NECAP - NASA'S ENERGY-COST ANALYSIS PROGRAM Part II ...NECAP - NASA'S ENERGY-COST ANALYSIS PROGRAM Part II - Engineering Manual R. H. Henninger, Editor Prepared by "GENERAL AMERICAN

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NECAP - NASA'S ENERGY-COST ANALYSIS PROGRAM

Part II - Engineering Manual

R. H. Henninger, Editor

Prepared by

"GENERAL AMERICAN TRANSPORTATION CORPORALr- "J

Nites, 111. 60648 C. /. >

for Langley Research Center

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTO

NO- 19753

eitnicai Library' '

MBER 1975

https://ntrs.nasa.gov/search.jsp?R=19760003664 2020-07-14T22:33:16+00:00Z

TECH LIBRARY KAFB, NM

1. Report No.

NASA CR-2590

2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

NECAP - NASA's Energy-Cost Analysis ProgramPart II - Engineering Manual

5. Report DateSeptember 1975

6. Performing Organization Code

7. Author(s)

Editor - R. H. Henninger8. Performing Organization Report No.

10. Work Unit No.9. Performing Organization Name and Address

General American Transportation Corporation.General American Research Division7449 North Natchy AvenueNites, IL 60648

11. Contract or Grant No.

NAS1-12843

12. Sponsoring Agency Name and Address

National Aeronautics & Space Administration

Washington, DC 20546

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

15. Supplementary Notes

The Technical Monitor for this project was Ronald N, Jensen, The members of the GHRD's TechnicalStaff were Messrs. R. H. Henninger, J. T. McNally and R. W, Wallace.Final report. -

16. Abstract

The NASA's Energy-Cost Analysis Program (NECAP) is an extremely powerful and sophisticatedcomputerized system to determine and minimize building energy consumption^'

The program complies with ASHRAE's "Procedures for Determining Heating and Cooling Loadsfor Computerized Energy Calculations" manuTT ITTalculate's tfie thermoriynamic heal'gaTnsand losses of a structure, taking accound of the building's thermal storage and hourlyweather data. It uses new weighting factors for building lightsj and environmental equipmentschedules. Infiltration is allowed to vary in accordance to wind velocity. Internal temperatureare allowed to vary when equipment capacity is scheduled or does not meet loads, Standard wallsand schedules can be used to simplify program input. System simulation models systems now ingeneral use.

Users of NECAP can obtain data for selection of the most economical system, system size, fuels,window area, thermal barries, etc,,' during the design phase. After installation, users canoptimize operating schedules, most economical temperature settings for components, and othervaluable data.

17. Key Words (Suggested by Author(s))

Calculation of building thennodynamicheat gains and losses

18. Distribution Statement

Unclassified — Unlimited

Subject Category 61 Computer Programming

and Software

19. Security Classif. (of this report)

Unclassified20. Security Classif. (of this page)

Unclassifiad21. No. of Pages 2. Price*

$9.50

For sale by the National Technical Information Service, Springfield, Virginia 22161

This version of NASA's Energy-Cost Analysis Program (NfCAP)Is for Internal NASA use.

The National Aeronautics and Space Administration (NASA)can not assume any responsibility for the application ofthe manual or the program beyond the control of itsengineers. Users that apply the program do so withoutrecourse to the Government.

TABLE OF CONTENTS

Section Page

1 INTRODUCTION . .. . . . . . .,. .. . . ..... 1-1

2 'RESPONSE FACTOR PROGRAM . . . '^ . . ... ... ,.'..'...'... 2-1

2.1 Objective and Description .......... . . 2-12.2 Algorithms of Subroutines 2-1

3 THERMAL LOAD ANALYSIS PROGRAM 3-1

3.1 Objective and Description 3-13.2 The Convolution Principle 3-63.3 Main Routine Algorithms 3-11

3.3.1 Building Input Segment 3-113.3.2 Calculate Heat Transfer Through

Internal Partitions 3-143.3.3 Job Processing Control Segment 1 3-143.3.4 Hourly Energy Analysis Segment 3-143.3.5 Job Processing Control Segment 2 3-22

3.4 Algorithms of Subroutines 3-23APOL 3-23CCM 3-24CENTER 3-26DAYMO 3-26DST 3-28DESDY 3-29FILM 3-34HD 3-35HL 3-37HOLDAY 3-40HQ 3-41INPUT1 3-42INPUT2 3-43INF 3-46LEEP 3-47MATCON 3-47MONFIN 3-50NDOW 3-51PSY & PPWNVMS 3-52QMAX 3-54

iii

TABLE OF CONTENTS(continued)

Section PageRECTAN , , . 3-58RECAP1 3-60RECAP2 3-61REPRT1 3-64REPRT2 3-67REPRT3 3-68REPRT5 3-68REPRT6 3-71RMRSS 3-81SCHDUL 3-86SCHED 3-87SEARCH 3-89SETBK 3-89ASHADOW 3-90SHG 3-94STNDRD 3-96SUN1 3-113SUN2 3-116SUN3 3-120TAR 3-125WBF 3-128WEATHER 3-129

4 VARIABLE TEMPERATURE PROGRAM 4-1

4.1 Objective and Description 4-14.2 Input 4-14.3 Output 4-24.4 Main Routine Algorithms 4-11

5 SYSTEM AND EQUIPMENT SIMULATION PROGRAM • . . 5-1

5.1 Objective and Description 5-15.2 Main Routine Algorithms 5-55.3 Algorithms of Subroutines 5-29

CDATA 5-29TDATA 5-29FSIZE 5-30MZDD 5-37SZRHT 5-44FHTG2 5-50FCOIL 5-54INDUC 5-59

. VARVL 5-67RHFS2 5-74FANOF 5-81ZL03 5-84BRAD2 5-87AHU 5-89MXAIR 5-93ECONO 5-95CCOIL 5-97

IV

TABLE OF CONTENTS(continued)

Section Page

TRSET , , , . 5-100PTLD 5-101TEMP 5-103PSYCH 5-107PSY1 & PSY2 , 5-108PPWVM . . . . 5-109HUM! 5-110DENSY , , 5-110MAX , . , . , 5-111ERROR 5-111ALOG1 5-111H20ZN , 5-112WZNEW , . 5-113EQUIP , . . , , , . . 5-114STTUR , 5-123CENT , 5-126RECIP 5-128ABSOR , 5-129SNOWM , , . , . . , , 5-131ENGYC , 5-133HTC0N 5-135

6 OWNING AND OPERATING COST ANALYSIS PROGRAM 6-1

1.1 Objective and Description , 6^11.2 Input 6-11.3 Output 6-11.4 Main Routine Algorithms 6-1

J. •

IN ORDER TO MINIMIZE THE AMBIGUITIES INVOLVED IN MATHEMATICAL

OPERATIONS, THE FOLLOWING FORTRAN OPERATIONAL SYMBOLS ARE USED

PARTIALLY IN THE MAIN BODY OF THIS TEXT.

/ : Division

* : Multiplication

** : Exponentiation

vi

SECTION 1INTRODUCTION

NECAP is a sophisticated building design and energy analysis toolwhich has embodied within it all of the latest ASHRAE state-of-the-arttechniques for performing thermal load calculation and energy useagepredictions. NECAP is actually a set of six (6) individual computerprograms whose descriptions are given briefly below:

1. RESPONSE FACTOR PROGRAM

For wall or roof structures different from the typical onesbuilt into NECAP, the Response Factor Program, using a layer-by-layer description of the surface, will calculate and output theset of response factors required to perform transient heat trans-fer analysis.

2. DATA VERIFICATION PROGRAM

The Data Verification Program interrogates the building descrip-tion input data to check for proper order, range and format ofthe card input data.

3. THERMAL LOAD ANALYSIS PROGRAM

Performs hourly transient heat transfer calculations for eachbuilding space utilizing actual hourly recorded weather, geometryand construction of the building, scheduled internal loads andastronomy of the sun.

4. VARIABLE TEMPERATURE PROGRAM

Corrects the thermal loads calculated above to account fortemperature swings occurring within each space due to thermostataction, equipment capacity and equipment scheduling.

5. SYSTEM AND EQUIPMENT SIMULATION PROGRAM

For a specified type of distribution system allocation and typeof energy conversion equipment, the Simulation Program determinesthe total load on each distribution system, transfers it to theenergy conversion equipment, and based upon part load efficienciesdetermines the building's monthly demand and consumption of allforms of fuels and energy.

6. OWNING AND OPERATING COST PROGRAM

For the expected life of the building, the Owning and OperatingCost Program calculates the expected annual expenditure to ownand operate the building utility systems.

1-1

Each building design and analysis problem might not require use ofall of the 6 programs enumerated above. To illustrate the suggestedsequential use, refer to Figure 1.1.

The remaining sections of this manual deal with each segment ofNECAP and sets forth the algorithms that were programmed into eachsubroutine.

1-2

Figure 1.1 NECAP FLOWCHART1-3

SECTION 2RESPONSE FACTOR PROGRAM

2.1 OBJECTIVE AND DESCRIPTION

the Response Factor Program generates the set of heat transferfactors called response factors required to accurately determinethe transient flow of heat into, through and out of buildingexterior walls and roofs as they react to temperature differencesacross them. These response factors are a function of the type ofmaterials used and their order of placement and therfore requirethat the following be known for each layer:

1. XL, thickness, ft.2. XK, thermal conductivity, BTU per (hr.)(ft.)(°F)3. D, density, Ib. per cu. ft.4. SH, specific heat, BTU per (Ib.) (°F)5. RES, Resistivity, (hr.)(sq.ft.)(°F) per BTU.

Using this data, the Response Factor Program calculates the setof response factors peculiar to the wall or roof construction inquestion and then outputs this data onto punched computer cardsfor direct insertion into the Thermal Load Analysis Program inputdata deck. The Response Factor Program need not be used if allwall and roof types desired are among the standard walls and roofsbuilt into the Thermal Load Analysis Program and available for usesimply by the calling out of an input code. A flow chart explainingthe use of the Response Factor Program is given in Figure 2.1.

2.2 ALGORITHMS OF SUBROUTINES

RESFACand

PER. FALSE. MATRIX, SLOPE, ZERO

The calculation of the response factors involve a matrix-typesolution of the Laplace transform of the heat conduction equationand inversion integral using the residue theorem, detail of whichcan be found in:

1. "Conduction of Heat in Solids", by H. S. Carslaw andJ. C. Jaeger, Second Edition, p. 326.

2. "FORTRAN IV Program to Calculate Heat Flux Response Factorsfor a Multi-layer Slap", by G. P. Mitalas and J. G. Arseneault^NRC, June 1967.

3. "Thermal Response Factors for Multi-layer Structures of VariousHeat Conduction Systems", by T. Kusuda, ASHRAE, January, 1969.

2-1

i

/ASSEMBLEf WALL ANDI ROOF DATA

! i/PREPARE

DATA FORSURFACE TYPE

1i

/PREPAREDATA FORSURFACE TYPE

2

('PREPAREDATA FORSURFACE TYPE

N

* 1 ^ '

RESPONSEFACTORPROGRAM

| SURFACE N

| SURFACE

REPORTFORSURFACE 1

^>— ^

2

—

\ /SURFACE N

SURFACE

1

PUNCHEDOUTPUTSURFACE 1

Figure 2.1 RESPONSE FACTOR PROGRAM FLOWCHART

2-2

INPUT

NOC : Number of surfaces to be analyzed

NOL : Number of layers to be considered for the analysisof the particular wall or roof

XK-. : Thermal conductivity of each layer, Btu/hr-ft-°FIf the layer was no thermal mass, XK. = 0where i = 1, 2, . . . , NOL '

D. : Density of each layer, Ib/cu ftIf the layer has no thermal mass, D. = 0where i = 1, 2, .... NOL 7

SH1 ? Specific heat of each layer, Btu/lb-°FIf the layer has no thermal mass, SH. = 0where 1 * 1 , 2 NOL 1

XL.- : Thickness of each layer, ftIf the layer has no thermal mass, XL. = 0where i = 1, 2 NOL 1

RES., : Thermal resistance of the layer which has no thermal1 mass, hr-sq ft-°F/Btu

If the layer has thermal mass, RES. = 0where i = 1, 2, . . ., NOL

DT : Time increment for the response factors calculation(set to 1 in program), hr.

The sequence of inputting the values of above properties is impor-tant. It must follow the way each layer is laid one after anotherfrom the outside or exterior surface to the inside air. It shouldbe noted that when the inside surface heat transfer coefficient FIIs constant, it can be included as a single resistance on the insideof the last layer of wall.

Response factors series for j = 1, 2, . . ., M wherethe value of M, number of the factors in the series,depends upon the type of wall, roof or overhang floorconstructionCommon ratio between successive terms of each seriesbeyond M calculated by

CR = XMfl/XM = Vl/YM = ZM*1/ZM2-3

Definitions of X, Y and Z Response Factors

Consider the wall in Figure 2.2 and assume that the heat flow rateinto side A is Q., and the heat flow rate out of side B is (L.

B

Figure 2.2 A WALL

If a unit pulse of temperature is applied to side A at time zero,the values of QA at times 0, 1, 2, . . . are called, respectively,XQ» Xl» Xg, . . . and the values of QB at times Ovi 1,2,.. .arecalled, respectively Y0, Y-j, ¥2 ....

If a unit pulse of temperature is applied to side B at time zero,the values of Qg at times 0, 1,2, .-. . are called, respectively,ZQ, Z-,, Z2». . • and the values of Q/\ at times 0, 1, 2, . . . arecallea, respectively YQ, Y,, Y'p. ....

Therefore:

The time series XQ, Xj, X2, X3 .. .. ., or more briefly, X. is the

heat flux at A due to a temperature disturbance at A.

The time series ZQ, Z^, Z2, Z3 . . ., or more briefly, Z, is the

heat flux at B due to a temperature disturbance at B.

The time series YQ. Y-|» Y2* Y3 ' ' " or more Drief^y» Y» s tne

heat flux at either side of the wall due to a temperature disturbance

at the other side.

These definitions are shown schematically in Figure 2.3

2-4

Unit Pulse at A

Unit Pulse at B

Figure 2.3 MEANING OF X, Y AND Z

2-5

SECTION 3THERMAL LOAD ANALYSIS PROGRAM


The Thermal Load Analysis Program, a complex of heat transfer,psychrometric, and geometric subroutines, computes the thermalloads, both heating and cooling, resulting in each building spaceeach hour due to:

1. Transmission gains and losses through walls, roofs, floorsand windows.

2. Solar gains through windows.

3. Internal gains from people, lights and building equipment.

4. Infiltration gains and losses due to wind and thermal pressuredifferences across openings.

5. Ventilation air gains and losses due to fresh air requirements.

Using these capabilities, the Thermal Load Analysis Program can per-form two types of analysis:

1. Design load analysis - Utilizing user-defined design weatherdata, a 24-hour design day analysis is done for each month todetermine peak heating and cooling requirements for each spaceand the entire building.

2. Hourly energy analysis - Utilizing actual hourly weatherdata, hourly heating and cooling loads for each space arecalculated for an entire year of building operation andresults stored on magnetic tape for use by other programs.

The input to the Thermal Load Analysis Program reflects buildingarchitecture, building construction, building surroundings, localweather, and pertinent astronomy of the sun. The output consists ofhourly weather and psychrometric data and hourly sensible loads,latent loads, return air lighting loads, and equipment and lightingpower consumption for each building space. All calculations areperformed in accordance with algorithms set forth by ASHRAE in theirpublication entitled "Procedures for Determining Heating and CoolingLoads for Computerized Energy Calculations". Figure 3.1 briefly depictsthe overall methodology built into the Thermal Load Analysis Program.Table 3.1 gives a brief description of each subroutine making up theprogram.

3-1

INPUT PROGRAM FUNCTION OUTPUT

r BUILDINGDESCRIPTIONCARD INPUT

HEATHERTAPE

( BEGIN )

ÎNPUT SEGMENT:

READ AND ORGANIZEINPUT DATA

IINTERNAL PARTITION HEAT TRANSFER

IJOB PROCESSING

CONTROLSEGMENT-!

JHOURLY ENERGYANALYSIS SEGMENT

JOB PROCESSINGCONTROL

SEGMENT-2

I( END

OPTIONALSHADOWPICTURES

OPTIONALHOURLYWEATHER& LOADDATA

SUMMARY REPORTS:• Design Analysist Hourly EnergyConsumptionAnalysis

Figure 3.1 THERMAL LOAD ANALYSIS PROGRAM MACRO-FLOW DIAGRAM

3-2

TABLE 3.1

THERMAL LOAD ANALYSIS PROGRAM SUBROUTINES

Name of theSubroutine Function

APOL

CCM

CENTER

OAYMO

DESDY

DST

FILM

HD

HL

HOLDAY

HQ

INF

INPUT!

INPUT2

LEEP

MATCON

MONFIN

NDOW

PPWVMS

PSY

Calculates area and orientation of an.irregular surface

Calculates cloud cover modifier

Centers the headings of output

Determines the day of month

Determines design day temperature correction factors

Determines Daylight Savings Time

Calculates outside heat transfer film coefficient

Calculates heat gain through slowly respondingsurfaces (Delayed surfaces)

Calculates sensible and plenum return air heatingand cooling load due to a space

Determines holidays of year

Calculates heat gain through quickly respondingsurfaces (Quick surfaces)

Calculates space infiltration air loads

Reads surface geometric data for shading surfaces

Reads surface geometric data for delayed, quickand window surfaces

Determines whether the year is a leap-year

Converts shadow picture matrix for pictorial display

Determines name of month for printing in reports

Determines day of week

Calculates water vapor pressure of saturated air

Calculates psychrometric data

3-3

TABLE 3.1 (CONT'D)

Name of theSubroutine Function

QMAX

RECTAN

RECAP!

RECAP2

REPRT1

REPRT2

REPRT3

REPRT5

REPRT6

RMRSS

SCHOUL

SCHED

SEARCH

SHADOW

SHG

STNDRD

SUN!

SUN2

SUNS

TAR

WBF

WEATHER

Keeps track of space peak heating and cooling loads

Calculates vertex coordinates of a rectangular surface

Echos initial portion of input data

Echos surface geometric description data

Prints title page

Prints weather information page

Prints load tape parameter labels

Prints summary of design day weather

Prints summary of design load results

Calculates room hourly weighting factors

Generates operating schedules for people, lights,and equipment

Assigns proper lighting, people, and equipmentschedules

Limits shadow pictures to certain times and certainsurfaces

Calculates shadow shapes and areas

Calculates heat gain through windows

Generates response data for standard walls and roofs

Calculates daily data on solar radiation

Calculates hourly data on solar radiation

Calculates solar data which depends on orientationof a surface

Calculates glass absorption and transmission factors

Calculates wet-bulb temperature

Decodes weather tape

3-4

There is a difference between thermal load calculation proceduresfor use in the design of the heating and cooling facilities and theprocedures for estimates of energy requirements. The load calcula-tion procedure as described in the 1967 ASHRAE Handbook of Fundamentalsis for the design calculation. It is valid for simplified designconditions that assume steady-state conditions (such as is largelythe case for heating load calculations) or a steady periodic heatflow (as is the case for the cooling load calculation).

The load calculated under these design conditions may be adequatefor sizing or selecting heating and cooling equipment and systems, butit is unsatisfactory for predicting the actual hourly thermal loads.

A good load calculation procedure for the determination of energyrequirements should be able to predict the performance of the buildingheating and cooling system when combined with a total system simula-tion program under actual (randomly fluctuating) climatic and opera-ting conditions.

An important distinction between the design load calculation andenergy calculation, therefore, is that the former uses a singlevalue while the latter generates a series of values or time seriesof thermal loads evaluated at every hour of the year.

Since the load determination of energy requirements involves manymore calculations as compared with an ordinary design load determina-tion, the use of a computer is considered mandatory.

The Thermal Load Analysis Program uses a number of subroutines insteadof a long continuous algorithm. The rationale behind this arrange-ment is as follows:

(1) The subroutine algorithms are easier to describe and under-stand than a long and continuous algorithm of the wholeprogram.

(2) If required, it is easier for the user to alter, delete, orreplace portions of his load calculation program.

(3) Many of the subroutine algorithms can be made independentlyavailable for many other heat transfer problems such ascalculation of refrigeration load, heating and cooling ofsolid objects, temperature rise of a building wall duringfire, propagation of smoke within a building and design ofexterior shading devices of buildings.

The basic scheme of the load calculation procedure is first toevaluate the instantaneous heat gains due to solar radiation andheat conduction as accurately as possible. These heat gains arethen balanced with those due to infiltration, lighting and other

3-5

internal sources with a specific consideration that the sum of all ofthe instantaneous heat gains is not the instantaneous cooling load.

The solar radiation is first absorbed by solid objects in thespace and is not manifested as a cooling load until some time later.Exact evaluation of the space cooling load requires solution of aset of the heat "balance equations for all the space surfaces, spaceair and space heat gains.

In order to simplify this calculation procedure, the weightingfactor concept is introduced in such a manner that each heat gaincontributes to the space cooling load through its own weightingfactors.

3.2 THE CONVOLUTION PRINCIPLE

The program takes account of heat storage in the building's struc-ture by a mathematical device called the convolution principle. Theexample of heat gain through a thick wall will illustrate how theconvolution principle works.

The value of heat gain (Q) into the building through a thick wall,for a constant inside air temperature, depends on the present value,and the past history, of the temperature difference (AT) betweenthe inside air and the outside surface of the wall. In other words,the graph of the schedule of Q versus time (t) depends on the graphof the schedule of AT versus t (see Figure 3.2).

0) H9 9> H3 O OJ-P O >

t<U -H

EH P

.V 01JH 0<M JH

O

Time, t Time, t

Figure 3.2 DEPENDENCE OF HEAT (SAIN SCHEDULE ONTEMPERATURE DIFFERENCE SCHEDULE

3-6

Were it necessary to compute Q for each hour, on the basis of thehourly history of AT, the differential equation of heat conductionwould have to be repeatedly solved by numerical methods, and thecomputation time would be prohibitive even with a fast computer.Fortunately, the problem can be simplified so that Q need bedetermined as a function of t for only one temperature differenceschedule. The one temperature difference schedule for which theprogram must compute a heat gain schedule is called the triangularpulse, and the values of Q which the triangular pulse elicits, atsuccessive equal time intervals after the peak of the pulse, arecalled the response factors (rn,-r, , r9, . . .) of the wall(see Figure 3.3). u i <:

Any arbitrary schedule of AT may be squared off to give a scheduleof approximate temperature differences, AT1 , whose values agree withthose of AT at integral multiples of the time interval, 6. Thisschedule of approximate temperature differences, AT1, may be resolvedinto a series of triangular pulses (AT-|, AT?, AT3, AT4, and ATs) which,when added together, give exactly AT1. Each of these component pulseshas a base width, or duration, of 26, a peak occurring at each integralmultiple of 6, and a height equal to the value of AT' at the time ofthe pulse's peak. Each such pulse alone would elicit its own scheduleof heat gains as shown in Figure 3.4. The pulse AT2 would elicit Q2and so on. The heat gain schedules elicited by the individual pulsesare all the same except for two differences. Their heights are pro-portional to the heights of the pulses which elicit them, and eachis moved to the right, on the time axis, as far as the pulse whichproduced it.

The values of the individual responses, Q-j . . . Q5, may be addedat each value of time, to give the curve of sums. A mathematicalprinciple known as the superposition theorem asserts that thecurve of sums is exactly the heat gain schedule which would beelicited by the approximate temperature difference schedule, AT'.Due to the smoothing effect of the heat transfer process, AT andAT1 give nearly the heat gain schedule elicited by the originaltemperature difference schedule, AT. This method of resolution andrecombination is called the convolution principle.

To the air conditioning engineer, the convolution principle meansthat the difficult problems of transient heat transfer can be solved,for each simulated hour, by adding and multiplying very few numbers.The convolution principle as applied to heat gain through a thickwall, is expressed mathematically by the equation.

where Q-j equals the heat gain at the hour J;Alj_.j equals the tempera-ture difference i hours previous to hour j; r-j equals the ith response

3-7

o:

IUJ(T

5

I!<O'NIVO 1V3H

UJo<

fe

UiQ.5UJ

•»

IU

UJO

|OIII-

o:3

oCOz '

" "oI- I-

C0

QC LU

oLU O._l CO3 UiootfUIac CD<_> zto i-i

3"UI

oca.

CO

a>vo

CM O

3-8

tr\ FIGURE Q

TIME

AT'

ACTUAL AT SCHEDULE ACROSS WALL

FIGURE b

TIME

APPROXIMATE AT SCHEDULE

FIGURE C

TIME

THE COMPONENT PULSES

AT,

FIGURE d

FIRST COMPONENT PULSE AND HEAT GAIN IT ELICITS

"lA FIGURE eTIME TIME

SECOND COMPONENT PULSE AND HEAT GAIN IT ELICITSo,

A FIGURETIME TIME

THIRD COMPONENT PULSE AND HEAT GAIN IT ELICITS

A FIGURE g JTIME TIME

FOURTH COMPONENT PULSE AND HEAT GAIN IT ELICITS

AT5<

A FIGURE hTIME TIME

FIFTH COMPONENT PULSE AND HEAT GAIN IT ELICITS

FIGURE i

CURVE OF SUMS

TIME

Figure 3.4 THE CONVOLUTION PRINCIPLE

3-9

factor for the wall; and n equals the number of hours of the tempera-ture difference history which significantly effect Qj. Notice thatthe response factors are the only information about the wall whichappears in equation 1. Thus, the response factors, characterizecompletely the thermal properties of the structure of the wall and,alone describe'how the structure-'absorbs and releases heat over aprolonged period of time.

The program allows the user to specify either actual thermal data -that is, layer by layer thicknesses", conductivities, and specificheats - which the program will convert to response factors, or theresponse factors themselves. Tables of response factors are nowavailable for a variety of structures. Where neither the layerby layer thermal data nor the response factors of a wall or roof areknown, a feature is available to generate approximate responsefactors from these simplified data: U-factor conditions (summer orwinter to which the U-factor applies; material of outside layer, andthickness of insulation, if present. The wall and roof constructionsubroutine works by selecting a wall or roof construction from astored library of constructions standardized by ASHRAE, to fit thesimplified data. The load program uses the response factors ofthe selected construction.

A cost saving feature of the Load Program is the use of asubtle modification of equation 1 which allows n to equal infinitywhile saving a good deal of computer time. That is, all previoushours of the temperature difference schedule are taken into account -very inexpensively.

The Load Program uses the convolution principle for the followingthree purposes.

1. To compute the exterior surface temperature of a thick wallat each simulated hour on the basis of past temperatures andpresent radiation and convection data.

2. To compute heat gain as already described.

3. To compute the time delay between heat gain to a space andthe resulting loads on the air conditioning system. In thislast case, the series of numbers which characterizes thestructures (room furnishings, floors, partitions) are calledroom weighting factors, rather than response factors.

To summarize, the convolution principle is used by the thermal loadanalysis program to simulate, with great accuracy, the transient heatconduction taking place within the structures of the building. Variousexperiments with the program indicate that the convolution principle,when used in heating and cooling load calculations, gives more realisticvalues of the maximum loads and more accurate estimates of the timesof their occurrence. For example, the program shows that maximum

3-10

cooling loads occur several hours after the hottest time of the day,at which time some buildings are unoccupied. For practical purposes,this means that the equipment specified with the help of the programwill be smaller than equipment specified as a result of hand compu-tation, and that the elusive demand figures for utility services canbe determined accurately, allowing a realistic estimation of energycosts.

3.3 MAIN ROUTINE ALGORITHMS

The main routine of the Thermal Load Analysis Program is dividedinto five segments whose relationship is expressed graphically inFigure 3.1. These segments are as -follows:

Building inputInternal partition heat transferJob Processing Control-!Hourly energy analysisJob Processing Control-2

3.3.1 Building Input Segment: Read and Organize BuildingDescription Data

In this segment of the program, building description informationis read into the program and organized for processing by segmentswhich follow. A summary of card input data requirements (with cardtype numbers in parentheses) is given below. Refer to the User'sManual for a complete listing and discussion of card input variables.

READ - identifiers (LC-1,5)

- general program control variables (LC-6,10)

- schedules [people, lighting, and equipment] (LC-11,13)• standard (built into program)• specific (card input)

READ - common shading polygons (LC-14,161)++• short form0 long form

READ - delayed surfaces (LC-17,29)t response factors

- standard (built into program)- specific (card input)

• general characteristics• geometry4"1"

- short form- long form

• deleted common shading surfaces• added shading to specific delayed surface"1"1"


3-11

t pictorial output, delayed surface

READ - quick surfaces (LC-30,38)t general characteristics• geometry"1"1"


t deleted common shading surfaces• added shading surfaces to specific quick surface


t pictorial output, quick surface

READ - glazed surfaces (LC-39,47)• general characteristicst geometry"1"1"


• deleted common shading surfaces• added shading surfaces to specific glazed surface


• pictorial output, glazed surface

READ - internal heat transfer surfaces (LC-48,49)• area, U-value, adjoining space numbers

READ - underground walls (LC-50,51)• area, U-value

READ - underground floors (LC-52,53)t area, U-value

READ - ground temperatures for each month (LC-54)

READ - zone description (LC-55,56)area of floor, volume, weight of floorsetpoint temperaturepeople, lights, equipment peaks and associated schedulesinfiltrationindices of previously described heat transfer surfaces

- delayed- quick- glazed- internal surfaces- underground walls- underground floors

BEGIN THERMAL ANALYSIS

Refer to Figure 3.5 which indicates how polygons are read in and inputdata organized by the program for later processing.

3-12

C Enter

ShadingSurface

Heat TransferSurface

/READ:characteristicsof delayed, quickor glazed surface

Applies to:

1. Common shading sur-faces

2. Delayed heat transfersurfaces

3. Shading surfaces addedto specific delayedsurfaces

4. Quick heat transfersurfaces

5. Shading surfaces addedto specific quick sur-faces

6. Glazed heat transfersurfaces

7. Shading surfaces addedto specific glazedsurfaces

READ: Height,Width, Orienta-tion, etc.

READ: X,Y,ZCoordinatesof Vertices

V

Convert toX, Y, Z Coor-dinate System

IC Continue^

Figure 3.5 POLYGON INPUT FLOW DIAGRAM

3-13

3.3.2 Calculate Heat Transfer Through InternalPartitions (QIHTS

QIHTS. = Z CFIHTSjj *'(TSPACadj- TSPAC.)];jj = 1, NIHTS.

where1 - is a subscript referring to the space

FIHTS.J.J - heat transfer factor (Btu/hr-°F-sq ft)

NIHTS - number of internal partitions, space i

TSPAC.J - setpoint temperature, space i (°F)

TSPAC ri.- setpoint temperature of space on otheraaj side of partition (°F)

3.3.3 Job Processing Control Segment-!

If design run is to be done, set up summer design daydry and wet-bulb temperature arrays (TDBSUM, TWBSUM) for March bycalling subroutine DESDY.

Initialize building and space peak load and peak load thermalcharacteristics.

BHMAX

BCMAX

SSHMAXi

STCMAX.iQCBLDGAl

QHBLDG^

= 0

= 0

= 0

= 0

= 0

= 0

BEGIN HOURLY CALCULATION

3.3.4 Hourly Energy Analysis Segment

Refer to Figure 3.6 for Hourly Energy Analysis SegmentFlow Diagram.

• initialize flags which indicate if heat transfer through asurface has already been calculated for this hour

3-14

Figure 3.6 THERMAL LOAD ANALYSIS PROGRAM, HOURLY ENERGYANALYSIS SEGMENT FLOW DIAGRAM

3-15

ICALDi = 0 (delayed surfaces)

ICALQi = 0 (quick surfaces)

ICALW.. = 0 (glazed surfaces)

• net hour number

IHOURP = IHOUR - JSTART + 1

• initialize test case variables'for maximum building heatingand cooling loads and characteristics

BHEATT = 0

BCOOLT = 0

QCCOMP.CC = 0

QHCOMP1cc = 0 (where ice = 1,17)

• establish time references for this hour

IDOY - day of year

ITIME - time of day

• if ITIME =1 (i.e., 1 AM)

1. Call subroutine SUN1 to calculate:

SUNRAS - hour angle when solar altitude is zero

DEABC(l) - tangent of declination angle

DEABC(2) - equation of time, ET (hours)P

DEABC(3) - apparent solar constant (350-390 Btu/hr-ft )

DEABC(4) - atmospheric extinction coefficient (air mass )

DEABC(5) - sky diffuse factor2. Call subroutine DAYMO to calculate day of the month and

month of the year.

3. Establish value of CN (Clearness Number) = CNS (summer)= CNW (winter)

4. Call subroutine DST to determine whether or not DaylightSaving Time is in effect,

3-16

5. In the first hour of the run, call function NDOW toestablish the day of the week (IDAY).

6. Call subroutine HOLDAY to establish if the day is aholiday.

• calculate hour angle for current hour (HANG, radians)

f if Design Load Analysis, by-pass day type flag and weather tapecall. Define hourly weather from design load weather tables.

• if Energy Consumption Analysis,

1) Call subroutine SCHED to determine type of schedules forthis day.

2) Call subroutine WEATHR to read weather data from input tape.

• call subroutine PSY to calculate outside air psychrometricconditions:

HUMRAT - Humidity Ratio (Ibs H20/lbm-dry air)

ENTH - Enthalpy (Btu/lbm-air)

DENS - Density (lbsm/ft3)

• if | HANG | <. | SUNRAS |, sun above horizonJl = 0Call subroutine SUN2 to calculate:

RAYCOSy v 7 - solar angle direction cosines (X,Y,Z)A, I >t-

RON - direct normal radiation (Btu/hr-ft2)

BS sky brightness

SA - sine of building azimuth (Sin(BAZ))

CA - cosine of building azimuth (Cos(BAZ))

If Energy Consumption Analysis, call subroutine CCM tocalculate cloud cover modifier (CC) and adjust RDN and BS.

RON = RDN * CC

BS = BS * CC

• if | HANG | >. | SUNRAS |, sun below horizon.Jl = 1

3-17

Call subroutine CCM to calculate cloud cover modifier (CC).

BS = 0

BG = 0

BEGIN SPACE LOAD CALCULATION (repeat for each space)

t calculate ground temperature,

TGROND = TGRNDmontn+ 460.0

• underground wall heat transfer

QUWi = z [FUW . * (TGROND - TSPAC^] for ii = 1, NUV^

t delayed surface heat transfer (repeat for each delayed surfaceof zone 1)

If | HANG | <. | SUNRAS |, sun above horizon.

Call subroutine SUN3 to calculate:

GAMMA - cosine of surface tilt angle (Cos(WT))

ETA - angle of Incidence of direct solar ray upon surface

RDIR - direct solar radiation incident upon surface

RDIF - diffuse solar radiation incident upon surface

RTOT - direct + diffuse solar radiationo

BG - ground brightness (Btu/hr-ft )

Check if picture is to be made of this surface (pictures maybe printed on the first day of the month).

Call subroutine SEARCH to determine if a shadow picture Iscalled.

Set up deleted common shading polygon array (ILETE) forsubroutine SHADOW.

Set up added shading surface arrays (XA, YA, ZA) for subroutineSHADOW.

Call subroutine SHADOW to calculate the percent of a surfacewhich is shaded and, if desired, to print a shadow picture ofthe surface.

3-18

• Calculate solar radiation on delayed surface.

If | HANG | > | SUNRAS |, sun below horizon.Solar radiation on surface = 0

Call subroutine FILM to calculate heat transfer coefficientof the outside air film.

Call subroutine HD to calculate heat transfer through delayedsurfaces.

Sum heat transfer through delayed surfaces, zone 1.

• Quick surface heat transfer (repeat for each quick surface ofzone i).


Call subroutine SUNS to calculate solar radiation characteristicson quick heat transfer surface.

Check if picture is to be made of this surface (pictures aredone for the first day of the month). Call subroutine SEARCHto determine if a picture is to be made.

Set up deleted COMMON shading polygon array (ILETE) forsubroutine SHADOW.

Set up added shading surface arrays (XA, YA, ZA) for subroutineSHADOW.

Call subroutine SHADOW to calculate the percent of a surfacewhich is shaded and, if requested, to print a shadow pictureof the surface.


Call subroutine FILM to calculate heat transfer coefficient ofthe outside air film.Call subroutine HQ to calculate heat transfer through quicksurfaces.

Sum heat transfer through quick surfaces, zone i.

• Glazed surface heat transfer(repeat for each glazed surface ofzone i).


Call subroutine SUN3 to calculate solar radiation characteristicson glazed heat transfer surface.

3-19

Check if picture is to be made of this surface. Call sub-routine SEARCH to do this.

Set up deleted common shading polygon array (ILETE) forsubroutine SHADOW.

Set up added shading surface arrays (XA, YA, ZA) for sub-routine SHADOW.

Call subroutine SHADOW to calculate the percent of a surfacewhich is shaded and, if requested, to print a shadow pictureof the surface.

Call subroutine TAR to calculate transmission, absorption, andreflection of solar radiation through single and dual glazing.


Call subroutine FILM to calculate heat transfer coefficient ofthe outside air film.

Call subroutine SHG to calculate heat transfer through glazedsurfaces.

Sum heat transfer through glazed surfaces, zone i.

Calculate people loads.

People, sensible

QPS = 28 + Qp(266.4 - 10.25 * Qp) + (T-460.) * (1.2-Qp *(3.07 - 0.128 * Qp)

People, latent

QPL = 206. - Qp(214.9 - 13.8 * Qp) - (T-460.)* (6.7 -

Qp * (4.44 . 0.222 * Qp))

where Qp - activity levels of occupants (Btu/hr) •

T - space temperature (°F)

Sum thermal loads entering zone at current hour.Solar radiation (HINEW)

HI NEW = QRAD

where QRAD - sum of instantaneous solar radiation into zone.3-20

Transmission and internal loads (H2NEW)

H2NEW = Qeqs * SCHEDeq * Qdwall + Qqwall + Q ., + Qqceil

+ <>u + Qint + Qps * SCHEDpeo * NFOLK + Qgc

where Q - peak equipment sensible heat (Btu/hr)

SCHEDe - equipment part load operation schedule

Q,i..aii ~ sun> °f delayed wall surface heat transferdwa" (Btu/hr)

Q« «n ~ sum of quick wall surface heat transfer(BtU/hr)

~ sum of delayed ceiling surface heattransfer (Btu/hr)

~ sum °f quick ceiling surface heat transfer(Btu/hr)

Q - sum of quick underground surface heatu transfer (Btu/hr)

Q,-«* ~ Sum of internal partitions heat transferint (Btu/hr)

QPS - Sensible heat given off by one person(Btu/hr)

SCHED - Occupancy part load schedule

NFOLK - Maximum number of people in the space

Q . - Sum of conduction heat transfer through^ glazed surfaces

Light heat (H3NEW)

H3NEW = 3413. * SCHEDm *PLITE

where SCHED,. f - Internal lighting part load operation111 schedule

PLITE - Peak lighting power of the space (KW)

• Call subroutine HL to calculate thermal loads to room airand plenum air by adjusting instantaneous loads by theproper weighting factors.

3-21

t Call subroutine INF to calculate sensible and latentinfiltration thermal loads ( Q S , QLinf)

• Sura latent space loads (HLAT)

HLAT = QPL * SCHEDpeo * NFOLK + QLg * SCHED + QL1nf

• If energy consumption run, write weather and zone data tooutput tape and line printer (line printer write optional).

• Call subroutine QMAX to sum zone loads and calculate peakloads and thermal characteristics at peak conditions.

END OF SPACE LOAD CALCULATION.

• Calculate building peak loads and associated thermal con-ditions.

