

Dump the numbers which are controlling the shadowing calculations

(RN0S=15 - 1.2.1). MODE is set by the calling to routine to tell which

values to print.

DUMPS3(M0DE) subroutine

Dump details of the shadowing calculations (RN0S=16 - 1.2.1). These

are primarily the coordinates of the shadow and overlap figures. MODE

determines which values to print.

DUMPTC(NZ) subroutine

Dump temperature profile control points for zone NZ (RNOS=22 - 1.2.1).

DUMPTH subroutine

Dump all temperature and flux history values (RNOS=24 - 1.2.1).

DUMPTM subroutine

Dump time and date values (RN0S=21 - 1.2.1).

DUMPVC(NZ) subroutine

Dump ventilation profile control points for zone NZ (RNOS=22 - 1.2.1).

DUMPZL subroutine

Dump zone load values for all zones (RN0S=21 - 1.2.1).

ERROR ( MSG, ETYPE) subroutine

Print error message (character string MSG),

type (ETYPE).

Process according to error

ETYPE=0

ETYPE=1

ETYPE=2

ETYPE=3

informative message.

'warning' — unusual, but not fatal, value or action,

'severe' — unusual value or action usually leading to

incorrect answers or ETYPE=3 error.

'fatal' — immediate run termination usually caused by

exceeding iteration limit, exceeding valid control range,

or invalid arithmetic operation (division by 0, etc.).

222
GAUSSY(A,B,X,N,MAX) subroutine

Solve a system of simultaneous linear algebraic equations (A * X = B)

by Gauss elimination. There are no safety check or pivoting in this

routine: it will not fail gracefully for an invalid set of equations.

It is used in the Newton iteration for pressure where the A matrix

is diagonally dominant and known to produce valid equations.

HBAIR(CNVG) subroutine

Compute the zone air temperatures for normal control (K.1.4) or ventilation control (K.3). Check heat balance convergence and set CNVG

false if it has not been achieved.

HBOUT subroutine

Compute surface outside temperatures for building envelope surfaces.

Use the algorithms in 1.4.

HBSRF subroutine

Compute surface inside temperatures according to algorithms in J.3,

J . 4 j and J • 5

HTRANS( I ,NS ,NV) subroutine

Convert Cartesian coordinates to homogeneous coordinates (E.3) and

compute the area (E.4.1) of the figure.

IBLRPT subroutine

Initialize the building loads report varaibles.

IMRTNW subroutine

Initialize the mean radiant temperature network algorithm. Compute the

MRT view factors (H.2.2) and the constant part of the radiative

conductance (H.2.3).

IMVINS(I,N) subroutine

Determine presence of inside movable insulation for heat transfer

surface I in zone N. If present, set UM(I) to the insulation U-values.

Otherwise, set UM(I) to zero.

INCL0S(N1 , NV1 ,N2 ,NV2 ,NV3 ,NIN) subroutine

Determine which vertices of HC figure N1 lie within figure N2. N1 has

NV1 vertices, and N2 has NV2 vertices. NIN is the number of enclosed

vertices. NV3 is a running count of the number of vertices in the

overlap of N1 and N2. The algorithm is described in E.4. The

coordinates of the inclosed vertices are stored in XTEMP and YTEMP.

223
INITBL subroutine

Direct the set-up of the simulation data. This is the root routine in

the initailization segment. The segmentation is helped by temporary

storage of data on units 4 and 5. The report of array limits is the

first action. It will occur even if there is no SINPFL or ENVTFL

attached. Next, those files are opened and the environment header is

read. Then the SINPFL is read [READER] and the required array space

reported. Some calculations are made that require data simultaneously

for all zones and surfaces [SETIZP, CISAF, and CIVAF] . Dumps [DUMPEH,

DUMPIN] ( RN0S=8 , 1.2.1) and reports [ REPTZD] (RN0S»9, 1.2.1) are written. Inter-segment scratch files 4 and 5 are written.

INITSG subroutine

Direct the calculation of the solar gains multipliers. This is the

root routine of the solar gains segment. The segmentation is helped by

the temporary storage of data on unit 5. Determine shadowing

combinations [SGCOMB]. Read the environment file to determine solar

position and days to be simulated.

INITTH subroutine

Initailize temperatures and temperature/flux histories.

INITZP subroutine

Initialze values for computing zone pressures. In particular, set the

ZZ(0) and PZ(0) values (for ambient air) to zero. Set system flows to zero. Set wind pressures to zero (needed to allow inclusion of PW term

in the equation for internal surfaces).

INTCPT subroutine

Determine all intercepts between the sides of figure NS2 and the sides

of figure NS1 (E.3.4 and E.4).

I ZERO ( ARRAY, LEN) subroutine

Set ARRAY (length LEN) of integers to 0.

JDS( JFLAG , JD ,YR,M0 ,DM) subroutine

If JFLAG = 1, compute the Julian date (JD) from the year (YR) , month

(MO), and day-of-month (DM) (B.1.2). Otherwise, compute YR, MO, and DM

from YR (B.1.3).

L0CRAN(LIST,LEN, ITEM) integer function

Determine the location of ITEM in a LEN long array (LIST) of unordered

words. A linear search is used. An unsuccessful search returns the

value zero.

224
MRL( OUTPUT , SINPFL ,ENVTFL) program

Multi-room loads program. This is the main (or root) program of the

loads calculator. It calls the three segments of the loads

calculation.

MRTNET subroutine

Compute the zone mean radiant temperatures for the second and

subsequent heat balance iterations. Use the simple (H.2.3) or the

detailed (H.2.4) algorithm. This routine includes equations to improve

heat balance convergence.

MRTNT1 subroutine

Compute the zone mean radiant temperatures for the first heat balance

iteration of the hour. Use the simple (H.2.3) or the detailed (H.2.4)

algorithm. This routines includes equations to improve convergence of

the MRT on the first iteration. Development of those equations is not

complete.

MULTOL(NNN,LOCO,NRFIGS) subroutine

Determine the overlaps of figure NNN with previous figures stored in

locations LOCCH-1 through LOCCH-NRFIGS of the HC arrays.

OCNVCO(I ,HM,OABS ,T0 ,HO,HS ,HG) subroutine

Evaluate the heat exchange coefficients HA (=H0), HS, and HG for heat

transfer surface number I. Input also includes the U-value of movalbe

insulation, if present, the solar absorptance of the surface/movable

insulation, and the most recently computes surface outside temperature

TO. Use the algorithms in (1.2). The surface temperature of movable

insulation is estimated from (1.3.8) with HO as input computed from the

simple algorithm.

OMVINS( I ,OABS) subroutine

Evaluate external movable insulation for heat transfer surface number I.

If it is present, return its solar absorptance in OABS and set UM(I).

Otherwise, set UM(I) to zero.

ORDER(NS3,NV3) subroutine

Sort the unordered vertices found by enclosure [INCLOS] and intercept

[INTCPT] into clockwise sequence for use by subsequent overlap

calculations. Results are placed in location NS3 in the HC arrays.

OVRLAP subroutine

Use homogeneous coordinate techniques (E.4) to compute the overlap

between two convex polygons.

225
PAGE (IACT, NEED) subroutine

Write output report page heading. See PAGE description in the list of

IP subroutines.

P0LY1F(X,A,N) real function

Evaluate simple polynomial expression (D.1.7a):

P = A( 1 ) + A(2)*X + A(3)*X2 + ... + A(N)*XN_1

P0LY2F(X,A,N) real function

Evaluate simple polynomial expression (D.1.7b):

P = A(1)*X + A(2)*X2 + ... + A(N)*Xn

QINSRC subroutine

Compute (or set up parameters and pointers) for scheduled internal

loads. First initialize the loads arrays. Then process every element

in the CGS arrays (that is not off for the day) according to type

(CGSTYP)

.

QSDIST subroutine

Distribute short wavelength radiant gains (solar and lights) on the

inside surfaces of the zones. This includes a single pass of light

through transparent interzone partitions and calculation of the light

converted to instantaneous convective gain on internal shades.

Determine if the radiant gain should be placed on movable insulation

instead of the surface. Include the transmission of light through

windows ut of the zone and to the environment.

QSUN subroutine

Determine solar gains. Use the solar gains multipliers and the solar

radiation intensities to determine the diffuse solar gains in the zones,

the solar gains on outside surfaces, and the beam soalr gains on inside

surfaces. Also evaluate placement of movable insulation for the hour

[ IMVINS and OMVINS].

READIN subroutine

Read the simulation input file (SINPFL) and determine the array space

used. Data which was prepared in single element arrays in the IP is

read into multiple element arrays. The reading is directed by

two-element records that tell which arrays will be filled when the next

record is read. The unformatted read statements must match the IP write

statements. Note that each data read is protected to prevent array

overflow. Also note that a simulation control information (created in

FINISH) must be the last record read. Otherwise, an end-of-file is

encountered which terminates the run.

226
REPTBL subroutine

Report building loads (a default action).

REPTSM(KEY) subroutine

Report simulation values like numbers of iterations and execution time.

Time is determined by the non-ANSI function SECOND. This function can

be removed without otherwise effecting the program.

REPTZD subroutine

Report a description of the zone (RN0S=9 - 1.2.1).

RPTASU( NR, MAX, NAME, LIMIT) subroutine

Report array space utilization. For PARAMETERized arrays, print a message giving the number (NR) of elements utilized and the short

parameter name (NAME). If NR is greater than the size (MAX) of the

arrays, print a string of stars to highlight the message and set LIMIT

true.

SETIZP subroutine

Set interzone pointers for interzone partitions, MIX and FAN

operations, and interzone air flow openings. Unmatched items cause run termination.

SGACTN subroutine

Determine which groups of days are used for shadowing calculations.

This is based on the shadowing group dates (Table IV.G.l) and the dates

of any shadowing surface or movable insulation actions which change the

building shadowing configuration. The angles (declination and equation

of time) from which solar position is calculated are determined by

averaging the values for all days in the period.

SGBEAM subroutine

Direct the calculation of solar gains multipliers for a day. For each

hour, compute the angle of incidence of the sun's rays on every surface

(E.2.2); compute the solar multipliers [SHADOW]; store the results on unit 3 for later heat balance calculations.

SGCOMB subroutine

Determine which surfaces can shade each other. This is constant for

the entire simulation and can, therefore, be used to avoid (recomputing

such data at every hour. Data is stored in the SHDCMB array and is

used to direct the calculation sequence of the SHADOW subroutine.

Shadowing combinations are computed for heat transfer, exterior, base

surfaces. All surfaces which can shade the base surface are determined

[ CHK.GSS ] . All heat transfer subsurfaces are determined [CHKSBS]. For

227
the detailed solar distribution algorithm, all inside surfaces which

might receive beam sunlight are determined [CHKBKS]. Complex building

configurations which cause SHDCMB to overflow are handled by reducing

the level of shadowing detail, if possible.

SHADOW( IHOUR ) subroutine

Compute the sunlit areas and solar gains multipliers for all building

envelope surfaces at time IHOUR. From the shadow combinations array,

determine the number of shadowing surfaces (NGSS), inside (back)

surfaces (NBKS), and heat transfer subsurfaces (NSBS). If the surface

faces away from the sun, its sunlit area (and all subsurfaces) must be zero. If it faces the sun and there are no shadowing surfaces, it must

be totally sunlit. Otherwise, compute the shadow patterns on the

surface [SHDGSS]. For window subsurfaces and the detailed solar

distribution call SHDBKS. Then process the subsurfaces [SHDSBS] to

compute their sunlit areas and solar gains multipliers and to determine

how they modify the gross sunlit area of the base surface. Finally,

compute the solar gain multiplier of the base surface.

