BUILDING SCIENCE SERIES 45

llllil

Dynamic Thermal Performance

of an Experimental

Masonry Building
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Dynamic Thermal Performance of an

Experimental Masonry Building

3^ \ O i ' CCl ti' ^XLv '^-t^ National Bureas af Standards

MAY S 'i374 Bradley A. Peavy, Frank J. Powell, and

Douglas M. Burch

Building Environment Division

Center for Building lechnology

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretory

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts, Director

IssuedJuly 1973
Library of Congress Catalog Card Number: 72-600347

National Bureau of Standards Building Science Series 45

Nal. Bur. Stand. (U.S.), Bldg. Sci. Ser, 45, 103 pages (July 1973)

CODEN: BSSNBV

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. C13.29/2:45). Price: S1.25. Stock Number 0303-01119
Page

1. Introduction 1

2. Prediction and evaluation analyses 3

3. Description of building 3

4. Instrumentation and transducers 5

5. Experimental procedure 6

5.1. Floating tests 6

5.2. Thermostated tests 7

6. Results and discussion 8

6.1. Floating tests 9

6.2. Thermostated tests 2f

6.3. Heating load predictions 25

7. Conclusions 26

Appendix A. Air infiltration measurements on the NBS experimental building 27

Appendix B. Noise transmission measurements of the NBS experimental building 29

Appendix C. Computer programs (NBSLD) to obtain heating and coohng loads and to estimate room air temperature change using thermal response factors 33

Appendix D. Computer program used in evaluation for the experimental building 71

Appendix E. Input and output for the response factor program 91

iii

Dynamic Thermal Performance of an Experimental Masonry Building

B. A. Peavy, F. J. Powell, and D. M. Burch

Measurements of the dynamic heat transfer in an experimental masonry building were made in a large environmental chamber to explore the validity of a computer program developed at NBS,

labeled NBSLD, for computing heating and cooling loads, and indoor air temperatures. This study was

jointly supported by the National Bureau of Standards and the Department of Housing and Urban

Development, and is a part of a broader research program being supported by both agencies to improve

performance test procedures and criteria for housing.

The experimental structure was a one-room house 20 ft long, 20 ft wide, and 10 ft high with walls of solid concrete blocks and a flat roof made of reinforced precast concrete slabs. During the tests changes were made in fenestration, the amount and location of insulation, and the indoor mass; and

the building was exposed to a diurnal temperature cycle.

It was found that the combination of mass in the masonry walls and roof, and insulation placed on the outside of the masonry was very effective in reducing and controlling the variation of indoor

air temperature. The NBSLD computer program realistically predicted the heat storage effects and maximum heating loads during these tests. For five heating tests, the greatest difference between computed maximum heating load and measured values was 8 percent and the average difference was

4.3 percent. It was shown that steady-state methods of heating load calculation could result in oversizing

heating equipment by 30 percent or more for this particular building and imposed exterior conditions

if the lowest outdoor temperature was selected as the design temperature.

Key words: Building heat transfer; computer programs; dynamic thermal performance; heat

flow analysis; heating and cooling loads; temperature predictions; thermal analysis; thermal behavior;

transient heat flows.

1. Introduction

To provide a functional and habitable indoor en- vironment for a building requires careful consideration of the properties and performance of the materials that cover the building frame together with careful design, specification, and installation of its mechanical and electrical systems. The building

materials and systems taken together are a major

part of the cost of a new building and the fuel con- sumption also constitutes a substantial long-term ex- pense in the operation of a building.

The indoor thermal environment of a building is influenced by the weather, by the thermal behavior

of the walls, roof and floors, by heat-producing occupant-related activities, and especially by the

mechanical and electrical systems that serve to make living spaces habitable.

This study explores the actual dynamic or timevariable flow of heat into and out of the fabric of a

building and the resulting temperature patterns of

the indoor air and the building itself. Present practice in calculating heat transfer and in selecting

equipment sizes is based largely on steady-state as- sumptions and techniques. The actual performance

is dynamic because of the changing patterns of weather and cHmate. Therefore, analysis and predictions of hourly, daily, and seasonal system per- formance should be based on dynamic considerations. The theory and basic mathematics for the

dynamics of such a system were first explained by

Fourier about 1820, but the complexity of calculation

and the time and expense involved have deterred

architects and engineers from using such so- phisticated procedures to design and evaluate

buildings. Simplified steady-state approaches have

been and are still used in combination with engineering judgment.

Design calculations for the heating and cooUng

loads for buildings have been performed by a mul1
tiplicity of arithmetic and algebraic computations. It was not practical to make an extensive type of design

analysis and the loads were generally determined by

employing simple equations using selected fixed

winter and summer design temperatures. Experience has shown that systems designed on this basis are sometimes oversized and may never

operate at full load and optimum efficiency.

With the advent of high speed electronic digital

computers with a large memory bank, it is now possi- ble to make a comprehensive design analysis which

includes the dynamic performance of buildings as af- fected by diurnal and seasonal patterns of the

weather and the time dependent interactions within

the building itself. This approach allows an engineer

to calculate rapidly and inexpensively: (a) energy

requirements with consideration of operating costs,

(b) heating and cooling load profiles for equipment

design or selection and operation, (c) the information

needed to evaluate rapidly a large number of options

in the design process, (d) optimum energy utilization,

and (e) the need for zoning in large buildings.

Computer programs usually contain approximations that require experimental verification before

being adopted for wide-scale use. In addition, the

performance data on building materials and ele- ments, design weather data, and boundary conditions at surfaces need better definition to assure ac- curacy of predicted results.

It is the objective of this study to utilize a computer program suited to the variable temperature

and heat flow regimes in most real situations and to compare results as predicted by this program with

measurements made in the laboratory on fuU scale

buildings that are subjected to changing simulated

weather patterns. Further, it was hypothesized that building walls, roofs, and floors can be better

designed to take advantage of thermal lags that occur due to the mass of the building and thereby

allow a reduction of the installed capacity of

mechanical equipment for heating and cooling while

stiU maintaining performance satisfactory for human

comfort and health. For example, it was hypothesized that if the masonry of a building is located on

the indoor side of walls and roofs with thermal insulation on the outside, the stability of indoor temperature changes should be improved with less gross energy expended for maintaining a selected indoor

temperature level. Also, locating masonry on the in- side of the walls and an insultion with appropriate

weather surface on the outside provides other potential advantages such as: a reduction of cracking and

spaUing because the masonry remains unexposed to weather and at essentially a constant temperature

and moisture content; the use of strong durable in- door surfaces should allow a reduction in the costs

of maintenance and redecorating; and a greater re- sistance of the building to an interior fire or its rapid

spread. When compared with the usual construction

of walls with masonry outside and insulation inside,

the proposed inverted system with insulation outside

has elicited considerable interest. A concerted effort towards the experimental

verification of computer calculation methods and the

technical merits of the inverted system was needed.

At the Natioucd Bureau of Standards the initial ex- perimental phases in this regard included laboratory

testing in a high-bay environmental chamber employing an experimental building where the time

varying external environment could be controlled

and reproduced, and where variations in important

parameters could be studied.

This report presents a computer program for prediction of dynamic thermal and energy loads of

buildings, the experimental results obtained from

laboratory measurements made on an experimental

building, and the comparison of experimental results with those calculated by the computer program. In conjunction with the experimental phases involving

the dynamic thermed performance of a building, two

other significant experiments were performed on the

building. The first experiment was concerned with

the air infiltration rate of the building. The method,

procedure, and results are contained in appendix A

of this report. The second experiment involved a series of noise transmission measurements made on

the building. The method, procedure, and results are contained in appendix B of this report. Other observations included monitoring of the moisture content

of the experimental building and the movement of

the walls of the building under the influence of the

changes in simulated outdoor air temperatures. The

moisture content reached low equilibrium values

early in the program and remained steady thereafter. Wall movement was little and about what would be

expected using predictive engineering calculations.

No surface or through-the-wall cracks in masonry

were observed at any time in the program.

This work was cosponsored by the National Bureau of Standards and the Department of Housing

and Urban Development. This report represents the

initial stage of a research program. It is planned to

2
perform further measurements on completely

furnished full-scale houses that encompass a range

of types of construction from lightweight (wood) to heavyweight (masonry). It is expected that results of

those measurements will be published in future is- sues of the Building Science Series.

2. Prediction and Evaluation

Analyses

In order to evaluate the dynamic, rather than

steady-state thermal behavior and response of the

fabric of a building as affected by diurnal and

seasonal variations of weather and the time dependent interactions within the building, it was necessary to make a comprehensive mathematical analysis

of the various heat transfer problems and translate the derived expressions into computer programs. It was found that the heat conduction portion of the

overall problem could not be satisfied by purely

rigorous mathematical solutions to the appUcable

partial differential equations because some of the

boundary conditions at solid surfaces cannot be

represented in a rigorous closed form in a reasonable manner. For these reasons, the Response Factor

method was employed for those portions of the

problem involving heat conduction. It allows a time

variation of boundary conditions and can readily be

related to modes of heat flow other than conduction,

such as radiation and time varying changes in the nature of convection heat flow. Basically, the Response Factor method predicts

one-dimensional heat flow by utilizing the superposition principle in such a manner that the overall ther- mal response of a solid at a selected time is the sum

of the responses caused by many individual temperatures or heat flux pulses during preceding time

steps. Thereby, transient boundary conditions are simulated by a train of pulses. By summing up the

fluxes or temperatures caused by each pulse, the

total heat flux or temperature at a given time can be

determined. The differential equations of heat con- duction for multilayer systems of a building may be

solved in this method by employing matrix equations

of the Laplace transforms. The matrix algebra, su- perposition principle, and inversion of the Laplace

transforms are shown and discussed by Kusuda^ Experience has shown that when this method is comThermal Response Factors for Multi-layer Structures of Various Heat Conduction

Systems, American Society of Heating, Refrigerating, and Air-Confiitioning Engineers (ASHRAE)Transactione, 1969, pp. 246-271.

pared with a rigorous analytical solution under simplified conditions, the agreement is very good, ex- cept for the case where sudden changes or amplitude peaks of a weather cycle are encountered.

This is probably due to the time steps employed and

is not considered to be a serious drawback.

Appendix C contains the complete computer pro- gram, NBSLD, Computer Programs to Obtain Heating and Cooling Loads and to Estimate Room Air

Temperature Change Using Thermal Response Factors. For the purpose of predicting performance in the experiment, certain subroutines of NBSLD were

not needed. Appendix D is the computer program as adapted from NBSLD for use in this report for comparing predicted results with experimentally measured results. Appendix E gives a sample set of input

and a printout of corresponding computer results as used with the program of appendix D. For this thermal analysis, the following assumptions were made:

1. The conduction heat transfer through all the components of the experimental building was assumed

to be one-dimensional.

2. All building materials were assumed to be

homogeneous having constant physical and thermal

properties over the operating temperature range of

the tests.

3. For the tests considered in this report, the heat- transfer coefficients at the inside and outside sur- faces of the experimental building were assumed to be constant.

4. Heat and mass transfer of water in vapor or liquid

form or the latent heats of condensation and

evaporation were not considered in the analysis. For

most tests, the dew point temperature of the outside

air was maintained below that for any temperature

occurring in daily cycle.

5. Infiltration of air from the outside to the inside

and from the inside to the outside was considered to be a constant for a particular test. Two tests were

performed for determining the air infiltration rates of the building, one with and the other without windows installed. The description and results for the

air infiltration tests are in appendix A.

3. Description of Building

The building was constructed in a high-bay en- vironmental laboratory of approximately 70,000

cubic feet in volume. A photograph of the experi3
Figure 1. Experimental building in environmental chamber. mental building located in the environmental

chamber is shown in figure 1. In this laboratory, the

temperature and relative humidity can be controlled over the ranges — 50 to 150 °F and 15 to 85 percent,

respectively. Temperatures and relative humidities can be changed as a function of time using camoperated controllers. The floor of the laboratory is undisturbed earth suitable for placing building foundations.

The outside plan dimensions of the building w^ere 20 X 20 ft with 10-ft-high walls. The flat roof consisted of five 20-ft-long by 4-ft-wide and 4-in-thick

steel reinforced concrete roof slabs as shown in figure 2. The walls were made of nominal 8-in-high

by 8-in-wide and 16-in-long solid cinder aggregate concrete blocks joined with fully bedded mortar

joints. The blocks were of a nominal 100 Ib/ft^ density. Eight concrete lintels were installed at appropriate locations; one above each of the seven windows that were 40 in high and 32 in wide and one

Figure 2. The basic experimental building.

4

Figure 3. The experimental building showing windows, internal mass, heaters, and insulation on the outside ofthe building.

above the solid wood door measuring 79 in high X 32

in wide X 2 in thick. For the first two tests, there were no openings for windows and the spaces below

these seven lintels were filled with blocks. The

blocks were removed and the windows installed for the remaining tests. The exposed glass area was

about 8 percent of the exposed wall area or about 18

percent of the floor area. Figure 3 shows the configuration. A detailed illustration of the floor and the footing

supporting the walls is given in figure 4. Below the

ground level, 4-in-thick polystyrene insulation was

placed on the outside and a 1-in thickness on the in- side of the concrete blocks to a depth of 16 in. Below

the 16-in depth, a 1-in thickness was placed on the

outside of the footing. The floor was made of 2 in of polystyrene insulation placed on the earth with a 2- in-thick concrete slab on top of the insulation. Considerable insulation was purposely placed below

grade to reduce the known long-term influence of heat flow to the earth from the building and to minimize the time necessary for experimental test. Cracks at the roof-wall interface and between the

roof slabs were caulked with a polysulfide sealant. When the windows were installed, all cracks including those at the glass-wood frame interface were also caulked with the same sealant. Windows were as shown in figure 4. Commercial expanded polystyrene board-type in- sulation 2 in thick, vyhen used, was spot glued to either the inside or outside surfaces and aU cracks were tape sealed. The identical insulation was used

inside and outside. An internal mass consisting of
GROUND LEVEL- -I

-SOLID CONCRETE BLOCK

-POURED CONCRETE

FLOOR

-POURED CONCRETE FOOTING

3/32 STORM GLASS

SEALANT

.3/32 GLASS

-3/4" WOOD FRAME

Figure 4. Floor, footing and window details.

2600 lbs of solid concrete blocks stacked on the

floor, as shown in figure 3, was used to simulate the

heat capacity effect of interior partitions, furniture,

etc.

4. Instrumentation and Transducers

Temperatures were measured using 24 gage

copper-constantan thermocouples. The dots on

figure 5 indicate thermocouple locations. The five vertical planes A, B, C, D, and E, as shown on the

plan view of figure 6, each contained the same ther- mocouple configuration given in figure 5, except for the indoor air thermocouples which were located

only in the vertical plane B. Four thermocouples were placed in the air 1 ft from the outside surfaces.

One of these was located at the center of the roof and

the other three were located at the midheight of the

three walls denoted by vertical planes B, D, and E of

figure 6. Six heat flow meters were placed on inside sur- faces, five of them in vertical plane B of figure 6. One

was placed at the center of the floor and a second

meter was placed on the floor at a distance 2 ft from

the waU. Two meters were placed on the ceiling opposite those on the floor. The fifth meter was placed on the wall at midheight. The sixth meter was placed

midheight on the wall of vertical plane D. The heat

flow meters were circular disks 2.0 in in diameter

and 0.13 in thick, made of tan polyvinylchloride fiUer

r r

Figure 5. A vertical section through the experimental building

showing thermocouple locations.

material, each having an embedded spiral of heli- cally wound wire comprising a large number of ther- mojunctions in series (with internal resistance range

of 135 to 170 ST) distributed over a circular area 1 5/8

in in diameter located centrally in the disk. Two

wires attached in each meter acted as leads for the

series thermopile of the meter. The meters were

calibrated in an 8 in guarded hot plate apparatus

Figure 6. Plan view ofthermocouple locations.
conforming with the requirements of Standard

Method of Test ASTM C177.

All thermocouple and heat flow meter leads were

connected to thermally isolated terminal strips at the center of the room from which copper leads went to a data acquisition system. The terminal strips were mounted on a 1/4-in-thick aluminum plate which in turn was surrounded by 3 in of polyurethane insulation. All lead wires were surrounded by 3 in of the same insulation for a distance of 7 in. This assembly

is termed a zone box. Four additional thermocouple

leads were connected to the terminal strips at ends

of the zone box and their junctions were placed in an

ice point reference external to the building. The

readings from these four thermocouples gave the

temperature of the zone box as a reference temperature for the other thermocouple leads. Copper leads from the zone box were connected

to terminals of the data acquisition system which

converted the analog signals to digital information

which in turn was recorded on punched cards.

Electric energy supphed to the building was measured using a calibrated single-phase watthour meter

equipped with an impulse generator. The impulse

generator is a photoelectric device which counts the

revolutions of the disk inside the watthour meter. A

digital signal (number of revolutions of the disk) was

fed into the data acquisition system which in turn recorded the digital signal on punched cards at selected time intervals.

5. Experimental Procedure

Figure 7 is a representative sample of the outside

air temperature wave-form imposed on the experimental building for each 24-h time period. For most

of the tests, the limits 40 to 100 °F were selected for experimented convenience and because their

average would be approximately a normal room temperature. In test 10, the limits were changed to the

range 10 to 70 °F. The curve was used to control the

average of the four individual temperatures in- dicated by thermocouples in the air 1 ft from the exterior surface of the building. The maximum dif- ference in temperature between any of these four lo- cations was always less than 4 °F. The outside dew

point temperature was maintained constant at ap- proximately 5 °F below the lowest temperature of a

cycle. The temperature cycle of figure 7 was derived

as a simulated sol-air temperature pattern from the

100

I

UJ

q; 90

70-

4U-I =^1

'

1 1 1 1 1 1

1 0 3 6 9 12 15 18 21 24 TIME OF DRY - HOUR

Figure 7. Outside sol-air temperature cycle.

data in table 25, page 490 of the "Handbook of Fundamentals," published by the American Society of

Heating, Refrigerating, and Air-Conditioning Engineers, 1967. Sol-air temperatures were area- averaged for orientations north, east, south, west,

and horizontal. The temperature variation as in- dicated on figure 7 was maintained for a period of

from 3 to 4 days before a final set of data was taken.

This conditioning period was deemed to be necessary and sufficient to eliminate transient heat flows

thereby giving only those heat flows that would recur

in a periodic fashion.

A complete set of data for each test consisted of

recording the digital output from analog signals of

171 sensing elements (thermocouples, etc.) every 30

min during a 24-h period. The raw data were con- verted by computer into temperatures, heat flows,

etc. The converted data were then transferred to magnetic tape for use in analysis, and plotting as temperature and heat flow patterns.

The results from 10 tests given in this report are derived from the five floating tests and five thermostated tests summarized in tables 1 and 2.

5.1. Floating Tests

Floating tests are defined as those tests where no

heat energy was added to or taken away from the in- terior air of the experimental building by mechanical

equipment. The temperature of the interior air was

allowed to "float" or respond to changes in the out- side air temperature. Five floating tests were con- ducted with variations in test conditions as shown in table 1.

6
Table 1. Floating tests

Test No. Insulation Windows Internal Mass

1 None None None

2 None None Mass*

3 None Single Pane None

4 Inside Single Pane Mass*

5 Outside Single Pane Mass*

*2600 lbs of concrete blocks.

5.2. Thermostated Tests

Thermostating tests are defined as those tests where heat energy was added to the interior air of

the experimental building by four electric heaters

under thermostatic control. The variations in test conditions are shown in table 2 along with the

average inside air temperature maintained and its root mean square RMS deviation.

The sensing element for thermostating was a ther- mocouple placed in the middle of the room at midheight. It controlled the operation of four fan heaters

placed as shown in figure 3, in an on-off type of control with a differential of approximately ± 2 °F. Each

drum-type fan heater, as shown in figure 8, consisted

of a heating element and a blower which takes air from the floor level, passes it through the heater

chamber and into the room through peripheral holes near the top of the drum. Each electric heating ele- ment was rated at 600 W for 110-V input, and each

blower delivered 100 W. Heat was supplied by the

elements, blowers, and the thermostat and voltage

control equipment. For test 10, the daily temperature

cycle for the outside air ranged from 10 to 70 °F as shown in figure 31, but the cycle was similar in shape

to that given in figure 7.

r

Figure 8. (a) Fan heater; (b) Fan heater with top cover removed.

Table 2. Thermostated tests

Test No. Insulation Windows Internal Mass

Inside Air Temp.

Average RMS

deviation

6 None Single Pane None 78.9 ±1.2

7 Inside Single Pane Mass* 76.9 ±0.8

8 Outside Single Pane Mass* 77.6 ±0.6

9 Outside Double Pane Mass* 77.6 ±0.6

10 Outside Double Pane Mass* 74.2 ±0.8

*2600 lbs of concrete blocks.

7
6. Results and Discussion

The thermal and physical properties of the materials comprising the building used in the computer

program are given in table 3.

Table 3. Thermal and physical properties

Thick- Thermal Specific ness Conduc- Density Heat

in tivity Btu h-i

ft-' F-'

lb ft-3 Btu lb-' F-'

Concrete Block 7.5 0.29 100 0.18 Roof Slab 4. .80 150 .2 Polystyrene

Insulation 2. .018 2.5 .27 Concrete

Floor 2. .80 150 .2 Earth .5 120 .2

Measurements of thermal conductivity, thickness,

and density were made on oven-dried samples of the concrete block and polystyrene insulation in ac- cordance vsrith the hot plate method given in ASTM

C177. All other properties were obtained from the

apphcable literature. The areas used for computing heat flows through

the roof, walls, and floor were the arithmetic average

of the inside and outside areas for each of the components. The mean heat transfer areas of tests 1 through 10 are summarized in table 4.

Table 4. Mean heat transfer areas, ft"^

Test No. Window

Area Roof Area Wall Area Floor Area

1 none 375 814 375

2 none 375 814 375

3 58 375 750 375

4 58 369 738 369

5 58 381 763 381

6 58 375 750 375

7 58 369 738 369

8 58 381 763 381

9 58 381 763 381

10 58 381 763 381

Values for the coefficients of heat transfer at the

various surfaces were selected and used in the computer program as constants for the time period of a

test. The coefficients used for the inside surfaces at the ceiling, walls, and floor were 1.08, 1.1, and 1.08 Btu h~' ft"^ °F"\ respectively. The heat transfer

coefficient selected for the outside surfaces was 1.47

Btu h~* ft~^ °F~^ In general these values are based

on a value of 0.9 for the radiation component of heat

transfer and time-averaged temperature differences

between surfaces and adjacent air of 1 and 14 °F for the inside and the outside, respectively. For test 10,

where the outside temperature was considerably

lower, the outside surface coefficient selected was

3,0 Btu/h"' ft"^ °F~\ owing to the larger temperature

difference between the outside surface and the sur- rounding air. The surface film coefficient varies considerably with the direction of heat flow, air velocity,

and the temperature difference from surface to air. Reasonable variations in these coefficients as high

as 20 percent have shown a negligible effect on

results from the computer program.

For the computer program, the heat capacity ef- fects of the door and windows were assumed to be

negligibly small and only the thermal resistance of

these components was used. For the door and singleand double-pane windows, the overall coefficients of

heat transfer were calculated to be 0.25, 0.55, and

0.41 Btu/h"^ ft"^ °F"\ respectively, for the conditions

of tests 1 through 9. For the double-pane windows of

test 10, the calculated coefficient was 0.47. These

overall heat transfer coefficients were calculated by

the series resistance method. The film resistances at the inside and outside surfaces were taken to be the same as the corresponding waU values.

For heat flow to or from the floor, the underlying

earth was considered to be a one-dimensional semiinfinite medium for the Response Factor program,

and the average of temperatures measured at the 1-ft depth in the earth was used as the earth temperature

at a depth considerably removed from the floor. For

the duration of the tests, this was deemed an adequate assumption because the root mean square

deviation of the earth temperatures at the 1-ft level was less than 0.2 °F for all tests where the diurnal

outside air temperature varied from 40 to 100 °F and

less than 0.3 °F for the 10 to 70 °F cycle. For the 40 to 100 °F tests, the average temperature at the top of

the footing (fig. 5) was about 0.5 °F lower than the

earth temperature at the 1-ft level, and for the 10 to 70 °F test was about 2 °Y lower. This indicates that some of the heat is flowing from the earth underlying

the floor toward the footing and was not accounted

for in the one-dimensional heat transfer approach of

the Response Factor program. The error due to this

8
heat flow is believed to be very small in relation to other heat flows. A mathematical analysis was per- formed for the heat flow at the ground level in the

wall section below ground level to the top of the foot- ing (fig. 4) using the temperature variations with time

from thermostated test 6. The computed heat flows

showed that heat was flowing into and out of this section with time, but the magnitude of these heat flows was small in relation to other heat flows.

Air infiltration rates were determined by a tracer gas method using helium as the tracer gas (see ap- pendix A). For the building without and with windows, measured values were 0.06 and 0.38 air changes per hour, respectively. The above values are considered maximum rates for air infiltration because the tests were performed when the thermal

head (difference in temperature between the inside

and outside) was the greatest. It would be expected

that the air infiltration rate would be proportional to the thermal head. Based on the average indoor-outdoor temperature difference, average air infiltration rates were selected as being 2 cfm for tests with no windows and 10 cfm for test with windows. The tests of appendix A were performed on the building

without thermal insulation. Placing insulation on

either the inside or outside surfaces would increase

the resistance to air infiltration. For this reason, a

rate of 5 cfm was used for tests with insulation.

Noise reduction measurements were made on the

experimental building as given in appendix B. The

results for conditions of no windows, single-pane

windows only, single-pane windows with insulation

inside, and single-pane windows with insulation out- side are shown in figure 2 of appendix B. As in- dicated and expected, the noise reduction was

greatest without windows and some improvement is shown when insulation was apphed. Comparison of

noise reduction measurements for the tests with in- sulation on the inside and on the outside indicate

that insulation on the inside provided better characteristics because of the higher noise reduction values

in the range from 500 to 2500 Hz. This range is considered to contain the most objectionable portion of

the audible frequency spectrum.

As mentioned in the introduction, an equilibrium

moisture content of the block was rapidly achieved

and the influence of moisture in these tests is considered to be negligible. The moisture content of the

block was monitored by observing the changes of

weight of two initially oven dried concrete blocks.

One block was placed in the environmental chamber

and the other in the test room throughout the tests. The equilibrium moisture content of the monitored

blocks was 4 percent by weight. Similarly, vertical and horizontal thermal expansion of the concrete block wall was measured and attained an equilibrium range and was considered to be desirably low

especially since no surface or through-the-wall

cracks were visible.