END HOURLY CALCULATION

• Job processing control Segment-2 (see para. 3.3.5)

t Call output report subroutines

• Rewind input and output tapes of energy consumption analysis.

3.3.5 Job Processing Control (JPC) Segment-2

The thermal load analysis program may be operated in threemodes as defined by input variable CODE (see input card type LC-7)

1. Design load analysis only.

2. Design load analysis and hourly energy analysis.

3. Hourly energy analysis only.

The above-mentioned types of analysis are accomplished by multiplepasses through the hourly analysis segment of the program. The jobprocessing control (JPC) segment governs the mode in which the hourlyenergy analysis segment is used.

If CODE = 1. (design load analysis only), let: KODE = 1, summerdesign day analyses for the months of March throughNovember are performed.

KODE = 2, winter design day analysis for the month ofDecember is performed.

3-22

If CODE = 2, (design load analysis and hourly energy analysis),let:

KODE = 2'] as per KODE = ] above>KODE = 3, hourly energy consumption analysis for

the period specified.

If CODE = 3, (hourly energy analysis only),KODE = 3, hourly energy consumption analysis for

the period specified.

3.4 ALGORITHMS OF SUBROUTINES

APOL

A geometry subroutine which calculates, for a polygon of knownvertices, its area, tilt angle (Bangle from zenith) and azimuth angle ofthe right-handed normal.

INPUT

n : Number of vertices

xi

Coordinates of vertices, ft

OUTPUT2

AREA : Area of polygon, ft

TILT : Tilt angle (Bangle from zenith), degrees

AZIM : Azimuth angle of the right-handed normal, degrees,clockwise from y axis

CALCULATION SEQUENCE

1. AREA = A = |A| = 1 z (V. x V,)* i=l 1 J

where j =i + 1 when i < n

j = 1 when i = n•»• -*•V^, V., ... position vectors of the vertices

3-23

2. XCOMP

YCOMP

ZCOMP

i2

= 2

= 7

Zi=lnz

i=lnz

(yizj

(zixj

K-yi

- yjzi>

- ZJX1>

- x.y.)

3.

4.

5.

6.

TILT = Cos"' (ZCOMP/A)

PROJ = "V(XCOMP)2 + (YCOMP)2

If PROJ « A AZIM =0.0

If PROJ is appreciable compared to A, use the properequation given in Table 3.2for the calculation of AZIM.

TABLE 3.2

EQUATIONS FOR THE CALCULATION OF AZIM

i:os>-( -0

en•r~00

1

+i~o0

SIGN 0

-

n , .,-1 /-XCOMP,n ' oln ( PROJ j

LSn.SiV1 ({gg!i)

F XCOMP

0 or +

n .. -1 ,-YCOMP,2 ' oin i pROJ ;

„. -1 /XCOMPxSin (PROJ~)

CCM

A subroutine which calculates as a function of solar altitude angle,cloud type and total cloud amount, the coefficients for modifying solarradiation intensity which are calculated for a clear atmosphere.

INPUT

AL

ICLTP

ICLD

Solar altitude angle,radians~0 Cirrus, Cirrostratus

Cloud type index = 1 Stratus_2 Other

Weather Bureau total cloud amount index

3-24

OUTPUT

CC : Cloud Cover Modifier


The values of CC as a function of AL, ICLTP and ICLD are given inTable 3.3, which is derived from Boeing Company Report, "Summary ofSolar Radiation Observation D2-90577-1, December 1964".

TABLE 3.3

CLOUD COVER MODIFIER, CC

ICLTP-*-

ICLDf

12345678910

STRATUS

AL <_ 45°

.60

.60

.58

.58

.57

.53

.49

.43

.35

.27

AL > 45°

.88

.88

.88

.87

.85

.83

.79

.73

.61

.46

CIRRUS, CIRROSTRATUS

AL i 45°

.84

.83

.83

.82

.80

.77

.74

.67

.60

.49

AL > 45°

1.1.1.1..99.98.95.90.84.74

The values in Table 3.3 are curve fitted and the coefficientscalculated.

1. SQ = ICLD * ICLD

2a. STRATUS CLOUDS, AL ±45° (0.707=Cos of 450)

CC = 0.598 + 0.00026 * ICLD + 0.00021 * SQ - 0.00035

* ICLD * SQ

2b. STRATUS CLOUDS, AL > 45°

CC = 0.908 - 0.03214 * ICLD + 0.0102 * SQ - 0.00114

* ICLD * SQ

3-25

3a. CIRRUS, CIRROSTRATUS CLOUDS, AL £ 45°

CC = 0.849 - 0.01277 * ICLD + 0.00360 * SQ - 0.00059

* ICLD * SQ

3b. CIRRUS, CIRROSTRATUS CLOUDS, AL > 45°

CC = 1.010 - 0.01394 * ICLD + 0.00553 * SQ - 0.00068

* ICLD * SQ

4. Other than Cirrus, Cirrostratus and Stratus clouds, useaverage value of CC for ICLTP = 0 and 1.

CENTER

A subroutine which centers titles, names, etc. for output pagesof reports.

INPUT

IDEN : Left-justified title, name, etc.

KODE : processing indicator

KAGIT : print output device

OUTPUT

IDEN : Centered title, name, etc.


1. Check IDEN column-by-column to determine number of blanksat righthand.

2. Reallocate IDEN in field with half of blanks of either side.

3. Print IDEN on output device KAGIT.

4. If KODE > 3, write IDEN onto output device 2.

DAYMO

A calendar subroutine which identifies the day of the month andthe month of the year.

3-26

INPUT

LEAP : Leap yearlndex =

IDOY : Day of the year, from start of year

OUTPUT

IDAY : Day of the month

MONTH : Month of the year


1. If IDOY < 31, MONTH = 1 and IDAY = IDOY

2. If 31 < IDOY < (59 + LEAP), MONTH = 2, IDAY = IDOY - 31

3. If (59 + LEAP) < IDOY < (90 + LEAP), MONTH = 3,

IDAY = IDOY - 59 - LEAP

4. If (90 + LEAP) < IDOY <. (120 + LEAP), MONTH = 4,


5. If (120 + LEAP) < IDOY <. (151 + LEAP), MONTH 5,




7. If (181 + LEAP) < IDOY £ (212 + LEAP), MONTH = 7,




9. If (243 + LEAP) < IDOY < (273 + LEAP), MONTH 9,


10. If (273 + LEAP) < IDOY < (304 + LEAP), MONTH 10,


3-27

11. If (304 .+ LEAP) < IDOY <_ (334 + LEAP), MONTH = 11,

I DAY = IDOY - 304 - LEAP

12. IF (334 + LEAP) < IDOY, MONTH = 12 IDAY = IDOY - 334 - LEAP

DST

A subroutine which determines Daylight Saving Time and the datewhen it commences and when Standard .Time resumes.

INPUT

OAHR : Year AD

MONTH : Month of the year

IDAY : Day of the month

^-Standard Time=IDST : The Dayling Saving Time indicator = ht Sav1ng

/ Time period

DSTS : The day when Daylight Saving Time commences

DSTF : The day when Standard Time resumes


1. If MONTH is less than 4 and greater than 10, IDST » 0

2. If MONTH is greater than 4 and less than 10, IDST = 1

3. If MONTH = 4 and IDAY is less than 24, IDST = 0

4a. If MONTH = 4 and IDAY is greater than 23, find JDAY > 23for which DAY OF THE WEEK = NDOW (JAHR, 4, IDAY) is equalto 1 , DSTS = JDAY.

4b. If IDAY is less than DSTS, IDST = 0; otherwise, IDST = 1

5. If MONTH = 10 and IDAY is less than 25, IDST = 1

6a. If MONTH = 10 and IDAY is greater than 24, find JDAY >24for which DAY OF THE WEEK = NDOW (JAHR, 10, IDAY) is equalto 1, DSTF = JDAY.

6b. If IDAY is less than DSTF, IDST = 1; otherwise, IDST = 0

3-28

DESDY

A subroutine for calculating design hourly dry-bulb and wet-bulbtemperature for months other than the design summer and winter monthsusing Carrier temperature correction factors.

INPUT

MONTH

TMAX

TMIN

TDEW

TWIN

PATH

OUTPUT

TDB

TUB

DEN

IER

REFERENCE

Month number, 1 to 12

Maximum dry-bulb temperature for summer designday, °F

Minimum dry-bulb temperature for summer designday, op

Average dew point temperature for summer designday, OF

Minimum dry-bulb temperature for winter designday, °F

Atmospheric pressure, inches of mercury

Hourly dry-bulb temperature for design day, F

Hourly wet-bulb temperature for design day, °F

Density of air at 3 PM hour, Ib per cu ft0 Summer design day calculationsuccessful

Error indicator^ 1 Winter design day calculationsuccessful

2 Correction had to be made towet-bulb calculation for atleast one hour

"Handbook of Air Conditioning System Design", Carrier CorporationChapter 2, Design Conditions.

Table 2 - Corrections in Outdoor Design Temperature for Time ofDay.

Table 3 - Corrections in Outdoor Design Conditions for Time ofDay.

3-29


Let the following define the correction factors as listedin subject reference.

a) IDD1 - DBT correction factors for 1 AM hour

IDD2 - DBT correction factors for 2 AM hour• • • • • • •

IDD24- DBT correction factors for 12*nridnite.

b) IDW1 - WBT correction factors for 1 AM hour

IDW2 - WBT correction factors for 2 AM hour• • • • • • *• • * « • * •

IDW24- WBT correction factors for 12 midnite

c) IMD1 - DBT correction factors for March

d)

IMD2 - "

3 - " "

4 _ " "

5 - " "

6 - " "

7 _ " "

8 - " "

g _ It II

IMW1 - WBT correction

IMW2 - "

3 - "

4 - " "

5 - "

6 - " "

7 _ " "

8 - "

q _ ii ii

11 April11 May

" June

" July11 August

" September

" October11 November

factors for March11 April

" May11 June11 July

" August

" " September

" October

" " November3-30

2. Initialize correction factors

CORM1 =0.0 Month correction for DBT

CORM2 =0.0 Month correction for WBT

CORD1 =0.0 Day correction for DBT

CORD2 =0.0 Day correction for WBT

3. Calculate Month index

If March, M = 1

If April, M = 2

If May, M = 3

If June, M = 4

If July, M = 5

If August, M = 6

If September, M = 7

If October, M = 8

If November, M = 9

4. Calculate index corresponding to yearly temperature range

RY = TMAX - TMIN

If RY i 50, L = 1

50..< RY < 55, L = 2

55 < RY S 60, L = 3•••

RY < 115, L = 15

5. Calculate index corresponding to daily temperature range

RD = TMAX - TMIN

If RD < 10, K = 1

10 < RD 515, K = 2••

RD * 45, K = 83-31

6. For months March through November:

a) Set CORM1 = ICORM(L,M,1)

CORM2 = ICORM(UM,2)

b) Call PSY to get W, the humidity ratio, at thedew point temperature.

c) Calculate enthalpy at 3 PM, using TMAX and W.

H = 0.24 * TMAX + (1061. + 0.444 * TMAX) * W

d) Call WBF to get wet-bulb temperature, TWREF,corresponding to enthalpy H.

e) Calculate DBT and WBT for 3 PM and call PSY toget DEN.

CORD! = ICORD(K,15,1)

CORD2 = ICORD(K,15,2)

TDNEW = TMAX - CORM1 - CORD1

TWNEW = TWREF - CORM2 - CORD2

Call PSY (TDNEW, TWNEW, TDEW, PATM, W, H, DEN)

f) For hours 1=1 to 24, repeat the following:

CORD1 = ICORD(K,I,1)

CORD2 = ICORD(K,I,2)

TDB(J)= TMAX - CORM1 - CORD1

H = 0.24 * TDB(I) + (1061. + 0.444 * TDB(J) * W

TWB(I) = WBF(H.PATM)

If (TWB(J)+3) <TDB(I), set

TWB(I) = TDB(I) - 3

7. For months January, February and December, generate24 hours of design weather using following approximation:

a) Let PI = 3.14

ALFA = PI/12.0

3-32

BETA = 2.0 * ALFA

GAMA = PI/2.4

TETA = 2.0 * GAMA

A = (TMAX-TMIN) * COS(TETA)

B = 0.5 * (TMAX-TMIN) * COS(GAMA)

C = COS(GAMA)*SIN(TETA)-2.0*COS(TETA)*

SIN(GAMA)

b) For hours I = 1 to 24, repeat following:

TDB(I) = 0.5 * (TMAX + TMIN) - (A * SIN(ALFA *

(I-10)))/L + (B*SIN(BETA*(I-10)))

H = 0.24 * TDB(J)+(1061. + 0.444 *

TDB(I)) * W

TWB(I) = WBF(H.PATM)

If (TWB(I)+3) < TDB(I), set

TWB(I) = TDB(I) - 3

3-33

FILM

A subroutine which determines the outside surface heat transfer co-efficient as a function of wind velocity and the type of surface con-structions.

INPUT

V

IS

OUTPUT

FO

Wind velocity, mph

Exterior surface index =

1 Stucco2 Brick and rough plaster3 Concrete4 Clear pine5 Smooth plaster6 Glass, white paint on pine

Outside surface heat transfer coefficient,Btu/hr-sq ft-°F


FO = A * V2 + B * V + C

The values of A, B, and C as a function of type of exterior surfaceare given in Table 3-4

TABLE 3.4

VALUES OF A, B, AND C FOR CALCULATIONOF OUTSIDE HEAT TRANSFER COEFFICIENT

IS

12345

6

A(IS)

00.001329

0

-0.002658

0

-0.001661

B(IS)

0.535

0.369

0.380

0.363

0.2810.302

C(IS)

2.04

2.201.90

1.45

1.80

1.45

3-34

HO

A subroutine which computes the heat transferred into a spacefrom an outside opaque thick wall (or roof). This is accompli shed'using the Y response factors and the history of the wall's outsidesurface temperature. This history of TO, includes the presenttemperature, T0-j, which must be computed using the X response factors.

INPUT

AiYiIR

RATOS

FO

CC

TM

TDB

TO.

AB

SOLI

SUMN

SUMR

QN

QR

Self response factors, BTU/HR - sq. ft. - °F

Transfer response factors, BTU/HR - sq. ft. - °F

Number of response factor terms

Common ratio

Overall film coefficient for the outside surface ofwall (includes convection and long wave radiation),BTU/HR - sq ft - °F

Cosine of angle between zenith and outward normalof wall.

Total cloud amount index (previously called ICLDin subroutine CCM).

Constant space temperature, °R

Ambient outside air dry-bulb temperature, °R

Outside wall surface temperature history,(TO. is present outside wall surface temperature),°R.

Absorptivity of outside surface of wall toradiation in solar spectrum

Total solar radiation intensity, BTU/HR - sq.ft.

For previous hour;Used to accomplish the recursive summation>of the response factors and outside surfacetemperature

3-35

OUTPUT

QR

QN

SUMN

SUMR

Space heat gain (+) or loss (-) per unit areaof surface, BTU/HR - Sq. ft.

For Present Hour;Used to accomplish the recursive summation'of the response factors and outside surfaceTemperature.

Heat Balance Equation:

QINSIDE <

Figure 3.7 CONCEPTS OF HD SUBROUTINE

Using the diagram given in Figure 3.7, the heat balance equation of a wallmay be constructed as follows:

By the use of response factors:

OUTSIDE

'INSIDE ._ (TO. - TM)Y.

(EQ. l)t

(EQ. 2)f

t Note that the response factors include the inside convection film co-efficient.

3-36

Outside Wall Surface Heat Balance:

QOUTSIDE = "1 + <2 - 3 (EQ' 3)

where

q1 = AB * S0LI (EQ. 4)

q2 = F0 * (TDB - TO^ (EQ. 5)

q3 = 2.0 * A * (10.0 - CC) (EQ. 6)

Combining equations 1, 3, 4, 5 and 6:

? (TO. - TM)X. = AB * S0LI + FO * (TDB - TOJi=l n n '

- 2.0 * A * (10.0 - GC) (EQ. 7)

Equation 7 is the heat balance equation of the outside wall surface atthe time in question. Since T02» T03, etc. are known from past calculations,TO-, may be solved from this equation.

Rearranging equation 7 as:

T01 * (X] + FO) = X1 * TM+ AB * SOI I + FO * TDB - 2.0

* A * (10.0 - CC) - z (TO, -TM)X. (EQ. 8)i*2 1 '

and solving equation 8 for TO, gives:

X1*TM+AB*SOLI+FO*TDB-2.0*A*(10.0-CC) - z (TO.-TM)*,i=? ' 'TO - ll£

IU1 X1 + FO

Now that TO, is known, equation 2 may be used to compute QTMCTni:directly. ' 1Nblut

HL

A subroutine which determines the total space sensible load bycombining the different sensible components after being multipliedby their appropriate weighting factors.

3-37

INPUT

I

HI

H2

H3

HI NEW

H2NEW

H3NEW

RMRG1

RMRGC

RATRG

RMRX1

RMRXC

RATRX

RMRIS1

RMRISC

RATRIS

RMRPS1

RMRPSC

RATRPS

HRLDS

HRLDL

Space Number

Window solar load from previous hour, BTU/HR

Total transmission and internal load from previoushour, BTU/HR

Plenum return air load from previous hour, BTU/HR

Window solar load for present hour, BTU/HR

Total transmission and internal load for presenthour, BTU/HR,

Plenum return air load for present hour, BTU/HR

Window solar load weighing factors

>Space sensible load weighting factors

>Space lighting load weighting factors

Return plenum lighting load weighting factors

space sensible load for present hour, BTU/HR

Total plenum sensible load for present hour, BTU/HR

3-38

SA

SB

SC

H2P

H2NEWP

SBP(I)

OUTPUT

HI

H2

H3

HRLOS

HRLDL

SA

SB

SC

SBP

H2P

Weighted window solar load for present hour, BTU/HR

Weighted space sensible load for present hour, BTU/HR

Weighted space lighting load for present hour,BTU/HR

Components of sensible load from previous hour, BTU/HR

Components of sensible load for present hour, BTU/HR

Components of weighted sensible load for presenthour, BTU/HR, where

1 = 1 equipment2 quick walls3 delayed walls4 underground floors5 underground walls6 internal walls7 people8 window conduction9 quick ceilings10 delayed ceilings

Window solar load from previous hour, BTU/HR

Total transmission and internal load from previoushour, BTU/HR

Plenum return air load from previous hour, BTU/HR

Total space sensible load for present hour, BTU/HR

Total plenum sensible load for present hour, BTU/HR

Weighted window solar load for present hour, BTU/HR

Weighted space sensible load for present hour, BTU/HR

Weighted space lighting load for present hour, BTU/HR

Components of weighted sensible load for presenthour, BTU/HR

Components of sensible load for previous hour,BTU/HR

3-39


LOAD), =j=0

(SPACE SENSIBLE LOAD), = E ? (LOAD)l , * (WEIGHTING FACTOR)!1 1=0 i=l *~J t-

where i is a superscript which corresponds to the typeof loads and n is the number of the type of loads.

HOLDAY

A subroutine which identifies the National holidays of the UnitedStates of America.

Month of the year

Day of the month

Day of the week (Sunday = 1 , etc. )

JOL : Holiday Indicator =\


1. Set JOL equal to 1 for the following situations:

If MO = 1 and JAY = 1MO = 12, JAY, = 31, and NDAY = 6MO = 1, JAY = 2, and NDAY = 2MO = 2, and JAY = 22MO = 2, JAY = 21, and NDAY = 6MO = 2, JAY = 23, and NDAY = 2MO =5, and JAY = 30MO = 5, JAY = 29, and NDAY = 6MO = 5, JAY = 31, and NDAY = 2MO = 7, and JAY = 4MO = 7, JAY = 3, and NDAY = 6MO = 7, JAY = 5, and NDAY = 2MO = 12 and JAY = 25MO = 12, JAY = 24, and NDAY = 6MO = 12, JAY = 26, and NDAY = 2MO = 9, JAY is less than 7 and NDAY = 2MO = 1, JAY ig greater than 23, and NDAY = 5

2. Otherwise, set JOL equal to 0.

3-40

UP,A subroutine which computes the heat transferred into a space

from an outside opaque quickly-responding wall, door, etc. Thissubroutine is very similar to the HD subroutine except that itrequires no use of response factors.

INPUT

FO : Overall film coefficient for the outside surfaceof wall (includes convection and long wave radiation)BTU/HR - sq. ft. - °F *

U : Overall heat transfer coefficient of wall, BTU/HR -sq. ft. - °F

A : Cosine of angle between zenith and outward normalof wall

CC : Total cloud amount index (previously called ICLDin subroutine CCM)

TM : Constant space temperature, °R

TDB : Ambient outside air dry-bulb temperature, °R

AB : Absorptivity of outside surface of wall toradiation in solar spectrum

SOLI : Total solar radiation intensity, BTU/HR - sq. ft.

OUTPUT

Q : Space heat gain (+) or less (-) per unit area ofsurface, BTU/HR - sq. ft.

CALCULATION SEQUENT

Using the same terminology of the HD subroutine, we can write:

QOUTSIDE = QINSIDE = U * <T01 ' ™} (EQ. 1)

where U is the overall heat transfer coefficient.

The heat balance equation of the outside wall surface becomes:

U * (T01 - TM) = AB * SOLI + FO * (TDB - T0]) - 2.0

* A * (10.0 - CC) (EQ. 2)

Solving this equation for TO, gives:-m - U *TM + AB * SOLI + FO * TDB - 2.0 * A * (10.0 - CC) ,cn _.IU1 " U + FO (t(*' *'

Now that TO-, is known, equation 9 may be used to compute QTMCTQC directly.

3-41

INPUT!

A subroutine used to read surface geometric data required for commonshading surfaces and shading surfaces added to delayed, quick andwindow surfaces.

INPUT

KARD

KAGIT

NV

Logical unit number for card input device

Logical unit number for line printer

Number of vertices contained in surface

OUTPUT

coordinates of lower lefthand vertex* ft

coordinates of vertices


1. If NV = 1, the short form of description for a rectangularsurface is desired, therefore go to calculation 2; ifNV > 3, go to calculation 3.

2. Short form input for rectangular surface

a) Read the following card input data:

XCORN

YCORN

ZCORN_^

height, ft

width, ft

azimuth angle, degrees

tilt angle, degrees

b) Convert azimuth and tilt angles to radians

AZIM = 0.01745 * AZIM

TILT = 0.01745 * TILT

3-42

c) Call RECTAN which returns XX, YY, ZZ.

d) Call RECAP2 to echo data.

e) Reset NV = 4.

3. Long form input for any surface shape

a) For each of NV vertices, read XX, YY, and ZZ fromcard input data.

b) Call RECAP2 to echo data.

INPUT2

A subroutine used to read input surface data required for delayedand quick surfaces.

INPUT

KARD

KAGIT

OUTPUT

NY

ND

NA

Logical unit number for card input device



coordinates of vertices

Surface azimuth angle, degrees

Surface tilt angle, degrees

Surface area, sq ft

Number of X-divisions that surface is to bedivided into for shadow calculations

Number of Y-divisions that surface is to bedivided into for shadow calculations

Number of common shading surfaces deleted

Number of local shading surfaces added

3-43

ISR : Surface roughness index

IRF : Surface construction type index (used only fordelayed surfaces)

H : Height, ft .,

W : Width, ft


1. Read input card identifying the following surface factors:

FNV, FNX, FNY, FND, FNA, FISR, FIRF.

2. Convert these factors to integer number.

NV = FNV + 0.1

NX = FNX + 0.1

NY } = FNY + 0.1

ND = FND + 0.1

NA = FNA + 0.1

ISR = FISR + 0.1

IRF = FIRF + 0.1

and echo data.

3. If NV = 1, the short form of geometric description for arectangular surface is desired, therefore go to calculation4; if NV > 3, go to calculation 5.

4. Short form input for rectangular surface

a) Read the following card input data:

^YÔDM •/\wV/l*i * /

YCORN \ coordinates of lower lefthand( vertex, ft

ZCORN \

HT - height, ft

WD - width, ft

3-44

AZIM - azimuth, angle, degrees

TILT - tilt angle, degrees

b) Convert azimuth and tilt angles to radians andcalculate surface area.

AZIM = 0.01745 * AZIM

TILT = 0.01745 * TILT

AREA = HT* WD

c) Call RECTAN which returns XX, YY, ZZ.

d) Call RECAP2 to echo data.

e) Reset NV = 4.

5. Long form input for any surface shape

a) For each of NV vertices, read XX, YY, and ZZfrom card input data.

b) Call RECAP2 to echo data.

3-45

INF

A subroutine which estimates sensible and latent components ofthe outside air load which infiltrates through openings.

INPUT

DB

HUMRA

DEN

VO

TSPA

CODE

OUTPUT

QSIN

QLIN

Outside air dry-bulb temperature, °F

Outside air humidity ratio, Ibs water/lb dry air

Outside air density, Ibs dry air/cu ft

Outside air specific volume, cu ft

Space temperature, °R

Number of air changes per hour

Sensible infiltration load, Btu/hr

Latent infiltration load, Btu/hr


1. If DB is greater than 50°F, cooling coil is probablyoperating, therefore estimate space humidity ratio asfollows

54 ™

DPT DPT = dew point temperatureof air leaving coolingcoil50

50 DB 90WRA = SPACE HUMIDITY RATIO

53.2 + 0.245 * (DB - 50.0)7000.0

2. If DB is less than 50°F, only heating coil is probably operating,therefore,

WRA = HUMRA

3-46

3. QSIN = 14.4 * DEN * VO * (DB + 460.0 - TSPA)*CODE/60.0

QLIN = 63300.0 * DEN * VO * (HUMRA - WRA) * CODE

LEEP

A subroutine which determines whether a year is a leap year or not.

INPUT

JAHR : Year AD

OUTPUT

LEEP : Leap year index =


0 Not leap year1 Leap year

If (JAHR - 1900) is evenly divisible by 4, then LEEP = 1,otherwise LEEP = 0

MATCON

A subroutine which examines the grid elements of a shaded surfaceand defines an alphameric matrix made up of blank characters for sunlitelements or an asterisk character for shaded or border elements.

INPUT

ISHADE : A two-dimensional matrix representing the grid intowhich a surface is broken for shadow analysis. Eachelement of the matrix has a value of either 0, 1,or 2 to indicate respectively:

-sunlit element of surface-shaded element of surface .-element falling outside surface

See Figure 3.9 for example.

MM : Number of grid elements in the x-axis direction

NN : Number of grid elements in the y-axis direction

OUTPUT

ISHADE : Redefined grid matrix filled with either blankor asterisk characters

3-47


1. For each element of matrix, i.e., I = 1 to MM and J = 1, NN

a) If ISHADE (I,J) is greater than 0, go to 2

b) If ISHADE (I.J) is equal to 0, check to see if elementis on border of surface, i.e., I = 1 or MM, J = 1 or NN.If so, set ISHADE (I, J) = 1.

c) If ISHADE (I,J) is equal to 0, and I M or MM or J ? 1 or NN,check to see if element is on a diagonal border; i.e.,element above, below, to right, or to left is equal to 2.If so, set ISHADE (I, J) = 1.

2. For each element of matrix, i.e., 1=1 to MM and J = 1to NN

a) If ISHADE (I, J) = 0, set element equal to ablank character

b) If ISHADE (I,J) is greater than 0, set element equalto an asterick character.

See Figures 3.8 - 3.11 for a visual explanation of the steps performedin making a shadow calculation. Also refer to subroutine SHADOW forfurther insites into the mechanics of performing such calculations.

-SurfaceNN

122222P

0

2222,2-0

2222,1)0

222000

22

/cf'o00

2?^0000

00000

000000

000000

000000

000000

000000

00000&

0000p2

000V'22

00o.22

00,4222

0*2222

X22222MM

Figure 3.8

Step 1 - Surface broken into grid elements with 0 and 2indicating if grid midpoint is without or withinthe surface boundary

3-48

Shaded

2 2 2 2 2 2 2 ^ 0 0 0 02 2 2 2 2 2 T V 0 0 0 02 2 2 2 X r 0 0 0 0 0 0

0 0 0 0 0 0 00 0 0 0 0 0 0 0

2 220 0 0 0 0 0 0 0 0 0

ShadedFigure 3.9 .

Step 2 - Surface broken into grid elements with1 indicating portion that is shaded

2 2 2 2 2 22 2 2 2 2.2 2 22 2

1 1 1 10000000

0 0 0 0 0 10 0

1 1 1 1 1 1

Figure 3.10

Step 3 - Surface broken into grid elements with1 indicating a shaded element or a boundaryelement

* * * * * * * * * * * ** *******

* * ****** * * * *

* * * ** * * * * * * * * * * *

Figure 3.11

Step 4 - Transformed matrix ready for pictorial display

3-49

MONFIN

A subroutine to define the alphameric name of a month giventhe numeric equivalent.

INPUT

MONTH: : Month of year, 1 to 12

OUTPUT

MONT : Alphameric name of month corresponding to MONTH.


If MONTH = 1, MONT = JAN.= 2, = FEB.= 3, » MAR.= 4, = APR.=5, = MAY=6, = JUNE=7, = JULY=8, = AUG.=9, = SEP.=10 = OCT.=11, = NOV.=12, = DEC.

3-50

NDOW

A subroutine which determines the day of the week.

INPUT

: Year AD

: Month of the year

: Day of the month

JR

MO

JAY

OUTPUT

NDOW

1 if Sunday12 if Monday'3 if Tuesday

Week day indicator =^4 if Wednesday|5 if Thursday'6 if Friday7 if Saturday


1. Let JSTMJST(5JST(9)

= 31, JST= 151, JST= 273, JST

2) = 59, JST(3) = 90, JST(4) = 1206) = 181, JST(7) = 212, JST(8) = 24310)= 304, JST(11)= 334, JST(12)= 365

2. Let N = Integer part of JR/4

ND = N - 485IY = 2, IAAD = 2If ND = 0, go to (4)If ND is less than 0, ND = -ND and IADD = -2.

3. Repeat the following steps ND times

IY = IY - LADD

If IY is greater than 7, IY = IY - 7If IY is equal to 0, IY = 7If IY is less than 0, IY + 7

4. Let MD = JR - N * 4

If MD is equal to 0, IWK = IY1, IWK = IY + 22, IWK = IY + 33, IWK = IY + 4

If IWK is greater than 7, IWK = IWK - 7

3-5]

5. Repeat the following for j = 1 through 12.

If MO is equal to j, let JDAY = JST(j) - 31 + JAY - 1

6. If MD is equal to 0 and MO is greater than 2, JDAY = JDAY + 1

7. NTX = Integer part of JDAY/7NDX = JDAY - 7 * NTX + INK

If NDX is greater than 7, let NDS = NDX - 7

8. Let NDOW = NDX

PSY AND PPWVMS

A subroutine which calculates humidity ratio, enthalpy and density ofoutside air.

INPUT

DBT : Outside air dry-bulb temperature, °F

WBT : Outside air wet-bulb temperature, °F

DPT : Outside air dew point temperature, °F

PATM : Atmospheric pressure, inches of mercury

OUTPUT

HUMRAT : Humidity ratio, Ibs water/lb dry air

ENTH : Enthalpy, Btu/lb dry air

DENS : Density, Ibs dry air/cu ft


In the calculation of psychrometric properties of moist air, partialpressure of water vapor is needed. This is calculated by the PPWVMS sub-function.

1. If DPT is less than 32, calculate partial pressure of water vaporfor DPT.

PPWV = PPWVMS(DPT)

Go to step 3.

3-52

2. If DPT is greater than 32, calculate partial pressure of watervapor in moisture-saturated air for WBT and obtain partial pressureof water with

PPWV = PPWVMS(WBT) - 0.000367 * PATM * (DBT - WBT)/

(1.0 + (WBT - 32.0)71571.0)

3. HUMRAT = 0.622 * PPWV/(PATM - PPWV)

4. ENTH = 0.24 * DBT + (1061.0 + 0.444 * DBT) * HUMRAT

5. DENS = 1.0/(0.754 * (DBT + 460.0) * (1.0 + 7000.0 * HUMRAT/

4360.0)/PATM)

CALCULATION OF PARTIAL PRESSURE OF WATER IN MOISTURE-SATURATED AIR:

1. Let t be either DBT, WBT or DPT.

2. Let A(l) = -7.90298A(2) = 5.02808A(3) = -1.3816 E-7A(4) = 11.344A(5) = 8.1328 E-3A(6) = -3.49149

3. Let T = (t + 459.688)/1.8

If T is less than 273.16, go to 4.

Otherwise

B(2) =B(3) =B(4) =

-9.09718-3.566540.8767930.0060273

z =PI =P2 =P3 =P4 =

Go to 5.

373.16/TA(l) * (z-1)A(2) * LoglO (z)A(3) * (10 ** (A(4)A(5) * (10 ** (A(6)

l-l/z))-l)z-l))-l)

Let z = 273.16/TPI = B(l) * (x-1)P2 = B(2) * LoglO (z)P3 = B(3) * (1-1/z)P4 = Log 10 (B(4))

PVS = 29.921 * 10 ** (PI + P2 + P3 + P4)

3-53

QMAX

A subroutine that sums space loads each hour to get total buildingload; also keeps track of the peak heating and cooling load for each space.

INPUT

I

HRLDS

SSHMAX

TOTAL

STCMAX

SUMA

SUMBP(L)

SUMC

HLATP

QSINF

QLINF

HRLDL

QLEQ

MONTH

DBT

WBT

Space Number

Space sensible load for hour, Btu/hr

Maximum space sensible heating load, Btu/hr

Space total load for hour, Btu/hr

Maximum space total cooling load, Btu/hr

Space window solar load, Btu/hr

Space sensible load components, Btu/hrwhere:

L = 1 equipment2 quick walls3 delayed walls4 underground floors5 underground walls6 internal walls7 people8 window conduction9 quick ceilings10 delayed ceilings

Space lighting load, Btu/hr

Space latent load due to people, Btu/hr

Space sensible load due to infiltration, Btu/hr

Space latent load due to infiltration, Btu/hr

Space plenum return air load, Btu/hr

Space latent load due to equipment, Btu/hr

Month number

Ambient dry-bulb temperature, °F

Ambient wet-bulb temperature, °F

3-54

HUMRAT Ambient air humidity ratio, Ib/lb

DENS Ambient air density, Ib/cu ft

CFMSF Estimated amount of ventilation air, CFM/sq ft

FLORA Space floor area, sq ft

TROOM Space setpoint temperature, °F

MULT Number of times space is repeated in building

ITIME Time of day, 1 to 24

IDAY Day of month

BHEATT Summation of space heating loads for the hour, Btu/hr

QHCOMP(K) Components of hourly building heating load, Btu/hr,where K takes on the following definition

K = 1 delayed walls2 window conduction3 window solar4 quick walls5 internal walls6 underground walls7 underground floors8 people sensible9 people latent10 lighting11 equipment sensible12 infiltration sensible13 infiltration latent14 plenum return air15 equipment latent16 quick ceilings17 delayed ceilings

QCCOMP(K) : Components o;* hourly buildign cooling load, Btu/hr,where K has same definition as above.

OUTPUT

QHCOMP(K) : Same definition as above

QCCOMP(K) : Same definition as above

QWIN(M,I) : Components of space peak heating load, Btu/hr, whereI is the space number and M takes on the followingdefinition

3-55

M = 1 delayed walls2 window conduction3 window solar4 quick walls5 Internal walls6 underground walls7 underground floors8 people sensible9 people latent10 lighting11 equipment sensible12 infiltration sensible13 infiltration latent14 plenum return air15 equipment latent16 month17 ambient dry-bulb temperature18 ambient wet-bulb temperature19 ambient humidity ratio20 hour of day21 quick ceilings22 delayed ceilings23 day of month

QSUM(M,I) : Components of space peak cooling load, Btu/hr; M and Ihave same definition as for QWIN


1. If HRLDS is zero or positive go to 3.If HRLDS is negative, go to 2.

2. Heating hour

a) Add space heating load and space ventilation air load intobuilding heating load for the hour

BHEATT = BHEATT + HRLDS + QOA

QOA = 14.4*DENS*CFMSF*FLORA(I)*(DBT-TROOM(I))

b) Add space heating load components into building heatingload components

QHCOMP(l) = QHCOMP(l) + SUMBP(I,3)*MULT(I)(2) = (2) + SUMBP(I,8)*MULT(I)3) = (3) + SUMA (I) * MULT(I)4) = (4) + SUMBP(I,2)*MULT(I)5) = (5) + SUMBP(I,6)*MULT(I)(6) = (6) + SUMBP(I,5)*MULT(I)(7) = (7) + SUMBP(I,4)*MULT(I)

3-56

(8) =(9) =

(10) =(11) =(12) -(13) =(14) -(15) -(16) -(17) =

(8) + SUMBP(I,7)*MULT(I)(9) + HLATP * MULT(I)(10) + SUMC(I) * MULT(I)(11) + SUMBP(I,1)*MULT(I)(12) + QSINF * MULT(I)(13) + QLINF * MULT(I)(14) + HRLDL(I) * MULT(I)(15) + QLEQ * MULT(I)(16) +:$UMBP(I) * MULT(I)(-17) + SUMBP(I,10) * MULT (I)

c) Check for peak load, i.e., if |HRLDS| > |SSHMAX|, andupdate peak load data as follows:

QWIN(1,I(2,1!

=

(3,1) =(4.1!5,16,17,1

} ====

8,1) =(9,1) =(10,1) =

(12',I(13,1,(14,1(15,1!(16,1!17,1!18,119,1

1 =i =i =s

1 => ===

(20,1) =(21,1(22, I!(23,1!

!S

1 -=

SUMBP(I,SUMBP(I,SUMA (I)SUMBP (ISUMBP (ISUMBP (ISUMBP (ISUMBP (IHLATPSUMC(I)SUMBP(I,QSINFQLINFHRLDL(I)QLEQMONTHDBTWBTHUMRATITIMESUMBP(I,SUMBP(I,I DAY

3)8)

,2),6),5),4),7)

1)

9)10)

3. Cooling hour

a) Add space cooling load and space ventilation air load intothe building cooling load for the hour.

BCOOLT = BCOOLT + TOTAL + QSOA + QLOA

QSOA = 14.4*DENS*CFMSF*FLORA*(I)*(DBT - TROOM(I))

QLOA = 63000.*DENS*CFMSF*FLORA(I)*(HUMRAT - 0.0093)

(Room humidity condition is assumed to be approximately75°F and 50% R.H.)

If QLOA < 0.0 set QLOA =0.0

3-57

b) Add space cooling load components into building coolingload components. Follow same procedures as are outlinedin 2b above except use QCCOMP instead of QHCOMP.

c) Check for peak load, i.e., if |TOTAL| > |STCMAX|, andupdate QSUM peak load data using same procedures as areoutlined in 2c above.

RECTAN

A subroutine which calculates coordinates of three verticesof a rectangle, two sides of which are horizontal, if tilt angle,azimuth angle and coordinates of one vertex are given.

INPUT

X

Y

Z

H

W

A

B

OUTPUT

Coordinates of one vertex, ft

Height of surface, ft

Width of surface, ft

Azimuth angle, degrees

Tilt angle, degrees

XV(I)

YV(I)

ZV(I)


Coordinates of 4 vertices

1. Let CA =CB =SA =SB =

COS (A)COSSINSIN

B)A)B)

2. XV(1) = X - H * CB * SAYV(1) = Y - H * CB * CAZV(1) - Z + H * SB

3-58

XV(2) = XXV(2) = YZV(2) = Z

XV(3) = X - W * CAYV(3) = Y + W * SAZV(3) - Z

XV(4) = X - W * C A - H * C B * S AYV(4) = Y + W * S A - H * C B * C AZV(4) = Z + H * SB

Figure 3.12 DEFINITION OF SURFACE ANGLESAND DIMENSIONS

3-59

RECAP1

A subroutine thatLC-1 through LC-10.