SHDBKS (NGRS) subroutine

Project the zone inside surfaces along the sun’s rays to the plane of

the current general shadow receiving surface. This is done for the

detailed internal solar distribution (3.1.2) if there are windows on

the base surface and if the sun might shine through the window onto the

inside surface. This is not possible if the inside surface faces the

sun. The projected figure of the inside surface is reduced to fit

within the base surface by the overlap algorithm (E.4) [OVRLAP]

.

SHDGSS (NGRS) subroutine

Compute the shadow figures on surface (base surface - 4.13.2) number

NGRS. If there are no shadowing surfaces, the surface must be fully

sunlit. Otherwise, determine the shadows from all shadowing surfaces.

If the shadowing surface is sunlit, it cannot be casting a show (E.2)

so skip it. Also skip if indicated by shadowing surface dates.

Transform and clip the coordinates of the shadowing surface to the

receiving surface coordinate system (E.2). Determine the overlap of

the shadow on the surface (E.4). Also determine how it overlaps any

previous shadows. Add (signed) shaded areas to compute the gross

sunlit area of the base surface. The effects of subsurfaces is not yet

computed.

SHDINT(L) subroutine

Determine the distribution of solar gains from a single window of

optical type L (index to optical coefficients). Compute multipliers

for zone diffuse gains. Compute multipliers for beam gains using

detailed or simple internal solar distributions. The detailed

distribution involves overlapping the window sunlit pattern with the

228
projections of the internal surfaces along the sun’s rays to the plane

of the base surface and computing the sunlit area of each internal

surface. Tf the internal surface is transparent, its diffuse

transmittance is used to pass sunlight into the adjacent zone. The

simple distribution puts the sunlight on the floor(s) of the zone according to ISABSF [CISAF]. In either case, that portion of the

sunlight which is not directly absorbed by the internal surface becomes

a diffuse gain for the entire zone.

SHDRVL subroutine

Evaluate the shadowing effect of a subsurface setback (4.13.6). The

shadow from the setback reduces the potential sunlit area of the

subsurface. This potential area is still rectangular. It is

overlapped with the shadow figures already known to lie within the

subsurface opening [SHDSBS] to compute the actual sunlit area.

SHDSBS(IHOUR) subroutine

Evaluate the sunlit areas of the subsurfaces (windows, doors). The

shadow patterns have already been accurately determined on the base

surface and stored in the homogeneous coordinate arrays [SHDGSS]. The

subsurfaces are evaluated one at a time. Each subsurface figure is

overlapped with the shadow figures. This determines a sunlit area which must be removed from the gross sunlit area of the base surface.

Check for movable insulation [SMVINS] and if it applies skip most of

the following calculations. Evaluate the shadowing effect of a setback

[REVEAL]. If the surface is transparent, compute its optical properties

and determine the windows contribution to the distribution of sunlight

in the zone [SHDINT]. Finally, compute the solar multipliers for the

subsurface

SIMBLD subroutine

Simulate the building thermal performance. This is the root routine of

the loads segment. The segmentation is helped by temporary storage of

data on unit 4. There are several initializations [IMRTNW, REPTSM(l),

and IBLRPT] . The largest initialization requires several days

simulation [SIMDAY] to remove the transients in the temperature

histories. This initialization is terminated in accordance with the

hourly heat balance convergence criteria. Then the actual simulation

[SIMDAY] is done for the number of days required. A summary report is

printed [REPTBL].

SIMDAY subroutine

Do the simultaneous multizone heat balance calculations for one day.

This involves an initialization of values which are constant for the

day [DAILY] followed by a loop of heat balance calculations for 24

(standard time) hours. The loop involves setting up the constant

values for the hour (weather data, solar gains [QSUN], scheduled loads

229
[QINSRC] , control profiles [CHACS] , distribution of short wavelength

radiation [QSDIST]), doing the first iteration of the multizone heat

balance (compute variable coefficients [VARTMP] , air movements [AIRMVO

or AIRMV1], surface outside heat balances [HBOUT] , mean radiant

temperatures [MRTNT1], surface inside heat balances [HBSRF] , the zone

air heat balances [HBAIR]), do subsequent iterations to convergence,

summarize the hour’s loads data [CALOAD] , and prepare for the next hour

[UTHRMH] . Various data dumps are available as the calculations

proceed.

SMVINS(K,IHOUR,OABS) subroutine

Evalaute exterior movable insulation (EMI). K is the pointer stored in

SSCPTR(heat transfer surface number). It points to data about the EMI

in the ISSC/RSSC arrays. Time (IHOUR), environmental conditions, and

the type of control will determine if the EMI is applied or if it is

not. If it is not, OABS is set to zero. If it is applied, OABS is set

to the solar absorptance of the EMI.

SOLVZP subroutine

Solve the detailed air flow equations for the zone pressures. On the

first iteration of the hour approximate the zone pressures (PZ) by

solving a linear set of equations (flow exponents set to one). This

gives a reasonable set of starting values for PZ. Then use a modified

Newton’s method to solve the simultaneous non-linear algebraic

equations (G.3.5, G.4.1a to c). This method always produces a diagonally dominant matrix which can be solved by GAUSSY, a simplified

Gauss elimination routine.

STATUS (UNIT) subroutine

Print the status of unit number UNIT as determined by the FORTRAN

INQUIRE function. This routine is used for program debugging purposes

only.

SUN3 ( DAYYR , SINDEC ,EQTIM) subroutine

Compute the sine of the solar declination angle (SINDEC) and the

equation of time value (EQTIM) for a given day-of-year (DAYYR)

.

SUN4(H0UR) subroutine

Compute the solar direction cosines for a given HOUR.

UTHRMH subroutine

Update the surface temperature and flux history values. All histories

are stored contiguously in the TFH array. New values of temperature

and flux are added to the array by overwriting old values (that will

not be needed next hour) of other surfaces. This causes the histories

230
to "crawl" slowly through the TFH array. Compute the inside (C.1.4)

and outside (C.1.6) conductive fluxes and store in the TFH array.

Compute KIP (C.1.5) and KOP (C.1.7) for the next hour. Shift the

history values back one hour by incrementing TSHIFT. If the histories

have reached the bottom of the TFH array, shift all values back to the

top of the array and reset TSHIFT.

VARTMP subroutine

Evaluate variables that are directly influenced by zone air

temperature. These variables are the occupant sensible/latent gains

(F.1.1), and the interior convection coefficients (J.l and J.2).

ZERO ( ARRAY,LEN) subroutine

Set ARRAY (length LEN) of real numbers to 0.

231
This diagram (continued over several pages) shows the general relationship

of the loads calculator subroutines to ech other. A subroutine calls other

subroutines which are to the right and below it on the diagram. Multiple calls

to the same routine are not shown, only the first. Circled letters are continuation points for often used groups of subroutines. Not all subroutines and

functions are included. The intrinsic FORTRAN 77 have been left out. The

simple utility routines ERROR and PAGE which are called from many places are

not always shown.

PAGE

INITBL

—INITSG

BDMRL

BDSIM

MRL —

-READIN

j-IZERO

I—ZERO

Udumpin

•-ERROR

RPTASU

-ERROR —SETIZPTERROR

LOCRAN —CISAF —CIVAF

-DUMPEH

-DUMPIN —REPTZD

•SGCOMB —

—CHKGSS

T —CHKSBS-

—CHKBKS

—DUMPSC

-ERROR

CROSS

DOT

-CTRANS —HTRANS —OVRLAP

•—ERROR

CROSS

DOT

ERROR

(A). r* mm

$

i -INCLOS 1

i —INTCPT •

i -ORDER

i -HTRANS ;

i -DUMPS3

l

i L-error

j

i

i 1

Figure VI.B.l Tree structure of the loads calculator program

232
t

GACTN —

|

rL-s

GBEAM—

|

Ud

r

s r

z L-s

DUMPS

SUN3

ZERO

HADOW-

-DUMPS2

-CTRANS

-HTRANS

-DUMPS3

-SHDGSS

-DUMPS2

-CTRANS

-CLIP

-HTRANS

-DUMPS3 —OVRLAP (A)

-MULTOL (B)

—SHDBKS—

I-DUMPS2

[-CTRANS

[-HTRANS

I-DUMPS3

Lovrlap—

j|—DUMPS3

[ t-OVRLAP—

(A) —SHDSBS*

-DUMPS2

-HTRANS

-DUMPS3

-MULTOL —SMVINS

-SHDRVL

•(B)

"I

I-DUMPS2

I—HTRANS

I-DUMPS3

Lmultol —(B)

-POLY IF

-P0LY2F

-SHDINT

-ERROR

~

1_DUMPS2

L-ERROR

Figure VI.B.l (continued)
SIMBLD-

-IMRTNW

.REPTSM

IBLRPT

•INITTH

-INITZP

-SIMDAY-

•REPTBL

DUMPTH

-DAILY

DUMPTM

-DUMPHW

QSUN

•QINSRC

-CHACS

BTWEEN

IMVINS

OMVINS

“fc

DUMPTM

DUMPTC

•QSDIST

DUMPSG

•VARTMP

•AIRMVO

-AIRMV1—

•HBOUT

-MRTNT1

-HBSRF

•HBAIR*

-SOLVZP

-DUMPTM

-DUMPHW —DUMPQB —DUMPAF

OCNVCO

DUMPST

-DUMPQB

-DUMPTM

-DUMPHW

-DUMPTC

—DUMPVC

-DUMPSG

—DUMPST

-DUMPTH

"UAUSSY

-MRTNET

-CALOAD

-UTHRMH

-DUMPTH

-DUMPZL

Figure VI.B.l (concluded)

234
VI.

c

VARIABLES

PARAMETERS are extensively used to set array dimensions. This allows

the same common block to describe only a single surface, schedule, etc., in

the IP program and hold all surfaces, schedules, etc. in the LC. The IP

computes the required dimensions necessary for the LC to simultaneously hold

all descriptions. The following list describes the TARP parameters. "Short

names" are those used to describe parameters in IP and LC reports.

short

parameter

ALEN

name description

maximum number of words decoded at one time

DESLEN - maximum number of characters in a description

MAXAFS AFS maximum number of air flow openings

MAXCDS CDS maximum number of control day-schedules

MAXCGS CGS maximum number of control/general schedule descriptions

MAXCON CON maximum number of constructs

MAXCMB - maximum number of shadowing combinations

MAXCTF CTF maximum number of conduction transfer functions (CTF)

MAXCWS CWS maximum number of conrol week-schedules

MAXDSH DSH maximum number of day-scheduled

MAXENV - maximum number of environments

MAXGTP GTP maximum number of optical constructs

MAXHCS - maximum number of homogeneous coordinate figures

MAXHCV - maximum number of vertices in an HC figure

MAXHTS HTS maximum number of heat transfer surfaces

MAXLNM - maximum number of library names (entries)

MAXNL - maximum number of layers in a construct

MAXNRF - maximum number of response factors

MAXNRT - maximum number of roots for CTF calculation

MAXNWL - maximum number of wavelengths

MAXPFL PFL maximum number of control profiles

MAXPNT - maximum number of user defined points in control profile

MAXRNG - maximum number of control ranges (=MAXPNT+1)

MAXSSC ssc maximum number of special surface coefficients

MAXSRF SRF maximum number of surfaces (ex MASS, inc shadowing)

MAXTFH TFH maximum number of temperature and flux histories

MAXTMP - maximum number of control points (=MAXPNT+2)

MAXWSH WSH maximum number of week-schedules

MAXZON ZON maximum number of zones RFGLEN - number of report flags

UINLEN - number of characters in one user input record

WRDLEN - maximum number of characters in a word

Nearly all significant variables in the TARP are in common blocks. The

list below describes all such variables by giving the name, common block,

subprogram using the variable (IP, LC, or BOTH), type, dimensions (including

parameters), and units on one line followed by a verbal description.

