Preface

What would the world look like without ASHRAE Research? Since its beginnings in 1919, ASHRAE Research has grown and expanded to address the ever changing questions and topics facing both its members and the HVAC&R Industry and the world as a whole. The ASHRAE Handbook is constantly evolving to address these new challenges, fueled by the knowledge and principals developed through ASHRAE Research. As the focus of the industry has evolved from home refrigeration and food safety to improved indoor air quality to sustainability and energy efficiency, this four-volume series continues to be the cornerstone in every ASHRAE Member’s career.

The power behind ASHRAE Research and the four-volume Handbook comes directly from YOU: your financial support is the driving force behind every research project conducted world wide; your financial investment is an investment in the future of the HVAC&R industry; your donation to ASHRAE Research fills the more than 3,600 Handbook pages.

What would the ASHRAE Handbook look like without your support of ASHRAE Research? Take a look at just one chapter and imagine a world without this guidance from ASHRAE over the last 90 years.

Thank you for all your support

Research Promotion Committee

Reprinted and altered with the written permission of ASHRAE and for chapter distribution only.

The publication may not be reproduced without permission from ASHRAE RP Fundraising Staff. 404/636-8400 or researchpromotion@ashrae.org 1791 Tullie Circle, Atlanta GA 30329

CHAPTER 18 NONRESIDENTIAL COOLING AND HEATING LOAD CALCULATIONS

Cooling Load Calculation Principles ...... 18.1 Radiant Time Series (RTS) Method ...... 18.20 Internal Heat Gains ...... 18.3 Heating Load Calculations ...... 18.28 Infiltration and Moisture Migration System Heating and Cooling Load Effects...... 18.32 Heat Gains ...... 18.12 Example Cooling and Heating Load Calculations ...... 18.35 Fenestration Heat Gain...... 18.14 Previous Cooling Load Calculation Methods...... 18.49 Heat Balance Method ...... 18.14 Building Example Drawings ...... 18.52

EATING and cooling load calculations are the primary design Many cooling load components vary widely in magnitude, and pos- Hbasis for most heating and air-conditioningair-conditioning systems and com-com- ssiblyibly didirection,rection, dduringuring a 24 h perperiod.iod. Because these cyclic changes in ponents. These calculations affect the size of piping,piping, ductwork, difdif-- load comcomponentsponents often are not in pphasehase with each other, each comcompo-po- fusers,fusers, air handlershandlers,, boboilers,ilers, chillers, coils,coils, compressors,compressors, fans, anandd nent must bebe analyzedanalyzed to establishestablish the maximum cooling load for a every ototherher component ooff systesystemsms tthathat conconditiondition iindoorndoor envenviron-iron- building or zone. A zoned system (i.e., one serving several indepen- ments. Cooling and heating load calculations cann sisignificantlygnificantly affect dent areas, each with its own temperature control) needs too provide no firstfirst cost ooff buildingbuilding construction,construction, comfortcomfort andand productivityproductivity ooff occuoccu-- greater total cooling load capacity than the largest hourly sum of pants, and operating costt and energy consumption. simultaneous zone loads throughout a design day; however, it must Simply put, heating and cooling loads are the rates of energy handle the peak cooling load for each zone at its individual peak hour. inputinput (heating)(heating) or removalremoval (cooling)(cooling) requiredrequired to maintainmaintain an indoorindoor At some times off day during heatingheating or intermediateintermediate seasons, some environment at a desired temperattemperatureure and humidity condition. Heat- zones maymay require heatingheating while others require cooling.cooling. The zones’ ing and air conditioning systems are designed, sisized,zed, anandd controcontrolledlled vventilation,entilation, hhumidification,umidification, or ddehumidificationehumidification needsneeds must alsoalso be to accomplishaccomplish thatthat energy transfer.transfer. TheThe amount ofof heatingheating or coolingcooling cconsidered.onsidered. required at ananyy particuparticularlar time varies widelwidely,y, dependindependingg on externalexternal (e.g.,(e.g., outdoor temperaturetemperature)) and iinternalnternal ((e.g.,e.g., number of peoplpeoplee Heat Flow Rates occupyingoccupying a space)space) factors.factors. In air-conditioning design, the following four related heat flow Peak design heating and cooling load calculations, which are this rates, each of which varies with time, must be differentiated. chapter’s focus, seek to determine the maximum rate of heating and Space Heat Gain. This instantaneous rate of heat gain is the rate coolingcooling enerenergygy transtransferfer neeneededded aatt any point in time. Similar princi- aatt which heat enters into and/or is generatedgenerated within a space. Heat gaingain ples, but with different assumptions,assumptions, data,data, andand application,application, can be iiss classifiedclassified by itsits modemode ofof entryentry intointo thethe space andand whetherwhether itit isis sen- usedused to estimateestimate buildingbuilding energy consumption,consumption, asa described in Chap- sible oror lalatent.tent. EntryE modes include (1)) solar radiation through trans- ter 19. parent surfaces; ((2)) heat conduction through exterior walls and roofs; This chapter discusses common elementselements of cooling load calcu- (3) heat conduction through ceilingsceilings,, floors, and interior partitions; lation (e.g., internal heat gain, ventilation and infiltration, moisture (4) heat generated in the space by occupants, lighlights,ts, anandd appappliances;liances; migration,migration, ffenestrationenestration hheateat ggain)ain) and two methods off heating and (5) energy transfer through direct-withdirect-with-space-space ventventilationilation anandd iinfiltra-nfiltra- coolingcooling load estimation: heat balance ((HB)HB) and radiant time serieseriess tionn oof outdoor air; aand (6)) miscellaneous heat gains. Sensible heat is (RTS).(RTS). addedadded directly to the conditioned space by conduction, convection,convection, and/orand/or radiation. Latent heat gain occurs when moisture is added to thethe space ((e.g.,e.g., ffromrom vapor ememitteditted by occupants anandd equequipment).ipment). TToo COOLING LOAD CALCULATION maintainmaintain a constant humidityhumidity ratio,ratio, water vapor must condensecondense on thethe PRINCIPLES coolingcooling apparatus and be removed at tthehe sasameme rrateate it iiss added toto thethe space. The amount of energyenergy required to offset latent heat gaingain essen-essen- Cooling loads result from manyy conduction, convection, and radi- tiallytially equalsequals thethe productproduct ofof thethe condensationcondensation rate andand latentlatent heatheat ofof ation heat transfer processes through the building envelope and frofromm condensation.condensation. In seselectinglecting coocoolingling equequipment,ipment, didistinguishstinguish bbetweenetween internal sources and ssystemystem components.components. Building components or sensible and latelatentnt heat ggain:ain: eveveryery coolincoolingg apparatus has differendifferentt contents thatt may affect cooling loads include the following: maximummaximum removaremovall capaccapacitiesities fforor senssensibleible versus latentlatent heatheat forfor par- • External: Walls, roofs, windows, skyliskylights,ghts, doors, partitions, ceil-ceil- ticularticular operatingoperating conditions.conditions. In extremelyextremely drydry climates,climates, humidifica-humidifica- ings,ings, and floorsfloors tiontion maymay be required, rather than dehumidification, to maintainmaintain • Internal: LLights,ights, people,people, appliances,appliances, andand equipmentequipment thermalthermal cocomfort.mfort. • Infiltration: Air leakage and moisture migration Radiant Heat Gain. Radiant energy must first be absorbed by sur- • System: Outdoor air, duct leakaleakagege aandnd heat ggain,ain, reheat, fan and facesfaces tthathat encencloselose tthehe space ((walls,walls, flfloor,oor, anandd ceceiling)iling) anandd oobjectsbjects in ppumpump energy, anandd energy recovery the space (furniture, etc.). When these surfaces and objects become warmer than the surrounding air, some of their heat transfers to the air TERMINOLOGY by convection. The composite heat storage capacity of these surfaces and objects determines the rate at which their respective surface The variables affecting cooling load calculations are numerous, temperaturestemperatures increase for a givengiven radiant input, and thus ggovernsoverns ththee oftenn difficult to define precisely, andd always intricately interrelated. relationship between the radiant portionporrtion of heat gain and its corre- sponding part of the space cooling load (Figure 1). The thermal stor- The preparation of this chapter is assigned to TC 4.1, Load Calculation Data age effect is critical in differentiating between instantaneous heat and Procedures. gain for a given space and its cooling load at that moment. PredictingP 18.1 18.2 2013 ASHRAE Handbook—Fundamentals