INPUT

STALAT :

STALON :

TZN :

CNS :

CNN :

BAZ :

LCODE :

CFMSF :

FPRES :

DTC :

DTH

ALTUD :

TDBS :

RANGS :

TOPS :

WINDS :

TDBW :

RANGW :

TDPW

WINDW :

JAHR :

JMONTH :

echos beginning portion of input data, i.e.,

Station latitude, degrees

Station longitude, degrees

Time zone number

Summer clearness number

Winter clearness number

Building azimuth angle, degrees

Job processing code

Ventilation air rate, cfm/sq ft

Estimated total fan pressure, inches of water

Cold air supply temperature, °F

Hot air supply temperature, °F

Building altitude, ft.

Summer maximum DBT, °F

Summer daily range of DBT, °F

Summer dew point temperature, °F

Summer wind speed, mph

Winter minimum DBT, F

Winter daily range of DBT, °F

Winter dew point temperature, °F

Winter wind speed, mph

Weather year

Starting month of analysis

3-60

LENGTH

IXMAS

TDB

KPRINT

KAGIT

Length of analysis, days

Length of Christmas period, days

Initial temperature of exterior surfaces, °F

Print code ''

Logical unit number for Hne printer

OUTPUT

A report similar to that shown in Figure 3.13.

RECAP2

A subroutine that echos surface geometric description input data.

INPUT

NV

XCORN

YCORN

ZCORN

HT

WD

AZIM

TILT

X

Y

Z

KAGIT

OUTPUT


Coordinates of lower left-hand vertex, ft.

Height, ft.

Width, ft.

Azimuth angle, radians

Tilt angle, radians

Coordinates of all surface vertices, ft.

Logical unit number of line printer.

Several lines of output similar to those indicated in Figure 3.14.

3-61

ft aN a•O .4

nn

o.s

* * *

I************ *****************

>**

***************

****

»*»

**•*

<**

*»

<**

EC

HO

O

F

INP

UT

D

ATA

**

»**

F

OR

LO

AD

PR

OG

RAM

«*

<**

«»<

>******************»

*********4

* «

O0

in

o•»•

o0•

oo<v

10«4•0

o0

•4

0 0O 0• •

pi

0 O0 0• •«or-

o o0 O• »vOK»v4

000 00 0 O O

rt O> OJ

0o•4

Q.

O

to

CO

S-3•f"Lu

10«a>

<<a

caMUlUO

o uj a o u< a ui zo 3 or a: a u_1 1- UJUI O CD

*-•£»• Uz i-'r z u.ts -i 3»-« v> o>-(«</> 3 ZO) M •Ul K Oa a. z

3-62

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3-63


1. If NV = 1, go to calculation 2; otherwise go to calculation 3.

2. Echo Input data for rectangular surface.

a) Convert azimuth and tilt angle to degrees.

M = AZIM/0.01745

BB = TILT/0.01745

b) Print XCORN, YCORN, ZCORN, HT, WD, AA, and BB.

3. Echo Input data for surface.

a) Print column label.

b) For each of NV surface vertices, print X, Y and Z

coordinate.

REPRT1

A subroutine that prints a one-page report summarizing the name ofbuilding being studied, its location, name of analyst, project number anddate.

INPUT

IDEN1 Facility name

IDEN2 Facility location

IDENS Analyst's name

IDEN4 Project number

IOEN5 Date

KODE Print code indicating 1f writing on outputcomputer tape is desired

KAGIT : Logical unit number for line printer.

OUTPUT

A one-page report similar to that shown 1n Figures 3.15 and 3.16.

3-64

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3-65

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3-66


1. Print upper part of border.

2. Print first line of report.

a) If KODE =1 or 2, print title "Design LoadAnalysis For".

b) If KODE > 2, print title "Analysis of EnergyUtilization of".

3. Print IDEN1, first calling subroutine CENTER to position

title within center of 35 column field.

4. Print IDEN2, again calling subroutine CENTER to position

title within center of 35 column field.

5. Print IDEN3, IDEN4 and IDEN5.

6. Print lower part of border.

7. If KODE < 3, write IDEN3, IDEN4 and IDEN5 on output

computer tape.

REPRT2

A subroutine that prints a one-page report summarizing calendar dataand weather data required for hourly energy analysis run.

INPUT

JSTAT

JHOUR

LMONTH

LDAY

JAHR

LENGTH

ITDB

KAGIT

Weather station number

Hour of day when analysis is to start

Month when analysis is to start

Day of month when analysis is to start

Year when analysis is to start

Length of analysis in days

Initial estimate of exterior surface temperature,OFLogical unit number for line printer

3-67

OUTPUT

A one-page report similar to that shown in Figure 3.17.

REPRT3

A subroutine that prints a one-page report summarizing data that isprinted each hour on load output tape and on line printer, if desired.

INPUT

KAGIT : Logical unit number of line printer.

OUTPUT


REPRT5

A subroutine that prints a one-page report summarizing the designweather data generated by subroutine DESDY.

INPUT

TDBS : Maximum summer dry-bulb temperature, °F

RANGS : Daily swing of dry-bulb temperature for summerdesign day, °F

TOPS : Average dew point temperature for summer designday, OF

WINDS : Wind speed for summer design day, mph

TDBW : Minimum winter dry-bulb temperature, °F

RANGW : Daily swing of dry-bulb temperature for winterdesign day, °F

TDPW : Average dew point temperature for winter designday, OF

WINDW : Wind speed for winter design day, mph

PATM : Atmospheric pressure, inches of mercury

IPRNT : Logical unit number for line printer.

3-68

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3-69

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3-70

OUTPUT



1. Print top part of report summarizing user Input data,

I.e., TDBS, RANGS, TOPS, WINDS, TDBW, RANGW, TDPW and

WINDW.

2. Calculate minimum dry-bulb temperature for summer design day.

TWIN = TDBS - RANGS

3. For months March through November:

a) Call subroutine DESDY to calculate the hourlydesign dry-bulb temperature, TDB, and wet-bulbtemperature, TWB for the month.

b) Print TDB and TWB.

4. Calculate maximum dry-bulb temperature for winter design day.

TMAX = TDBW + RANGW

5. For month of December:

a) Call subroutine DESDY to calculate the hourlydesign dry-bulb temperature, TDB, and wet-bulbtemperature, TWB, for month.

b. Print TDB and TWB.

REPRT6

A subroutine which prints one-page reports for each space and buildingsummarizing peak load data results. .

INPUT

IPRNT : Logical unit number for line printer

FAC : Facility name

CITY : Facility location

PROJ : Project number

ENGR : Engineer name

3-71

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3-72

DATE

NSPAC

AREA

VOL

TSPAC

DENS

DENW

QSUM(I.N)

QWIN(I,N)

T2(I)

Date

Number of spaces In building

Space floor areas, sq ft

Space volumes, cu ft

Space set point temperature, °F

Outside atr density for summer peak load hour,Ibs/cu ft

Outside air density for winter peak load hour,Ibs/cu ft

Components of space peak cooling load, Btu/hr,where N is the space number and I takes on thefollowing definition:

1=1 delayed walls2 window conduction3 Window solar4 quick walls5 internal walls6 underground walls7 underground floors8 people sensible9 people latent10 lighting11 equipment sensible12 infiltration sensible13 infiltration latent14 plenum return air15 equipment latent16 month17 ambient DBT18 ambient WBT19 ambient humidity ratio20 hour of day21 quick ceilings22 delayed ceilings23 day of month

Components of space peak heating load, Btu/hr;I and N have same definition as for QSUM.

Components of building peak cooling load, Btu/hr;I has same definition as for QSUM.

Components of building peak heating load, Btu/hr;I has same definition as for QSUM.

3-73

CFMSF : Ventilation air rate, cfm/sq ft

FPRES : Estimated total fan pressure, inches of water

MULT : Space repetition factor

OUTPUT

A one-page report for each space similar to that shown inFigure 3.20. Also a one-page report for the building similar tothat shown in Figure 3.21. Finally, a one-page report summarizingheating and cooling capacities required for each space (see Figure3.22).


1. For each space, N, print following:

a) Identification information, i.e., page header,page number, FAC, CITY, space number, MULT, AREAand VOL.

b) Time and conditions for summer peak load, i.e.,dry-bulb temperature, wet-bulb temperature, hourof day, month, and day of month.

c) Time and conditions for winter peak load, 3.e.,dry-bulb temperature, wet-bulb temperature,hour of day, month, and day of month.

d) Components of summer and winter peak load in orderindicated in Figure 3.20.

e) Total summer sensible, summer latent and wintersensible load which are simply the summations oftheir respective columns.

f) Total space cooling expressed in Btu/hr, whichis simply the summation of the total summer sensibleand latent loads.

g) Total space heating expressed in Btu/hr, the totalwinter sensible load.

h) The supply air cfm required to meet the total spacesensible cooling load for two values of requiredzone supply air temperatures:

CFM1 = TOT1/(14.4*DENS*(TSPAC(N) - DTC(l))

3-74

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3-75

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3-76

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3-77

CFM2 = TOT1/(14.4*DENS*(TSPAC(N) - DTC(2))

where TOT1 ts total summer sensible load.

i) The supply atr cfm required to meet the total spacesensible heattng load for two values of requiredzone supply air temperatures:

CFM3 = TOT3/(14.4*DENW*(DTH(1) - TSPAC(N))

CFM4 = TOT3/(14.4*DENW*(DTH(2) - TSPAC(N))

.where TOTS is total winter sensible load.

j) The supply cfm required per square foot of floorarea.

SQFT1 = CFM1/AREA(N)




2. Calculate following summations for building.

a) Total floor area

TAREA = z(AREA(N)*MULT(N)), for N*l to NSPAC

b); Total volume

TVOL = Z(VOL(N)*MULT(N)), for N=l to NSPAC

c) Total cooling cfm at both temperature conditions

TCFM1 = z(CFMl*MULT(N)), for N=l to NSPAC

TCFM2 = E(CFM2*MULT(N)),-for N=l to NSPAC

d) Total heating cfm at both temperature conditions

TCFM3 = z(CFM3*MULT(N)), for N=l to NSPAC

T&FM4 = z(CFM4*MULT(N)), for N=l to NSPAC'r|

3. For the building peak load conditions, print the following:

a) Identification information, i.e., page header,page number, FAC, CITY, number of spaces inbuilding, TAREA and TVOL.

3-78

b) Time and conditions for summer peak load, I.e.,dry-bulb temperature, wet-bulb temperature, hourof day, month, and day of month.

c) Time and conditions for winter peak load, I.e.,dry-bulb temperature, wet-bulb temperature, hourof day, month, and day of month.

d) Components of summer and winter peak load in orderIndicated In Figure 3.21.

e) Subtotals for summer sensible (SUMT1), summerlatent (SUMT3) and winter sensible (SUMT2) loadswhich are simply the summations of their respec-tive columns.

f) Return air load created by light heat which 1spicked up by return air as it passes through aventilated light fixture.

g) Fan heat load

QFAN = 0.4014 * TCFM1 * FPRES

h) Ventilation air load for summer peak cooling hour

QSOAS - 14.4 * DENS * CFMSF * TAREA

* (Tl(17) - 75.0)

QLOA = 63000. * DENS * CFMSF * TAREA

* (Tl(19) - 0.0093)

where It is assumed that 75°F and 50% R.H.are the average conditions within the build-Ing during the peak cooling hour.

1) Ventilation air load for winter peak heating hour

QSOAW = 14.4 * DENW * CFMSF * TAREA

* (T2(17) - 75.0)

j) Total loads for summer sensible, summer latentand winter sensible loads which are simply thesummations of their respective columns.

k) Total building cooling load expressed in Btu/hrand tons, which is the summation of the totalsummer sensible and latent loads.

3-79

1) Total building Keating load expressed in Btu/hrand 1000's Btu, the total winter sensible load.

m) The supply air cfm and cfm per square foot requiredfor a variable volume system to meet the buildingpeak sensible heating and cooling loads for twovalues each of required supply air temperatures.

• Cool ing

TCFM5 = SUMT1/(14.4*DENS*(75.0 - DTC(l))

TCFM6 = SUMT1/(14.4*DENS*(75.0 - DTC(2))

TSQFT5 = TCFM5/TAREA


t Heating

TCFM7 = -SUMT2/(14.4*DENW*(DTH(1) - 75.0))

TCFM8 = -SUMT2/(14.4*DENW*(DTH(2) - 75.0))



n) The supply air cfm and cfm per square foot requiredfor a constant volume system to meet the buildingpeak sensible heating and cooling loads for twovalues each of required supply air temperatures.

• Cooling

TCFM1 = see 2c.

TCFM2 = see 2c.



• Heating

TCFM3 = see 2d.

TCFW = see 2d.



4. Print a table (Figure 3.22) summarizing the maximum heatingand cooling capacity required for each space.

3-80

RMRSS

A subroutine that sets the weighting factors required to delay theheat transfer between the space and the heating-cooling equipment.

INPUT

IL

W

PERCT

OUTPUT

RMRIS1

RMRISC

RATRIS

RMRPS1

RMRPSC

RATRPS

RMRX1

RMRXC

RATRX

RMRG1

RMRGC

RATRG

Type of lighting fixture (see Figure 3.23)

= 1 Fluorescent fixture recessed into suspendedceiling, ceiling plenum not vented.

= 2 Fluorescent fixture recessed into suspended ceiling,return air through ceiling plenum.

= 3 Fluorescent fixture recessed into suspendedceiling, supply and return through ceiling plenum.

= 4 Incandescent lights exposed in the room air.

Weight of floor, Ibs/sq ft

Percent of light heat that goes directly into space(obtain from manufacturer's data)

Weighting factors for relating light heat enteringfspace to room cooling load.

Weighting factors relating heat released into plenum byAlights to return air heat pick-up.

Weighting factors relating heat gain through walls'and roofs to room cooling load.

Weighting factors relating solar heat gain through^glass to room cooling load.

3-81

L

CEILING AIRSPACE

SUSPENDEDCEILING

NOT VENTED

VENT=1

FLOOR

v ' <J -

VENTED TORETURN AIR

VENT=2

"1

• ' • *

VENTED TOSUPPLY AIRRETURN AIR

VENT=3

FLUORESCENT FIXTURES

VENT=4

INCANDESCENTLIGHT

Figure 3.23 TYPES OF LIGHT FIXTURES

3-82


1. Set of the type of construction on basis of weight of floor.

If W <_ 50, set IW = 1 (Light)

If 50 < W <. 100, set IW = 2 (Medium)

If 100 < W, set IW = 3 (Heavy)

2. Set value of weighting factors for handling solar heat gain throughglass.

Table 3.5

WEIGHTINGFACTORSYMBOL

RMRG1

RMRGC

RATRG

TYPE OF CONSTRUCTION

LIGHT

0.224

-0.044

0.82

MEDIUM

0.197

-0.067

0.87

HEAVY

0.187

-0.097

0.91

3.

Source: "Procedure For Determining Heating and CoolingLoads For Computerized Energy Calculations", ASHRAE, 1971Revised Edition.

Set value of weighting factors for handling wall and surfaceheat gain.

Table 3.6


RMRX1

RMRXC

RATRX


LIGHT

0.703

-0.523

0.82

MEDIUM

0.681

-0.551

0.87

HEAVY

0.676

-0.586

0.91

Source: "Procedure of Determining Heating and CoolingLoads For Computerized Energy Calculations", ASHRAE, 1971Revised Edition.

3-83

4. If IL = 1 or 4, set PERCT = 100.0; otherwise leave user definedas Is.

5. Set value of weighting factors required for handling space heatgain from lights. Obtain values of RMRIS1, RMRISC and RATRISfrom Table 3.7, and then modify the first two for percentage oflight heat that goes into space as follows:

RMRIS1 = RMRIS1 * (PERCT/100.)

RMRISC = RMRISC * (PERCT/100.)

6. Check for ceiling plenum and set weighting factors accordinglyfor handling heat added to plenum as a function of lightingload.

a) If IL = 1 or 4, there is no return plenum, therefore set

RMRPS1 =0.0RMRPSC =0.0RATRPS =0.0

b) IfIL = 2or3, there is a return plenum, therefore obtainvalues of RMRIS1, RMRISC and RATRIS from Table 3.7 and thenperform following

RMRPS1 = RMRIS1 * (100. - PERCTJ/100.

RMRPSC = RMRISC * (100. - PERCT)/100.

RATRPS = RATRIS

3-84

Table 3.7



LIGHT MEDIUM HEAVY

Type 1 - Fluorescent fixture recessed intosuspended ceiling, ceiling plenumnot vented.

RMRIS1

RMRISC

RATRIS

0.53

-0.35

0.82

0.53

-0.40

0.87

0.53

-0.44

0.91

Type 2 - Fl orescent fixture recessed intosuspended ceiling, return airthrough ceiling plenum.

RMRIS1

RMRISC

RATRIS

0.59

-0.41

0.42

0.59

-0.46

0.87

0.59

-0.50

0.91

Type 3 - Fluorescent fixture recessed intosuspended ceiling, supply andreturn air through fixtures.

RMRIS1

RMRISC

RATRIS

0.87

-0.69

0.82

0.87

-0.74

0.87

0.87

-0.78

0.91

Type 4 - Incandescent lights exposed in theroom air

RMRIS1

RMRISC

RATRIS

0.50

-0.32

0.82

0.50

-0.37

0.87

0.50

-0.41

0.91

Source: "Procedure For Determining Heating and CoolingLoads for Computerized Energy Calculations, ASHRAE, 1971,Revised Edition.

3-85

SCHDUL

A subroutine forfor people and lights

INPUT

CFKSCH

CLTSCH

FISCH(J,K)

I

KARD

KAGIT

KKMAX

OUTPUT

SCHFLK(I,J,K)

SCHLIT(I,J,K)

SCHEQ(I,J,K)

reading a generating operating schedule to be usedand equipment.

People schedule requirement, no = 0, yes = 1

Lighting schedule requirement, no = 0, yes = 1

Coded schedule number, where

J = 1, people schedule2, light schedule3, equipment schedule

K = 1, Sunday2, Weekday3, Saturday4, Holiday5, Special period at year end

Space schedule type number

Logical unit number for card input


Number of types of daily schedules used

Hourly people schedule where

1=1 to 3, space schedule type number

J = 1 to 9, type of day (Sunday through Saturday,Holiday and Special)

K = 1 to 24, Hour of day

Hourly lighting schedule where I, J and K havesame definitions as above.

Hourly equipment schedule where I, J and K have samedefinitions as above.

3-86


1. Fill in matrix for standard non-standard schedules; for each ofpeople, lights and equipment performance following:

a) For each type of day, if FISCH £ 10, standard schedule(Figure 3. 24) is desired, therefore enter standard 24 hourschedule into appropriate matrix, i.e., SCHFLK, SCHLIT, orSCHEQ.

b) For each type of day, FISCH > 10, a user defined schedule isdesired; therefore, if the non-standard schedule has not beenpreviously defined, read it from card input and enter it intoappropriate matrix, i.e., SCHFLK, SCHLIT or SCHEQ.

2. Echo schedules.

SCHED

A subroutine which assigns the proper lighting, people and equipmentschedules to spaces and corrects time for Daylight Saving time.

INPUT

«IDST : Daylight Saving Time indicator - ng

ITIME : Hour of day, 1 to 24

IDOW : Day of Week, 1 to 7

I FEAST : Holiday indicator = 1°

: Chrises period indcator = °

OUTPUT

J : Type of day, 1 to 9

K : Corrected time, 1 to 24


1. a) If JC = 1, J = 9

b) If JC = Oand IFEAST = 1, J = 8

c) If JC = 0 and IFEAST = 0, J = IDOW

2. a) If IDST = 0, K = ITIME

3-87

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SEARCH

A subroutine which indicates a shadow pictorial output is desiredfor the present hour and surface.

INPUT

N Number of pictorial outputs desired

NA Month for which pictorial outputs are desired

NB Hour for which pictorial outputs are desired

NC Surface index for which pictorial outputs are desired

IA Present month number

IB Present hour number

1C Present surface index number

J Pictorial output indicator


For I = 1 to N

1. If NA(I) = IA and NB(I) = IB and NC(I) = 1C, then J = 1.

2. If NA(I) not equal to IA orNB(I) not equal to IB orNC(I) not equal to 1C,

Then J = 0

jr

*= noyes

3-89

SETBAK

A sub-routine which calculates coordinates of verticesfor three added shading surfaces. Window must be a rectangle.This routine used only in windows.

INPUT

XXYYZZ

HHWWAB

SBKDB

OUTPUTXV(I,K)YV(I,K)ZV(I,K)

Coordinates of upper left handwindow vertex

Height of window, feetWidth of surface, feetAzimuth angle of surface, degreesTilt angle, degreeAmount of set back, inchesBorder, inches

Coordinates of four vertices of three surfaces


1 Let S = SBK/12.0D = BD/12

:CA = COS (A)CB = COS (B)SA = SIN (A)SB = SIN (B)

H = HH+DW = WW+D+D

2. VERTEX 1

XV (1,1)YV (1,1)ZV (1,1)

VERTEX 2

XV (1,2)YV (1,2)ZV (1,2)

VERTEX 3

XV(1,3)YV(1,3)ZV(1,3)

of the first shading surface

XX+D*CAYY-D*SAZZ

of the first shading surface

XX+D*CA+S*SAYY-D*SA+S*CAZZ

of the first shading surface(also vertice 2 of the second shading surface)

XX+S*SA-H*CB*SAYY-D*SA+S*CA-H*CB*CAZZ+H*SB

3-89A-1

VERTEX 4

XV(1,4)YV(1,4)ZV(1,4)

—and so on - -

of the first shading surface(also vertice 1 of the second shading surface)

XX+D*CA-H*CB*SAYY-H*CB*CAZZ+H*SB

FIGURE 3.24A

DEFINITION OF SURFACE DIMENSIONS

3-89A-2

SHADOW

A major portion of the air conditioning load on a building comes fromsolar radiation. To improve the accuracy of load assessment and thus permita less conservative, and therefore less expensive, cooling system design, theair conditioning engineer must know how much of a building is shaded andhow much lies exposed to the sun's rays.

Development of the digital computer has now made shading amenableto rational solution. In the program, a newly-developed technique isutilized. This technique attacks the general problem and treats com-plicated shapes with as much ease as it deals with simpler configurationsThe basis of the technique is the representation of all architecturalforms as a series of plane polygons. Even curved surfaces can be sorepresented with great accuracy. For example, a sphere may be approximatedby the 20 sides of a regular icosohedron. This approximation gives amaximum error of only 3% in the shadow area cast by the sphere.

The output of the computer program is a pictorial display of theshadows and the surface upon which they are cast. Shadow areas are alsoprinted as floating point numbers. Where shadows are cast by perforatedstructures, e.g., trees, the pictorial output shows the shadow as amottled pattern.

INPUT

NVERTF : Number of vertices on receiving Polygon (R.P.)

XVERTF : x - coordinates of receiving Polygon (R.P.)

YVERTF : y - coordinates of receiving Polygon (R.P.)

ZVERTF : z - coordinates of receiving Polygon (R.P.)

NUXDIV : Number of x - divisions

NUYDIV : Number of y - divisions

NP0LY : Number of shading Polygons (S.P.)

NVERT : Number of vertices of each shading Polygon (S.P.)

PERM : Permeability of each shading Polygon (S.P.)

XVERT : x - coordinates of shading Polygon vertices (S.P.)

YVERT : y - coordinates of shading Polygon vertices (S.P.)

ZVERT : z - coordinates of shading Polygon vertices (S.P.)

3-90

NPOLYD

IDLETE

NPOLYA

NVERTA

PERMA

XVERTA

YVERTA

ZVERTA

RAYCOS

ARECI

LOOK

Number of shading Polygons deleted

Index number of deleted Polygons

Number of added Polygons

Number of vertices of added Polygons

Permeability of added S.P.'s

x-coordinates of added Polygons

y - coordinates of added Polygons

z-coordinates of added Polygons

Direction cosines of solar ray

Area of receiving Polygon

Picture?ft:= No picturePicture

OUTPUT

ASHADE : Shaded area of receiving Polygon


1. Coordinate Transformation

Designate the polygons which cast shadows as shading polygons (S.P.)and those upon which shadows are cast as receiving polygons (R.P.). Thevertex coordinates of each R.P., and its relevant SP's are transformedfrom a base coordinate system, xyz, to a new coordinate system, x'y'z1,with origin 0 attached to the plane of the R.P. The first three verticesVT» V?» V3, of the R.P. being examined are used to define this newcoordinate system. The x1 axis passes through V2 and V3, while the y'axispasses through Vi. In order that the z1 axis point outward from the surface,angle V]VoV3 must be convex and the vertices must be numbered counterclockwise.The equation of transformation is written in matrix form as

where

Y , A Scalar =

y «

_^

X0 =

ar =

A(x-xQ)"^ /"*"X 4- A/f y 'o i V o

b O

/•** •* \(X^Xg) •

/->• •*•(-r -f \x3-x2)

3-91

1st row of A = (x3-x0)/|x3-x0|

2nd row of A = (X-|-XO)/|X^-XQ|

3rd row of A = 1st row of a x 2nd row of ASolar altitude, a, and azimuth, g, must also be transformed, into

the solar direction vector, as

Sine • CosaSi no

Cos3 Cosa

2. Clipping Transformation

Any part of an S.P. whose z' is negative cannot cast a shadow onthe R.P. These "submerged" portions of the S.P.'s must be clipped off,prior to projection, lest they project "false" shadows (see Figure 3.25).This is done by finding, through linear interpolation, the points A and B,on the perimeter of the S.P. which pierce the plane of the R.P., and takingthese points as new vertices. All submerged vertices are deleted. Thisresults in a new polygon with line AB as a side, which will project onlyreal shadows.

WITHOUT ClIPPIH* APT**

Figure 3.25 CLIPPING

3. Projection Transformation

To simulate the actual casting of a shadow, the following transformation projects, along the sun's rays, all the vertex points of thetransformed and clipped R.P. 's

X = x1 -

Y =y' -- z,

4. Enclosure Test

The coordinate, clipping and projection transformation haveconverted all R.P. and S.P.'s in space into two dimensional figures in the

3-92

R.P. plane. It remains only to find the points in the R.P. plane which lieInside the R.P. and inside one or more of the S.P. projections, i.e., pointsof the R.P. which are shaded. At this point, the two-space XY is dividedinto grid and the center of each element of this grid is tested forenclosure by the R.P. and the S.P. projections. A point, P, whose coordi-nates are XpYp, is inside the polygon V-j, V2,...Vn if the followingInequality holds.

The angular change, A0-j, subtended at P by the ith side, and countedpositive counterclockwise, is given by the following formulae.

A0.(e, -

3j - 0i I

if i < n

if i = n

if |ej - 0,1 <2

if |ej - e.| > 2

YVPxrVYryp

in 1stquadrant

in 3rdquadrant

Xp-X.

Xi"XP

in 2ndquadrant

in 4thquadrant

These approximate formulae, which express A9. in right angles, replacethe time-consuming square root and arcosine computer library routines. Theyhave, by set theory, been proved adequate for the purpose.

5. Display Matrix and Typical Problem

An alphameric matrix is created corresponding to the grid elements1n the R.P. plane. A blank component represents a grid element either out-side the R.P. or exposed on the sun. An asterisk component represents ashaded grid element or one on the R.P.'s boundary. Grid elements shadedby a transmissive structure are randomly asterisked with a probabilityequal to the fraction of incident light stopped by the shading structure.Figure 3.26 shows the solution of a typical problem involving a trans-missive structure. Also see Figures 3.8 to 3.11.

3-93

>0BUILDINGBEINGEXAMINED

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Figure 3.26 THE COMPUTER OUTPUT OF A TYPICAL PROBLEM

SHG

A subroutine which calculates solar heat gain through windows.

INPUT

RDIR

BS

BG

FWS

FWG

RO

RA

RI

Intensity of direct solar radiation normal to window,Btu/hr-sq ft

Sky brightness, Btu/hr-sq ft

Ground brightness, Btu/hr-sq ft

Form factor between the window and the sky++

Form factor between the window and the ground++

(Thermal resistance at outside surface, air space, and(inside surface, sq ft~hr-°F/Btu

If more accurate data are not available, use FWS = FWG = 0.5.

3-94

SHAW : Sunlit area factor

SC : Shading coefficient if the window is shaded bydrapes or blinds.or if it has an interpaneseparation of more than 1 inch

* ~). i Transmission factors of direct and diffuseTDIF :j radiation

'outer ' (Absorption factors of direct solar radiationsflnTDT . ( through outer and inner window paneADIRI,inner 'J

ADIFO,outer :1 Absorption factors of diffuse radiation through

.n.CT . ( outer and i nner wi ndow paneAD1FI'inner >J

Note: When the value of SC is given, these Transmission andAbsorption factors should be for the standard 1/8" thickdouble strength glass (or k*fl, = 0.05 of TAR) regardlessof the type of glass used.

T : Space temperature, °R

TDB : Ambient outside air temperature, °R

OUTPUT

QRAY : Radiant heat gain through glass, Btu/hr-sq ft

QCON : Conductive heat gain through glass, Btu/hr-sq ft


1. Calculate inward flowing fraction of the radiation absorbed by theinner and the outer pane, respectively.

FI = (RO + RA)/(RO + RA + RI)

FO = RO/(RO + RA + RI)

2. Calculate components of solar load

a) Direct

QDIR = SHAW * RDIR

3-95

b) Diffuse

QDIF = BS * FWS + BG * FWG

c) Transmitted

QTRANS = QDIR * TDIR + QDIF * TDIF

d) Absorbed

QABS = QDIF * (FO * ADIFO + FI * ADIFI)

+ QDIR * (FO * ADIRO + FI * ADIRI)

3. Calculate solar heat gain through glass

If SC = 0, QRAY = QTRANS + QABS

If SC f 0. QRAY = SC * (QTRANS + QABS)

4. Calculate heat conduction through glass

QCON = U * (TDB-T)U = 1.0/(RO + RA+ Rl)

STNDRD

A subroutine that generates the response factor data required forstandard wall and roof constructions.

INPUT

ISTD : Standard surface number, 1 to 16

OUTPUT

Rl : Common ratio

NRFT : Number of response factor terms

RFX : X-Response factor set, Btu/hr-sq ft-°F

RFY : Y-Response factor set, Btu/hr-sq ft-°F

RFZ : Z-Response factor set, Btu/hr-sq ft-°F

See Figures 3.27 through 3.42 for a description of standard wallsand roofs built into the subroutine as well as the accompanying valuesof Rl, NRFT, RFX, RFY, and RFZ.

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3-112

SUN!

Day of Year, 1 to 366

Tangent of Latitude -angle

A subroutine to calculate the daily solar radiation data.

INPUT

IDOY

TL

OUTPUT

SUNRAS Hourly angle (radians) when solar altitude is zero

DEABC(l) Tangent of declination angle, TAN6

DEABC(2) Equation of time, ET, hours

DEABC(3) Apparent solar constant, A, BTU/hr-sq ft

DEABC(4) Atmospheric extinction coefficient, B

DEABC(5) SRy diffuse factor, C

Table 3.8 lists, as function of date, five variables related to solarradiation. These variables are declination angle, 6; the equation of time,ET; the apparent solar constant, A; the atmospheric extinction coefficient,B; and sky diffuse factor, C.

Table 3.8 VALUES OF 6, ET, A, B AND C FOR NORTHERN HEMISPHERE

DATE

Jan. 21Feb. 21Mar. 21Apr. 21May 21June 21July 21Aug. 21Sept. 21Oct. 21Nov. 21Dec. 21

6DEGREES

-20.0-10.80.011.620.023.4520.612.30.0

-10.5-19.8-23.45

ETHOURS

-.190-.230-.123.020.060

-.025-.103-.051.113.255.235.033

ABtu per

(hr)(sq ft)

390385376360350345344351365378387391

B

1AIR MASS"1

0.1420.1440.1560.1800.1960.2050.2070.2010.1770.1600.1490.142

C

0.0580.0600.0710.0970.1210.1340.1360.1220.0920.0730.0630.057

3-113

Table 3.8 could be stored in the computer memory, but this wouldnecessitate an interpolation procedure. In order to avoid such a problemand to save computer core, Tans, ET, A, B and C are expressed in FourierSeries form and the values are calculated as a function of the day of theyear, d, from the following truncated Fourier series.

A2*Cos(2*a>*d) + A3*Cos(3*u>*d)

+B1*S1n(u*d) + B2*Sin(2*a>*d) + B3*Sin(3*u>*d)

where U) = 2*Tr/366. = 0.01721

d = IDOY

The proper Fourier coefficients are given in Tabel 3.9.

Table 3.9 FOURIER COEFFICIENTS

Tan«S

ET

A

B

C

A0-.00527

0. 696x1 0"4

368.44

.1717

.0905

Al-.4001

. 00706

24.52

-.0344

-.0410

A2

-.003996

-0.0533

-1.14

.0032

.0073

A3

-.00424

-0.00157

-1.09

.0024

.0015

Bl.0672

-0.122

.58

-.0043

-.0034

B20.0

-0.156

-0.18

0.0

.0004

B30.0

-.00556

.28

-.0008

-.0006


1. Calculate Tans, ET, A, B and C using the following equation whereI varies from 1 to 5 and coefficients take on values shown inTable 3.9.

DEABC(I) = AQ + A] * Cl + A2 * C2 + A3 * C3

+ B1 * SI + B2 * S2 + B3 * S3

Where

Cl = cos (w*d)

SI = sin (o»*d)

3-114

and by trigometric identity

C2 = cos (2*u»*d) = C1*C1-S1*S1

C3 = cos (3*uj*d) = C1*C2-S1*S2

52 = sin (2*o)*d) = 2*S1*C1

53 = sin (3*oj*d) = C1*S2+S1*C2

2. Calculate sun rise angle

SUNRAS = cos"1 (-TL*DEABC(1))

which is obtained from general equation

sin(h) = sin(6)*sin(L)+cos(6)*cos(L)*cos(t)

(this equation is RAYCOS(3); see subroutine SUN2 forderivation)

whereh = solar altitude, radians

L = latitude, radians

t = hour angle, radians

and where SUNRAS is gotten by setting h=0, and solving for t.

3-115

SUN2

A subroutine to calculate the hourly solar radiation data.

INPUT

H

DEABC(l)

DEABC(2)

DEABC(3)

DEABC(4)

DEABC(5)

SL

CL

CN

SA

CA

OUTPUT

RAYCOS(l) :

RAYCOS(2) :

RAYCOS(3) :

RON :

BS :

Calculatedin SUN1

Hour angle, radians (calculated in main program)

Tangent of declination angle

Equation of time, hours

Apparent solar constant, Btu/hr-sq ft

Atmospheric extinction coefficient

Sky diffuse factor

Sin of latitude angle

Cosine of latitude angle

Clearness number

Sin of building azimuth angle

Cos of building aximuth angle

Direction cosine of sun in x-direction (WEST)

Direction cosine of sun in y-direction (SOUTH)

Direction cosine of sun in z-direction (UPWARD)

Intensity of direct normal solar radiation, Btu/hr-sq ft

Brightness of sky, Btu/hr-sq ft.

3-116


1. Calculate direction cosines of sun

kZSun

X (west)

Y (south)

cos(h) * cos(A) NOTE: This coordinate systemapplies only to thisderivation

From the schematic presented above, the direction cosines are asfollows:

RAYCOS(l) = cos(w) = cos(h)*sin(AZ)

RAYCOS(2) = cos(s) = cos(h)*cos(AZ)

RAYCOS(3) = SIN(h)

hwhere

AZ

= altitude of sun measured from horizontal,degrees

= azimuth of sun measured from south towardswest, degrees

From spherical trigonometry , the following relationships hold

sin(h) = sin(6)*sin(L)+cos(6)*cos(L)*cos(t)

cos(AZ)=-(sin(6)*cos(L)-cos(6)*sin(L)*cos(t))/cos(h)

sin(AZ)= *(cos(6)*sin(t))/cos(h)

J. L. Threlkeld, "Thermal Environmental Engineering", Chapter 14 - SolarRadiation, Prentice-Hall Inc., 1962.

3-117

where 6 = declination of sun, degrees

L = station latitude, degrees

t = hour angle of sun measured from south towards west,degrees

Substitution gives

RAYCOS(l) = tcos(6)*sin(t)

RAYCOS(2) =-sin(5)*cosUHcos(6)*sin(j>)*cos(t)

RAYCOS(3) = sin(6)*sin(4>)+cos(6)*cos(<|>)*cos(t)

We must build into these equations the ability to account forbuilding rotation, which is represented by the building azimuth angle, A.This rotation correction is about the z-axis and therefore will onlyaffect RAYCOS(l) and RAYCOS(2). From trigonometry, the new values afterrotation can be found by using the relationships

x =-x'*cos(A) + y'*sin(A)

y =-x'*sin(A) - y'*cos(A)

Substitution yeilds

RAYCOS(l) = -(cos(6)*sin(t))*cos(A)

-(sin(5)*cosU)-cos(6)*sinU)*cos(t))*sin(A)

RAYCOS(2) = -(cos(6)*sin(t))*sin(A)

+(sin(6)*cos(<j.)-cos(6)*sin((|>)*cos(t))*cos(A)

RAYCOS(3) = sin(6)*sinU)+cos(6)*cosU)cos(t)

To get into form in subroutine let

cos(6) = CDsin(6) = SDcos(A) = CAsin(A) = SAcos(<j>) = cos(L) = CLsin(<|>) = sin(L) = SLcos(t) = cos(h) = CHsin(t) = sin(h) = SH

3-118

Finally, by substitution of these identities,

RAYCOS(l) = -CD*SH*CA-SD*CL*SA+CD*SL*CH*SA

RAYCOS(2) = -CD*SH*SA+SD*CL*CA-CD*SL*CH*CA

RAYCOS(3) = SD*SL+CD*CL*CH

2. Calculate intensity of direct normal solar radiation

a) If RAYCOS(3) is <_ 0.001, sun has not risen yet, andtherefore set

RAYCOS(3) =0.0RON =0.0BS =0.0

b) If RAYCOS(3) is greater than 0.001, sun is up, andtherefore

RON = DEABC(3)*CN*EXP(-DEABC(4)/RAYCOS(3))

BS = DEABC(5)*RDN/(CN*CN)

Value of clearness number, CN, can be gotten from Figure 3.43

S -SUMMER(M-J-J-A-S-O)W-WINTER(N-D-J-F-M-A)

Figure 3.43 CLEARNESS NUMBERS OF NON-INDUSTRIALATMOSPHERE IN UNITED STATES

3-119

SUN3

A subroutine which calculates solar data depending upon orientationof a surface.

INPUT

WT

WA

RAYCOS

RON

BS

ROG

OUTPUT

GAMMA

ETA

RDIR

RDIF

RTOT

BG

Surface tilt angle from horizontal, radians

Surface azimuth angle, radians, clockwise fromy-axis of building

Direction cosines of sun's ray

Intensity of direct normal solar radiation, Btu/hr-sq ft(already corrected for cloud cover)

Brightness of sky (diffuse sky radiation on horizontalsurface, Btu/hr-sq ft

Ground reflectivity

Cosine of angle between zenith and outward normal ofsurface

Cosine of the solar angle of incidence, n

Intensity of direct solar radiation on surface,Btu/hr-sq ft

Intensity of diffuse radiation on surface, Btu/hr-sq ft

Intensity of total radiation on surface, Btu/hr-sq ft

Brightness of ground, Btu/hr-sq ft

For a pictorial illustration of the various angles referred to in SUN1,SUN2 and SUN3, see Figures 3.44 and 3.45.