235
A /GLAS3/ IP real (2,4,2)

Absorptances of single panesof glass

(polarization, pane number, side of incidence).

A / ZONL/ LC real (MAXZON) C/W

Temperature independent part of the zone heat balance equation.

For example (K.1.4) and (K.4.1).

AA /GLAS3/ IP real (2,5,2)

Absorptances of layers in a window system

(polarization, surface number, side of incidence).

AAB /GLAS6/ IP real (16,2,5)

Absorptances of a window system for beam light

(angle number, polarization, surface number).

AABW /GLAS8/ IP real (16,5)

Beam absorptances integrated over wavelength and polarization

(angle number, surface number).

AAD / GLAS5/ IP real (2,5,2)

Absorptances of a window system for diffuse light

(polarization, surface number, side of incidence).

AADW /GLAS7/ IP real (5)

Diffuse absorptances integrated over wavelength and polarization

(surface number).

ABI / SHDCTL/ LC real

Fraction of beam solar radiation absorbed at the inside surface of

a window.

ABO /SHDCTL/ LC real

Fraction of beam solar radiation absorbed at the outside surface of

a window.

ACHAR /UINDAT/ IP integer

Pointer to current character in AWORD.

ACNVG1 /RUNCTL/ IP real - -

/ SIMCTL/ LC

Relative air flow convergence (3.1.4).

ACNVG2 /RUNCTL/ IP real — m^/

/SIMCTL/ LC

Absolute air flow convergence (3.1.4).

ACNVG3 /RUNCTL/ IP real m3/s Pa

/SIMCTL/ LC

Minimum pressure across any opening (3.1.4).

236
AD /RF4/ IP real

Upper left element of the layer derivative matrix.

AFAREA /AFSDAT/ IP real - m

2

Air flow opening area for matching interzone openings.

AFEXP /AFSDAT/ IP real

Air flow opening exponent for matching interzone openings.

AFLOW /RUNCTL/ IP integer

/ SIMCTL/ LC

Flag for detailed (1) or simple (0) air flow modeling (3.1.4).

AFSNAM / AFSNAM/ LC chr*WRD (MAXAFS)

Name of zone on opposite side of interzone opening.

AFSPTR / AFSIL/ LC integer (MAXAFS)

Number of the zone on the opposite side of the opening (0 means ambient).

AI / SOLFAC/ LC real (MAXHTS)

Beam solar radiation factor for the inside of a surface.

AID /GLASO/ BOTH real (MAXGTP)

Fraction of diffuse solar radiation absorbed at the inside surface

of a window.

AIRDEN /AIR/ LC real - kg/m3

Density of ambient air.

All /GLAS/ BOTH real (5, MAXGTP)

Polynomial coefficients for window inside beam solar absorptance

( ci in D. 1 .7a)

AI2 /GLAS/ BOTH real (6, MAXGTP)

Polynomial coefficients for window Inside beam solar absorptance

(ci in D.l .7b)

AL /RF4/ IP real

Upper left element of the layer matrix.

ALIST /ALIST/ IP char*WRD (ALEN)

List of words decoded from user input: a section name, key name,

or subkey name and data.

ALTD /EFLHDR/ BOTH real - m

Altitiude of site (not yet used).

AMAXIT /RUNCTL/ IP integer

Maximum number of air flow iterations for convergence (3.1.4).

237
AN /GLAS9/ IP real

Index of refraction of air (=1.0).

AO / SOLFAC/ LC real (MAXHTS)

Beam solar radiation absorption factor for the outside of a surface.

AOD /GLASO/ BOTH real (MAXGTP)

Fraction of diffuse solar radiation absorbed at the outside surface of

a window.

A01 /GLAS/ BOTH real (5, MAXGTP)

Polynomial coefficients for window outside beam solar absorptance

( c^ in D. 1 .7a)

.

A02 /GLAS/ BOTH real (6, MAXGTP)

Polynomial coefficients for window outside beam solar absorptance

(c^ in D. 1 ,7b)

.

AP /IZPDAT/ IP real - m2 Area of interzone partition.

AREA /HTSISL/ BOTH real (MAXHTS) m

2

Area of heat transfer surface.

AS /RF4/ IP real

Upper left element of the total construct matrix.

ASD /GLASO/ BOTH real (MAXGTP)

Absorptance for diffuse radiation of the interior shading device.

AS1 /GLAS/ BOTH real (5, MAXGTP)

Polynomial coefficients for beam absorptance of the interior shading

device (c-^ in D.1.7a).

AS2 /GLAS/ BOTH real (6, MAXGTP)

Polynomial coefficients for beam absorptance of the interior shading

device (c-^ in D.1.7b).

AT /RF4/ IP real

Upper left element of the total derivative matrix.

AWORD /UINDAT/ IP integer

Pointer to current word in ALIST.

AZS /AFSDAT/ IP real - m

Height of air flow opening for matching interzone openings.

B / ZONL/ LC real (MAXZON) W

Temperature dependent part of the zone air heat balance equation.

For example (K.1.4) and (K.4.1).

238
BAREA /BASES/ IP real - m

2

Net area of base surface (** gross area minus subsurface areas).

BASE /BASES/ IP real - m

Distance from surface origin to first vertex (for imaging).

BAZM /BASES/ IP real - degrees

Azimuth angle of base surface (4.13.3).

BBLOAD / ZONL/ LC real (MAXZON) Wh

Baseboard heating load.

BCA /BASES/ IP real

Cosine of azimuth angle of base surface (4.13.3).

BCLD /BLDRPT/ LC real - Wh

Total sensible cooling load for the building.

BCT /BASES/ IP real

Cosine of tilt angle of base surface (4.13.4).

BD /RF4/ IP real

Upper right element of the layer derivative matrix.

BDRELN /RUNCTL/ IP real - degrees

Angle from true north to Y-axis of building coordinate system

(3.1.1 and E . 1 . 1 )

BETA /RF2/ IP real (MAXNL)

Layer thickness divided by the square root of the thermal diffusivity.

BHOC /BASES/ IP real

Value of HOC for the base surface.

BHLD /BLDRPT/ LC real - Wh

Total sensible heating load for the building.

BHTS /BASES/ IP integer

Heat transfer surface number of the base surface.

BKSNR / SHDCTL/ LC integer

Back (inside) surface number.

BL /RF4/ IP real

Upper right element of the layer matrix.

BMNT /BLDRPT/ LC real - C

Minimum temperature of any zone in the building.

BMXC /BLDRPT/ LC real - W

Peak cooling load for the building.

239
BMXH /BLDRPT/ LC real - W

Peak heating load for the building.

BMXT /BLDRPT/ LC real - C

Maximum temperature of any zone in the building.

BS /RF4/ IP real

Upper right element of the total construct matrix.

BSA /BASES/ IP real

Sine of azimuth angle of base surface (4.13.3).

BST /BASES/ IP real

Sine of tilt angle of base surface (4.13.4).

BT /RF4/ IP real

Upper right element of the total derivative matrix.

BTILT /BASES/ IP real - degress

Tilt angle of base surface (4.13.4).

BTYP /BASES/ IP integer

Type number of the base surface: l=envelope, 2=interior.

BZS /BASES/ IP real - m

Average Z coordinate of base surface.

BZT /BASES/ IP real - m

Maximum Z coordinate of base surface.

C /GLAS12/ IP real (6)

Coefficients of the window properties curve fit.

C / SHDCTL/ LC real

X displacement of a shadow in the surface coordinate system (E.2.3a).

CA / SRFIS/ BOTH real (MAXSRF)

Cosine of surface azimuth angle (3.2.1 and 4.13.3).

CALCS /RUNCTL/ IP logical

Opposite of SYNTAX.

CAP /TCDESC/ LC real (MAXPNT+1) V/ Heating/cooling capacities at the control point temperatures

(Lp in K.1.1).

CB / SOLFAC/ LC real (MAXZON)

Beam solar radiation convection factor for the zone.

CBI /SHDCTL/ LC real

Fraction of beam solar radiation convected at an interior shade.

240
CC /RF/ IP real - W/m2 K

Layer thickness * density * specific heat (= thermal capacitance).

CD /RF4/ IP real

Lower left element of the layer derivative matrix.

CDATE /SIMCTL/ LC

Cyclic date (B.1.4).

integer

CDSH /CNTPTR/ LC integer (24,MAXCDS)

Control day-schedules (pointers to control profiles).

CDSNAM /LIBNMS/ LC char*WRD (MAXCDS)

Names of control day-schedules (2.7.1).

CDSO /LIBCTL/ IP integer

Pointer to control day-schedules in LNAMES (location 0).

CFA /REPORT/ BOTH real

Area conversion factor: ft 2 * CFA(2) m'

CFC

CFD

CFH

CFK

/REPORT/ BOTH real - * Specific heat conversion factor: Btu/lbF * CFC(2) “ kJ/kgK

/REPORT/ BOTH real - * Density conversion factor: lb/ft^ * CFD(2) kg/rn^

CFE /REPORT/ BOTH real

Energy conversion factor: Btu * CFE(2) Wh

/REPORT/ BOTH real - * Enthalpy converstion factor: Btu/lb * CFH(2) - kJ/kg

/REPORT/ BOTH real - * Conductivity conversion factor: Btu/hrftF * CFK(2) = W/mK

CFL /REPORT/ BOTH real

Length conversion factor: ft * CFL(2) m

CFM /REPORT/ BOTH real - * Mass conversion factor: lb * CFM(2) ** kg

CFMF /REPORT/ BOTH real - * Mass flow conversion factor: lb/hr * CFMF(2) kg/s

CFP /REPORT/ BOTH real - * Pressure conversion factor: in(H20) * CFP(2) » N/m2 (* Pa)

CFQ /REPORT/ BOTH real

Power conversion factor: Btu/hr * CFQ(2) W

241
CFS

CFT

CFU

CFV

/REPORT/ BOTH real

Speed conversion factor: ft/min * CFS(2) = m/s

/REPORT/ BOTH real

Temperature conversion factor: R * CFT(2) K

/REPORT/ BOTH real - * U-value conversion factor: Btu/hrft^F * CFU(2) = W/m^K

/REPORT/ BOTH real

Volume conversion factor: ft^ * CFV(2) mCFVF /REPORT/ BOTH real - * Volumetric flow conversion factor: ft^/min * CFVF(2) = m^/s

CGSDX / CGSIL/ BOTH integer (MAXCGS)

Pointer to week-schedule (or control week-schedule)

CGSHX /CGSIL/ BOTH integer (MAXCGS)

Pointer to day-schedule (or control day-schedule)

CGSNAM / CGSNAM/ LC chr*WRD (MAXCGS)

Name of zone to which the scheduled load applies. This identifies

the adjacent zone for which MIX and FAN operations apply.

CGSOFF /CGSIL/ BOTH integer (MAXCGS)

Date (cycilc date form - eq B.1.4) week-schedule ends.

CGSON /CGSIL/ BOTH integer (MAXCGS)

Date (cyclic date form - eq B.1.4) week-schedule begins.

CGSTYP /CGSIL/ BOTH integer (MAXCGS)

Type of action:

1 = people

2 = lights

3 = electric equipment

4 = gas equipment

5 = steam equipment

6 = hot water equipment

7 = other equipment

8 = infiltration

9 = ventilation

10 = controls

11 = day lighting

12 = steam baseboard heat

13 = hot water baseboard heat

CGSZON /CGSIL/ BOTH integer (MAXCGS)

Number of the zone for which the action applies.

242
CL /RF4/ IP real

Lower left element of the layer matrix.

