... 0._

-----------.-.---------. "~---------_._------._--'----------_._--

DOCUMENTATION GUIDETABLE' OF CONTENTS",

Chapter I - ThermalLO Introduction !-J

U Wall and Roof Transmission Loads 1-L2 Glass Transmission ]·21.3 Solar Gain Loads ]·21.4 Heat Gains due to People ]-31.5 Lighting Heat !A1.6 Miscellaneous Electrical Heat Gains IAL7 Miscellaneous Intemal Gains 1-4L8 Transmission Loads through P~lrWions 1-5L9 Infiltration Loads 1-5

1.10 Ground Element Transmission Loads , ]-61.11 Safety Factor ]·8

Chapter 2 - Design System Calculations2.0 Introduction 2-]2.1 Analysis for Design Cooling Conditions 2-J

2.].] Thermal Load Calculations 2- I2.1.2 Supply Air Sizing Calculations 2-22.1.3 Air System Simulation Calculations 2-4

2.2 Analysis for Design Heating Conditions 2-72.2. I Thermal Load Calculations 2-72.2.2 System Analysis and Sizing Calculations 2·8

._J . ' + +. -,-_' • ++~_.,~.

A key facet of the design load and energy analyses isA "thermal" load is the sum of transmission,for a region of the building. In the program theas a "space load".

calculation of thermal loads.internal and solar gain loads

load is sometimes referred to

load is the amount of heatload as well as ventilation,

The thermal load is distinguished from a coil load. Aremoved or added at the coil. It incorporates thefan gain and p1enum load characteristics.The purpose of this chapter is to document the basic thyrmalload calculationprocedures used in HAIP. These calculations apply to design as well as average loadanalyses. The procedures here are based on the Carrier rQO Load Estimating Method.The primary reference for the method is the Carrier Sys'lem Design Manual Pari I:Load E"!:;timating. Separate sections of this chapter deal with each thermal loadcomponent. Specific details concerning design thermal !()<id calculations are foundin Chapter 2.Finally, in the formulas below, it convention is used in which cooling loads (Ilealgains) are positive and heating loads (heat losses) are negative.

Heat transmission through walls and roofs is due to the indoor-outdoor temperaturedifference and to the transmission of absorbed solar energy. The fundamentaltransmission equation is:

Qw == Uwwhere:

Qw - Wall transmission load (lHU/IJr orWall LJ..value (BTLJ/(hr-sqft-F) or W I(sqm-K))

I\w -- Wall area (sqft or sqm).ETD -- Equivalent Temperature Difference or K).

The ETD value incorporates the considerations of heat transfer due to both the actualindoor-outdoor temperature difference and absorbed solar energy. The basic ETDequation may be expressed as:

ETD == Kw (Rs/Rm)C[em" Tes) +Tes +where:

Kw == Wall or roof color correction factor (dimensionless). This factoraccounts for varied absorptivity characteristics of different colorsurfaces.1.00 for dark color surfaces (reference color).0.78 for medium color surfaces.0.55 for light color surfaces.Solar heat gain for wall or roof exposure (BTU/(hr-sqft) or W Isqm).This value is a peak solar heat gain (IPSHG) for design calculations; itis an solar gain (ASHG) for typical calculations.Solar heat gain for the reference condition (BTU I(hr-sqft) orW Isqm). The reference conditions are 40 deg. north latitude, July,sea level, design dewpoint temperature of 67 F (19.4 and clear skyconditions. Thus, the (Rs/Rm) ratio COHects for the magnitude ofthe solar flux on the surface.

!-I

LOAD CALCULATIONS

The equation for heat transmission through glass is:

Qg:;;: Ug Ag (T a - Ti)

Tes

Tam

Ti

where:

QgUg

Ag

--.

::;:

--

Equivalent temperature difference for sunlit exposures for thereference condition (F or K). Values are obtained from the CarrierDesign Manual Tables! 9 and 20. Valucs vary for cach hour, for wallor roof weights and by exposure.

Equivalent temperature difference for sh',lded exposures for thereference condition (F or K). Values are.lobtained from the CarrierDesign Manual Tables 19 and 20. Values vary for each hour, for wallor roof weights and by exposure.