6.1. Floating Tests

For the floating tests numbered 1 through 5, table

I, the measured and computer-calculated inside air temperatures are plotted in figures 9 through 13,

respectively, each with its measured outdoor air temperatures. The curve of measured indoor air temperature is the arithmetic average of the six in- door air thermocouples as shown in figure 5. The

vertical distribution of temperature within the room

will be treated later in this discussion. There was

generally good agreement between the measured

and predicted average inside air temperatures in all cases, although there is a trend for the predicted

values to have slightly higher maximum values and

lower minimum values during the 24-h cycle. This in- dicates that the mass of the building dampens temperature changes more than is accounted for in the

predictive computer program. This may result from

the design of the theoretical model that was used in the computer program which neglects the additional

thermal capacitance introduced at the corners of the

building and the slight changes in material physical

properties during exposure as compared with measured dry values. Comparing the indoor air temperature curves of

figures 9 through 13, it can be seen that placing insulation on inside and outside building surfaces had a marked influence on the inside air temperature

profiles. (Compare especially figs. 12 and 13 with fig. II. ) In order to examine differences, the observed

temperature deviations from the daily average inside

air temperature for the building with windows are plotted in figure 14 for the cases of no insulation, in- sulation on the inside building surface, and insulation on the outside building surface (corresponding

to figs. 11, 12, and 13). Adding insulation on the in9
A SUTSIDE niR HEBSUREO O CBLCULflTEO

TIME - HOURS

NO INSULATION, NO WINDOWS, NO INTERNAL MASS.

Figure 9. Comparison between measured and calculated inside air temperatures for floating test 1.

* OUTSIDE BIR nEflsUREO O CBLCULBTED

9 12 IS TIME - HOURS NO INSULATION,NO WINDOWS, INTERNAL MASS.

Figure 10. Comparison between measured and calculated inside air temperatures for floating test 2.
* OUTSIDE MR a HEflSURED O CflLCULBTEO

1 r 1 1 1 1 1 0 3 6 9 12 15 18 21 24 TIME - HOURS NO INSULATION, WINDOWS, NO INTERNAL MASS.

Figure 1L Comparison between measured and calculated inside air temperatures for floating test 3.

cr

A OUTSIDE nm O nEBSURED O CBLCULflTED

9 12 15 TIME - HOURS

INSULATION INSIDE, WINDOWS, INTERNAL MASS.

Figure 12. Comparison between measured and calculated inside air temperatures for floating test 4.

11
A OUTSIDE RIR a nEflSUREO O CfiLCULflTED

TIME - HOURS

INSULATION OUTSIDE, WINDOWS, INTERNAL MASS

Figure 13. Comparison between measured and calculated inside air temperatures for floating test 5.

U.

I z

o

LJa

UJ

ZD

(Xcn

UJ

-6-

NO INSULATION o INSULATION INSIDE

A INSULATION OUTSIDE

1 12 TIME - HOURS

15 18 21 24

Figure 14. Comparison of inside air temperature deviations from daily average inside air temperature

for identical buildings for cases of no insulation, insulation inside, and insulation outside.
Figure 16. Comparison of the inside air temperature deviations from daily average inside air temperature for identical uninsulated buildings with windows (test 3) and without windows ( test 1 ).

side surface of the building reduced the variations of the inside air temperature from about 10.5 to 5.5 °F. The effect of the insulation then was to damp out the

cyclic fluctuations of inside air temperature.

Furthermore, when insulation was placed on the out- side surfaces instead of the inside, the variation was

reduced to about 2 °F. This experimental finding is considered to be significant because no heat energy was purposely added to or taken away from the in- door air during the tests, and the performance

results illustrate that considerable reduction of the

indoor air temperature variations can be obtained by

simply placing the mass of the walls and roof inside

with insulation outside.

To investigate the effect of an interior mass on the

inside air temperature for a floating test, a com497-811 O - 73 - 2

parison was made between tests 1 and 2 (figs. 9 and

10). Temperature deviations from the measured mean inside air temperature for these two tests are

plotted in figure 15. It can be seen that for these cases with no insulation, the presence of an internal mass slightly dampens the inside air temperature cycle. This effect was also predicted by the Response

Factor program. For floating tests with insulation

either on the inside or outside surfaces (figs. 10 and

11) , the effect of an internal mass is reduced to negligible proportions. This is because the heat absorption and rejection by the internal mass is very

small when the cyclic fluctuations of the inside air temperature are small. To examine the effect of windows on the inside air temperature, a comparison was made between tests

13
numbered 1 and 3. The measured temperature

deviations from the mean inside air temperature for these two tests are plotted in figure 16. From figure

16, it may be seen that for the two cases without in- sulation the effect of adding windows had little effect on the cyclic fluctuations of the inside air temperature. The glass area was about 8.4 percent of the

total wall area. For cases with insulation, one would

expect the addition of windows would have a more

pronounced effect on the cyclic fluctuations of the

inside air temperature, since the heat flow through

windows would be a larger percentage of the total heat flow. Direct experimental comparison is not

possible because measurements were not made on

the building with insulation either inside or outside

without windows. For practical purposes, an improvement in the indoor temperature profile as shown in figure 16 by elimination of windows is considered to be negligible.

Figures 17 and 18 show the inside and outside wall

surface temperature variations for test 1; no insulation, no windows, and no internal mass. Each curve

represents the average temperature of five ther- mocouples located at the same height above the floor

and at the wall positions as shown in figure 6. From

these graphs it can be seen that the wall surface temperatures for this floating test differ from each other

within a 2 °F band except for the temperatures at the

0- and 10-ft levels. This suggests that the assumption

of one-dimensional heat transfer is valid over a major

area of the wall surface, multi-dimensional effects being confined in a region near the junctures of the

floor to wall and the roof to wall. Figures 17 and 18

also show by comparison the effect of thermal re- sistance and mass of the building, i.e., at the 10-ft level, the outside surface changed in temperature by

about 30 °F while the inside surface at the same level changed by about 16 °F. Also, the highest and lowest

temperatures on the outside surface occurred about

2 hours sooner than the inside surface. The use of

thermal insulation resulted in a much more uniform

inside wall temperature distribution. For instance,

when insulation was placed on the outside surface of

the building (floating test numbered 5), a maximum

inside waU surface temperature fluctuation of 2.3 °F occurred over the 24-h cycle at the juncture of the

wall and the ceiling. In addition, at any instant the

maximum floor to ceiling temperature difference

along the inside wall surface was 1.8 °F.

cr

aoINSIDE WALL SURFACE TEMPERATURE

0 FOOT LEVEL O 2 FOOT LEVEL A 4 FOOT LEVEL

-f 6 FOOT LEVEL X 8 FOOT LEVEL O 10 FOOT LEVEL

1 12 TIME - HOURS

Figure 17. Variations of inside wall surface temperatures for test 1.

14
1 1 1 L

OUTSIDE WALL SURFACE TEMPERATURE

Figure 18. Variations of outside wall surface temperatures for

test 1.

Comparisons between the measured and calculated heat fluxes at the inside surfaces of major

building components for floating test 1 are shown in figures 19 through 21 where negative values denote

heat flow into the room. Measured heat fluxes shown

for the floor, roof, and the wall were obtained using

heat flow meters located at the center of the floor,

the center of the roof, and at the midpoint of wall in plane B, respectively (see fig. 6). Since both the measured and calculated data contain many small fluc- tuations due to local variations of the inside air temperature, it was necessary to apply a harmonic aucdysis to each set of heat flux data, maintaining only

the first eight terms to give the smoothed curves shown in the graphs. From figures 19 and 20 it can be

seen that the agreement between the measured and

calculated heat fluxes at the inside surface for floor and the roof was reasonably good.

Figure 21 shows fairly large deviations for the

smoothed measured wall heat flux from the calculated values. The same type of behavior was obtained in other tests where the floor and ceiling also showed good agreement. The calculated heat flux values were computed assuming a constant film re- sistance for all heat flow conditions. Because of air

motion the film resistance wiU not be a constant, but

will be a function of the heat flow conditions that promote air flow adjacent to the surfaces. Figures

19-21 show that zero heat flux occurred at different

times for the floor, roof, and walls, and, therefore,

the time of reversal of direction of heat flow by convection was different for the different surfaces. Thus, there would be different degrees of reinforcement or interference to convection heat flow near the

floor-wall and ceiling-wall junctions for an hour or so

just before and just after the time of zero heat flux at the various surfaces. This may account for some of

the disparity between calculated and measured heat

flux for the walls shown in figure 21. To study the processes which combine together to produce the thermal performance of the air inside a building, the profiles of the heat flux at the separate

inside surfaces during the outside air temperature

cycle were plotted. Figure 22 shows the variations of

the heat flux at the inside surfaces of the roof, walls,

floor, and window for the case of no insulation (float- ing test 3). The heat flux profiles appearing in this graph were calculated by the Response Factor computer program. Positive values signify heat flow in a direction from the inside to the outside. The net heat

15
a - MEASURED O - CALCULATED

12 15 16 21 TIME - HOURS

Figure 19. Comparison between the measured and calculated

heat fluxes at the inside surface ofthefloorfor test 1.

-MEASURED O- CALCULATED

12 IS TIME - HOURS

Figure 20. Comparison between the measured and calculated

heat fluxes at the inside surface of the rooffor test 1.

TIME - HOURS

Figure 21. Comparison between the measured and calculated heatfluxes at the inside surface of the wallfor test 1

.

transfer to or from the indoor air at any instant of

time is equal to the algebraic sum of the products of

the heat fluxes at the surfaces and their respective areas plus the heat exchange resulting from air infil- tration. For the floating tests this sum should be

equal to zero. The heat flux at the inside surface is affected by the resistance to heat flow and the ther- mal heat capacity of the materials across which heat

must flow to the surface as well as the dynamic conditions of the temperature of the outside and inside

air. For this reason, heat is simultaneously flowing

out of and into different surfaces of the building. The

heat flow at the windows is in phase with the temperature potential created by the difference in the

outside and inside air temperature because heat

storage (mass) of the windows was negligible. The

roof and walls are not in phase with this potential

TIME - HOURS

Figure 22. Computed variations of the heat flow rates at the in- side surfaces of the roof, walls, floor, and the windowfor the case of no insulation (test 3). 16
ROOF (LEFT SCALE) OV/ALL (LEFT SCALE) AFLOOR (LEFT SCALE)

+ V/INDOW (RIGHT SCALE)

J ] I I 150

a 3 6 9 12 IS 18 21 24 TIME - HOURS

Figure 23. Computed variations of the heat flow rates at the in- side surfaces of the roof, walls, floor, and the windows for

the case of insulation placed on the outside surfaces of the building (test 5).

due to their appreciable heat storage capacity and

their minimum values (maximum heat flows into the

room) lag behind that for the windows by about 3 and

9 hours, respectively. The roof was approximately

one-half the thickness of the walls, and a smaller

delay time to reach a maximum or minimum was ex- pected. Heat flow into and out of the floor was ap- proximately in phase with the inside air temperature

cycle shown in figure 11. This was as expected

because the ground temperature beneath the floor was relatively constant with time.

A similar analysis of heat flow was performed for the case of insulation placed on the outside surfaces

(floating test 5). Figure 23 shows the profiles of the

heat flow at the inside surfaces for this test condition. With the peak outside air temperature at the

fourteenth hour, the delay times for maximum heat

flows into the room were 12 and 5 hours for the walls

and roof, respectively. The effect of placing insulation on the outside surface was to increase the delay

time (from 9 and 3 to 12 and 3) and considerably

reduce the amplitude of the heat flux profiles for the

wall and roof.

Figure 24 is a plot of deviations of the inside air temperature at each of six points from their instan- taneous average (floating test 3). As in all previous

plots, the peak outside air temperature occurred at the fourteenth hour. Positive deviations signify that the air temperature at that location was higher than

the average inside air temperature. On a daily average, the air adjacent to the ceihng was about 2 °F warmer than the air layer next to the floor with the

floor being as much as 3 °F warmer and 8.5 °F colder

than the ceiling during portions of the cycle. The

portion of the cycle with the largest floor to ceiling

temperature difference (about hour 18) shows a good

example of a heated surface facing downward (ceil- ing) and a cooled surface facing upward (floor) where

the air flows adjacent to the two surfaces were in the

laminar range thus producing little mixing of air and

large vertical temperature gradients. Conversely, the

portion of the cycle with the smaller temperature dif- ferences (about hour 5) shows an example of a cooled

surface facing downward (ceihng) and a heated sur- face facing upward (floor) where the air flows adjacent to the surfaces were more turbulent producing mixing of air by natural convection and smaller

vertical temperature gradients. One must conclude

from figures 22 to 24 that the indoor convection pat- tern is continually changing, as well as surface coefficients of heat transfer. The same observations can

be made from the plots of deviations from the

average inside air temperatures given in figures 25

and 26 for insulation placed on the inside (test 4) and

the outside (test 5) surfaces, respectively. In these

two cases, the vertical temperature gradients are considerably dampened due to the addition of insulation and subsequent reductions in variations of the

surface temperatures.

17
i I I I 1 L

3" above floor, 2' from wall

3" above floor, center of room

-6-( 1 1 1 1 1 1 1 1 0 3 6 9 12 15 21 24

TIME - HOURS

Figure 24. Deviations of the inside air temperature from instantaneous average of the six indoor air thermocouples for the case of no

insulation (test 3).

18
1

-2-

-3-

3" above floor, 2' from wall

+ 3" above floor, center of room A 3" below ceiling, 2' from wall

O 3" below ceiling, center of room O 5'3" above floor, 2' from wall

X 5*3" above floor, center of room

12 15 18 21 24

TIME - HOURS

Figure 25. Deviations of the inside air temperature from instantaneous average ofthe six indoor air thermocouples for the case of insula- tion placed on the inside surfaces ofthe building ( test 4).

19
-2-

-&

Q 3" above floor, 2' from wall

4* 3" above floor, center of room A 3" below ceiling, 2' from wall

<^ 3" below ceiling, center of room O 5*3" above floor, 2' from wall

X 5 '3" above floor, center of room

T 1 r- 9 12 15 Time - HOURS

le 21 24

Figure 26. Deviations of the inside air temperature from instanlaneoiis average of the six indoor air thermocouples for the case of insul tion placed on the outside surfaces ofthe building ( test 5).

20
6.2. Thermostated Tests

For the therpiostated tests, the inside room air temperature was maintained within an approximate

2 °F band by controUing the heat input to the experimental building.. The room air temperature was obtained by averaging the six air temperatures (fig. 5)

at each time interval. Figures 27 through 31 are graphs for tests numbered 6 to 10 which compare the measured power

supplied to the electric heating equipment and the

heating load calculated by the Response Factor pro- gram over the 24-h outdoor air temperature cycle as shown in each figure. The calculated load was computed by summing the net heat flows through each

building component and heat flow due to air infiltra- tion at each time interval. Areas used for computing

heat flows were the arithmetic averages of the inside

and outside areas of each building component as shown in table 4. Since both the measured and cal- culated heating load data contained many small fluc- tuations due to variations of the inside air temperature, it was necessary to apply a harmonic analysis

to each set of heat load data. Only the first eight

terms were maintained to give the smoothed curves shown in the graphs.

As shown on figures 27 through 31, the minimum

measured and calculated heating load usually oc- curred later in the day than the peak outside air temperature (hour 14) because of the effect of the mass

of the building and insulation retarding heat flow

through building components. Comparing the cases

without and with insulation, figure 27 with figures 28,

29, 30, and 31, it can be seen that the effect of placing insulation on either the inside or outside surfaces

of the building was to substantially reduce the

amount of heating needed to maintain a constant in- side air temperature. Generally the correlation

between computer prediction and the measured

heating load profiles is reasonably good. There was

less than an 8 percent difference between the max- imum computed and measured heating loads for all cases. The average difference was 4.3 percent for the five tests.

120CH

lOOCM

a

CEo

crUJX

6000-

400&-

2000-

MEASURED HEATING LOAD

O CALCULATED HEATING LOAD - OUTSIDE AIR TEMPERATURE

NO INSULATION

NO INTERNAL MASS

S. p. WINDOWS

-2000

TIME - HOURS

Figure 27. Comparison between the measured and calculated heating loads for test 6.

21
For test 9 (fig. 30) and test 10 (fig. 31), the building was identical but for test 10 the outdoor temperature

cycle was changed from 40-100 to 10-70 °F and the

indoor air temperature was changed from 77.6 to 73.8 °F. The shape of the heating load profiles are

similar but for test 9 the maximum and minimum

loads were about 2500 and 400 Btu/h, respectively,

and for test 10 about 6100 and 3500 Btu/h, respectively. The maximum loads for both tests are lower

than the values that would be estimated on the basis

of steady-state procedures as is discussed in detail

later in this paper. For the thermostated tests with insulation (tests 7 through 10), the measured heating loads lag the cal- culated heating loads over part of the 24-h cycle.

Consistently, the phase lag occurred on the profiles

in the time period between the maximum and

minimum loads. Also, some phase lags occurred fol- lowing the minimum loads. The reasons for these

phase lags are not obvious because the phase lags

varied from one test to the other and the lag is especially evident in test 9, figure 30. It was found during

analysis that the calculated heating load was influenced by whether the inside, outside, or average

area was used, lack of heat flow allowance for cor- ners and the building foundation, variations of inside

air temperature, and heat transfer coefficients at the

inside and outside surfaces.

To illustrate the effect of windows on the thermal

behavior of the experimental building, calculations were made using the Response Factor method for the cases of seven single-pane windows, seven double-pane windows, and no windows with insulation on the outside surfaces. The outside air temperature

cycle used was 40-100 °F and the inside air temperature was 77.6 °F. Figure 32 shows the computed

heating load profiles for the above cases. The peak

heating load for single-pane windows was 57 per- cent higher and occurred approximately 2 1/2 hours

earlier than the case without windows. The peak

heating load for double-pane windows was 9 percent

lower than single-pane windows. Some validation by

measurement of the latter can be seen by comparing

the peak heating loads as shown in figures 29 and 30,

about 4 percent difference.

t- 2000-

MEASURED HEATING LOAD O CALCULATED HEATING LOAD

OUTSIDE AIR TEMPERATURE

INSULATION INSIDE INTERNAL MASS

y r

S. P. WINDOWS

y 76.9 ±.8 \ fj6

y

y

y

\ 1

1 1 -1 ^ ^ 9 12 IS TIME - HOURS

Figure 28. Comparison between the measured and calculated heating loads for test 7. 22
MEASURED HEATING LOAD

0 3 6 9 IZ IS 18 21 24 TIME - HOURS

Figure 29. Comparison between the measured and calculated heating loads for test 8.

Figure 30. Comparison between the measured and calculated heating loads for test 9.
3400-1 1 1 , 1 1 1 1

1 lb 0 3 6 9 12 15 18 21 24 TIME - HOURS

Figure 31. Comparison between the measured and calculated heating loads for test 10.

B NO WINDOWS

i 1 1 1 1 1 1 1 0 3 6 9 12 IS le 21 2 TIME - HOURS

Figure 32. Comparison of the calculated heating load profiles for

the cases of no windows, single-pane windows, and double- pane windows for the same building.
6.3. Heating Load Predictions

Steady-state methods are usually used for predicting maximum heating loads from which the size of

heating equipment is selected. Sometimes this process results in oversizing of heating equipment.

To illustrate and compare the steady-state procedure

and the dynamic procedure as given by the computer

programs in appendices C and D, table 5 was

prepared.

The values Usted in the column under SteadyState Method in table 4 were calculated for the ex- perimental building as used in tests 6 through 10,

and for the outside air temperature cycles used during the tests. The steady-state maximum heat flow

rate was calculated using the following formula:

9= UMf (Ti - Tg) + (Ti - To) ^U„An

+ lMV(Ti- To)

where q — heating load, Btu h~^

Ur- coefficient of transmission for the floor. Btu h-i ft-2 F-^

Af = area of the floor, ft^ Ti^ average inside air temperature, F

T,= average ground temperature, F

To = outdoor temperature, F

Un = coefficient of transmission for the nth

surface, Btu h-i, ft-^ F'^

An — area of the nth surface, ft^ air infiltration rate, cfm

The first term corresponds to the heat transferred

through the floor. The second term is for heat trans- ferred through the walls, windows, and roof. The

third term is heat transfer due to air infiltration. When the above equation was used to predict the

maximum heating load, the minimum outdoor temperature was used for To. When the above equation was used to calculate the daily average heating load,

the daily mean outdoor temperature was used for To.

The maximum and daily average heating loads as calculated using the steady-state and Response Factor methods are presented for comparison with measured values in table 5. The maximum heat flow rates as calculated by the

steady-state method for the conditions during tests

6, 7, 8, 9, and 10 were 32, 63, 69, 67, and 29 percent,

respectively, higher than the measured rates. The

maximum heat flow rates as predicted by the

Response Factor method were within 8 percent of the rates measured during the tests. The above high

percentages indicate that when steady-state max- imum rates are used with the temperature profile of figure 7 to size heating equipment without taking

into account the heat capacity effects of the building,

considerable oversizing could result. When comparing daily average heat flow rates between the steady-state method, the Response Factor method, and measured values, table 5 shows that

all values are reasonably close to each other for a given test number (about 10% or less). This was ex- pected because a minimum quantity of heat energy

is necessary to maintain the indoor air temperature

over a period of 24 hours.

There is no way to make a good comparison

between the design heating load that would result from application of the current steady-state

procedures in the Guide and Data Book of the American Society of Heating, Refrigerating, and Air-Conditioning Engineers, and the maximum heating load

determined by the computer techniques used in this investigation. The design winter outdoor temperature used in the ASHRAE procedure is that temperature for which 97 1/2 or 99 percent, or some

other chosen percentage, of the total hours are less severe in the location under consideration. The

procedure does not take into account the effect of sunshine, the mass of the building, of the diurnal

temperature pattern, or the relative location of the

insulation in the building. Once the design outdoor

Table 5. Comparison of maximum and average heating loads

Maximum heat flow rate (Btu/h)

Test

Steady- Response Steady- Response

state factor Measured state factor Measured

method method method method

6 15135 11558 11372 4849 4899 5346

7 4470 2814 2748 1365 1421 1475

8 4748 3047 2811 1554 1612 1664

9 4499 2525 2700 1455 1515 1639

10 8150 6144 6321 4981 5047 5062

Daily average heat flow rate (Btu/h)

25
temperature is selected, the design heating load is calculated as a steady-state heat transfer problem.

There is no way to convert the diurnal temperature

cycle used in this investigation into an equivalent

ASHRAE design outdoor temperature. Furthermore,

it is not possible to select a design winter day in terms of the diurnal temperature pattern using

present ASHRAE procedures. Thus the present

ASHRAE steady-state procedures constitute an ap- proximate approach to the determination of heating

loads that, due to experience and judgment,

minimizes the likelihood of serious prolonged un- derheating of buildings.

7. Conclusions

The NBSLD computer program was experimentally verified for predicting the daily indoor air temperature as it is influenced by known outdoor temperature conditions and the mass and thermal re- sistance of the building. Furthermore, when the in- side air temperature was thermostated, this program

predicted the maximum and daily average heating

loads and may therefore be used to size equipment

needed to condition the interior of a building and to predict energy requirements. It was shown that steady-state methods of heating load calculations

could result in oversizing heating equipment by 30

percent or more for this particular building and imposed exterior conditions if the lowest outdoor temperature was selected as the design temperature.

The NBSLD dynamic method takes into account

heat storage effects and therefore predicts the max- imum heating load more realistically. The maximum

percent difference between the computer calculated

maximum heating load and measured values was 8

percent, and the average difference was 4.3 percent

for the five tests. The combination of mass in the walls and roof fac- ing the interior with insulation placed on the outer

surfaces of the building was very effective in reducing and controlling the variation of the indoor air temperature. This desired effect was also predicted

by the computer program. When the inside air temperature was not thermostated and the building

floated in response to the outside air temperature

condition, placing insulation on the inside building

surface reduced the variation of the inside air temperature from 10 1/2 to 5 1/2 °F. Furthermore, when

this insulation was placed on the outside surface of

the building, the variation in the inside air temperature was reduced to 2 °F. In addition, comparing

cases of no insulation, insulation inside, and insulation outside, the temperature distribution from floor

to ceiling on walls and in the indoor air was a minimum when insulation was placed on the outside

of the building.

The effect of an internal mass on the thermal

behavior of the experimental building was generaUy

small. An internal mass to simulate furnishings may

have a greater effect in a less massive building. On

the other hand, windows had a significant effect on

the computed thermal behavior of the experimental

building. For instance, the maximum heating load for the experimental building with windows and insulation was 57 percent higher than the same building

with insulation but without windows. Use of storm

windows reduced the maximum heating load by 9

percent.

The authors wish to thank H. E. Robinson for his many ideas, conceptual approach, and technical sug- gestions prior to and during the experimental phases

of this investigation. Also, appreciation is expressed

to D. R. Showalter, J. D. Allen, J. M. Dungan, and J. W. Grimes for their technical assistance in the in- stallation of the instrumentation and day-to-day

operation of the experiments. The very helpful sug- gestions and comments made during review of this paper by P. R. Achenbach are gratefully

acknowledged.

26
Appendix A

Air Infiltration Measurements on the NBS Experimental Building

Thomas K. Faison

Thermal Engineering Systems Section, Building Environment Division

Center for Building Technology, Institute for Applied Technology,

National Bureau of Standards, Washington, D.C. 20234
1. Introduction

In the early stages of the project on thermal per- formance of the experimental building, measure- ments were made to determine the magnitude of air exchange between the building and the surrounding

chamber during the process of cyclic temperature

changes. Since wind forces were negligible during

the testing period, the major driving force influencing the change of air was the thermal difference

between the air inside of the building and that of the

surrounding air in the chamber.

2. Analysis and Instrumentation

The instrumentation used in the determination of

the air exchange rates was developed at the National

Bureau of Standards', and the process of measure- ment was the tracer gas method using helium as the

tracer gas. The rate of change in concentration of a tracer gas caused by exchange or infiltration of outside air under a steady-state temperature difference is ex- pressed by the formula:

-V (dcldt) = Kc (1)

where

V= volume of enclosure

c = concentration of tracer gas at time t K= average volume of air infiltration per unit time

for the time interval

« = time

When c = Co at time = 0, the solution of eq 1 is as fol- lows:

c=coe-'''"' (2)

or

KtlV=\oge(colc) (3)

Equation 3 shows that the number of air changes oc- curring during time t is equal to the natural

logarithm of the ratio of the tracer gas concentrations at the beginning and at the end of the time in- terval.