1. Calculate brightness of ground

BG = ROG * (BS+RDN*RAYCOS(3))

2. Calculate the direction cosines (a, e and y) of the normal tothe surface. By definition

3-120

Normal to Horizontal Surface

Surface (Wall) in Consideration

Horizontal Surface

SolarAltitude,

SALT

Projection ofSun's Ray onHorizontal /Surface / Normal to

Surface (Wall)in Consideration

Figure 3.44 DEFINITION OF ANGLES

Projection of Normal to Surface (Wall) inConsideration on Horizontal Surface

NORMAL TOHORIZONTAL SURFACE

SUN

Figure 3.45 SCHEMATIC SHOWING APPARENT PATH OF SUN ANDHOUR ANGLE

3-121

a = cos(WT) = CWT

3 = sin(WA)*sin(WT) = SWA*SWT

Y = cos(WA)*sin(WT) = CWA*SWT

Since most building surfaces have tilt angles that are generallyeither 0° (roofs) or 90° (walls) and azimuth angles that generally coincidewith the four cardinal directions of the compass (0°, 90°. 180° and 270°)much computer computation time can be saved by checking for these conditionsand setting the values of the sin(WT), cos(WT), sin(WA) and cos(WA)directly instead of letting the computer software evaluate the sine andcosine.

Therefore, the following preliminary checks have been made part of SUN3.

a) If WT = 0.0 RAD (0°), surface is horizontal facing upward

CWT = cos (0) = 1.0SWT = sin (0) = 0.0

b) If WT = 1.5708 RAD (90°), surface is vertical

CWT = cos (90) =1.0SWT = sin (90) =0.0

c) For all other tilt angles

CWT = cos (WT)SWT = sin (WT)

d) If WA = 0.0 RAD (0°)

CWT = cos (0) = 1.0SWT = sin (0) =0.0

e) If WA = 1.5708 RAD (90°)

CWT = cos (90) =0.0SWT = sin (90) = 1.0

f) If WA = 3.1416 RAD (180°)

CWT = cos (180) = -1.0SWT = sin (180) =0.0

g) If WA = 4.7114 RAD (270°)

CWT = cos (270) = 0.0SWT = sin (270) = -1.0

3-122

h) For all other azimuth angles

CWT = cos (WA)SWT = sin (WA)

3. Calculate ETA, the cosine of the incident radiation on thesurface

ETA = cos (n) = o*RAYCOS(3)+g*RAYCOS(l)+Y*RAYCOS(2)

4. Calculate the intensity of the direct normal solar radiation

a) If ETA <_ 0.0, sun is not up yet

RDIR • 0.0

b) If ETA > 0.0, sun is up

RDIR * RON * ETA

5. Calculate the intensity of diffuse radiation

a) If WT <_ 0.7854 RAD (45°) surface is oriented toward sky

RDIF = BS

b) If WT > 2.35619 RAD (135°), surface is oriented toward ground

RDIF = BG

c) If WT between 45° and 135°, diffuse radiation is estimatedusing curve shown in Figure 3.46 .

If ETA < -0.2,y = 0.45

If ETA i-0.2,y = 0.55 + 0.437*ETA + 0.313*ETA**2

Then RDIF = y*BS + 0.5*BG

6. Calculate total -radiation incident upon surface

RTOT = RDIR + RDIF

J.L. Threlkeld, "Thermal Environmental Engineering", Chapter 14, SolarRadiation, Figure 14.18, Prentice-Hall Inc., 1962.

3-123

s '••»

1, «•O-2S o

llo.8

if 06

e*!S^ 0.4•sio 0.2

. iii

x- ^ss

/>•

I/1/

(

!/

, ,.. _.„ ... -0.2 0 0.2 0.4 0.6 0.8 1.0Cosine of the incidence angle to the vertical surface

° -1.0 -0.8 -0.6 -0.4

Figure 3.46 RATIO OF DIFFUSE SKY RADIATION INCIDENTUPON A VERTICAL SURFACE TO THAT INCIDENTUPON A HORIZONTAL SURFACE DURING CLEAR DAYS

3-124

TAR

A subroutine which calculates transmission, absorption and reflectionfactors for windows.

INPUT

L : Code for thickness times extinction coefficient (k*A),see Table 3.10 and Figure 3.47

C : Cosine of angle of incidence, n

NPANE : Number of panes (1 or 2)

Note: In some cases, glass manufacturers use value of transmission atNormal Incidence. In this case, using the curve given in Figure 3.47,it is possible to obtain the value of k*A. The data for the curveare taken from National Research Council of Canada Report No. 7104

OUTPUT

TDIR : Transmission factor for direct solar radiation

TDIF : Transmission factor for diffuse solar radiation

:1 Absorption factors for direct solar radiation throughADIRI • [outer and 'inner window pane

ADIFO • T' I Absorption factors for diffuse radiation through outerADIFI • 1 inner window pane

The data for the polynominal coefficients aj and tj are given inTable 3.11. These coefficients are curve-fitted and the equation formsused In the subroutine.


1. Compute transmission factors for direct solar and diffuseradiation.

5TDIR = I t. * (C**j)

j=0 J5

TDIF = 2 * I t./(j + 2)j=0 J

3-125

Table 3.10

CODE FOR THICKNESS TIMESEXTINCTION COEFFICIENT

CODE

1

2

3

1*

56

78

MEANING

1/8" sheet

}a*l = 0.10

k*^ = 0.15k*^ = 0.20

k*.g = O.UO

k*£ = 0.60

50$> transparent H.A. plate

k*£ = 1.00

.90

.80

Figure 3.47 k*£ VS TRANSMISSION AT NORMAL INCIDENCE FORSINGLE SHEET GLASS

3-126

Table 3.11

POLYNOMIAL COEFFICIENTS FOR USE IN CALCULATION OFTRANSMITTANCE AND ABSORPTANCE OF GLASS

**t

0.051/8" Sheet

0.10

0.15

1/V1 Reg.Plate

0.20

O.UO

0.60

0.80

50$ Trans.H.A. Plate

1.00

i

0123It5

0123U5

012

1*5

012

1*5

012

U5

012345

0123U5

0i23i*5

Single Glazingaj

0.01151*0.77671*

-3. 9^6578.57881

-8.381353.01188

0.016361.1+0783

-6.79030lU. 37378

-13.833571*. 921+39

0.018371.921+97

-8.89131+18.1+0197

-17.1+861+86.175^

0.019022.35^17

-10.1+715121.21+322

-19.959786.99961+

0.017123.50839

-13.8639026.31+330

-23.81+81+68.17372

0.011+06U. 15958

-15.0627927.181+92

-23.885188.03650

0.011531+. 559^6

-15.J*329U26.70568

-22.879937.57795

0.00962l+. 81911

-15.1+713725.86516

-21.691067.08711+

*d

-0.008852.71235

-0.62062-7.073299.75995

-3.89922

-0.01111+2.393710.1+2978

-8.9826211.51798-l+. 52061+

-0.012002.130361.13833

-10.0792512.1+1+161-1+. 8328(5

-0.012181.909501.61391

-10.61+87212.83698-1+. 95199

-0.010561.297112.28615

-10.3713211.95881+-*+. 51+880

-0.008350.927662.15721

-8.711+299.87152

-3.73328

-0. 0061+60.682561.821+99

-6.953257.8061+7

-2.91+1+5!+

-o. 001+960.5101+31.1+7607

-5.1+19856.0551+6

-2. "28162

Double Glazingaj, outer

0.011+071.06226

-5.5913112.1503!+

-11.780921+. 20070

0.018191.86277

-9.21+83119. ^^S

-18. 5609!* •6.539^0

0.019052.1+7900

-11.71+2662l+. 11+037

-22.6U2997.89951+0.018622.961+00

-13.1+870127.13020

-25.118778.688950.011+23l+. 11+381+

-16.6670931.301+81+

-27.819559.36959

0.01056l+.7ll+1+7

-17.331*5'+30.91781

-26.638988. 79^95

0.008195.01768

-17.2122829.1+6338

-2l+. 769158.0501+0

0.006705.18781

-16,81+82027.90292

-22.996197.3811+0

aj, inner

0.002280.31+559

-1.199082.22366

-2.052870.72376

0.001230.29788

-0.922561.58171

-l.l+OOl+O0.1+8316

0.000670.26017

-0.727131.11+950

-0.971380.32705

0.000350.22971+

*o. 583810.81+626

r.0. 676660.22102

-0.000090.1501+9

-0.275900.25618

-0.129190.02859

-0.000160.10579

-0.150350.061+870.02759

-0.02317

-0.000150.07717

-0.090590.000500.06711

-0.03391*

-0.000120.0571+6

-0.05878-0.018550.06837

-0.03191

*3

-O.OOUOl0.71*0507.20350

-20.1176319.68821*-6.71*585-0.001*380.578187.1*2065

-20.2681*819.79706-6.79619

-O.OOl*280.1*57977.1*1367

-19.9200!*19.1+0969-6.66603

-0. 001*010.366987.27321*

-19.29361*18.751*08-6.1*3968

-0.002790.161+686.17715

-15.81+81115.28302-5.23666

-0.001920.081801*. 91*753

-12.1+31+8111.921+95-l+. 07787

-0.00136o.oW+193.87529

-9.590699.16022

-3.12776

-0.000980.025763.001+00

-7.33831*6.9871*7

-2.38328

3-127

2. Compute absorption factors for direct solar and diffuseradiation.

5ADIRO = I a, __ * (C**j)

ADIRI = I a.

ADIFI = 2 * JQ ajj1nner/(j + 2)

WBF

A subroutine for calculating the wet-bulb temperature of moist airgiven the enthalpy and barometric pressure

INPUT

i H : Enthalpy, Btu/lb

PB : Barometric pressure, Inches of mercury

OUTPUT

WBF : Wet-bulb temperature, °F


; 1. If PB = 29.92 and H > 0

i Let Y = log(H)i

For H < 11.758

WBF = 0.6040 + 3.4841 * Y + 1.3601 * (Y**2) + 0.9731 * (Y**3)

For H » 11.758

WBF = 30.9185 - 39.682 * Y + 20.5841 * (Y**2) - 1.758 * (Y**3)

2. If PB 29.92, or H < 0 solve the following equation by IteratingWBF

H = 0.24 * WBF + (1061 + 0.444 * WBF) * W2

Where W2 = 0.622 * PV2/(PB - PV2)

PV2 = PPWVMS (WBF)

3-128

WEATHER

The weather subroutine obtains the hourly values of the data listedbelow, together with Station Number, Year, Month, Day and Hour (StandardTime) from "1440 Magnetic Tapes" of the National Weather Record Center,which are required by the hourly load calculation procedure.

DBT : Dry-bulb temperature, °F

DPT or : Dew point or wet-bulb temperature, °FWBT

TCA : Total cloud amount index

TOC : Cloud type index

V . :,.:. Wind velocity, knots ,

PATM : Atmospheric pressure, in. Hg

The hourly values of the data listed above can be obtained eitherin punch card or magnetic tape form from the National Weather RecordCenter, NWRC, Asheville, N.C. Detailed information on these data maybe found in:

(1) Reference Manual WBAN Hourly Surface Observations 144, April, 1966.

(2) Reference Manual WBAN Solar Radiation-Hpurly 280, April 1967.

(3) Tape Reference Manual, Airways Surface Observations, TDF 14.

See Appendix C of Volume I, User's Manual for Decoding Algorithms.

3-129

SECTION 4VARIABLE TEMPERATURE PROGRAM


The space loads calculated by the Thermal Load Analysis Programdescribed in Section 3 are determined on the basis of the followingtwo assumptions:

1. space heating and/or cooling is available any time it isrequired.

2. space temperature is always maintained at its specifiedset point.

In reality, however, the space temperature is not maintained at aconstant, but rather varies from its set point from time to time dueto:

1. throttling range and deadband of thermostat

2. undersized space heating and/or cooling capacity

3. shutdown of equipment during specified periods.

If the user wishes to investigate the effects of the above items onbuilding performance and energy usage, he can do so with the use ofthe Variable Temperature Program.

Utilizing such information as the type of thermostat, operatingcharacteristics of thermostat, heating and cooling capacity avail-able to each space, and seasonal start-up/shutdown dates for theheating and cooling plant, the Variable Temperature Program correctsthe basic loads calculated by the Thermal Load Analysis Program forthese effects and generates a new output tape containing correctedhourly space loads.

4.2 INPUT

The Variable Temperature Program requires two forms of input:

1. the output tape generated by the Thermal Load AnalysisProgram and containing hourly weather and basic space loads.

2. the card input data described in Table 5.1 of User's Manual.

In attempting to simulate the effect of varying space temperature, ,all surfaces and objects having mass, and therefore thermal inertia,have their Influence on the room's response to that effect. For thisreason, the Variable Temperature Program requires the user to define

4-1

some additional information that may not have been required by theThermal Load Analysis Program, i.e., the types of floors, ceilingsand furnishings that are part of each space. If, however, the userdesires not to go into this kind of detail, an alternative approachcan be used, i.e., make use of typical default values built into theprogram. The default values set by the program are determined asfollows:

1. For floors, the default parameters are a function of theweight of floor (Ibs per sq. ft.) which are specified inTable 4.3 of User's Manual, Reading Order LC-57, and passedalong to the Variable Temperature Program via the inputtape.

2. For ceilings, the default parameters are a function of theweight of ceiling (Ibs per sq. ft.) which is assumed to beone-half of the weight of floor.

3. For furnishings, the default parameters are a function ofthe weight of furnishings (Ibs per sq. ft.) called for inTable 5.1 of User's Manual, Reading Order VT-16.

The more detailed solution requires that the make-up of the floors,ceilings and furnishings be known and use be made of the ResponseFactor Program (Section 2) to generate the response factors corres-ponding to each.

4.3 OUTPUT

Results of the variable temperature analysis are summarized in aone-page report (Report VI) entitled "Summary of Variable TemperatureLoad Calculations" (see Figure 4.1). At the user's option, additionalreports can be called for which echo input data and detail resultsfor various phases of the analysis. The optional reports include:

1. Report V2 - Hourly Summary of Results (Figure 4.2)

2. Report V3 - Echo of Building Description Data Read FromTape (Figure 4.3)

3. Report V4 - Echo of Floor, Ceiling and Furnishing InputData .(Figure 4.4)

4. Report V5 - Echo of Space Description Input Data (Figure 4.5)

5. Report V6 - Echo of Thermostat Scheduling Input Data(Figure 4.6)

6. Report V7 - Summary of Internal Surface Data and Calculation(Figure 4.7)

7. Report V8 - Summary of Calculated Space Response Factors(Figure 4.8)

4-2

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4-10

4.4 mH ROUTINE ALGORITHMS

The calculations performed by the Variable Temperature Program areas follows:

1. Read building description data from basic load Input tape.Order of data Is as follows:

a) IOEN1 - Facility name

b) IOEN2 - Facility location

c) IOEN3 - Engineer's name

d) IDEN4 - Project number

e) IDEN5 - Date

f) NRF - Number of types of response factor surfaces

g) For each surface type

NRFT - Number of response factor terms

Rl - Common ratio

RX "

RY \ Surface response factors

RZ _

h) NDB - Number of delayed surfaces

1) For each delayed surface

IRF - Response factor type Index

AD - Surface area, sq. ft.

j) NQB - Number of quick surfaces

k) For each quick surface

ISQ - Surface roughness Index

UQ - Surface U-factor less outside filmcoefficient, Btu/hr-sq ft-F

AQ - Surface area, sq.ft.

1) NWB - Number of windows

4-11

m) For each window

NPW - Number of panes of glass

AW - Window area, sq. ft.

n) NIHT - Number of Internal heat transfer surfaces

o) For each internal heat transfer surfaceISPCllISPC2 I Spaces connected to surfaceFIHTS - Surface V*A, Btu/hr. °F

p) NUWB - Number of underground walls

q) For each underground wall

AUW - Underground wall area, sq. ft.

FUW - U-factor, Btu/hr-sq ft-°F

r) NUFB - Number of underground floors

s) For each underground floor

AUF - Underground floor area, sq. ft.

FUF - U-factor, Btu/hr-sq ft-°F

t) NS - Number of spaces in building

u) For each space

ND - Number of delayed surfaces in space

NQ -. Number of quick surfaces in space

NW - Number of windows in space

NIHTS - Number of internal H.T. surfaces inspace

NUW - Number of underground walls in space

NUF - Number of underground floors in space

MULT - Space repetition factor

FLORB - Floor area, sq. ft.

VOL - Space volume, cu. ft.

4-12

TSPAC - Set point temperature, °F

WOF - Weight of floor, Ibs/sq. ft.

ID - Index associated with each of ND delayedsurfaces

IQ - Index associated with each of NQ quicksurfaces

IW - Index associated with each of NW windows

IHTS - Index associated with each of NIHTS internalH.T. surfaces

IUW - Index associated with each of NUW undergroundwalls

IUF - Index associated with each of NUF undergroundfloors

v) JMONT - Starting month, 1 to 12

LENGH - Number of days

NOHIE - Number of hours in each month

ISTRT - Starting hour of analysis, 1 to 8760

IEND - Ending hour of analysis, 1 to 8760

2. Write all of the data read above onto the output tape inthe same order as above.

3. For each window, calculate the resistance and U-factor(less the outside film coefficient).

a) For single pane windows

REI = 0.5 inside film resistance

REA = 0.0 interpane resistance

R = REI + REA total resistance

UGW = 1.0/R U-factor

b) For multi-pane windows

REI = 0.5 inside film resistance

REA = 1.6 Interpane resistance

4-13

R - REI t REA total resistance

UGW = 1.0/R U-factor

4. Read card input data as outlined in Table 5.1 of User'sManual.

5. Calculate hour of year that boiler and chiller are to beturned on and off.

IBS = IHOY (MONS, IDAYS, NOHIE)

IBE = IHOY (MONE, IDAYE, NOHIE)

ICS = IHOY (MONS, IDAYS, NOHIE)

ICE = IHOY (MONE, IDAYE, NOHIE)

6. Calculate each space's set of response factors by accountingfor heat storage effect of delayed surfaces, undergroundwalls and floors, ceilings, intermediate floors, and fur-nishings. Effects of quick surfaces and windows will beadded within the hour loop, where the outside film co-efficient can be calculated as a function of wind speed.For each space I = 1 to NS, perform the following:

a) Determine the highest number of response factor termsthat any delayed surface in the space has.

0 MNRF = 1 (initialization)

t If ND(I) = 0, go to (6b).

• For each delayed surface J4 = 1 to ND(I),

Jl = ID(I,J4) (delayed surface index)

J3 = IRF(Jl) (response factor surface typeindex)

MNRFT = IR(J3)

If MNRF < MNRFT, reset MNRF = MNRFT.

b) Limit the minimum number of response factor terms to10.

If MNRF < 10, reset MNRF = 10.

c) Set index J=l (first term of space response factor set),

4-14

d) Initialize space response factor variable correspond-ing to 0.

SRMRT(J) = 0.0

e) Underground Walls - calculate and add into SRMRT acorrection factor to correct the underground wallload for space temperatures other than that assumedin basic load calculation.

• This correction factor should only be added inone time; therefore if J > 1, skip to calculation(6g).

• If NUW(I) <. 0, space has no underground walls;therefore skip to calculation (6f).

• For each underground wall Jl = 1 to NUW(I),

SRMRT(O) = SRMRT(J) - AUW(J2) * FUW(J2)

where 02 = IUW(I,J1).

f) Underground Floors - calculate and add into SRMRT acorrection factor to correct the underground floorload for space temperatures other than that assumedin basic load calculation.

• This correction factor should only be added inone time; therefore if J > 1, skip to calcula-tion (6g).

• If NUF(I) <, 0, space has no underground floors;therefore skip to calculation (6g).

• For each underground floor Jl = 1 to NUF(I),

SRMRT(J) = SRMRT(J) - AUF(J2) * FUF(J2)

where J2 = IUF(I,J1).

g) Delayed Surfaces - calculate response factor termfor all delayed heat transfer surfaces and add theircontribution into SRMRT(J).

• Let number of delayed surfaces in space ND1 =

• If ND1 <.0, skip to calculation (6h).

• For each del ayed surface J2 = 1 to ND1 ,

4-15

01 * 10(1,02) (delayed surface index)

A = AD(J1) (area)

03 = IRF(Ol) (response factor tndex)

If 0 > IR(03), use common ratio to determineresponse factor.

RZ(03,0) = RATOS(03) * RZ(03,0-1)

SRMRT(0).= SRMRT(O) - A * (RZ(03,0))

h) Ceilings - calculate response factor term for allceilings, if any, in space and add their contributioninto SRMRT.

• Let number of ceiling surfaces in space NCI = NC(I).

• If NCI <_ 0, skip to calculation (61).

0 For each ceiling surface 01 = 1 to NCI.

02 = ICD(I,01) (ceiling index type)

A = ACEIL(I,01) (area)

If 0 > IRC(02), use common ratio to determineresponse factor.

CRX(02,0) = CRC(02) * CRX(02,0-1)

CRZ(02,0) = CRC(02) *CRZ(02,0-1)

SRMRT(O) = SRMRT(0) + A * (CRX(02,0) - CRZ(02,J))

1) Non-underground Floors - calculate response factor termfor all non-underground floors, if any, in space and addtheir contribution into SRMRT(O).

• Let number of non-underground floors in spaceNF1 = NF(I).

t If NF1 <.0, skip to calculation (63).

• For each non-underground floor 01 = 1 to NF1,

02 = IFD(I.Ol) (floor index type)

A = AFLOR(I.Ol) (area)

4-16

If 0 ?• IRFL(J2), use common ratio to determineresponse factor.

FLRX(J2,J) « CRFUJ2) * FLRX(J2,J-1)

FLRZ(J2,J) = CRFL(J2) * FLRZ(J2,J-1)

SRMRT(J) = SRMRT(J) + A * (FLRX(J2,J) - FLRZ(J2,J)

j) Furnishings - calculate response factor term for allfurnishings in space, if any, and add their contribu-tion into SRMRT(J).

• Let area of furnishings in space AFN1 = AFN(I).

t If AFN1 <_ 0.0, skip to calculation (6k).

0 If J > IRFU(J2), use common ratio to determineresponse factor.

FURZ(J2,J) = CRFU(J2) * FLRZ(J2,J-1)

where J2 = IFND(I).

• SRMRT(J) = SRMRT(J) - AFN1 * FURZ(J2,J).

k) Add in default values for floors and ceilings, ifrequired.

t Check to see if default values for floor andceiling are required.

If user entered his own floor and ceiling viainput data, (i.e., NC(I) + NF(I) > 0, then skipto calculation (60).

i i

1) Underground Floors - using default values (DFURZ) builtinto program for underground floors, calculate theresponse factor term to account for heat storageeffect; add its contribution into SRMRT.

• If space has no underground floors (i.e.,NUF(I) £0, skip to calculation (6m).

• For each underground floor Jl = 1 to NUF(I):

J2 = IUF(I,J1) (underground floor number)

++Default values taken from Dr. T. Kusuda, "Thermal Response Factors forMulti-layer Structures of Various Heat Condition Systems", p.V.3.23,"Basement Floor", ASHRAE Semiannual Meeting, January, 1969.

4-17

If J > 10, use common ratio to calculatedefault value.

DFURZ(J) * DFURZ(J-l) * DFUCR

Update SRMRT and adjust response factor forU-factor other than the 0.665 (6" concreteon soil) upon which default values are based.

SRMRT(J) = SRMRT(J) - AUF(J2) * DFURZ(J) *

(FUF(J2)/0.665)

m) Underground Walls - using default values (DFURZ) builtinto program for underground walls, calculate theresponse factor term to account for heat storage effect;add its contribution into SRMRT.

• If space has no underground walls (i.e., NUW(I)<0),skip to calculation (6p).

t For each underground wall, Jl = 1 to NUW(I).

J2 = IUW(I) (underground wall number)

If J > 10, use common ratio to calculatedefault value.

DFURZ(J) = DFUCR * DFURZ(J-l)

Update SRMRT and adjust response factor forU-factor other than the 0.791 (6" concrete wallagainst soil) upon which default values arebased (see same reference as used in (6 1).

SRMRT(J) = SRMRT(J) - AUW(J2) * DFURZ(J) *

(FUF(J2)/0.791)

n) Ceilings - using default values (DFFRZ) built intoprogram for ceilings, calculate the response factorterm and add its contribution into SRMRT.

t There is no bypass around this calculation sinceeach space is assumed to have a ceiling andsince the user did not define one, i.e.,NC(I) = 0, a default value must be entered.

• If J > 7, use common ratio to calculate defaultvalue.

DFFRZ(J) = DFFCR * DFFRZ(J-l)

4-18

0 Update SRMRT and adjust response factor termfor weights other than the 70 lbs/sq. ft. uponwhich default values are based. (It is assumedthat the ceiling is also serving as a floor tothe space above, therefore the total weight ofsurface (140 Ibs/sq. ft.) Is being split betweena floor and a ceiling.)

SRMRT(J) = SRMRT(J) - FLORB(I) + DFFRZ(J) *

(WOF(I)/70.0) * 1.26

where 1.26 is the correction to the overallU-factor for a ceiling.

o) Non-underground Floor - using default values (DFFRZ)built into program for non-underground floors, calcu-late the response factor term and add its contributioninto SRMRT.

• Check to see if a floor has been previouslydefined, i.e., NUF(I) > 0, and if so, skip tocalculation (6p).


DFFRZ(J) = DFFCR * DFFRZ(O-l)

• Update SRMRT and adjust response factor termfor weights other than 70 Ibs/sq. ft. upon whichdefault values are based .

SRMRT(J) = SRMRT(J) - FLORB(I) * DFFRZ(J) *

(WOF(I)/70.0)

p) Furnishings - using default values (DFNRZ) built intoprogram for furnishings, calculate the response factorterm and add its contribution into SRMRT.

t Check to see if user entered his own furnishingdata, i.e., IFND(I) > 0, and if so, skip tocalculation (6q).


++ Default values taken from Dr. T. Kusuda, "Thermal Response Factors forMulti-layer Structures of Various Heat Condition Systems", p. V.3.22, "Con-crete Floor", ASHRAE Semiannual Meeting, January, 1969.

4-19

DFNRZ(O) - DFNCR * DFNRZ(J-l)

• Update SRMRT and adjust response factor termfor weights other than the 20 Ibs/sq. ft. uponwhich default values are based. (It is assumedthat the heat storage capacity of furnishings isequivalent to approximately 3" paper.)

SRMRT(O) = SRMRT(J) - FLORB(I) * DFNRZ(J) *

(WOFN(I)/20.0)

q) Store the space response factor into a matrix for lateruse.

SRF(I.J) = SRMRT(J)

r) Check to ensure at least 3 space response factor termshave been calculated, and if not, go to calculation(6w) and proceed to next term calculation.

s) Perform check to determine if space is fast responding,i.e., J = 3 and |SRMRT(J)| <.1.0 * E-15, and if so, goto calculation (6x).

t) Check to determine if all space response factor termshave been calculated. If J < MNRF, go to calculation(6w).

u) Perform the relative end test. If |SRF(I,J)/SRF(I,1)|<.1.0*E-3, go to calculation (6x).

v) Limit the number of space response factor terms to 100.If 0 >. 100, go to calculation (6x).

w) Increment 0 = J + 1 and go to calculation (6d) to begincalculation for next term.

x) Set the number of terms defined for space in question.

NSRF(I) = J

7. Calculate the sum of U * A for all internal heat transfersurfaces in each space. For each space I = 1 to NS,

JLIM = NIHTS(I) (number of surfaces)

Default values taken from Dr. T. Kusuda, "Thermal Response Factors forMulti-layer Structures of Various Heat Condition Systems", p. V.3.23,"Solid Slab", ASHRAE Semiannual Meeting, January, 1969.

4-20

SIHTC(I) * 2 FIHTS(02) for 01 =• 1 to OHM

02 = IHTS(I,01) (surface Index)

8. Initialize run parameters for each space I = 1 to NS.

SMH(I) = 1.0E10 space maximum heating

SMC(I) = -1.0E10 space maximum cooling

SLT(I) = 1.0E10 space lowest temperature

SHT(I) = -1.0E10 space highest temperature

ESHT(I) = 0.0 heat extraction difference

ETEMP(I,0) =0.0 space temperature deviation

where 0 = 1 to NSRF(I)

9. Initialize run parameters for building.

TCOOL = 0.0 total building cooling consumption

THEAT =0.0 total building heating consumption

10. Begin hourly analysis, perform following for each dayODAY = ISTRT to IEND incrementing 24 hours each time.

a) Check condition of boiler. If

"IBE > ODAY

IBS < ODAY

LIBC = 1

boiler should be off, therefore set IBOF = 0.Otherwise, set IBOF = 1.

b) Check condition of chiller. If

TICS < ODAYl

LICE > ODAYJ

chiller should be ON, therefore set ICOF = 1.Otherwise, set ICOF * 0.

c) For each hour of day, i.e.,

4-21

IHOUR = JDAY to ODAYE

ODAYE = JDAY + 23

perform following calculations.

d) Read from the input the hour's time and weatherparameters.

IDUMY - hour of year 1 to 8760

MONTH - month of year 1 to 12

IDAY - day of month 1 to 31

NDAY - day of week 1 to 7 (l=Sunday)

ITIME - hour of day, 1 to 24 corrected for DST

Jl - sun flag, 0 = up, 1 = down

KA - dry-bulb temperature, °F

LA - Wet-bulb temperature, °F

IWS - wind speed, knots

HUMRAT - humidity ratio, Ibs/lbs

PATM - barometric pressure, inches of mercury

DEN - density, Ibs/cu. ft.

ENTH - enthalpy, Btu/lb

JSC - type of day, 1 to 9

CC - cloud cover modifier.

e) Set type of day indicator for thermostat operationschedule.

If JSC =1 or JSC > 7, set IDT = 2.

If JSC = 2 to 6, set IDT = 1.

f) Begin space calculation repeating the following cal-culations for I = 1 to NS.

g) Initialize space parameters.

4-22

UQT * 0.0 sura of U * A for quick surfaces(outside film included)

UGWT= 0.0 sum of U * A for glass surfaces(outside film included)

PIHT= 0.0 partial internal heat transfer term

SUM1= 0.0 response factor sum for space

h) Read from the input tape the space load set.

IDUMY - space number

HRLDS - sensible load, Btu/hr

HLAT - latent load, Btu/hr

HRLDL - plenum return air load, Btu/hr

SPOW - space power consumption by lights andequipment, KW

QSINF - sensible infiltration load, Btu/hr

QLINF - latent infiltration load, Btu/hr

1) Calculate the sum of U * A for quick surfaces. Foreach quick surface in space Jl = 1 to NQ(I), performfollowing calculations:

JQ = IQ(I,J1) (quick surface index)

U = UQ(JQ) (surface U-factor)

IRUF = ISQ(JQ) (roughness factor index)

CALL FILM (VEL.IRUF.F)

where VEL = IMS

F = outside film resistance

UQT = UQT + AQ(JQ) * (U/(1.0 + F * U))

j) Calculate the sum U * A for window surfaces. For eachwindow in space Jl =1 to NW(I) perform following cal-culations:

JW = IW(I,J1) (window index)

U = UGW(JW) (U-factor)

4-23

ITYPE * 6

CALL FILM (YEL.mfPE.f)

where VEL = IWS

F = outstde film resistance

UGWT = UGWT + AW(JW) * (U/0-0 + F * U))

k) Calculate the Internal surface load correction factor.For each internal surface in space Jl = 1 to NIHTS(I),perform following calculations:

J2 = IHTS(I.Jl) (surface index)

J3 = ISPC1(J2) (adjacent space number)

If J3 = I, set J3 = ISPC2(J2)

PIHT = PIHT + FIHTS(J2) * ETEMP(J3,1)

1) Calculate final space response factors and set value ofETEMP. For Jl = 1 to JL1M1 where JL1M1 = NSRF(I)-1,perform the following calculations:

J2 = JL1M - Jl

ETEMP(I,J2+1) = ETEMP(I,J2)

SUM1 = SUM1 + SRF(I,J2+1) * ETEMP(I,J2+1)

m) Initialize plenum variables.

CFM1 = 0.0

CFM2 =0.0

UCFM =0.0

n) Check if space is a ceiling plenum, and if so,perform the following calculations:

• If IPLS(I) = 0, space is not a plenum, thereforeskip to calculation (10 o).

• Check if fan is operating-. If

ITIME < IVON(I,IDT)

or ITIME > IVOFF(I.IDT)

fan is off; therefore skip to calculation (10 o).

4-24

• Fan is operating; therefore perform the following:

Jl = IVS(I)

UCFM * CFM(I)

CFM1 = 1.08 * CFM(I)

CFM2 = 1.08 * CFM(I) * (TSPAC(I) -

ETEMP(Jl.l) - TSPAC(Jl) + HRLDL(Jl)

o) Calculate temperature difference between outside dry-bulb and constant space temperature assumed in basicload calculation.

TOMCS = LA - TSPAC(I)

if |TOMCS| <.o.i, set TOMCS = LOESS

p) Define various terms to be used in equations later.

SUMS = UQT + UGWT

SUM4 = SUM1 + PIHT + HRLDS + CFM2

SUMS = -SRF(I,1) + SUMS + SIHTC(I)

+ QSINF/TOMCS + CFM1

q) Set space thermostat type and check for no thermostat,i.e., floating space temperature. Also set thermostatschedule that applies.

IJUMP = ISTT(I)

If IJUMP = 0, skip to calculation (lOu).

JUMP = IVTSD(IJUMP,IDT,ITIME)

r) Set the high and low thermostat limits deviations andspace heating and cooling capacity.

TL = VTSD2(IJUMP,IDT,ITIME) - TSPAC{I)

TH = VTSD1(IJUMP,IDT,ITIME) - TSPAC(I)

HEAT = -HCAP(I) * IEOF

COOL = CCAP(I) * ICOF

4-25

s) Analysis for a Type 1 thermostat (linear or propor-tional control) (see Table 4.1).

• Calculate slope of thermostat function line.

D = (HEAT -H COOL)/(TH - TL)

• Calculate intercept of thermostat function line.

C = -(HEAT + D * TL)

• Calculate space temperature deviation fromTSPAC(I) that exists at end of hour.

TEMPS = (SUM4 - C)/(SUM5 + D)

0 Calculate heat extracted from or supplied tospace during hour.

HE = TEMPS * D + C

• Check if more heat is required than the spacehas capacity for.

If TEMPS < TL, set

HE = -HEAT

TEMPS = (SUM4 + HEAT)/SUM5

• Check if more cooling is required than thethan the space has capacity for.

If TEMPS > TH, set

HE = COOL

TEMPS = (SUM4 - COOL)/SUM5

• Go to calculation (lOv).

t) Analysis for a Type 2 thermostat (hi-low or on-offcontrol) (see Table 4.1). This thermostat suppliesno heating or cooling between the high and low limits.If the limits are hit, the extraction rate (+ or -)at that temperature is calculated and compared to theheating or cooling capacity of the space. If the spacecapacity is exceeded, the temperature is allowed tofloat the necessary amount to satisfy heat balanceequation.

4-26

Table 4.1

TYPES OF THERMOSTATS

TYPE DESCRIPTION ACTION

CoolingRate

LINEAR ORPROPORTIONALCONTROL

°FBelowSetpoint

Heating Capacity

Cooling Capacity

°FAbove

SetpointHi Limit

HeatingRate

HI-LOW ORON-OF CONTROL

CoolingRate

I°FBelo\r*—Setpoint

Lo Limit

Heating Capacity

Cooling Capacity

-^ AboveSetpoint

Hi Limit

HeatingRate

4-27

t Calculate space temperature deviation fromTSPAC(r) that exists/at end of hour.

TEMPS = SUM4/SUM5

0 Initialize heat extraction rate.

HE = 0.0

• Check if lower thermostat temperature limit isexceeded and if so, reset TEMPS and HE.

If TEMPS < TL, set

TEMPS = TL

HE = SUM4 - TEMPS * SUMS

• Check if space heating capacity has beenexceeded and if so, reset TEMPS and HE.

If |HE| > HEAT, set

TEMPS = (SUM4 + HEAT)/SUM5

HE = -HEAT

0 Check if high thermostat temperature limit isexceeded and if so, reset TEMPS and HE.

If TEMPS > TH, set

TEMPS = TH

HE = SUM4 - TEMPS * SUMS

• Check if space cooling capacity has beenexceeded and if so, reset TEMPS and HE.

If |HE| > COOL, set

TEMPS = (SUM4 - COOL)/SUMS

HE = COOL

• Go to calculation (10v).

u) Analysis for a Type 0 thermostat (floating control orno thermostat at all). This will be simulated usinga Type 2 thermostat analysis, but with high and lowlimit set at extremely large values.

4-28

t Set limit values at quantities that will neverbe exceeded.

TL -• -1.0E10

TH = 1.0E10

• Zero out space heating and cooling capacities.

HEAT =0.0

COOL = 0.0

t Proceed to calculation (lot).

v) Store space end-of-hour temperature deviation foruse next hour.

ETEMP(I,1) = TEMPS

w) Calculate end-of-hour space temperature.

STEMP = TEMPS + TSPAC(I)

x) Write out space data onto output tape.

IDUMY - space number

HE - system sensible load, Btu/hr

HLAT - system latent load, Btu/hr

ZERO - plenum return air load

SPOW - space power consumption, KW

ZERO - sensible infiltration load, Btu/hr

QLINF - latent infiltration load, Btu/hr

STEMP - resulting space temperature, °F

UCFM - CFM being circulated through a plenumspace when fan is operating.

y) Keep track of space maximum heating and cooling ratesand their time of occurrence.

• Maximum heating check

If SMH(I) > HE , reset maximum

4-29

SMHU) = HE

ITSMH(I.l) • ITIME

ITSMH(I,2) = IDAY

ITSMH(I,3) = MONTH

• Maximum cooling check

If SMC(I) < HE, reset maximum

SMC(I) = HE

ITSMC(I.l) = ITIME

ITSMC(I,2) = IDAY

ITSMC(I,3) = MONTH

z) Keep track of maximum and minimum space temperaturesand their time of occurrence.

0 Lowest space temperature check

If SLT(I) > STEMP, reset minimum

SLT(I) = STEMP

ITSLT(I,1) = ITIME

ITSLT(I,2) = IDAY

ITSLT(I,3) = MONTH

• Highest space temperature check

If SHT(I) < STEMP, reset maximum

SHT(I) = STEMP

ITSHT(I,1) = ITIME

ITSHT(I,2) = IDAY

ITSHT(I,3) = MONTH

aa) Update consumption totals for building.

If HE < 0.0, THEAT = THEAT + HE * MULT(I)

If HE > 0.0, TCOOL + HE * MULT(I)

4-30

END op SPACE LOOPcc) END OF HOUR LOOP

11. Write final report. See Figure 4.1.

NOTE: For further information on the algorithms contained within theVariable Temperature Program refer to the following additionalreferences.

1. K. Kimura, "Simulation of Cooling and Heating Loads UnderIntermittent Operation of Air Conditioning, ASHRAE SemiannualMeeting, New Orleans, January 1972.

2. G. Mitalas and D. Stephenson, "Room Thermal Response Factors",ASHRAE Semiannual Meeting, Detroit, January 1967.

3. ASHRAE Handbook of Fundamentals, Chapter 22, Air ConditioningCooling Loads Part II - Extension of Cooling Load CalculationFor Intermittent and Variable Operating Conditions, P. 425, 1972.

4-31

SECTION 5SYSTEM AND EQUIPMENT SIMULATION PROGRAM


Due to outside air requirements and the limitations imposed byvarious component control schedules, the hourly heating and coolingrequirements of a building's boilers and chillers may differ markedlyfrom the summation of hourly heating and cooling space loads. TheSystem and Equipment Simulation Program, therefore, performs two func-tions. First, it translates hourly space loads, including the ventila-tion air requirements, by means-of the individual performance charac-teristics of each fan system, into the hourly thermal requirementsimposed upon the heating and cooling plants. Second, it converts thesehourly thermal requirements into energy requirements based upon thepart-load characteristics of the heating and cooling .plant equipment.