Temperature correction factor (F or K). Tern and Tes valucs arcbased on a reference outdoor air tempenHure profile. To adapt theETDs to actual outdoor conditions, corrections for the amplitude andmagnitude of the actual temperature pro~le must be made. Thisfactor is derived in part from Table 20A of the Carrier DesignManual.Tam -Ti - .5 - 5 for English units.Tam - - .5 - 2.78 for S.I. Metric

Maximum temperature in outdoor air temperature profile (F or C).

Indoor air temperature (F or C).

Daily temperature range (F or K). This is the difference betweenmaximum and minimum temperatures in the daily profile.

Glass transmission load (BTU/hr or W).

Glass U-value (BTU/(hr-sqft-F) or W /(sqrn-K».

Glass area (sqft or sqm).

Outdoor air temperature (F or C).

Indoor air temperature (F or C).

Throughout the day the sun shines through windows in the building. This solarenergy is absorbed by interior floors, walls and ceilings and is released by convectionand radiation over time. To analyze this transient heat gain a set of hourly solarresponse factors are These factors been normalized for the maximum dailysolar flux. Different sets of factors are defined in the Carrier Design Manual forvarious building weights and for bare glass elements and glass with internal shadingdevices. The basic solar gain equation for glass with no external shading is:

Qsg ::;:(SHG)(SLF) Fg Agwhere:

QsgSHG

Solar gain load (RTU/hr or W).

I\Aaximum solar heat value (BTU/(hr-sqft) or W /sqm). Thisvalue is the peak solar heat gain for design cooling calculations or theaverage solar heat gain for aver:'l:ge

1-2

-.

SLF = Storage load factor (dimensionless). This is the solar response valueobtained from Carrier Design Manual. Tables 7 through I I for theappropriate glass condition, building weight, cooling equipmentoperation schedule, exposure and hour.

Fg = Glass factor (dimensionless). SHG values are derived for solar nuxthrough a single pane of ordinary glass. To account for differenttransmission and reflection characteris~ics of other types of glass andinternal shading devices a correction f<ictor is applied.

Ag 0- Glass area (sqft or sqm).

For solar gains for glass with external shading, the equation is:

Qsg = (FeSHGe + FsSHGs)(SLF) Fg Ag

where:

Fe _. Fraction of glass area exposed to sunlight (dimensionless). This valueis determined first by evaluating the angIe of incidence for the beamcomponent of solar flux for the hour. Using the angle of incidencewith the physical characteristics of the external shading device, theportion of the glass pane exposed to sunlight can be computed.

Fraction of glass area shaded (dimensionless).

I - FeMaximum solar heat gain for the exposed glass (BTU/(hr-sqft)or W /sqm).

Maximum solar heat gain for shaded glass (BTU/(hr-sqft) orW /sqm). Different SHG values are used because the exposed glassreceives beam and diffuse components of the solar flux; the shadedglass receives only diffuse solar.

The human body continuously releases quantities of sensible heat and nlOisture. Themagnitude of these heat gains depends upon the level of physical exertion. It isassumed body heat is released directly to the surrounding air. The basic sensible andlatent heat gain equations are as follows:

where:

Qps = Np Qs Qp! = N p QI

Qps--

--

=

Sensible component of heat gain (BTU/hr or W).

Latent component of heat gain (BTU/hr or W).

Scheduled number of people occupying space for the hour.

Sensible heat gain rate (BTU/(hr-person) or W /person). This value isdefined by the user.

Latent heat gain rate (BTU/(hr-pcrson) or W /person). This value isdefined by the user.

1-3

LOAD CALCULATIONS

LIGHTINGHEATGAIN

Heat gain lights is assumed to be instantaneous. The basic equation for the totallighting heat gain is:

where:

=:

=:

=: Lighting heat gain (BTU/hr or W).

Scheduled lighting power level for the hour (W).

Ballast multiplier (dimensionless). When fluorescent lights are used,the heat gain from the ballast starter device must be considered also.A ballast multiplier factor is used to increase the lighting power PIaccordingly. This multiplier is defined by the user and typicallyranges from 1.0 to 1.25. For incandescent lights the multiplier is notused.

Fu Unit conversion factor used to provide heat gain in proper units.

(3.4]2 BTU/hr)/(W) for English units.

1.0 fOf S.L Metric units.

HEATGAINS

This load element is used to model heat gain due to miscellaneous electricalmachinery such as computers, typewriters, vending machines, etc ... Heat gain fromthese machines is assumed to be instantaneous. The basic heat gain equation is:

=: Fu Pme

where:

Pme =:

Fu

=

Miscellaneous electrical heat gain (BTU/hr or W).