CLKTIM / SIMCTL/ LC integer - hr

"Clock time" (=t<j in B.1.1) for selecting scheduled activities.

CNAME /ZNAMES/ IP char*WRD - Construct name (4.13.1).

CND /RF/ IP real - W/m2 K

Conductivity of the construct.

CNTCAP / CNTPFL/ BOTH real ( HAXPNT , MAXPFL) W

Heating/cooling capacity at the control point.

CNTTMP /CNTPFL/ BOTH real (MAXPNT, MAXPFL) C

Effective zone temperature of the control point.

CNVMRT / ZONL/ LC real (MAXZON)

Parameter user to predict the mean radiant temperature (TR) and

speed zone heat balance convergence.

COND /MATDAT/ IP real (MAXNL) W/mK

Conductivity of each layer of construct (from outside).

CONNAM /LIBNMS/ LC char*WRD (MAXCON)

Construct names (2.5.1).

CONSO /LIBCTL/ IP integer

Pointer to constructs in LNAMES (location 0).

CONTEM /TCDESC/ LC real (MAXTMP , MAXZON) C

Control point temperatures.

COSBR /RUNCTL/ IP real

Cosine of the building rotation angle.

COSD / SLPSSH/ BOTH real

Cosine of the solar declination angle.

COSINC / GLAS 1 / IP real

Cosine of the angle of incidence.

COSL /EFLHDR/ BOTH real

Cosine of the latitude angle.

COSZR /BASES/ IP real

Cosine of the zone rotation angle.

CP /TCDESC/ LC integer (MAXZON)

Pointer to control profile.

243
CPAIR /AIR/ LC real Ws/kgK

Specific heat of air.

CPFLO /LIBCTL/ IP integer

Pointer to control profile in LNAMES (location 0).

CPOLD / ZONL/ LC integer (MAZON)

Prior hour's pointer to control profile.

If CP = CPOLD, it is not necessary to recompute the control profile.

CR /TCDESC/ LC real (MAXZON)

Zone temperature control radiant fraction (b in eq K.1.3).

CS /RF4/ IP real

Lower left element of the total construct matrix.

CSDECL /ENVDAT/ BOTH real

Cosine of the solar declination angle.

CT / SRFIS/ BOTH real (MAXSRF)

Cosine of surface tile angle (3.2.2 and 4.13.4).

CT /RF4/ IP real

Lower left element of the total derivative matrix.

CTF /BLDCTF/ LC real (MAXCTF)

Array of conduction transfer fucntions for all constructs.

CTFXO /CONDAT/ BOTH real (MAXCON) W/m2K

X conduction transfer function for each construct for time = 0.

CTFYO /CONDAT/ BOTH real (MAXCON) W/m2 K

Y conduction transfer function for each construct for time = 0.

CTFZO /CONDAT/ BOTH real (MAXCON) W/m2 K

Z conduction transfer function for each construct for time =0.

CTHETA /SRFIS/ BOTH real (MAXSRF)

Cosine of the angle of incidence of the sun's rays on the surface.

CTILT /HTSISL/ BOTH real (MAXHTS)

Cosine of the heat transfer surface tilt anlge.

CTQ /RF1/ IP real (5)

Flux conduction transfer functions (orders 0 through 5).

CTX /RF1 / IP real (0:5 ,0:MAXNRF) W/m2 K

X (external) conduction transfer functions (orders 0 through 5).

CTY /RF1/ IP real (0:5,0: MAXNRF ) W/m2 K

Y (cross) conduction transfer functions (orders 0 through 5).

244
CTZ /RF1/ IP real (0:5,0:MAXNRF) W/m2 K

Z (internal) conduction transfer functions (orders 0 through 5)

CWSH / CNTPTR/ LC integer (12, MAXCWS

)

— Control week schedules (2.8): pointers to control day schedules

CWSNAM /LIBNMS/ LC char*WRD (MAXCWS) — Names of control week shcedules (2.8.1).

CWSO /LIBCTL/ IP integer _ — Pointer to control week-schedules in LNAMES (location 0).

D /RF1/ IP real (5) _

1.0 - RATIO

DAYOFM /ENVDAT/ BOTH integer — — Day of the month number (DM in B .1.2)

DAYOFS / SIMCTL/ LC integer — — Number of days simulated.

DAYOFW /ENVDAT/ BOTH integer — — Day of the week number (DW in B. 1.2).

DAYOFY /ENVDAT/ BOTH integer — — Day of the year number (DY in B. 1.2).

DAYTYP /SIMCTL/ LC integer - — Day type number (used to select schedules)

DB / SOLFAC/ LC real (MAXZON) — Beam radiation factor for zone (beam converted to diffuse by shade).

DD /RF4/ IP real

Lower right element of the layer derivative matrix.

DDBP /DDENVT/ IP real - Pa

Design day barometric prpessure (1.6.6).

DDCLR /DDENVT/ IP real

Design day clearness number (1.6.9).

DDDOFM /DDENVT/ IP integer

Design day day-of-month number (1.6.5).

DDDTYP /DDENVT/ IP integer

Design day type number (1.6.12).

DDMDBT /DDENVT/ IP real - C

Design day maximum dry bulb temperature (1.6.2).

245
DDMON /DDENVT/ IP integer

Design day month number (1.6.5).

DDRN /DDENVT/ IP integer

Design day rain indicator (l=rain) (1.6.10).

DDSNW /DDENVT/ IP integer

Design day snow indicator (l=snow) (1.6.11).

DDTRNG /DDENVT/ IP real - C

Design day temperature range (from 1.6.2 and 1.6.3).

DDWBT /DDENVT/ IP real - C

Design day wet bulb temperature (1.6.4).

DDWDIR /DDENVT/ IP real - degrees

Design day wind direction (1.6.8).

DDWSPD /DDENVT/ IP real - m/s

Design day wind speed (1.6.7).

DELT /REPORT/ BOTH real - * Temperature conversion factor: (F+DELT(2)) * CFT(2) = C

DEM /RUNCTL/ IP logical

Detailed error messages (1.1.3).

DENS /MATDAT/ IP real (MAXNL) kg/m3

Material density (2.4.5).

DG / SOLFAC/ LC real (MAXZON)

Ground reflected diffuse radiation factor for the zone.

DIR /ENVDAT/ BOTH real (24) degress

Wind direction (G.1.3).

DL /RF4/ IP real - Lower right element of the layer matrix.

DS /RF4/ IP real

Lower right element of the total construct matrix.

DS /SOLFAC/ LC real (MAXZON)

Diffuse sky radiationn factor for the zone.

DSH / SCHDLS/ LC real (24.MAXDSH)

Day schedules (2.2).

DSHNAM /LIBNMS/ LC char*WRD (MAXDSH)

Day schedule names (2.2.1).

246
DSTIND /ENVDAT/ BOTH integer

Daylight savings time indicator.

DSO /LIBCTL/ IP integer - Pointer to day schedules in LNAMES (location 0).

DT /RF4/ IP real - Lower right element of total derivative matrix.

DTR /REPORT/ BOTH real * Conversion factor: degrees * DTR = radians.

DYS /CALNDR/ BOTH char*3 (12) - Names of day types (2.3.3).

EELOAD / ZONL/ LC real (MAXZON) Wh

Zone electric load (lights plus electric equipment).

EFILL /ENVDAT/ BOTH integer (3)

Array filler.

EFSTR /TCDESC/ LC integer (MAXZON)

Pointer to temperature control range (p in K.1.1).

EMIT /MATDAT/ IP real (MAXNL)

Emittance o material for thermal wavelength radiation (2.4.8).

EMUI /RUNCTL/ IP integer

Input in English (2) or metric (1) units (1.1.7).

EMUO /REPORT/ BOTH integer

Output in English (2) or metric (1) units (1.1.7).

ENDATE / SIMCTL/ LC integer

Cyclic date on which current shadowing data ends.

ENVDAT /ENVDAT/ BOTH integer (256)

Environment data - all equivalenced to this array.

ENVREC /SIMCTL/ LC integer

Environment record number (index to ENVTFL direct access file).

ENVTNR /SIMCTL/ LC

Environment number.

integer

EQTIME /ENVDAT/ BOTH

Equation of time.

real - hr

EQTM / SLPSSH/ BOTH

Equation of time.

real - hr

247
ETITLE /TITLES/ BOTH char*DESC (13)

Environment titles (1.5.1 and 1.5.1).

EVDATE /ENVDAT/ BOTH integer

Julian date (JD in B.1.2).

EXTC /GLAS9/ IP real (4)

Product of pane extinction coefficient times thickness.

EXTCW / GLAS 10/ IP real (4,MAXNWL)

Product of pane extinction coefficient times thickness for each

wavelength.

EVTR . /TCDESC/ LC integer (MAXZON)

Pointer to ventilation control temperature range.

FACTOR / ZONL/ LC real (MAXZON) C

Intermediate result for computing mean radiant temperature

(TRLnif H.2.4c)

.

FAFS / ZONISL/ BOTH integer (MAXZON)

Number of the first air flow opening in the zone description.

FAHS /ZONL/ LC real (MAXZON) m

3 /s

Net air flow from the air handling system into the zone (set to 0).

FAREA / AFSIL/ BOTH real (MAXAFS) m

2 Air flow opining area (4.14.1).

FBKSHC / SHDCTL/ LC integer

Pointer to HC location for inside (back) surface calculations.

FC0S1 /AFSIL/ BOTH real (MAXAFS)

Direction cosine of opening for computing relative wind direction.

FC0S2 /AFSIL/ BOTH real (MAXAFS)

Direction cosinf of opening for computing relative wind direction.

FCOUNT / SIMCTL/ LC integer

Number of air flow iterations from start of simulation.

FEXP /AFSIL/ BOTH real (MAXAFS)

Air flow opening exponent (4.14.2).

FD / GLAS9/ IP real (2,4)

Thickness of reflective films (D in D.4.4a).

(side, pane number)

FGSSHC /SHDCTL/ LC integer

Pointer to HC location for general shadowing surface calculations.

248
FHTS / ZONISL/ BOTH integer (MAXZON)

Number of the first heat transfer surface in the zone description.

FINSHC / SHDCTL/ LC integer

Pointer to HC location for inside solar distribution calculation.

FK /GLAS9/ IP real (2,4)

Reflective film extinction coefficient (k£ in D.4.1).

(side, pane number)

FKW /GLAS10/ IP real (4.MAXNWL)

Reflective film extinction coefficient (k-2 in D.4.1).

(pane number, wavelength)

FLRTFP /CONDAT/ BOTH integer (MAXCON)

Pointers to flux components of conduction transfer functions.

FLXHPE /HTSIL/ BOTH integer (MAXHTS)

Pointers to external flux histories.

FLXHPI /HTSIL/ BOTH integer (MAXHTS)

Pointers to internal flux histories.

FN /GLAS9/ IP real (2,4)

Reflective film index of refraction (n£ in D.4.1).

(side, pane number)

FNW /GLAS10/ IP real (4,MAXNWL)

Reflective film index of refraction (n£ in D.4.1).

(pane number, wavelength)

FP / ZONL/ LC integer (MAXZON)

Pointer to scheduled fan action (RCGS).

FRVLHC /SHDCTL/ LC integer

Pointer to HC location for setback (reveal) calculations.

FSBSHC /SHDCTL/ LC integer

Pointer to HC location for subsurface calculations.

FSG /HTSISL/ BOTH real (MAXHTS)

Angle factor between the surface and the ground (4.13.8 and E.5.1 and

I. 2. 6c)

FSRF /ZONISL/ BOTH integer (MAXZON)

Number of first surface in zone description.