Fig. 1 Origin of Difference Between Magnitude of Instantaneous Heat Gain and Instantaneous Cooling Load Fig. 2 Thermal Storage Effect in Cooling Load from Lights the nature and magnitude of this phenomenon to estimate a realistic cooling load for a particular set of circumstances has long been of interest to design engineers; the Bibliography lists some early work a simplification of the HB procedure. Both methods are explained on the subject. in their respective sections. Space Cooling Load. This is the rate at whichh sensible and latent Cooling load calculation of an actual, multiple-room building heat must be removed from the sspacepace to maintain a constant sspacepace requires a complex computer program implementing the principles aairir temperature andand humidity.humidity. TheThe sum ofof allall spacespace instantaneousinstantaneous of either method. hheateat ggainsains at ananyy gigivenven ttimeime ddoesoes not necessarnecessarilyily ((oror even ffre-re- quentquently)ly) equalequal thethe coolingcooling loadload forfor thethe space at thatthat same time.time. Cooling Load Calculations in Practice Space Heat Extraction Rate. The rates at which sensible and Load calculations should accurately descridescribebe tthehe bbuilding.uilding. AllAll llatentatent hheateat are removeremovedd ffromrom tthehe conconditionedditioned space equalequal thethe spacespace lloadoad cacalculationlculation iinputsnputs sshouldhould bbee aass accuraaccuratete as rereasonable,asonable, wwithoutithout coolincoolingg load onlyonly if the room airair temperature and humidityhumidity are con- uusingsing safetysafety factors.factors. IntroducingIntroducing compouncompoundingding sasafetyfety ffactorsactors aatt stant. Along with the iintermittentntermittent ooperationperation of coocoolingling equequipment,ipment, mmultipleultiple llevelsevels iinn tthehe lloadoad cacalculationlculation resuresultslts iinn an unreaunrealisticlistic anandd controlcontrol ssystemsystems usuausuallylly aallowllow a mminorinor cycliccyclic varvariationiation or swingswing inin oveoversizedrsized load. room temperature; humidityhumidity is often allowed to float, but it can bbee VVariationariation iinn heatheat transmtransmissionission ccoefficientsoefficients ooff ttypicalypical bbuildinguilding controlled. Therefore,T proper simulationsimulation ofof thethe controlcontrol systemsystem givesgives mmaterialsaterials anandd composcompositeite assemassembblilies,es, diffdifferingering motmotivationsivations andand a more realisticrealistic valuevalue ofof enerenergygy removaremovall over a fixedfixed perperiodiod tthanhan sskillskills of those who construct the buildinbuilding,g, unknown infiltrationinfiltration using values of the space cooling load. However, this is primarily rrates,ates, andand thethe manner inin whichwhich tthehe building is actually operated are importantimportant forfor estimatingestimating energyenergy use over time;time; itit isis not neededneeded toto some of the variables that make precise calculation impossible. calculate design peakk cooling load for equipment selection. Even if the designer uses reasonable procedures to account for these Cooling Coil Load. The rate at which energy is removed at a factors, the calculation can never be more than a good estimate of coolingcooling coilcoil servingserving one or more conditionedconditioned sspacespaces eequalsquals thethe sumsum the actual load. Frequently, a cooling load must be calculated before ofof instantaneousinstantaneous space coolingcooling loadsloads (or(or space heatheat extractionextraction rate,rate, every parameter in the conditioned space can be properly or com- ifif it is assumed that sspacepace temtemperatureperature and humidithumidityy varvary)y) for allall pletely defined. An example is a cooling load estimate for a new spaces served by the coilcoil,, plus any system loads. System loads building with many floors of unleased spaces for which detailed includee fan heat gain, duct heat gain,gain, andand outdooroutdoor airair heatheat andand mois-mois- partition requirements, furnishings, lighting, and layout cannot be ture broughtbrought intointo thethe coolingcooling equipmentequipment to satisfysatisfy tthehe ventventilationilation aairir predefined. Potential tenant modifications once the building is occu- requirement.requirement. pied also must be considered. Load estimating requires proper engi- neering judgment that includes a thorough understanding of heat Time Delay Effect balance fundamentals. Energy absorbed by walls, floor, furniture, etc., contributes to Perimeter spaces exposed too high solarsolar heat gaingain often need cool- space cooling loadd only after a time lag. Some of this energy is still iingng during sunlit portions of tradtraditionalitional heating mmonths,onths, as do com- present and reradiating even afafterfter tthehe hheateat sources havehave beenbeen ppletelyletely interiorinterior spaces withwith significantsignificant iintenternarnall hheateat gain.gain. TheseThese switched off or removed, as shown in Figure 2. sspacespaces can aalsolso havehave significantsignificant hheatingeating lloadsoads dduringuring nonsunlitnonsunlit There is always significant delay between the time a heat source hhoursours or afterafter perperiodsiods ooff nonoccupnonoccupancy,ancy, whenwhen adjacentadjacent spaces havehave iiss activated, and the point when rreradiatederadiated enerenergygy equals that beinbeingg ccooledooled belowbelow interiorinterior designdesign temperatures. TheThe heatingheating loadsloads iinstantaneouslynstantaneously stored.stored. ThisThis timetime laglag must bebe consideredconsidered whenwhen cal-cal- iinvolvednvolved can bbee estestimatedimated conventionallyconventionally to offsetoffset or to compensatcompensatee culatinculatingg coolincoolingg load, because the lloadoad required for the space can bbee fforor themthem anandd prevent overoverheating,heating, bbutut ttheyhey hhaveave no didirectrect rerelation-lation- mucmuchh lowerlower tthanhan tthehe iinstantaneousnstantaneous hheateat gagainin bbeingeing generated,generated, andand shishipp to tthehe spaces’ ddesignesign hheatingeating lloads.oads. the space’s peak load mamayy be sisignificantlygnificantly affected.affected. Correct design and sizing of air-conditioning systems require AccountAccountinging forfor thethe timetime delaydelay effecteffect isis thethe majormajor challengechallenge in more than calculation of the cooling load in the space to be condi- coolincoolingg load calculations. SeveralSeveral methods, includinincludingg the two pre- tioned. Thee type of air-conditioningair-conditioning system, ventilationventilation rate,rate, reheat,reheat, sented in this chapter,chapter, have been developed to take the time delay ffanan energy,energy, fan location, duct heat lossloss and gain,gain, duct leakage,leakage, heatheat eeffectffect intintoo coconsideration.nsideration. extraction lighting systems, type off return air system, and any sen- ssibleible oror latentlatent heatheat recoveryrecovery all affect systemsystem load and componentcomponent ssizing.izing. Adequate systemsystem design and component sizing require that COOLING LOAD CALCULATION METHODS system performance be analyzed as a series of psychrometric pro- This chapter presents two load calculation methods that vary cesses. significantly from previous methods. The technology involved, System design could be driven by either sensible or latent load, however (the principle of calculating a heat balance for a given and both need to be checked. In a sensible-load-driven space (the space) is not new. The first of the two methods is the heat balance mmostost common casecase),), the coolincoolingg ssupplyupply air has surplus capacitcapacityy toto (HB) method; the second is radiant time series (RTS), which is ddehumidify,ehumidify, butbut thisthis isis usuallyusually permissible.permissible. For a space driven by Nonresidential Cooling and Heating Load Calculations 18.3 latent load (e.g., an auditoriumauditorium),), suppsupplyly aairflowirflow bbasedased on senssensibleible Internal Heat Gains and Operating Schedules. Obtain lloadoad iiss liklikelyely not to hhaveave eenoughnough ddehumidifyingehumidifying capability,capability, so sub-sub- planned density and a proposed schedule of lighting, occupancy, coocoolingling anandd rereheatingheating or some ootherther ddehumidificationehumidification process iiss internal equipment, appliances, and processes that contribute to the neeneeded.ded. internal thermal load. This chapter is primarily concerned with a given space or zone in Areas. Use consistent methods for calculation of building areas. a building. When estimating loads for a group of spaces (e.g., for an For fenestration, the definition of a component’scomponent’s area must bebe concon-- air-handling system that serves multiple zones), the assembled ssistentistent with associated ratinratings.gs. zones must be analyzed to consider (1)) the simultaneous effects tak- Gross surface area. It is efficient and conservative to derive gross ing place; (2) any diversification off heat gains for occupants, light- surface areas from outer building dimensions, ignoring wall and ining,g, or other internal load sourcesources;s; (3) ventilation; and/or (4) any floor thicknesses and avoiding separate accounting of floor edge and other unique circumstances.circumstances. With large buildings that involve moremore wall corner conditions. Measure floor areas to the outside of adjacent than a single HVAC system, simultaneous loads and any additionaadditionall exterior walls or to the center line of adjacent partitions. When diversity also must be consideredd when designing the central equip- apportioning to rooms, façade area should be divided at partition ment that serves the ssystems.ystems. Methods presented in this chapter are center lines. Wall height should be taken as floor-to-floor height. expressed as hourly load summaries, reflecting 24 h input schedules The outer-dimension procedure is expedient for load calculations, and profiles of the individual load variables. Specific systems and but it is not consistent with rigorousrigorous definitionsdefinitions usedused inin building-building- applications may require different profiles. related standards. The resulting differences do not introduce signifi- cacantnt errorserrors inin thisthis chapter’schapter’s procedures.procedures. DATA ASSEMBLY Fenestration area. As discussed in Chapter 15, fenestration rat- iingsngs [U-factor and solar heat ggainain coefficient ((SHGC)]SHGC)] are based oonn Calculating space cooling loadss requires detaileddetailed buildingbuilding designdesign tthehe entire product area, includinincludingg fframes.rames. ThusThus,, for load calcula- information and weather data att design conditions. Generally, the titions,ons, ffenestrationenestration area isis tthehe area ooff tthehe rougroughh openopeninging inin thethe wallwall following information should be compiled. oorr rroof.oof. Building Characteristics. Building materials, component size, Net surface area. Net surface area is the gross surface area less external surface colors, and shape are usually determined from any enclosed fenestration area. building plans and specifications. Configuration. Determine building location, orientation, and INTERNAL HEAT GAINS external shading from building plans and specifications. Shading from adjacent buildings can be determined from a site plan or by Internal heat gains from people, lights, motors, appliances, and visiting the proposed site, but its probable permanence should be equipment cann contribute the majoritymajority of the cooling load ini a mod- carefully evaluated before it is included in the calculation. The pos- ern building. As building envelopes have improved in response to ssibilityibility ooff aabnormallybnormally high gground-reflectedround-reflected sosolarlar raradiationdiation (e.g.,(e.g., more restrictive energy codes, internal loads have increased because ffromrom aadjacentdjacent water, sansand,d, or parparkingking llots)ots) or solarsolar loadload fromfrom adja-adja- of factors such as increased use of computers and the advent of cent rereflectiveflective bbuildingsuildings should not be overlooked. dense-occupancy spaces (e.g., call centers). Internal heat gain cal- culation techniques are identical for both heatt balance (HB) and Outdoor Design Conditions. Obtain appropriate weather data, rradiantadiant timetime seriesseries (RTS)(RTS) cooling-loadcooling-load calculationcalculation methods,methods, soso and select outdoor design conditions. Chapter 14 provides informa- iinternalnternal hheateat gaingain ddataata are presepresentednted here independentt of calculacalculationtion tion for many weather stations; note, however, that these design mmethods.ethods. dry-bulb and mean coincident wet-bulb temperatures may vary considerably from data traditionally used in various areas. Use judgment to ensure that results are consistent with expectations. PEOPLE Also, consider prevailing wind velocity and the relationship of a Table 1 gives representative rates at which sensible heat and project site to the selected weather station. moisture are emitted by humans in different states of activity. In Recent research projects have greatly expanded the amount of high-density spaces, such as auditoriums, these sensible and latent available weather data ((e.g., ASHRAE 2012). In addition to the con- heat gains comprisee a large fraction of the total load. Even for short- ventional drydry bulb with mean coincident wet bulb, data are nownow term occupancy, the extra sensible heat and moisture introduced by available for wet bulb and dew point with mean coincident drdryy bulb.bulb. people may be significant. See Chapter 9 forf detailed information; PeaPeakk space lloadoad ggenerallyenerally cocoincidesincides wwithith peapeakk sosolarlar or peapeakk drydry however, Table 1 summarizes design data for common conditions. bulb, but peak ssystemystem load often occurs at peak wet-bulb tempera- The conversion of sensible heat gain from people to space cool- ture. TThehe rerelationshiplationship bbetweenetween spacspacee anandd system lloadsoads iiss didiscussedscussed ing load is affected by the thermal storage characteristics of that further in following sections of the chapter. space because some percentagepercentage off thethe sensiblsensible lloadoad iiss raradiantdiant To estimate conductive heat gain through exterior surfaces and energy. Latent heat gains are usually considered instantaneous, but infiltration and outdoor air loads at any time, applicablee outdoor dry- research is yielding prpracticalactical models and dataa for the latent heat and wet-bulb temperatures must be used. Chapterr 14 gives monthly sstoragetorage ofof andand releaserelease fromfrom common buildingbuilding mamaterterials.ials. coolincoolingg load designdesign values of outdoor conditions for manymany locations. TThesehese are generallygenerally mmidafternoonidafternoon conditions;conditions; forfor otherother timestimes ofof day,day, LIGHTING the daily range profile method described in Chapter 14 can be used Because lighting is often a major space cooling load component, ttoo estimate drdry-y- and wet-bulb temperatures.temperatures. Peak coolingcooling load isis an accurate estimate of the space heat gain it imposes is needed. Cal- ooftenften ddeterminedetermined by sosolarlar hheateat ggainain tthroughhrough ffenestration;enestration; tthishis peapeakk culation of this load component is not straightforward; the rate of mamayy occur in winter months and/or at a time of dadayy when outdoor airair ccoolingooling lloadoad ffromrom lighlightingting at ananyy gigivenven moment can bbee qquiteuite differ-differ- temperature is not at its maximummaximum.. eentnt fromfrom thethe heatheat equivalentequivalent ofof power suppliedsupplied instantaneouslyinstantaneously toto Indoor Design Conditions. Select indoor dry-bulb temperature, ththoseose lights,lights, becausebecause ofof heatheat storagestorage.. indoor relative humidity, and ventilation rate. Include permissible variations and control limits. Consult ASHRAE Standard 90.1900..1 for Instantaneous Heat Gain from Lighting energy-savings conditions, and Standard 55 for ranges of indoor The primary source of heat from lighting comes from light- coconditionsnditions neededneeded forfor thermalthermal comfort.comfort. emitting elements, or lamps, although significant additional heat 18.4 2013 ASHRAE Handbook—Fundamentals