!The System and Equipment Simulation Program is made up of a number

of functions and subroutines. (See Table 5.1 for a description ofthese routines.) The main routine, SYSIM, directs the flow of logicthrough the program and controls the order in which calculations areto be performed. The sequence of the calculations is as follows.First, the zone air flows are determined using the peak hourly heatingand cooling zone loads. Next, fans and fan motors are sized based onair flows and system pressures. In this segment, central equipment isalso sized. Then, an hour-by-hour analysis of the building's energydistribution systems is performed. Each system is examined each hourand the hourly heating and/or cooling loads calculated and summed togive the building's heating and/or cooling requirements. At the endof an hour's calculations, after the last thermal distribution systemhas been examined and any snow-melting load accounted for, the EQUIPsubroutine is called upon to convert the hourly building thermal re-quirements into hourly heating, cooling and on-site generation (ifapplicable) energy requirements. This series of calculations isrepeated hourly for the length of time called for (up to 1 year)'. Theoutput is organized in terms of monthly energy and resource require-ments for the building equipment combination in question. An annualsummary of the energy and resource consumption is then printed out asa permanent record.

The sequence of calculations outlined above is the same for a heatconservation equipment combination, except that: 1) zone air flowsare sized differently, 2) other supplemental heating requirementsmust be accounted for, and 3) specialized treatment of the double-bundled condenser refrigeration machines is necessary.

In order to follow the notations of the engineering manual, anunderstanding of variable organization as it pertains to zonelabeling is required (see Figure 5.1). The re-numbering of zonesinternally by the program has resulted in increased flexibility tothe user and a reduction of computer storage requirements. As

5-1

regards assigning zones to energy distribution systems, the user neednot be concerned with, zone sequence when generating the load tape.They may be specified in any order. Zones may be omitted or repeated.

Regarding the program structure, a storage requirement savings isrealized since variables which were once doubly-subscripted may now besingly subscrpted. An example of this potential savings using theexample of Figure 5.1 zone/system relationships is illustrated inFigure 5.2. Input tape variables (V numbers) are assigned via vari-able •SPACN|(:jv Each zone "j" of system "k" has a corresponding "i".Thus one doubly-subscripted variable (SPACNkj) is used to identifythe particular "£" variable location of a given zone on a given sys-tem.LOAD PROGRAM SPACENUMBERING

SIMULATION PROGRAMINTERNAL NUMBERING

U)

(i)

1

1

2 3

2 3

4

4

5

5

6

6

7 8 9 10

7 8 9 10

^-^

11 12 13 »\LOAD PROGRAMNUMBERING (SPACNj

ZONE NUMBERING

SYSTEM NUMBERING

(j)(k)

4

1

10

2

1

3

3

4

5

5

1

5

1

8

2

7

3

2

6

1

2

2

4

3

3

6

1

4

2

4

3

1

5

Figure 5.1 SYSTEM SIMULATION PROGRAM NUMBERINGORGANIZATION w/example

co

1 2 3 4 5

Number of zones (j)

Figure 5.2 SYSTEM/ZONE MATRIX using doubly-subscripted variables (k,j)

5-2

TABLE .5.1

SYSTEM AND EQUIPMENT SIMULATIONSUBROUTINES AND FUNCTIONS

NAME FUNCTION

SYSIM

HTCON

TDATA

CDATA

FSIZE

MZDD

SZRHT

FHTG2

FCOIL

INDUC

VARVL

RHFS2

FANOF

ZL03

BRAD2

AHU

MXAIR

ECONO

CCOIL

TRSET

PTLD

TEMP

PSYCH

PSY1

PSY2

PPWVM

Main routineHeat conservationReads off header data from LOAD tapeReads card inputFan sizingMulti-zone and dual duct fan system simulationSingle-zone/sub-zone reheat fan systemFloor panel heating systemsFancoil unit simulation (2- and 4-pipe)Induction unit fan system simulation (2- and 4-pipe)Variable volume fan system simulationSimulation of: Single-zone fan system w/face and bypass

dampers ,Unit ventilator,Unit heater,Constant volume reheat fan system.

Load handler when fan system is offZone load organizer: calculates reheating and recooling

loadsBaseboard radiation simulationAir Handling Unit simulationMixed air calculationEconomizer cycle simulationCooling coil simulationLinear interpolation routinePart load fan power calculationTemperature calculationPsychrometricsPsychrometricsPsychrometricsPsychrometrics

5-3

TABLE 5.1 (CONT'D)

NAME FUNCTION

ALOG1

HUM!DENSY

ERROR

MAX

H20ZNWZNEW

EQUIP

STTUR

CENT

RECIPABSOR

SNOWMENGYC

Base 10 logarithmsHumidity ratio calculationA1r density calculationPrints error messagesMaximum value calculationZone moisture change and requirement calculationHumidity ratio calculationBoilers, chillers and on-site generation systemsSteam turbineCentrifugal water chillerReciprocating water chillerSteam absorption water chillerSnow meltingEnergy consumption output table

5-4


The main routine of the System and Equipment Simulation Program.SYSIM controls the flow through the program. This routine is dividedroughly into three sections.

t Initial Sizing. Subroutines are called to read card input data(CDATA) and to read off header data from the LOAD tape (TDATA).A third subroutine (FSIZE) is then called to size zone and systemair flows. Finally, central system power consuming equipment(i.e., pumps, fans, cooling towers, motors, engine generators,steam turbines) are sized/

t Hourly Calculations. The function of this mode is to firstread hourly weather data and zone loads from the LOAD tape.Secondly, the appropriate energy distribution subroutines arecalled to calculate energy conversion system loads (heating,cooling, water and power requirements). Thirdly, subroutineEQUIP is called to calculate resource requirements necessary tosatisfy heating, cooling and power needs. An account of energydistribution and conversion system loads not met is kept andprinted in this mode at the end of each month.

• Monthly summaries. The third mode indicates the activity of theprogram by printing a central equipment size summary and a tableof energy and resource requirements (demand and consumption) foreach month.

INPUT

Cards - A description of card input variables may be found inSection 6 of the Users Manual (Vol. I).

Tape - Hourly data required by the program is defined in Table 5.2.This includes both weather and zone load information.

OUTPUT

Printer - Printed output is discussed in Table 5.3. Also refer toSection 6 of the User's Manual for examples of the program'soutput.

COMMON

The System and Equipment Simulation Program is organized such thatuse of common by second-, third-, etc. order subroutines andfunctions is the exception rather than the norm. However, most ofthe variables required by first-order subroutines are located inCOMMON. These variables are defined in Table 5.4.

5-5

TABLE 5.2

ORGANIZATION OF INPUT LOAD TAPE TO SYSTEM ANDEQUIPMENT SIMULATION PROGRAM

On the input tape, after the header data, the following variablesappear for each hour:

I HOUR

IMOY

IDOM

NDOW

IHOD

ISUN

TOA

TWB

VEL

WOA

PATH

DOA

HOA

JSC

CCM

Hour number, hour of year

Month of year

Day of month

Day of the week

Hour of the day

Sun index which indicates whether or not thesun is up (0 = sun up; 1 = sun not up)

Outside air dry-bulb temperature (°F)

Outside air wet-bulb temperature (°F)

Wind velocity (knots)

Outside air humidity ratio (Ib water/lb dry air)

Barometric pressure (inches of mercury)

Outside air density (lbm/ft3)

Enthalpy of outside air (Btu/lb dry air)

Day type (i.e., weekday,Saturday, Sunday,Holiday, Xmas)

Cloud cover modifier

For each zone, the following variables appear on the input tape:

IS

SLPOW

Space number

Zone sensible load (Btu/hr)

Zone latent load (Btu/hr)

Zone lighting load picked up by return air(Btu/hr)

Zone internal lighting and machinery powerconsumption (KW)

5-6

TABLE 5.2 (CONT'D)

QSINF. : Zone sensible infiltration load (Btu/hr)

QLINF. : Zone latent infiltration load (Btu/hr)* 4

STEMP. : Zone temperature (°F) (calculated in VariableTemperature Program)

UCFM . : Air flow if zone is a ceiling plenum (ft3/m1n)(calculated in Variable Temperature Program)

5-7

TABLE 5.3

OUTPUT OF SYSTEM AND EQUIPMENT SIMULATIONPROGRAM

(NOTE: optional printout not covered here)

PROGRAM VARIABLE DESCRIPTION

Input Recap

Recapitulation of input card data

Energy Analysis Header

FAC - Building or project name

CITY - Location

ENGR - Name of userPROJ - Project numberDATE - Date

Energy Distribution System Summary

FBHPS. - Supply fan brake horsepower, system k

FBHPR. - Return fan brake horsepower, system k

FBHPEk - Exhaust fan brake horsepower, system k

JMAXk - Number of zones on system k

CFMAXk - Supply air, system k (CFM)

CFMINk - Minimum outside air, system k (CFM)

CFMEXk - Exhaust air, system k (CFM)

ALPCTk - "Minimum outside air percent of supply air,system k

Zone Air Flow Summary

CFMSi - Supply air, zone i (CFM)

CFMXi - Exhaust air, zone i (CFM)

- Set point temperature, zone i (°F)

5-8

TABLE 5.3 (CONT'D)


Loads Not Met

QCLNM1

QCPNM1

IHCNM,

QHLNM

QHPNM1

IHHNM1

QRCNM

QR6NM

IHRNM

QBCNM

QBPNM

IHBNM

1

Monthly accumulation of cooling loads notmet, zone 1 (MBTU)

iPeak cooling load not met, zone 1 (MBH)

Number of hours 1n month cooling load notmet, zone 1 :

Monthly accumulations of heating loads notmet, zone 1 (MBTU) ;

Peak heating load not met, zone 1 (MBH)

Number of hours in month heating load notmet, zone 1 \

Monthly accumulation of central coolingsystem loads not met due to undersizedequipment (MBTU)

Peak central cooling system load not met (MBH)

Number of hours in month central coolingsystem load not met

Monthly accumulations of boiler loads notmet due to undersized equipment (MBTU)

Peak boiler load not met (MBH)

Number of hours in month boiler load not met

NOTE: Loads not met are tabulated only once (I.e., zoneloads not met are not carried over Into centralequipment loads not met).

5-9

TABLE 5.3 (CONT'D)


Summary of Equipment Sizes

NUMC

SIC

NUMB

SZB

NUMT

SZT

M4

SZE

CAPH

CAPC

CFMCT

HPCTF

HPBLA

GPMCL

HPCLP

GPMCN

HPCNP

GPMBL

HPBLP

Number of chillers

Size of chillers (tons)

Number of boilers

Size of boilers (MBH)

Number of steam turbines

Size of steam turbines (HP)

Number of on-site generation engines

Size of on-site generation engines (KW)

Total heating capacity (MBH)

Total cooling capacity (tons)

Cooling tower air flows (CFM)

Horsepower of cooling tower fan motor (HP)

Horsepower of boiler auxiliaries (HP)

Chilled water flow (gpm)

Chilled water pump horsepower (HP)

i Condenser water flow (gpm))Condenser water pump horsepower (HP)

Boiler water flow (gpm)

Boiler water pump horsepower (HP)

5-10

TABLE 5.3 (CONT'D)


ENGY : Monthly resource consumptions and demands.A 12 x 2 x 18 matrix with indices definedas Indicated below. This variable is trans-ferred to subroutine ENGYC where themonthly tabulation is printed.

FIRST SUBSCRIPT: MONTH

1 is January2 is February3 is March4 is April5 is May6 is June7 is July8 is August9 is September10 is October11 is November12 is December

SECOND SUBSCRIPT: MODE OF ENERGY

1 is Demand2 is Consumption

THIRD SUBSCRIPT: TYPE OF ENERGY

1 is Maximum monthly heating2 is Maximum monthly cooling3 is Electric, internal lights and

building equipment4 is Electric, external lights5 is Electric heat (boiler and auxiliaries,

and hot water pumps)6 is Electric cool (chillers, chilled

water pumps, and cooling tower fan)7 is Gas heat8 is Gas cooling9 is Gas generation10 is Steam heat11 is Steam cooling12 is Oil heat13 is Oil cooling14 is Diesel fuel generation15 and 16 not used17 is City water18 is Fan power

5-11

TABLE 5.4DEFINITION OF

VARIABLES IN COMMON

IPRT1

IPRT2

IPRT3KO

1C

IT

IBOIL

ICHIL

I FAN

QSj)

QLj>

SLPOWJ-QSINF^

QLINFJ(

STEMPi

TSPj}

TOAWOA

HOA

DOA

PATM

TCO

KBLDG

KMAX

IZNMX

MSTRT

Optional print flag-1Optional print flag-2Optional print flag-3Line printer unit numberCard reader unit numberInput tape unit number

Boiler on/off flag (l=on; 0=off)Chiller on/off flag (l=on; 0=off)Fan system shut-off flag (0=fans run continuously,

l=fans may be shut off)2=fans and baseboard radia-

tors may be shut off)Zone sensible load (Btu/hr)Zone latent load (Btu/hr)Light heat into ceiling plenum above zone (Btu/hr)Space light and power (KW)Zone sensible loss due to infiltration (Btu/hr)Zone latent loss due to infiltration (Btu/hr)Space temperature at a given hour (°F)Air flow through zone if it is a plenum space(ft3/min)Zone set point temperature (°F)

qZone volume (ft )

Outside air dry-bulb temperature (°F)Outside air humidity ratio ( airOutside air enthalpy (Btu/lbm)

oOutside air density (Ibm/ft )Barometric pressure (in.Hg.)Changeover temperature (°F)Heat conservation building flagNumber of energy distribution systemsNumber of zones to be studiedMonth in which study begins

5*12

TABLE 5.4 (CQNT'D)

NDAYS

MEND

I MAXm

KFAN^

JMAXk

CF.MAXkCFMEXkALFAMkOACFM

RHSPkwspkDAVEk

WRAk

DRAk

PW6ALk

FMASSkFMASRkFMASXR

TFNPSk

TFNPRk ; ...

TFNPEk :

FBHPSkFBHPRkFBHPEkDTFNS.

K

DTFNR.N

MXAOkIVVRHk

Length o f study (days). . 'Last month of study - .^ / : - • "Number of hours in montji m Xra - 1 ,12)

' • • ' • " .'•'.'..'•' .'':"•./•'"'"•'•. '

Energy distribution system index

Number of zones on system kDesign supply air. of system k (ft /min)Exhaust air, system i< (ft /min)Minimum fraction .outside air, system k

O

Minimum ventilation air, system k (ft /min)Relative humidity set point, system k (% R.H.)

Humidity ratio set point, system K v^bm-dry air'o

Average air density, system k (Ibm/ft )

— rsctut ii air ii HIM i u i uy r a u i u , oy o icin N \-> > i\y*\/ an J»o

Return air density, system k (Ibm/ft )

Process water volume, system k (gals)

Supply air mass, system k (Ibm-air/hr)Return air mass, system k (Ibm-air/hr)Exhaust air mass, system k (Ibm-air/hr)

Total supply fan pressure, system k (inches)

Total return fan pressure, system k (inches)Total exhaust fan pressure, system k (inches)Supply fan brake horsepower, system k (bhp)Return fan brake horsepower, system k (bhp)Exhaust fan brake horsepower, system k (bhp)Air temperature rise across supply fan, system k,at full load (°F)Air temperature rise across return fan, system k,at full load (°F)Mixed air option, system kVariable volume reheat option, system k

5-13

TABLE 5.4 (CONT'D)

ICZNk

ITMPCk>1

ITMPC

NVFCkVVMINk

TCOFCk

k,2

TFIXlk

TFIX2kRIPA,,

Zone in which, humidistat is located, system k,(a "j" number).:Atr temperature .control mode, system k

Air temperature control mode, system kType of .'fan damper control, system kMinimum-al r f 1 ow through var i abl e vol ume boxes,system: Jcy:;v' ;.•''.-' •' '... .: '' •Two-pipe(Itidyctlon unit fan system changeovertemperature, of" -floor panel heating system hotwater shut-off temperature, system k ( F)Fixed hot. deck or. AHU discharge temperature,system fc;i(PF) :: ,:>:•;Fixed cold deck:temperature, system k (°F)Ratio of induced to primary air, system k

CFMiCFMSCFMR

ZMASSiZMASiZMASR,

ZMASX

QSI,TSWZ

WREQD1ALFBR iCBTUi

QCLNM,

QCPNM

IHCNM

QHLNM1

Supply air flow rate, zone i (constant)(cu ft/min)Supply air flow rate; zone i (variable) (cu ft/min)Return air flow rate'i zone i (cu ft/min)Exhaust air flow rate, zone i.(cu ft/min)Supply air mass flow, zone i (constant)(Ibm-air/hr)Supply air mass flow, zone i (variable)(lbm-air/hr)Return air mass flow, zone i (Ibm-air/hr)Exhaust air mass flow, zone i (Ibm-air/hr)Sensible heating load, zone i (Btu/hr)Supply air temperature, zone i (°F)Calculated humidity ratio, zone i (lbm-H20/lbm-dry air)Required humidity ratio .zone i (lbm-H20/lbm-dry air)Active length baseboard radiation, zone t-:-(i:$fuft)Baseboard radiation heat output per linear foot itstandard conditions, zone i (Btu/hr-lin.ft), . ;.Monthly accumulation of cooling loads not met,(zone 1) * MULTi (Btu) : ;

Monthly peak cooling load not met, zone 1 (Btu/hr-)Number of hours cooling load not met, zone i (hrsj

K?iP^hl^D5c9umulation of heating loads not met,(zone •!)*nULI •»

5-14

TABLE 5.4 (CONT'D)

QHPNM1IHHNM1

IPLEfL

Monthly peak heating load not met, zone i (Btu/hr)Number of hours heating load not met, zone 1 (hrs)

LOAD program space number of plenum above zone 1

SPACNk,J

MULT,

Number of space as per LOAD program, applied tosystem k, zone jMultiplication factor,zone iVariable subscript i

TOALO,n

TO AH In

nTLOTHInI SETk,m

TFBHP

EFF

Low outside air temperature at which system tem-perature is THIn, reset schedule n ( F)High outside air temperature at which system tem-perature is TLO , reset schedule n ( F)Low system fluid temperature, reset schedule n (°F)High system fluid temperature, reset schedule n (°F)

Reset temperature schedule index, system k, resetitem m (an "n" number) (V is defined in Table 6.4,User Manual)

Total fan brake horsepower (bhp)Pump and fan motor efficiency

PLOCkPAREAkPERIM^

KFLCV

CINSL

DINSL

Location of floor heating panels, system k2

Floor area covered by heating panels, system k (ft )Exposed perimeter of floor, system k (lin.ft)Type of floor covering (l=bare concrete; 2=tile;3=carpeting)Floor insulation conductance (Btu/hr-sq-ft-°F)Floor insulation thickness (ft)

TLCHLTPSPPSTESTM

PESTM

SZT

Chilled water set point temperature (°F)Steam turbine entering steam temperature (°F)Steam turbine entering steam pressure (psig)Boiler supply and absorption chiller enteringsteam temperature (°F)Boiler supply and absorption chiller enteringsteam pressure (psig)Steam turbine size (hp)

5-15

TABLE 5.4 (CONT'D)

NUMT

RPMSZE

FFLMN

KREHT

HVDF

HVHO

CFMBN

CFMBX

CFMBE

PWBIL

PWOL

TLCNM

TLCMN

TCWIN

TWWIN

TECMN

HDCLPHDCNP

HDBLPHDWWP

GPMCL

GPMCN

GPMBLGPMWW

HPCLP

HPCNP

Number of steam turbinesSteam turbine speed (rpro)Engine/Generator set sizeMinimum part load cut-off for chillersSource of reheat coil energy

Heating value of diesel fuel (Btu/gal)Heating value of heating oil (Btu/gal)

Building total minimum outside air (cii ft/min)Building total design load supply air (cu ft/min)Building total exhaust air (cu ft/min)

Building peak base power load (KW)Power of external lighting (KW)

Maximum allowable condenser water temperature (°F)Well or city water design return water temperature

City water supply temperature (°F)Well water supply temperature (°F)Cooling tower water low limit temperature (°F)

Total chilled water pump head (ft)Total condenser water pump head (ft)Total boiler water pump head (ft)Total well water pump head (ft)

Chilled water flow rate (gpm)Condenser water flow rate (gpm)Boiler water flow rate (gpm)Well water flow rate (gpm)

Chilled water pump power (bhp)Condenser water pump power (bhp)

5-16

TABLE 5.4 (CONT'D)

HPBLP

HPWWP

HPCTF

HPBLACFMCT

Boiler water pump power Cbhp)Well water pump power Cbhp)Cooling tower fan power (bhp)Boiler accessory power (bhp)Cooling tower air flow (cu ft/m1n)

IHSRTIHSIP

NCASE

NRSET

KHCST

Hour of year at which simulation may beginHour of year at which simulation may endNumber of cases to be runNumber of reset schedules to be readHeat conservation system flag

NUMBSZB

BON

BOFF

Number of boilers

Size of each boiler (MBH)

Hour of seasonal boiler start-up (hour of year)Hour of seasonal boiler shut-down (nour of

NUMCSZCCONCOFF

Number of chillersSize of each chiller (tons)Hour of seasonal chiller start-up (hour of year)Hour of seasonal chiller shut-down (hour of

KSNOWQSNOWSAREA

Type of snow melting systemSnow melting system design load (Btu/hr)Snow melting slab area (sq ft)

ASYSncABLDGncAM1ncAM2ncAM3ncAREHTnc

System identification number, run ncHeat conservation flag (l=no; 2=yes), run ncType of chiller, run ncSource of chiller energy, run ncSource of general heating energy, run ncSource of reheat coil energy, run nc

5-17

TABLE 5.4 (CONT'D)

AM6nc - Type of auxiliary chiller, run ncAM7nc - Type of supplemental heat, run ncAM4nc - Number of engine/generator sets, run ncAM5nc : - Type of engine/generator set, run nc

QRCNM - Monthly accumulation of chiller loads not metdue to undersizing (MBTU)

QRPNM - Monthly peak chiller load not met (MBH)IHRNM - Number of hours chiller load not metQBCNM - Monthly accumulation of boiler loads not met

due to undersizing (Btu)QBPNM - Monthly peak boiler load not met (Btu)IHBNM - Number of hours boiler load not met

5-18


1. Call subroutine CDATA to read and recap card input data.

2. Call subroutine TDATA to read off input tape header datastopping before hourly weather and building load informationis encountered.

3. Read daily snowfall data, if snow-melting system is used.

4. Call subroutine FSIZE to calculate the following quantities:

PWBIL

CFM.J

CFMR.

CFMAXc

CFMEX

ALFAM

OACFM

WRA.

FBHPS

FBHPR

FBHPE.

TFBHP

: Peak building base power (KW)

: Peak supply air volume for zone i (CFM)

: Return air volume for zone i (CFM)

: Total air supplied by fan system k

: Auxiliary exhaust air removed from zonesserved by system k (CFM)

: Minimum outside air required for fan system k(CFM)

: Percent of minimum outside air required forfan system k

: Minimum outside air for system k

: Initialize return air density for system k

: Initialize return air humidity ratio, system k(lbm-H20/lbm-dry air)

: Supply fan brake horsepower required for fansystem k (bhp)

: Returfi fan brake horsepower required for fansystem k (bhp)

: Exhaust fan brake horsepower required for fansystem k (bhp)

: Summation of fan brake horsepowers for allsystems (bhp)

5-19

DTFNSk : Temperature rise across supply fan, system k

DTFNRk : Temperature rise across return fan, system k

ZMAS.J : Supply air mass flow to zone f at design load (Ibm/hr)

ZMASX^ : Exhaust air mass flow from zone i (Ibm/hr)

ZMASRj : Return air mass flow from zone i at design load1 (Ibm/hr)

FMASS^ : Total supply air mass flow of system k at designconditions (Ibm/hr)

FMASXk : Total exhaust air mass flow of system k (Ibm/hr)

FMASR^ : Total return air mass flow of system k at designconditions (Ibm/hr)

CFMBE : Z CFMEX,k=l,kmax

CFMBX : Z CFMAX,.k=l,kmax *

CFMBN : Z CFMIN.k=l,kmax K

5. Check type of system

If conventional or on-site generation, go to calculation 6.If heat conservation, call HTCON and then go to 31.

6. Size Central Equipment

6.1 Heating and cooling capacities

CAPH = SZB * NUMB

CAPC = SZC * NUMC

SZT = SZC

NUMT = NUMC

6.2 Steam turbines (to drive centrifugal chillers).

If Ml=5, determine number of steam turbines required.

NUMT = NUMC

5-20

Determine size of steam turbines required, if used,assuming 1 HP per ton of cooling.

SZT = SZC

6.3 Compute total heating capacity required.

If Ml = 4 (steam absorption chiller),

Check boiler size with steam turbine requirementsfor possible updating. Steam turbine require-ments based upon peak cooling hour assuming20 Ibs steam per ton of cooling

CAPH1 = CAPC * 20.0 * 33.472/34.5

If CAPH < CAPH1,

CAPH = CAPH1

SZB = CAPH/NUMB

6.4 Size all pump water flows.

Chilled water flow rate (gpm)

GPMCL = 2.4 * CAPC

Condenser water flow rate (gpm)

If Ml f 4, 6PMCN = 3.0 * CAPC

If Ml = 4 (steam absorption chiller),

GPMCN = 3.5 * CAPC

Boiler water flow rate (gpm)

6PMBL = CAPH * 1000.0/(500.0 * 20.0)

6.5 Size pump motors assuming a pump efficiency of 60%.

Chilled water pump horsepower

HPCLP = GPMCL * HDCLP/(3962.0 * 0.6 * EFF)

Condenser water pump horsepower

HPCNP = GPMCN * HDCNP/(3962.0 * 0.6 * EFF)

5-21

Boiler water pump horsepower

HPBLP = GPMBL * HDBLP/C3962.0 * 0.6 * EFF)

6.6 Horsepower requirement for motors running boiler auxiliaryequipment such as fans, blowers, pumps, etc. should becomputed. From American Standard catalog for packagedboilers ranging invsize from 20 to 750 HP, the auxiliaryhorsepower requirement was approximately 1/20 of the totalboiler horsepower capacity; therefore

HPBLA = CAPH * 1000.07(33472.0 * 20.0)

6.7 Size cooling tower fan.

Cooling tower air flow requirement

For all chillers except steam absorption, use300 cfm per ton of cooling; therefore

CFMCT = 300.0 * CAPC

For steam absorption system, use 350 cfm per tonof cooling; therefore

CFMCT = 350i.O * CAPC

Cooling tower fan horsepower requirement assuming1.0 inch water total pressure

HPCTF = CFMCT * 1.0/(6346.0 * EFF)

6.8 Sum heating and cooling equipment brake horsepowerdemand.

HPHEQ = HPBLA + HPBLP where HPHEQ has units of horsepower

HPCEQ = HPCTF + HPCLP + HPCNP where HPCEQ has units ofhorsepower

6.9 Size on-site generation plants.

Calculate maximum building electrical demand assumingall electrical equipment operating (electric resist-ance heating and electrically-driven compressivecooling not allowable with on-site generation).

BKWDM = PWBIL + PWOL + (TFBHP + HPCEQ + HPHEQ)

* 0.7457

5-22

Calculate number and size of on-slte generation units.

If M4 ? 0, set

NUME = M4 where NUME 1s number of engines.

Size of engines 1s then

SZE = BKWDM/NUME

If SZE > 500 KW, Increase the number of enginesuntil SZE <_ 500 KW.

Finally, set M4 = NUME.

If M4 = 0, set

NUME = 2 where NUME is number of engines

Size of engines is then

SZE = BKWDM/NUME

If SZE > 500 KW, increase NUME untilSZE <. 500 KW.

Finally, set M4 = NUME.

7. Begin hourly energy consumption analysis repeating calculations7 through 14 for every hour of the analysis.

Read hourly weather data which includes:

IHOUR Hour number, hour of year

IMOY Month of year

IDOM Day of month

NDOW Day of the week

IHOD Hour of the day

ISUN Sun index which indicates whether or not thesun is up

TOA : Outside air dry-bulb temperature (°F)

TWB : Outside air wet-bulb temperature (°F)

VEL : Wind velocity (knots)

5-23

WOA

PATM

DOA

HOA

JSC

CCM

Outside air humidity ratio Ob water/lb dry air)

Barometric pressure (inches of mercury)o

Outside air density (lbm/ft )

Enthalpy of outside air (Btu/lb dry air)

Day type (i.e., weekday, Saturday, Sunday,holiday, Xmas)

Cloud cover modifier (0=opaque, l=clear)

Read zone load data for all zones on tape.

IS A : Space number

QSj : Zone sensible load (Btu/hr)

Zone latent load (Btu/hr)

QLITEf) : Zone lighting load picked up by return air* (Btu/hr)

SLPOWo : Zone internal lighting and machinery power* consumption (KW)

QSINFn : Zone sensible infiltration load (Btu/hr)

QLINFft : Zone latent infiltration load (Btu/hr)

STEMP£ : Zone temperature (°F)

Initialize total net fan brake horsepower (TNFBP).

TNFBP = TFBHP

8. Call energy distribution systems.

Check type of fan system.

If KFAN. = 1, call RHFS2K 2, call MZDD

3, call MZDD4, call SZRHT5, call RHFS26, call RHFS27, call FHTG28, call FCOIL9, call FCOIL10, call INDUC11, call INDUC12, call VARVL13, call RHFS2

5-24

Each of the above subroutines simulates the performanceof a given system and returns the following quantities:

QFPCk - system cooling requirement (Btu/hr)

QFPH. - system primary heating requirementK (Btu/hr

QFPRH., - system reheat coil heating requirementK (Btu/hr)

QFPPH. - system preheat coil heating requirementK (Btu/hr)

TQB. - heating requirement of baseboard radia-tion in zones served by system k (Btu/hr)

WATER. - steam humidifier water requirementK (Ibm/hr)

PWI_k - base power (KW)

TNFBP - total net fan brake horsepower, all fansystems (bhp)

9. Sum building hourly cooling, heating, reheat, zone power, andwater resource requirements.

QHBC = E QFPCkk=l,kmax -WATER.

QHBRH = E QFPRHkk=l,kmax

PWILM = E PWLkk=l,kmax

H20 = E WATERkk=l,kmax

10. Determine if cooling tower fan is operating.

If chiller is off (ICHIL=0), set KCTF=0, andgo to calculation 11.

If chiller is on (ICHIL=1), assume a 7°F approach fortower, therefore temperature of water entering condenser is

TECON = TWB + 7.0

If from previous hour,tower is on (KCTF=1), and if(TECON >.TECMN + 10), set KCTF=1; otherwise KCTF=0.

5-25

If from previous hour, tower is off (KCTF=0), and if(TECON < TECMN), set KCTF=0; otherwise KCTF=1.

11. Determine hourly electrical demand of the building (ELDEM) foron-site generation, if used.

If ISUN = 0, exterior lights are OFF; therefore, set

PWEL =0.0

If ISUN = 1, exterior lights are ON; therefore, set

PWEL = PWOL

If cooling equipment only is ON,

ELDEM = PWILM + PWEL + (TNFBP + HPCLP + HPCNP

+ HDCTF * KCTF) * 0.7457

If heating equipment only is ON,

ELDEM = PWILM + PWEL + (TNFBP + HPHEQ) * 0.7457

If heating and cooling equipment are ON,

ELDEM = PWILM + PWEL + (TNFBP + HPCLP + HPCNP

+ HDCTF * KCTF + HPHEQ) * 0.7457

12. Check type of snow-melting system.

If KSNOW = 0, no snow-melting system. Go tocalculation 13.

If KSNOW = 1 or 2, snow-melting considered.

Calculate amount of snowfall for the hour, assumingthat 1/24 of the day's total fell during the hour.

SNOW = 0.1 * SNOWF(ID)/24.0

where SNOW has units of equivalent inches of water,SNOWF(ID) has units of inches of snow and ID is theday number of the year, calculated as follows:

ID = 1 + IHOUR/24

Call SNOWM subroutine which calculates QTOT, thesnow-melting load.

Add QTOT to heating requirement of building.

5-26

If KSNOW = 1, liquid type snow-meltingsystem; therefore,

QHBH = QHBH - QTOT

If KSNOW = 2, electric type snow-meltingsystem; therefore,

ELEH = ELEH + QTOT/3413.0

13. Calculate hourly energy consumption.

Call EQUIP which calculates the following:

GASCGASHGASGOILC See subroutine EQUIP algorithms for?J:JP explanation of these variablesSTMHELECELEHFUELChiller loads not met due to undersized equipmentBoiler loads not met due to undersized equipment

14. Keep running total of hourly energy consumption for eachmonth. Update the following quantities each hour.

ENGY (M.2,3)ENGY (M.2,4)ENGY (M.2,5)ENGY (M,2,6)ENGY (M,2,7)ENGY (M.2,8)ENGY (M.2,8)ENGY (M,2,9) See subroutine ENGTG algorithms

ENGY iS'l'l? for exPlanation of ENGY matrix.ENGY (M',2J2ENGY (M.2,13ENGY (M.2,14ENGY (M,2,15)ENGY (M,2,1.6)ENGY (M,2-,17)ENGY (M,2,18)

15. Keep a record of maximum hourly energy demands by checking,at the end of each hour's calculation, and updating thefollowing energy demand quantities.

ENGY (M.l.l)ENGY (11,1,ENGY (M,.l>3ENGY -01,1,4) ^

" '' - 5-27

ENGY (M.1,5)ENGY (M,l,6)ENGY (M,l,7)ENGY (M,l,8)ENGY (M,l,9)ENGY (M,l,10)ENGY (M,l,ll)ENGY (M,l,12)ENGY (M,l,13)ENGY (M.1,14)ENGY M.1,15)

M.1,16)ENGY M,l,17)ENGYENGYENGY (M.1,18)

END OF HOURLY ANALYSIS FOR ENTIRE YEAR

16. Write out summary of equipment sizes. See Table 5.3 for listof the items printed out.

17. Call ENGYC to write out annual summary of building monthlyenergy consumption and demands.

18. Check to see if there is another case to be run.

If YES, go to calculation 5 and continue.

If NO, PROGRAM FINISHED.

5-28

5.3 ALGORITHMS OF SUBROUTINESCDATA

A subroutine to read card input data and assign default values. SeeVolume I, System and Equipment Simulation Input Tables for reading orderand default values of card input variables.

TDATA

A subroutine to read off load tape header data (building descriptioninformation). This advances the tape to the hourly analysis data.

Building description information read in this subroutine used by thesystem simulation program is as follows:

Facility Name

Facility Location

Name of User

Project Number

Date

Number of zones on load tape

Volume of each zone (cu ft)

Set point temperature of each zone (°F)

Month in which analysis begins

Length of study (days)

Number of hours per month

5-29

FSIZE

A Subroutine to size energy distribution system characteristics.These properties Include:

Zone peak heating and cooling loadsZone air flowsFan system air quantities and motor brake horsepowerFan systemMinimum outside air percentage

INPUT

FAC

CITY

ENGR

PROJ

DATE

MSTRT

MEND

IMAXmSPACNi

F

MULT1

IZNMX

QLj|

QLITEj(

SLPOWJJ

KMAX

Name of facility

Name of city 1n which facility Is located

Name of user

Project number

Date of computer run

First month on LOAD tape

Last month on LOAD tape

Number of hours In month m

Variable relating load program zone numberingwith system simulation zone numbering

Zone duplication factor

Number of fan zones 1n building

Volume of load program, zone$, fan system k (cu ft)

Hourly zone sensible load, zone j| (Btu/hr)

Hourly zone latent load, zone % (Btu/hr)

Hourly zone lighting load picked up by return air,zone { (Btu/hrJ

Hourly zone Internal lighting and machinery powerconsumption* zone Ji (KM)

Total number of fan systems within the building

5-30

INPUT (CONT'D)

KFAN

JMAXR

TFNPS

TFNPR

TFNPE

OACFM

RHSPk

RIPA

EFF

KBLDG

CFMXi

OUTPUT

CFMR1

ZMASS1

ZMASR1

ZMASXi

CFMIN^

ALFAM,

FBHPS,

Type of energy distribution system, system k ~ ;

Set point temperature! zone/ ( F)

Number of zones on system k

Total supply fan pressure of system k

Total return fan pressure of system k

Total exhaust fan pressure of system k

Minimum outside ventilation air of system k (cfm)

Relative humidity set point of system k (% RH)

Ratio of induced to primary air for induction unitsof system k

Efficiency of fan and pump motors (decimal)

Type of building system (1 .-conventional; 2.-heatconservation)

Auxiliary exhaust air quantity for zone i (cfm)

Supply air volume required for zone i (cfm atstandard density)

Return air volume for zone i at standard density

Supply air mass flow of zone 1 (Ibm/hr)

Return air mass flow of zone 1 (Ibm/hr)

Exhaust air mass flow of zone i (Ibm/hr)

Total air supplied by fan system k (cfm)

Minimum outside air required for fan system k (cfm)

Percent of minimum outside air required for fansystem k (fraction) •

Supply fan brake horsepower required for fan system k(bhp)

5-31

OUTPUT (CONT'D)

FBHPRk :

FBHPEk

CFMEXR :

WSPk

CFMBX

CFMBN :

CFMBE :

PWBIL :

DTFNSk :

DTFNRk :


Return fan brake horsepower required for fansystem k (bhp)

Exhaust fan brake horsepower required for fansystem k (bhp)

z CFMX. (cfm)j=l,jmax

Humidity ratio set point for system k(lbm-H20/lbm-dry air)

z CFMAX,. (cfm)k=l,kmax *Z CFMIN. (cfm)k=l,kmax K

Z CFMEX,. (cfm)k=l,kmax K

Maximum hourly building internal lighting andmachinery power consumption (KW)

Temperature rise across supply fan at full load,system k (OF)Temperature rise across return fan at full load,system k (°F)

1. Segment One. Read through the load input tape and find thefollowing quantities:

QSZCM. Maximum zone sensible cooling load for eachzone, i

QSZHMi Maximum zone sensible heating load for eachzone, i

PWBIL Maximum hourly building internal lightingand machinery power consumption

2. Segment Two. Calculate zone and system peak load airquantities and system peak load power requirements for eachzone within the building.2.1 Calculate cooling and heating temperature differences.

TDC - TSPS - (TPAC*f * TIAC * ARIPA,)

* (1. •+ ARIPAk)

5-32

CALCULATION SEQUENCE (CONT'D)

TDH = TSP, - (TPAHkf t TIAH * ARIPAk)* (1 . + ARIPAk)

where TDC : terminal unit cooling design temperaturedifference ( F)

TDH : terminal unit heating design temperaturedifference (°F)

ARIPA. : ratio of induced to primary air (equalszero for all but induction unit fan systems),system k

TIAC : design ury-bulb temperature of induced airafter passing through coil, cooling mode = 62 F

TIAH : design dry-bulb temperature of induced airafter passing through coil, heating mode = 120 F

TPAC,f: primary air design temperature, cooling mode,fr ssm kf. S abl b l w .for system type

TPAH . fi primary air design temperature, heating mode,for system type Kf. See table below.

TABLE 5.5 HEATING & COOLING PRIMARY AIR DESIGN TEMPERATURE

SYSTEMTYPE(kf)

12345678910111213

SYMBOL

SZFBMZSDOSSZRHUVTUHTFPH2PFC4PFC2PIU4PIUVAVSRHFS

PRIMARY AIRCOOLING DESIGN

(OF)

55.55.55.52.55.55.0.55.55.53.53.55.55.