' Coblentz, C. W. , and Achenbach, P. R., "Design and Performance of a Portable Infiltration Meter," Transactions, American Society of Heating and Air Conditioning Engineers, Vol. 63, 1957.

3. Procedure and Results

Prior to the test, the apparatus was calibrated and

brought into equilibrium with its surroundings, then

hehum, the tracer gas, was released into the building. As the helium was introduced, it was mixed with

the room air by means of a portable fan and the final mixture of air and helium contained about 1/2 per- cent of helium by volume.

Four helium-sensing elements were distributed

within the space. Each sensor was positioned 3 ft above floor level and 4 ft from an outside wall near each of the four corners. Air temperature measure- ments of the two spaces were recorded during the

test.Initially a test was made to determine the amount

of air exchange through the building with the sur- rounding environmental chamber prior to cutting

openings for the glass windows. Later, additional

tests were made to determine the rate of air exchange when glass windows were introduced into the building. The windows were of a fixed type and were caulked in place. The door was closed for all tests. Measurements were made at the time of day when

the air temperature in the environmental chamber

was lowest and unchanging, providing a maximum

temperature difference and air exchange between

the inside and outside. Measurements of air exchange were made when the tightly fitting

weatherstripped door was normally closed and when

aU cracks around the door were taped.

For the building without windows, the measured

values of air exchange were 0.03 and 0.06 air changes per hour for the conditions of the taped and

untaped door, respectively. These air exchange rates

for the basic structure are very small. They do pro- vide a minimum value for comparison with other

tests and show that heat gain or loss to the building was almost solely by heat conduction and the in- fluence of air leakage for the test without windows was practically negligible.

After the windows were installed, single glass

only, additional measurements were made to deter- mine the exchange rate under these conditions. The

same procedure was followed and approximately the same temperature difference was observed. Under

these conditions, but with the windows installed, the

door not taped and no insulation on the walls, the

measured value was 0.38 air changes per hour, a significant increase over the first tests having no window openings.

28
Appendix B

Noise Transmission Measurements of the NBS

Experimental Building

John S. Forrer

Applied Acoustics Section, Mechanics Division

Institute for Basic Standards, National Bureau of Standards

Washington, D.C. 20234

1. Objectives of Tests

Measurements were made of the sound attenuation provided by the concrete block experimental

building located in the NBS high-bay environmental

laboratory in order to establish the feasibility of

noise reduction testing in such a space and to determine the sound transmission characteristics cor- responding to four different conditions of the building.

2. Building Variations Tested

The building construction during the first series of

tests was a simple concrete block cubicle with a 20

ft X 20 ft floor plan and a 10-ft-high ceiling (outside

dimensions). The walls were made of 8-in X 8-in X

16-in solid concrete blocks. A concrete slab floor and

a flat 4-in-thick precast concrete slab roof completed

the enclosure. A 2-in-thick solid wooden door (foam

rubber gasketed) provided the only break in the

otherwise solid shell of the building.

The building configurations employed during the

noise transmission tests were as follows:

1. Concrete block shell with a single wooden door

(described above).

2. Seven 32-in X 40-in X 3/32-in single-pane windows

installed as shown in figure 1 (bottom of sills 40 in above floor).

3. 2-in-thick rigid polystyrene thermal insulation applied to the inside walls and ceiling.

4. Insulation removed from inside the building and

similar material used to cover the outside walls and

roof.

3. Test Procedures

Measurements were made in accordance with

ASTM E336-67T, Tentative Recommended Practice

for Measurement of Airborne Sound Insulation in Buildings. The procedures, referred to in appendix

A. 1.1 of E336-67T, for determining noise reduction

(a measure of the isolation between two enclosed

spaces) were followed. This is in contradistinction to the field insertion loss which is typically measured

when a complete building is tested out of doors.

Figure B-1 shows the location of each of the five microphones of the receiving room array (inside the

T10'

I

Source Room

(height: 31 ft)

window I

X

90

48

X

93

X

A9

X

50

X

58

Receiving Room X

71

door

88

X

90

10' high

X microphone (height given in inches)

I S I speaker

g

concrete block stack 38 in. high

Figure B-1. Floor plan of NBS High-Bay Environmental Laboratory and experimental building. Microphone and speaker

positions usedfor the noise reduction tests are indicated.

building) and the six microphones of the source room

array (outside the building). The microphone

systems employed 1-in pressure-type condenser

microphone cartridges with attached preamplifiers.

Each array was powered by a six-channel

microphone energizer and multiplexer which

scanned the microphone array at a rate of five channels per second. The multiplexer output was fed into a one-third octave band-pass filter set. The filtered signal was measured by means of a precision sound

level meter or a graphic level recorder (see table B1). Calibration of the measurement system was per- formed using a calibrated piston phone — a precision

sound source which produces a sound pressure level of 124 ±0.2 dB at a frequency of 250 Hz at the

microphone diaphragm.

The signal for the noise transmission tests was

provided by four speakers energized with pink ran- dom noise'. These speakers were located opposite

' Pink random noise is white noise passed through a network which weights at — 3 dB

per octave.

31
Table B-1. Instrumentation for noise reduction measurements*

1. Briiel and Kjaer Model 4220 Pistonphone

2. Briiel and Kjaer Model 4132 Pressure Microphone

3. Bruel and Kjaer Model 2619 FET Preamplifiers

4. Briiel and Kjaer Model 221 Microphone Energizer and

Multiplexer

5. Briiel and Kjaer Model 1612 Band-pass Filter Set

6. Briiel and Kjaer Model 2204 Precision Sound level Meter

(used during design stages 1,2. and 3).

7. Briiel and Kjaer Model 2305 Graphic Level Recorder (used during design stages 3 and 4).

8. Kudelski (Nagra III) tape recording of pink noise used as

signal source in design stages 1,2, and 3.

9. Briiel and Kjaer Model 1024 Sine Random Generator used as pink noise source in design stage 4.

*Commercial instruments are identified in this report in order

to adequately specify the experimental procedure. In no case does such identification imply recommendations or endorsement

by the National Bureau of Standards, nor does it imply that the equipment identified is necessarily the best available for the purpose.

the outside corners of the building as shown in figure

B-1. The noise reduction provided by the building at each test frequency was determined by subtracting

the one-third octave band sound pressure level measured in the receiving room from the corresponding

level measured in the source room.

4. Results

The curves plotted in figure B-2 present the measured noise reduction provided by the building for each of the four variations in construction. As

shown, the use of windows caused an average loss of

sound isolation of about 10 dB for frequencies above

200 Hz. The addition of thermal insulation either on

the inside or the outside improved the acoustic per- formance but not enough to compensate for the ef- fect of the windows.

Data were gathered at frequencies below 500 Hz

but the short integration times used in the rms detection system, along with difficulties encountered in achieving a uniform sound field in the test space

60

50

10

Before windows

> /'/ \

\' - After ^ windows Insulation

outside -

1 III 11 1

1 Insulation

inside

C 1 1 100 1000 10,000

Frequency, Hz

Figure B-2. Noise reduction versus frequency for various construction modifications of the experimental building in the High-Bay Environmental Laboratory.

rendered the measurements inconclusive for frequencies below 500 Hz. Specifically, measure- ments of the sound distribution inside and around

the building with the speakers energized revealed

differences among the sound pressure levels measured at microphones in the same array of 4-12 dB

for frequencies below 200 Hz in the receiving room

and for frequencies below 500 Hz in the source room.

Differences of this magnitude render a spatial

average achieved by a five- or six-microphone array

of Uttle value. No attempt was made to compute the sound trans- mission loss (the difference between the incidence

sound intensity level and the transmitted sound in- tensity level) of the walls of the building or to relate the results of the present tests to laboratory tests on

similar walls. The intent of the present work was

merely to investigate the feasibility of measuring the

noise reduction between one enclosed space contained within another enclosed space.

32
Appendix C

Computer Programs (NBSLD) to Obtain Heating and Cooling Loads and t Estimate Room Air Temperature Change Using Thermal Response Factors

Tamami Kusuda

Thermal Engineering Systems Section, Building Environment Division

Center for Building Technology, Institute for Applied Technology

National Bureau of Standards, Washington, D.C. 20234

1. Introduction

The NBS computer programs called NBSLD are

a group of routines to permit the determination of heating and cooling loads of a room based upon a cal- culation methodology adopted by the American

Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) Task Group on Energy

Requirements.

For a given 24-hour weather pattern, the program

calculates heat exchange due to solar and sky ther- mal radiation through windows, heat conduction

through walls and roofs, heat convection due to air infiltration and internal heat generation. Heat

exchange is computed for every hour and later con- verted into the room heating or cooling load in conjunction with weighting factors. Details of these cal- culation procedures and the theoretical background

for the weighting factors' application are not given

here. The calculation procedures are available in the

1971 ASHRAE publication entitled "Procedures for Determining Heating and Cooling Loads for Computerized Calculation of Energy Requirements." These

procedures were developed and published by the

ASHRAE Task Group on Energy Requirements with

the assistance of the National Bureau of Standards

and the National Research Council of Canada.

The ASHRAE Task Group procedures incorporate

what is considered to be the most up-to-date computation methodology for evaluating the dynamic

aspects of building heat conduction by the response

factor method. Since the algorithms employed in this procedure are new and rather complex, their use has

been limited. Presented in this report is the general feature of

the NBS program of the ASHRAE Task Group al- gorithms to illustrate the use of this modern and

powerful technique on small computers'.

AU of the routines are, therefore, written in a close

accordance with the ASHRAE Task Group al- gorithms and made into many subroutines, each of

which could be used independently for other pro- grams.

Attached are the Fortran V listings of NBSLD

(designed to be run by the NBS UNIVAC 1108 under

the version of EXEC H). The program in the form of

punched cards or on magnetic tape is available from

the Thermal Engineering Systems Section of NBS

' This documentation is not intended to serve as a User's Guide or Manual, but rather

to describe the program in general. More detailed documentation in the form of a User's Manual will be published subsequently.

I HESF \-

FlGURE C-1. Logic networkfor NBSLD.

including assistance for its use, if desired. Figure

C-1 shows the logic network for NBSLD.

1. ABCD2, ABCDP2, DERVT, GPF, MULT, RESF,

RESFX, RESPTK: These routines are parts of a response factor calculation package and are needed for the accurate evaluation of thermal time

lag, damping, heat storage in exterior facing sur- faces as well as the internal furnishings.

2. DPF: Calculates dew point temperature when

the partial vapor pressure is known.

3. GLASS: Calculates solar heat gain through glass

when given the shading coefficient, orientation

type of glass, type of fenestration.

4. OUTSID: This routine calculates the outside sur- face temperature and wall heat gain by taking into account solar heating, back radiation to the sky,

convective heat loss to the ambient air and

transient heat conduction.

5. PSYl: This is a simplified psychrometric routine

that determines the thermodynamic properties of

moist air when given dry-bulb temperature, wet- bulb temperature, and barometric pressure.

6. PSY2: This is the same as PSYl except that the

dew point temperature is used instead of the wet- bulb temperature.

7. PVSF: This routine determines the saturated

vapor pressure as a function of temperature.

8. SHG: This is the ASHRAE routine for calculat- ing solar heat gain through glass.

9. SUN: Calculates basic sun data such as angles,

cloud cover, direct and diffuse radiation needed

for solar heat gain and solar heating of the building

exterior surfaces.

35
10. TAR: Calculates transmission and absorption

characteristics of glass.

11. WBF: Approximates the wet-bulb temperature

when provided with the enthalpy of moist air and

the barometric pressure.

12. WF: Determines the cooling load by multiplying

the heat gain by the ASHRAE weighting factors. (This routine was not used in this report because

it incorporates the basic calculation used for deriving the weighting factors.)

13. RMTMP: Determines the room temperature as a balance of heat gains and cooling capacity of an

air conditioning unit. Since this routine is not

available in ASHRAE Task Group Algorithms,

detail is given in the following pages.

14. SOLVP: Solves simultaneous linear algebraic

equations needed in RMTMP.

15. WEATHE, WD, DECODE: This package is a weather decoding program and was not included

because the weather input is implicitly defined in the following section on input data.

16. CCM: This routine modifies the solar radiation

for a cloudless sky by the instantaneous cloud

cover. (This routine is not included.)

17. FO: This routine calculates the outside surface

heat transfer coefficients from the weather data. (This routine is not included where the coeffi- cients are considered to be input data.)

2. RMTMP

Room Temperature Calculation Routine

Input: NS = number of heat transfer surfaces in the room

(S(I), I —I, NS) = area of the heat transfer surfaces, ft^ {M{I), 1=1, NS) = number of response factor terms for each heat transfer surface

(IX{I), 1=1, NS) = index for the thermal storage effect for each heat transfer surface

IX (I) = 1 for thermal storage surface

IX (I) = 0 for nonthermal storage surfaces such as windows and door

(CRil), 1=1, NS) = common ratio for the thermal response factor of each heat transfer

surface

M{I) = 1,CR{I) = 0 if IX{I) = 0

( iX{I, J) , F(/, J) for 1=1, NS) ,7=1, M{I) ) thermal response factors for each surface

X{I, 1), Y{I, 1) = overall thermal conductance of the nonthermal storage surface and all the other response factor terms should be treated as zero if IX (I) = 0.

Note: For the calculation of X{I, J), Y(I, J), the surface heat transfer coefficients (both inside

and outside) are not included.

{{T(j){I, t-J) for 1=1, NS), J =1, M(I)) = outside surface temperature history, °F

{{TI{I, t-J) for /= 1, A^S), y= 1, M{I)) =inside surface temperature history, °F TA = air temperature of the room

(//(/), /= 1, NS) = convection coefficient of the interior surface, °F (F(/, K) , I = 1, NS) , K= 1, NS) = radiant heat exchange factors between surfaces / and

K, where F(/, K) = 0 if I = K

(/?(/, t) , I = 1, NS) = heat input per unit indoor surface at time t to the surface, such as

solar heat or radiation heat from the lighting, equipment and occupants to the surface

(£(/), /= 1, NS) = emissivity of the surface

Q{I, t — 1) = heat flow at the /th surface at the previous time period or time = (t — 1)A,

Btu h-i ft-2 A = time increment

t = time index for the clasped time ^ A hours

CFML = outdoor air leakage, CFM

36
CFMV=' ventilation air rate, CFM/°F (at time «A)

DB{t) = outdoor air temperature, °F TV{t) — ventilation air temperature, °F (at time fA)

QEQUP: convective component of internal heat from equipment, Btu/h

Q0CPS: convective component of internal sensible heat from occupants, Btu/h

QLITE: convective component of heat from lights suspended in air, Btu/h

1. Basic heat balance equation at the / surface (at time

Q(I, t) = ^{X{IJ)*TI{I, t-J+l)-Y{I,J)*T0{I, t-J+l)} + CR(I)*Q{I,t-\)

Ns = H(I)*{TA{t)-TI(l, 0) + X (^(L K) *iTI{K, t)-TI{I, t)) + R{I, t)

where 6(7, K) =^*E(I)*F{I, K)*{TA + ^60)^*0. UiES

2. Total heat balance for the room air

Ns£S(/)*(r/(/, t)-T.4{t)) + 1.08*CFM

1=1 *{DB{t)-TA{t))

+ im*CFMV*{TV{t)-TA{t})

+ QEQUP + QOCPS + QfJTE^O

3. Letting matrix elements

Ns A{I, I)=X(L !)+//(/) + £ 6(7, K)

A{I, K) = -C(I, K), A{K, I) = -G{K, 7), for 7=1, NS andK=l, NS

A{I, Ns+l) = -H{I)

M(l) '''W B{I) = -J^X{I,J)*TI{I, t-J) + ^Y{I,J)*T0{I, t-J)-CR{I)*QiI, t-l)+R{I, t)

A{Ns + l, K)^S{K)*H{K) {oT K^l,Ns

Ns AiNs + 1, Ns + l) = -l.08*{CFML + CFMV)-^H{K)*S{K)

B{Ns+l)^-QEQUP-Q0CPS- QLITE - 1 . 08 *

( CFML*DB(t)+ CFMV*TV{t))

TI{I, t) and TA can be obtained by solving the following yV5+ 1 simultaneous equations

^(1,1), ^(1,2)

A{2, 1),^(2,2)

^(1,A^5+1)

A{2,Ns+l)

AiNs,l),A{Ns,2) . ..A{Ns,Ns + 1)

AiNs+1, l),A{Ns+l, 2) . . . A{Ns+l, Ns+1)

TIil,t) 5(1)

•*

TI{2,t) B{2)

TI{Ns,t) BiNs)

TA B{Ns+l)

37
3. Input Data Needed for the Fortran

Listing of NBSLD

Input data needed for the heating/cooling load

calculation are listed on the following pages but

not necessarily in the card reading sequence of the Fortran version listed in this report.

Building Number (BLDGNO)

CeiUng Height (HT)

Floor Area (AG)

Number of Floors (N0FLR)

Number of Occupants (QCU)

Winter Window Overall Heat Transfer Coeffi- cient (UGW)

Ground Floor Heat Transfer Coefficient (UG)

Air Change Per Hour (AIRCHG)

Latitude (LAT)

Longitude (L0NG)

Time Zone Number (TZN)

Month (M0NTH)

Day (DAY)

Elapsed Hour Since Midnight of January 1st (FLAPS)

Electric Power to the Light Watts Per Square

Foot of Floor (OLITY)

Electrical Power to Equipment, Watts Per

Square Foot of Floor Area (QEQPX)

Ventilation Air Rate (CFMV)

Air Leakage Rate (CFML)

Maximum Temperature of the Design Day

(DBMAX)

Daily Temperature Range of the Design Day

(RANGE)

Design Indoor Temperature Condition (DBIN)

Design Outdoor Wet-Bulb Temperature

(WBMAX)

Design Indoor Wet-Bulb Temperature (WBID)

Design Winter Outdoor Temperature (DBMWT)

Design Summer Ground Temperature (TG)

Design Winter Ground Temperature (TGW)

Total Number of Exterior Surfaces to be Considered for the Heat Gain Calculation (NEXP)

Index for the Room Temperature Calculation

Index for the Standard ASHRAE Task Group

Calculation in the Special and Detailed NBS

Calculation

Repeat the following cards for NEXP times

Type of Heat Transfer Exposures (ITYPE)

1. Roofs

2. Walls

3. Windows

4. Doors

5. Floors

Type of Response Factors to be Used (IRF)

1. Heavy roof construction

2. Light weight roof

3. Heavy weight exterior walls

4. Light weight exterior walls

5. Heavy ceiling/floor

6. Light ceiling/floor

7. Heavy partition wall

8. Light partition wall

U Value of the Exposures (U)

Area of the Exposures (A)

Orientation of the Exposures (AZW)

0. South facing

90. West facing

180. North facing — 90. East facing

Radiant Heat Exchange Factors Among

Exposure Surfaces

If the construction of roof, wall and floor is nonstandard, the following information is needed in addition to the standard data indicated above.

Roof, Wall, Floor Data

1 Time increment of the temperature data

2 Number of roof layers (NR)

3 Thermal resistance of the roof inside surface

4 /, K, p, c, and resistance of the 1st layer counted

from inside surface . . . (NR-2) Cards

5 Thermal resistance outside surface of the roof

6 Description of the 1st layer of the roof

7 Description of the 2d layer of the roof

8 Description of the NRth layer of the roof

9 Number of wall layers (NW)

10 Thermal resistance of the inside surface

11 /, K, p, c and resistance of the 1st layer counted

from inside (NW-2) Cards

12 Thermal resistance of the outside surface layer

13 Description of the 1st layer of the wall

14 Description of the 2d layer of the waU

15 Description of the NWth layer of the wall

16 Number of layer of the floor and the semiinfinite layer (NF) index (if basement floor) 17 Thermal resistance of the inside surface /, k, p,

c and Res of the 1st layer of the floor counted

from the inside surface

18 /, K, p, c and Res of the 2d layer of the floor (NF-1) Cards

19 K, p, and c of the earth ... if basement floor 20 Description of the 1st layer

21 Description of the 2d layer

22 Description of the NFth layer

38
C BASE HEATINS/GOOLINS LOAD CALCULATION PROGRAM

C INCLUDIWG THE ROOM TEMPERATURE CHANGE PREDICTIONS

C I=EXPOSURE NUMBER* 1=1 »2»-NEXP

C ITYPE(l) ^EXPOSURE TYPE NUMBER

C 1 ROOF

C 2 EXPOSED WALLS

C 3 WINDOWS

C DOORS

C 5 GROUND HEAT TRANSFER SURFACES

C 6 FURNISHIN6S»PARTITI0N WALLS»PARTY WALLS AND FLOOR/CEILINGS

C 7 OPEN SURFACE

C 8 EXPOSED FLOORS

C PB BAROMETRIC PRESSURE IN OF H6

C ITEMPS TEMPERATURE RISE INDEX

C IHTCI) HEAT TRANSFER INDEX

C AVEHTG—AVERAGE HEAT GAIN FOR SITE

C TSITHT—TOTAL SITE HEAT GAIN FOR 2U HOURS

C IHT=.l GLASS SURFACE(TRANSPARENT)

C IHT=0 OPAQUE

C IHT=1 OTHERWISE

C 01—HEAT FLOW THROUGH EACH EXPOSURE

C QSUM—SENSIBLE HEAT GAIN

C QTLAT—LATENT HEAT GAIN

C TOTHT—TOTAL HEAT GAIN

C QC—SENSIBLE COOLING LOAD

C SITEQS—ENTIRE SITE SENSIBLE HEAT GAIN

C SITEQL—ENTIRE SITE LATENT HEAT GAIN

C SITETH—ENTIRE SITE TOTAL HEAT GAIN

C BLDMAX—BUILDING MAX HEAT GAIN

C QSUMT—AVERAGE HEAT GAIN

C SITELD--ENTIRE SITE COOLING LOAD

C SITMAX—SITE MAX HEAT GAIN

C AVESIT—SITE AVERAGE HEAT GAIN

C SQWINT—SITE HEAT LOSS

C IRF(I) RESPONSE FACTOR NUMBER APPLICABLE TO THE SURFACE

C ABSP(I) SURFACE SOLAR HEAT COEFFICENT

C SHADE(I) SHADING COEFFICIENTS

C U(I) EXPOSURE U VALUE

C UT(I)—U VALUE WITHOUT EXTERNAL SURFACE RESISTANCE

C H(l) EXPOSURE EXTERIOR SURFACE THERMAL CONDUCTANCE

C Ad) EXPOSURE AREA

C WAZ(I) WALL AZIMUTH ANGLE MEASURED CLOCKWISE FROM SOUTH

C TG--GROUND TEMPERATURE FOR COOLING LOAD CALCUATION

C TV = VENTILATION AIR TEMPERATURE

C UG—GROUND HEAT TRANSFER COEFFICIENT

C AG—GROUND HEAT TRANSFER SURFACE(=0 WHEN NO GROUND FLOOR)

C TGW—WINTER GROUND TEMP

C DBMWT—WINTER OUTDOOR TEMP

C LAT=LATITUDE DEGREE

C LONG=LONGITUDE DEGREE

C TZN—TIME ZONE NUMBER

C MONTH—MONTH OF YEAR

C DAY—DAY

C QLITX—MAXIMUM LIGHTING LOAD IN WATT/FT2

C OEQPX—MAX EQUIP LOAD IN WATT/FT2

C NEXP—NUMBER OF EXTERIOR HEAT TRANSFER SURFACES

C 3LDGN0—BUILDING NUMBER

C HT—BUILDING OR DWELLING UNIT HEIGHT

C QPSX—MAX OCCUPANT SENSIBLE LOAD BTU/HR* PERSON

C QPLX—MAX OCCUPANT LATENT LOAD BTU/HR» PERSON

C DP—OEWPOINT TEMP* F

C QCU—MAX NUMBER OF OCCUPANTS
C ELAPS=OArS ELAPSED SINCE JAN. 1 C UGLAS—WINTER GLASS HEAT TRANSFER COEFFICIENT

C HI——INNER SURFACE CONVECTIVE HEAT TRANSFER COEFFICIENT

C HR INNER SURFACE RADIATIVE HEAT TRANSFER COEFFICIENT

C G»GG RADATION HEAT EXCHANGE SURFACES SHAPE FACTORS

C X»Y»Z RESPONSE FACORS

C THESE RESPONSE FACTORS SHOULD NOT INCLUDE OUTSIDE SURFACE

C THERMAL RESISTANCE WHEN ITEMP.EO.O

C THEY SHOULD NOT INCLUDE BOTH THE OUTSIDE AND INSIDE THERMAL

C RESISTANCES WHEN ITEMP.EQ.l

C CFML AIR LEAKAGE

C CFMV VENTILATION

C R A FRACTION OF LIGHTING POWER THAT GOES INTO FLOOR

C DBMAX DESIGN OUTDOOR DRY-BULB TEMPERATURE

C RANGE DAILY RANGE OF THE OUTDOOR TEMPERATURE

C WBMAX DESIGN OUTDOOR WET-BULB TEMPERATURE

C WBID DESIGN INDOOR WET-BULB TEMPERATURE

C DBIN DESIGN INDOOR DRY-BULB TEMPERATURE

C ITK INDEX TO CALCULATE ROOM TEMPERATURE RISE WHEN NOT AIR CONOIT

C ITK=1 WHEN NOT AIR CONDITIONED

C ITEMP INDEX To USE ASHRAE WEIGHTING FACTOR

C IF ITEMP=0 ASHARE WEIGHTING FACTOR

COMMON /CC/ X(10»100) »Y(10»100) »Z(10»100) »ITYPE(10) »IHT(10) »IRF(10

1) »ABSP(10) »U(10> »H(10) »HI(10) »A(10) »UT(10) »TOS(10»i*8) »TIS(10»«»8) »8

2(10»10) »TOY(i*B) »DB(2«+) »QLITE^2^^) »0EQUP(2f) »00CPS(2^) » 01(10) »CR< 10)

3»NR(10) »QSLAS(10»2«*) »ITHST

DIMENSION XXdOOrlO) »YY(100»10)»ZZ(100»10) »TNEW(24) »TIX(2i^) »Tl(t^9)

1»Q0CUP(2'*) »QTL(2«») f XDUM(IOO) rYDUMdOO) »ZDUM(100) »TDUM(100) »00(10)

REAL LG(8) »LX(8) »LIS(8) »0G(8) »0X(8) »QIS(8) »OGZ(e) »0XZ(8) »0ISZ<8) »S

IITEQSC2«») »SITE0L(2t») »SITETH(2tf) »SITELD( 2tf) » TIF( 10)

DIMENSION QLITX(2«f) »QEQUX(2'*) »QDESlNCl0r2«») »QPE0PL(2'*) »ODFS(10)

DIMENSION QSUN(10»2f) »QSKY ( 10 » 2'») » SHADE ( 10 ) » AZW( 10

)

DIMENSION NAMEBD(6) »VT(10) »DRC10) »MR(10) »OGX{10)

DIMENSION DBNBS(2'»)/.26» ,20» .15» .10» ,05» .0» .03» ,1» .19» .30* .f3».57»

1.69» ,80» ,90» .96» .99» 1 . 0 » . 97» .90 » . 75» . 57» . tf3» , 33/

REAL LAT»LONG»MONTH»NOFLR

DIMENSION LTYPE(IO) »GG(10»10)

COMMON /SOL/ LAT»L0NG»TZN»WAZ»WT?CN»D5T»LPYRrS(35)

READ (5»900) OLITX

READ (5»900) QEQUX

READ (5f900) QOCUP

SlGMA=0.17mE-8

HR=J».*(535.**3)*SIGMA

00 790 IJKLMN=1»20

READ (5»910»END=800) NAMEBD

READ (5»880) IR0T»ISKIP

IF (NAMEBO(l) .EQ« •) GO TO 800

IF (ISKIP.NE.O) GO TO 30

DO 10 I=l»10

DO 10 JsiflOO

X(I»J)=0.