Table 1 Representative Rates at Which Heat and Moisture Are Given Off by Human Beings in Different States of Activity Total Heat, Btu/h % Sensible Heat that is Sensible Latent Radiantb Adult Adjusted, Heat, Heat, Degree of Activity Location Male M/Fa Btu/h Btu/h Low V High V Seated at theater Theater, matinee 390 330 225105 Seated at theater, night Theater, night 390 350 245 105 60 27 Seated, very light work Offices, hotels, apartments 450 400 245 155 Moderately active office work Offices, hotels, apartments475 450 250 200 Standing, light work; walking Department store; retail store550 450 250 200 58 38 Walking, standing Drug store, bank 550 500 250 250 Sedentary work Restaurantc 490 550 275 275 Light bench work Factory 800 750 275 475 Moderate dancing Dance hall 900 850305 545 49 35 Walking 3 mph; light machine work Factory 1000 1000 375 625 Bowlingd Bowling alley 1500 1450 580 870 Heavy work Factory 1500 1450 580 870 54 19 Heavy machine work; lifting Factory 1600 1600 635 965 Athletics Gymnasium 2000 1800 710 1090 Notes: aAdjusted heat gain is based on normal percentage of men, wowomen,men, anandd childrenchildren fforor thethe applicationapplication listed,listed, 1. Tabulated values are based onn 7575°F°F room dry-bulbdry-bulb temperature.temperature. ForFor anandd assumes tthathat ggainain ffromrom an aadultdult female is 85% of that for an adult male, and gain from a child is 75% 80°F room drydry bulb,bulb, totaltotal heatheat remainsremains thethe same, butbut sensiblesensible heatheat of that for an adult male. vavalueslues sshouldhould bbee ddecreasedecreased by approxapproximatelyimately 20%, anandd llatentatent hheateat b Values approximated from data in Table 6, Chapter 9, where V is air velocity with limits shown in that vavalueslues iincreasedncreased accoraccordingly.dingly. table.table. 2. Also see Table 4, Chapterr 9, for additional rates of metabolic heat cAdjusted heat gain includes 60 Btu/h for food peperr iindividualndividual ((3030 Btu/hBtu/h sensiblesensible andand 30 Btu/hBtu/h latent).latent). generation. d Figure one person per alley actually bowling,bowling, andand allall othersothers as sittingsitting (400(400 Btu/h)Btu/h) or standingstanding or walkingwalking 3. All values are rounded to nearest 5 Btu/h. slowlyslowly (550(550 Btu/h).Btu/h). may be generated from ballasts and other appurtenances in the lumi- power density (LPD) (lighting heat gain per square foot) allowed by naires. Generally, the instantaneous rate of sensible heat gain from ASHRAE Standard 90.1-2010 for a range of space types. electric lighting may be calculated from In addition to determining the lighting heat gain, the fraction of qelel = 3.41WFFulFsa (1) lighting heat gain that enters the conditioned space may need to be distinguished from the fraction that enters an unconditioned space; wherewhere of the former category, the distribution between radiative and con- qelel ==h heateat gain,gain, Btu/hBtu/h vective heat gain must be established. W =tota totall lightlight wattage,wattage, W Ful ==li lightingghting use factorfactor Fisher and Chantrasrisalai (2006) experimentally studied 12 Fsa ==li lightingghting specspecialial aallowancellowance factorfactor luminaire types and recommendedd fifiveve different categories of lumi- 3.413.41 = conversionconversion factorfactor naires, as shown in Table 3. The table provides a range of design The total light wattage is obtained from the ratings of all lamps data for the conditioned space fraction, short-wave radiative frac- installed, both for general illumination and for display use. Ballasts tion, and long-wave radiative fraction under typical operating con- are not included, but are addressed by a separate factor. Wattages of ditions: airflow rate of 1 cfm/ft², supply air temperature between 59 magnetic ballasts are sisignificant;gnificant; tthehe energy consumptconsumptionion ooff hihigh-gh- and 62°F, and room air temperature between 72 and 75°F. The rec- ommended fractions in Table 3 are based on lighting heat input rates efficiencyefficiency electronicelectronic bballastsallasts mmigightht bebe iinsignificantnsignificant comparedcompared toto 2 that of the lamps.lamps. range of 0.9 to 2.6 W/ft . For higher design power input, the lower The lighting use factor is thee ratio of wattage in use, for the con- boundsbounds ofof thethe space andand short-waveshort-wave fractions should be used; for ditionsditions underunder whichwhich thethe loadload estimateestimate is beingbeing made, to totatotall design power input below this range, the upper bounds of the space installedinstalled wattage. For commerccommercialial appapplicationslications sucsuchh as stores, tthehe and short-wave fractions should be used. The space fraction in the use factor is generallygenerally 1.0. table is the fraction of lighting heat gain that goes to the room; the The special allowance factor is the ratio of the lighting fixtures’ fraction going to the plenum can be computed as 1 – the space frac- power consumption, including lalampsamps anandd ballast,ballast, to tthehe nomnominalinal tion. The radiative fraction is the radiative part of the lighting heat power consumption of the lamps. FoForr incandescent lights, this factor gain that goes to the room. The convective fraction of the lighting isis 1. For fluorescent lights,lights, itit accounts for power consumed byby thethe heat gain that goes to the room is 1 – the radiative fraction. Using ballastballast as wellwell as thethe ballast’sballast’s effect on lamp power consumption.consumption. values in the middle of the range yieldss sufficiently accurate results. The special allowance factor can be less than 1 for electronic bal- However, values that better suit a specifspecificic situation may be deter- lastslasts thatthat llowerower eelectricitylectricity consumptconsumptionion belowbelow thethe lamp’slamp’s ratedrated mined accordingaccording to the notes for Table 33.. power consumption. UUse manufacturers’ values for system (lamps + Table 3’s data apply too both ducted and nonducted returns. How- ballast) power, when available. ever,ever, application of the data, pparticarticularlularlyy the ceilinceilingg plenum frac- For high-intensity-discharge lamps (e.g. metal halide, mercury tion, may vary for different returnn configurations. For instance, for vapor, high- and low-pressure sodium vapor lamps), the actual light- a room with a ducted return, althoughalthough a portion of the lightinglighting ing system power consumption should be available from the manu- energyenergy initiallinitiallyy dissipated to the cceilingeiling plenum is quantitativelquantitativelyy facturer of the fixture or ballast. Ballasts available for metal halide equalequal to thethe plenumplenum fraction,fraction, a largelarge portionportion ofof thisthis energy wouldwould and high pressure sodium vapor lamps may have special allowance likelylikely end up as the conditioned spacespace coolingcooling load and a small por-por- factors from about 1.3 (for low-wattage lamps) down to 1.1 (for tiontion wouldwould endend up as thethe coolingcooling lloadoad to tthehe return aair.ir. high-wattagehigh-wattage lampslamps).). If the space airflow rate is differentdifferent from the typicaltypical condition An alternative procedure is to estimate the lighting heat gain on a (i.e., about 1 cfm/ftcfm/fft2), Figure 3 can be used to estimate the lighting per square foot basis. Such an approach may be required when final heat gain parameters. Design data shown in Figure 3 are only appli- lighting plans are not available. Table 2 shows the maximum lighting cable forfor thethe recessedrecessed fluorescentfluorescent luminaireluminaire withoutwithout lens.lens. Nonresidential Cooling and Heating Load Calculations 18.5