Scheduled miscellaneous electrical power level for the ham (W).

Unit conversion factor used to provide load in proper units.

12 BTU/hr)/(W) for English units.

1.0 for S.L Metric units.

INTERNALHEAT

GAINS

This load element is used to consider heat gain from miscellaneous non-electricalsources. Heat gai,n is assumed to be instantaneous. Gains considered for bothsensible and latent load components. Hourly heat gain quantities are directly specifiedby the user in the form of a maximum heat gain and hourly scheduling factors. Heatvalues may be positive or negative. Negative heat values are used to model loads dueto refrigeration cases or similar equipment.

AND

L LOAD CALCULA

--'---.--- --- - -----~-Heat transmission through partitions adjacent to a non-conditioned region areconsidered with this load element. non-conditioned we mean such regions asadjacent parking garages, freezer storage rooms and unconditioned warehouses, Theair temperature in these regions may vary in different ways. Therefore two options foranalyzing transmission loads through partitions are offered,

Adjacent Region Temperature. The first option is to consider the temperature in theadjacent region as being fixed, This option should be used for regions such as arefrigerated storeroom or an equipment room in which the temperature is relativelyconstant. The transmission load for this case is computed

Qpl = Up Ap (T",-Tj)

where:

Qpt = Transmission load through partition (BTU/hr or W).

Up = Partition U-value (BTU/(hr--sqft-F) or W I(sqm-K»,

Ap = Partition area (sqft or sqm).

Tar = Air temperature in adjacent region (F or C). This value is defined by theuser.

'Ii = Air temperature in conditioned space (F or C),

Pcrcenlage 01' huJoor-O!!hloor Tempen!lure Dillercnce. Thc second optionevaluates the partition temperature difference as a fraction of the indoor-outdoortemperature difference. This method may be used to model regions such as a parkinggarage or unconditioned warehouse in which the temperature varies with outdoor airtemperature. The basic transmission equation is:

Qpt ::::Up

where:

Qpt

'Ii

::::

--.

Partition transmission load (IBTU/hr or W),

Partition U-value (BTU/(hr-sqft-F) or W I(sqm-K)).Partition area (sqft or

Temperature difference fraction (dimensionless), The fraction ofindoor-outdoor ternpcraturc difference to be applied to the partition.Values may range from 0 (0%) to 2,0 (200%).

Outdoor air temperature or C).

Indoor air temperature (F or C).

Sensible and latent heat gains due to infiltration air arc considered with this loadelement. Infiltration air is assumed to enter the space at outdoor conditions and leaveat the room conditions. The basic equations for this load are:

Qis ::::Pa Vi Cpa Fu (Ta - TnQil ::::Pa Vi hfg Fu (wa - wi)

where:

Qis =Qil

Sensible infiitration (BTlJ lor or W).

Latent infiltration load (BTU/hr or W).

1-5

LOAD CALCULATIONS

Pa ==::::

Ps! ==

Pba -

--

PsI ==

E

Cpa

Fu

TaTj

hfg

Density of Value is adjusted for site elevation.

Psi Pba / PsiDe'o.sity of air standard sea leve! conditions (0.075 Ibm/ft3or 1.201 kg/m3).

Standard atmospheric pressure at site elevation (psia or kPa).

14.696 (l - 6.87535 x J 0-6E)5.256! for English units.

10 1.3 (1 - 2.25569 x 1O-5E)5.2561 for Metric units.

Standard atmospheric pressure at sea !eve! (14.696 psia or101.3 kPa).

Site elevation (fed or meters above sea level).

Infiltration air flow rate (CFM or Lis).

Specific heat of air. Standard values used arc 0.24 BTU/(lbm-F) orlO04.832 J/(kg-K).Conversion factor used to provide load in correct units.

60 min/hr for English units.

m3/(lOOO L) for SJ. Metric units.

Outdoor air temperature or C).

Indoor air temperature or C).

Heat of vaporization for water. Values used are 1054.8 BTU/lbm or2.4535x106 J/kg.

Heat loss through floors on or below grade and through walls below grade arecomputed only for the heating design condition. Heat transmission through groundclements for other conditions is not evaluated.