FSS /HTSISL/ BOTH real (MAXHTS)

Angle factor between the surface and the sky (4.13.7 and E.5.1 and

I .2 .6a,b)

249
FTRANS /MATDAT/ IP real (MAXNL) - Transmittance of pane of glass with reflective film (2.4.11

G /HTSL/ LC real (MAXHTS) W/m2 K

Constant part of HR (H.2.4a).

GELOAD / ZONL/ LC real (MAXZON) Wh

Gas equipment load.

GN /GLAS9/ IP real (4) — Index of refraction of pane.

GNW / GLAS10/ IP real ( 4 , MAXNWL

)

_ Wavelength dependent indices of refraction.

GRSNR /SHDCTL/ LC integer - - Surface number of the general (base) shadow receiving surface.

GSSNR / SHDCTL/ LC integer

Surface number of the general shadowing surface.

GTND / SIMCTL/ LC logical

"Go to next day.” (False during temperature history initialization.)

HC /HTSL/ LC real (MAXHTS) W/m2 K

Inside convection coefficient.

HCA /HCFS/ LC integer (MAXHCV ,MAXHCS)

'A 1 homogeneous coordinates of side of figure.

HCAREA /HCFS/ LC real (MAXHCS) m

2 Area of homogeneous coordiante figure.

HCB /HCFS/ LC integer (MAXHCV, MAXHCS)

' B' homogeneoues coordinates of sides of figure.

HCC /HCFS/ LC integer (MAXHCV , MAXHCS)

'C' homogeneous coordinates of sides of figure.

HCMULT /SHDCTL/ LC real

Homogeneous coordinate multiplier: convert dimensions in meters to

integer values in millimeters.

HCNS /HCFS/ LC integer (MAXHCS)

Surface numbers of back surface homogeneous coordinate figures.

HCNV /HCFS/ LC integer (MAXHCS)

Number of vertices of homogeneous coordinate figures.

HCOUNT /SIMCTL/ LC integer

Number of heat balance iterations in current hour.

250
HCT /HCFS/ LC real (MAXHCS)

Transmittances of homogeneous coordinate figures.

HCX /HCFS/ LC integer (MAXHCV, MAXHCS)

'X' homogeneous coordinates of vertices of figure.

HCY /HCFS/ LC integer (MAXHCV, MAXHCS)

* Y' homogeneous coordinates of vertices of figure.

HOC /HTSIL/ BOTH real (MAXHTS)

Constant part of detailed outside convection coefficient.

HOLIND /ENVDAT/ BOTH integer

Holiday indicator (1 = holiday; 0 not holiday;

2 = special 1; 3 * special 2, ...)

HR /HTSL/ LC real (MAXHTS) W/m2 K

Surface radiative conductance (H.2.3 and H.2.4d).

HRS / CALNDR/ BOTH char*2 (24)

Hours (for reports).

HTBAL /RUNCTL/ IP integer

/ SIMCTL/ LC

Heat balance method (3.1.5).

HTS /SHDCTL/ LC integer

Heat transfer surface number.

HTSS /SHDCTL/ LC integer

Heat transfer subsurface number.

HWLOAD / ZONL/ LC real (MAXZON) Wh

Hot water load.

ICOUNT /SIMCTL/ LC integer

Number of non-convergent heat balance iterations.

IHALG /RUNCTL/ IP integer

/SIMCTL/ LC

Inside convection algorithm (3.1.7).

INF /ZONL/ LC real (MAXZON) W/C

Simple infiltration capacity rate.

INTSHD / GLAS1/ IP integer

0 = no interior shade; 1 * interoir shade present.

IP /ZONL/ LC integer (MAXZON)

Pointer to scheduled infiltration (RCGS).

251
ISABS /CONDAT/ BOTH real (MAXCON)

Inside surface short wavelength absorptance (2.4.7 and 2.5.7).

ISABSF /HTSIS/ BOTH real (MAXHTS)

Fraction of beam solar gain absorbed directly by surface.

The remainder becomes a diffuse gain to the zone.

ISENV /HTSISL/ BOTH integer (MAXHTS)

Surface inside environment number (= zone number).

ISHC / GLAS1 1/ IP integer

1 indicates properties of interior shade are independent of theta.

0 not yet used.

ISSC / SSCISL/ BOTH integer (9,MAXSSC)

Equivalenced to RSSC.

ITABS /CONDAT/ BOTH real (MAXCON)

Inside surface thermal absorptance/emittance (2.4.8 and 2.5.8).

IVABSF /CONDAT/ BOTH real (MAXCON)

Fraction of visible diffuse light absorbed by each surface.

IZPHTS /HTSISL/ BOTH integer (MAXHTS)

Heat transfer surface number of opposite side of interzone surface.

Equivalenced to FSS to save storage space.

JDATE / SHDCTL/ LC integer

Julian date.

JDATEO /SHDCTL/ LC integer

Julian date at start of shadow group-of-days

.

JJ / GLAS4/ IP integer

Inner or outer surface indicator.

KELVIN /REPORT/ BOTH real - C

Conversion factor: C + KELVIN = K

KEY1 /ALIST/ IP char*WRD - Name of current input section.

KEY2 /ALIST/ IP char*WRD - Name of current input key.

KK /RF2/ IP real (3 ,MAXNRT)

Combination of residue elements.

KIP / HTSL/ LC real (MAXHTS) W/m2

Constant part of inside conductive flux (C.1.5).

252
KOP /HTSL/ LC real (MAXHTS) W/m2

Constant part of outside conductive flux (C.1.7).

KPTR / HTSISL/ BOTH integer (MAXHTS) - Pointer to construct data.

LAFS /ZONISL/ BOTH integer — — Number of the last air flow opening in the zone description.

LALOAD / ZONL/ LC real (MAXZON) Wh

Latent heat gain.

LAMBDA / GLAS1/ IP real — nm

Wave length of light for optical calculations.

LATD /EFLHDR/ BOTH real — degrees

Location latitude (1. 3.2).

LCNVG1 /RUNCTL/ IP real _ —

/ SIMCTL/ LC

Loads convergence.

LCNVG2 /RUNCTL/ IP real — W

/SIMCTL/ LC

Minimum load.

LDESC /LIBNMS/ IP char*DESC — — Location description (1.3.1).

LENGTH / MATDAT/ IP real (MAXNL) m

Thickness of layer (21.5.3).

LFLAGS /LIBCTL/ LIBCTL logical (7) - Library report flags (2.1.3).

LFLAGS /SIMCTL/ LC logo cal (4) - Temporary report flags corresponding to RFLAGS 21-24.

LUTS /ZONISL/ BOTH integer (MAXZON)

Number of the last heat transfer surface of the zone.

LIBNAM /LIBNMS/ IP char*WRD - Library name (2.1.1).

LNAMES /LIBNMS/ IP char*WRD (256)

Names of library entries - used as index to library data.

LOCHCA /SHDCTL/ LC integer

Current location in the homogeneous coordinate arrays.

253
LOCSCM / SHDCTL/ LC integer

Current location in the shadowing combinations (SHDCMB) array.

LONG /EFLHDR/ BOTH real

Location longitude (1.3.3).

LR /RF2/ IP real (MAXNL)

Thermal resistance of layer.

LRAIN / SIMCTL/ LC logical

Rain indicator for the hour.

LSRF / ZONISL/ BOTH integer (MAXZON)

Surface number of the last surface of the zone.

degrees

m2 K/W

LTITLE /TITLES/ BOTH char*DESC - Location title (1.3.1).

LUSED /LIBCTL/ IP logical (MAXLNM)

Set to TRUE when a library name is referenced.

MATLO /LIBCTL/ IP integer

Pointer to matrials (location 0).

MAXIT /RUNCTL/ IP integer

/SIMCTL/ LC

Maximum number of heat balance iteration in an hour (3.1.3).

MAXPAN / GLAS9/ IP integer

Maximum number of glass pane in a window.

MCPI / ZONL/ LC real (MAXZON) W/K

Mass flor rate time specific heat for infiltration.

MCPM /MIXING/ LC real (MAXZON) W/K

Mass flow rate times specific heat for mixing.

MCPTM /MIXING/ LC real (MAXZON) W

MCPM times air temperature for mixing.

MCPV /ZONL/ LC real (MAXZON) W/K

Mass flor rate times specific heat for ventilation.

MDHMNT / BLDRPT/ LC integer - Month/day/hour at which minimum temperture (BMNT) occurs.

MDHMXC /BLDRPT/ LC integer

Month/day/hour at which maximum cooling load (BMXC) occurs.

MDHMXH /BLDRPT/ LC integer

Month/day/hour at which maximum heating load (BMXC) occurs.

254
MDHMXT / BLDRPT/ LC integer

Month/ day/hour at which maximum temperture (BMXT) occurs

ME RID / EFLHDR/ LC real

Degrees east of time zone central meridian.

MIRRX /BASES/ IP logical

Mirror X coordinates (4.1.5).

MIRRY /BASES/ IP logical

Mirror Y coordinates (4.1.6).

MISS / SHDCTL/ LC integer

Results of polygon overlap calculation:

1 = no overlap

2 = NS1 completely within NS 2

3 = NS2 completely within NS1

4 = partial overlap

MNAMES /MATNMS/ IP char*WRD (MAXNL)

Names of materials (2.4.1).

MNS / CALNDR/ BOTH char*3 (12)

Month names.

MONTH /ENVDAT/ BOTH integer - Month number.

MP / ZONL/ LC integer (MAXZON)

)

Pointer to scheduled mixing (RCGS).

MTYPE /MATDAT/ IP integer (MAXNL)

Material type (2.4,.15, 2.4.16, 2 .4.17):

0 =* opaque , 1 * glass, 2 shade, 3 -

MXCDS /LIBCTL/ IP integer - Maximum number of control day=schedules (2.

MXCONS /LIBCTL/ IP integer - Maximum number of constructs (2.1.3).

MXCPFL /LIBCTL/ IP integer

Maximum number of control profiles (2.1.3).

MXCWS /LIBCTL/ IP integer

Maximum number of control week-schedules (2.1.3).

MXDS /LIBCTL/ IP integer

Maximum number of day-schedules (2.1.3).

degrees

255
MXMATL /LIBCTL/ IP integer

Maximum number of materials (2.1.3).

MXWS /LIBCTL/ IP integer

Maximum number of week-schedules (2.1.3).

NAFS / SIMCTL/ LC integer

Total number of air flow opening descriptions.

NBKS /SHDCTL/ LC integer

Number of back surfaces.

NBKSHC /SHDCTL/ LC integer

Number of back figures in HC arrays.

NC /IZPDAT/ IP integer

Number of temperature CTF to determine interzone surface match.

NCDS /LIBCTL/ IP integer

/SIMCTL/ LC

Number of control day-schedules.

NCGS /RUNCTL/ IP integer

/SIMCTL/ LC

Number of zone control and general schedules (RCGS).

NCMB / SHDCMB/ LC integer

Number of shadowing combinations.

NCL /RF/ IP integer

Number of conductive layers in construct.

NCON /SIMCTL/ LC integer

Number of constructs.

NCONS /LIBCTL/ IP integer

Number of constructs.

NCPFL /LIBCTL/ IP integer

Number of control profiles.

NCTF /RUNCTL/ IP integer

/SIMCTL/ LC

Number of conduction transfer functions coefficients.

NCWS /LIBCTL/ IP integer

/SIMCTL/ LC

Number of control week-schedules.

NDS /LIBCTL/ IP integer

Number of day-schedules.

256
NDSH / SIMCTL/ LC integer

Number of day-schedules.

NEVTRC /EFLHDR/ BOTH integer

Number of ventilation temperature ranges.

NFRTFC /CONDAT/ BOTH integer (MAXCON)

Number of flux referring CTF coefficients.

NGSS / SHDCTL/ LC integer

Number of general shadowing surfaces.