Y(I»J)=0.

10 Z(I»J)=0.

DO 20 J=l»2'*

SITEQS(J)=0.

SITEQL( J)=0.

SITETH(J)=0.

SITELD(J)=0.

20 CONTINUE

SQWINT=0.

CALL RESFX (X* Y»Z»XX»YY»ZZ»MR»DR»VT»10)

WRITE (6»820)

40
PB=29.92

READ (5»900) LAT»L0NG»T2N»M0NTH»DAY»ELAPS»UG»USLAS

WRITE (6»850)

WRITE (6»8t0) LAT»L0NS»TZN»M0NTH»DAY»ELAP5»US»USLA5

READ (5»900) 9LITY»QE0PX»CFMV»CFML

WRITE (6»860)

WRITE (6»8i*0) GILITY»QEQPX»CFMV»CFML

READ (5»900) DBMAX»RANGE»DBIN»WBMAX» WBI0»DB»^WT»TG»T6W»TV

WRITE <6»870)

WRITE (6»8«f0) OBMAX»RANGE»DBlN»WBMAX»WBID»DBMWT»TG»TGW»TV

CALL PSYl (DBMAX»WBMAX»P8»DP»PV»W0UT»H0UT»V0UT»RH0UT)

CALL PSYl (DBIN»WBID»PB»DPID»PV»WID»HIN0»VIN»RHIN)

WV=WOUT

WIN=WID

WA=WOUT

TI0=DBIN

30 READ (5»900) ROOMNO* HT» AG» NOFLR » QCL>» AIRCHG

WRITE (6»830)

WRITE (6»8«»0) R00MNI0»HT»AG»N0FLR»QCU»AIRCHG

READ (5»890) MEXP» ITK » ITEMP* ITHST

00 110 I=1»NEXP

READ (5»920) ITYPEd) »IRF(I) »U(I) »A(I) » AZWd) »OUM»SHAOE(I) fABSPd)

READ {5»900) (6(I» J) » J=1»NEXP)

LTYPE(I)=ITYPE(I)

IF (ITYPE(I).E0,7) GO TO 110

KsIRFCI)

IF (Y(K»l).6T.l.) IRF(I)=10

NR(I)=MR<K)

UT(I)=VT(K>

CR(I)=DR{K>

IF (NRCD.GT.t^e) NR(I)=«»8

IF (ITYPE(I).EQ.3> ABSP(I)=0.

IF (ITYPE(I).EQ.5) ABSP(I)=0,

IF (ITYPE(I).EQ,6> ABSP(I)sO.

IHT(I)=1

IF <ITYPE(I).EQ.3) IHT(I)=-1

H(I)=U,OB

HI(I)r0.5t»2

IF (ITYPECD.EO.e) H(I)=0.

IF (ITYPE(I).E9.5) HICI)=0,162

IF (U(I)) <»0»t*0»50

«^0 RU=1./UT(I)*1./HI{I>

IF <ITYPE(I).NE.6) RU=RU-«-l ./H( I

)

U(I)=1./RU

50 CONTINUE

IF (X(K»2)) 110»60»110

60 IF (H(I)) 70»80»70

70 R=1./U(I)-1./H(I)

60 TO 90

80 R=1,/U(I)

90 UT(I)=1./R

IF (ITEMP.NE.O) UT(I>=l./(R-l./tHl{!)*0,9))

IF (UT(I)) 100rlOO»110

100 UT(I)=100,

110 CONTINUE

WRITE (6»1170)

00 120 I=1»NEXP

AZW(I)=AZW(I)+IROT

IF (AZW(I) .GT.IBO.) AZW(I)=AZW(I)-360.

WRITE <6»930) I » ITYPE« I ) » IHT J I > » IRF ( I ) » ABSP( I ) »U( I ) »H( T ) » A ( I ) » AZW(

1I)»SHADE<1)»UT(I)

120 CONTINUE
NEXPl=NEXP-l

NEXP2=NEXP-2

00 160 I=1»NEXP

GSUM=0«

NEX=NEXPl

IF (I.EQ.NEXP) NEX=NEXP2

MEX=NEX+l

DO 130 J=1»NEX

IF (I.ST. J) Gdf J)=S(J»I)*A(J)/AC1>

130 SSUM=SSUM*S(I» J)

IF (GSUM-l.) m0»150»150

mo S(I»MEX)=1.-SSUM

80 TO 160

150 6(I>MEX)=0.

160 CONTINUE

WRITE (6»1180)

WRITE (6»1190)

00 170 I=lrNEXP

WRITE {6»1200)I»(6(I»J)»J=1»NEXP)

170 CONTINUE

00 180 I=1»NEXP

00 180 J=1»NEXP

180 6(I» J)=HR*S(I» J)

11=0

00 200 I=1»NEXP

IF (ITYPE(I).EQ.7) GO TO 200

IISII-H

ITYPE(II)=ITYPE<I)

IRFCIDsIRFd)

U(II)=U(I)

A(II)=A(I)

AZW(II)=AZW(I)

SHADE(II)=SHADE(I)

ABSP(II)2ABSP(1)

NR(II)=NR(I)

UT(II)=UT(I)

CR(II)=CR(I)

IHT(II)=IHT(I)

H(II)=H(I)

HI(II)=HI(I)

JJ=0

00 190 jslfNEXP

IF (LTYPE(J).EQ.7) GO TO 190

JjrjJ^l

SG{II»JJ)=6(I»J)

190 CONTINUE

200 CONTINUE

NEXPrll

WRITE (6»1210)

DO 210 I=1»NEXP

00 210 J=1»NEXP

210 G(I>J)=66(I>J)

WRITE (6»1180)

WRITE (6»1190)

DO 220 I=l»NEXp

220 WRITE (6»1200) I » (G( I » J) » J=l » NEXP)

WRITE (6»1170)

DO 230 I=1»NEXP

230 WRITE (6»930) I » ITYPE< I ) » IHT( I ) » IRF( I ) » ABSP( I ) »U( I ) »H( I ) » A ( I) » AZW(

1I)»SHADE(I)»UT(I)

R=0.5

WRITE (6»9i*0)

42
00 2«*0 I = l»2^

2H0 DB(I)=(0BMAX-RANGE)+(RANGE*DBNB5(I) )

SUM=0.

00 250 1 = 1 »2'* 250 SUM=SUM+DB{I)

OBM=SUM/2«4.

WRITE (6»950) ( DB ( I ) » 1 = 1 » 2t» ) » DBM

DO 260 I = l»2'*

260 TIX(I)=TIO

SUM=0.

00 270 I=1»2U

270 SUM=SUM+TIX(I)

TIM=SUM/2«I.

WRITE (6»960) ( TIX ( I ) » 1 = 1 » 2'*) » TIM

WRITE (6»970) OLITX

WRITE (6*980) QEQUX

WRITE (6»990) OOCUP

CFMWT=AS*HT/60,*AIRCHS

CFML=0.5*CFMWT

CFM=CFML+CFMV

9LIT0=QLITY*AP*3.tH3*N0FLR

0EQP0=QEQPX*AG*3.t»13*N0FLR

DO 280 J=l»2«t

QLITE(J)=QLITX( J)*GILIT0

QEQUP(J)=QEQUX(J)*QEQPO

QTL ( J ) =t»8'»0 . CFM*WOUT

280 CONTINUE

00 290 I=l»9

Q0(I)=0.

QI(I)=0.

290 TNEW(I)=0.

C OBM=TIM= REFERENCE TEMPERATURE

DBM=TIM

S(1)=LAT

5(2)=L0NG

S(3)=TZN

S(t*)=ELAPS

S(6)=l.

S(7)=0.2

5(8)=1,0

5(33)=1.

WRITE (6»1220)

00 350 I=1»NEXP

IF (ITYPE(I) .LT.5) GO TO 310

DO 300 J=lf2f

95UN(I» J)=0.

QGLASd' J)=0.

300 05KY{I»J)=0.

GO TO 3t*0 310 WAZ=AZW(I)

S(9)=WAZ

S(10)=90.

IF (ITYPE(I).EO.l) S(10)=0.

DO 330 J=l»2«t

QSKYdf J)=0.

IF (ITYPE(I) .EO.l) QSKY<I»J)=20.

TIME=J

S(5)=TIME

CALL SUN

IF (5(25). GT.O.) 60 TO 320

0SUN(I» J)=0.

QGLAS(I» J)=0.

43
so To 330

320 !5SUN(I» J)=S(25)*A85P(I)

Q6LAS(I» J>=0

IF (IHT(I) .GT.O) GO TO 330

CALL GLASS ( SHADE ( I ) » 1 . » 1 . » QGLAS( I » J)

)

330 CONTINUE

3«*0 WRITE (6»1000) I WRITE (6»1010) (QSUN(I» J) » J=l»2^)

350 WRITE (6»1010) ( QGLAS( I » J) » J=l » gt^)

00 360 J=l»24

TK J)=TIX(2'*-J+1)-TIM

DO 360 I=l»NEXP

360 TOS(I» J)=DB(2^-J+1)-DBM

DO 370 JsaSri+e

TI( J)=TI(J-24)

DO 370 I=l»NEyP

370 T0S(I» J)=T0S(T» J-24)

IF (ITEMP.NE.O) GO TO 390

00 380 L=l»8

LG(L)=0.

LX(L)=0«

LIS(L)=0.

3G(L)=0.

9X(L)=0.

380 aiS(L)=0.

390 CONTINUE

DO ^00 I=1»NEXP

DO ^OO J=l»«t8

«+00 TIS(I»J)=0.

TA=TIV

DO 720 N=lr7

IF (N.NE.7) GO TO HiO

QSUMT=0.

BLDV|AX=0.

«H0 CONTINUE

DO 720 NK=l»2n

DO ^^o i=i»nexp

DO 120 NTT=2»1S

^20 T0Y(NTT)=T0S(I»NTT-1)

DO «»30 NTT=2»'*8

'30 T0S(I»NTT)=T0Y(NTT)

''0 CONTINUE

IF (ITEMP.NE.O) GO TO «»9n TA=TIX(MK)

DO f+SO L=2»8

QGZ(L)=3G(L-1)

QXZ(L)=QX(L-1)

QISZ(L)=QIS(L-1)

•SO CONTINUE

DO tf60 L=2»8

3G(L)=QGZ(L)

QX(L)=9XZ(L)

QIS(L)=0ISZ(L)

'60 CONTINUE

DO •70 NTT=2»t*s

•70 T0Y(NTT)=TI(NTT-1)

DO •SO NTT=2»«*R

'80 TI(NTT)=TOY(NTT)

SUMQG=0.

'90 CONTINUE

DO 5^0 I=1»NEXP

K=IRF(I)

44
DO 500 J=l»«*8

XDUM( J)=X(K» J)

YDUM( J)=Y(K» J)

ZDUM(J)=Z(K» J)

TDUM(J)=TOS(I»J)

IF (ITYPE(I) .p:q.6) TDUM(J)=TIS(I» J)

IF (ITYPE(I) .F0.5) TDUM(J)=TG-TIM

IF (ITEMP.NE.O) TI(J)=TIS(I» J)

IF (T0Uy(J).GT,100,.OR.TI(J),GT.100,) GO TO 760

IF (TOUM{J).LT.-100,.OR.TI(J),LT,-100.) GO TO 760

500 CONTINUE

UX=U(I)

IF (Hd)) 520»5?0»510

510 RX=1./U{I)-1./H(I)

UX=1,/RX

520 CONTINUE

CALL OUTBID ( XDUM» YDUM» ZDUM» CR ( I ) » UX» H( I ) r DB(NK) » TIVI» Q0( I ) »QI ( I) »0

1SUN(I»NK) »QSKY(I»NK) »TDUV|»TI»TNEW0»TA»ITEMP)

DO 530 J=l»'»8

530 TOS(I» J)=TDUM(J)

TNEW(1)=TNEW0+TIM

5t»0 CONTINUE

0OCPS(NK)=OOCUP(NK)*10.*(100.-TA)*QCU

QOCPL=10 . ( TA-60 ) *QOCUP ( NK ) OCU

IF (TA-IOO.) 560»550»550

550 QOCPS(NK)=0.

QOCPL='»00.*Q0CUP(NK)*OCU

GO TO 580

560 IF (TA-60.) 570»580r580

570 0OCPS(NK)=«*00.*OOCUP(NK)*QCU

QOCPL=0,

580 QPEOPL{NK)=OOCPL

SUML=QTL(NK)-'lRt»0.*CFM*WIN-»-OOCPL

OTLAT=-SUML

C QSUM INSTANTANEOUS HEAT GAIN

C SUWQC INSTANTANEOUS SOLAR HEAT GAIN

C 01 CONDUCTION HEAT TRANSFER

aSUM=l,08*CFML*(TA-DB(NK) )+1.0B*CFMV*(TA-TV)-OLlTE(NK)-QEOUP(NK)-0

lOCPS(NK)

DO 590 I=1»NEXP

590 QSUM=OSUM+A(I)*(QI(I)-OGLAS(I»NK)

)

IF (N.NE.5) 60 TO 650

IF (NK.NE.l) SO TO 600

WRITE (6»1020) NAMEBD

600 CONTINUE

WRITE (6fl030) NK» (TNEW(I) I=l»9) »DB(NK)

IF (ITEMP) 720, 720*650

610 IF (NK.NE.l) GO TO 620

WRITE (6rlO«*0) NAMEBD

620 CONTINUE

TOTHT=QL+QTLAT

WRITE (6rl050) NK » (QI ( I ) » 1 = 1 » <>) » OSUM» OTLAT, QL» TOTHT

DO 630 I=1»NEXP

9DESIN(IrNK)=0I(I)*A(I)

630 CONTINUE

SI TEQS ( NK ) =SI TEOS ( NK ) QSUM

SITEQL(NK)=SITEQL(NK)-»-QTLAT

SITETH(NK)=SITETH(NK)+TOTHT

SITELO < NK ) =SI TELD ( NK ) QL

IF (QL.GT.BLDMAX) GO TO 6«*0 3LDMAX=0L

T0THTX=TOTHT

497-811 O - 73 - 4 45
IMAX=NK

6*0 IF (N.E0.7) QSUWIT=0SUMT+T0THT

SO TO 720

650 00 680 I=1»NEXP

DO 660 NTT=2»»^8

660 T0Y(NTT)=TIS(I»NTT-1)

DO 670 NTT=2»'»8

670 TIS(I»NTT)=TOY(NTT)

680 CONTINUE

TV=DB(NK)

CALL RMTMP (NE:XPrNK»TV»CFML»CFMV»R»TIM»TA»TIF»QU» ITK)

IF (TA.GT.TIM) GO TO 690

DPI=DPID

WBINzWBIO

HIN=HIND

iriN=wio

SO TO 700

690 CONTINUE

QOCPL=QOCPL/1060.

i#I=(«».5«CFML*WA+'».5*CFMV*WV+Q0CPL>/<'*.5*CFML+H,5*CFMV)

PVI=PB*Wl/(0.622**fI)

OPI=DPF(PVI)

CALL PSY2 (TA»DPI»PB»WBIN»PVI»WIN»HIN»VIN»RHIN)

700 CONTINUE

IF <N.LT.6) GO TO 720

IF (N.E0.7) SO TO 610

IF (NK.NE.l) GO TO 710

IIRITE (6»1060) NAMEBO

710 WRITE (6»1070) NK» (TIF ( I ) r 1=1 » 9) »TA, W9IN

720 CONTINUE

QSUMT=QSU»flT/2«»,

QWINT=1 • 08*CFMWT* ( TIM-DBMWT ) +UG* ( TI M-TGW) *AG

QWINT=1.08*CFMWT*(TIM-DBVIWT)

DO 7i»0 I=1»NEXP

IF (IHT(l).LT.O) LJ(I)=UGLAS

IF (ITYPE(I).NE.5> GO TO 730

Q«INT=0WINT*US*A ( I ) ( TIM-TGW

)

60 TO 7*0

730 IF (ITYPE(I).E9.6) 60 TO 740

IF (ITYPE(I).E0.7) 60 TO 740

QWINT=QWINT+A(I)*U(I)*(TIM-DBWWT)

7*0 CONTINUE

SQWINT=SQWINT*QWINT

WRITE (6»11*0) QWINT»T0THTX»Q5U>1T

IF (ITK.NE.O) GO TO 790

00 750 I=1»NEXP

06X(I)=0GLAS(I»IMAX)*A(I)

750 QDES(I)=QDESIM(If IMAX)

CFM=CFML*CFMV

CALL OUTPUT CDBMAX»WBMAX»DBIM» WBI0»W0UT»WINrQ6X»CFM»QLlTE(IMAX) »Q0

1CPS(IMAX)»QPE0PL(IMAX) f QDES»A7W»ITYPE»NFXP»NAME:BD)

GO To 790

760 WRITE (6»1080) N

WRITE (6»1090)

DO 770 J=l*48

770 WRITE (6»1110) J» (TOS(I» J) r I=l»10)

WRITE (6»1080) N

WRITE (6»1100)

00 780 J=l»«»8

780 WRITE (6»1110) J» (TIS( I » J) f 1=1 » 10

790 CONTINUE

800 CONTINUE

46
»*RITE (6»1120)

WRITE (6»1130)

SITMAX=0»

T5AVE=0,

TSITHT=0.

00 810 I=l»2't

SQLLD=SI TEQL ( I ) SITELO ( I

)

TSITHT=TSITHT+SITETH( I

)

IF (SITETHCI) .LT.SITMAX) SITMAX=SITETH( T

)

IF (SQLLD.LT.TSAVE) TSAVE=SQLLO

WRITE (6»1150) I»SITEQS(I)»SITE0L(I)»SITETH(I),5ITELD(T)»SOLLO

810 CONTINUE

AVEHTS=TSITHT/2'».

WRITE (6rll60) SQWINT»SITVIAX» AVEHTG»T5AVE

WRITE (6»1120)

STOP

820 FORMAT (IHl)

830 FORMAT (8H1 BL0GN0»8X» HT» » 8X» AG» » 5X»N0FLR » 7X' OCU» »«»X» AIRCMS*

)

8«»0 FORMAT (lOFlO.l)

850 FORMAT (7X»LAT» »6X»L0NG» »7X»TZN» »5X»M0NTH» »7X»0AY« »5X«ELAPS» »ftX»US

1» »5X»UGLAS»

)

860 FORMAT (SX'QLITY* »5X»QEQPX» »6X»CFMV» »6X»CFyL»

)

870 FORMAT (5X»DBMAX»5X»RANGE» »6X»DBIN» »5X» WBMAX» »6X»WBID» »5X»PBMWT» #8

1X»TG»»7X»T6W»»8X»TVM

880 FORMAT (1017)

890 FORMAT (1017)

900 FORMAT (10F7,0)

910 FORMAT (6A6)

920 FORMAT (2I7»6F7.0)

930 FORMAT (I3»3I10#8F10.2)

9tfO FORMAT (•! ENVIRONMENTAL DATA')

950 FORMAT (»ODB TEMP»/12F10.2/12F10,2/'OMEAN VALUE=»F10.3)

960 FORMAT ( OTI • /12F10.2/12F10 .2/» OMEAN VAtUE=»Fl0.3)

970 FORMAT (• OOLITE' /( 12F10. 3)

)

980 FORMAT ( •0QEQUP»/(12F10.3)

990 FORMAT ( •OQOCUP»/(12F10.3)

)

1000 FORMAT (I10»F10.0)

1010 FORMAT (2'*F5.0)

1020 FORMAT (1H120X»EXPOSURE SURFACE TEMPERATURE* DEGREES F FOR •6A6//

17X»TIME»5X» (1) •7X» (2) •7X» (3) 'TX* (t») »7X» (5) 7X» (6)»7X»(7) •7Xf (8)»7X

2»(9)»7X»DB»)

1030 FORMAT ( 110 » 10F10.2)

10^0 FORMAT (lH130X6A6///7X»TIME»i'»X»EXPOSURE HEAT FLUX •'JOX' HEAT SAIM

IS 'SX* SENSIBLE L0AD»1X» TOTAL LOAO»/30X»BTU/HR»FT2»i»5X»BTU/HR»12X

2»BTU/HR»5X»BTU/HR»/»0»81X» SENSIBLE* 3X 'LATENT* /1«»X» (1) •«»X* (2) ti»X» (3

3) »^X» («) 'UXr (5) »«»X» (6) •'X* (7) 'itX* (8) tc^X* (9) »7X»HEAT'7X«HEAT»/)

1050 FORMAT (I10»9F7.2»«»X»«»G10.i^)

1060 FORMAT (1H120X» INSIDE SURFACE TEMPERATURE' DEGREE F FOR •6A6//7X'

1TIME»5X» (1) •7X» (2) •7X» (3) •7X» (U) »7X« (5) •7X* (6) »7X* (7) •7X» (B) •7X* (9

2) 7X»TA»TA»8X»WB»/)

1070 FORMAT ( I10» 11F10,2)

1080 FORMAT CI CONVERSION ERROR AT N=*I10)

1090 FORMAT ('0 TOSM

1100 FORMAT CO TIS»)

1110 FORMAT (I10»10F10,2)

1120 FORMAT (IHl)

1130 FORMAT (30X»SITE SUMMARy»//7X»TIME'9X»HEAT GAINS* 15X»T0TAL HEAT*«>X

1 * COOLI NG LOAD » 7X • TOTAL * /22X » BTU/HR * 19X • 9TU/HR * 9X • BTU/HR • 7X • COOLING

2 L0AD»//1«»X»SENSIBLE HEAT*3X*LATENT HEAT*//)

imO FORMAT (////• HEAT LOSS* lOX* COOLING L0A0»7X» AVERAGE HEAT GAlN*3X//

47
11X3(G10,H»10X))

1150 FORMAT (6(G10.t|»5X)

)

1160 FORMAT (////» HEAT LOSS»10X»MAX HEAT GAIN»7X» AVERAGE HFAT 6AIN»3X»

IMAX TOTAL COOL LOAD' //1X4 ( 610 . 1 » lOX )

)

1170 FORMAT ('O SURFACE NO ITYPE ' tfX» IHT» 7X» » IRF» 7X » A8SP» 6Xr HI' 9X» 'H* 9

1X»»A»9X» 'WAZ'SXf SHADE' 8X » 'UT*

)

1180 FORMAT CO RADIATION INTERCHANGE FACTORS*)

1190 FORMAT ('O SURFACE 1 2 3 H

1 5 6 7 8 9 lOM

1200 FORMAT ( I10»10F10.3)

1210 FORMAT CO MODIFIED SURFACE DATA')

1220 FORMAT CI SOLAR DATA (QSUN/0GLAS5)

)

END

SUBROUTINE ABCD2 (Z»K»L»G»A»B»C»D»NL)

DIMENSION AX(IO) »BX(10) »CX(10) »DX(10) fG(lO)

REAL K(10)»L(10)

PI=tf.*ATAN(l.)

OP=PI*0,5

DO 50 I=1»NL

IF (6(1)) if0»£»0»10

10 IF (Z) 30»30»20

20 ZQ=5QRT(Z/G(I))

ZQL=ZO*L(I)

C0=SIN(ZQL)

C1=C0S(ZQL)

S1=C0/Z0L

S2=(S1-C1)/Z0L/ZQL

AX(I)rCl

BX(I)rL(I)/K(T)*Sl

CX ( I) =-ZQL*K ( I ) /L ( I ) CO

DX(I)rCl

GO TO 50

30 AX(I)rl.

CX(I)=0,

DX(I)=1.

BX(I)=L(I)/K(I)

60 TO 50

AX(I)=1,

BX(I)=1/K(I)

CX(I)=0,

DX(I)=1.

50 CONTINUE

A=AX(1)

B=BX(1)

C=CX(1)

D=DX(1)

IF (NL.LT.2) GO TO 60

CALL MULT (AX»BX»CX»DX» A»B»C»0»NL)

60 RETURN

END

48
SUBROUTINE DERVT (A»B»C»D» AP»BP»CP»DPr APP»BPP»CPP»DPP»N)

DIMEMSIONI A(N) »B(N) »C(M) »D(N) »AP(N) »BP(^J) »CP(M) ,DP(N) »AT(10) »BT(10

1) »CT{10) »DT(10) »ATT(10) »BTT(10) »CTT(10) »DTT(10)

00 30 I=1»N

DO 20 J=lfN

IF (I.E9.J) GO TO 10

AT(J)=A( J)

3T(J)=B( J)

CT( J)=C(J)

OT(J)=D(J)

GO TO 20

10 AT(J)=AP(J)

8T(J)=BP(J>

CT(J)=CP(J)

DT(J)=DP( J)

20 CONTINUE

30 CALL MULT <ATfBT»CT»DT»ATT(I)f3TT(I)»CTT(I)rDTT(I)»M)

APP=ATT(1)

8PP=BTT(1)

CPP=CTT(1)

0PP=DTT(1)

DO tfO I=2»N

APP=APP+ATT(I)

3PP=BPP+BTT(I)

CPP=CPP-»-CTT(I)

'0 DPP=DPP+DTT(I)

RETURN

END

FUNCTION DPF (PV)

C THIS SUBROUTINE CALCULATES DEW-POINT TEMPERATURE FOR GIVEN VAPOR PRE

Y=L06(PV)

IF (PV.GT. 0.1836) GO TO 10

DPF=71 . 98+2t* . B73*Y+0 . 8927*Y*Y

GO TO 20

10 DPF=79«0t»7+30.579*Y+l.ft893*Y*Y

20 RETURN

END

SUBROUTINE GLASS (SHDCF»GLTYP»6LAZE»SHGP)

DIMENSION TR(9)»SH(25>

COMMON /SOL/ LAT»L0NG»TZN»WAZ»WT»CN»DST»LPYR»S(35)

TR(7)=S(19)

TR(8)=GLTYP

TR(9)=GLAZE

CALL TAR (TR)

SH(l)=S(2t»)

SH(2)=S(22)

SH(3)=S(23)

SH(«f)=S(19)

SH(5)=0.5

SH(6)=0.5

5H(7)=0.25

SH(8)=0.