Table 2 Lighting Power Densities Using Space-by-Space Method Common Space Types* LPD, W/ft2 Building-Specific Space Types* LPD, W/ft2 Building-Specific Space Types* LPD, W/ft2 Atrium Automotive Library First 40 ft in height 0.03 per ft Service/repair 0.67 Card file and cataloging 0.72 (height) Bank/office Reading area 0.93 Height above 40 ft 0.02 per ft Banking activity area 1.38 Stacks 1.71 (height) Convention center Manufacturing Audience/seating area—permanent Audience seating 0.82 Corridor/transition 0.41 For auditorium 0.79 Exhibit space 1.45 Detailed manufacturing 1.29 For performing arts theater2.43 Courthouse/police station/penitentiary Equipment room 0.95 For motion picture theater 1.14 Courtroom 1.7272 Extra high bay (>50 ft floor-to- 1.051.05 Confinement cells 1.10 ceiling height) Classroom/lecture/training 1.24 Judges’ chambers 1.17 High bay (25 to 50 ft floor-to- 1.231.23 Conference/meeting/multipurpose 1.23 Penitentiary audience seating0.43 ceiling height) Corridor/transition 0.66 Penitentiary classroom 1.341.34 Low bay (<25 ft floor-to-ceiling 1.191.19 Penitentiary dining 1.07 height) Dining area 0.65 Dormitory Museum For bar lounge/leisure dining 1.31 Living quarters 0.38 General exhibition 1.05 For family dining 0.89 Fire stations Restoration 1.02 Dressing/fitting room for 0.40 Engine room 0.56 Parking garage performing arts theater Sleeping quarters 0.25 Garage area 0.19 Gymnasium/fitness center Post office Electrical/mechanical 0.95 Fitness area 0.72 Sorting area 0.94 Food preparation 0.99 Gymnasium audience seating 0.43 Religious buildings Playing area 1.20 Audience seating 1.53 Laboratory Hospital Fellowship hall 0.64 For classrooms 1.28 Corridor/transition 0.89 Worship pulpit, choir 1.53 For medical/industrial/research 1.81 Emergency 2.26 Retail Exam/treatment 1.66 Dressing/fitting room 0.87 Lobby 0.90 Laundry/washing 0.60 Mall concourse 1.10 For elevator 0.64 Lounge/recreation 1.07 Sales area 1.68 For performing arts theater2.00 Medical supply 1.27 Sports arena For motion picture theater 0.52 Nursery 0.88 Audience seating 0.43 Nurses’ station 0.87 Court sports arena—class 4 0.72 Locker room 0.75 Operating room 1.89 Court sports arena—class 3 1.20 Lounge/recreation 0.73 Patient room 0.62 Court sports arena—class 21.92 Pharmacy 1.14 Court sports arena—class 13.01 Office Physical therapy 0.90.911 Ring sports arena 2.68 Enclosed 1.11 Radiology/imaging 1.32 Transportation Open plan 0.98 Recovery 1.15 Air/train/bus—baggage area 0.76 Hotel/highway lodging Airport—concourse 0.36 Restrooms 0.98 Hotel dining 0.82 Waiting area 0.54 Sales area 1.68 Hotel guest rooms 1.11 Terminal—ticket counter 1.08 Stairway 0.69 Hotel lobby 1.06 Warehouse Storage 0.63 Highway lodging dining 0.88 Fine material storage 0.95 Workshop 1.59 Highway lodging guest rooms 0.75 Medium/bulky material storage0.58 Source: ASHRAE Standard 90.1-2010. *In cases where both a common space type and a building-specific type are listed, the building-specific space type applies.