NGSSHC /SHDCTL/ LC integer

Number of general shadowing figures in homogeneous coordinate arrays.

NGTP /RUNCTL/ IP integer

/SIMCTL/ LC

Number of constructs with optical coefficients.

NHCS /SHDCTL/ LC integer

Maximum number of homogeneous coordinate figures used.

NHTS /RUNCTL/ IP integer

/SIMCTL/ LC

Number of heat transfer surfaces.

NINSHC /SHDCTL/ LC integer

Number of inside surfaces (shadow overlaps on back surfaces) in HC

arrays

NIN1 /SHDCTL/ LC integer

Number of vertices of HC figure NS1 within HC figure NS2.

NIN2 /SHDCTL/ LC integer

Number of vertices of HC figure NS2 within HC figure NS1.

NIZP / IZPDAT/ IP integer

Number of unmatched interzone surfaces.

NL /RF/ IP integer

Number of layers in construct.

NMATL /LIBCTL/ IP integer

Number cf materials in library.

NOFOCC / ZONL/ LC integer (MAXZON)

Number of occupants (4.2.2).

NOIMI /HTSISL/ BOTH integer (MAXHTS)

True if there is never inside movable insulation (4.18) on the surface.

Equivalenced to FSG to save space.

257
NOSC /SIMCTL/ LC integer

Number of "other side coefficient” (4.16) descriptions.

NPANES / GLAS1/ IP integer

Number of glass panes in window construct.

NPFL /SIMCTL/ LC integer

Number of contol profiles.

NQ / IZPDAT/ IP integer

Number of flux CTF coefficients for matching interzone surfaces.

NRATIO /RF2/ IP integer - - Number of RATIO.

NRCTR /TCDESC/ LC (MAXZON) - Number of control temperature ranges in control profile.

NRDAYS /EFLHDR/ BOTH integer (13)

Number of days in the simulation environment.

NRENVS /EFLHDR/ BOTH integer

Number of environments on the environemnt file.

NRF /RF/ IP integer - - Number of temperature CTF calculated.

NRSTAT /CNTPFL/ BOTH integer (MAXPFL)

Number of control points in control profile.

NRT /RF/ IP integer

Number of roots computed.

NRVLHC /SHDCTL/ LC integer

Number of reveal figures in HC arrays.

NRVTR /TCDESC/ LC integer (MAXZON)

Number of ventilation temperature ranges.

NSBS /SHDCTL/ LC integer

Number of door/window subsurfaces.

NSBSHC /SHDCTL/ LC integer

Number of subsurface figures in the homogeneous coordinate arrays

.

NSRF /RUNCTL/ IP integer

/ SIMCTL/ LC

Number of surfaces (all except internal mass).

NS SC /RUNCTL/ IP integer - Number of special surface coefficients (RSSC).

/SIMCTL/ LC

258
NSURFS / GLAS1/ IP integer

Number of optical surfaces in window construct (glass + shade).

NS1 / SHDCTL/ LC integer

Number of the HC figure being overlapped.

NS2 /SHDCTL/ LC integer

Number of the HC figure doing the overlapping.

NS3 /SHDCTL/ LC integer

HC location to place results of overlap.

NTFH /RUNCTL/ IP integer

/ SIMCTL/ LC

Number of temperature/flux history terms (with space for time shift)

.

NTIMES /PSYCOM/ IP integer

Number of times specific psychrometric errors have occurred.

NTRTFC /CONDAT/ BOTH integer (MAXCON)

Number of temperature CTF coefficients.

NUAFS1 / AFSDAT/ IP integer - - Number of unmatched interzone air flow openings.

NV /SRFIS/ BOTH integer (MAXSRF) — Number of vertices of surface

.

NVERTS /VERTS/ IP integer — — Number of vertices of surface.

NVS / SHDVRT/ LC integer - — Number of vertices of the shadow.

NVT /SHDVRT/ LC integer - — Number of vertices of the transformed/ clipped surface .

NV1 /SHDCTL/ LC integer - — Number of vertices of figure NS1.

NV2 /SHDCTL/ LC integer - - Number of vertices of figure NS2.

NV3 /SHDCTL/ LC integer - - Number of vertices of figure NS3.

NWL /GLAS10/ IP integer - - Number of wavelengths used to evaluate optical properties

NWS /LIBCTL/ IP integer - - Number of week-schedules.

259
NWSH /SIMCTL/ LC integer

Number of week-schedules

.

NXMI /SIMCTL/ LC integer

Number of exterior movable insulation (4.17) descriptions.

NZON /RUNCTL/ IP integer - /SIMCTL/ LC

Number of zones.

OAMFL / ZONL/ LC real (MAXZON)

Infiltration mass flow rate.

kg/s

OBP /KNVDAT/ BOTH real (24)

Barometric pressure (absolute).

ODB /ENVDAT/ BOTH real (24)

Ambient dry bulb temperature.

OFFDAT / SRFIS/ BOTH integer (MAXSRF)

Stop date (cyclic) for shadowing surfaces.

OHALG /RUNCTL/ IP integer

/SIMCTL/ LC

Outside surface coefficient algorithm (3.1.6).

Pa

C

OHR /ENVDAT/ BOTH real (24)

Humidity ratio of ambient air.

OLDW /RUNCTL/ IP logical

Use old WTHRFL (1.1.6).

ONDAT /SRFIS/ BOTH integer (MAXSRF)

Start date (cyclic) for shadowing surfaces.

ORDER /RF/ IP integer

Order (number of flux coefficients) of conduction transfer functions.

OROUGH /CONDAT/ BOTH integer (MAXCON)

Surface outside roughness number (2.4.14 and 2.5.6).

OSABS /CONDAT/ BOTH real (MAXCON)

Surface outside solar absorptance (2.4.7 and 2.5.4).

OSENV /HTSISL/ BOTH integer (MAXHTS)

Surface outside environment number:

>0 = adjacent zone number

-1 = internal mass

-2 = partition

-3 = envelope surface

-4 = surface with OSC (4.16)

260
OTABS /CONDAT/ BOTH real (MAXCON)

Surface outside thermal absorptance/emittance (2.4.8 and 2.5.8).

OTLOAD / ZONL/ LC real (MAXZON) Wh

Load from "other” sources (4.4.7).

OWB /ENVDAT/ BOTH /real (24) C

Ambient wet bulb temperature.

PFC /RF2/ IP real (MAXNRT)

Components of pulse functions.

PFLNAM /LIBNMS/ LC char*WRD (MAXPFL)

Names of control profiles.

PI /REPORT/ 30TH

n - 3.14159...

real

pp /ZONL/ LC

Pointer to people gains

integer

(in RCGS)

(MAXZON)

•

-

PRAIR /AIR/ LC

Prandtl number of air.

real - -

PS /AFSIL/ BOTH

Stack pressure (G.2.3).

real (MAXAFS) Pa

PTITLE /TITLES/ BOTH

Project title (1.1.1).

char*DESC - -

PW /AFSIL/ BOTH

Wind pressure (G.1.3).

real (MAXAFS) Pa

PZ /ZONL/ LC

Zone pressure (G.1.3).

real (MAXZON) Pa

Q /GLAS12/ IP real (16)

Dependent varaible in optical properties curve fits

.

QBV /ZONL/ LC real

Total beam sunlight entering zone (MAXZON)

(for daylight

W

calculations)

QC /ZONL/ LC real (MAXZON)

Solar gain convected from shading devices.

W

QD /ZONL/ LC real (MAXZON) W

Total diffuse solar gain in zone (includes beam radiation diffused

after first surface absorption in zone).

QDV /ZONL/ LC real (MAXZON) W

Total diffuse sunlight entering zone (for daylight calculations).

261
QFSTDC /TCDESG/ LC real (MAXRNG, MAXZON) W/K

LT in (K.1.2a).

QFSTIF / TCDESC/ LC real (MAXRNG,MAXZON) W

LC in (K.1.2a).

QFVTDC /TCDESC/ LC real (4, MAXZON) W/K

Ventilation coefficient (similar to QFSTDC).

QFVTIF /TCDESC/ LC real (4, MAXZON) W

Ventilation coefficient (similar to QFSTIF).

QL /ZONL/ LC real (MAXZON) W

Total long wave radiant gains in zone (QLn in H.2.5).

QOCCON /ZONL/ LC real (MAXZON) W

Convective gains from occupants.

QOCLAT /ZONL/ LC real (MAXZON) W

Latent gains from occupants.

QOCRAD /ZONL/ LC real (MAXZON) W

Radiant gains from occupants.

QS /ZONL/ LC real (MAXZON) W

Total diffuse , short wavelength gains in zone.

QSA /ZONL/ LC real (MAXZON) W

Solar radiation available for daylighting.

QSI /HTSL/ LC real (MAXHTS) W/m2

Short wave radiant flux absorbed by inside surfaces.

QSM /HTSL/ LC real (MAXHTS) W/m^

Short wave radaint flux absorbed by movable insulation.

QSO /HTSL/ LC real (MAXHTS) W/m2

Short wave radaint flux absorbed by outside surface.

R / GLAS2/ IP real (2,4,2) - Reflectances of single pane of glass

(polarization, pane number, side of incidence).

RAIN / ENVDAT/ BOTH integer

Rain indicator (24 hours, compressed).

RALOAD /ZONL/ LC real (MAXZON) Wh

Return air load (part of sensible gain from lights 4.3.3).

RATIO /RF/ IP real (MAXNRT)

Ratios defining higher order conduction transfer functions.

262
RCGS / CGSIL/ BOTH real (5,MAXCGS)

Data for scheduled loads; varies according to CGSTYP.

Type = 1 (people - 4.2)

1 = number of occupants

2 = activity level W

3 = fraction radiant

Type = 2 (lights - 4.3)

1 = design lighting load W

2 = fraction of load to return air

3 = fraction radiant (long wavelengths)

4 = fraction visible (short wavelengths)

5 = fraction of load replaceable *by daylight

Types = 3, 4, 5, 6, and 7 (equipment - 4.4)

1 = design load W

2 = fraction latent

3 = fraction radiant

4 = fraction lost

5 = fraction convected

Type = 8 (infiltration - 4.5)

1 = design volumetric flow m-Vs

2 = constant part of Achenbach-Coblenz equation

3 = temperature part

4 = velocity part s/m

5 = velocity squared part s^/m^

Type = 9 (ventilation - 4.6)

1 = design volumetric flow m^/s

2 = minimum temperature C

3 = maximum temperature C

4 = temperature difference C

Type = 10 (two-zone mixing - 4.7)

1 = design volumetric flow m^/

s

4 = temperature difference C

Type = 11 (whole house fan - 4.8)

1 = design volumetric flow m^/

s

4 = desired temperature C

Type = 12 (controls - 4.9)

1 = maximum heating capacity W

2 = maximum cooling capacity W

3 = fraction of control based on mean radiant temperature

Type =13 (daylight - 4.10)

1 = fraction beam usable

2 = fraction diffuse usable

Types = 14 and 15 (baseboard heat - 4.11)

1 = temperature at lower control point C

2 = temperature at upper control point C

3 = capacity at upper control point W

4 = slope of curve W/C

5 = fraction radiant

RCOUNT / SIMCTL/ LC integer

Number of heat balance iterations.

263
REFRAC /MATDAT/ IP real (MAXNL)

Index of refraction (2.4.10).

REPEAT /RF/ IP logical

If true, repeat root search with smaller SINC.