SH(9)=0.7

SH(10)=1.0

SH(H)=SHDCF

SH(12)=TR(1)
5H(13)=TR(2)

5H(m)=TR(3)

SH(15)=TR(5)

SH(16)=TR(t)

SH(17)=TR(6)

CALL SHG (SH)

SHGF=SH(18)

RETURN

END

SUBROUTINE GPF (U»ZL»Z)

DIMENSION Z(l)

PI=i+,*ATAN(l.)

5QTPI=S0RT(PI)

PI2=2./PI

EB=0,001

DB=0.1

WRITE (6»30>

WRITE (6»'+0)

Z{l)r2*ZL*S9RT(U)/S0TPI

ZZ=Z(1)

Z(2)=Z(l)*{SQRT(2.)-2.)

DO 10 K=3»50

ZK—

10 Z(K)=Z(l)*{SQRT(ZK)-2.*S0RT(ZK-l)+SQRT(ZK-2.)

)

DO 20 K=l»50

20 WRITE (6»50) K,Z{K)

RETURN

C

C

C

30 FORMAT (50H0 RESPONSE FACTORS FOR SEMI-INFINITE BED

•0 FORMAT (50H0 K Z(K)

50 FORMAT ( 1110 » I^FIO .5)

END

SUBROUTINE MULT ( A »B» C # D» AT» BT » CT» DT» N)

DIMENSION A(N)»B(N)»C(N)»D(N)

ATT=A(1)

BTT=B(1>

CTT=C(1)

DTT=D(1)

IF (N.LT.2) SO TO 20

00 10 J=2»N

AT=ATT*A( J)+BTT*C(J)

BT=ATT*B( J)+BTT*D(J)

CT=CTT*A( J)+DTT*C( J)

DT=CTT*B( J)+DTT*D( J)

ATT=AT

3TT=BT

CTT=CT

10 DTT=DT

SO To 30

20 AT=ATT

3T=BTT

CT=CTT

DT=DTT

30 RETURN

END

50
10

SUBROUTINE OUTPUT ( DB» WB» DBI » WBI » WA » WI » 9GX» CFML» QLITE» OOCS» QOCL» Q»

1WAZ»ITYPE»NEXP»NAME)

DIMENSION Q(10) rWAZdO) »ITYPE(10) »NAME(6) rQGXdO)

OWS=0.

9WW=0.

QWN=0.

OWE=0.

06S=0.

QGE=0.

96W=0.

9GN=0.

OD5=0.

QDW=0.

9DE=0.

ODN=0.

WRITE (6»20) (NAME(I) »I=1»6)

WRITE (6»30) DB»WB»WA

WRITE ISff^O) r)BI»WBl»WI

OBD=OB-DBI

WD=WA-WI

WRITE (6»50)

WRITE (6»60) DBDrWD

DO 10 I=1»NEXP

Q(I)r-Q(I)

II=ITYPE(I)

IF (II,EQ.3) 0(I)=0{I)+QGX{I)

IWAZ=WAZ(I)

IF (lI.EQ.l) 9R00F=Q(I)

IF (Il.EQ.S) 9FL00R=Q(I)

IF (II.EQ.6) QFL00R=QFL00R+Q(I)

IF (I1.E0.2.ANJD.IWAZ.EO.O) QW5=9(I)

IF (II.EQ.2.AND.IWAZ.EQ.90) QWW=Q{I)

IF (II.EQ.2.AND.IWAZ.EQ.-90) 0WE=Q<I)

IF (II.EQ.2.AND.IWAZ.EQ.IR0) 0WN=Q(I)

IF (I1,EQ.3.AN0.IWAZ.EQ.0) OGS=Q(I)

IF (II.EQ.3.AND.IWAZ.EQ.90) QGW=Q(I)

IF (II,EQ.3.AMD.lWAZ.EQ.-90) OGE=0(I)

IF <II,EQ.3.AMD.IWAZ.EQ.180) QGN=Q(I)

IF (II.EQ.^.AND.IWAZ.EO.O) QDS=0(I)

IF (II.EQ.^.ANO.IWAZ.EQ.90) QOW=Q(I)

IF (IIEQ.^.ANO.IWAZ.EQ.-90) ODE=Q(I)

IF (H.EQ.<*.AND.IWAZ.EQ.180) 0DN=9(I)

WRITE (6i 350)

WRITE (6< 70) QROOF

WRITE (6i 80) QWS

WRITE (6i 90) 9WE

WRITE (6i-100) QWW

WRITE (6i 110) OWN

WRITE (6i• 180)

WRITE (6i 190) 9DS

WRITE (6i 200) ODE

WRITE (6i 220) 9DW

WRITE (6<'210) ODN

WRITE (6i»120) QFLOOR

WRITE (6i• 130)

WRITE (6ifmo) QGS

WRITE (6i• 150) QGE

WRITE (6i• 160) 9GN

WRITE (6i• 170) QGW

OINFIL = 1<,08*CFML*OBD

WATT=0LITE/3.m5

WRITE (6»3«»0)
c

cc20

30

'O

50

60

70

80

90

100

110

120

130

mo

150

160

170

180

190

200

210

220

230

2f0

250

260

270

280

290

300

310

320

330

3^0

350

WRITE

WRITE

WRITE

WRITE

WRITE

WATTfQLlTE

QOCS

CFMLtDBDrOINPIL

SUMSQROOF+QWS+OWE+QWW+OWM+QFLOOR+QOS+QDE+ODW+ODN+OGS+OGW+OGE+OGN

WRITE (6»270) 5UM

(6»230)

(6*250)

(6»260)

(6»2'f0)

(6r3'*0)

SUM=SUM-K3LITE+QINfIL+OOC5

WRITE (6»280) SUM

G(INFIL=«I8'*0.*WD*CFML

WRITE (6»320) CFML» WD» QINFIL

WRITE (6»330) OOCL

WRITE (6»3^0)

SUML=QIMFIL+QOCL

WRITE (6»290) 5UML

5UMT=SUM+SUML

WRITE (6»300)

WRITE (6r310) SUMT

RETURN!

FORMAT

FORMAT

IDTY RAT

FORMAT

IDTY RAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

1)

FORMAT

FORMAT

FORMAT

FORMAT

FORMAT

END

(IHllOX'SUMMARY OF CALCULATIONS F0R»6A6)

CONDITIONS F5.1r DB» FlO , 1 »

» WB • FIO . f» 'HUMT

DB*F10.1» WB»Fln•t^»HU^1T

0 OUTDOOR )

0 SPACE CONDITIONS *F5,1**

•)

2t*X» »20X» »

)

0 DIFFERENCE 'FS. 1»F25.'*)

ROOF =»36X»F10.0)

SOUTH WALL='36X»F10.0)

EAST WALL =»36X»F10.0)

NORTH WALL=»36X»F10.0)

WEST WALL =»36X»F10.0)

FLOOR =»36X»F10.0)

0 SOLAR HEAT GAIN AND T

SOUTH =»36X»F10.0)

EAST =»36X»F10.0)

NORTH =»36X»F10,0)

WEST =»36X*F10.0)

ODOORS'

)

SOUTH =»36X»F10.0)

EAST =»36X»F10.0)

NORTH =»36X»F10.0)

WEST =»36X»F10.0)

0 INTERNAL LOAD')

THROUGH GLASS')

INFILTRATION»F10.0» 'CFMX l.OB X FlO . 1 »F13. 0)

LIGHTS»F10.1» 'X 3.t*l = »23X,FlO,0)

OPEOPLH = »37X»F10.0)

8X»Fln.0)

0 TOTAL SENSIBLE SPACE LOAD»20X»F10.0)

0 TOTAL LATENT SPACE LOAO«20X=+1 + +

0 GRAND TOTAL LOAD •30X»F10.0)

0INFTLTRATION»F5.1» 'CFM X ^840 X»F6.'»» • = » 10X»F10.0)

PEOPLE = 27X»F20.0)

(50X»»—^ )

(IHO)

52
SUBROUTINE OUTSID ( X» Y» Z» CR » UX» F0» DB » TI vi» Q0» QI r OSUN» 05K Y » T0» TI » TON

1EW»TA» ITEMP)

DIMENSION T0(1)»TI(1)»X(1)»Y{1)»2(1)

XNUM=GlSUN-QSKY-»-FO*(DB-TlV|)

IF (X(2)) 50»l0»50

10 IF (FO) 20»20»30

20 T0NEW=T0(1)

GO TO 'O

30 TAM=TA-TIM

T0NEW= ( XNUM+UX*TAM ) / ( UX+FO

)

"O CONTINUE

30=UX*(TAVI-T0NEW)

IF (ITEMP.EQ.O) OI=QO

T0(1)=T0NEW

RETURN

50 SUMZ=0.

SUMY=Y(1)*TI(1)

SUMX=X(1)*TI(1)

SUMXY=0.

00 60 J=2»tf8

SUMY=SUyY+Y(J)*TI(J)

SUMX=SUMX+X(J)*Tl(J)

SUMXY=SUMXY-»-Y( J)*TO( J-1)

60 SUMZ=SUN^Z*2( J)*TO( J-1)

XNUM=SUV1Y-SUMZ+CR*Q0+XNUM

T0NEW=XNUM/ ( Z ( 1) +F0

)

IF (FO) 70»70»80

70 TONEw=TO(l)

80 T0(1)=T0NEW

SUMZ=SUMZ+Z(1)*T0(1)

SUMXY=5UMXY+Y( 1 ) TOd ) 90=SUMY-SUMZ-»-CR*Q0

IF (ITEMP.EQ.O) QI=SUMX-5UMXY+CR*QI

RETURN

END

SUBROUTINE PSYl (0B» W8»PB»0P»PV» W»H, V#RH)

C THIS SUBROUTINE CALCULATES VAPOR PRESSURE(PV) »HUVIIDITY RATIO (W)

C ENTHALPY(H) »VOLUyE(V) »RELATIVE HUMIOITY(RH) AND DEW-POINT

C TEMPERATURE WHEN THE DRY-BULB TEMPERATUPE(DR> »WET-BULB TFMPERATURE

C (WB) And BAROMETRIC PRESSURECPB) ARE GIVEN

PVP=PVSF(WB)

IF (DB-WB) 30»30»10

10 WSTAR=0.622*PVP/(PB-PVP)

IF (wB-32.) 20,20»«+0

20 PV=PVP-5 . 70'*E-^*PB* ( DB-WB ) /1 .

8

60 TO 50

30 PV=PVP

60 To 50

•0 CDB=(DB-32.)/1.8

CWB=(WB-32.)/1.8

HL=597. 31+0 . ^'*09*CDB-CWB

CH=0, 2^02+0. ''*09*WSTAR

EX=(wSTAR-CH*(CDB-CWB)/HL)/0.622

PV=PB*EX/(1.+EX)

50 W=0.622*PV/(P3-PV)

V=0.75«**(DB+f59.7)«(l+7000*W/«*360)/PB

H=0.2'**0B+(1061-»-0.«»«m*DB)*W

0P=DPF(PV)

RH=PV/PVSF(OB)

RETURN

END - 53

497-811 O - 73 - 5
SUBROUTINE PSY2 (OB»DP»PB»WB»PV»W»Hf V»RH)

C THIS SUBROUTINE CALCULATES THE FOLLOWING WHEN DRY-BULB TEMPERATURE

C (03) »DEW-POINT TEMPERATURE { OP) » AND BAROMETRIC PRESSURE(PB) ARE GIVEN

C WB WET-BULB TEMPERATURE

C W HUMIDITY RATIO

C H ENTHALPY

C V VOLUME

C PV VAPOR PRESSURE

C RH RELATIVE HUMIDITY

IF (OP-OB) 20»10»10

10 OP=OB

20 PV=PVSF(DP)

PVS=PVSP(DB)

RH=PV/PVS

W=0.622*PV/(PB-PV)

V=0.75«t*(DB+tf59.7)*(l+7000*W/«»360)/PB

H=0 . 2'**0B+ ( 1061+0 . '+'f'**DB ) *W

WB=WBF(H»PB)

RETURN

END

FUNCTION PVSF (X)

DIMENSION A(6)/-7.9029R»5.02808»-1.3816E-7»li.3^^»8.13?8E-3»-3,t^91

l'»9/»B('f)/-9.09718»-3.56654»0.976793»0.0060273/»P('»)

T=(X+tf59.688)/1.8

IF (T.LT.273.16) GO TO 10

Z=373.16/T

P(1)=A(1)*(Z-1)

P(2)=A(2)*LOGIO(Z)

Zl=A(i4)*(l-l/Z)

P(3)=A(3)*(10**Z1-1)

Z1=A(6)*(Z-1)

P(«t)=A(5)*(10**Zl-l)

GO TO 20

10 Z=273.16/T

P(1)=B(1)*(Z-1)

P(2)=B(2)*L0G10(Z)

P(3)=B(3)*(1-1/Z)

P('*)=LOG10(B('*)

)

20 5UM=0

00 30 I=l»f

30 5UM=SUM+P(I)

PVSF=29.921*10**SUM

RETURN

END

54
SUBROUTINE RESF (XXrYY»ZZ» IRUM)

C THIS PROGRAM IS DEVELOPED BY T.KUSUDA OP THE NATIONAL BljREAU OF

C STANDARDS FOR CALCULTING THE THERMAL RESPONSE FACTORS FOR

C COMPOSITE WALL5rFL00R5»R00FS»BASEMENT WALLS» BASEMENT FLOORS

C AND INTERNAL FURNISHINGS OF SIMPLE SHAPES

C RESPONSE FACTORS ARE USED IN THE FOLLOWING MANNER

C X»Y»Z ARE RESPONSE FACTORS

C QI=X*TI-Y*TO*GMA INSIDE WHERE R IS MINIMUM

C QO=Y*TI-Z*TO OUTSIDE WHERE R IS MAXIMUM

C TI INSIDE TEMPERARURE WHERE R IS MINIMUM

C TO OUTSIDE TFMPFRATURE WHERE R IS MAXIMUM

C K THERMAL CONDUCTIVITY

C G THERMAL DIEFUSIVITY

C L THICKNESS

C IN=0 FINITE THICK WALL

C IN=1 SEMI-FINITE WALL

C IN=2 SOLID OBJECT

C IF RESPONSE FACTORS OF THE SOLID CYLINDER OR SPHERE OF HOMOGENEOUS

C PROPETY ARE DESIRED* TREAT THE PROBLEM OF MULTILAYER BUT WITH THE

C IDENTICAL PROPERTIES FOR ALL THE LAYERS EXCEPT THE RADIUS

REAL K(10) »G(in) »L(10) »KG

DIMENSION X(lOn) »Y(100) »7(100) »C(10) »D(10) »RES(10) »RMK(10»tf)

DIMENSION RMKG(4) »F ( lOO ) » XX ( 100 » 1 ) » YY ( 100 » 1 ) r ZZ ( 100 » 1 ) » FF ( 1 00 » 20

)

10 READ (5»2U0) DELTAT

IRUN=0

20 READ (5»230) NLAYR»IN

IF (NLAYR.EQ.O) GO TO 200

IRUN=IRUN+1

IF (NLAYR.6T.10) GO TO 200

NNLAYR=NLAYR-»-l

IF (NLAYR.EQ.O) GO TO

00 30 I=1»NLAYR

30 READ (5»2«I0) L ( I ) » K ( I ) » D( I ) » C ( I ) » RES( I

)

IF (IN.EQ.2.AN0.IM.EQ.0) GO TO 50

C READ K»RHO» AND C OF GROUND IF IN=1

C FOLLOWING ARE GROUND THERMAL CONDUCTIVITY » DENSITY AND SP.HT IF

C IN=2» OTHERWISE THE SAME PROPERTIES OF THE INTERNAL SLAB

'^0 IF (IN.NE.O) READ (5»2«»0) KG»OG»CG

C AG THERMAL DIFFUSIVITY OF EARTH

IF (IN.NE.O) A6=KG/CG/0G

IF (NLAYR.EQ.O) GO TO 100

IF (IN.EQ.2) RFAD (5»330) (RMKG( J) » J=l t») 50 00 60 I=1»NLAYR

60 READ (5»330) ( RMK ( I » J> » J=l » «)

IF (IN.EQ.l) RPAD (5»330) {RMK6( J) J=l » «») DO 90 I=1»NLAYR

IF (L(I)) 80»70»80

70 G(I)=0.

K(I)=1./RES(I)

GO TO 90

80 6(I)=K(I)/C(I)/D(I)

90 CONTINUE

100 WRITE (6»350)

CALL RESPTK (K»L»G»AG»KG»X»Y»Z»NLAYR»DELTAT»NRT»CR»UT» iNrF)

WRITE (6»220) IRUN

WRITE(6»360)

WRITE (6»250)

WRITE (6»260)

WRITE (6»210)

IF (NLAYR.EQ.O) GO TO 130

IF (IN.EQ.2.ANn.IM.NE.O) WRITE (6»370) KGfPGrCSr (RMKG( J) » J=l»«*)

00 120 I=1»NLAYR

IF (L(I)) 120»110»120
110 K(I)=0.

120 WRITE (6»270) T » L ( I ) » K ( I ) » D ( I) » C ( I > » RES ( I) » (R^^K ( I » J) » J=l

IF (IhJ.EQ.l) WRITE (6»370) KG»DG»CG» (RMKG( J) » J=l »U)

130 WRITE (6»290) OELTAT

WRITE (6»280) UT

WRITE (6»300)

WRITE (6»210)

IF (IN.ME.O) GO TO 150

WRITE (6»310)

XX(1»IRUN)=FL0AT(NRT)

YY(lrIRUN)=FLOAT(NRT)

ZZdf IRUN)=FLOAT(NRT)

XX(2»IRUN)=CR

YY(2»IRUN)=CR

ZZ(2»IRUN)=CR

XX(NRT+3»IRUN)=UT

DO mo NJ=1»NRT

XX(N+2»IRUN)=X(M)

YY(N+2»IRUN)=Y(N)

ZZ(N+2»IRUN)=Z(M)

JN=N-1

It^O WRITE (6»320) JN»X(N) »Y(N) »Z(N)

GO TO 190

150 WRITE (6»380)

IF (IN.EQ.l) GO TO 170

IF (IN.EQ.2) GO TO 170

XX(1,IRUN)=FL0AT(NRT)

XX(2»IRUN)=CR

XX(NRT+3»IRUN)=UT

DO 160 N=1»NRT

JN=N-1

X(N)=-X(N)

XX(N+2»IRUN)=X(N)

160 WRITE (6»390) JN'»X(N)

GO TO 190

170 DO 180 N=1»NRT

JN=N-1

FF(N+2»IRUN)=F(NJ)

180 WRITE (6»390) JM»F(N)

FF(1,IRUN)=FL0AT(NRT)

FF(2»IRUN)=CR

FF(NRT+3»IRUN)=UT

190 WRITE (6»210)

WRITE (6»210)

WRITE (6»3»f0) CR

GO TO 20

200 RETURN!

C

C

c210 FORMAT (2H0 ) 220 FORMAT (lOHl IRUN= 110)

230 FORMAT (1017)

2«*0 FORMAT (10F7.0)

250 FORMAT (77H0 LAYER L(I) K(I) (I) C(I) RES(

II) DESCRIPTION ) 260 FORMAT {77H NO

1 OF LAYERS ) 270 FORMAT ( 1I6» IFl 1 ,3» IFIO .3» IFIO . 2» IFlO .3» 1FP.2* 2X» UA6)

280 FORMAT (58H0 THERMAL CONDUCTANCE

1 U=1F7,3)

56
290 FORMAT CigHO TIMF INCREMENT DT=lF3.0)

300 FORMAT (50HO RFSPONSE FACTORS)

310 FORMAT (120H0 J y Y

1 Z

2)

320 FORMAT (lI17rlF23.^r2F15.^)

330 FORMAT (^A6)

3«»0 FORMAT (iftfHO COMMON RATIO CR=1F7.5)

350 FORMAT (2H1 ) 360 FORMAT (50H0 WALL COMPOSITION ) 370 FORMAT (1F27.3»1F10.2»1F10.3»10X»I+A6)

380 FORMAT (50H0 J F ) 390 FORMAT

END

(1I2'*»1F21.5)

SUBROUTINE RESPTK { K » L» G» AG» KG » X » Y » Z» ML r DT»NR » CR »U» IS»F)

DIMENSION K(10)»L(10)»6(10)»X(100)»Y(100)»Z(ino)»AP(10)»BP(lO)»CP(

110) »DP(10> »A(10) »B(10) »C(10) »0(10> »ZR1(3) »ZR2(:^) »RB(3) »RAP(3) »ROOT

2(100) fRA(3»l00) »ZRK(3»100) »RX(100) »RY(100) »AZ(100) »F(ino)

REAL K»L»KG

PI=l»,*ATAN(l,)

M3=3

IF (IS.NE.l) GO TO 10

ZL=K6/10.

UY=100./AG/DT

CALL GPF (UY»ZL»AZ)

IF (I5.EQ.1.AND.NL.EQ.0) GO TO 330

10 CALL ABCD2 ( 0 . » K » L» G» AX» BX» CX» DX» NL)

RB(1)=0X

RB(2)=1.

RB(3)=AX

J=1./BX

00 20 I=1»NL

PX=0

CALL ABCDP2 ( PX» K ( I) » L ( 1) » G ( I ) » AP( I ) » BP ( I ) » CP ( I ) f DP ( I )

)

20 CALL ABCD2 (PX » K ( I ) »L ( I ) » G ( I ) » A ( D » B ( I ) »C ( I ) » D ( I ) » 1

)

IF (NL.LT.2) 60 TO 30

CALL DERVT (A»B»Cf D» AP»BP»CP»DP» APP»BPP»CPP»DPP»NL)

GO To 'O

30 APP=AP(1)

8PP=BP(l)

CPP=CP(1)

0PP=DP(1)

40 RAP(1)=0PP

RAP(2)=0.

RAP(3)=APP

00 50 I=l»3

C1=RAP(I)/BX/0T

C2=RB( I ) *BPP/8X/BX/DT

ZR2(I)=-C1+C2

50 ZR1(I)=-ZR2(I)4^RB(I)/BX

WRITE (6»t^80)

WRITE (f>ff^90) (ZR1(I)»I = 1»M3)

WRITE (6»'»90) (ZR2(I) »I = 1»M3)

C ROOTS OF B(P)=0,

NMAX=10

TESTMX=«*0.

PX=0,001

OPO=0.1/DT

OLX=0.0001
NJ=0 WRITE (6»500)

60 DL=DPO

CALL ABC02 ( PX » K »L» G» AX» BX» CX »DX» ML)

70 PXP=PX+DL

CALL ABCD2 (PXP» K »L» G» AXP » BXP» CXP» DXP»NL)

IF (BX*BXP) 90»110»80

80 PX=PXP

BX=BXP

TESTX=PX*OT

IF (TE5TX-TESTMX) 70»170»170

90 IF (DL-DLX) l'^0»ltfO»100

100 DL=DL/2,

GO TO 70

110 IF (BX) 150»120»130

120 RXX=PX

GO TO 150

130 RXXrpXP

GO TO 150

mo AB=ABS(BX/BXP)

RXX=(PX+A8*PXP)/{1,+AB)

150 M=N-»-l ROOT(NJ)=RXX

' IF (M.6T.1) DP0=R00T(M)-R00T{M-1)

NRT=NJ

WRITE (6»510) NJ»ROOT(M)

PX=RXX+DLX

TESTX=RXX*DT

IF (TESTX-TESTVX) 160»160»170

160 IF (N.LT.MMAX) GO TO 60

170 WRITE (6»520)

IF (ROOT(NRT)-IOO.) 190»180»180

180 MRT=NRT-1

190 DO 250 JJ=1»NRT

PX=ROOT(JJ)

DO 200 J=1»ML

CALL ABCD2 ( PX » K ( J) » L< J) » G ( J) r A ( J) » B ( J) » C ( J) » D ( J) » 1

)

200 CALL ABCDP2 ( ox » K ( J) » L ( J) » G ( J) » AP ( J) » BP ( J) » CP( J) »0P( J)

)

CALL ABCD2 (PX » K »L» G» AX rBX » CX » DX » ML)

IF (NL.LT.2) GO TO 210

CALL DERVT ( A » B » C »D» AP» 8P» CP» DP» APP»BPP» CPP» OPP» ML)

GO TO 220

210 APP=AP(1)

3PP=BP(1)

CPP=CP(1)

DPP=DP(1)

220 PY=BPP*PX*PX*DT

RA(1» JJ)=DX/PY

RA(2»JJ)=1./PY

RA(3» JJ)=AX/PY

PZ=PX*OT

IF (PZ-20.) 2(+0»2t»0»230

230 RX(JJ)=0.

RY( JJ)=25.E16

GO TO 250

2«*0 RX( JJ)=EXP(-PZ)

RY(JJ)=(1.-EXP(PZ))**2

250 WRITE (6»530) ROOT ( JJ) » ( RA ( M» JJ) » M=l » M3)

00 260 JJ=1»MRT

DO 260 M=1»VI3

ZRl(M)=RA(M»vJJ)*RX( JJ)+ZR1(M)

260 ZR2(M)=RA(M» JJ)*(RX( JJ)*RX(JJ)-2.*RX( JJ) )+ZR2{M)

58
11=1

111=2

WRITE (6»5«*0)

WRITE (6r550)

IF (ZR1(2) .LT.O) ZRl(?-)=0.