Transmission loads are computed using empirical equations derived for the Carrier~QO Method. This method is appropriate only for heat loss through concrete ormasonry walls and floors, and only for the heating design condition. A study ofground heat loss showed that ground temperatures below 8 ft (2.44 m) are relativelystable regardless of outdoor air temperature. Between the 8 ft (2.44 m) depth and thesurface, ground temperature varies with outdoor temperature more appreciably.Further, research showed that heat loss through floor elements was relativelyindependcnt of depth below grade, while heat loss through the perimeter of the floorwas dependent upon depth. Because of these considerations, the E20 method analyzesground transmission loads ill components. These arc floor loss, perimeter floorloss, wall transmission below an 8 ft (2.44 depth and wall transmission abovc an 8ft (2.44 m) depth. These load components are discussed below.

Floor Loss. Heat transmission through the floor to the ground below is evaluatedwith the following equation.

== Uf(Tg _ Tj)

Perimeter Floor Loss. To evaluate heat loss through the perimeter of floors, a set ofthermal resistance factors were derived to account for the insulating effcct of the floormaterial and of the ground at various depths. Heat loss is computed Ilsing thefollowing equation:

Qfp == Lfp Fp (Tad - Tn

1-6

Qn

Qfp

1 =

Qw2

Af =

Aw

Uf

Uw

Lfp =

Lwp

IFp =

-~. __ ._-----------------~---~_._._-_._--

THERMAL LOAD CALCULAI10NS

Wall Loss Above a Depth of 8 n m). To analyze heat loss through the portionof the wall between grade level and 8 ft (2.44 m) below grade, a set of factors wereempirically derived to account for the insulating effect of the wall and ground atvarious depths. The basic tra~smission equation for this load component is:

Qw! = Lwp Fp (Tad - Ti)

Heat Loss for Wails More thalli 8 n (2.44 m) Below Grade. If basement walls existbelow a depth of 8 ft (2.44 m), a separate analysis is used to determine the heat I.ossfor this section of waIL The transmission equation for this section of the wall is:

Qw2 = Uw Aw (Tg - Ti)

Variable Defilliitiollls:

Floor transmission load (BTU/hr or Vv').

Heat loss through floor perimeter (BTU Ihr or W).

Heat loss through wall area between grade and 8 ft (2.44 m) belowgrade (BTU/hr or W).

Heat loss through wall area below 8 ft (2.44 m) depth (BTU/hror W).

Floor area (sqft or sqrn).

Basement wall area (sqft or sqrn). For Qw I this is the area betweengrade and an 8 ft (2.44 m) depth. For Qw2 this is the area below an8 ft (2.44 m) depth.

Floor U-value. An assumed value of .05 BTU/(hr-sqft-I<') or .28W I(sqm-K) is used. This value models a concrete or masonry floor.

Wall U·~value. An assumed value of .08 BTU/(hr-sqft-F) or .45\V I(sqm-K) is used to mode! concrete or masonry walls.

Floor perimeter (ft or

Wall perimeter length or m).

Perimeter factor (BTU/(hr-ft-F) or W I(m-K»). This factor accountsfor the thermal resistance of the floor or wall and the ground atvarying depths. The perimeter factor is applicable from grade level to8 ft (2.44 m) below grade. For floors more than 8 ft (2.44 m) belowgrade, the perimeter factor at the 8 ft (2.44 m) level is used. Theempirical equation for the factor is:0.60 -+ 0.075(D) for English Units1.0384 -+ .4259(D) for S.I. Metric Units

Ground temperature below floor (IF or C). This value is obtainedfrom an empirical equation:55 -+ .s Tad for English units.21.67 -+ .5 Tad for SJ. Metric units.

Indoor air temperature (F or C).

Heating design outdoor air temperature or C).

Depth below grade or m). For floors, this is the distance fromgrade level to the of the walL

1-7

CALCULATIONS

For desngn load calculations a factor is introduced to provide a margin of safetyin the design. The safety factor is defined by the user. The safety load is computed bymultiplying each·of"the space sensible and latent thermal load componenl<; by thefactor.

1-8

~-----_._---_._------_._------_._._---------_._._---_.--- ..--

CIIAPTER

DESIGN SYSTEMANALYA-9IS CALCULATIONS

~'h..._J '~~-'''''~'_'-;'' '_'_''''_'T'k~- ..-------.---------------.----.--

YSISFOR

DESIGNCOOLING

CONDITIONS

The purpose of the design analysis is to determine system coil loads and air flowcharacteristics for cooling or heating design conditions. The analyses typically involvethree stages:

The Thermal Load Calculation Stage determines the heat quantity to be addedor removed from the spaces in order to maintain comfort conditions.