RFLAGS /REPORT/ BOTH logical (RFGLEN)

Reports flags:

1 = dump PROJECT and LIBRARY data

2 = dump DDY and WTAP data

3 = dump CTF calculations

4 = dump glass calculations

5 = dump DSS data

6 = dump ZONE data

7 = dump cross reference values

8 = dump SIMBLD as read by LC

9 = report description of zone

13 = report sunlit areas

14 = report shadowing combinations

15 = dump shadow calculation controls

16 = dump shadow calculations

20 = dumps 21-24 during warm-up period

21 = dump primary zone data

22 = dump constant load components

23 = dump variables

24 = dump temperature and flux histories

25 = dumps 21-24 on WED nearest 21st of month

RHO / GLAS4/ IP real (2,4)

Energy reflectances of the air-glass interfeces

(polarization, interface and direction)

ROOT /RF2/ IP real (MAXNRT)

Roots for computing response factors.

ROUGH /MATDAT/ IP integer (MAXNL)

Material roughness number (2.4.14).

RR /GLAS3/ IP real (2,2)

Reflectance of a window system (polarization, side of incidence).

RR /RF/ IP real - m2 K/W

Thermal resistance of single layer slab.

RRB / GLAS6/ IP real (2,16)

Reflectance of a window system for beam light

(angle number, polarization).

RRBW / GLAS8/ IP real (16)

Outside beam reflectances integrated over wavelength and polarization

(angle number).

264
RRD / GLAS5/ IP real (2,2)

Reflectances of a window system for diffuse light

(polarization, side of incidence).

RRDW / GLAS7/ IP real

Outside diffuse reflectance integrated over wavelength and

polarization.

RSD / GLAS1 1/ IP real (2)

Reflectance of shade for diffuse light.

RSSC / SSCISL/ BOTH real (9.MAXSSC)

Array of special surface coefficients created by OSC (4.16), EMI (4.17)

and IM1 (4.18). Equivalenced to ISSC for integer values.

For OSC, RSSC(N, SSC) =

N=l: 3 (integer)

N=2: convection coefficient (4.16.1)

N=3: zone air temperature part (4.16.2)

N=4: ambient air temperature part (4.16.3)

N=5: constant temperature (4.16.4)

N=6: constant temperature part (4.16.5)

N=7 : ground temperature part (4.16.6)

N=8: wind speed factor (4.16.7)

N=9: heat transfer surface number of base surface (integer)

For EMI, RSSC(N,SSC) = N=l: 1 (integer)

N=2: U-value of construct

N=3: outside solar absorptance

N=4: outside thermal absorptance

N=5: surface roughness number (integer)

N=6: start date (cyclic) (4.17.3) (integer)

N=7 : stop date (cyclic) (4.17.3) (integer)

N=8: positive value = pointer to day-schedule (4.17.2),

-1 = sun up control, -2 = sun down control (integer)

N=9 : heat transfer surface number of the base surface (integer)

For IMI , RSSC(N,SSC) = N=1 through N=7 and N=9 : same as EMI

N=8: positive value = pointer to day-schedule (4.18.2),

-1 = maximum heat gain, -2 = maximum heat loss (integer)

RSO / GLAS1 1/ IP real - - Reflectance of shade at normal incidence (2.4.12).

RTD /REPORT/ BOTH real - * Conversion factor: radians * RTD = degrees

RVAL / MATDAT/ IP real (MAXNL) m^K/W

R-value of material (2.4.6).

S / SHDCTL/ lc real - - Y displacement of a shadow in the surface coordinate system

265
SA /SRFIS/ BOTH real (MAXSRF)

Sine of surface azimuth angle (4.13.3).

SABS /MATDAT/ IP real (MAXNL)

Solar absorptance of the material (2.4.7).

SAREA / HTSIS/ BOTH real (MAXHTS) m

2 Sunlit area of the surface.

SBSNR /SHDCTL/ LC integer

Subsurface number; pointer to SRFIS arrays.

SFAZIM /HTSIL/ BOTH real (MAXHTS) degrees

Surface azimuth angle (3.2.1 and 4.13.3).

SHAPE /VERTS/ IP integer

Surface shape number: l=triangle, 2=quadrilateral , 3=rectangle,

4=door/window, 5=overhang, 6=projection, 7=left fin, 8=right fin.

SHDCF /MATDAT/ IP real (MAXNL)

Shading coefficient of material (2.4.13).

SHDCMB / SHDCMB/ LC integer (MAXCMB)

Shadowing combinations array. For each base, envelope surface:

surface number, number of shadowing surfaces, number of back surfaces

number of subsurfaces, list of shadowing surfaces, list of back

surfaces, list of subsurfaces.

S HDGRP / SIMCTL/ LC integer

Shadow group (of days) number.

SHDREC /SIMCTL/ LC integer

Shadow file record number.

SHDSRF /SRFIS/ BOTH integer (2, MAXSRF)

Surface data array (for shadowing).

SHRSRF(1 ,NS) = Heat transfer surface number (HTS or I) of surface NS

Detached shadowing surface.

Shadowing subsurface.

+1 to +MAXHTS

0

-1

SHRSRF(2 ,NS) = +1 to +MAXHTS

-1 to -MAXHTS:

Coordinates are relative to global origin.

Coordinates are relative to surface -HTS.

SINBR /RUNCTL/ IP real

Sine of the building rotation angle (3.1.1).

SINC /RF/ IP real

Root search increment.

266
SIND / SLPSSH/ BOTH real

Sine of the solar declination angle.

SINL /EFLHDR/ BOTH real

Sine of the location latitude (1.3.2).

SINZR /BASES/ IP real - - Sine of the zone rotation angle (4.1.2).

SKY /ENVDAT/ BOTH real (24) C

Sky temperatures (B.3 .4).

SNAME /ZNAMES/ IP chr*WRD _ _ Schedule name

SNLOAD / ZONL/ LC real (MAXZON) Wh

Sensible heating (+) or cooling (-) load in the zone.

SNOW /ENVDAT/ BOTH integer - - Snow indicator (compressed 24 hours).

SOLDIS /RUNCTL/ BOTH integer

Solar distribution algorithm (3.1.2).

SPC2 /RUNCTL/ IP logical

If true, double space the echo of user input (1.1.4).

SPD /ENVDAT/ BOTH real (24) m/s

Wind speed.

SPHT /MATDAT/ IP real (MAXNL) kJ/kgK

Specific heat of material (2.4.4) •

SQTRDZ /ZONL/ LC real (MAXZON) /kg/m^ Square root of zone air density.

SQRTV /AIR/ LC real - / (m/s)

Square root of wind velocity.

SRADBM /ENVDAT/ BOTH real (24) W/m2

Intensity of beam solar radiation •

SRADDF /ENVDAT/ BOTH real (24) W/m2

Intensity of diffuse solar radiation (sky brightness) •

SRADGR /ENVDAT/ BOTH real (24) W/m2

Intensity of ground reflected solar radiation.

SREF /MATDAT/ IP real (MAXNL) - Reflectance of shade (2.4.12).

267
SSCPTR /HTSISL/ BOTH integer (MAXHTS)

Pointer to special surface coefficients.

SSDECL / ENVDAT/ BOTH real

Sine of the solar declination angle.

ST / SRFIS/ BOTH real (MAXSRF)

Sine of the surface tilt angle (3.2.2 and 4.13.4).

STATM /BLDRPT/ LC integer (6, MAXZON)

System status hours: Total for run in 6 categories.

1 = heating capacity exceeded.

2 = in heaing mode.

3 = in ventilation mode.

4 = in cooling mode.

5 = cooling capacity exceeded.

6 = no heating, cooling, or ventilating.

STDTIM / SIMCTL/ LC integer

Standard time (t s in sec B.1.1).

STLOAD / ZONL/ LC real (MAXZON) Wh

Steam load in zone (steam equipment plus steam baseboard heat)

.

SUMB /RF/ IP real

Sum of BETA values for all layers.

SUMC /ZONL/ LC real (MAXZON) W

Sum of scheduled convective gains.

SUMDTI /ZONL /LC real (MAXZON)

Sum of outside temperature derivatives.

SUMHA /ZONL/ LC real (MAXZON) W/K

Sum of (HI*AREA) for zone surfaces (HCi*Si in K.2.2).

SUMHAD /ZONL/ LC real (MAXZON)

Sum of air temperature derivatives (J.3.4a, J.4.2a, J.5.8a, J.5.10a).

SUMHAT /ZONL/ LC real (MAXZON) W

Sum of (HI*AREA*T) for zone surfaces (HC^*Si*T^ in K.2.2).

SUMLJA /ZONL/ LC real (MAXZON)

Sum of (HR*AREA) for zone surfaces (H.2.5).

W/K

SUMUAD /ZONL/ LC real (MAXZON)

Sum of radiant temperature derivatives (J.3.4b, J.4.2b, J.5.8b,

and J. 5.10b).

SUMUAT /ZONL/ LC real (MAXZON)

Sum of (HR*AREA*T) for zone surfaces (H.2.5).

W

268
SUMX /RF1/ IP real (5)

Sum of X CTF to test convergence (C.2.1).

SUMY /RF1/ IP real (5)

Sum of Y CTF to test convergence (C.2.1).

SUMZ /RF1/ IP real (5)

Sum of Z CTF to test convergence (C.2.1).

SUNCOS / SLPSSH/ BOTH real (3)

Solar direction cosines.

SYNTAX /RUNCTL/ IP logical

Process input to only check syntax (1.1.2).

T / GLAS2/ IP real (2,4)

Transmittances of single panes of glass (polarization, pane number).

T /HTSL/ LC real (MAXHTS) C

Temperature of inside of surface (or inside movable insulation) for

computing mean radiant temperature and convective gain to zone.

TAU / GLAS4/ IP real (2,4)

Energy transmittances of the air-glass interfaces

(polarization, interface in direction).

TBM / SHDCTL/ LC real

Transmittance of window for beam radiation.

TCNVG /RUNCTL/ IP real - C

/ SIMCTL/ LC

Temperature convergence (3.1.3).

TD /GLASO/ BOTH real (MAXGTP)

Fraction of diffuse solar radiation transmitted through window.

TE / ZONL/ LC real (MAXZON) C

Zone effective temperature for control purposes (K.1.3).

TFH /BLDTFH/ LC real ( MAXTFH) C & W/m2

Array of surface temperature and flux histories for CTF calculations.

TGRND /EFLHDR/ BOTH real (12) C

Ground temperatures (monthly values; 1.4.1).

TI /HTSL/ LC real (MAXHTS) C

Temperature of inside of surface.

TINC /RF/ IP real - s Time increment for CTF calculations.

269
TMKUP /EFLHDR/ BOTH real (12) C

Make-up water temperatures (not used).

TMPHPE /HTSIL/ BOTH integer (MAXHTS)

Pointers to external temperature histories.

TMPHPI /HTSIL/ BOTH integer (MAXHTS)

Pointers to internal temperature histories.

TO /HTSL/ LC real (MAXHTS) C

Temperature of outside (side away from zone) of surface.

TR /ZONL/ LC real (MAXZON) C

Mean radiant temperature of zone (H.2.5).

TRANS /MATDAT/ IP real (MAXNL)

Transmittance of material (2.4.9).

TRANS / SRFIS/ BOTH real (MAXSRF)

Transmittance of shadowing surface (3.2.5 and 4.15.4).

TRRAIN /EFLHDR/ BOTH integer

Terrain classification (1.3.6 and sec B.4).

TRTFPC /CONDAT/ BOTH real (MAXCON) W/m2 K

Cross (Y) temperature conduction transfer functions.

TRTFPE /CONDAT/ BOTH real (MAXCON) W/m2K

External (X) temperature conduction transfer functions.

TRTFPI /CONDAT/ BOTH real (MAXCON) W/m2K

Internal (Z) temperature conduction transfer functions.

TSD / GLAS1 1/ IP real (2)

Transmittance of shading device (polarization).