Although design data presented in Table 3 and Figure 3 can be uusedsed forfor a ventedvented lluminaireuminaire withwith sisidde-slote-slot returns, theythey are likelylikely notnot aapplicablepplicable fforor a ventedvented lluminaireuminaire wwithith llampamp compartment returns, bbecauseecause in the latter casecase,, all heaheatt convected in the vented luminairluminairee iiss likelylikely to go directlydirectly to tthehe ceceilingiling pplenum,lenum, resuresultinglting iinn zero con- vvectiveective ffractionraction anandd a muchmuch lowerlower space fraction.fraction. TTherefore,herefore, tthehe ddesignesign ddataata sshouldhould ononlyly bbee useusedd fforor a conconfigurationfiguration wwherehere concondi-di- titionedoned airair isis returnedreturned throughthrough thethe ceceilingiling grgrilleille or lluminaireuminaire sideside sslots.lots. For other luminaire types, it mamayy bbee necessary ttoo estestimateimate tthehe hheateat gagainin fforor eaceachh component as a ffractionraction of thethe totaltotal lightinglighting heatheat ggainain bbyy usinusingg jjudgmentudgment to estimatestimatee heat-to-space andand hheat-to-returneat-to-return percentages.percentages. Because of the directional nature of downlight luminaires, a large portion of the short-wave radiation typically falls on the floor. When Fig. 3 Lighting Heat Gain Parameters for Recessed converting heat gains to cooling loads in the RTS method, the solar Fluorescent Luminaire Without Lens radiant time factors (RTFs)(RTFs) maymay be more appropriate than nonso-nonso- (Fisher and Chantrasrisalai 2006) larlar RTFs. ((SolarSolar RTFs are calccalcuulatedlated assumassuminging most solarsolar radiationradiation 18.6 2013 ASHRAE Handbook—Fundamentals