The Sizing Stage involves computation of supply air characteristics required tomeet the thermal loads. In the special case of hydronic heating system design,sizing involves computing a required water flow rate.

The System Analysis Stage. System operation is simulated to determine thecooling or heating coil load. Coil loads arc in turn used to size the cooling orheating plant

The purpose of this chapter is to describe procedures for both cooling and heatingdesign analyses. The following discussions will be useful in interpreting and utilizingdata on program printouts. Separate sections arc devoted to each analysis.

Design cooling analyses are performed onan hourly basis. Each of the three analysisstages is described below. For these calculations the indoor temperature is fixed at thespecified cooling setting. The outdoor conditions are obtained from the designtemperature profiles.

1.1 Thermal Load CalculationsThe first stage in the analysis involves the calculation of thermal loads. Generalthermal load calculation procedures were described in Chapter!. To apply theseprocedures for cooling design conditions, loads arc computed using considerationslisted in the Table 2.1.

2-1

DESIGN ANALYSIS CALCULATIONS

TABLE 2.1 Considerations For Cooling Design Thermal Loads-----------------_.

TlJermalload Component

Wall & Roof Transmission

Glass Transmission

So!ar Gains

!otemal

Par!i!ioo Transmission

Considerations-------------

Compute nos using peak solar gains. coolingdesignlemperature profile data and the daily rangelor design days.

-----------Compute using design temperature profile data.

---"------.-----Utilize peak solar gain data to mode! clear skyconditions.

______ H _

Compute using design day schedules.--------~--._------"-----------

Uiifize specified cooling values for the temperaturedillerence across the partition.

----------------- ..-----.<---"---.-

Infiltration Use specified cooling design infiltration air!low rales.

Ground Element Transmission This load is not considered lor cooling calculalions.Tim E20 load calculation procedure lor this elementis appropriate only lor healing design calculations.

------------. _._-------_.~--Safety Faclor load Compute using specified cooling salely lactor.

------~ --------Plenum load Computed as a percentage 01 the tolal mol and Iota!

lighting loads. Individual percentages lor eachcomponent are liseI' -supplied.

--------------------

1.2 Supply SizingThe next stage in the analysis is to derive supply air characteristics. The purpose of thecooling system is to provide conditioning to meet a thermal load. To do this a quantityof chilled air at a certain temperature is provided to the space. Thus, characteristics ofsupply air are air How quantity and temperature. The user has specified one of thesecharacteristics. It is the program's job to compute the other quantity. ~uppIy airf1Qwrates are computed both on a space and zone basis. Supply temperature iscomputedol1Iyon basis. SIzing calculations on the zone and space levels are describedbelow.

2-2

DESIGN SYSTEJv! ANALYSiS

Space Slupply Air Calculations. These computations take one of three formsdepending upon the user supply air specification.

I. Given the supply flow rate per unit !loor area, the flow rate is computed asshown below. Note that this quantity is not ,elated 1.0 a specific system supplytemperature, or even to the space load.

Vsa == Vaf Afswhere:

Vsa '. Supply air flow rate (CFM or Lis).

Vaf == Supply !low rate per unit nom area (CFM/sqft or L/(s·sqm)).

== Space floor area (sqft or sqm).

2. If the total supply air flow rate is given for the zone, the program has no basisfor computing a space How rate. Consequently, none is computed or reported.

3. Given the supply temperature, the space supply flow rate is computed by solvingthe following equation for

Qss::: Pa Vsa Cpa Fu (Tc .. Tsa)

\/ '" % / Co ( .~) ~Space sensible thermal load or W). This load does notinclude plenum heat gains.

Density of air. Value is adjusted for site elevation.

Psi Psi/ PbaDensity of air for standard sea leve! conditions (0.075 Ibm/ft.3or 1.201 kg/m]).Standard atmospheric pressure at site elevation (psia or kPa).14.696 (! - 6.87535 x lO-6E)5.256! for English units.

J 0 1.3 (I .. 2.25569 x IO-~:E)5.2561 for Metric units.

Standard atmospheric pressure at sea leve! (i 4.696 psia orlOJ.3 kPa).

Site elevation (feet or meters above sea level).