PRIMARY AIRHEATING DESIGN

(°F)

120.120.120.95.

120.120.0.

110.110.53.53.

120.120.

INDUCEDHEATING

(°F)_

--------

120.120.--

AIRCOOLING

(°F)

.---__

---62.62._

-

5-33

2.2 Calculate zone supply air quantities

If

If

QSZCM1TDC

CFM, =i

QSZHMiTDH

CFM.

FMXi > C

4

(0.245*(

<

QSZH

QSZHMtTDH

D. 075*60

QSZCMjTDC

Mi

>

.*TDH)(l.+ARIPAk)

»

(0.245*0. 075*60. *TDC)(1.+ARI PA)

FMi

CFM. = CFMX1

2.3 Calculate zone return air

CFMRi = CFMn. - CFMX.

2.4 Sum system supply and exhaust air flows

CFMAXk = E CFM. **j=l,jmax

CFMEXk = E CFMX.**j=l,jmax 1

2.5 Average system temperature -TAVEk

TAVE,E (CFM. * TSP * MULT.)

_ j=l Jmax(CFMi *MULT-T•k E

j=l,jmax2.6 Minimum outside air fraction - ALFAM

If CFMEXk < OACFM > CFMAX

CFM.

k ' """"k '

CFM1 * (OACFMk/CFMAXR)

CFMAXj = OACFMk

ALFAMk = OACFMk/CFMAXk =1.0

NOTE: There is a correspondingby the variable SPACN. ..

K, J

for each i; a relationship defined

5-34

If CFMEXk< OACFMk <; CFMAXk ,

ALFAMk = OACFMk/CFMAXk

If CFMEXk > OACFMk < CFMAXk ,

OACFMk = CFMEXk

ALFAMk = CFMEXk/CFMAXR

2.7 Calculate fan power*

Supply Fan:

FBHPS, = CFMAXk * TFNP$k6346 * EFF

Return Fan:

FBHPR = (CFMAXk - CFMEXR) * TFNPRkk 6346 * EFF

Exhaust Fan:

= CFMEXk - TFNPEk6346 * EFF

2.8 Sum building fan power

TFBHP = I (FBHPSR + FBHPRk + FBHPEk)j=l,kmax

2.9 Calculate temperature rise across fans at full load

Supply Fan:

nTPNC = (TFNPS * 0.4014)mhru>k (0.245 * 0.075 * 60.0)

Return Fan:/TFNPR * n dnid^RTCMD — \ITMrr\k U.HUIH^

Ul rlNKi, ~ KK (0.245 * 0.075 60TOT

2.10 Calculate mass flows

Zones:

ZMASS1 = CFM1 * 0.075 * 60.0

ZMASXi = CFMXi * 0.075 * 60.0

5-35 -

ZMASR1 = ZMASS1 - ZMASYi

Systems:

FMASSk = CFMAXk * 0.075 * 60.0

FMASXk = CFMEXk * 0.075 * 60.0

FMASRk = FMASSk - FMASXk

3. Segment Three. Write FSIZE information.

3.1 For each fan system, write out the following:

KFANkfFBHPSkFBHPRkFBHPEkJMAXkCFMAXkCFMINkCFMEXkALFAMk

3.2 For each zone, write out the following:

kj

MULT.!CFM1CFMXi

5-36

MZDD

A subroutine to simulate the performance of a multi-zone or dualduct fan system.

INPUT

K - Energy distribution system number

Various items held in COMMON (see Table 5.4 for definitions ofvariables in COMMON).

OUTPUT

QCC - Cooling coil load (Btu/hr)

QHC - AHU heating coil load (Btu/hr)

QRHC - Reheat coil load (Btu/hr)

QPHC - Preheat coil load (Btu/hr)

TQB - Baseboard heating load (Btu/hr)

WATER - Steam humidification supplied at air handlingunit (lbm-H20/hr)

BPKW - Base power (KM)

TNFBP - Total net [updated] fan brake horsepower (bhp)

Various items held in COMMON.


1. Fan off/on check.

Using subroutine FANOF, determine whether the fan has beenturned off for the current hour.

If the system is off, terminate MZDD simulation for thecurrent hour.

If the system is on, continue.

2. Identify sensible thermal load of each zone on this system.

5-37

s QSJ!**3. Baseboard radiation.

If boiler on, call subroutine BRAD2 to calculate baseboardradiation heat (QB.) and to adjust QSI, for QB,.

Sum baseboard radiation heat,

TQB = z QB,j=l, jmax J

If boiler off, continue.

4. Calculate base power (KW); includes internal power, lightsreceptacles, equipment, misc.

BPKW = z SLPOWt) *MULT. **j=l,jmax 1

5. System and zone mass flows remain constant.

FMAS. = Z ZMASS. * MULT.K j=l,jmax ] 1

FMR. = Z ZMASR. * MULT,K j=l.,jmax ] 1

6. Calculate return air temperature (TRAk).

NOTE: Since the System and Equipment Simulation Program iscapable of using LOAD or VARIABLE TEMPERATURE tapes as input,the following logic sequence is required.

If ceiling plenum is calculated as a separate zone,

If LOAD tape is used,

DTL2. = 0.**

QLITI = QLITE£ + QS « + QLITE o + QSINF o

If VARIABLE TEMPERATURE tape is used,DTL2i = STEMPp£- TSPjj

QLITI = QLITEj,

**Yhere 1s a corresponding 5 for each i; a relationship defined by thevariable SPACNk ,. Hence, i and j are defined by system number (k) andzone number(j). See Para. 5.1 for zone labeling organization.

5-38

If ceiling plenum is not calculated as a separate zone,

DTL21 = 0.

QLITI = QLITEj(

DTL1 = QLITI/(0.245 * ZMAS^)

TRA,, = Z (TSPO + DTL. + DTL2.) * ZMASR. * MULT.k >1 .Jmax ] ! 1 1

+ DTFNRZ ZMASR. * MULT. * UiFNKkj=l Jmax ] 1

where DTL2. - difference between zone and plenumtemperatures as calculated by VARIABLETEMPERATURE program.

QLITI - thermal load of plenum pi above zonejas calculated by LOAD program.

pi - LOAD program space number of plenum abovezone 5 •

7. Calculate required supply air temperature of each zone.

TS1 = TSP$ - QSI/(0.245 * ZMASS^

8. Calculate zone humidification requirements.

Using subroutine H20ZN, calculate total moisture requirementsIncluding set point recovery load (H20AD.) and moisture changesin current hour due to environmental and room effects (HZOAD ).

9. Calculate hot deck and cold deck air temperatures. Generally,three control options are available:

1. Fixed settings for both hot and cx>ld decks.

2. Fixed cold deck temperature but allowing hot decktemperature to vary inversely with outside airtemperature.

3. Reset temperature control as governed by the spaces.Control for this mode involves setting the hot deckleaving air temperature equal to that of air suppliedto the space requiring warmest air. The cold deckleaving air temperature is set equal to the tempera-ture of air supplied to the space requiring coolestair.

5-39

Call subroutine TEMP to calculate hot and cold deck leavingair temperatures (THC and TCC).

10. Calculate destred economizer approach temperature enteringsupply fan.

EAT = TCC - DTFNSk

11. Calculate mixed air conditions.

Call subroutine MXAIR to simulate the performance of:

1. Fixed outside and return air dampers.

2. An enthalpy/temperature type economizer cycle,

or

3. A temperature type economizer cycle.

Subroutine MXAIR also calculates the thermal properties(temperature, humidity ratio, and density) of the mixedair stream.

12. Calculate preheat coil load by comparing to mixed air tempera-ture desired.

If boiler on,

If TMA < EAT,

QPHC = 0.245 * FMASSk * (TMA-EAT)

TMABF = EAT

If TMA >_ EAT,

QPHC = 0.

TMABF = TMA

(TMABF = temperature of mixed air before fan (°F))

If boiler off,

QPHC = 0.

TMABF = TMA

13. Calculate mixed air temperature after supply fan.TMAAF = TMABF + DTFN$k

5-40

rcc

Ifoff,

THC B

QHPJVM. .

TS7- = THC

QCP/V«f .

76 c TS7

CMASS = .*

- CMASS

„

5-41

17. Calculate heating coil load.> • . ' . • ' . '

QHC = HMASS * 0.245 * (TMAAF - THC)

WHC = WMA - ,

18. Calculate cooling coil load.

Call subroutine CCOIL to calculate cooling coil load (QCC),cold deck humidity ratio (WCC), and sensible heat ratio (SHR).

19. Calculate humidification requirements.

19.1 Calculate required hot deck humidity ratio (WHRQD).

CMESS = ZMASSicz * PCTC1cz

HMESS = ZMASS1.cz * (1. - PCTCicz)

WZRQD = WZicz - H20RD.CZ/ZMASS.CZ

WHRQD = (ZMASS. * WZRQD - WCC * CMESS)/HMESS1 \»tL

where:

icz - zone in which humidistat is located.

19.2 Check that WHRQD does not exceed a high limit of 80% R.H.within the duct. Call subroutine HUM! to do this.

19.3 Hot deck humidity ratio.

If WHRQD <. WMA

WHC = WMA

If WHRQD > WMA

WHC = WHRQD.

19.4 Calculate amount of humidification water required.

WATER = HMASS * (WHC - WMA)

20. Calculate zone humidity ratio.

Using function WZNEW, calculate the humidity ratio of eachzone (WZn.).

5-42

21. Calculate return atr humidity ratio and density.

MRAk • Z WZ * ZMASR. * MULT,JalJmax -1 1 1I ZMASR, * MULT,

j=l .jmax 1 i

DRAk = _ PATM(0 45 * (TRAk + 460.)(1.0 + 7000.0 * WRAk/4360.)

5-43

SZRHT

A subroutine to simulate the operation of a single-zone fan systemwith sub-zone reheat.

INPUT



OUTPUT

QCC - Cooling coil load (Btu/hr)


QTRHC - Reheat coil load (Btu/hr)

QPHC - Preheat coil load (Btu/hr)



BPKW - Base power (KW)






If the system is off, terminate SZRHT simulation for thecurrent hour.



5-44

3. Baseboard radiation.

If boiler on, call subroutine BRAD2 to calculate baseboardradiation heat (QB-) and to adjust qsi. for qB..

J I J


TqB = 1 QB, '• : - j=l , jmax J


4. Calculate required supply air temperature to each zone,

TS^ = TSP - QSIt/(0.245 * ZMASj)

5. Calculate AHU discharge temperature.

TLVG = IS., (equals supply air temperature of air to centralzone which in "j" sequence is assumed to be No. 1)

6. Calculate fraction of primary air required.

BETAi = (TSi - TRPRI)/(TLVG - TRPRI)

If BETA.J <_ 0.5, reheat coil required.

QZRHCi = 0.245 * IWSS. * (0.5 * (TRPRI + TLVG) - TS^

If BETAi > 0.5,

If BETA _> 1.0, cooling load not met.

Call subroutine CCOIL to calculate cooling loadnot met (QLNM..).

Update as required the following variables:

QCLNMi -

IHCNMi -

TS. = TLVG

**NOTE: There is a corresponding S. for each 1; a relationship defined by thevariable SPACN^ .. Hence, i and i are defined by system number (k)and zone number'0 (j). See Para. 5.1 for zone labeling organization.

5-45

If BETA <, 1.0, continue.

7. Calculate zone mass flows.

ZMAS1 = ZMASS. * BETA1

ZMASR1 = ZMAS1 - ZMASXi

If ZMASR < 0.0,

ZMASR = 0.

8. Calculate system mass flows.

FMAS = i ZMAS. * MULT,j=l Jmax 1 1

FMAR = z ZMASR. * MULT.j=l .jrnax n n

9. Calculate percent of full load.

PCTSA = FMAS/FMASSk

PCTRA = FMAR/FMASRk

10. Calculate return air temperature (TRAk).




DTL2i = 0.

QLITI = QLITEJ + QSpft + QLITEpj+ QSINFpjj **

If VARIABLE TEMPERATURE tape is used,

DTL2.. = STEMP ft-

QLITI = QLITEjj


DTL21 = 0.

QLITI = QLITEjt

5-46

DTL1 * QHTI/(0.245

TRAt » E (TSPO + DTL. + DTL2.) * ZMASR. * MULT.K j=l.jmax T 1 T 1E ZMASR. * MULT.j=l,jmax

+ DTFNRk * PTLD(NVFCk,PCTRA)

where DTL2., - difference between zone and plenumtemperatures as calculated by VARIABLETEMPERATURE program.

QLITI - thermal load of plenum px above zone X.as calculated by LOAD program.

pj^ - LOAD program space number of plenum abovezonejj .

11. Calculate desired economizer approach temperature (EAT).

EAT = TLV6 - DTFNSk * PTLD(NVFCk , PCTSA)

12. Calculate mixed air conditions entering preheat coil.




or


Subroutine MXAIR also calculates the thermal properties(temperature, humidity ratio, and density) of the mixedair stream.

13. Air Handling Unit (AHU).

13.1 If boiler and chiller on, if chiller on and coolingcalled, or if boiler and heating called,

Call subroutine AHU (mode 2) to simulate theoperation of a central system air handling unit.Calculate heating and cooling coil operation (QHCand QCC), the effect of fan heat, and the additionof steam (WATER) by a humidifier on the dischargeside of the unit.

Go to 14.

5-47

13.2 If boiler off and heating required at AHU,

TLVG = TMA t DTFNSk * PTLDCNVFCk,PCTSA)

Go to 13.4.

13.3 If chiller off and cooling required at AHU,

TLVG = TMA + DTFNSk * PTLD(NVFCk , PCTSA)

Go to 13.4.

13.4 If TLVG-TLVG2 < 0.001,TLVG


Go to 14.

If TLVG-TLVG2 > 0.001,TLVG

TLVG = TLVG2 = TLVG.

Go to Step 2.

14. Adjust total fan brake horsepower.

PCTSA = SMCFM/CFMAXi

TNFBP = TNFBP + (PTLD(NVFCk> PCTSA) - 1.0) * FBHP$k

+ (PTLD(NVFCk, PCTRA) - 1.0) * FBHPRR


BPKW = £ SLPOW8* MULT.j=l,jmax


Using function WZNEW, calculate the humidity ratio of eachzone (WZ..).

17. Calculate return air humidity ratio and density.

5-48

WRA,, * E WZ. * ZMASR. * MULT

E ZMASR. * MULT.0=1 ,jmax '

DRAk = ________ ________ PATH(0.754 * (TRAk + 460.)(1.0 + 7000.0 * WRAk/4360.)

5-49

FHTG2

A subroutineheating system.

INPUT

TOA

K

JMAXK

QLITE/

SLPOwy

TCO

PERIM,k

PAREA |<.

PLOCk

CINSL

DINSL

TSP/

KFLCV

OUTPUT

QFPC

QFPH

QFPRH

BPKW

for simulating the system performance of the floor panel

Dry-bulb temperature of outside air, F

Fan system number

Number of zones on fan system No. K

Hourly sensible load for zone No.,/ Btu/hr

Hourly latent load for zone No. ji Btu/hr

Hourly lighting load picked up by return airin zone No. Btu/hr.

Hourly zone internal lighting and machinerypower consumption, KW, for zone No.^

Building changeover temperature, °F

Exposed perimeter of floor for distribution systemNo. k, ft.

Floor area available for heating panels, system k sq. ft.

Location of floor heating panel for system No.k

Floor insulation conductance, Btu/hr-sq.ft.-°F

Floor insulation thickness, ft.

Set point temperature of zone No.^, °F

Type of floor covering

Hourly cooling requirement, Btu/hr

Hourly heating requirement, Btu/hr

Hourly reheat requirement, Btu/hr

Total internal lights and machinery powerconsumption for zones served by system underconsideration, KW

5-50

CALCULATION SEQUENCE*

1. Read load input tape for zones required and calculate:

BPKW = £SLPOW/ *MULT; , for j = i to JMAXKQSIj = QS^ + QLITE^

QSSUM = £QSI , for all zones on this system requiring heating

2. If TOA > TOACOj, , go to calculation 2.1, otherwise go to calculation2.2 *

2.1 No heating available since building system is operatingin cooling mode, therefore set

QFPC =0.0

QFPH = 0.0

QFPRH = 0.0

Go to 3.

2.2 Heating available within building, therefore performthe following:

2.2.1 Calculate panel temperature, TPAN, required fordesired heating flux, QPAN.

QPAN = QSSUM/ PAREAji,

Calculate set point temperature of systemTSPJ1 = TSP^ where TSP0 is the setpoint of the first zone.

Initially, set TPAN = 76.0

QCALC = 0.15 * ((TPAN + 460.0)/100.0)

** 4.0 - 0.15 ((TSPJ1 + 460.0)7100.0)

** 4.0 + 0.32 * (TPAN - TSPJ1 ) ** 1.31

If (QPAN - QCALC) is greater than (0.01 * QPAN),calculate a new TPAN

TPAN = TPAN + 0.5 * (QPAN - QCALC)

and repeat above calculation. If necessary,repeat again until QCALC is within (0.01 * QPAN).

*See 1967 ASHRAE Guide and Data Book, Systems and Equipment Volume,Chapter 58, for derivation of all equations.

5-51

2.2.2 Calculate surface temperature of floor requiredas a function of the type of floor covering.

2.2.2.1 If KFLCV = 1, bare concrete floor,therefore

TSUR = TPAN

2.2.2.2 If KFLCV = 2, tile covering, therefore

TSUR = TPAN + QPAN * 0.05

2.2.2.3 If KFLCV * 3, carpeting, therefore

TSUR = TPAN + QPAN * 1.4

2.2.3 If TSUR as calculated above is greater than85.0 F, reset

TSUR =85.0

2.2.4 Calculate the downward and edgewise losscoefficient, C3.

2.2.4.1 If CINSL = 0.0, no insulation,therefore

C3 =1.8

2.2.4.2 If CINSL > 0.0, and DINSL = 0.0, thenonly perimeter insulation, therefore

C3 = 1.32 + 0.25 * CINSL

2.2.4.3 If CINSL > 0.0 and DINSL > 0.0, then

C3 = 0.932 + 0.523 * CINSL

- 0.479 * CINSL ** 2.0

- 0.271 * DINSL + 0.046 * DINSL

** 2.0 + 0.786 * CINSL * DINSL

- 0.72 * DINSL * CINSL ** 2.0

- 0.182 * CINSL * DINSL ** 2.0

+ 0.24 * (DINSL * CINSL) ** 2.0

5-52

2.2.5 Calculate downward and edgewise heat loss, QLOSS.

2.2.5.1 If PLOCjj = 1. then

QLOSS = PERIMfc * C3 * (TPAN - TOA)/'

2.2.5.2 If PLOC (K) = 2, then

QLOSS = 0.15 * ((TPAN + 460.0)/100.0)

** 4.0 - 0.15 * (TSPJ1 + 460. O)/

100.0) ** 4.0 + 0.021

* (TPAN - TSPJ1) ** 1.25

2.2.6 Calculate heating requirement of system.

QFPH = 1.0 * (QPAN + QLOSS) * PAREAj,

QFPC =0.0

QFPRH = 0.0

3. Distribute unmet heating and cooling loads, finding:

Heating and cooling peak, consumption, and number of hoursheating and cooling loads were not met.

5-53

FCOIL

A subroutine to simulate the operation of two- and four-pipe fancollsystems consisting of blow-through type fancoil units,

INPUT

k : Energy distribution system number

Various items held in COMMON (see Table 5.4 for definition of variablesin COMMON).

OUTPUT

QC : Cooling load (BTU/HR) (QC = I QC.)**j=l, jmax

QH : Heating load (BTU/HR) (QH = I QH.)**j=l, jmax

TQB : Baseboard heating load (BTU/HR)

BPKW : Base power (KW)

TNFBP : Total net (updated) fan brake horsepower (BHP)



Using subroutine FANOF, determine whether fancoil units have been turnedoff for the current hour.

If fancoil units are off, terminate fancoil simulation.

If fancoil units are on, continue.

2. For two-pipe fancoil units, use subroutine TEMP to determine processwater mode (i.e., hot water, chilled water, or changeover) for thecurrent hour.

**NOTE: There is a corresponding i for each i, a relationship defined by thevariable SPACNkj. Hence, i and $ are defined by system number (k)and zone number'of system (j). See Para. 5.1 for zone labelingorganization.

5-54

3. Calculate base power (KW), includes internal power, lights, receptacles,equipment, miscellaneous.

BPKW = I SLPOVty* MULT. **j=l, jmax

Calculation sequence 4 through 12 is repeated for each fancoil zone onsystem k.

4. Calculate sensible thermal load.

QS^ = QSjj + QLITEfl **


If boiler is on, call subroutine BRAD2 to calculate baseboard radiationheat (QB.) and adjust QSI.


TQB = I QB.j=l, jmax J

If boiler is off, continue.


Call subroutine MXAIR to calculate thermal properties (temperature,humidity ratio, and density) of mixing outside air and room air by thefancoil unit.

7. Calculate mass flow through fancoil unit.

ZMAS = CFM1 * DMA * 60.0

where DMA = mixed air density (LBM/FT3)

8. Calculate required supply air temperature.

TSA1 = TSP1 - QSIj/CO.245 * ZMASi) **

**NOTE: There is a corresponding j? for each i, a relationship defined by thevariable SPACN^ ,-„ Hence, i and X are defined by system number (k) andzone number of System (j). See Para. 5.1 for zone labeling organi-zation.

5-55

9. Calculate fan heat and mixed air temperature downstream of blower.

QFAN = CFM1 TFNPSk * 0.4014

TMA = TMA + QFAN/(0.245 * ZMASj)

10. Zone humidity calculations.

Using subroutine H20ZN, calculate total moisture requirements includingset point recovery load (H20RD.) and moisture changes in current hourdue to environmental and room effects (H20AD,).

11. Calculate fancoil performance and distribute thermal loads.

11.1 Two-Pipe Fancoil System

11.1.1 Heating Mode (IPW = -1)

If TMA £ ISA, heating required.

If boiler on, call subroutine ZLJJ3 to calculate QH anddistribute unmet load, if any.

If boiler off, heating load not met,

QLNM1 = ZMASi * 0.245 * (TMA - ISA)

Update as required:

QHLNM. : Sum of all heating loads not met, zone 1.

QHPNM. : Peak heating load not met, zone 1.

IHHNMj : Hours heating load not met, zone 1.

If TMA > TSA, cooling Toad not met.

Call subroutine CCOIL to calculate cooling load not met.


QCLNM^ : Sum of all cooling loads not met, zone i.

QCPNM.. : Peak cooling load not met, zone 1.

IHCNM.J : Hours cooling load not met, zone i.

5-56

11.1.2 Changeover Mode (IPW = 0)

During the changeover hour, it is assumed that both heating andcooling loads may be met. Therefore, the four-pipe fancoil systemzone analysis is used (see 11.2). In addition, there is a thermalload due_to changing the tempdrature of the hydronic system (see 13.).

11.1.3 Cooling Mode (IPW = +1)

If TMA <_ TSA, cooling required,,

If chiller on, call subroutine ZL03 to calculate QC. anddistribute unmet load, if any.

If chiller off, cooling load not met. Call subroutineCCOIL to calculate cooling loads not met.

Update as required:

QCLNM. : Sum of all cooling loads not met, zone i.

QCPNM. : Peak cooling load not met, zone i.

IHCNM. : Hours cooling load not met, zone i.

If TMA > TSA, heating load not met.

QLNMj = ZMASi * 0.245* (TMA - TSA)

Update .as required:

QHLNM. : Sum of all heating loads not met, zone i.

QHPNM. : Peak heating load not met, zone i.

IHHNM• : Hours heating load not met, zone i.

11.2 Four-Pipe Fancoil System

If TMA £TSA, heating required.

If boiler on, call subroutine ZL03 to calculate QH- anddistribute unmet load, if any.

If boiler off, heating load not met.

QLNMi = ZMASi * 0.245 * (TMA - TSA)


QHLNM. : Sum of all heating loads not met, zone i.

QHPNM. : Peak heating load not met, zone i.

IHHNM. : Hours heating load not met, zone i.

5-57

If TMA > ISA, cooling required.

If chiller on, call subroutine ZL03 to calculate QC1 anddistribute unmet load, if any.

If chiller off, cooling load not met. Call subroutineCCOIL to calculate cooling load not met.


QCLNM.. : Sum of all cooling loads not met, zone 1.

QCPNM.. : Peak cooling load not met, zone i.

IHCNM. : Hours cooling load not met, zone 1.


Using function WZNEW, calculate the humidity ratio of each zone.

13. Calculate heat of changeover (for two-pipe fancoil systems only).

If IPW = 0, changeover.

Calculate hot water temperature (THW) using function TRSET.

Calculate changeover heat : QCO

QCO = PWGALk *8.3 * (THW'-'TLCHL)

where PWGAI_k : Water volume of two-pipe system (GALS)

TLCHL : Chilled water temperature (°F)

If heating-to-cool ing changeover:

QC = QC + QCO

If cool ing-to-heating changeover:

QC = QH - QCO

If IPW ^ 0, continue.

5-58

INDUC

A subroutine to simulate the operation of two and four pipe induc-tion unit fan systems having induction units whose primary and inducedroom air streams mix after induced air is tempered. Induction unit cool-Ing coll limited to sensible cooling only.

INPUT

K : Energy distribution system number.

Various items held in COMMON (See Table 5.4 for definition ofvariables in COMMON).

OUTPUT

QCC

QHC

QTRHC

TQB

WATER

BPKW

TNFBP

Total cooling load (Btu/hr) (QCC = E QC.)0=1, jmax

Heating load at AHU (Btu/hr) (QHC = QH,)j=l, jmax

Heating load at induction unit (Btu/hr)(QTRHC = E QRHCJ**

j=l, jmax

Baseboard heating load (Btu/hr)

Steam humidification supplied at air handling unit(lbs-H20/hr).

Base power (KW)

Total net [updated] fan brake horsepower (Bhp)




Using subroutine FANOF, determine whether air handler has been turnedoff for the current hour

If the system is off, terminate induction system simulation.


5-59

2. Calculate temperature leaving air handler (TLVG).

If two-pipe induction unit fan system, call subroutine TEMPto calculate primary atr temperature and induction unit watermode indicator (IPW). This is graphically represented asfollows:

TOALO

o8 (/)Uloc a.

THI . f I(Hot WaterH

TLO(Hot Waterrt~

THI(Primary Air);§

</> i- (Primary Air)

(chilled water;

TOAHI>(Hot Water)

LEGEND

TOALO TOAHI(Primary Air) (Primary Air)

OUTSIDE AIR DB TEMPERATURE (°F)

Figure 5.3 TWO-PIPE INDUCTION UNIT AIR AND WATER SCHEDULING

NOTE: TOAHI [hot water] should be set equal to TOALO (pri-mary air).

If four-pipe induction unit fan system, primary air is heldconstant (set equal to TFIX1.).

3. Calculate fraction of primary to total air (ALFIU)

ALFIU = 1.0/(1.0 + RIPA. )k4. Calculate base power (KW); includes internal power, lights, recepta-

cles, equipment, miscellaneous.

BPKW = E SLPOW-* MULT. **j=l, jmax * 1


QSI. = nc - **

**NOTE: There is a correspond!ng£ for each i, a relationship defined bythe variable SPACN^j. Hence, i and jl are defined by systemnumber (k) and zone'number of system (j). See Table 5.1 for zonelabeling organization.

5-60


If boiler on, call subroutine BRAD2 to calculate baseboardradiation heat (QB,) and adjust QSI. for QB..

J 1 1*

Sum baseboard radiation heat.

TQB = £ QB,j=l, jmax J


7. Calculate return air temperature (TRA. .)•

NOTE: Since the system and equipment simulation program is capableof using LOAD or VARIABLE TEMPERATURE tapes as input, thefollowing logic sequence is required.



DTL2. =0.0

QLITI = QLITEf + QS „ + QLITE + QSINF A **D Jr D 9 QJL


DTL2. = STEMPp^- TSPj

QLITI = QLITEj|


DTL2i =0 .0

QLITI = QLITE/

DTL- = QLITI/(0.245 * ZMASR^

( Z (TSP/ + DTL. + DTL2.) * ZMASR, * MULT.)• i • ^ ~ 1 1 1 1j=l, jmax

DTFNRk

ZMASR1 *

where DTL2. — Difference between zone and plenum tempera-tures as calculated by VARIABLE TEMPERATUREprogram.

QLITI — Thermal load of plenum p^ above zone ji ascalculated by LOAD program.

5-61


Using subroutine H20ZN, calculate total moisture requirementsIncluding set point recovery load (H20RD.) and moisture changesin current hour due to environmental and room effects (H20AD,).

9. Calculate economizer approach temperature (EAT).

If TLVG > 125.0°F,

TLVG = 125.0°F

EAT = TLVG - DTFNSk

If EAT < 40.0°F

EAT = 40.0°F

TLVG = EAT + DTFNSk



1. Fixed outside and return air dampers2. An enthalpy/temperature type economizer cycle.

3. A temperature type economizer cycle

Subroutine MXAIR also calculates the thermal properties (temper-ature, humidity ratio, and density) of the mixed air stream.

11. Air handling unit.

Call subroutine AHU (mode 1) to simulate the functioning of a centralsystem air handling unit. Calculate heating and cooling coilthermal response (QHC and QCC) of fan heat, and operation ofsteam humidifier on discharge side of unit (WATER).The heating coil is locked out when the boiler scheduled off.The cooling coil Is locked out when the chiller scheduled off.The humidifier is locked out when the cooling coil is functioning.

5 62

12. Calculate Induction unit coil sensible thermal load and inducedair mass flow.

_.*-*

QSIU1 = QSIt + ZMASSt * 0.245 * (TLVG - TSJ )

ZMASj = ZMASSj * RIPAk

13. Induction unit simulation.

13.1 Two-pipe induction unit.

13.1.1 Hot water mode (IPW = -1).

If QSIUt £0.0,

If boiler on,

= -QSIU1/(ZMASi * 0.245) + TSF£

where TLC. - Temperature of induced air after coil

Call subroutine ZL03 to calculate induction unit heatingload and distribute an unmet load, if any.


QLNM1 = QSIUi


QHLNM. -QHPNM! -IHHNM: -

If QSIU. > 0.0, cooling load not met.

QLNM1 = QSIU1


QCLNM, -QCPNM,. -IHCNM! -

13.1.2 Changeover mode (IPW = 0).

During the changeover hour, it is assumed that both heatingand cooling loads may be met. Therefore, the four-pipe fan-coil system zone analysis is used (see 13.2.). In addition,there is a thermal load due to changing the temperature ofthe hydronic system (see 17.).

5-63

13.1.3 Cooling mode (IPW « +1)

If QSIU. > 0.0, cooling required.

If chiller on,

TLC, = -QSIU,/(ZMAS. * 0.245) + TSP*i i i j &

Call subroutine ZL03 to calculate cooling load anddistribute an unmet load, if any.

If chiller off, cooling load not met.

QLNM1 = QSIU1


QCLNM, -QCPNM] -IHCNM] -

If QSlU.j< 0.0, heating load not met.

QLNMj = QSIUi


QHLNM. -QHPNM] -IHHNMI -

13.2 Four-pipe induction unit.

If QSIU^ <_0.0, heating required.

If boiler on,

TLC1 = -QSIU1/(ZMAS1 * 0.245) + TSP

Call subroutine ZL03 to calculate induction unit heatingload and distribute an unmet load, if any.


QLNMi = QSIU.


QHLNM, -QHPNM] -IHHNMJ -

5-64

If QSIU. ? 0.0, cooling required,

If chiller on,

TLCt = -QSIUt/(ZMASt * 0.245) +

Call subroutine ZL03 to calculate cooling load and dis-tribute an unmet load, if any.

If chiller off, cooling load not met.

QLNMi = QSIl .


QCLNM, -QCPNMJ -IHCNM] -

14. Calculate thermal properties (temperature and humidity ratio) ofair leaving the induction unit.

TTLV6.= (TLVG * ZMASSi + TLC * ZMAS. )/(ZMAS$i + ZMAS..)

WTLVG.= (WSUP * ZMASSi + WCLVG * ZMASi)/(ZMAS$i + ZMAS^


Using function WZNEW, calculate the humidity ratio of eachzone (WZ.).


WRAk " (j^jmax WZi * ZMASRi * ^V/^l'jmax ZMASRi * MULTi>

DRAk = PATM/((0.754 * (TRAk + 460.0)*(1.0 + 70bO.O * WRAk/4360.0))

17. Calculate heat of changeover (for two-pipe induction systems only).

If IPW = 0 (changeover), I

Calculate hot water temperature using function TRSET.iI

Calculate changeover heat, QCO |i

QCO = PWGALk * 8.3 * (THW - TLCHL) j

where, PWGAL. - Water volume of two-pipe induction unitsystem (gal.) j

TLCHL - Chilled water temperature (°F)

5-65

If heating to cooling changeover:

QC = QC + QCO

If cooling to heating changeover:

QH = QH - QCO

If IPW f 0, continue.

5-66

VARVL

A subroutine to simulate the operation of a variable volume fansystem with optional reheat.

INPUT



OUTPUT

QCC - Cooling coil load (Btu/hr) i


QTRHC - Reheat coil load (Btu/hr)



BPKW - Base power (KW)






If the system is off, terminate VARVL simulation for thecurrent hour.


2. Identify leaving AHU air temperature,

TLVG = TFIXlk

TLVG2 = TLVG

5-67


QSI = QSjj **


If boiler on, call subroutine BRAD2 to calculate baseboardradiation heat (QB.) and to adjust QS . for QB..


TQB = Z QB.j=l,jmax 'J


5. Calculate air mass flow and temperature to each zone,

ZMAS1 = QSIi/(0.245 * (TSP - TLVG))

If ZMASi > ZMASSi

ZMASi = ZMASSi

If ZMASi < ZMASSf * VVMINk

ZMASi = ZMASS1 * VVMINk

ZMASRn. = ZMAS. - ZMASXi

If ZMASRi < 0.0,

ZMASRi = 0.

TSi = TSPj} -QSI./(0.245 * ZMA$i)

6. Calculate system mass flows.

FMAS. = Z ZMAS. * MULT..j=l,jmax

FMR. = I ZMASR. * MULT.K j=l,jmax 1

7. Calculate supply and return air full load flows.

PCTSA =' FMASk/FMASSk

PCTRA = FMRk/FMASRk

** There is a corresponding X for each i; a relationship defined by thevariable SPACN... Hence, i and 8 are defined by system number (k)and zone number*J (j). See Para. 5.1 for zone labeling organization.

5-68

8. Calculate return air temperature




DTL21 = 0.QLITI = QLITEg + QSp + QLITEpj + QSINFpj


DTL2t -

QLITI «


DTL21 = 0.

QLITI = QLITEJDTL1 = QLITJ/(0.245 * ZMASR^

TRA. = I (TSPj + DTL. + DTL2.) * ZMASR, * MULT,' A i ' 1 i i

**

E ZMASR. * MULT.=l , jmax ] 1

DTFNRk * PTLD(NVFCk,PCTRA)

where DTL2^ - difference between zone and plenum-i temperatures as calculated by VARIABLETEMPERATURE program.

QLITI - thermal load of plenum pi above zonejlas calculated by LOAD program.

pi - LOAD program space number of plenum abovezone { .


Using subroutine H20ZN, calculate total moisture requirementsincluding set point recovery load (H20AD.) and moisture changesin current hour due to environmental and room effects (H20AD.)-

5-69


If TLVG > 125.°F

TLV6 = 125.°F

EAT = TLVG - DTFNSk

If EAT < 40.°F

EAT = 40.°F

TLVG = EAT + DTFNSk





or


Subroutine MXAIR also calculates the thermal properties(temperaure, humidity ratio, and density) of the mixedair stream.

12. Air Handling Unit (AHU).

12.1 If boiler and chiller on, if chiller on and coolingcalled, or if boiler and heating called,


Go to 13.

12.2 If boiler off and heating required at AHU,

TLVG = TMA + DTFNSk* PTLD(NVFCk,PCTSA)

Go to 12.4.

12.3 If chiller off and cooling required at AHU,

TLVG = TMA + DTFNSk * PTLD(NVFCk , PCTSA)

Go to 12.4.

5-70

12.4 If TLVG-TLVG2 < 0.001,TLVG


Go to 13.

If TLVG-TLVG2 > 0.001,TLVG

TLVG = TLVG2 = TLVG.

Go to Step 3.

13. Adjust total fan brake horsepower.

PCTSA = SMCFM/CFMAXk

TNFBP = TNFBP + (PTLD(NVFCk, PCTSA)-1.0)*FBHP$k

+ (PTLD(NVFCk, PCTRA)-1.0)*FBHPRk


BPKW = z SLPOWjj* MULTjj=l,jmax

15. Terminal unit performance.

QT,. = ZMAS, .< 0.245 * (TLVG - TS^

If no reheat coils,

If QT.j < 0.0, heating load not met.

QLNM. = QT.


QHLNMi -

QHPNMn. -

IHHNMi -

5-71

TS^ = TLVGj

WTLVQ = WSUP (WSUP = supply air humidity ratio. It iscalculated in subroutine AMD.)

If QT 0.0,

WTLVG = WSUP

If QT.> 0.0, cooling load not met.

QLNM1 = QT.


QCLNMi -

QCPNMi -

IHCNM- -

TS1 = TLVG

WTLVGn. = WSUP

If terminal has reheat coil,

If QT.< 0,

If boiler on,

Call subroutine ZL03 to calculate and sum reheatcoil loads and distribute loads not met, if any.


QLNM. = QT.


QHLNM. -

QCLNMi -

IHHNMi

TSi = TLVG

WTLVGi = WSUP

5-72

If QT 0.0,

WTLVG = WSUP

If QT. > 0.0, cooling load not met.

Call subroutine CCOIL to calculate cooling load notmet (QLNM^.


QCLNM1 -

QCPNM1 -

IHCNM1 -

TS1 = TLVG

WTLVG1 = WSUP

Go to 13.


Using function WZNEW, calculate the humidity ratio of eachzone


WRAt = z WZ. * ZMASR. * MULT.K j=1 . jmax n _ ] _ ].

Z ZMASR. * MULT.j=l ,jmax

DRAt = PATM* (0.754 * (TRAk + 460.)(1.0 + 7000.0 * WRAk/4360.)

5-73

RHFS2

.A subroutine to simulate the operation of a single-zone fan systemwith face and bypass dampers, a unit ventilator, a unit heater, or aconstant volume reheat fan system.

INPUT

K - Energy distribution system number.


OUTPUT

QCC - Cooling coil load (Btu/hr.)

QHC - AHU heating coil load (Btu/hr.)

QTRHC - Reheat coil load (Btu/hr.)

TQB - Baseboard heating load (Btu/hr.)

WATER - Steam humidification supplied at air handlingunit (lbm-H20/hr.)

BPKW - Base power (Kw)





Using subroutine FANOF, determine whether the fan has been turnedoff for the current hour.

If the system is off, terminate RHFS2 simulation for the currenthour.


2. Identify sensible thermal loss of each zone on this system.

= QSj **

5-74


If boiler on, call subroutine BRAD2 to calculate baseboard radia-tion heat (QB.) and to adjust QSI^ for QB..


TQB = £ QB.j=l,jmax J


4. Calculate required zone supply air temperatures.

TS. = TSP» - QSI./(0.245 - ZMASS.)1 ^ 1 1

5. Calculate base power (Kw); includes internal power, lightsreceptacles, equipment, misc.

BPKW = A . SLPOWQ * MULT. **J-l» Jmax A i

6. Calculate return air temperature, TRA.

NOTE: Since the System and Equipment Simulation Program iscapable of using LOAD or VARIABLE TEMPERATURE tapesas input, the following logic sequence is required.