Table 3 Lighting Heat Gain Parameters for Typical Operating Conditions Luminaire Category Space Fraction Radiative Fraction Notes RecessedRecessed fluorescentfluorescent luminaireluminaire 0.64 to 0.74 0.48 to 0.68 ••U Usese middlemiddle valuesvalues inin most situationssituations withoutwithout llensens • Mayygp use higher space fraction, and lower radiative fraction for luminaire wiwithth sideside-slot-slot returnsreturns •Ma Mayy use lowerlower valuesvalues ofof bothboth fractionsfractions forfor direct/indirectdirect/indirect luminaireluminaire •Ma Mayy use higherhigher vavalueslues ofof bothboth fractionsfractions forfor ductedducted returnsreturns RecessedRecessed fluorescentfluorescent luminaireluminaire 0.40 to 0.50 0.61 to 0.73 • Mayyj adjust values in thethe sasameme wawayy as fforor recesserecessedd fluorescentfluorescent lluminaireuminaire withwith lenslens withoutwithout lenslens DownlightDownlight compact fluorescentfluorescent 0.12 to 0.240.95 to 1.0• Use middle or highg values if detailed features are unknown luminaireluminaire • Use low value for spacepg fraction and highh value for radiative fraction if there are largelarge hholesoles inin luminaire’sluminaire’s reflectorreflector DownlightDownlight incandescentincandescent 0.70 to 0.80 0.95 to 1.0 • Use middle valuesvalues if lamplamppyp typetype isis unknownunknown luminaireluminaire • Use lowlow valuevalue fforor sspacepace ffractionraction if stanstandarddard lamplampp( (i.e.(i.e. A-lamp)A-lam p) isis usedused • Use high valuevalue forfor space fractionfraction if reflectorreflector lamplamp (i.e.(i.e. BR-lamp)BR-lamp) isis usedused Non-in-ceilingNon-in-ceiling fluorescentfluorescent 1.0 0.5 to 0.57 • Use lower value for radiradiativeative ffractionraction forfor surface-mountedsurface-mounted luminaireluminaire luminaireluminaire • Use higherhigher valuevalue forfor radiativeradiative fractionfraction forfor pendantpendant luminaireluminaire Source: Fisher and Chantrasrisalai (2006).