Specific heat of air. Standard values used are 0.24 BTU/(lbm-F) or1004.832 J/(kg-K).

where:

-

Psi --

E -

Cpa ==

Fu ==

--

Tc

Tsa

Qss

pa

PsI

==--

Con version f~lctor to provide load in proper units.

60 min/hr for English units.

013/(1000 L) for S.!. Metric units.

Indoor air temperature for cooling (F or C).

Supply air temperature (F or C).

Zone Supply Air Calculations. Calculations again take three forms depending uponthe user supply air specification.

2-3

SYSTEM ANALYSIS CALCULAI10NS

i. Given the supply air flow rate per unit 1100r area, the zone flow rate is computcdas:

Vsa:::: Vsf Afz

where:

Vsa = Zone supply air flow rate (CFM or Lis).

Vsf Supply air flow per unit floor area (CFM/sqft or LI(s-sqrn)).

Afz Zone floor area (sqft or sqm). This is the sum of space floor areas forall spaces in the zone.

Next, the required supply air temperature is computed by solving the followingequation for Tsa.

Qzs ::::Pa Vsa Cpa Fu (T c - Tsa)where:

Q5ZL7 ::::

Pa

Cpa

Fu

Tc --Tsa

Zone sensible thermal load (BTU /hr or W).

Density of air (lbm/ft3 or kg/m3). Values arc adjusted for siteelevation. See previous discussion for calculation.

Specific heat for air. Values used are .24 BTU/(lb-F) or1004.832 J/(kg-K).

Conversion factor used to provide load in proper units.

(60 min)/hr for English units.

m3/(l000 L) for S.L Metric units.

Indoor air temperature for cooling (F or C).

Supply air temperature (F or C).

2. If given the total supply air flow rate, only the supply temperature needs to bedetermined. The following equation is solved for Tsa.

Qsz:::: Pa Vsa Cpa Fu (Tc - Tsa)

3. If given the supply air temperature, only supply air flow rates needs to bedetermined. The following equation is solved for Vsa.

Qsz = Pa Vsa (Tc - Tsa)

1.3 Air System Simulation CalculationsThe final stage is the system simulation. The analysis procedure involves computingair flow rates, dry-bulb temperatures and humidities at all key points in the system.The coil inlet and outlet conditions are then used to determine the cooling coil load.Space sensible, latent and plenum thermal loads, supply air characteristics, systemoperating characteristics and weather conditions are utilized in the analysis. Individualaspects of the simulation are discussed below.

Zone Thermal Loads are computed as the sum of space thermal loads for all spacesin the zone. Separate totals are determined for the sensible, latent and plenum loadcomponents.

~""---_._------ -----~-_.-

----------------------------------------------- ._---~--------DESIGN SYSTEM ANALYSIS CALCULATIONS

Ventilation Loads. The quantity of air entering the system through the ventilationduct and quantities of air exhausted directly from the zone and exhausted from thereturn duct result in a heat gain or loss for the system. The ventilation load iscomputed separately for sensible and latent components:

Qvs =, Pa Vva Cpa Fu (Ta - Tzc)+ Pa Vre Cpa Fu (Tze - Tre)

Qvl '" Pa Vva hlg Fu (wa - we)

Pa

Fu

Cpa

hfg

where:

QvsQvt -~Vva

Sensible ventilation load (BTU/hr or W).

Latent ventilation load (BTU/hr or W).

Ventilation air flow rate (CFM or Lis).

Air flow exhausted from return duct (CFM or

Air density (lbm/ft3 or kg/013). This value is adjusted for siteelevation, See 2.1.2 for calculation details.

Heat capacity of air (.24 BTU/(lbm-F) or 1004832 J/(kg-K».

Heat of vaporization for water. Values used are 1054.8 BTU/lbrn or2.4535 x 106 J/kg.Outdoor air temperature (F or C).

Air temperature for air exhausted from return duct or return plenum(F or C). This temperature may differ fro-m-T-ze-'d~le to--plenum heat gains.

Air temperature for air exhausted directly from the zone (F orThis is the specified indoor temperature for cooling.

Outdoor air specific humidity (Ibm/Ibm or kg/kg).

Exhaust air specific humidity (Ibm/Ibm or kg/kg).

Conversion factor used to provide load in proper units.

60 min/hr for English units.

m3/(l000 for S.I. Metric units.