T SHIFT /BLDTFH/ LC integer

Time shift for temperature and flux histories in TFH array.

TSO / GLAS1 1/ IP real

Transmittance of shade at normal incidence.

TT / GLAS3/ IP real (2)

Transmittances of layers in a window system (polarization)

TTB /GLAS6/ IP real (16,2)

Transmittances of a window system for beam light

(angle number, polarization).

TTBW /GLAS8/ IP real (16)

Beam transmittances integrated over wavelength and polarization

(angle number).

270
TTD /GLAS5/ IP real (2)

Transmit tances of a window system for diffuse light (polarization).

TTDW / GLAS7 / IP real

Diffuse transmittances integrated over wavelength and polarization.

TVENT /TCDESC/ LC real (5,maxzon) C

Ventilation control point temperatures.

TZ /ZONL/ LC real

Zone air temperature.

(MAXZON) C

TZNR /EFLHDR/ BOTH real

Time zone number (1.3.4).

- -

T1 /GLAS/ BOTH (5.MAXGTP)-

Polynomial coefficients for beam solar transmittance (c^ in D.1.7a)

T2 /GLAS/ BOTH (6,MAXGTP)-

Polynomial coefficients for beam solar transmittance (c^ in D.1.7b)

UCHAR /UINDAT/ IP integer

Current character in line (record) of user input.

UIERR /UINDAT/ IP integer

User input error:

0 no error

1 invalid subkey value:

continue processing

2 invalid subkey name:

skip input to next / or ) or ] 3 error in key name processing:

skip input to next ) or ] 4 error in section name processing:

skip input to next ] 5 at end of information:

set UISTAT=6

UILINE /UINDAT/ IP integer

User input line number.

UINREC /UINREC/ IP char*80

User input record (line of 80 characters).

U ISTAT /UINDAT/ IP

User input status:

integer

0 initial setting in subroutine READER

1 at / at end of subkey

2 at ) at end of key, end subkey also

3 at ( at end of key name

4 at ] at end of section

5 at [ at end of section name

6 at end-of-inf ormation

271
UM /HTSL/ LC real (MAXHTS) W/m2 K

U-value of movable insulation. 0 means no movable insulation

UV / IZPDAT/ IP real — W/m2 K

U-value of surface for matching interzone surfaces •

UVAL /CONDAT/ BOTH real (MAXCON) W/m2 K

Construct U-value.

VCONV /ZONL/ LC real (MAXZON) - Visible to convective factor.

VMULI /ZONL/ LC real (MAXZON) — Visible multiplier.

VP /ZONL/ LC integer (MAXZON) - Pointer to Ventilation control.

VVF /ZONL/ LC real (MAXZON) m^/s

Ventilation design volumetric flow.

WA /VERTS/ IP real - degrees

Surface azimuth angle (3.2.1 and 4.13.3).

WFDAYS /WFLHDR/ IP integer

Number of days on BLAST weather file.

WFEDAT /WFLHDR/ IP integer

Julian date of last day on BLAST weather file.

WFEFCD /WFLHDR/ IP real

Cosine of solar declination on first day of BLAST weather file.

WFEFET /WFLHDR/ IP real - hr

Equation of time on first day of BLAST weather file.

WFEFSD /WFLHDR/ IP real

Sine of solar declination on first day of BLAST weather file.

WFFDAY /WFLHDR/ IP integer —

WFFILL /WFLHDR/ IP

Array filler.

integer (46) -

WFLATD /WFLHDR/ IP

Location latitude of

real

BLAST weather file.

degrees

WFLONG /WFLHDR/ IP

Location longitude of

real

BLAST weather file.

degrees

WFSDAT /WFLHDR/ IP integer

Julian date of first day on BLAST weather file.

-

272
WFSDAY /WFLHDR/ IP integer

Day-of-month of first day of BLAST weather file.

WFSMON /WFLHDR/ IP integer

Month of first day of BLAST weather file.

WFSTTN /WFLHDR/ IP integer

Weather station number of BLSAT weather file.

WFSYR /WFLHDR/ IP integer

Year of first day of BLAST weather file.

WFTMZN /WFLHDR/ IP real

Time zone of BLAST weather file.

WL / GLAS10/ IP real (1) nm Wavelength at which optical properties are computed.

WREC /WFLHDR/ IP integer (64)

BLAST weather file header array (all values equivalenced to this array.

WS /VERTS/ IP real - degrees

Surface slope (tilt) angle (3.2.2 and 4.13.4).

WSH / SCHDLS/ LC integer (12,MAXWSH)

Week-schedules (pointers to day-schedules).

WSHNAM /LIBNMS/ LC char*WRD (MAXWSH)

Names of week-schedules.

WSTATN / EFLHDR/ BOTH integer

Weather station number.

WSO /LIBCTL/ IP integer

Pointer to week-schedules (location 0).

WTITLE /WFLHDR/ IP integer (4)

BLAST weather file title.

WTYPE /CONDAT/ BOTH integer

Window type (=1 if window; =0 if opaque).

X / GLAS12/ IP real (16)

Independent variable (cos 6) for curve fit.

X /VERTS/ IP real (4) m

X-coordinate (surface relative or global) of surface vertices.

XLLC /VERTS/ IP real - m

X-coordinate (global) of surface origin (Xso in E.1.2a).

273
XLOAD / ZONL/ LC real (MAXZON) Wh

Previous value of zone sensible load.

XREF /RUNCTL/ IP logical — —

If true, print cross reference data (1.1.5).

XTEMP /HCFS/ LC integer (MAXHCS) - X homogeneous coordinates of overlap before sequencing.

XTR /ZONL/ LC real (MAXZON) C

Previous value: of the :zone mean radiant temperature.

XTZ /ZONL/ LC real (MAXZON) C

Previous value: of zone air temperature.

XV / SRFIS/ BOTH real (4.MAXSRF) m

X-coordinates (global) of surface vertices.

XVC / SHDVRT/ LC real (5) m

X-coordinates (surface relative) of clipped shadowing surface

XVS /SHDVRT/ LC real (5) m

X-coordinates (surface relative) of shadow.

XVT /SHDVRT/ LC real (5) m

X-coordinates (surface relative) of shadowing surface •

XX /VERTS/ IP real (4) m

X-coordinates (surface relative) of surface vertices.

Y /VERTS/ IP real (4) m

Y-coordinates (surface relative or global) of surface •

YEAR /ENVDAT/ BOTH integer - - Year (4 digits)

.

YLLC /VERTS/ IP real — m

Y-coordinate of surface origin (Yso in E.1.2b).

YTEMP /HCFS/ LC integer (MAXHCV) - Y homogeneous coordinates of overlap before sequencing.

YV /SRFIS/ BOTH real (4 ,MAXSRF) m

Y-coordinates (global) of surface vertices.

YVC /SHDVRT/ LC real (5) m

Y-coordinates (surface relative) of slipped shadowing surface

YVS / SHDVRT/ LC real (5) m

Y-coordinates (surface relative) of the shadow.

274
YVT / SHDVRT/ LC real (5) m

Y-coordinates (surface relative) of the shadowing surface.

YY /VERTS/ IP real (4) m

Y-coordinates (surface relative) of the surface.

Z /VERTS/ IP real (4) m

Z-coordinates (surface relative or global) of surface vertices.

ZCLD /BLDRPT/ LC real (MAXZON) Wh

Total sensible cooling load for zone

ZHLD /BLDRPT/ LC real (MAXZON) Wh

Total sensible heating load for zone.

ZLLC /VERTS/ IP real - m

Z-coordinate of surface origin (Z s0 in E.1.2c).

ZMNT /BLDRPT/ LC real (MAXZON) C

Minimum zone air temperature.

ZMXC /BLDRPT/ LC real (MAXZON) W

Peak sensible cooling requirement.

ZMXH /BLDRPT/ LC real (MAXZON) W

Peak sensible heating requirement.

ZMXT /BLDRPT/ LC real (MAXZON) C

Maximum zone air temperature.

ZNAMES /ZNAMES/ LC char*WRD (MAXZON)

Names of zones.

ZNAMIN /ZNAMES/ IP char*WRD - Name of current zone.

ZNMOUT /ZNAMES/ IP char*WRD - Name of far side zone.

ZNRELN /BASES/ IP real - degrees

Angle from the building Y-axis (north) to the zone Y-axis

(4.1.2 and E.1.2).

ZNXORG /BASES/ IP real - m X-coordinate of zone origin (Xzo in E.l.la).

ZNYORG /BASES/ IP real - ra Y-coordinate of zone origin (Yzo in E.l.lb).

- m

in E.l.lc).

ZNZORG /BASES/ IP real

Z-coordinate of zone origin (Z

27 5
ZRRES /RFO/ IP real (3) - Residues at the double pole at 0.

ZS /AFSIL/ BOTH real (MAXAFS) m

Height of the air flow opening.

ZT /AFSIL/ IP real (MAXAFS) m

Height of top of surface (for evalauting PW)

.

ZV / SRFIS/ BOTH real (4.MAXSRF) - Z-coordinates (global) of surface vertices.

ZVC / SHDVRT/ LC real (5) m

Z-coordinates (surface relative) of clipped shadowing surface

.

ZVMOD /AFSIL/ BOTH real (MAXAFS) - Height modifier for computing wind pressure.

ZVS /SHDVRT/ LC real (5) m

Z-coordinates (surface relative) of the shadow (= 0)

.

ZVT /SHDVRT/ LC real (5) m

Z-coordinates (surface relative) of shadowing surface »

ZZ /ZONISL/ BOTH real (MAXZON) m

Height of zone for computing zone pressure.

27 6
VI.

FILES

INPUT PROCESSOR FILES:

UNIT FILE ACCESS DESCRIPTION

11 SINPFL seq Simulation input file

12 ENVTFL dir Environment file

13 WTHRTP seq Weather tape from BLAST program

14 - dir Materials data

15 - dir Constructs data

16 - dir Interzone surface data

17 - dir Interzone opening data

21 - seq Day-schedules library report

22 - seq Week-schedules library report

23 - seq Materials library report

24 - seq Constructs library report

25 - seq Control profiles library report

26 - seq Control day-schedules library report

27 — seq Control week-schedules library report

LOADS CALCULATOR FILES:

11 SINPFL seq Simulation input file

12 ENVTFL dir Environment file

13 - dir Solar gains multipliers

14 - seq Input segment to loads segment data

15 - seq Input segment to shadowing segment data

277
U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSTR 83-2655

2. Performing Organ. Report No 3. Publication Date

February 1983

4. TITLE AND SUBTITLE

Thermal Analysis Research Program Reference Manual

5. AUTHOR(S)

G. N. Walton

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

national bureau of standards

7. Contract/Grant No.

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

S. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

National Bureau of Standards and U.S. Department of Energy

Building Energy Sciences Branch

Office of Building Energy Research and Development

Washington, D.C. 20545

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

The Thermal Analysis Research Program (TARP) has been developed as a research tool

for the thermal analysis of buildings. It especially aims to study the interactions

of many complex heat transfer phenomena. TARP uses the detailed heat balance method

for the simultaneous calculation of the energy requirements of multiple rooms. Interroom conductive and convective processes are simulated in detail. This program

reference manual describes the algorithms, input, output, and program structure of

TARP. The program is written to be portable and modifiable. It is written in FORTRAN

77 and has run on CDC and UNIVAC computers. Future expansions of the program are anticipated, particularly for the simultaneous simulation of equipment performance

and building thermal response.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Building energy analysis; load calculation; computer modeling; building

heat transfer.

13.

AVAILABILITY

• £3] Unlimited For Official Distribution. Do Not Release to NTIS

r~] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

* [_XJ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

286

15. Price

$22.50

USCOMM-DC 6043-P80