DTL2i = 0.

QLITI = QLITEjj + QS + °.LITEpfc + QSINF » **


DTL2i = STEMP .- TSPjj

QLITI = QLITE|


DTL2]. = 0

QLITI =

**NOTE: There is a corresponding Jl for each i; a relationship defined b,the variable SPACN^ .. Hence, i and % are defined by system number (kand zone number (j/.'J See Para. 5.1 for zone labeling organization.

5-75

y)

DTL. = QUTI/(0.245 *

TRAk = £ (TSP Hj=l ,jjnax

I ZMASR.j=l ,jmax

h DTLi + DTL2t) * ZMASRi * MULTj

* MULT1+ DTFNRk

where DTL2. - difference between zone and plenum temperaturesas calculated by VARIABLE TEMPERATURE program.

QLITI - thermal load of plenum px above zone x ascalculated by LOAD program,

p^ _ load program space number of plenum above zone |7. Zone humidity calculations

Using subroutine H20ZN, calculate total moisture requirementsincluding setpoint recovery load (H20AD.) and moisture changesin current hour due to environmental ana room effects (H20AD^)

8. Calculate air temperature leaving unit.

8.1 For single-zone fan system, unit ventilator, and unit heater,

TLVG = TS, , v1 (one)8.2 For constant volume heat fan system, air handler discharge

temperature (TLVG) is controlled in one of three ways:

1. constant leaving air temperature

2. set equal to lowest TS.

3. reset as an inverse function of ambient air temperature.

Call subroutine TEMP to calculate TLVG for one of the abovecontrol modes.


If TLVG 125.°F

TLVG = 125.°F

EAT = TLVG-DTFNSk

If EAT 40.°F

EAT = 40.°F

TLVG = EAT + DTFNSk

5-76





or


Subroutine MXAIR also calculates the thermal properties (temperature,humidity ratio, and density) of the mixed air stream.

11. Air handling unit.

11.1 Single-zone system with face and bypass dampers aroundcooling coil.

Call subroutine AHU (mode 2) to simulate the functioning ofthis air handling unit. Calculate bypass damper operation,heating and cooling coil thermal response (QHC and QCC), effectof fan heat, and steam humidifier functioning (WATER).

11.2 Unit ventilator.

Heating and the addition of outside air are provided by thissystem type.

Call subroutine AHU (mode 1) to calculate the functioning ofthe heating coil (QHC) and effect of fan heat.

11.3 Unit heater.

Same as unit ventilator, without outside air option.

11.4 Constant volume reheat fan system.

Call subroutine AHU (mode 1) to simulate the operation of acentral system air handling unit. Calculate heating andcooling coil operation (QHC and QCC), the effect of fan heat,and the addition of steam (WATER) by a humidifier on the dis-charge side of the unit.

11.5 Controls applicable to all system types.

The heating coil is locked out when the boiler is scheduled off.

The cooling coil is locked out when the chiller is scheduled off.

5-77

The humidifier is locked out when the cooling coil isfunctioning.

12. Calculate reheat coil loads (QT ) and distribute loads not met.

12.1 Single-zone fan system and constant volume reheat fan systems.

QTj = ZMASS1 0.245 (TLVG1 - TSj)

If QTj < 0.0,

If boiler on,Call subroutine ZL03 to calculate and sum reheat collloads and distribute loads not met, if any.Go to 13.


QLNM. = QT.

Update as required the following variables: .

QHLNMi -

QHPNM1 -

IHHNM, -I . . .y. . .

TS1 = TLVG

WTLVG. = WSUP (WSUP = supply air humidity ratio.It 1s calculated in subroutine AHU.)

If Q^ = 0.0,

WTLVGi = WSUPGo to 13.

If QT. > 0.0, cooling load not met.

Call subroutine CCOIL to calculate cooling load not met(QLNM.).Update as required the following variables:

QCLNMj -

QCPNM1 -

IHCNM1 -

TSi = TLVG

5-78

WTLVG1 = WSUP

Go to 13.

12.2 Unit ventilator and unit heat systems.

QTi = ZMASS1 * 0.245 * (TLVGj - TS^

If QT.. < 0.0, heating load not met.

QLNM1 = QTi


QHLNM1 -

QHPNM1 -

IHHNMi -;

TS1 = TLVG

WTLVG1 = WSUP

Go to 13.

If QT.. > 0.0, cooling load not met.

QLNM. = QT.


QCLNM1 -

QCPNM. -

IHCNMi -

TS1 = TLVG

WTLVG1 = WSUP

Go to 13.


Using function WZNEW, calculate the humidity ratio of each zone (WZ )


5-79

WRA., = 2 WZ, * ZMASR. * MULT,K j=l, jmax 1 ] 1

~ Z Z M A S R . * MULT.j=l,jmax n 1

DRA = , PATMUKrtk (0.754 * (TRAk+460.)(l-0+7000.0*WRAk/4360.)

5-80

FANOF

A subroutine to handle loads for a given hour when a fan system 1soff. This routine should only be "called when IFAN =1.

INPUT

k : Energy distribution system number.

Various items held in COMMON (see Table 5.4 for definition ofvariables in COMMON).

Fan operation indicator (0, fan on; 1, fan off).

Cooling load (Btu/hr).

Heating load (Btu/hr).

Reheat coil load (Btu/hr).

Preheat coil load (Btu/hr).

Baseboard radiation load (Btu/hr).

Steam humidification supplied at air handling unit(lbm-H20/hr).

Base power (KW).

Total net [updated] fan brake horsepower (Bhp).

BPKW

TNFBP



1. Check for zero sensible zone load.

If I |QS,| ? 0, **.j=l, jmax

RETURN.

**NOTE: There is ^corresponding for each 1; a relationship defined byeflned by system nifor zone labeling

• i i w i w i«* v* \»wi i ^.?|swiivj i ny i I/I cav*ii i j a re

the variable SPACN|< ,-. Hence, 1 and are defined by system num-ber (k) and zone number .(j). See Para. 5.1organization.

5-81

If I |QSJ "0,** .-. . :j=l, jmax

CONTINUE.

2. Fan system turned off, distribute loads not met.

2.1 Initialize general variables.

QCC = 0.

QHC = 0.

WATER =0.

QTRHC =0.

QPHC =0.

TQB =0.

2.2 Zone load distribution.

2'.2.1 Sum base power requirements.

BPKW = I SLPOW. * MULT.j=l, jmax ' T

2.2.2 Sum baseboard radiation heat.

QLNM1 = QSg + QLITEjL

If boiler on, call subroutine 6RAD2 to calculate baseboardradiation heat (QB..) and adjust QLNM...

If boiler off, CONTINUE.

2.2.3 Distribute sensible load not met (QLNM^.

If QLNM^ < 0.0, heating load not met.

Update the following variables as required:

QHLNM1

QHPNM1

IHHNM1

GO TO 2.2.4

5-82

If QLNMi =0.0,

GO TO 2.2.4

If QLNMj > 0.0, cooling load not met.


QCLNMf

QCPNMt

IHCNM.

GO TO 2.2.4

2.2.4 Turn off all system fans.

TNFBP = TNFBP - FBHPSk - FBHPRk - FBHPEk

100 = 1.

5-83

ZL03

Zone load organizer. A subroutine to calculate terminal unit ther-mal loads to reheat and recoolfng cotls. These are then checked againstmaximum and minimum leaving coll temperatures. Thermal loads met and un-met, positive and negative are broken out and summed.

INPUT

IQ

AMULT

TLC

TEC

WEC

TLCMX

TLCMN

Coil type index (1 = heating; 2 = cooling).

Zone multiplication factor.

Desired leaving coil temperature (°F).

Entering coil temperature (°F).

Entering coil humidity ratio (Ibm-Ô/lbm-dry air),

Maximum allowable leaving coil temperature (°F).

Minimum allowable leaving coil temperature (°F).

Variables in COMMON. See Table 5.4 for definitions.

OUTPUT

WLVG : Leaving humidity ratio (Ibm-fÔ/lbm-dry air),

QTRHC : System reheat load (Btu/hr).

QTRCC : System recooling load (Btu/hr).

Also, some variables in COMMON.


1. Heating supplied.

If TLC > TLCMX,

TDIF = TLCMX - TLC

TLC = TLCMX

QTDIF = ZMASt * 0.245 * (TDIF - TLC)

5-84

QLNM1 * QTDIF


QHLNMf

QHPNMt

IHHNMi

QT = ZMASt * 0.245 * (TEC - TLC)

QTRHC = QTRHC + QT * AMULT

WLVG = WEC

If TLC <JLCMX,

QT = ZMASi * 0.245 * (TEC - TLC)

QTRHC = QTRHC + QT * AMULT

WLVG = WEC

2. Cooling supplied.

If TLC < TLCMN,

Call subroutine CCOIL to calculate cooling load (QCTLC) if TLCwere allowed to be met.

Call subroutine CCOIL to calculate cooling load (QT) with TLClimited to TLCMN.

TLC = TLCMN

QTDIF *,QCTLC - QTV*i

QLNM1 = QTDIF


QCLNMt

QCPNM1

IHCNMi

QTRCC = QTRCC + QT * AMULT

5-85

If TLC >. TLCMN,

Call subroutine CCOIL to calculate cooling load QT

QTRCC = QTRCC + QT * AMULT

5-86

BRAD2

A subroutine to calculate the heat (QB) added to a zone by a base-board radiation heating system and to correspondingly adjust the zone'sbase sensible heat load (QS).

INPUT

QS

TSP

CBTU -

ALFBR -

TOA

THWHI -

THWLO -

TOAHI -

TOALO -

Base sensible heating load (Btu/hr)

Set point temperature of zone (°F)

Heat output of baseboard radiation at standard conditions(215°F avg. water temp., 65°F entering air temp.)(Btu/hr-lin.ft.)

Active length baseboard radiation (lin.ft.)

Dry-bulJ^ temperature outside air (°F)- U./Oc\ o i( p) tu THWHI -

(°F)£F> THW£2 THWLO

(°F)*£o ui

(OF)=:K-

i

. 1 . ^_

TOAL'O' T()A TÂHIOUTSIDE AIR TEMPERATURE (F)

Figure 5.4 Graphic illustration of baseboardhot water temperature reset as functionof outside air temperature

OUTPUT

QB - Heat given off by baseboard radiation (Btu/hr)


1. Baseboard heating off.

If TOA > TOAHI,

QB = 0.

2. Baseboard heating on.

If TOA* TOAHI,

TAIR = TSP - 10.

5-87

Calculate THW using function TRSET.

«•• -3. Adjust QS.

QS = QS - QB

5-i

AHU

A routine to simulate the performance of air handling units calcu-lating thermal requirements of colls, fan heat, and humidifier.

INPUT

NAHU : Air handling unit type:

1) Draw-through unit—heating coil, cooling coll, fan,discharge

2) Draw-through unit—heating coil, cooling coil withface and bypass dampers, fan, discharge.When heating required, bypass full open and heatingcoil modulates to meet load, coolino coil off. Whencooling required, heating coil locked out, coolingcoil runs wild, dampers modulate to meet requireddry bulb temperature.

PATH Barometric pressure (in. Hg).

MFAN Fan mass air flow (Ibm-air/hr).

NVFC Fan volume control index (see PTLD).

PCTLD Fan full load fraction.

DTFAN Temperature rise across fan at full load (°F).

TLVG Desired air temperature leaving AHU (°F).

TCD Cold deck temperature (°F).

H20RD Net humidity control zone water requirement.

MZONE Humidity control zone mass air flow (Ibm-air/hr).

WZ Humidity control zone humidity ratio (lbm-H20/lbm-dry air),

TMA Inlet dry bulb temperature (°F).

WMA Inlet humidity ratio (lbm-H20/lbm-dry air).

DMA Inlet air density (lbm/ft3).

OUTPUT

QCC : Cooling coil load (Btu/hr).

SHR : Sensible heat ratio.

5-89

QHC : Heating coil load (Btu/hr),

WLYG : Humidity ratio entering humidifier section (Ibm-HeO/l bin-dry air)air),

DLVG : Atr density entering humfdtfter section (Ibm/ft ).

WSUP : Humidity ratio after humidifier section (lbm-H20/lbm).

WATER : Water added to air by humidifier (lbm-H20/hr).


1. Simple draw-through unit simulation.

TLC = TLVG - DTFAN * PTLD * (NVFC, PCTLD)

If TMA < TLC,

QHC = MFAN * 0.245 * (TMA - TLC)

QCC = 0.0

WLVG = WMA

SHR = 1.0

GO TO 3.

If TMA = TLC,

... QHC = 0.0

QCC = 0.0

WLVG = WMA

SHR =1.0

GO TO 3.

If TMA > TLC,

Call subroutine CCOIL to calculate WLVG, QCC, and SHR.

QHC = 0.0

GO TO 3.

5-90

2. Draw-through unit with bypass around cooling coil.

TLC - TLVG - DTFAN * PTLD * (NVPC, PCTLD)

If TMA « TLC,

QHC = MFAN * 0.245 * (TMA - TLC)

QCC = 0.0

WLVG = WMA

SHR = 1.0

GO TO 3.

If TMA =• TLC

QHC = 0.0

QCC = 0.0

WLVG = WMA

SHR = 1.0

GO TO 3.

If TMA > TLC,

Call subroutine CCOIL to calculate cooling coil performance for1. Ibm-air/hr (QCC1).

Call subroutine MXAIR to calculate position of face and bypassdampers (ALFA = portion of air through bypass).

QCC = MFAN * (1.0 - ALFA) * QCC1

3. Humidifier simulation.

Using function DENSY, calculate DLVG.

If QCC > 0.0

WATER =0.0

WSUP = WLVG

5-91

If QCC £0.0,

WSUP - -H20RD/MZONE + WZ

(Limit WSUP by high limit switch on humidifier set at 80% R.H.)

WATER = -MFAN * (WLVG - WSUP)

5-92

MXAIR

A subroutine to calculate the thermal properties of mixed air giventhe properties of the two mixing air streams. The basic application ofthis routine is in simulating the function of three types of outside aircontrol.

INPUT

Air Stream #1

Air Stream #2

MXAO : Type of outside air control.

1 Fixed percent outside air.2 Enthalpy/temperature type economizer cycle

control.3 Temperature type economizer cycle control.

TOA : Outside air dry bulb temperature (°F)

DOA : Outside air density (lbm/ft3)

HOA : Outside air enthalpy (Btu/lbm)

.WOA : Outside air humidity ratioIbm-dry air)

PATH : Barometric pressure (in. Hg)

TRA : Return air temperature (°F)

DRA : Return air density (lbm/ft3)

WRA : Return air humidity ratio (lbm-H20/Ibm-dry air)

EAT : Desired mixed air temperature (economizerapproach temperature ) (°F)

ALFAM : Minimum fraction of outside air (for MXAOtype 1, ALFAM is the fixed portion of out-side air.

OUTPUT

ALFA

TMA

WMA

Actual portion of outside air which meets or approaches EAT.

Mixed air dry bulb temperature (°F)

Mixed air himidity ratio (Ibm-Ô/lbm-dry air)

5-93

OUTPUT (Concluded)

DMA : Mixed air density (lbm/ft3)


1. Using subroutine PSYCH, calculate return air enthalpy (HRA).

2. MXAO » 1 (fixed percent outside air)

ALFA = ALFAM

GO TO 5.

3. MXAO = 2 (enthalpy/temperature type economizer cycle control)

If HOA < HRA,

Calculate ALFA using subroutine ECONO

If HOA > HRA,

ALFA = ALFAM

GO TO 5.

4. MXAO = 3 (temperature type economizer cycle control)

Calculate ALFA using subroutine ECONO.

GO TO 5.

5. Mixed air thermal properties.

TMA = (TOA * DOA * ALFA + TRA * DRA * (1. - ALFA))/(DOA * ALFA

+ DRA * (1. - ALFA))

WMA = (WOA * DOA * ALFA + HRA * DRA * (1. - ALFA))/(DOA * ALFA

+ DRA * (1. - ALFA))

DMA = PATM/((-754 * (TMA + 460.)) * (1. + (7000. * WMA/4360.)))

5-94

ECONO

A subroutine to simulate the operation of a temperature type econo-mizer cycle, calculating that portion of outside air yielding a mixedair temperature closest to the desired mixed air dry bulb temperature.

INPUT

OA

DOA

RA

DRA

LV6

ALFAM

OUTPUT

ALFA

Outside air dry bulb temperature (°F)

Outside air density (lbm/ft3)

Return air dry bulb temperature (°F)o

Return air density (lbm/ft )

Desired mixed air dry bulb temperature (°F)

Minimum fraction of outside air

: Portion of outside air yielding mixed temperature closestto desired mixed air temperature


1. Select appropriate mode.

Mode 1. Return air temperature greater than outside air temperature.

If LVG <_ OA, ' '

ALFA =1.0

If LVG > OA, ' '

If LVG < RA,

ALFA = (DRA * (RA - LVG))/(RA * DRA - OA * DOA + LVG

* (DOA - DRA))

If LVG >_ RA,

ALFA = ALFAM

GO TO 2.

5-95

Mode 2. Return air temperature equals outside air temperature.

ALFA = 1.0

RETURN

Mode 3. Return atr temperature less than outside air temperature.

If LVG <.RA,

ALFA « ALFAM

If LVG > RA,

If LVG < OA,

ALFA = (DRA * (RA - LVG))/(RA * DRA - OA * DOA + LVG

* (DOA - DRA))

: I f L V G > _ O A ,

ALFA = 1.0

GO TO 2.

2. Check range of ALFA.

If ALFA < ALFAM,

ALFA = ALFAM

If ALFA > 1.0,

ALFA = 1.0

5-96

CCOIL

A subroutine to stmulate the performance of a cooling coil. It cal-culates the sensible and latent heat extracted by a cooling cotl assumingit to be of adequate capacity. The coil cools air to dry bulb tempera-ture (TDBO) and calculates the humidity ratio at that condition.

INPUT

MASS : Rate of air flow through coil (lbm-air/hr)

PATM : Barometric pressure (inches Hg.)

TDBI : Dry bulb temperature of entering air (°F)

WI : Humidity ratio of entering air (Ib-Ô/lb-dry air)

TDBO : Dry bulb temperature of leaving air (°F)

OUTPUT

WO : Humidity ratio of leaving air (lb-H20/lb-dry air)

QCC : Total heat extracted by coil (Btu)

SHR : Sensible heat ratio


1. Estimate leaving wet bulb temperature.

TWBO = TDBO - 1.5

2. Simulate cooling coil.

DT = TDBI - TDBO

If DT <_0.0,

QCC = 0.0

SHR =1.0

WO = WI

5-97

If DT > 0.0,

QSC - MASS * 0.245 * DT

Use subroutine PSY1 to calculate leaving air humidityratio (WO)

DW * WI - WO

If DW <_0.0,

WO = WI

QCC = QSC

SHR = 1.0

If DW > 0.0,

QIC = MASS * 1090.0 * DW

QCC = QSC + QIC

SHR = QSC/QCC

The functioning of the cooling coil simulation is illustratedgraphically in Figure 5.5, where it is plotted on an HVAC equip-ment manufacturer's psychrometric chart.

It shows a strong correlation with the manufacturer's publishedcooling coil performance curves and it is also in accord withrecommendations of Stoecker, et.al. (1973) (ASHRAE PublicationNo. 2290-RP-131), recommending cooling coil discharge air condi-tions to be 90% RH for simulation purposes when latent heat isbeing extracted.

5-98

' ^

-i \ \ \ I'l i nYrrtmhrfrrnTnT ;

patooosso puo jio Ajp jo qj Jad nig-JkdlVHlN3

5-99

TRSET

A function to calculate TRSET as a linear function of TOA between thecoordinates (THI, TOALO) and (TLO, TOAHI). TRSET Is allowed to float be-tween THI and TLO but not to exceed those bounds as illustrated in thefigure below.

INPUT

TOA

THI

TLD

TOAHI

TOALO

OUTPUT

TRSET *

TRSET -

TOATOALO TOAHI

Figure 5.6 GRAPHIC ILLUSTRATION OF FUNCTION TRSET.


If TOA <_ TOALO,

TRSET = THI

If TOA > TOALO,

If TOA >_ TOAHI,

TRSET = TLO

If TOA < TOAHI,

TRSET = (THI - (THI - TLO) * (TOA - TOALO))/(TOAHI - TOALO)

5-100

PTLD

A function to calculate the part load power requirement of variablevolume fans.

, INPUT

NC : Curve Number

1 : Variable Speed Motor.

2 : Inlet Vane Damper

3 : Discharge Damper

PC : Fraction of full load for a volume

OUTPUT

PTLD : Percent part load power

LIMIT VALUES

0.20 <_PC <_1.10


1. Variable Speed Motor

PTLD = 0.0015302776 + PC * (0.0052080574 + PC * (1.1086242

+ PC * (-0.11635563)))

5-101

2. Inlet Vane Damper

PTLD = 0.35071223 + PC * (0.3080535 + PC * (-0.54137364 +

PC * (0.87198823)))

3. Discharge Damper

PTLD = 0.37073425 + PC * (0.97250253 + PC * (-0.34240761))

20 30 40 50 60 70 80 SO 100

Rated fan volume, percent (PC)

Figure 5.7 POWER SAVINGS VS AIR QUANTITY REDUCTION FORTHREE COMMON METHODS OF CONTROLLING DUCTSTATIC PRESSURES

5-102

TEMP

A subroutine to calculate the dry bulb air temperature of air leav-ing an air handler and/or Indicate the mode (heating or cooling) of pro-cess water in a two-pipe distribution system.

INPUT

ICO

K

JMAXK

TOA

TFIX

SPACN(K.J)

TS(I)

Type of control option selected:1) Fixed or predefined (constant).2) Determined by room with coldest supply air require-

ment.3) Reset as inverse function of outside air dry bulb

temperature.4) Reset as direct function of outside air dry bulb

temperature to a maximum, then lower to a minimum(spike). For two-pipe induction units with water-side changeover.

5) High/low step function with hysteresis at change-over. Used for two-pipe fancoil waterside change-over.

6) Determined by room with warmest supply air require-ment.

Fan system number.

Number of zones on currently analyzed system.

Dry bulb outside air temperature (°F)

Fixed leaving air temperature for control mode one ( F)

Variable which defines zone/Q-distrib. system relation-ships.

Required supply air temperatures to each zone ( F)

Following variables used for control mode three:

TLAHI

TLALO

TDBLO

TDBHI

Highest air temperature leaving AHU ( F)

Lowest air temperature leaving AHU (°F)

Low ambient DB temperature corresponding to high leav-ing AHU temperature (TLAHI) (°F)

High ambient DB temperature corresponding to low leav-ing AHU temperature (TLALO) (°F)

5-103

TCOFC : Two-pipe fancojl unit changeover temperature.

OUTPUT

TLVQ : Required dry bulb temperature of air leaving airhandler.

TOACO : Induction unit changeover temperature.

IPW : Induction or fancoil unit process water temperatureindicator: -1 = Hot water available.

0 = Changeover condition and/or hot andchilled water available.

+1 = Chilled water available.


1. Fixed or predefined.

TLVG = TFIX

2. Determined by room with coldest air requirement.

Scan applicable TS. values. Set TLVG equal to lowest TS...

3 Reset as inverse-function of outside air dry bulb temperature

Use function TRSET to calculate TLVG.

Input variables:

TOA

TLAHI

TLALO

TDBHI

TDBLO

4. Two-pipe induction unit primary air schedule and process water modeindicator. See INDUC for graph of this TEMP function.

5-104

If TOAGO < TOA,

If TDBHI TOA,

TLVG = TLALO. /•

IPW = 1

TOACO = TDBLO

If TDBHI > TOA,

Calculate TLVG using function TRSET.

IPW = 1

TOACO = TDBLO

If TOACO = TOA,

Calculate TLVG using function TRSET.

If TOACO i TDBLO,

TOACO = TDBLO +5.0

IPW = -1

If TOACO > TDBLO,

TOACO = TDBLO

IPW = -1

If TOACO > TOA,

TLVG = TLALO

TOACO = TDBLO +5.0

IPW = -1

5-105

5. Two-pipe fancoil waterside changeover. Based on changeover temper-ature with (+) or (-) 2,5°F lag.

If TOA « TOACO, ...

If TOACO > TCOFC

IPW = -1

If TOACO <_ TCOFC ; ,

TOACO = TCOFC +2.5

IPW = 0 : . . -

If TOA « TOACO,

If TOACO <_ TCOFC

TOACO = TCOFC + 2,5

IPW = 0

If TOA > TCOFC,

TOACO = TCOFC - 2.5

IPW = 0

If TOA > TOACO,

If TOACO >_ TCOFC

TOACO = TCOFC n 2.5

IPW = 0

If TOACO < TCOFC

IPW = +1

6. Determined by room with warmest supply air requirement.

Scan applicable TS^ values. Set TLVG equal to largest TS...

5-106

PSYCH

A subroutine for calculating the psychrometrlc properties of moistair.

INPUT

T : Dry-bulb temperature of moist air (°F)

W : Humidity ratio of moist air (Ib water/1b dry air)

PATH : Barometric pressure (inches of mercury)

OUTPUT

DEN : Density of moist air (Ib dry a1r/cu ft)

H : Enthalpy of moist air (Btu/lb dry air)


1. Calculate enthalpy.

H = 0.24 * T + VI * (1061.0 + 0.444 * T)

2. Calculate specific volume.

V = 0.754 * (T + 459.688) * (1.0 + 7000.0 * W/4360.0)/PATM

3. Calculate specific density.

DEN = 1.0/V

5-107

PSY1 AND PSY2

A subroutine which calculates humidity ratio, enthalpy and densityof outside air.

INPUT

DBT : Outside air dry-bulb temperature (°F)

WBT : Outside air wet-bulb temperatjre (°F)

DPT : Outside air dew point temperature (°F)

PATM : Atmospheric pressure (inches of mercury)

OUTPUT

HUMRAT : Humidity ratio (ibs water/lbs dry air)

ENTH : Enthalpy (Btu/lb dry air)(PSYl only)

DENS : Density (ibs dry air/cu ft)(PSYT only)


In the calculation of psychrometric properties of moist air partialpressure of water vapor is needed. This is calculated by the PPWVM sub-function.

1. Calculate partial pressure of water vapor in moisture-saturatedair for WBT and obtain partial pressure of water (applies whendewpoint temperature is greater than 32.0 °F).

PPWV = PPWVM'(WBT) - 0.000367 * PATM * (DBT - WBT)/

(1.0 + (WBT - 32.0)/1571.0)

2. HUMRAT = 0.622 * PPWV/(PATM - PPWV)

3. ENTH = 0.24 * DBT + (1061.0 + 0.444 * DBT) * HUMRAT

4. DENS = 1.07(0.754 * (DBT + 460.0) * (1.0 + 7000.0 * HUMRAT/

4360.0)/PATM)

5-108

PPHVM

A function which calculates the partial pressure of water inmoisture-saturated air.

INPUT

TEMP : may be a wet-bulb, dry-bulb, or dewpoint temperature (°F)OUTPUT

PPWVM : partial pressure of water in moisture-saturated air(in. Hg)


1

3.

Let A(l)A 2)A(3)A(4)A(5)A(6)

= -7.902985

-1118

,02808,3816 E-7,344,1328 E-3

B 1B 2)B(3)B(4)

-9.09718-3.566540.8767930.0060273

= -3.49149

2. Let T = (t + 459.688)/1.8

If T is less than 273.16, go to 3.

Otherwise

z =PI =P2 =P3 =P4 =

373.16/TA(l) * (z-1)A(2) * LoglO (z)A(3) * (10 ** (A(4)A(5) * (10 ** (A(6)

* (l-l/z))-l)* (z-l))-l)

Go to 4.

Let z =PI =P2 =P3 =P4 =

273.16/TB(D * (x-1)B(2) * LoglOB(3) * (1-1/z)Log 10

(z)

4. PVS = 29.921 * 10 ** (PI + P2 + P3 + P4)

5-109

HUM!

A subroutine to calculate the humtdlty ratio (Ib-HpO/lb-dry a''r)given

T - dry-bulb temperature (°F)

RH - relative humidity (%)

PATM - barometric pressure (in. Hg.)

1. Using subroutine PSY2, calculate humidity ratio of saturatedair (WSAT) at temperature, T.

2. Humidity ratio (W) = RH * 0.01 * WSAT

DENSY

A function to calculate the density of moist air (Ib-air/cu.ft.)given

T - dry-bulb temperature (°F)

W - humidity ratio (lb-H20/lb-dry air)

PATM - barometric pressure (in. Hg.)

DENSY = 1.0/(0.754 * (T+460.0) * (1.0+7000.0 * W/4360.)/PATM)

5-110

MAX

A subroutine to replace current values of A with X and IB with IYif the absolute value of X exceeds A. A and X are real numbers. IBand IY are integers.

VARIABLE ORDER

A, X, IB, IY


1. If |X| exceeds |A|,

A = X

IB = IY

ERROR

A subroutine to print terminal and warning messages due to inputdata abnormalities.

ALOG1

A function to calculate logarithms to base 10.

Log1Q(X) = 0.434294481 * Loge(X)

5-111

H20ZN

A subroutine to calculate hourly moisture changes and net moisturerequirements.

INPUT

QL

ZMASS

WSP

QLINF

WZON

WOA

Latent load from zone (Btu/hr)

Mass flow through zone (Ibm-air/hr)

Zone humidity ratio set point (lbm-H20/lbm-dry air)

Latent load due to infiltration from load tape (Btu/hr)

Current zone humidity ratio (lbm-H20/lbm-dry air)

Outside air humidity ratio (lbm-H20/lbm-dry air)

OUTPUT

H20AD : Zone water change in current hour

H20RD : Net zone water requirement


1. Zone load water.

H20RM = QL/1090.0

2. Infiltration water.

H20IN = (QLINF/1090.0) * (WOA - WZON)/((WOA - WSP)

3. Set point recovery load.

H20VL = (WZON - WSP) * ZMASS

4. Summaries.

H20AD = H20RM + H20IN

H20RD = H20AD + H20VL

5-112

WZNEW

A function to calculate space humidity ratios based on a water bal-ance of the following sources: QL moisture, infiltration moisture, sup-ply air moisture.

INPUT

TSP

TLC

WLC

PATM

CFMS

VOL

H20AD

WZ

Set point tepperature (°F)

Supply air temperature (°F)

Supply air humtdity ratio (Ibm-Ô/lbm-dry air)

Barometric pressure (inches Hg)

Supply air flow rate (ft3/min)

Zone volume (ft )

Zone water change incurrent hour (Ibm-HÔ)

Current zone humidity ratio (Ibm-HJVlbm-dry air)

OUTPUT

WZNEW : New humidity ratio (lbm-H20/lbm-dry air)


1. Calculate supply air moisture and net moisture to zone.

Call function DENSY to calculate supply air density (DLVG)

H20S2 = CFMS * DLVG * 60-.0 * (WLC - WZ)

DH20 = H20S2 + H20AD

2. Calculate new humidity ratio.

AIR = CFMS * 60.0

If AIR < VOL, AIR = VOL

WZNEW = DH20/(AIR * DLVG) + WZ

5-113

EQUIP

A subroutine for calculating the energy consumption of conventionalheating and cooling systems, on-site generation systems and conventionallyoperated heat conservation systems.

INPUT

Ml

M2

M3

M4

M5

M6

M7

KREHT

NUMC

SZC

NUMAC

SZAC

QHBC

QHBH

QHBRH

TECON

ELDEM

TLCHL

IPS

PPS

TESTM

PESTM

Type of chiller

Source of chiller energy

Source of heating energy


Type of on-site generation engines

Type of auxiliary chiller

Source of supplemental heat

Source of reheat coil energy

Number of chillers

Size of chillers (tons)

Number of auxiliary chillers

Size of auxiliary chillers (tons)

Hourly building cooling load (Btu/hr)

Hourly building heating load (Btu/hr)

Hourly building reheat load (Btu/hr)

Entering condensing water temperature (°F)

Hourly electrical demand of the building (KW)

Chilled water set point temperature (°F)

Temperature of high pressure purchased steam (°F)

Pressure of high-pressure purchased steam (psig)

Temperature of low pressure steam (°F)

Pressure of low pressure (psig)

5-114

HZRHETICIECIFROCATIKJ

CAU. RECXP

/HERMETIC

CENTRIFUGAL

CALL CENT

^

GAS ^ ^1

yOIL If

COMPUTEGAS

COKSUMmOB

CCMFUTEOIL

CONSUMPTION

X r

I^STEAM

COMPUTESTEAM

CONSUMPTION

COMPOTEELECTRIC

CONSUMPTION

' X

OIL If

COMPUTECAS

CONSUMPTION

COMPUTEOIL

CONSUMPTION

1

REHEAT

^^

S '

J^STEAM

COMPUTESTEAM

CONSUMPTION

COMPUTEELECTRIC

CONSUMPTION

1

Figure 5.8 LOGIC FLOW CHART OF SUBROUTINE EQUIP

5-115

INPUT. (CONT'D)

-SZT

NUMT

-- RPM

SZE

HVHO

HVDF

FFLMN

OUTPUT

GASC

GASH

GASG

OILC

OILH

STMC

STMH

ELEC

ELEH

FUEL

Size of steam turbines (HP)

Number of steam turbines (rpm)

Speed of steam turbines (rpm)

Size of on-site generation engines (KW)

Heating value of heating oil (Btu/gal)

Heating value of diesel fuel (Btu/gal)

Minimum part load cutoff point for chillers (decimal)

Hourly gas consumption for cooling (therms)

Hourly gas consumption for heating (therms)

Hourly gas consumption for on-site generation(therms)

Hourly oil consumption for cooling (gals)

Hourly oil consumption for heating (gals)

Hourly steam consumption for cooling (Ibs)

Hourly steam consumption for heating (Ibs)

Hourly electrical consumption for cooling (KW)

Hourly electrical consumption for heating (KW)

Hourly diesel fuel consumption for on-sitegeneration (gals)


1. Convert hourly building cooling load into tons.

QHBC = QHBC/12000.0

2. Calculate the enthalpy of entering and leaving steam (forboilers and absorption chillers).

5-116

2.1 For entering condition, use

AH = 1068.0 - 0.485 * PESTM

BH = 0.432 + 0.000953 * PESTM

CH = 0.000036 - 0.000000496 * PESTM

HESTM = AH + BH * TESTM + CH * TESTM * TESTM

where HESTM is enthalpy of entering steam (Btu/lb).

2.2 For leaving conditions, assume saturated water,therefore

HLSTM = 180.07

where HLSTM is enthalpy of leaving steam (Btu/lb)

3. Check the type of building system.

If M4 =0, then conventional system or conventionally-operatedheat conservation system.

Go to calculation 4.

If M4 > 0, then on-site generation system.


4. Calculate the number of chillers operating.

4.1 If the quantity (1.0 - QHBC/(0.9 * NUMC * SZC)) is (+),then building system is a conventional system or aconventionally-operated heat conservation system withno auxiliary chillers needed.

Set NC = 1 (number of chillers operating).

Calculate fraction of full load.

FFL = QHBC/(NC * SZC)

If necessary, increase NC until FFL £0.9.

IF NC = 1, and-FFL < FFLMN, then no cooling available.

If NC = NUMC, and FFL > 1.1, chiller load not met.

FFL = 1.1

QRNM = (QHBC - NC * SZC * FFL) * 12where QRNM = chiller load not met

5-117

QHBC * NC * SZC *

Update as required the following ch.tller load notmet variables.

QRCNM -

QRPNM -

IHRNM -

4.2 If the quantity (1.0 - QHBC/(0.9 * NUMC * SZC)) is (-),then building system is a conventionally-operated heatconservation system with auxiliary chillers needed.

Set NAC = 1 (number of auxiliary chillers operating).


FFL = QHBC/(NUMC * SZC + NAC * SZAC)

If necessary, increase NAC until FFL <.0.9.

5. Calculate the energy consumption required for cooling.

5.1 If the quantity (1.0 - QHBC/(0.9 * NUMC * SZC)) is (+),proceed as follows:

If Ml =1, (reciprocating chiller), call RECIP, whichcalculates ELEC.

If Ml = 2, (hermetic centrifugal chiller), call CENT,which calculates ELEC.

If Ml = 3, (open centrifugal chiller), call CENT,which calculates ELEC, then adjust as follows:

ELEC = ELEC/O.Q + 0.02133 * ELEC/QHBC)

If Ml = 5, (centrifugal chiller powered by steam turbine)*call CENT, which calculates POWER, then call STTUR, whichcalculates STMC and equivalent heating requirement, QHMC.

For cases where Ml = 4 or 5, check for source of chillerenergy.

If M2 = 1, GASC = QHMC/80000.0

. STMC = 0.0

5-118

If M2 * 2, OILC B QHMC/(0.8 * HVRO)

STMC * 0.0

If M2 = 3, STMC = STMC

If M2 « 4, ELEC = QHMC/3413.0

STMC = 0.0

5.2 If the quantity (1.0 - QHBC/(0.9 * NUMC * SZC)) is (-),proceed as follows:

If Ml = 1, call RECIP, which calculates PW1.

If Ml = 2, call CENT, which calculates PW1.

If Ml = 3, call CENT, which calculates PW1, thenadjust as follows:

PW1 = PWL/0.0 + 0.02133 * PW1/(FFL * NUMC * SZC))

If M6 = 1, (reciprocating auxiliary chiller), callRECIP, which calculates PW2.

If M6 = 2, (Hermetic centrifugal auxiliary chiller),call CENT, which calculates PW2.

If M6 = 3, (open centrifugal auxiliary chiller), callCENT, which calculates PW2, then adjust as follows:

PW2 = PW2/(1.0 + 0.02133 * PW2/(NAC * SZAC * FFL))

Total energy consumption for cooling

ELEC = PW1 + PW2

6. Calculate the energy consumption required for heating.

If QHBH > NUMB * SZB * 1000.0, boiler load not met.

QBNM = QHBH + SZB * NUMB * 1000.0 (QBNM = boiler load not met)

QHBH = SZB * NUMB * (-1000.0)

Update as required the following boiler load not met variables:

5-119

QBCNM -

QBPNM -

IHBNM

If M3 = 1, (gas-fired boiler), GASH = -QHBH/80000.0

If M3 = 2, (oil-fired boiler), OILH = -QHBH/(0.8 * HVHO)

If M3 = 3, (purchased steam heat, STMH = -QHBH/(HESTM-HLSTMO

If M3 = 4, (electric boiler), ELEH = -QHBH/3413.0

7. Calculate the energy consumption required for reheat.

If KREHT = 0, no reheat energy available.

If KREHT = i, (heat from gas-fired boiler),GASH = GASH - QHBRH/80000.0

If KREHT = 2, (heat from oil-fired boiler),OILH = OILH - QHBRH/(0.8 *HVHO)

If KREHT = 3, (heat from purchased steam),STMH = STMH - QHBRH/(HESTM - HLSTM)

If KREHT = 4, (heat from electric boiler),ELEH = ELEH - QHBRH/3413.0

END OF CONVENTIONAL ANALYSIS

BEGIN ON-SITE POWER GENERATION ANALYSIS.

8. Calculate the number of on-site generation engines inoperation.

Set NE = 1 (number of engines operating).


FFLE = ELDEM/(NE * SZE)

If necessary, increase NE until FFLE <_ 1.1.

9. Calculate the energy consumption required for operation ofengines.

If M5 = 1, (diesel), FUEL = (8900.0 + 2000.0/FFLE)/HVDF

If M5 = 2, (gas), GASG = 0.085 + 0.0289/FFLE

5-120

10. Calculate the amount of engine heat able to be reclaimed.

If M5 = 1, (diesel), QEN = (69.2 + 21.2 * FFLE) * ELDEM

If M5 = 2, (gas), QEN = (60.51 + 16.64/FFLE > 14.0 * FFLE)* ELDEM

11. Compute the number of chillers operating.

Set NC = 1 (number of chillers operating).