WRITE (6»560) 1 1 # ( ZRl ( M) » M=l » VI3)

WRITE (6»560) T I I » { ZR? ( M) » M=i

,

m3)

00 270 M=1»M3

ZRK(M»1)=ZR1(M)

270 ZRK(M»2)=ZR2(vi)

MT=100

DO 300 M=3»NT

fvJR=N DO 280 M=1»M3

280 ZRK(y|»N)=0,

00 290 M=1»M3

DO 290 JJ=1»NRT

PZ=(RX( JJ) )**N

290 ZRK(M»N)=ZRK(M»N)+PZ*RY( JJ)*RA(M» JJ)

WRITE (6»560) N» ( ZRK ( M» N) » M=l » WI3)

IF (N.LT.5) GO TO 300

TESTl=ZRK ( 1 » N) /ZRK ( 1 r N-1

)

TEST2=ZRK ( 1 » N-1 ) /ZRK ( 1 » N-2

)

TEST3=A3S(TESTi-TEST2>

IF (TEST3-0. 00001) 3i0»310»300

300 CONTINUE

310 00 320 N=1»NR

X(N)=ZRK(1»N)

Y(N)=ZRK(2»N)

320 Z<N)=ZRK(3»N)

CR=TEST2

WRITE (6»570) CR

IF (IS.EQ.2) GO TO ISO

IF (IS.NE.l) GO TO '70

330 IF (NL.EQ.O) GO TO 390

GF=2*KG/SQRT(0T*A6*PI)

IF (NR.LT.SO) GO TO 350

DO 3^0 J=50»NR

ZJ=J

3H0 AZ( J)=GF*<SQRT(ZJ)-2.*SQRT(ZJ-1.)*-SQRT(ZJ-?.) ) NRR=NR

GO TO 370

350 00 360 J=NR»50

Z( J+1)=Z( J)*CR

X( J+l)=X(J)*CR

360 Y(J+1)=Y( J)*CR

NRR=50

370 DO 3B0 J=1»NRR

380 F(J)=X( J)-Y( J)*Y(J)/(Z(J)+AZ( J))

NR=NRR

GO TO '10

390 00 ^00 J=1»NR

'OO F(J)=AZ(J)

^HO WRITE (6»580)

CR1=1.

DO t*30 J=l»50

CR=F( J+l)/F( J)

TESTCR=ABS(CR-CR1)

IF (TESTCR-0. 00001) WfHHO»i*?0

'20 CR1=CR

JJ=J-1

'30 WRITE (6»590) JJ»F(J)

"•O NR=J

59
CR=CR1

SO TO 470

450 WRITE (6»580)

DO 460 J=1»NR

F(J)=X(J)+Z(J)-2.*Y(J>

JJ=J-1

460 WRITE (6»590) JJ»F(J)

470

Q

RETURN

C

li O A 480 FORMAT (50H0 PESIDUES AT P=0

FORMAT (3F20.f>)

500 FORMAT (50H0 ROOTS OF B(P)=0

510 FORMAT (I10»1F20.6)

520 FORMAT (50H0 RESUDUES AT P=R00T(N)

530 FORMAT (4F20.6)

540 FORMAT (50H0 RESPONSE FACTORS OF FINITE SLAB

550 FORMAT (120H0 J X( J)

1 Z{ J)

2)

560 FORMAT (I10»3F?0.6)

570 FORMAT (lOHO CR=1F10.6)

580 FORMAT (50H0 J F

590 FORMAT (1I10»1F20.5)

END

Y(J]

SUBROUTINE RMTmP (NEXP» NX

TV» CFML» CFMV»

» TIM» TA » TIF» QL» ITK ) COMMON /CC/ X(10»100) »Y(10»100) »2(10»100) rlTYPFdO) »IHT(10) »IRF(in

1) »ABSP(10) »U(10) »H(10) »HI(10) »A(10) »UT(10) » TOS ( 1 0 » 48)TIS ( 10 » 48)G

2(10»10) »T0Y(4B) »D8(24) »QLITE(?4) »0EQUP(24) »Q0CPS(?4) » (51 ( 10 ) » CR ( 10

)

3»NR(10) »0GLAS(10»24) rITHST

DIMENSION AA{20»20) »BB(20) »TT(20) »TIF(20) »A2(20»20) »B2(20) rB3(20)

1GSUM(20)

OBNX=OB(NX)-TTM

TU=TV-TIM

NEXP2=NEXP+1

DO 10 I=1»NEXP2

BB(I)=0.

B2(I)=0.

DO 10 J=1»NEXP2

A2(Ir J)=0.

10 AA(I,J)rO.

SHG=0.

HSUMrO.

ASUMrO.

ASUMT=0.

DO 70 I=1»NEXP

SHG=SHG+QGLAS ( I » NX) A ( I

)

ASUMT=ASUMT+A(I)

G5UM(I)=0.

DO 20 J=1»NEXP

20 GSUM(I)=GSUM(I)+G(I»J)

IF (ITYPE(I) .NE.3) ASUM=ASUM+A ( I)

HSUM=HSUM+HI(I)*A(I)

IR=IRF(I)

CRX=CR(I)

IF (X(IR»2)) 40»30»40

30 X(IR,1)=UT(I)

Y(IRrl)=UT(I)

CRX=0.

Z(IR»1)=UT(I)

40 AA(I,I)=X(IR»1)+HI(I)+GSUM(I)

60
00 50 J=1#NEXP

IF (I.EQ.J) GO TO 50

AA(I, J)=-S(I» J)

50 CONTINUE

AA(I»NEXP2)=-HI(I)

SUMy=Y(IR»l)*TOS(I»l)

SUMXrO.

DO 60 Jz2fH8

SUMYrSUMY+Y ( IR » J) *TOS ( I » J)

60 SUMX=SUMX+X(IR» J>*TIS(I» J)

B3( I ) =SUMY-CRX*OI ( I ) -SJMX

70 AA(NEXP2»I)=A(I)*HI(I)

OLT=QLITE(NX)/ASUMT*R

DO 80 I=1»NEXP

5HF=SHS/ASUM

IF (ITYPE(I) .EQ.3) SHF=0.

80 BB(I)=B3(I)-»-SHF+QLT

AA ( NEXP2 1 NEXP2 ) =-1 . 08* ( CFML+CFMV ) -HSUM

SUM=1.08*(CFML*DBNX+CFMV*TU)+00CPS(NX)+QEQUP(NX)+0LITE(NX)*(1,-R)

BB(NEXP2=-SUM

MEXP3=NEXP2+1

00 90 I=1»NEXP2

32(I)=B8(I)

00 90 J=lrNEXP2

90 A2(Ir J)=AA(I» J)

IF (ITHST.NE.O) GO TO 100

CALL SOLVP (NEyP2»NEXP3»AA»BB»TT»20)

TA=TT(NEXP2)+TIM

IF (ITK.NE.O) GO TO 110

IF (TA-TIM) 110»110»100

TA=TIM

CALL SOLVP (NEXP»NEXP2»A2»B2»TT»20)

110 9L=SUM-1 . 08* (CFML+CFMV ) * ( TA-TIM)

SUMQ=0,

DO H*0 I=1»NEXP

K=IRF(I)

TIS(I»1)=TT(I)

TEST=ABS(TT(I))

IF (TEST. 6T. 100.) GO TO 150

QI(I)=X(K»1)*TT(I)-B3(I)

IF (X(K»2)) 130»120»130

120 QI(I)=U(I)*(TA-DB(NX)

)

130 TIF(I)=TT(I)-«-TlM

li^O SUMQrSUMQ+A(I)*HI(I)*(TA-TIF(l))

QL=-QL-»-SUMQ

RETURN

150 CONTINUE

WRITE (6»170)

DO 160 I=1»NEXP2

160 WRITE (6»180) ( A2 ( I » J) » J=l » NEXP2 ) »82 ( I ) » TT ( I

)

RETURN

C

C

C

170 FORMAT CO ROOM TEMPERATURE MATRIX*)

180 FORMAT (12F10.3)

END

61
SUBROUTINE SHG (SH)

DIMENSION SH(20)

REAL LONG»LAT

C SH(1)=INTENSITY OF DIRECT NORMAL SOLAR RADIATION

C SH(2)=INTENSITY OF DIFFUSE SKY RADIATION

C 5H(3)=INTENSITY OF GROUND REFLECTED DIFFUSE RADIATION

C SH(i*)=COSINE OF INCIDENCE OF DIRECT SOLAR RADIATION

C SH(5)=F0RM FACTOR BETWEEN THE WINDOW AND THE SKY

C SH(6)=F0RM FACTOR BETWEEN THE WINDOW AND THE GROUND

C SH(7)=THERMAL RESISTANCE AT OUTSIDE SURFACE

C SH(8)=THERMAL RESISTANCE AT THE AIR SPACE (DOUBLE GLAZING)

C SH(9)=THERMAL RESISTANCE AT THE INNER SURFACE

C SH(10)=5UNLIT AREA FACTOR

C SH(ll)=SHADING COEFFICIENT »NON-ZERO VALUE WILL BE GIVEN ONLY

C WHEN THE WINDOW IS SHADED BY DRAPES OR BLINDS OR IF IT HAS

C AN INTERPANE SEPARATION OF MORE THAN 1-INCH

C SH(12)=TRANSMISSI0N FACTOR FOR DIRECT RADIATION)

C SH(13)=TRANSMISSI0N FACTOR FOR DIFFUSE RADIATION

C SH(m)=ABSORPTlON FACTOR FOR DIRECT RADIATION (OUTER PANE)

C SH(15)=A3S0RPTI0N FACTOR FOR DIRECT RADIATION (INNER PANE)

C SH(16)=ABS0RPTI0N FACTOR FOR DIFFUSE RADIATIONCOUTER PANE)

C SH(17)=AB50RPTI0N FACTOR FOR DIFFUSE RADIATION( INNER PANE)

C SH(18)=S0LAR HEAT GAIN

COMMON /SOL/ LAT»L0NG»TZN»WAZ»WT»CN»DST»LPYR,S(35)

REAL NI»N0

NI=(SH(7)+SH{8) )/(SH(7)+5H(8)+SH(9)

)

N0=(SH(7) )/(SH(7)+SH(8)+SH(9)

)

D=SH(10)*SH(l)*SH(t»)*(SH(12)+N0«SH(li*)+Nl*SH(15) ) DD=(SH(2)*SH(5)+SH(3)*SH(6) )*(SH(13)*N0*SH(16)*NI*SH(17)

)

IF (SH(H)) 20»10»20

10 SH(18)=D+DD

GO To 30

20 SH(18)={D+DD)*5H(11)

30 RETURN

END

SUBROUTINE SOLVP (M» N» C »D»X » I

)

C THIS IS A ROUTINE FOR SOLVING SIMULTANEOUS LINEAR EQUATIONS

C THE ROUTINE WAS DEVELOPED BY B,A. PEAVY OF NBS

C ROUTINE FAILS WHEN ANY OF THE DIAGONAL ELEMENTS IS ZERO

DIMENSION A(lOOrlOl) »C(I»1) »D(1) »X(1)

DO 10 IX=1»M

00 10 IY=1»M

10 A(IXrIY)=C(IX»IY)

DO 20 IZ=1»M

20 A(IZ»N)=D(I2)

L=l

30 AA=A(L»L)

DO t»0 K=L»N

40 A(L»K)=A(L»K)/AA

DO 60 K=1»M

IF (K.EQ.L) GO TO 60

AA=-A(K»L)

DO 50 IA=L»N

50 A(K»IA)=A(K»IA)+AA*A(L»IA)

60 CONTINUE

L=L+1

IF (L.LE.M) 60 TO 30

DO 70 IP=1»M

70 X(IP)rA(IP»N)

RETURN

END

62
SUBROUTINE SUN

DIMENSION A0(5)/.302»-.0002»36R.«*<*» .1717r0.09n5/»Al (5) /-22 .93 » . ^11*? 17f 2'*,52»-.03^f*»-.0^10/» A2(5)/-.229»-3.2265»-l.lU» .0032* .0073/» A3(5

2) /-.2t^3 0903»-l,09». 0024* .0015/* 81(5) /3.851» -7.351 » .58»-.00U3»-.

3003«*/»B2(5)/.n02»-9.3912»-.18»0. »0.000U/»B3(5)/-.nS5»-.3361» .28»-,

•foosr-.nooe/

COMMON /SOL/ LAT»LONG»TZN»WAZ»WT»CN#DSTf LPYR»5(35)

REAL LATD»LONG»MERIO»LOND

C S(l)= LATITUDE»DEGREE5(+N0RTH»-S0UTH)

C S(2)= LONGITUDE»DEGREES(+WEST»-EAST)

C S(3)= TIME ZONE- NUMBER

C STANDARD TIME DAYLIGHT SAVING TIME

C ATLANTIC «» 3

C EASTERN 5 «» C CENTRAL 6 5

C MOUNTAIN 7 6

C PACIFIC 8 7

C 5(^)= DAYS(FROM START OF YEAR)

C S(5)= TIME»HOUR AFTER MIDNIGHT)

C S(6)= DAYLIGHT SAVING TIME INDICATOR

C S(7)= GROUND REFLECTIVITY

C S(8)= CLEARNESS NUMBER

C S(9)= WALL AZIMUTH ANGLE# DEGREES FROM SOUTH

C S(10)=WALL TILT ANGLE* DEGREES FROM HORIZON

C S(11)=SUN RISE TIME (HOURS AFTER MIDNIGHT)

C S(12)=SUN SET TIME

C S(13)=C0SZ DIRECTION COSINES

C S(lt*)=COSN DIRECTION COSINES

C S(15)=C0S(S) DIRECTION COSINES)

C S(16)=ALPHA DIRECTION COSINES NORMAL TO SURFACE

C S(17)=BETA

C S(18)=6AMMA

C S(19)=COS(ETA)COSINE OF INCIDENCE ANGLE

C S(20)=S0LAR ALTITUDE ANGLE

C S(21)=S0LAR AZIMUTH ANGLE

C S(22)=DIFFUSE SKY RADIATION ON HORIZONTAL SURFACE

C S(23)=DIFFUSE GROUND REFLECTED RADIATION

C S(2«*)=DIRECT NORMAL RADIATION

C S(25)=T0TAL SOLAR RADIATION INTENSITY

C S(26)=DIFFUSE SKY RADIATION INTENSITY

C S(27)=GR0UND REFLECTED DIFFUSE RADIATION INTENSITY

C 5(28)=SUN DECLINATION ANGLE* DEGREES

C S(29)=EQUATI0N OF TIME »HOURS

C S(30)=A SOLAR FACTOR

C S(31)= SOLAR FACTOR

C S(32)= SOLAR FACTOR

C S(33)= CLOUD COVER MODIFIER

C 5(31+) INTENSITY OF DIRECT SOLAR RADIATION ON SURFACE

C S{35) HOUR ANGLE»DEGREE

PI=3,1«H5927

X=2*PI/366.*S(«»)

C1=C0S(X)

C2=C0S(2*X)

C3=C0S{3*X)

S1=5IN(X)

S2=SIN(2*X)

S3=SIN(3*X)

00 10 K=l»5

KS=(K-l)+?8

10 S{KS)=A0(K)+Al(K)*Cl+A2(K)*C2+A3{K)*C3-»-91(K)«Sl+B2(K)*S2+B3(K)*S3

S(29)=S(29)/60.

LATD=S(1)

L0NG=S(2)
MERID=15*S(3)

LOND=LONG-MERID

Y=S(28)*PI/180,

Yy=LATD*PI/180.

HP=-TAN(Y)*TAM(YY)

TR=12/PI*AC0S(HP)

5(ll) = {12-TR)-S<29)-»-L0ND/15.

S<12)=2t».«S(ll)

H=15*(S(5)-12+S(3)+S(29)-S(6) >-S(2)

5(35)=H

513=SIN(YY)*SIM(Y)+C0S(YY)*C0S(Y)*C0S(H*PI/18P.)

5(13)=S13

HP1=180,*ACOS{HP)/PI

X1=ABS(HP1)

X2=ABS(H)

IF (X1-X2) 130»20»20

20 5(m)=C0S<Y)*SlN(H*PI/180,)

S(15)=SQRT(1.-5(13)*S(13)-5(1U)*S(1«*) > STEST=S(15)

STEST1=C05(H*PI/180.)-TAN{Y)/TAN(YY)

IF (STESTl) t»0,30»30

30 S(15)=STEST

GO TO 50

•O 5(15)=-STEST

50 S(20)=A5IN(S(13))

IF (5(15)) 70»60f60

60 S(21)=ASIN(S(m)/COS(S(20) )

)

GO To 80

70 S(21)=PI-ASIN(S(1U)/COS(S(20) )

)

80 S(20)=180.*S(20)/PI

5<21)=180.*S(?1)/PI

S(2f )=S(30)*5(8)*S(33)*EXP{-S(31)/S(13)

)

S(22)=5(32)*S(2'»)/S(8)/S(8)

S{23)=S(7)*(S(?2)<»-S(2«*)*S(13))

WT=S(10)*PI/180.

S(16)=C0S(WT)

WA=S(9)*PI/180,

S(16)=C0S(WT)

S(17)=SIN(WA)*SIN(WT)

S(18)=C0S(WA)*5IN(WT)

S(19)=5(16)*S(l3)+S(l7)*S(l«t)+S(18)*S(15)

S(3i*)=S{2'*)*S(19)

Y=0.^5

IF (S(19)+0.2) 100»100»90

90 Y=0.55+0.'I37*5(19)+0.313*S(19)**2

100 IF (S(19)) 110»110»120

110 S(19)=0,

5(3t»)=0.

120 CONTINUE

S(26)=S(22)*Y

S(27)=S(23)*(l-S(16))/2.

5(25)=S(3t*)+S(26)-i-S(27)

GO TO 150

130 00 mo J=l«l»26

It^O S(J)=0.

5(3«»)=0

150 RETURN

END

64
SUBROUTINE TAR (TR)

REAL Al(6)/0.0ll5t»»0.7767i+»-3.9«»657»8.578Bl»-fl.3ei:55»3.011Rfl/

REAL A2<6)/0.0l636rl.»*0783»-6.79030»lU,37378f-J3.83357»«l.9?t*3q/

REAL A3(6)/0.0l837»1.92t*97»-8.89l3'*»18.e*0197»-17.'»86'*a»6.175«*t4/

REAL A«K6)/0.09902r2.35«*17»-10,^715r2l.2<t322»-19.95978»6.P996«t/

REAL A5(6)/0.01712»3.50839»-I3.8639»26.3«t330»-23.««^8«*6»8.1737?/

REAL A6 ( 6) /0. 0m06 »tf.l59«58» -15. 0628 » 27. 181*92 » -23. 88518 » 8. 03650/

REAL A7(6)/0.01153»^.559^+6»-15.^329»26.70568»-2?.87993»7.57795/

REAL A8(6)/0.00962f '.B1911»-15.»f71t»25.86516»-21.69106»7.087l«»/

REAL Tl(6)/-0.00885»2.71235»-0.62062»-7,07329»9.75995»-3.8992?/

REAL T2(6)/-0.0llH*»2.3937l»0.tf2978»-8.98262»11.51798»-«4.5206't/

REAL T3(6)/-0.Ol200»2.13O36»1.13833»-l0,07925»12.U4161»-'*.83285/

REAL TtK6) /-0. 01218* 1. 90950 »1. 61391 » -10. 6«»872» 12. 83698»-'*. 95199/

REAL T5(6) /-O. 01056* 1. 29711 » 2.28615* -10. 37132 »11.9588«t»-'*. 5^880/

REAL T6( 6) /-O. 00835* 0.92766* 2. 15721* -8. 71429* 9. 871 52* -3. 73328/

REAL T7( 6) /-O. 00646* 0.68256* 1.82499, -6. 95325* 7, 80647* -2. 9445t*/

REAL T8 ( 6) /-O. 00496* 0.51043* 1.47607, -5. 41985* 6. 00546* -2. 281 6?/

REAL AOK 6) /O. 01407* 1.06226* -5. 59131* 12, 15034* -11. 78092, 4. 20070/

REAL A02( 6) /O. 01819* 1.86277* -9. 24831* 19. 49443* -18. 56094* 6. 53940/

REAL A03( 6) /O. 01905* 2. 47900* -11. 7427* 24. 14037* -22. 64299, 7. 89954/

REAL A04(6)/0. 01862* 2. 96400* -13. 4870 27, 13020* -25. 11877, 8. 68895/

REAL AOS ( 6) /O. 01423* 4. 14384* -16. 66709* 31. 30484* -27. 81955* 9. 36959/

REAL A06(6>/0. 01056* 4. 71447* -17. 33454* 30. 91781* -26. 63898* 8. 79495/

REAL A07( 6) /O. 00819* 5. 01768* -17. 21228 ,29. 46388, -24. 7691 5* 8. 05040/

REAL A08 ( 6) /O. 00670* 5. 18781* -16. 84820* 27. 90292* -22. 99619, 7. 38140/

REAL All (6) /O, 00228* 0.34559* -1.19908* 2, 22336* -2. 05287* 0.72376/

REAL AI2 (6) /O. 00123* 0.29788* -0.92256* 1.58171, -1,40040* 0.48316/

REAL AI3( 6) /O. 00061* 0.26017* -0.72713* 1.14950, -0.97138* 0.32705/

REAL AI4 ( 6) /O. 00035* 0.22974* -0.58381* 0.84626* -0.67666* 0.221 02/

REAL A 15 ( 6) /-O. 00009* 0.15049* -0.27590*0. 25618 *-0. 12919* 0.02859/

REAL AI6( 6) /-O. 00016* 0.10579* -0.15035* 0.06487* 0.02759* -0.02317/

REAL AI7 ( 6) /-O. 00015* 0.07717* -0.09059* 0.00050* 0.06711* -0.03394/

REAL AI8 ( 6) /-O. 00012* 0.05746* -0.05878* -0.01855* 0.06837* -0.03191/

REAL TOl (6) /-O. 00401* 0.74050* 7, 20350* -20. 11763* 19. 68824, -6. 74585/

REAL TD2 ( 6) /-O. 00438* 0.57818* 7. 42065* -20. 26848* 19. 79706 *-6. 79619/

REAL TD3 ( 6) /-O. 00428* 0.45797* 7. 41367* -19. 92004* 19. 40969* -6. 66603/

REAL TD4( 6) /-O. 00401* 0.36698* 7, 27324* -19. 29364, 18. 75408, -6. 43968/

REAL TD5( 6) /-O. 00279* 0.16468* 6. 17715* -15. 8481 1*15. 28302* -5. 23666/

REAL TD6 (6) /-O. 00192* 0.08180* 4. 94753* -12. 43481* 11. 92495* -4. 07787/

REAL TD7( 6) /-O. 00136* 0.04419* 3. 87529* -9. 59069* 9. 16022* -3. 12776/

REAL TD8 ( 6) /-O. 00098* 0.02576* 3. 00400* -4. 33834* 6. 98747* -2. 38328/

DIMENSION TR(9) ,A(8*6) *T(S*6) »A0(8»6) »AI(8»6) *TD(8*6)

C TR(1)= TRANSMISSION FACTOR DIRECT

C TR(2)= TRANSMISSION FACTOR *DIFFUSE

C TR(3)= ABSORPTION FACTOR , DIRECT* OUTER

C TR(4)r ,DIFFUSE»OUTER

C TR(5)= *DIRECT *INNER

C TR(6)= *OirFUSE* INNER

C TR(7)= COSINE OF INCIDENT ANGLE

C TR(8)=TYPE OF GLASS

C TR(9)=I0 CODE FOR THE GLAZING

C ID =1 SINGLE GLAZING

C ID =2 D0U8LE GLAZING

DO 10 J=l*6

A(1*J)=A1(J)

A(2* J)=A2(J)

A(3* J)=A3(J)

A(4*J)=A4(J)

A(5*J)rA5(J)

A(6* J)=A6( J)

A(7*J)=A7(J)

A(8* J)rA8( J)
10

T(1»J)=T1(J)

T(2»J)=T2(J)

T(3» J)=T3(J)

T(^»J)=m(J)

T(5»J)rT5(J)

T(6» J)=T6(J)

T(7» J)=T7( J)

T(8» J)=T8(J)

A0( Ir J) =A01(J1

A0( 2f J) =A02( J)

A0( 3r J) =A03( J]

A0( (ft J) =AOU( J]

A0( 5» J) rA05( JI A0( bt J) =A06(J]

A0(I7f J) =A07(J1

A0( 8f J) =A08( j:

AK It J) =AT1(J]

AI( 2t J) =AI2(J]

AK 3» J) =AI3( J]

AK «*» J) zAIt^C J]

All[5» J) =AI5( J]

AKlb, J) =AI6( J]

AK If J) =AI7(J]

AK\bt J) =AI8(J1

TD<[Ir J) =T01(J1

TD [2r J) =TD2(J

TD [3» J) =T03(J

TD J) =TD«*(J

TD f5r J) =TD5(J

TD (6» J) =TD6(J

TD [7» J) rTD7{J

TO [8r J) =TD8(J

ETA=TR(7)

L=TR(8)

ID=TR(9)

IF (I0.EQ.2)

TR(1)=T(L»1)

GO TO 30

TR(2)=T(L»l)/2.

TR(3)=A(Lrl)

TR(^)=A(L»l)/2.

DO 20 J=2»6

TR(1)=TR(1)+T(L» J)*(ETA**( J-1)

)

TR(2)=TR(2)+T(L»J)/( J*l>

TR(3)=TR(3)+A(L» J)*(ETA**(J-1)

20 TR(<*)ZTR(^)+A(L» J)/(J+1)

TR(5)=0

TR(6)=0

GO To 50

30 TR(l)rTO(L»l)

TR(2)=T0(Lrl)/2.

TR(3)=A0(L»1)

TR(«*)=A0(L»l)/2.

TR(5)=AI(L»1)

TR(6)=AI(L»l)/2.