Supply Fan Heat Gain is due to friction between air and the 1~lI1 blades, energy addedto the air by compression, energy loss in the drive mechanism and heat gain from thefan motor. Assuming the fan motor is in the air stream, the fan heat gain equation is:

where:

Qf -'

Ts

flf

11m

Fu ==

==

'":::

Fan heat gain (BTU/hr or W).

Air !1ow rate through fan (CFM or L/s).

Total static pressure across fan (in wg or Pa).

Fan drive and mechanical efficiency (dimensionless). Value assumedto be 0.55 (55%).

Fan motor efficiency (dimensionless). Value assumed to be0.90 (90%).

Conversion factor used to provide heat gain in proper units.

.4003 for English units.

(62.3 Ibm water/cuft)(ft/J2 io)(60 min/hr)(.00J285 BTU/ft-Ib)

m3/(1000 L) for S.L Metric units.

2-5

SYSTEM ANALYSIS CALCULATIONS

Cooling Coil Loads. Once coil inlet and outlet conditions are defined, the cooling coilload is computed. Sensible and latent load components are calculated separately.

Qcs = pa Vsa Cpa Fu (Tci - Tco)

QcI = Pa Vsa hfg Fu (wci - wco)

where:

Qcs =QcI =

pa -.

CpaVsa -

hfg

Tci

Tco

Wci =Wco =

Fu ==--

Coil sensible load (BTU/hr or W).

Coil latent load (BTU/hr or W).Air density (lbm/H3 or kg/m3). Values are adjusted for site elevation.See 2.1.2 for calculation details.

Heat capacity of air (.24 BTU/(lbm·-F) or 1004.832 J/(kg-K).

Supply air flow rate (CFM or L/s).

Heat of vaporization of water (1054.8 BTU/lbmor 2.4535 x !O6 J/kg).Air temperature at coil inlet (F or C).

Air temperature at coil outlet (F or C).

Air humidity ratio at coil inlet (Ibm/Ibm or kg/kg).

Air humidity ratio at coil outlet (Ibm/Ibm or kg/kg).

Conversion factor used to provide load in proper units.

(60 min)/hr for English units.

m3/(1OOO L) for SJ. Metric units.

The coil outlet humidity is computed using the bypass factor relations. The coil bypassfactor is a measure of the approach of the outlet coil state to the apparatus dew point(AD?) condition. The first step in computing Wco is to determine the AD? state. It iscomputed using the equations:

BF:::: (T co-T adp)/(T ci-Tadp) ::::(wco-wadp)/(wci-wac!p)

::: (Tco - TciBF)/(I - BF)

where:

BFTadp

wac!p

-- Coil bypass factor (dimensionless).

Apparatus dew point dry buJb temperature (F or C).

Apparatus dew point humidity ratio (Ibm/Ibm or kg/kg).

Since the apparatus dew point state is a saturated condition, we can determine wadpusing Tadp and psychrometric relations. Next, Wco is computed using the equation:

Wco = BF (wci - wadp) + wadp

Finally, the total coil load is the sum of sensible and latent load components.

2-6

---------.-.----.---------------------------.-----------DESIGN SYSTEM ANALYSIS CALCULATIONS

Design heating loads are computed for one design condition. This condition is notassociated with a particular hour. For these calculations the outdoor winter designdry-bulb temperature, and the specified indoor heating temperature are utilized. Theanalysis stages are discussed separately below.

2.2.1 Thermal Load CalculationsThe first stage in the analysis is the calculation of thermal loads. General thermal loadcalculations were described in Chapter 1. Heating design thermal load calculationsfollow the traditional procedure of considering only transmission and infiltration loads.Internal heat gains are not evaluated. Individual considerations for each loadcomponent are listed in Table 2.2.

Table 2.2 Thermal Load Calculations ForHeating Design Condition

\---- ---~-_ ..._._._._-_. ------- ....-.---.-.--.----.--.--.--- .....--..-.--.- ..---.------ .-'-.-.--- .. --..

load Component Considerations

Wall & Roof Transmission

Glass Transimssion

Solar Gains

Intema! Gains---------~-_._.--

Partition Trallsmission

An actual temperature difference is used in place of theequivalent temperature difference (EHI). Thiseliminates the consideration of the transmission ofstored sofar hea!.

Computed using outdoor air temperature fordesign condition.

Not considered.---~._---"-------------------'------_._----_ .._------------~-------.--_._---------------_. __ ._--_..-

Nol considered.

Utilizes specified heating values for the temperaturedifference across the partition.