FFL = QHBC/(NC * SZC)

If necessary, increase NC until FFL < 0.9.

If NC = 1, and FFL < FFLMN, then no cooling available.

If NC = NUMC, and FFL > 1.1, chiller load not met.

FFL = 1.1

QRNM = (QHBC - NC * SZC * FFL) * 12

QHBC = NC * SZC * FFL

Update as required the following chiller load not metvariables:

QRCNM -

QRPNM -

IHRNM -

12. Calculate the energy consumption required for cooling.

If Ml =1, not applicable.

If Ml =2, not applicable.

If Ml = 3, not applicable.

If Ml =4, call ABSOR, which calculates STMC and theequivalent heating requirement, QHMC.

If Ml = 5, call CENT, which calculates POWER, then call STTUR,which calculates STMC and equivalent heatingrequirement, QHMC.

5-121

13. Calculate the energy consumption required for heating andcooling.

If -QHBH - QEN + QHMC > NUMB * SZB * 1000.0, boiler load not met.

QBNM = (QHBH + QEN - QHMC) + (NUMB * SZB * 1000.0)

QHBH = NUMB * SZB * (-1000.0)

Update as required the following boiler load not metvariables:

QBCNM -

QBPNM -

IHBNM -

If M3 - 1, GASH = (QHMC - QHBH - QEN)/80000.0

STMC =0.0

If GASH < 0.0, set GASH = 0.0.

If M3 = 2, OILH = (QHMC - QHBH - QEN)/(0.8 * HVHO)

STMC =0.0

If OILH < 0.0, set OILH = 0.0.

14. Compute energy consumption required for reheat.

If KREHT » 0, not applicable.

If KREHT = 1, GASH = GASH - QHBRH/80000.0

If KREHT = 2, not applicable.

If KREHT = 3, not applicable.

END OF ON-SITE POWER GENERATION ANALYSIS.

5-122

STTUR

A subroutine for calculating the energy consumption of a singlestage condensing steam turbine as a function of its power output.

INPUT

PPS : Pressure of high pressure steam (psig)

IPS : Temperature of high pressure steam (°F)

RPM : Speed of steam turbine (rpm)

SZT : Size of steam turbine, HP (taken as 1 HP/ton)

NSTON : Number of steam turbines operating; same as number ofchillers operating

POWER : Total power output required by all turbines (KW)

OUTPUT

STEAM : Hourly steam consumption (ib/hr)


1. Find the power output for each turbine (HP)

POWER = 1.341 * POWER/NSTON

2. Determine the enthalpy of entering steam (HI).

HI = AH + BH * TPS + CH * TPS * TPS

where AH = 1068.0 - 0.485 * PPS

BH = 0.432 + 0.000953 * PPS

CH = 0.000036 - 0.000000496 * PPS

3. Calculate the entropy of steam.

S = 2.385 - 0.004398 * TSAT1 + 0.000008146 * TSAT1 * TSAT1

-0.662 * E-08 * (TSAT1 ** 3.0) + 2.0 * CH * (TPS-TSAT1)

+ (BH - 920.0 * CH) * ALOG((TPS + 460.0)/(TSAT1 + 460.0))

5-123

where

TSAT1 = 1.0/(0.0017887 - 0.00011429 * ALOG (PPS)) - 460.0

4. Find the temperature of steam after isentropic expansion andexhausting at 2 psia (condensing turbine).

T2 = l.O/(0.0017887 - 0.00011429 * ALOG (2.0)) - 460.0

5. Find the enthalpy of leaving steam.

H2 = 1.0045 * T2 - 32.448 + (T2 + 460.0) * (S - 1.0045

* ALOG (T2 + 460.0) + 6.2264)

6. Calculate the theoretical steam rate Ob/HP-hr).

TSR = 3413.0/(H1 - H2)

7. Calculate base steam rate.

BSR = SLOPE * TSR + B

where

BO = 84.0 - 0.017 * SZT + 1.5625 * ((SZT/1000.0) ** 2.0))

Bl = -19.7 + 0.001025 * SZT

B2 = 1.4

B = BO + Bl * RPM/1000.0 + B2 * ((RPM/1000.0) ** 2.0)

50 = 3.88 - 0.011865 * SZT + 0.1173 * ((SZT/1000.0) ** 2.0)

51 = -1.1 + 0.000533 * SZT - 0.0581 * ((SZT/1000.0) ** 2.0)

52 = 0.116 - 0.000057 * SZT + 0.00709 * ((SZT/1000.0) ** 2.0)

SLOPE = SO + SI * RPM/1000.0 + S2 * ((RPM/1000.0) ** 2.0)

The base steam rate calculation was made by equation-fitting theElliott YR single stage steam turbine data.

.8. Calculate the horsepower loss again determined by equation-fit-ting the Elliott YT single stage steam turbine catalog data forcondensing turbine (2 psia).

HPLSS = 0.0334 * ((RPM/1000.0) ** 2.42)

* ((SZT/1000.0) ** 1.47)

5-124

9. Calculate the superheat correction factor determined by equation-fitting the Elliott YR single stage steam turbine catalog data.

See computer listing of STTUR subroutine for equation of SC.

10. Determine the full load steam rate (lb/HP-hr).

FLSR = (BSR/SC) * ((SZT + HPLSS)/SZT)

11. Determine the part load steam rate for one turbine (Ib/hr).

STEAM = FLSR * SZT (PLB + PLM * POWER/SZT)

12. Calculate the total hourly steam consumption (Ib/hr).

STEAM = STEAM * NSTON

5-125

CENT

A subroutine for calculating the energy consumption of an electrichermetic centrifugal water chiller as a function of part load.

INPUT

QHBC : Hourly building cooling load (.tons)

TECON : Temperature of entering condenser water (°F)

TLCHL : Temperature of leaving chilled water (°F)

FFL : Fraction of full load (decimal)

OUTPUT

POWER : Hourly electrical power consumption (kilowatt hours)


1. Calculate the temperature of leaving condenser water at fullload.

TLCON = TECON +10.0

2. Calculate the full load power per ton.

POPTN = 0.049 * ALOG (TLCON/TLCHL) * TLCHL ** 0.8

(This equation was excerpted from personal correspondencefrom R. S. Arnold of Carrier to J. M. Anders of P.O.D.)

3. Determine the error correction to be applied to above equationto make it conform with Carrier catalog data (Model 19C).

ERROR - 2.4531 - 0.041229 * TLCON - 0.0273842 * TLCHL

+ 0.000118191 * TLCON * TLCON + 0.00047537

* TLCHL * TLCON - 0.000197535 * TLCHL * TLCHL

4. Calculate the full load power per ton.

POPTN = POPTN - ERROR

5-126

5. Determine the total hourly part load power consumption.

POWER = (0.1641/FFL + 0.2543 + 0.73965 * FFL

- 0.15835 * FFL * FFL) * POPTN * QHBC

5-127

RECIP

A subroutine for calculating the energy consumption of an electrichermetic reciprocating water chiller as a function of part load.

INPUT

QHBC : Hourly building cooling load (tons)




OUTPUT

POWER : Hourly electrical power consumption (kilowatt hours)


1. Calculate the power per ton as determined from an equationfit of Carrier catalog data (Model 30HR).

POPTN = (0.3371 + 0.01223 * TECON - 0.009749 * TLCHL)

* (0.868 + 0.133 * FFL)

where POPTN has units of kilowatts per ton.

2. Determine total hourly power consumption.

POWER = POPTN * QBHC

5-128

ABSOR

A subroutine for calculating the energy consumption of a steam ab-sorption water chiller.

INPUT

QHBC : Hourly building cooling load (tons)



TDROP : Chilled water temperature drop at full load (°F)(setequal to 10°F in program)


PESTM : Pressure of low pressure steam (psig)

OUTPUTt

STEAM : Hourly steam consumption (ibs/hr)I

CALCULATION SEQUENCE (CARRIER 16HA) I

1. Determine the capacity factor which adjusts nominal capacityfor operation at conditions other than the standard of 12 psiginlet steam, 85°F entering condenser water and 44°F leavingchilled water.

RAT = -2.8246 + 0.06575 * TECON - 0.06011 * PESTM

+ 0.06433 * TLCHL + 0.0011862 * TECON * PESTM

+ 0.00023232 * TECON * TLCHL + 0.00025421 * PESTM

* TLCHL - 0.0006438 * TECON * TECON - 0.0015887

* PESTM * PESTM - 0.0006199 * TLCHL * TLCHL

2. Find the capacity factor which adjusts for chilled water tem-perature drop other than 10°F.

CMULT = 0.9190 + 0.010333 * TDROP - 0.0002222 * TDROP

* TDROP

5-129

3. Calculate the total capacity factor.

RAT = 0.91 * CMULT * RAT

where 0.91 is fouling factor.

4. Calculate the full load steam rate (Ib/hr-ton).

SRATE = 22.169 + 0.592 * PESTM - 0.0196 * PESTM * PESTM

- 6.9384 * RAT

5. Determine the part load steam consumption.

STEAM = SRATE * (0.0136/FFL + 0.7928 + 0.11843 * FFL ;

+ 0.0752 * FFL * FFL) * QHBC •

5-130

SNOWM

A subroutine for calculating the heat required to melt snow.

INPUT

TOA

MOA

PATH

WIND

SAREA

SNOW

OUTPUT

QTOT

Dry-bulb temperature of outside air (°F)

Humidity ratio of outside air (Ib water/1b dry air)

Barometric pressure (inches of mercury)

Wind velocity (mph)

Snow-melting slab area (sq ft)

Inches of snow water equivalent (inches)

Total hourly heating requirement of snow-melting system(Btu/hr) •

CALCULATION SEQUENCE*

1. Partial pressure of water vapor in moist air (inches of,mercury)

VP = (WOA/0.622 * PATM)/(1.0 + WOA/0.622)

2. Sensible heat required to raise temperature of snow from out-side air temperature to melting point (Btu/hr-sq ft)

QSEN = 2.6 * SNOW * (33.0 - TOA)

3. Latent heat required to melt snow (Btu/hr-sq ft)

QLAT = 746.0 * SNOW ^

4. Heat required to evaporate melted snow (Btu/hr-sq ft)

QEVAP = 1075.0 * (0.0201 * VWIND + 0.055) * (0.185 - VP)

*For derivation and justification of equations, see "Design of Snow-MeltingSystems", Heating and Ventilating. April, 1952, by William P. Chapman, and1967 ASHRAE Guide and Data Book. Systems and Equipment Volume, Chapter 67entitled "Snow Melting".

5-131

5. Heat transferred by convection and radiation CBtu/hr-sq ft)

QCONV = 11.4 * (0.0201 * VWIND + 0.055) * (33.0 - TOA)

6. Determine total heat required (Btu/hr)

QTOT = (SAREA * (QSEN + QLAT + 0.5 * QEVAP + 0.5 QCONV))/

0.7

where the edge loss factor is 0.3 and the area ratio of snow-free area to slab area is 0.5.

5-132

ENGYC

A subroutine for printing the monthly energy consumption summary.

INPUT

FAC Name of facility

CITY Location of facility

PROJ Project number

DATE Date of program run

ENGR Name of engineer

ENGY Monthly energy consumptions and demands. A 12 x 2 x 17matrix with indices defined as indicated below.

FIRST SUBSCRIPT: MONTH

1 January

2 February

3 March

4 April

5 May

6 June

7 July

8 August

9 September

10 October

11 November

12 December

5-133

OUTPUT

SECOND SUBSCRIPT: MODE OF ENERGY

1 Demand

2 Consumption

THIRD SUBSCRIPT: TYPE OF ENERGY

1 Maximum monthly heating, demand

2 Maximum monthly cooling demand

3, Electric, internal lights and building equipment

4' Electric, external lights

5 Electric heat (boiler and auxiliaries, and hot waterpumps)

6 Electric cool (chiller, pumps and cooling tower fan)

7 Gas heat

8 Gas cool

9 Gas generation

10 Steam heat

11 Steam cool

12 Oil heat

13 Oil cool

14 Diesel fuel generation

15 Not used

16 Not used

17 City water

18 Fans

Tabular summary of monthly energy consumption. See Figures 6.22 to6.25 In the User's Manual.

5-134

A subroutine for simulating the performance of heat conservationsystems. A heat conservation system is one where the refrigerationmachines have double-bundled condensers. During the summer months, thesystem acts as a conventional refrigeration system whereby the bundingheat gains are picked up in the chilled water coils, returned to therefrigeration machines, and rejected through condensers and the coolingtowers to the outside air. During winter months, the refrigerationmachines act as a heat pump wherein the building internal heat gains arepicked up by the chilled water coils and returned to the refrigerationmachines. Then, instead of being rejected to the outside through thecooling tower, this heat is redistributed by the hot condenser waterthrough the building to those areas that require heating. Supplementalheaters are provided in the chilled water return line to provide heatwhen the Internal gains are insufficient to offset the heat loss of thebuilding at peak heating conditions.

INPUT

VARIABLES PASSED FROM MAIN ROUTINE:

Ml

M2

M3

M4

M5

M6

M7

NUMB

SZB

NUMC

SZC

Type of chiller

Source of chiller energy

Source of heating energy


Type of on-site generation engines

Type of auxiliary chiller

Source of supplemental heat

Heating capacity multiplier

Heat conservation machine heating capacity (MBH)

Cooling capacity multiplier

Heat conservation machine cooling capacity (tons)

NOTE: Variables NUMB, SZB, NUMC, and SZC are dual functioning. Theyare redefined in HTC0N as given below.

5-135

C0MM0N INPUT VARIABLES;

See Table 5.4 for definitions of variables in C0MM0N.

OUTPUT

Number of heat conservation machinesNUMHC

SZHC

NUMC

SZC

NUMB

SZB

CAPH

CAPC

SZSCL

Size of heat conservation machines, tons

Number of auxiliary chillers (In C0MM0N)

Size of auxiliary chillers, tons (In C0MM0N)\

Number of boilers (In C0MM0N)

Size of boilers, MBH (In C0MM0N)

Total heating capacity, MBH

Total cooling capacity, tons

Size of supplementary heating unit in chilled watercircuit, MBH

ENGY : Energy resource peak and consumption matrix(See Table 5.3).


1. Calculate cooling capacity required.

QCR = NUMC * SZC * 12000

where QCR has unit of Btu/hr.

2. Calculate heating capacity required.

QHR = -1000. * NUMB * SZB

where QHR has units of MBH.

The input variable QSNOW should be set equal to 0.0 if snow-melting isnot to be considered or if snow-melting is considered, but the engineerdoes not wish to have a snow-melting load added to the capacity of the boil-er. If a snow-melting load is to be added to the capacity of the boiler,QSNOW can be obtained from the 1967 ASHRAE Guide and Data Book, Systems andEquipment Volume, Chapter 27, Table 2.

5-136

3. Compare peak cooling requirement to the peak heating require-ment expressed as equivalent cooling and size heat conserva-tion machines based upon the smaller of the two. Assume 1.3heat rejection ratio between condenser and evaporator, and a0.5 ratio of winter cooling capacity to summer cooling capa-city.

If QCR >_ lQHR/0.3 * 0.5)|, go to calculation 3.2.

If QCR < lQHR/0.3 * 0.5)|, go to calculation 3.1.

3.1 Size heat conservation machine based upon peak coolingload.

3.1.1 Compute total cooling capacity required.

CAPC = QCR/12000.0

where CAPC has units of tons.

3.1.2 Set NUMHC = 2 (number of heat conservation machines),

SZHC = CAPC * 1.3 * 0.5/NUMHC

where SZHC is the heat rejected at the condenserexpressed in tons during winter operation of heatconservation machines.

If necessary, increase NUMHC until SZHC < 600.0.

3.1.3 Compute heat conservation machine heating capacity(MBH).

CAPH = SZHC * NUMHC * 12000./1000.

3.1.4 Compute total heating requirements (MBH).

QHR = NUMB * SZB

3.1.5 Compute size of boilers required in condenser watercircuit. This is for supplemental heat.

SZB = (QHR - CAPH)/NUMB

where SZB has units of MBH. Note that the defini-tions of SZB and NUMB have changed from those a'tentry to HTCfJN, The number value of NUMB does notchange.

5-137

3.1.6 Compute size of supplementary heat element required1n chtlled water circuit.

SZSCL * CAPH/1.3

where SZSCL has units of MBH.


3.2 Size heat conservation machine based upon peak heatingload.

3.2.1 Compute the total heating capacity required.

CAPH = -QHR/1000.0

where CAPH has units of MBH.

3.2.2 Set NUMHC = 2 (number of heat conservation machines).

SZHC = CAPH/(12.0 * NUMHC)

where SZHC 1s the heat rejected at the condenserexpressed in tons during winter operation of heatconservation machines.

If necessary, increase NUMHC until SZHC < 600.0.

3.2.3 Compute amount of cooling available from heat con-servation machines during summer operation, Btu/hr.

QCA = (SZHC * NUMHC) * 12000.0/(1.3 * 0.5)

3.2.4 Compute amount of cooling which must be providedby auxiliary chillers, Btu/hr.

QDIF1 = QCR - QCA

3.2.5 Compute size of auxiliary chillers.Set NUMC = 1 (number of auxiliary chillers).

SZC = QDIF1/(12000.0 * NUMC)

where SZC has units of tons. Note that the defini^tions and number values of SZC and NUMC have changedfrom those at HTC0N entry.

5-138

3.2.6 Compute total cooling capacity.

CAPC = QCA/12000,0 + NUMC * SZC

where CAPC has units of tons. ,

3.2.7 Compute size of supplementary heating element inchilled water circuit, MBH.

SZSCL = CAPH/1.3

4. Size all pump water flows. _,

4.1 Chilled water flow rate, gpm.

GPMCL = 2.4 * CAPC

4.2 Condenser water flow rate, gpm.

GPMCN = 3.0 * CAPC

4.3 Boiler water flow rate, gpm.

GPMBL = CAPH * 1000.0/(500.0 * 20.0)

4.4 Well water flow rate, if used, gpm.

GPMWW = SZSCL * 1000.0/(60.0 * 8.3 * 1.0 *

(TWWIN - TCLMN))

5. Size all pump motors assuming pump efficiency of 60%.

5.1 Chilled water pump horsepower.

HPCLP = GPMCL * HDCLP/(3962.0 * 0.6 * EFF)

5.2 Condenser water pump horsepower.

HPCNP = GPMCN * HDCNP/(3962.0 * 0.6 * EFF)

5.3 Boiler water pump horsepower.

HPBLP = GPMBL * HDBLP/(3962.0 * 0.6 * EFF)

5.4 Well water pump horsepower,

HPWWP = GPMWW * HDWWP/(3962.0 * 0.6 * EFF)

5-139

6. Calculate the horsepower requirement for motors running boilerauxiliary equipment such as fans, blowers, pumps, etc. FromAmerican Standard Catalog for packaged boilers ranging in sizefrom 20 to 750 horsepower, the auxiliary horsepower require-ment was approximately 1/20 of the total boiler horsepowercapacity. Therefore,

HPBLA = CAPH * 1000,0/(33472.0 * 20.0)

7. Size cooling tower fan.

7.1 Cooling tower air flow requirement, cfm.

CFMCT = 300.0 * CAPC

7.2 Cooling tower fan horsepower requirement assuming 1.0inch of water total pressure.

HPCTF = CFMCT * 1.0/(6346.0 * EFF)

8. Begin hourly energy consumption analysis, repeating calcula-tions 9 through 20 for every hour of the year.

9. Read hourly weather and space load data. See Table 5.2 fordescription of variables.

10. Calculate wind velocity in units of mph.

VWIND = 1.151 * VEL

11. Determine if external lights are ON.

11.1 If ISUN = 0, set PWEL = 0.0.

11.2 If ISUN = 1, set PWEL = PWOL.

12. Check outside air temperature to determine if summer or winteroperation.

If TOA TCO, summer operation; therefore, go to calculation 13.

If TOA < TCO, winter operation; therefore, go to calculation 14.

13. Summer operation of heat conservation machines.

13.1 Begin fan system analysis repeating the following calcula-tions for each fan system within the building.

5-140

13.1.1 Check type of fan system.

If KFAN(K) • 1, call RHFS2 « 8, call FCfIL

• 2, call HZDO » 9. call FCfll

• 3, call NZDD * 10. call INOUC

• 4, call SZRHT " 11. call INDUC

» 5, call RHFS2 • 12. call VARVL

• 6. call RHFS2 - 13. call RHFS2

• 7. call FHT62

13.1.2 Keep running total of building cooling, heating,and power loads.

QHBC - I QFPCkk»l, kmax

QHBH , I QFPHK * QFPPH,, + TQB.k»l, kmax * *

QHBRH - I QFPRH.k«l, kmax

PWILM « I PWL.k*1, kmax

13.2 Calculate hourly energy consumption. Call EQUIP, whichthe following:

GASC

6ASH

GAS6

OILC

OILH See subroutines EN6YC for. explanation of these variable*.

STMC

STMH

ELEC

ELEH

5-141

13.3 Go to calculation 15.

14. Winter operation of heat conservation machines.

14.1 Begin fan system analysis repeating calculation 14.1.1through 14.1.6 for each fan system K.

14.1.1 Read zone loads from Input tape and form thefollowing summations:

QSUMC = ,8l E. QS(L)(pos) * MULT/*J ' » jura* I

QSUMH S J-l. jmaxk QS(L)(pos) * MULTj

14.1.2 Calculate supply air temperature required foreach zone,

TS(I) = TS(L) - QS(L)/(1.08 * CFM(I))**

14.1.3 Form the summation.

(CFM(I) * TS(I))"14.1.4 Calculate required leaving-condenser water temper-

ature assuming schedule below which 1s a functionof the hourly heating requirement of the building.

TLCON - TLCNN - 22.5 * (1.0 - QSUMH/QHR)

14.1.5 Calculate leaving-chilled water temperatureassuming the schedule shown below.

TOA 65

This schedule can be expressed 1n equation form as:

TLCHL = 44.0 + (65.0 - TOA)/5.0

unit: There is a corresponding L for each I, a relationship defined by thevariable SPACN(K.J).

5-142

If TLCHL as calculated by above equation is greaterthan 50°F, set TLCHL = 50.0.

If TLCHL as calculated by above equation is lessthan 44°F, set TLCHL =44.0.

14.1.6 Determine the ratio of cold air cfm to total cfmcirculated by fan system K. Let this ratio becalled GAMA(K). By definition, therefore,

- HBETA(J) + CFM(i)- CFMAX(K)

where BETA(J) is the fraction of total air flowinggthrough the cold duct to zone J.

A heat balance around any fan zone J yields

TS(I) = TCD * BETA(J) + THD(1 - BETA(J))

where TS(I) is the zone supply air temperaturerequired, °F

TCD is the temperature of air leavingcooling coil, °F

THD is the temperature of air leavingheating coil , °F

Solving for BETA(J) gives

BETAiJ) =btl/UJj THD - TCD

The heating and cooling coils used in heat conser-vation systems are deep coils and it is thereforeassumed that the discharge air temperature ap-proaches to within 5°F the entering water tempera-ture at maximum air flow. At partial air flow, itis further assumed that the discharge air tempera-ture varies linearly with the air flow rate throughthe coil.

The temperature of air leaving the heating coil(THD) is then

THD = TLCON - 5.0 * (1 - GAMA(K))

5-143

The temperature of air leaving the cooling coil(TCD) is then

TCD = TLCHL + 5.0 * GAMA(K)

Substituting the equation for BETA(J), THD and TCDinto the equation for GAMA(K) results in

CFMAX(K) * • (TLCON - 5.0) - SUMCT- CFMAX(K) * (TLCON - TLCHL - 10.0)

where .',: CMMP-T _ I (CFM(I) *.TS(I) * MULT(I))

bUm-' " j=l, jmaxk14.2 Calculate the quantity

SUMGX = (GAMA(K) * CFMAX(K)) for K=l to KMAX

14.3 Calculate fraction of total air circulated within buildingthat is passing through cooling coils.

GAMAB = SUMGX/CFMBX

14.4 Determine a weighted average return air temperature forthe building.

TPLB = 75.0 + QL1TB/(1.08 * (CFMBX - CFMEX))

14.5 Determine a weighted average cooling coil leaving airtemperature for building.

TCDB = TLCHL + 5.0 * GAMAB

14.6 Calculate a weighted average heating coil leaving airtemperature for the building.

THDB = TLCON - 5.0 * (1.0 - GAMAB)

14.7 Determine the amount of outside air required to create acooling load that will produce the required heating atthe condenser.

«-~. • --.•=-• >'• . •A heat balance about the building's heating coils, coolingcoilSj-.and outside air-return air damper systems yieldsthe following three equations:

QHBC = 1.08 * CFMBX * GAMAB * (TMA - TCDB)QHBH = 1.08 * CFMBX * (1.0 - GAMAB) * (THDB - TMA)

. , . . , TMAB = TPLB * (1.0 - ALFA) + TOA * ALFA

5-144

where

QHBC is hourly building cooling load

QHBH is hourly building heating load

TMAB is mixed air temperature

ALFA is fraction of outside air mixing withreturn air

Since the heat rejection ratio at the condenser of a heatconservation machine is approximately 1.3 times the cool-Ing load, find the fraction of outside air, ALFA, requiredsuch that

QHBH = 1.3 * QHBC

Substituting the equations for QHBC, QHBH, and TMAB Intothe equation yields

ALFA = TPLB/(TPLB - TOA) - (THDB * (1.0 - GAMAB)

+ 1.3 * GAMAB * TCDB)/((TPLB - TOA)

* (1.0 + 0.3 * GAMAB))

If ALFA > 1.0, the heating requirement can be obtainedwith 100% outside air; therefore, reset ALFA » 1.0.

If 0.0 <. ALFA <. 1.0, the heating requirement can be ob-tained with no need for supplementary heat.

If ALFA < 0.0, supplementary heat is required; therefore,reset ALFA =0.0. ;

14.8 Calculate actual building mixed air temperature, °F.

TMAB = TOA * ALFA + TPLB * (1.0 - ALFA)

14.9 Calculate actual building heating load, Btu/hr.

QHBH = 1.08 * CFMBX * (1.0 - GAMAB) * (TMAB - THDB)

14.10 Calculate any snow-melting load, if applicable, Btu/hr.

14.10.1 If KSNOW = 0, no snow-melting system.Go to calculation 14.11.

14.10.2 If KSNOW = 1 or 2, snow-melting 1s to be considered,

5-145

14.10.2.1 Calculate amount of snowfall for thehour assuming that 1/24 of the day'stotal fell during the hour.

SNOW = 0.1 * SNOWF(ID)/24.0

where SNOW has units of equivalentinches of water, SNOWF(ID) has unitsof inches of snow, and ID is the daynumber of the year, calculated asfollows:

ID = 1 + IHOUR/24

14.10.2.2 Call SNOWM subroutine which calculatesQTOT, the now-melting load.

14.10.2.3 Add QTOT to the heating requirement ofthe building.

If KSNOW = 1, liquid-type snow-meltingngsystem; therefore,

QHBH = QHBH - QTOT

If KSNOW = 2, electric-type snow melt-ing system; therefore,

ELEH = QTOT/3413.0

14.11 Calculate actual building cooling load, Btu/hr.

QHBC = 1.08 * CFMBX * GAMAB * (TMAB - TCDB)

14.12 Calculate energy required to produce the building heatingand cooling required.

14.12.1 If IQHBHJ >_ ISZHC * NUMHC * 12000.0), supple-mentary heat in condenser water line is required.

14.12.1.1 Calculate condenser water supplemen-tary heat requirement, Btu/hr.

QSHCN = QHBH + CAPHC

where

CAPHC = SZHC * NUMHC * 12000.0

and QHBH is negative.

5-146

14.12.1.2 If |QHBC| >. |CAPHC/1.3|, then nosupplementary heating 1s required 1nchilled water line; therefore* set

QSHCL = 0.0

If |QHBC| < |CAPHC/1.3|, then cal-culate supplementary heat requiredIn chilled water line, Btu/hr.

QSHCL = -(CAPHC/1.3 - QHBC)

14.12.1.3 Heat conservation machines are oper-ating at 100% capacity, therefore

FFL = 1.0

14.12.1.4 Calculate energy consumption requiredby heat conservation machines.

For SZHC < 200 tons:

POWER = QEVAP * (0.3371 + 0.01233

* TECON - 0.00974 * TLCHL)•'

* (0.868 + 0.0133 * FFL

* 16.0)

/ For SZHC >. 200 tons:

POWER = QEVAP * (1.74 - 1.0234

* FFL + 0.3707 * FFL

* FFL - 0.010025 * TDIF

+ 0.000175 * TDIF * TDIF)

where

QEVAP = QHBC/12000.0

TECON = TLCON +16.0

TDIF = TECON - TLCHL

5-147

14.12.1.5 Update monthly electric heat energyconsumption totals.

ELEH = ELEH + POWER

Go to calculation 14.13.

14.12.2 If |QHBH| <. |SZHC * NUMHC * 12000.0|, then heatconservation machines are operating at part load.

14.12.2.1 Calculate chilled water supplementaryheat requirement.

For |QHBH| > |1.3 * QHBCj, then

QSHCL = QHBH/1.3 + QHBC

For |QHBH| <jl.3 * QHBC|, then

QSHCL = 0.0

14.12.2.2 Calculate the number of heat conser-vation machines operating.

Estimated number operating is

ENHCM = -QHBH/0.3 * (12000.0

* 0.9 * SZHC))

Round ENHCN up to next whole numberand set equal to NHCON.

14.13.2.3 Calculate fraction of full load oneach machine operating.

FFL = QEVAP/(NHCON * SZHC/1.3)

where QEVAP = QHBC/12000.0 + QDIF2

QDIF2 = (-QHBH/1.3 - QHBC)

/12000.0

5-148

14.12.2.4 Calculate energy consumption of heatconservation machines operating.

For SZHC < 200 tons:

POWER = QEVAP * (0.3371 + 0.01223

* TECON - 0.00974 * TLCHL)

* (0.868 + 0.133 * FFL

* 16.0)

For SZHC >. 200 tons:

POWER = QEVAP * (1.74 - 1.0234 * FFL

+ 0.3707 * FFL * FFL

* 0.010025 * TDIF + 0.000175

* TDIF * TDIF)

14.12.2.5 Calculate condenser heat availablebased upon evaporator load and workdone.

QWORK = 002844 * POWER

QCOND = QEVAP + QWORK

14.12.2.6 Compare actual condenser heat availa-ble, QCOND, to that required, QHBH.

ERROR = 0.5 * (-QHBH/12000.0

* QCOND)

If |ERROR| > [0.005 * SZHC|, setQDIF2 = QDIF2 + ERROR and return tocalculation 14.12.2.3 and repeat pro-cedure until

| ERROR| <_ 10.005 * SZHC|

14.12.2.7 Check to see if FFL is below FFLMN.

If FFL >. FFLMN, then go to calcula-tion 14.13.

5-149

If FFL < FFLMN, heat conservationmachine not allowed to operate;therefore, set

QSHCL = 0.0

QHBH = 0,0

QHBC = 0.0

QHBRH = 0.0

Go to calculation 14.13.

14.13 Convert condenser supplementary heat requirement intoenergy requirements.

If M3 = 1, gas heating; therefore

GASH = GASH - QSHCN/80000.0

If M3 = 2, oil heating; therefore

OILH = OILH - QSHCN/(0.8 * HVHO)

If M3 = 3, steam heating; therefore

STMH = STMH - QSHCN/(HESTM - HLSTM)

If M3 = 4, electric heating; therefore

ELEH = ELEH - QSHCN/341300

14.14 Convert chilled water supplementary heat requirementinto energy requirements.

If M7 = I, gas heating source; therefore

GASH = GASH - QSHCL/80000.0

If M7 = 2, oil heating source; therefore

OILH = OILH - QSHCL/(0.8 * HVHO)

If M7 = 3, electric heating source; therefore

ELEH = ELEH - QSHCL/3413.0

If M7 = 4, well water heating source; therefore

ELEH = ELEH + HPWWP * 0.7457

5-150

15.

If M7 = 5, city water heating source; therefore

GALCW = -QSHCL/(8.3 * (TCMIN - TCLW))

Update the running totals of the following monthly energy con*sumption variables.

(M.2,3)M.2,4M.2.5M.2,6M.2,7M.2,10)M.2,12)M,2,15M.2.16;M.2,17M.2,18)

See subroutine ENGY for an explana-tion of these quantities.

16. Keep a record of maximum hourly energy demands by checking andupdating 1f necessary the following monthly demand variables.

ENGYENGYENGYENGYENGYENGYENGYENGYENGYENGYENGYENGYENGY

M.1,1M.1,2M,l,3M.1,4

Mê)M.1,7]

M|l!l2

M,'l,'l6M.1,17M,l,18

See subroutine ENGY for explanationof these quantities.

END OF HOURLY ANALYSIS

17. Return command to SYS IN.

5-151

SECTION 6OWNING AND OPERATING COST ANALYSIS PROGRAM


The Owning and Operating Cost Analysis Program performs a life cyclecost analysis for each building heating and cooling system analyzedby the System and Equipment Simulation Program. Life cycle costs arethose expenditures which occur singularly or periodically over thelife of the building and Includes cost of energy, cost of equipment1n terms of first costs and replacement costs which occur if the ex-pected life of the equipment 1s less than that of the building, costof maintenance (material and labor), salvage value of equipment atend of building life, and opportunity costs for floor space occupiedby equipment.

Most of the burden of assembling the cost data required by theprogram is placed upon the user. During these times of escalatingcosts for energy, fuel, material and labor, It is impractical toexpect the Owning and Operating Cost Analysis Program to accuratelyand automatically account for these factors.

6.2 INPUT

Only the punched card form of input data is required for the Own-ing and Operating Cost Analysis Program. Instructions for the pre-paration of this data are given in Table 7.1 of User's Manual.

6.3 OUTPUT

An owning and operating cost report similar to that shown in Figures6.1 through 6.3 is received for each set of input data given to theprogram. Most of the information appearing on this report is simplya recap of input data. The real results of the analysis are theannuities for each equipment category and for the total HVAC system.These annuities are calculated utilizing present worth techniques.


The calculations performed sequentially by the Owning and OperatingCost Analysis Program are summarized below:

1. Read all card input data as follows:

a) FAC - name of facility

b) CITY - location of facility

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6-4

c) ENGR - engineer's name

d) PROJ - project number

e) DATE - date of program run

f) BLGLF - building life, years

g) RINT - annual interest rate, %

h) RINL - annual increase of labor cost, %

i) RINM - annual increase of material cost, %

j) RINF - annual increase of floor space cost, %

k) RINE - annual increase of energy and fuel cost, %

1) CELE - unit cost of electricity, $/KW

m) CGAS - unit cost of gas, $/therm

n) COIL - unit cost of oil, $/gal

o) CSTM - unit cost of steam, $/1000 Ibs

p) CWAT - unit cost of water, $/1000 gals

q) CFUL - unit cost of diesel fuel, $/gal

r) CASES - number of cases or equipment combinationsto be analyzed

For "CASES" number of combinations, repeat (Is) through(lah).

s) DESC - system description label

t) ENCAT - number of energy categories

For "ENCAT" number of energy categories, repeat (lu)through (Iw).

u) ETYPE - energy type coded as follows:

1 electricity2 gas i3 oil4 steam5 water6 diesel fuel

6-5

v) ECQNS - annual consumption

w) ENLAB - energy category label

x) EQCAT - number of equipment categories

For each of "EQCAT" equipment categories, repeat (ly)through (lah).

y) EQLAB - equipment category label

z) COST - installed cost of equipment, $

aa) LIFE - expected life of equipment, years

ab) SV - is resale value to be considered at end ofbuilding life?, 0 » no, 1 = yes

ac) OHPD - major overhaul period, years

ad) AMI - estimated annual maintenance labor cost, $

ae) AMM - estimated annual maintenance material cost, $

af) DHL - estimated major overhaul labor cost, $

ag) OHM - estimated major overhaul material cost, $

ah) FLR - estimated cost of floor space occupied byequipment, $

2. Print title page as indicated in Figure 6.1.

3. Echo constants to be used for all analyses (see Figure 6.2).

4. Print first part of final report (Figure 6.3) summarizingenergy cost results.

a) Print system description label.

b) For each type of energy J = 1 to 6, and each category(I = 1 to ENCAT) entered for each type, calculate andprint the following:

• ENLAB(I,N) - energy category label

t UCOST(J) - unit cost

6-6

• ECONS(I) - energy consumption

t Total cost of energy for category

TOTAL * UCOST(J) * ECONS(I)

t Total consumption of J energy type

TCONS(J) = Z ECONS(I)

• Total cost of energy type J

TENGY(J) = Z TOTAL

• Annuity for energy type J

AE(J) = PE *((RINT * 100)/(1.0-1.0/(1.0+RINT *

100) ** BLGLF))

where PE the present value is

PE = Z (TENGY(J) *((1.0 + RINE * 100)/

(1.0 + RINT)) ** L) for L = 1 to BLGLF

c) Grand total cost for all energy consumed

UA = ZTENG(J) for J = 1 to 6

d) Grand total annuity for all energy consumed

UE = Z AE(J) for J = 1 to 6

5. Print second part of final report (Figure 6.3) summarizingequipment cost results. For each equipment category I = 1to EQCAT, calculate the following:

a) Present-value of installed equipment cost

PC = Z [COST(I) * ((1.0 + RINM)/(1.0 + RINT))

** ((J-l) * LIFE(I))] for J = 1 to L

where L = BLGLF/LIFE(I) + 1

If salvage value Is considered, adjust the present-value, PC, as follows:

PC = PC-COST(I) * (L-AL)/((1.0+RINT)**BLGLF)

6-7

Where AL = BLQLF/UFEU)

b) Present-value of floor space cost

PF = ?[FLR(I) * ((1.0 + RINF)/(1.0 + RINT))

** J] for J = 1 to LF

where LF = BLGLF

c) Present-value analysis of annual maintenance laborcost

PAML = z[AML(I) * ((1.0 + RINL)/(1.0 + RINT)) ** j]

for J = 1 to LF

d) Present-value analysis of annual maintenance materialcost

PAMM = Z[AMM(I) * ((1.0 + RINM)/(1.0 + RINT)) ** Jj

for J = 1 to LF

e) Present-value analysis of major overhaul labor cost

POHL = £[OHL(I) * ((1.0 + RINL)/(1.0 + RINT))

** (J * OHPD(I))] for J = 1 to K

where K = BL6LF/OHPD(I)

f) Present-value analysis of major overhaul material cost

POHM = Z[OHM(I) * ((1.0 + RINM)/(1.0 + RINT))

** (J * OHPD(I))] for J = 1 to K

g) Total present-value of system

P(I) = PC + PF + PAML + PAMM + POHL + POHM

h) Total owning and operating annuity for equipment I

A(D = P(D * (RINT/O.O - i.o/(i.o + RINT ** BLGLF))6. Print total owning and operating annuity for entire system.

TOOA = E A(I) + UE

7. If there is another system combination to be analyzed, returnto calculation (4) and repeat calculations 4 through 6 withthe new set of data.

6-8

NOTES AND COMMENTS

N-l

Page Intentionally Left Blank

NOTES AMD COMMENTS

N-3

NOTES AND COMMENTS

N-4

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Documents

NECAP - NASA'S ENERGY-COST ANALYSIS PROGRAM Part II ...NECAP - NASA'S ENERGY-COST ANALYSIS PROGRAM Part II - Engineering Manual R. H. Henninger, Editor Prepared by "GENERAL AMERICAN