DO ^0 J=2»6

X=ETA**(J-1)

TR(1)=TR(1)+TD(L» J)*X

TR(2)=TR(2)+TD(L» J)/(J+1)

TR(3)=TR(3)+A0(L» J)*X

TR(^)=TR(^t)+AO(L» J)/(

TR(5)=TR(5)+AT(L» J)*X

'»0 TR(6)=TR(6)+AI(L»J)/(J+1)

66
50 TR(2)=2*TR(2)

TR(H)=2*TR(f)

TR(6)=2*TR(6)

RETURN

END

PUNCTIOM WBF (H»PB)

C THIS PROGRAM APPROXIMATES THE WET-BULB TEMPERATURE WHEN

C ENTHALPY IS GIVEN

IF (PB-29.92) 10»30»10

10 Y=LOG(H)

IF (H.GT.ll.T'SR) GO TO 20

WBF=0,60«*l+3.'*8«tl*Y-H.36ni*Y«Y+0.97307*Y*Y*Y

GO TO 100

20 WBF=30. 9185-39, 68200*Y+20, 58m Y*Y-1,758*Y*Y*Y

60 TO 100

30 WB1=150.

PV1=PVSF(WB1)

W1=0,622*PV1/(PB-PV1)

X1=0,2'**WB1 + (1 061+0. '''**WR1)*W1

Y1=H-X1

tfO WB2=WB1-1

PV2=PV5F(WB2)

W2=0,622«PV2/(PB-PV2)

X2=0,2«**WB2+(1 061+0. ''«»*WB2)*W2

Y2=H-X2

IF (Y1*Y2) 90»60»50

50 WB1=WB2

Y1=Y2

GO To 'O

60 IF (YD 80»70»80

70 WBF=WB1

60 TO 100

80 WBF=WB2

GO TO 100

90 Z=ABS(Y1/Y2)

WBF= ( WB2*Z+WB1 ) / ( 1+Z

)

100 RETURN

END

SUBROUTINE WF(OG»QX»QlS»LG»LXf LIS»OL)

C THIS ROUTINE TAKES HEAT GAINS TO HEAT LOSS BY WEIGHTING FACTOR

C QG—HISTORY OF SOLAR HEAT GAIN

C 9X—HISTORY OF LONG WAVE LENGTH HEAT GAIN

C 9IS—HISTORY OF LIGHTING POWER INPUT

REAL QG(8) »QX(8) »GlIS(8) »LG(8) »LX(8) »LTS(8)

REAL AG ( 8) /0. 2060 »-0, 3989 »0.2?«*7»-0.02'+5»-0, 0026 »-0.0006»-0. 0002

10.0001/

REAL BG(B)/1.0nO»-2.'*586»2.0078»-0.5'^7»0. »0. »0. »0./

REAL AX(8)/0.6258»-1.2«t92f 0.7932 » -0.1573 r-0.0P03»0. »0.»0./

REAL BX ( 8) /1 . 000 » -2 . 0676 » 1 . 3651 r -0 . 2837 »0.»0.»0.»0./

REAL AIS(8)/0.2902»-0.1866»0. »0. »0. »0. »0. »0,/

REAL BIS(8)/1.000»-0.8781»0.»0.»0. »0. »0. »0./

DIMENSION QZ6(8) »0ZX(8) »0ZIS(8)

DO 10 L=2»8

0ZG(L)=LG(L-1)

QZX(L)=LX(L-1)

QZIS(L)=LIS(L-1)
10 CONTINUE

00 20 L=2»8

LG(L)=QZG(L)

LX(L)=QZX(L)

LIS(L)=QZIS(L)

20 CONTINUE

SUMAG=AG(1)*QG(1)

5UMBG=0.

SUMAX=AX(1)*QX{1>

SUMBX=0.

SUMAIS=AIS(1)*0IS(1)

5UM8IS=0.

DO 30 L=2»8

SUMAG=SUMAG+AG(L)*QG(L)

5UMBG=SUMB6+BG(L)*LG(L)

SUMAX=SUMAX+AX(L)*QX(L)

SU^1BX=SUMBX+BX(L)*LX(L)

SUMAIS=5UV!AIS+AIS(L)*0IS(L)

5UMBIS=SUMBIS+8IS{L)*LIS(L)

30 CONTINUE

LG(I)=SUMAG-SUMBG

LX(1)=SUMAX-SUMBX

LIS{1)=SUMAIS-SUMBIS

9L=LG(1)+LX(1)+LI5(1)

RETURN

END

SUBROUTINE ABCDP2 (Z » K » L » G» AP» BP» CP» DP)

REAL K»L

PI=t|,*ATAN(l.

)

IF (G) 30»30»10

10 PP=Pl/t»,/G

IF (Z) '*0»'t0»20

20 ZQ=5QRT(Z/G)

ZQL=ZQ*L

X=L*L*0.5/G

RES=L/K

C0=SIN(ZQL)

C1=C0S(ZQL)

S1=C0/Z(5L

52=(S1-C1)/ZQL/ZQL

AP=X*S1

BP=X*RES*S2

CP=X*(S1+C1)/RES

0P=X*S1

GO TO 50

30 AP=0.

BP=0,

CP=0,

DP=0.

GO TO 50

'O CONTINUE

X=L*L*0.5/G

AP=X

3P=X*L/K/3

CP=K/L*X*2.

OP=X

GO TO 50

50 RETURN

END
subroutine: RESFX (X»Y»Z»XX»Yy»ZZ»NR»CR»UT»NEXP)

DIMENSION XXdOOflO) »rY(100»10) »ZZ(10n»10) »X(10»100) »Y(10»100)

DIMENSION Z(10»100) »NR(10) fCRdO) rUTdO)

DO 10 K=l»10

DO 10 v>=l»100

XX( J»K)=0

YY(J»K)=0

10 ZZ(J»K)=0

CALL RESF (XX»YY»ZZ» IRUN)

DO 30 K=1»NEXP

I=K

IF (K»GT.IRUN) GO TO 30

X(I»1)=XX(3»K)

Y(If l)rYY(3»K)

Z(I»1)=ZZ(3»K)

NR{I)=XX(1»K)

CR(I)=XX(2f K)

JJJ=NR(I)+3

JT(I)=XX( JJJ»K)

NMAX=NR(I)

DO 20 J=2»NMAX

J3=J+2

J2=J+1

X(I» j)=XX(J3f K)

Y(I» J)=YY( J3»K)

20 Z(I» J)=ZZ(J3»K)

30 CONTINUE

RETURN

END

XX(J2»K)*CR(I)

YY(J2»K)*CR(I)

ZZ(J2»K>*CR(I)

497-811 0-73-7

69

Appendix D

Computer Program Used in Evaluation for the Experimental Building

T. Kusuda and D. M. Burch

Thermal Engineering Systems Section, Building Environment Division

Center for Building Technology, Institute for Applied Technology

National Bureau of Standards, Washington, D.C. 20234

C THIS PROGRAM CHECKS THE NBS INSIDEOUT HOUSE

C XX»YY»ZZ ARE RESPONSE FACTORS CALCULATED BY RE5PTK

C WHICH HAS BEEN DEVELOPED BY T. KUSUDA OF NBS

C X»YfZ ARE AUGUMENTED RESPONSE FACTORS TO SHORTEN THE CALCULATION

C A(l) AREA OF THE ROOF IN SQ.FT

C A(2) AREA OF THE WALLS IN SQ. FT

C A(3) AREA OF THE FLOOR IN SO. FT

C A{i*) AREA OF THE INTERNAL FURNISHINGS

C CFM AIR LEAKAGE IN CU.FT. PER MINUTE

C UD OVERALL HEAT TRANSFER COEFFICIENT OF THE DOOR

C AD AREA OF THE DOOR IN SQ.FT.

C UW OVERALL HEAT TRANSFER COEFFICIENT FOR WiNDOifl/S

C AW TOTAL WINDOW AREA SQ.FT.

C TG GROUND TEMPERATURE IN F

C- TA ASSUMED INITIAL AIR TEMPERATURE AT TtME 7ER0 IN F PARAMETER R=<+»S=100 rT=i+8»U=T + l » V=2*T

DIMENSION X(RrS)»Y(R»S)»Z(R»S)»XX(SfR)fYY(S»R)»ZZ(S»R),CR(R)»Q(R)»

1T0(5) »TI (5) »TOX(T) fA(R) r5UM(R) »T0Y(5) fTIME(T).TIX(T)»B{R)

3001 DO 700 K=lrR

DO 700 J=1»S

XX(JfK)=0.

YY(J»K)=0.

7oO ZZ{J»K)=0.

CALL RESF( IRUN»XXrYY»ZZ»QEL)

DO 1 I=1»IRUN

X(If l)=XX(3f I)

Y(I»l)=YY(3rI)

Z(I»l)=ZZ(3f I)

CR(I)=XX(2»I)

NMAX=XX(1»I)

DO 1 J=2»NMAX

J3=J+2

J2=J+1

X(I» J)=XX( J3»I)-XX( J2»I)*CR(I)

Y(If J)=YY(J3»I)-YY(J2»I)*CR(I)

1 Z(I»J)=ZZ{ J3f I)-ZZ(J2rI)*CR(I)

6o3 WRITE(6»605)

100 FORMAT(11F7.0)

3000 READ(5»100) RUN

WRITE(6»8007) RUN

8007 FORMATdHl'RUN NO='F10.0)

IF(RUN) 6000r6000»7000

7000 DEN=0.

DO 102 I=1»T

TIME( I)=DEN

102 DEN=DEN+DEL

READ(5»101) (TOX(I) f I=1»T)

READ(5»101) (TIX(I) »I=1»T)

READ (5^100) (A(I)»I=1»R) » CFM » UD » AD » UW » AW » TG » TA

101 F0RMAT(12F6.1)

WRITE(6»400n)

<+000 F0RMAT(30H0 OUTDOOR TEMPERATURE CYCLE

WRITE (6» 609) (TOX(I) »I=1»T)

IF(TIX(l)) 8001»8002»8001

BoOl WRITE(6»8003)

WRITE(6»609) ( TIX { I ) » 1=1 » T

)

NTI = 1 ao03 FORMAT( IHO' INSIDE AIR TEMPERATURE CYCLE')

609 FORMAT( 12F10.2)

GO TO 8010

8002 NTI=0

73
605 FORMAT(2H0 ) 606 FORMATdSOHO A(l) A(2) A(3) A ( ) CFM

1 UD AD UW AW TG TA ) 80l0 CONTINUE

WRITE(6»606)

WRITE(6»609) (A(I) »I=1»R) »CFM»UD»ADr W»AW»TG»TA

DO 500 J=1»T

IF(NTI.NE.O)TI ( J)=TIX(T-J+1)

500 T0( J)=T0XCT-J+1)

DO 501 J=U»V

IF(NTI.NE.O)TI ( J)=TI ( J-T)

501 T0{ J)=TO( J-T)

IF(NTI.NE.O) GO TO 8004

DO 2 I=1»V

2 TI(I)=TA

800'+ DO 502 J=1»V

T0( J)=TO( J)-TG

502 TI ( J)=TI ( J)-TG

DO 503 J=lrT

IF(NTI.NE.O) TIX( J)=TIX( J)-TG

503 TOX( J)=TOX{ J)-TG

DO U I=l»2

0( I)=0.

DO 5 J=1»V

5 Q(I)=Q{I)+(XX(J+2»I)*TI(J)-YY(J+2»I)*T0(J)

)

CONTINUE

DO 6 I = 3»'+ Q( I )=0.

DO 6 J=1»V

6 Q(I)=Q(I)+XX(J+2»I)*TI(J)

5o01 F0RV1AT(2H1 ) WRITE{6»5001

)

WRITE(6»5000)

5oOO FORMAT (10X»25H TEMPER ATURES » F »30X»30H HEAT FLOi«/S

1»BTU/HR ) WRITE(6»400)

400 FORMAT ( • TIME' »7X'T0' »8X»TI » 6X • ROOF » 6X • WALL ' » 5X FLOOR •» ^X • SOLI

1 • »6X'D00R' rUX'WlNDOW' »5X» INFIL* #7X»NET'

)

DO 200 N=l»10

DO 200 NK=1»T

IF(NTI.NE.O) TINEW=TIX(NK)

TNEW=TOX(NK)

DO 10 NTT=2»V

10 T0Y(NTT)=T0(NTT-1)

DO 11 NTT=2»V

11 TO(NTT)=TOY(NTT)

DO 12 NTT=2»V

12 TOY(NTT)=TI (NTT-1)

DO 13 NTT=2»V

13 TI(NTT)=TOY(NTT)

T0(1)=TNEW

IF(NTI.NE.O) TI(1)=TINEW

DO 7 I=l»2

SUM ( I ) =Q ( I ) *CR ( I) -Y ( I f 1 ) *T0 ( 1

)

NMAX=XX(1,I)

DO 8 J=2»NMAX

8 SUM(I)=SUM(I)+(X(I»J)*TI(J)-Y(I»J)*TO(J)

)

7 5UM{I)=SUM(I)*A(I)

DO 20 1=3.4

SUM(I)=CR(I)*Q(I)

NMAX=XX(1»I)

DO 9 J=2»NMAX

9 SUM(I)=5UM(I)+X(I»J)*TI(J)

74
20 5UVI(I)=5UM(I)*A(I)

IF(NTI.NE.O) GO TO 8005

DEN=UD*UW+UW*AW+1 .08*CFM

DEM=DEN

DO 15 Irl»R

15 DEN=DEN+A(I)*X(I»1)

XNEV-DEM*T0(1)

DO 16 Irl»R

16 XNEM=XNEM-SUM( I

)

TI(1)=XNEM/DEN

8005 DO 17 I=1»R

17 Q(I)=SUM(I)+A(I)*X(Irl)*TI{l)

QD=UD*AD*(TI (l)-TO(l)

)

QW=UW*AW*(TI (l)-TO(l)

)

QI=1 .08*CFM* (TI ( 1 )-T0( 1 )

)

T0N=T0(1 )+TR

TINrTK 1 )+TG

SUMQ=QD+QW+OI

DO 8006 I=lrR

8006 5UMQ=5Uf/Q+Q( I)

DO 201 I=1»R

IF{ A( I) )201»201»202

202 Q(I)=Q(I)/A(I)

20l CONTINUE

IF(N.NE,10) GO TO 200

DO 205 I=1»R

205 B(I)=A(I)*Q(I)

WRITE (6 » 300) NK»TON»TIN» (B(I)»I=1'R) » QD » QW » Ol » 5UMQ

300 FORMAT(I5»10F10.2)

C TON OUTSIDE AIR TEMPERATURE

C TIN INSIDE AIR TEMPERATURE

C Q(l) »! = !»'+ HEAT FLUX IN BTU PER HOURrSO.FT

C QD TOTAL HEAT TRANSFER THROUGH DOOR

C QW TOTAL HEAT TRANSFER THROUGH WINDOWS

C QI TOTAL HEAT TRANSFER DUE TO INFILTRATION

2o0 CONTINUE

GO TO 3000

6000 STOP

END

75
SUBROUTINE RESF ( IRUM » XX » YY » ZZ » DELTAT

)

C THIS PROGRA'*^ IS DEVELOPED BY T.KUSUDA OF THE NATIONAL BUREAU OF

C STANDARDS FOR CALCULTING THE THERMAL RESPONSE FACTORS FOR

C COMPOSITE WALLS»FL00RS»R00FS»BA5EMENT WALLS BASEMENT FLOORS

C AND INTERNAL FURNISHINGS OF SIMPLE SHAPES

C RESPONSE FACTORS ARE USED IN THE FOLLOWING MANNER

C X.YfZ ARE RESPONSE FACTORS

C QI=X*TI-Y*TO*GMA INSIDE WHERE R IS MINIMUM

C QO=Y*TI-Z*TO OUTSIDE WHERE R IS MAXIMUM

C TI INSIDE TEMPERARURE WHERE R IS MINIMUM

C TO OUTSIDE TEMPERATURE WHERE R IS MAXIMUM

C K THER^^AL CONDUCTIVITY

C G THERMAL DIFFUSIVITY

C L THICKNESS

C IM=0 OR BLANK PLANE WALL

C IM=1 CYLINDRICAL WALL

C IM=2 SPHERICAL WALL

C IN=0 FINITE THICK WALL

C IN=1 SEMI-FINITE WALL

C IN=2 SOLID OBJECT

C IF RESPONSE FACTORS OF THE SOLID CYLINDER ok SPHERE OF HOMOGENEOUS

C PROPERTY ARE DESIRED* TREAT THE PROBLEM OF MULTILAYER BUT WITH THE

C IDENTICAL PROPERTIES FOR ALL THE LAYERS EXCEPT THE RADIUS

C IF IHEATzO NO TEMPERATURE DATA THUS NO HEAT CALCULATION

C IF IHEAT=1 PERIODIC 80UNDATRY CONDITIONS

400 FORMAT(2H0 ) PARAMETER S=100 » T=10 » U=T+1 » TV=2*T

REAL K(T) »G(T) »L(T) »KG

DIMENSION X(S)»Y(S)fZ(S)»C(T)»D(T)»R{U) »RES(T) »RMK(T»T) »RMKG(T)

1F(S) »XX(S»TV) »YY(SrTV) .ZZ(S»TV)

1 FORWATC 1017)

2 FORMAT( 10F7.0)

100 FORMATdlHO EXPOSURE N0= 110)

101 FORVAT(77H0 LAYER L(I) K(I) (I) C(I) RES(I

1) DESCRIPTION ) 102 F0R^^AT(77H NO

2 OF LAYERS ) 103 FORMAT ( 1I6» IFll .3» 1F10.3»1F10.2» IFIO. 3 » 1F8.2»2XH4A8)

101+ FORMAT(58H0 THERMAL CONDUCTANCE

3U=1F7.3)

105 FORMAT('+9H0 TIME INCREMENT DT=1F3.1 ) 106 FORMAT(50H0 RESPONSE FACTORS ) 107 FORMAT(120Hn J X Y

1 Z ) 108 F0RMAT(lI17»lF23.t|»2F15.'+)

112 F0RMAT(t+A6)

117 F0R^^AT(i+£+H0 COMMON RATIO CR=1F7.5)

700 READ(5»2) DELTAT

IRUN=0

300 READ(5» 1)NLAYR»NTEST» IM. IN

IF(NLAYR.EQ.O) GO TO 800

IRUN=IRUN+1

IF(^JLAYR.GT.10) GO TO 600

NNLAYR=NLAYR+1

IF(NLAYR.EQ.O) GO TO 500

DO 200 I=1»NLAYR

200 REAn(5f2) L ( I ) . K ( I ) » D ( I ) r C ( I ) » RES ( I

)

IF( IN.EQ.2. AND. IM.EO.O) GO TO 301

500 IF(IN.NE.O) READ(5»2)KG»DG.CG

IF(IN.NE.O) AG=KG/CG/OG

IF(NLAYR.EQ.O) GO TO 501

IFdM.EO.O) GO TO 301

76
READ (5' 2) (R(I) »I=1»NNLAYR)

GO TO 302

301 R(l)=10.

DO 303 I=2»NNLAYR

303 R(I)=R(I-1)+L(I)

302 IF(IN,E0.2.AND.IM.NE.0)READ(5f 112) (RMKGCJ) »J=1.U)

DO 113 iritNLAYR

113 READ(5»112) (R>^K(I»J) » J=lr«+)

IF(IN.EQ.1)READ(5»112) (RMKG(J) »J=1»U)

DO 109 I=1»NLAYR

IF(L(I)) iinfiii,iio

111 6(I)=0.

K(I)=1./RES(I)

GO TO 109

110 G(I)=K(I)/C(I)/D{I)

109 CONTINUE

501 GMA=(R(NNLAYR)/R(1) )+*IV!

CALL RESPTK(K»L»R»Gf AG»KG»Xf Y»Z»NLAYR»DELTAT»NRT.CR»UT, IM» IN»F)

XX(1» IRUN)=FLOAT(NRT)

YY( 1 r IRUN) =FLOAT(NRT)

ZZ(1» IRUN)=FLOAT(NRT)

XX(2r IRUN)=CR

YY(2» IRUN)=CR

ZZ(2» IRUN)=CR

XX(NRT+3» IRUN)=UT

YY(NRT+3» IRUN)=UT

ZZ(NRT+3» IRUN)=UT

WRITE(6»100) IRUN

IF(IM.EQ.O) WRITE (6» 701)

701 FOR-^ATiSOHO PLANE WALL ) IF(IM.EQ.l) WRITE(6»702)

70? FORMAT(50H0 CYLINDRICAL WALL ) IF(IV|.EQ.2) WRITE(6f703)

703 FORVIAT(50H0 SPHERICAL WALL ) WRITE(6»101)

WRITE(6. 102)

WRITECeft+OO)

IF(NLAYR.EQ.O) GO TO 502

IF( IN.Eq.2. AND. I'^.NE.O) WRITE(6» 120)KG»DG»CG» (RMKG( J) f J=l »1)

DO 202 I=1»MLAYR

IF(L(I)) 202»2n3»202

203 K(I)=0.

202 WRITE{6»103)I»L(I)»K(I)»D{I)»C(I) »RES(I) » (RviK(I»J) » J=1.4)

IF( IN.EQ.1)WRITE(6» 120)KGrD6»CG» (RMKG( J) » J=l f't) 120 FORMAT ( 1F27. 3 f lF10.2r lF10.3r 10X»4A6)

502 CONTINUE

IF(IN.NE.O) GO TO 1535

DO 114 N=1»NRT

JN=N-1

XX(N+2» IRUN)=X(N)

YY(N+2»IRUN)=Y(N)

ZZ(N+2» IRUN)=Z(N)

llH CONTINUE

GO TO 501

1535 CONTINUE

555 FORV!AT(50H0 J F ) iFdN.EQ.l) GO TO 9999

GO TO 9998

9999 5I6rj=1.0

GO TO 505

9q98 IF(IN.EQ.2.AND.IM,EQ.O) GO TO 9997

77
GO TO 9996

9997 5IGN=-1.0

GO TO 505

9996 CONTINUE

DO 506 N=1»NRT

JN=N-1

X(N)=-X(N)

XX(N+2f IRUN)=X{N)

506 CONTINUE

GO TO 50'+ 505 DO 509 N=1»NRT

XX(N+2» IRUN)=5IGN*F(N)

JN=N-1

509 CONTINUE

508 F0RMAT(1I2'+p1F21.5)

501+ CONTINUE

GO TO 300

600 CONTINUE

. 800 RETURN

END

78
SUBROUTINE RESPTK ( K f L » R » G » AG » KG » X » Y » Z » ML » DT r NR , CR . U » I M , IS » F

)

C CALCULATES RESPONSE FACTORS BY MAKING USE OF THICKNESS » THERMAL

C CONDUCTIVITY* DENSITY* AND SPECIFIC HEAT OF EACH LAYER OF

C COMPOSITE WALL

DIMENSION K(10)fL(10)»R(10)»G(10)»X(100)»Y(lOO)»Z(l(JO).AP(10) pHP(1

10)»CP(10)»DP(10)»A(10)»B(10)»C(10)»D(10)»ZR1(3) »ZH2(3) rRR(3) »RAP(3

2) f ROOT (100) .RA(3»100) »ZRK(3»100) » RX (100 ) rRY ( 100 ) . AZ ( lOU

)

3»F(100)

REAL K»L»KG

PI = 3.1'+15927

M3=3

IF(IS.EQ.2.AND.IM.NE.O) M3=l

IF(IS.NE.l) GO TO 613

608 ZL=KG/R(NL+1)

UY=R(NL+1)**2/AG/DT

CALL GPF(UY»ZL» IMf AZ ) IF(IS.EQ.l.AND.NL.EQ.O) GO TO 901

613 CALL ABCD2{0. »K»L»R»G»AX»BXrCX»DXrIM»NL)

RB(1)=DX

R8(2)=l,

R8(3)=AX

U=1./BX

DO 1 I=1»NL

PX=0

CALL ABCDP2(PX»K(I) » L ( I ) » R ( I ) » G ( I ) » AP ( I) » BP ( I ) » CP ( I ) » DP ( I ) . IM

)

1 CALL ABCD2(PX»K(I) ,L(I) »R(I) »G{I) »A(I) »B(I) »C(I) »D(I) »IM.l)

IF(NL.LT.2) GO TO 502

CALL OERVT(A»B»C»D» AP»BPrCP»DP» APP»BPP»CPP»DPP»NL)

GO TO 503

502 APPrAPd)

BPP=8P(1)

CPP=CP( 1

)

DPP=DP{ 1 503 IF(IS.NE.2) GO TO 501

IF(IM.EQ.O) GO TO 501

CALL SOLID(0.»R(1)»KG»AG»IM»HF»HFP)

ZRK 1) = (-CPP+HFP*AX)/DX/DT

ZR2( 1)=-ZR1 (1)

1100 F0RMAT(1F20.5)

GO TO 1212

501 RAP(1)=DPP

RAP(2)=0.

RAP(3)=APP

DO 2 I=lf3

C1=RAP( I )/BX/DT

C2 = RB{I)*RPP/BX/Bx/DT

ZR2( I )=-Cl+C2

2 ZR1(I)=-ZR2(I)+RB(I)/BX

1212 CONTINUE

100 FORVIAT(3F20.6)

C ROOTS OF B(P)=0.

212 NV|AX=10

IF(I5.EQ.2.AND.IM.NE.O) NMAX=100

PX=0.001

DPO=0.1/DT

IF{ IS.EQ.2. AND. IM.NE.O) DP0=3. im6*3. l'+16*AG/R ( 1 ) /R ( 1 ) *0 .25

DLX=0.0001

IF { IS.EQ.2. AND. IM.NE.O )DLX=DP0/ 1000

79
N=0

11 DL=DPO

CALL ABCD2(PX»K»L»R»G» AX»BX»CX»DX» IV!»NL)

IFdS.EQ.a.AND.IM.NE.O) CALL SOLDX ( PX » R ( 1 ) r KG » AG » IM » BX » DX » TESTl

)

15 PXPzPX+DL

CALL ABCD2(PXP»K»L»R»6»AXP»BXP»CXP»DXP»IM»NL)

IF(I5.NE.2) GO TO 213

IFdM.EQ.O) 60 TO 213

CALL SOLDX (PXPrRd) » KG » AG r IM» BXP » DXP r TEST2

)

IF(TE5Tl*TEST2) 112»113»11'+

111+ PX=PXP

TEST1=TEST2

GO TO 15

112 IF(OL-DLX) 130»130»H7

117 DL=DL/2.

GO TO 15

113 IF(TESTl) lia»119»118

119 RXX=PX

GO TO 31

118 RXX=PXP

GO TO 31

130 AB=AB5(TE5T1/TEST2)

RXX=(PX+AB*PXP)/(1+AB)

GO TO 31

213 IF(BX*BXP) 12»13»1'+

1(+ PX=PXP

BX=BXP

TESTX=PX*DT

IF(TESTX-100. ) 15»43»t+3

12 IF(DL-DLX)30r30f 17

17 DL=DL/2.

GO TO 15

13 IF(BX) 18»19»18

19 RXX=PX

GO TO 31

18 RXX=PXP

GO TO 31

30 AB=ABS(BX/BXP)

RXX=(PX+AB*PXP)/{1.+AB)

31 N=N+1

ROOT(N)=RXX

IF(N.GT.l) DP0=R00T(N)-R00T(N-1)

NRT=N

41 FORMAT(I10»1F20.6)

PX=RXX+DLX

TESTMX = '+0 TESTX=RXX*DT

IF (TESTX-TESTMX)i+2»t|2»43

42 IF(N.LT,NMAX) GO TO 11

43 CONTINUE

DO 600 JJ=1»NRT

PX=ROOT(JJ)

DO 51 J=1»NL

CALL ABCD2(PX»K( J) »L(J)»R(J)rG{J)»A(J)»q(J)»C{J)»D(J)»TM.l)

51 CALL ABCDP2(PX»K( J) »L(J).R(J)»6(J)»AP(J)»BP(J)»CP(J)»DP(J)»IM)

CALL ABCD2(PX»K»L»R»G» AX»BX»CX»DX» IM.NL)

IF(NL.LT.2) GO TO 504

CALL DERVT( A»B»C»Dr AP»BP»CP»DPf APPfBPP»CPP»DPP»NL)

80
GO TO 505

50i| APPzAPd)

BPP=BP( 1)

CPP=CP( 1

)

DPP=DP( 1)

505 IF(IS.NE.2) GO TO 21«l IF(IM.EQ.O) GO TO 2m

CALL S0LID{PX»R(1) »KG» AGr IM»HF.HFP)

IF(HF) 401»i+00»«*01

t^Ol PYS =(HF*AX-CX)/PX/PX/(DPP-HFP*BX-HF*BPP)/OT

GO TO ^02

tfOO PYS=0.