-------------~----~---~----------------_._._--~----_ ..------.----------.------ ...-.---.

Infiltration---------------

Ground E!ement Transmission

Safely Factor load-----------

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Infiltration air flow fate for heating condition utilized.~-----------------------------------_._--_._-----

Considered as discussed in Chapter 1.-------------------------_.--.--------"---_.--

Computed using specified heating safety factor.------------------------ ...----

Pa

CpaVsa

Th

Tsa --

Fu =

SYSTEM ANALYSIS CALCULATIONS

2.2.2 System Analysis and Sizing CalculationsThe final two stages of the analysis are performed in different orders depending uponthe heating system type. These stages define system sizing characteristics and thedesign heating coil load. The purpose of the heating system is to provide conditioningto meet a thermal load. For warm air systems, this is done by providing the properquantity of air at a specified temperature. For hydronic systems, it is accomplished byproviding a quantity of hot water at a certain temperature level. Given sizingcharacteristics, the heating coil load can be computed and used to size the heatingplant Calculations for the two types of heating systems are discussed below.

Warm Air Heating Systems. Given space sensible thermal loads and the user-specified supply temperature, the required air now rate is computed by solving thefollowing equation for Vsa ..

Qss = Pa Vsa Cpa Fu (Th - Tsa)

where:

Qss Space sensible thermal load (BTU/hr or W). This load includes bothspace and plenum sensible thermal load components. By CtH1\('n(i\\\~,

a heating load is a negative quantity denoting heat loss fromthe space.

Air density (lbm/ft3 or kg/m3). Values are adjusted for site elevation.See 2.1.2 for calculation details.

Specific heat of air (.24 BTU/(lbm-F) or 1004.832 J/(kg-K).

Supply air flow rate (CFM or Lis).

Indoor temperature for heating (F or C).

Supply air temperature (F or C).

Conversion factor to provide load in proper units.

60 min/hr for English units.

m3/(lOOO L) for S.L Metric units.

The zone now rate is simply the sum of space flow rates.

Having sized the system, the heating coil load can be computed. Instead of simulatingsystem operation, the coil load is computed as the sum of space thermal loads and theventilation load. This procedure is used because fan heat gain is not considered for theheating design condition. The design load is:

Qhc = - (Sum of Qss values) - Pa Vva Cpa Fu (Ta - Th)where:

Qhc Design heating coil load (BTU/hr or W). For convenience, we reportthe heating coil load as a positive quantity. Note that in this equation,Qss values are negative indicating a thermal heating load.

Vva Ventilation air flow rate (CFM or L/s)_

= Indoor temperature for heating (F or C).

Ta Outdoor air temperature for heating design condition (F or C).

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Fu

CpwVw

WTD

DESiGN SYSTEM NALYSIS CALCULA110NS

Hydronic Heating Systems. Given space sensible thermal loads and a user-definedhot water temperature drop across heating coils, required water flow rates arecomputed by solving the following equation for V w:

- Qss = Pw Vw Cpw Fu (WTD)

where:

Space sensible thermal load (BTU/hr or W). Note that byconvention a sensible heating load is a negative quantity.

Pw -- Density of water (62.0 Ibm/ft3 or 993. I kg/m3). Conditions for waterat 100 17 (37.8 C) are used.

Specific heat ofwater(J.O BTU/(lbm-F) or 4186.8 J/(kg-K».= Hot water flow rate (gallons/min Of L/s).

= Hot water temperature drop across coil (F Of K).

Conversion factor used to provide load in proper units.

= (60 min/hr)(. J 3668 ft3/gaI) for English units.

- m3/(1000 L) for SJ. Metric units.

In addition, a water flow rate is computed to meet the ventilation load. The total zonehot water flow rate is the sum of space and ventilation load flow rates.

F"inally, the design heating coil load is the slim of space sensible thermal loads and theventilation load. Fan heat gains are not considered for this calculation.Mathematically, the design load is:

Qhc = - (Sum ofQss values) - Pa Vva Cpa Fu (Ta - Th)

where:

Qhc

-.

Design heating coil load (BTU/hr or W). Note that for conveniencewe report the heating coil load as a positive quantity. In this equation,Qss values arc negative since they represent thermal healing loads.

Ventilation air flow rate (CFM or Us).Indoor temperature for heating (F or C).

Outdoor air temperature for heating design condition (F or C).

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