402 RA(lfJJ)=PYS

GO TO 601

214 PY=BPP*PX*PX*DT

RA(1» JJ)=DX/PY

RA(2. JJ)=1./PY

RA(3» JJ)=AX/PY

601 PZ=PX*DT

IF(PZ.LT.<+0. )G0 TO 52

RX{ JJ)=0»0

RY( JJ)=1.0E30

GO TO 600

52 RX( JJ)=EXP(-PZ)

5 RY( JJ)=(1.-EXP(PZ) )**2

600 CONTINUE

54 FORMAT(4F20.6)

DO 154 JJ=1»NRT

DO 154 M=1»M3

ZR1(M)= RA(M» JJ)*RX( JJ)+ZR1(M)

I54 ZR2(M)=RA(Mf JJ)*RX( JJ)*{RX( JJ)-2. )+ZR2(vi)

11 = 1 111=2

80 FORVIAT{50H0 RESPONSE FACTORS OF FINITE SLAB ) 81 FORMAT(120H0 J X(J) Y(J)

1 Z(J) ) 701 FORMAT(120H1 RESPONSE FACTORS FOR SOLID CYLINDRICAL OrJECTS

1 ) 702 FORMAT(120H1 RESPONSE FACTORS FOR SOLID SPHERICAL ORJECTS

1 ) IF(ZR1 (2) .LT.O) ZR1(2)=0.

DO 67 M=lfM3

ZRK(V|»1)=ZR1(M)

67 ZRK(M»2)=ZR2(M)

55 F0RV1AT( I10»3F20.6)

NT=100

DO 58 N=3»NT

NR=N

DO 61 Mrl»M3

61 ZRK(M»N)=0.

DO 57 M=lfVI3

DO 57 JJ=1»NRT

PZ=(RX( JJ) )**N

57 ZRK(MrN)=ZRK (M»N)+PZ*RY( JJ) *RA{M» JJ)

IF(N.LT.5) GO TO 58

TEST1=ZRK(1»N)/ZRK(1»N-1)

TEST2=ZRK(lf N-l)/ZRK(l»N-2)

TEST3=ABS(TEST1-TEST2)

81
IF(TE5T3-0. 00001) 59»59»58

58 COMTINUE

59 DO 60 N=1»NR

X(N)=ZRK(1»N)

Y(N)=ZRK(2»M)

60 Z(1nI)=ZRK (3»N)

CR=TEST2

62 FORMATdOHO CR=1F10.6)

IF( IS.EQ.2.AND.IM.EQ.0) GO TO 800

IF(IS.NE.l) GO TO 900

901 IF(NL.EO.O) GO TO 905

GF=2*KG/SQRT(DT*AG*PI

)

IF(NR.LT.50) GO TO 610

DO 201 J=50»NR

ZJ=J

201+ AZ( J)=GF*(SQRT(ZJ)-2.*5QRT(ZJ-1. )+S0RT(ZJ-2. ) ) NRR=NR

GO TO 300

610 DO 301 J=NRr50

Z( J+1)=Z( J) CR

X( J+1)=X( J)*CR

301 Y( J+1)=Y{ J)*CR

NRR=50

300 DO 205 J=1»NRR

205 F( J)=X(J)-Y( J)*Y( J)/(Z( J)+AZ( J)

)

NR=NRR

GO TO 906

905 DO 90«+ J=1»NR

904 F(J)=AZ(J)

906 CONTINUE

207 FORVIAT(50HO J F ) CR1 = 1.

DO 208 J=l»50

CR=F{ J+l)/F( J)

TESTCR=ABS(CR-CR1)

IF(TE5TCR-0. 00001) ^Ilr611»6l2

612 CR1=CR

JJ=J-1

208 CONTINUE

209 FORMAT( 1I10» 1F20.5)

611 NR=J

CR=CR1

GO TO 900

800 CONTINUE

DO 210 J=1»NR

F( J)=2*Y( J)-{X( J)+Z( J)

)

JJ=J-1

210 CONTINUE

900 RETURN

END

82
SUBROUTINE DERVT ( A » B » C r D » AP » BP » CP » DP r APP » BPp » CPP , DPP » N

)

C COMPUTES DERIVATIVE OF MATRIX ELEMENTS FOR PLAiME LAYER

DIMENSION A(N) »B(N) »C (N) »D(N) » AP(N) »BP(N) »CP(N) »nP(N) » AT( in) f HT( 10

1) »CT( 10) f DT( 10) » ATT( 10) »BTT( 10) »CTT( 10) »DTT(10)

DO 1 I=1»N

DO 2 J=1»N

IF(I.EQ.J) GO TO 3

AT( J)=A( J)

BT( J)=B{ J)

CT( J)=C( J)

DT(J)=D(J)

GO TO 2

3 AT(J)=AP(J)

BT( J)=BP( J)

CT( J)=CP( J)

DT(J)=DP(J)

2 CONTINUE

1 CALL MULT(AT»BT»CT»DT»ATT(I)»BTT(I)»CTT(I)»DTT(I)»N)

APP=ATT(1)

BPP=8TT(1)

CPP=CTT(1)

DPP=DTT( 1)

DO ^ I=2rN

APP=APP+ATT( I

)

BPP=BPP+BTT( I CPP=CPP+CTT( I)

If DPP=DPP + DTT( I)

RETURN

END

SUBROUTINE ABCD2 ( Z » K » L » R » G » A » B » C » D » IM» NL)

C COMPUTES MATRIX ELEMENT FOR MULTI-LAYER PLANE AS SHOWN IN TABLE I C OF KUSUDA'S PAPER

DIMENSION AX(10)rBX(10)»CX(10)»DX(10)»R(10)»G(10)

DOUBLE PRECISION D3E J» OBEY » ZQl » ZQ2

REAL K(10) »L(10) » JOl. J02» Jll» J12

PI = 3.im5927

PP=PI*0.5

IF(NL.LT.2) R(2)=R(1)+L(1)

DO (+ I = 1»NL

IF(G(I)) 103»103»102

102 IF{Z) 1»1»101

101 ZQ=SQRT(Z/G(I)

)

ZQlrZQ*R(I)

ZQ2=ZQ*R( I+l)

ZQL=ZQ*L(I)

IF(IM.NE.l) 60 TO 3

J01=DBEJ(ZQ1»0)

J11=DBEJ(ZQ1»1)

J02=DBEJ(ZQ2»0)

J12=DBEJ(ZQ2»1)

83
Y01 = DE3EY{ZQ1 »0)

Yll=DBEY(ZQlrl)

Y02=DBEY(ZQ2»0)

Y12=DBEY(ZQ2»1)

AX( I )=-PP*Z02* ( J01*Y12-Y01*J12)

BX( I)=PP*R(I + l)/K(I)*(-Y01*J02-f J01*Yn2)

CX(I)=K(I)/R(I+1)*{-J11*Y12+Y11*J12)*PP*ZQ2*ZQ2

DX( I )=PP*ZQ2*( J11*Y02-Y11*J02)

60 TO

3 C0=5IN<ZQL)

C1=C05(ZQL)

S1=C0/Z0L

52=(51-C1)/ZQL/ZQU

IF(IM.EQ.2) GO TO 5

AX(I)=C1

BX(I)=L(I)/K(I)*S1

CX ( I ) =-ZQL*K ( I ) /L ( I ) *C0

DX(I)=C1

GO TO 4

5 GM=R( I+l )/R( I)

AX ( I ) =GM* ( C 1-L { I ) /R ( I+l ) *S1

)

BX(I)=L(I)/K(I)*GM*51

CX(I)=L(I)*L{I)/R(I)/R(I)*K(I)/L(I)*(-(Z01*ZQ2+l)*Sl+Ci

)

DX < I ) =GM* { C 1 +L ( I ) /R ( I ) *S1

)

GO TO 1+ 1 AX(I)=1.

CX(I)=0.

DX(I)=(R(I+1)/R(I) )**IM

IFdM.EO.O) BX(I)=L{I)/K(I)

IF(IM.EQ.l) BX(I)=R(I+1)/K(I)*L0G(R(I+1)/R(I)

)

IF(IM.E0.2) BX(I)=L(I)/K(I)*(R(I+1)/R(I)

)

GO TO 4

103 AX(I)=1.

BX(I )=1/K( I

)

CX(I)=0.

DX(I)=(R(I+1)/R(I) )**IM

t+ CONTINUE

A=AX(1)

B=BX(1)

C=CX(1)

D=DX(1)

IF(NL,LT.2) GO TO 6

CALL MULT(AXrBX»CX»DX» A»B»CrD»NL)

6 RETURN

END

84
SUBROUTINE ABCDP2(Z»K»L»R»G» AP»3P»CP»DP» IM)

C COMPUTES MATRIX ELEMENT FOR SINGLE-LAYER PLANE AS SHOWN IN TABLE I C OF KUSUDA'S PAPER

DOUBLE PRECISION ZQl » ZQ2 r DBEJ» DBEY

REAL K»L» JOlf J02» Jll» J12

PI=3. 1415927

IF(G) 103fl03»10'+

lOii PP=PI/«+./G

IF(Z) 101»101rl05

105 ZO=SQRT(Z/G)

ZQL=ZQ*L

ZQ1=ZQ*R

ZQ2=ZQ1+ZQL

IF(IM.NE.l) GO TO 3

X=R* (R+L)

Y=(R+L)**2

Z1=(R+L)/K

J01=DBEJ(ZQ1»0)

J02=DBEJ(ZQ2»0)

J11=DBEJ(ZQ1»1)

J12=DBEJ(ZQ2» 1)

Y01=DBEY(ZQ1»0)

Y02=DBEY(ZQ2»0)

Y11=DBEY{ZQ1»1)

Y12=0BEY(ZQ2»1)

AP=(-X*( J11*Y12-Y11*J12)+Y*( J01*Y02-Y01*J02) )*PP

BP=(X*( Jll*Y02-Yll*J02) Z1/ZQ2+Y*( J01+Y12-Y01+J12) *Z1/7Q2) PP

CP=PP*ZQ2/Z1*(X*( J01*Y12-Y01*J12)+Y*( JH*Y02-Y11*J02) ) DP=(X*(-J01*Y02+Y01*J02)-Y*(-J11*Y12+Y11*J12) )*PP

GO TO 1 3 X=L+L*0.5/G

R1=R+L

RES=L/K

C0=SIN(ZQL)

C1=C0S(ZQL)

S1=C0/ZQL

S2=(S1-C1)/ZQL/ZQL

IF(IM.EQ.O) GO TO 5

AP=X*(R1*S1/R-L*S2/R)

BP=RES*X*R1*52/R

ZP1=ZQ1

ZP2=ZQ2

CP=X*(L/R)**2/RES+( (2.*R*R1/L/L+1)*S1-{ZP1*ZP2+1. )*S2)

DP=X*(R1/R*S1+(L/R)*(R1/R)*S2)

GO TO 4 5 AP=X*51

BP=X*RES*S2

CP=X*(S1+C1)/RES

DP=X*S1

GO TO H 103 AP=0.

BP=0.

CP=0.

DP=0.

GO TO t+ 101 IF(IM.NE.O) GO TO 6

X=L*L*0.5/G

Ap=X

BP=X*L/K/3

CP=K/L*X*2.

DP=X

GO TO 4

85

497-811 O - 73 - 6
6 IF(IM.NE.l) GO TO 7

R1=R+L

AP=(0.5*(R*R-R1*R1 ) +R1*R1*L0G(R1/R) )*0.5/G

BP=Rl/'+/G/K*{ (R1*R1+R*R) *L06(R1/R)-(R1*R1-R*R) ) CP=K/R*0.5/G* (R1*R1-R*R)

DP=0.5/G*(0.5*(R1*R1-R*R)*R1/R-R*R1*L06(R1/R)

)

GO TO 4

7 X=L*L*0.5/G

R1=R+L

AP=X/3.*(2*R1/R+1.

)

BP=L/K*Rl/R*X/3.

CP=K/L*X*L/R*L/R*( 2. R*Rl/L/L+0. 666667)

DP=X/3.*Rl/R*(Rl/R+2)

1+ RETURN

END

SUBROUT I NE MULT (A»B»C»D»ATfBT»CT»DT»N)

C ROUTINE TO PERFORM MATRIX MULTIPLICATION

DIMENSION A(N) »B(N) »C(N) iD(N)

ATT=A(1)

BTT=B(1)

CTT=C{1

)

DTT=D(1)

IF(N.LT.2) GO TO 3

DO 1 J=2»N

AT=ATT*A(J)+BTT*C( J)

BT=ATT*B( J)+BTT*D( J)

CT=CTT*A( J)+DTT*C(J)

DT=CTT*B( J)+DTT*D( J)

ATT=AT

BTT=BT

CTT=CT

1 DTT=DT

GO TO 4

3 AT=ATT

BT=BTT

CT=CTT

DT=DTT

f+ RETURN

END

86
SUBROUTINE SOL ID ( Z » R 1 » KG » AG » I M r HF » HFP

)

C COMPUTES RESPONSE FACTORS FOR SOLID MATERIAL

REAL KG.JOl'Jll

DOUBLE PRECISION DBEJfZOD

ZQ=SQRT(Z/AG)

ZQ1=ZQ*R1

ZQD=ZQl

ZA=R1*R1/AG

C0N=KG/R1

IF(Z) 2»1»2

2 IFdM.NE.l) GO TO 100

J01=DBEJ{ZQD»0)

TX=ABS(J01)

IF(TX-0. 00001) 4»H»5

5 J11=DBEJ(ZQD»1)

HF=CON*ZQ1*J11/J01

HF1=J11/J01/ZQ1

HF2=( j01*JGl+Jll*Jll-J01*Jll/ZQl)/J0l/Jnl

HFP=-CON*0.5*ZA*(HF1+HF2)

GO TO 300

100 C=C05(ZQ1)

5=SIN(ZQ1)/ZQ1

TX=A3S{SIN(ZQ1 )

)

IF(TX-0, 00001 ) f+f^rS

3 HF=-C0N*(C/S-1)

HFP=-CON*0.5*ZA*(l+C*(C-S)/5/S/ZQl/ZQl)

GO TO 300

1 HF=0.

IF(IM,EQ.2) HFP=-C0N*ZA/3.

IFdM.EQ.l) HFP=-0.'i*CON*ZA

GO TO 300

HF=0.

HFP=0.

RETURN

END

87
SUBROUTINE GPF ( U » ZL » I M » Z

)

C COMPUTES RESPONSE FACTORS FOR GROUND HEaT TRANSFER

DIMENSION Z(IOO) »ZT( 5000) fZS( 5000)

DOUBLE PRECISION DBEJfDBEYrZQ

PI=3. 1415927

SQTPI=SQRT(PI)

PI2=2./PI

EB=0.001

08=0.1

Z(1)=2*ZL*SQRT(U)/SQTPI

ZZ=Z(1)

Z{2)=Z(l)*(SQRT(2.)-2.)

DO 2 K=3»50

ZK = K 2 Z(K)=Z(1 )*(SQRT{ZK)-2.*SQRT(ZK-l)+S0RT(ZK-2. )

)

IF(IM.EQ.O) GO TO 70

IF(IM.EQ.l) GO TO 1 Z(1)=Z(1)+ZL

GO TO 70

1 X=PI2 *LOG(0.5*EB )+0. 36746691

5UN=PI*0.5*( ATAN(X)+0.5*PI

)

IX = 0 B=ER-DB

DO 17 L=l»5000

B=B+DB

R ZQ=B

IF(IX.EQ.IO) GO TO 30

ZJO=OBEJ(Za'0)

ZYO=DBEY(ZQ»0)

TESTX=ZJ0*ZJ0+ZY0*ZY0

TESTY=PI2/B

TESTZ=AB5(TESTX-TESTY)

IF(TESTZ-0. 00001) 30»30»31

31 ZZ=8*B*B*TE5TX

GO TO 32

30 ZZ=B*B*PI2

IX = 10

32 ZT{L)=1./ZZ

LT=L

TEST=ABS(ZT(L) )*10

IF{TEST-0.0001) 11»11#17

17 CONTINUE

11 LTY=LT/2

LTX=LTY*2-1

BMAX=EB+(LTX-1)*DB

BB=1./BMAX

ZJ=1 ./U

SUT=SUN*ZJ

B=EB-DB

DO 28 L=1»LT

B=B+DB

ZB=B*B*ZJ

6 ZP=EXP{-ZB)

28 ZS(L)=(1 .-ZP)*ZT(L)

CALL SiMSCZSrDB »SUMfLTX)

GK=(SUM+SUT)*PI2 +BR

GG=GK*PI2

Z(1)=GG*ZL*U

70 CONTINUE

RETURN

END

88
SUBROUTINE SOLDX ( Z » R 1 » KG » AG » I M » B » D » TEST

)

DUMMY SUBROUTINE

END

SUBROUTINE DBEJ(Xfl)

DUMMY SUBROUTINE

END

SUBROUTINE DBEY(Xrl)

DUMMY SUBROUTINE

END

SUBROUTINE SIMS(XrY»Z»L)

DUMMY SUBROUTINE

END

Appendix E

Input and Output for the Response Factor Program

The Response Factor Program (Appendix D)

analyzes the thermal performance of the inside space

of the experimental building under a prescribed

outdoor air temperature cycle. When the inside air temperature is thermostated, this program calculates the rate of heat loss from the building at pre- scribed time intervals. If the inside building air temperature is not controlled and floats in response

to the outdoor air temperature cycle, the program

then calculates time dependent variations of the

inside building air temperature. Table E-1 contains

a sample set of data input.

A description of the data input is given below:

Card Sequence

1 Time increment of the temperature data in hours

2 Number of roof layers (includes the thermal

resistances of the inside and outside

surfaces)

3 Thermal resistance at inside surface of roof

4 Thickness, thermal conductivity, density,

and specific heat of roof

5 Thermal resistance at outside surface of roof

6 Description of the inside surface of the roof

7 Description of roof

8 Description of the outside surface of roof

9 Number of wall layers

10 Thermal resistance at inside surface of wall

11 Thickness, thermal conductivity, density, and

specific heat of wall

12 Thermal resistance of the outside surface of

wall

13 Description of the inside surface of wall

14 Description of wall

15 Description of the outside surface of wall

16 Number of layers of the floor and the semiinfinite layer index (if basement floor) 17 Thermal resistance at inside surface of floor 18 Thickness, thermal conductivity, density, and

specific heat of the first solid layer of the

floor counted from the inside surface

19 Thickness, thermal conductivity, density, and

specific heat of the second solid layer

20 Thermal conductivity, density, and specific

heat of the earth

21 Description of the inside surface of floor 22 Description of the first solid layer

,23 Description of the second solid layer

24 Description of the semi-infinite earth layer

25 Number of layers for inner mass

26 Thermal resistance at the outside surface of

the interior mass

27 Thickness, density, specific heat, and thermal

conductivity of the internal mass

28 Thermal resistance at the other outside

surface of internal mass

29 Description of the outside surface of interior mass

30 Description of the interior mass

31 Description of the other outside surface of

interior mass

32 Blank card (necessary to show end of above

data)

33 Run No. card

34-37 Outside air temperatures

38-41 Inside air temperatures

42 Roof area, wall area, floor area, inner mass

surface area, air flow (ventilation by air leakage), conductance of door, door area, conductance of window, window area, ground temperature, average inside air temperature.

Components possessing significant heat capacity

(such as walls, roof, etc.) are described in cards 2 through 31, while components having negligible heat

capacity are described on card 42. Some various

options available in the Response Factor program

are discussed below.

Additional layers can be readily handled. For

example, if the roof contains a second layer, then

the number of layers given in card 2 would be in- creased to four. Also, a card giving the thermal and

physical properties of this additional layer and a card giving a description of this layer would be

inserted in proper sequence (from inside to outside).

Additional layers in any component would be handled

in a similar manner. If the additional layer is an

air insulating layer, then only an average value of

the thermal resistance of the air layer would be

specified on the card giving layer properties.

Another option is a floor which has no semi-infinite

layer (such as the floor of a room of a multistory

building). This case may be handled by omitting the

semi-infinite layer index on card 16 and removing

the card giving the properties of the earth and the

card giving the layer description of the earth. Another option is the case of a building without a component (such as a building without windows).

This case is handled by setting the area of that component (given on card 42) equal to zero. And finally,

the option for determination of the inside building

air temperature (floating test) is handled by inserting

four blank cards for the inside air temperature

(cards 38 through 41). The computer printout for tests 6, 7, and 10 are found in tables E-2, E-3, and E-4, respectively. The

first page of each table gives the test number, out- side air temperature cycle, the inside air temperature cycle (if thermostated), and the data input given on card 42. The second page gives the description

and composition of each building component having

significant heat capacity. The third page of the print- out gives the inside and outside air temperatures,

the heat losses from the building at the inside sur- faces of the building components, the air infiltration loss, and the net heat loss from the room at pre- scribed time intervals, in Btu h^'. 91
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FORM NBS-n4A (1.71) U.S. DEPT. OF COMM. PUBLICATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA rcc / <; SHEET NBS BSS-45

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Dynamic Thermal Perforaance of An Experimental Masonry

Building

5. Publication Date July 1973

6. Performing Organization Code

7. AUTHOR(S)

B. A. Peavy, F. J. Powell, and D. M. Burch

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMFNT OF rOMMFRTF

WASHINGTON, D.C. 20234

10. Project/Task/ Work Unit No. 4624134

11. Contract/Grant No.

12. Sponsoring Organization Name and Address National Bureau of Standards

Department of Housing and Urban Development

Washington, D. C. 20410

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15, SUPPLEMENTARY NOTES

16- ABSTRACT (A 200*word or less factual summary of most significant information* If document includes a significant

bibliography or literature survey, mention it here.) Measurements of the dynamic heat transfer in an experimental masonry building were

made in a large environmental chamber to explore the validity of a computer program

developed at NBS, labeled NBSLD, for computing heating and cooling loads, and indoor

air temperatures. This study was jointly supported by the National Bureau of Standards

and the Department of Housing and Urban Development, and is a part of a broader research

program being supported by both agencies to improve performance test procedures and

criteria for housing.

The experimental structure was a one-room house 20' long, 20' wide, and 10' high with

walls of solid concrete blocks and a flat roof made of reinforced precast concrete slabs

During the tests changes were made in fenestration, the amount and location of insulation, and the indoor mass; and the building was exposed to a diurnal temperature cycle.

It was found that the combination of mass in the masonry walls and roof, and insulation placed on the outside of the masonry was very effective in reducing and con- trolling the variation of indoor air temperature. The NBSLD computer program realistically predicted the heat storage effects, and maximum heating loads during these tests.

For five heating tests, the greatest difference between computed maximum heating load

and measured values was 8 percent and the average difference was 4.3 percent. It was

shown that steady-state methods of heating load calculation could result in oversizing

heating equipment by 30 percent or more for this particular building and imposed exterior conditions if the lowest outdoor temperature was selected as the design temperature.

17. KEY WORDS (Alphabetical order, separated by semicolons) Building heat transfer; Computer programs;

dynamic thermal performance; heat flow analysis; heating and cooling loads; temperature

predictions; thermal analysis; thermal behavior; transient heat flows.

18. AVAILABILITY STATEMENT 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

fxl UNLIMITED.

UNCL ASSIFIED 103

1 1 FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

20, SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price S1.25

USCOMM-DC 66244.P71

U. S. GOVERNMENT PRINTING OFFICE : 1973 O - 497-811
Announcement of New Publications in

Building Science Series

Superintendent of Documents,

U.S. Government Printing Office,

Washington, D.C. 20402

Dear Sir:

Please add my name to the announcement list of new publications to be

issued in the series : National Bureau of Standards Building Science Series.

Name

Company . . .

Address

City State Zip Code

(Notification key N-339)
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system

with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry,

and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Nuclear

Sciences ' — Applied Radiation ^ — Quantum Electronics — Electromagnetics ' — Time

and Frequency ^ — Laboratory Astrophysics " — Cryogenics \

THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized

materials needed by industry, commerce, educational institutions, and Government; provides

advisory and research services to other Government agencies; and develops, produces, and

distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials and the following divisions: Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor

Radiation — Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to promote

the use of available technology and to facilitate technological innovation in industry and Government; cooperates with public and private organizations leading to the development of

technological standards (including mandatory safety standards), codes and methods of test; and provides technical advice and services to Government agencies upon request. The Institute consists of a Center for Building Technology and the following divisions and offices: Engineering and Product Standards — Weights and Measures — Invention and Innovation — Product Evaluation Technology — Electronic Technology — Technical Analysis — Measurement Engineering — Structures, Materials, and Life Safety* — Building

Environment * — Technical Evaluation and Application * — Fire Technology.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effec- tiveness in the conduct of their programs through the selection, acquisition, and effective

utilization of automatic data processing equipment; and serves as the principal focus within

the executive branch for the development of Federal standards for automatic data processing

equipment, techniques, and computer languages. The Center consists of the following offices and divisions: Information Processing Standards — Computer Information — Computer Services —

Systems Development — Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and

a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum

accessibility to the scientific information of the world. The Office consists of the following

organizational units: Office of Standard Reference Data — Office of Technical Information and Publications —

Library — Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

' Part of the Center for Radiation Research.

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* Part of the Center for Building Technology.
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