is intercepted by the floor; nonsolar RTFs assume uniform distribu- Table 4 Minimum Nominal Full-Load Efficiency for tion by area over all interior surfaces.) This effect may be significant 60 HZ NEMA General Purpose Electric Motors (Subtype I) for rooms where lighting heat gain is high and for which solar RTFs Rated 600 Volts or Less (Random Wound)* are significantly different from nonsolar RTFs. Minimum Nominal Full Load Efficiency (%) for Motors Manufactured ELECTRIC MOTORS on or after December 19, 2010 Open Drip-Proof Totally Enclosed Instantaneous sensible heat gain from equipment operated by Motors Fan-Cooled Motors electric motors in a conditioned space is calculated as Number of Poles ; 246 2 4 6 qem = 2545(P/EM)FUM FLM (2) Synchronous Speed (RPM) ; 3600 1800 1200 3600 1800 1200 where Motor Horsepower qem = heat equivalent of equipment operation, Btu/h 177.0 85.5 82.5 77.0 85.5 82.5 P = motor power rating, hp 1.584.0 86.5 86.5 84.0 86.5 87.5 EM = motor efficiency, decimal fraction <1.0 285.5 86.5 87.5 85.5 86.5 88.5 FUM = motor use factor, 1.0 or decimal fraction <1.0 385.5 89.5 88.5 86.5 89.5 89.5 FLM = motor load factor, 1.0 or decimal fraction <1.0 586.5 89.5 89.5 88.5 89.5 89.5 2545 = conversion factor, Btu/h·hp 7.588.5 91.0 90.2 89.5 91.7 91.0 The motor use factor may be applied when motor use is known to 10 89.591.7 91.7 90.2 91.7 91.0 be intermittent, with significant nonuse during all hours of operation 15 90.293.0 91.7 91.0 92.4 91.7 (e.g., overhead door operator). For conventional applications, its 20 91.093.0 92.4 91.0 93.0 91.7 value is 1.0. 25 91.793.6 93.0 91.7 93.6 93.0 The motor load factor is the fraction of the rated load delivered 30 91.794.1 93.6 91.7 93.6 93.0 under the conditions of the cooling load estimate. Equation (2) 40 92.494.1 94.1 92.4 94.1 94.1 assumes that both the motor and driven equipment are in the condi- 50 93.094.5 94.1 93.0 94.5 94.1 tioned space. If the motor is outside the space or airstream, 60 93.695.0 94.5 93.6 95.0 94.5 75 93.695.0 94.5 93.6 95.4 94.5 q = 2545PF F (3) em UM LM 10093.6 95.4 95.0 94.1 95.4 95.0 When the motor is inside the conditioned space or airstream but 12594.1 95.4 95.0 95.0 95.4 95.0 the driven machine is outside, 15094.1 95.8 95.4 95.0 95.8 95.8 20095.0 95.8 95.4 95.4 96.2 95.8 CS1.0 – E 25095.0 95.8 95.4 95.8 96.2 95.8 q = 2545PFDT------M- F (4) em EUE UM LM 30095.4 95.8 95.4 95.8 96.2 95.8 M 35095.4 95.8 95.4 95.8 96.2 95.8 Equation (4) also applies to a fan or pump in the conditioned 40095.8 95.8 95.8 95.8 96.2 95.8 space that exhausts air or pumps fluid outside that space. 45095.8 96.2 96.2 95.8 96.2 95.8 Table 4 gives minimum efficiencies and related data representa- 50095.8 96.2 96.2 95.8 96.2 95.8 tive of typical electric motors from ASHRAE Standard 90.1-2010. Source: ASHRAE Standard 90.1-2010 If electric motor load is an appreciable portion of cooling load, the *Nominal efficiencies established in accordance with NEMA Standard MG1. Design A motor efficiency should be obtained from the manufacturer. Also, and Design B are National Electric Manufacturers Association (NEMA) design class designations for fixed-frequency small and medium AC squirrel-cage induction motors. depending on design, maximum efficiency might occur anywhere between 75 to 110% of full load; if under- or overloaded, efficiency could vary from the manufacturer’s listing. current, fixed losses, and other reasons, FLM is generally assumed to be unity, and no adjustment should be made for underloading or Overloading or Underloading overloading unless the situation is fixed and can be accurately estab- Heat output of a motor is generally proportional to motor load, lished, and reduced-load efficiency data can be obtained from the within rated overload limits. Because of typically high no-load motor motor manufacturer. Nonresidential Cooling and Heating Load Calculations 18.7

Radiation and Convection Heat Gain for Generic Appliances. The average rate of appli- Unless the manufacturer’s technical literature indicates other- ance energy consumption can be estimated from the nameplate or wise, motor heat gain normally should be equally divided between rated energy inputt qinputp t by applying a duty cycle or usage factorr FU. radiant and convective components for the subsequent cooling load Thus, sensible heat gainn qs for generic electric, steam, and gas appli- calculations. ancesances installed under a hood can be estimated uusing one of the fol- lowing equations:

APPLIANCES qs = qinputt FU FR (5) A cooling load estimate should take into account heat gain from or all appliances (electrical, gas, or steam). Because of the variety of appliances, applications, schedules, use, and installations, estimates qs = qinputt FL (6) can be very subjective. Often, the only information available about where FL is the ratio of sensible heatheat ggainain to the manufacturer’manufacturer’ss heat gain from equipment is that on its nameplate, which can over- rated energy input. However, recent ASHRAE research (Swierc- estimate actual heat gain for many types of appliances, as discussed zyna et al. 2008, 2009) showed the design value for heat gain from in the section on Office Equipment. a hooded appliance at idle (ready-to-cook)(ready-to-cook) conditions based on its Cooking Appliances eenergynergy consumptconsumptionion rate iis,s, at bbest,est, a rouroughgh estestimate.imate. WWhenhen aappli-ppli- aancence heat gain measurements duringduring idle conditions were regressedregressed These appliances include common heat-producing cooking agagainstainst enerenergygy consumption rates fforor ggasas and electric appliancesappliances,, equipment found in conditioned commercial kitchens. Marn (1962) tthehe appliances’ emissivitemissivity,y, insulinsulation,ation, and surface coolincoolingg ((e.g.,e.g., concluded that appliancappliancee sursurfacesfaces contrcontributedibuted most ofof tthehe heatheat toto tthroughhrough ventilation ratrates)es) scattered the data points widely, with commercial kitchens and that whenn appliances were ininstalledstalled uundernder large deviations from the average values. BBecause large errors could an eeffectiveffective hhood,ood, tthehe coocoolingling lloadoad was iindependentndependent ooff tthehe ffueluel oorr occur in the heat load calculation for specific appliance lines by energy useusedd fforor ssimilarimilar equequipmentipment perperformingforming tthehe same operatoperations.ions. using a general radiation factor, heat gain values in Table 5 should Gordon et al. (1994) and Smith et al. (1995) found thatt gas appli- be applied in the HVAC design. ances may exexhibithibit slightlyslightly higherhigher heatheat gainsgains thanthan theirtheir electricelectric coun- Table 5 lists usage factors, radiation factors, and load factors terparts under wall-canopwall-canopyy hoods opoperatederated at ttypicalypical ventilation based on appliance energy consumption rate for typical electrical, rrates.ates. ThisThis is because heatheat containedcontained inin combustioncombustion productsproducts ex-ex- steam, and gas appliances under standby or idle conditions, hooded hhaustedausted ffromrom a gas appapplianceliance may iincreasencrease tthehe temperatures ooff thethe and unhooded. appapplianceliance anandd surrounsurroundingding sursurfaces,faces, as wewellll as tthehe hoodhood aboveabove thethe ap-ap- Recirculating Systems. Cooking appliances ventilated by recir- ppliance,liance, more so than the heaheatt produced bbyy its electric counterpart. culating systems or “ductless” hoods should be treated as unhooded TThesehese highhigher-temperatureer-temperature sursurfacesfaces radiateradiate heatheat to thethe kitchen,kitchen, addingadding appliancesappliances whenwhen estimatingestimating heatheat gain. InI other words, all energy momoderatelyderately to tthehe raradiantdiant ggainain didirectlyrectly assocassociatediated withwith thethe applianceappliance consumedconsumed byby the appliance and allall moisture produced byby cookingcooking isis coocookingking surface.surface. introducedintroduced to tthehe kikitchentchen as a ssensibleensible or llatentatent coocoolingling lload.oad. Marn (1962) confirmed that, whwhereere aappliancesppliances are iinstallednstalled Recommended Heat Gain Values. Table 5 lists recommended ununderder an eeffectiveffective hhood,ood, onlyonly raradiantdiant ggainain addsadds to thethe coolingcooling load;load; rates of heat gain from typical commercial cooking appliances. Data coconvectivenvective aandnd lalatenttent heaheatt ffromrom coocookingking anandd comcombustionbustion productsproducts in the “hooded” columns assume installation under a properly de- are exhausted and do not enter the kitchen. GGordon et al. (1994) and signed exhaust hood connected to a mechanical fan exhaust system Smith et al. (1995) substantiated these findings. Chapter 33 of the operating at an exhaust rate for complete capture and containment 2011 ASHRAE Handbook—HVAC Applications has more informa- of the thermal and effluent plume. Improperly operating hood sys- tion on kitchen ventilation. tems load the space with a significant convective component of the Sensible Heat Gain for Hooded Cooking Appliances. To heat gain. establish a heat gain value, nameplate energy input ratings may be used with appropriate usage and radiation factors. Where specific Hospital and Laboratory Equipment rating data are not available (nameplate missing, equipment not yet Hospital and laboratory equipment items are major sources of purchased, etc.), representative heat gains listed in Tables 5A to E sensible and latent heat gains in conditioned spaces. Care is needed (Swierczyna et al. 2008, 2009) for a wide variety of commonly in evaluating the probability and duration of simultaneous usage encountered equipment items. In estimating appliance load, proba- wwhenhen manmanyy components are concentrated in one area, such as a lab-lab- bilibilitiesties ofof simultaneoussimultaneous use andand operationoperation forfor differentdifferent appappliancesliances oratory, an operating room, etc. Commonly, heat gain from equip- llocatedocated inin thethe same space must bebe considered.considered. ment in a laboratory ranges from 15 to 70 Btu/h·fBtu/h·ftft2 or, in laboratories Radiant heat ggainain from hooded cookincookingg equipment can rangerange wwithith outdoor exposure, as much as fourfour times the heat gaingain from alalll from 15 to 45% of the actual appliance energy consumption ((Gor- ootherther sources comcombined.bined. don et al. 1994; Smith et al. 1995; Swierczyna et al. 2008; Talbert Medical Equipment. It is more difficult to provide generalized et al. 1973). This ratio of heat gain to appliance energy consumption heat gain recommendations for medical equipment than for general may be expressed as a radiation fafactor,ctor, and it is a function of both office equipment because medical equipment is much more varied appliance typetype and fuel source.source. The radiation factorr FR is applied to in type and in application. Some heat gain testing has been done, but the average rate of applianceappliance energyenergy consumption, determined byby the equipment included represents only a small sample of the type of applapplyingying usausagege factor FU to the nameplate or rated energy input. equipment that may be encountered. Marn (1962) found that radiant heatt temperature riserise can bebe sub-sub- Data presented for medical equipment in Table 6 are relevant for stantiallystantially reduced by shielding thethe fronts of cooking appliances.appliances. portaportableble anandd bbench-topench-top equequipment.ipment. MeMedicaldical equequipmentipment iiss very spe- AlthoughAlthough this approach maymay not alwaysalways be practical in a commer- ccificific and can varyvary greatlygreatly from applicationapplication to application.application. The data cialcial kikitchen,tchen, raradiantdiant gaiinsns can aalsolso bbee rereducedduced bbyy addiaddingng ssideide panepanelsls are presented to provide guidance in only the most general sense. or partial enclosures that are integrated with the exhaust hood.hood. For large equipment, such as MRI, heat gain must be obtained from Heat Gain from Meals. For each meal served, approximatelyapproximately the manufacturer. 5050 Btu/hBtu/h ofof heat,heat, ofof whichwhich 75% is sensiblesensible andand 25% isis latent,latent, is Laboratory Equipment. Equipment in laboratories is similar to transferredtransferred to tthehe didiningning spacespace.. medical equipment in that it varies significantly from space to 18.8 2013 ASHRAE Handbook—Fundamentals

Table 5A Recommended Rates of Radiant and Convective Heat Gain from Unhooded Electric Appliances During Idle (Ready-to-Cook) Conditions

Energy Rate, Btu/h Rate of Heat Gain, Btu/h Usage Radiation Sensible Sensible Factor Factor Appliance Rated Standby Radiant Convective Latent Total FU FR Cabinet: hot serving (large), insulated* 6,800 1,200400 800 0 1,2000.18 0.33 hot serving (large), uninsulated 6,800 3,500700 2,800 0 3,500 0.51 0.20 proofing (large)* 17,400 1,4001,200 0 200 1,400 0.08 0.86 proofing (small 15-shelf) 14,300 3,9000 900 3,000 3,900 0.27 0.00 Coffee brewing urn 13,000 1,200200 300 700 1,200 0.09 0.17 Drawer warmers, 2-drawer (moist holding)* 4,100 500 0 0 200 200 0.12 0.00 Egg cooker 10,900 700300 400 0 700 0.06 0.43 Espresso machine* 8,200 1,200400 800 0 1,200 0.15 0.33 Food warmer: steam table (2-well-type) 5,100 3,500 300600 2,600 3,5000.69 0.09 Freezer (small) 2,700 1,100500 600 0 1,1000.41 0.45 Hot dog roller* 3,400 2,400900 1,500 0 2,400 0.71 0.38 Hot plate: single burner, high speed 3,800 3,000900 2,100 0 3,0000.79 0.30 Hot-food case (dry holding)* 31,100 2,500900 1,600 0 2,500 0.08 0.36 Hot-food case (moist holding)* 31,100 3,300 900 1,800 600 3,300 0.11 0.27 Microwave oven: commercial (heavy duty) 10,900 00 0 0 0 0.00 0.00 Oven: countertop conveyorized bake/finishing* 20,500 12,6002,200 10,400 0 12,600 0.61 0.17 Panini* 5,800 3,200 1,200 2,000 0 3,2000.55 0.38 Popcorn popper* 2,000 200100 100 0 200 0.10 0.50 Rapid-cook oven (quartz-halogen)* 41,000 0 0 0 0 0 0.00 0.00 Rapid-cook oven (microwave/convection)* 24,900 4,100 1,0003,100 0 1,000 0.16 0.24 Reach-in refrigerator* 4,800 1,200300 900 0 1,200 0.25 0.25 Refrigerated prep table* 2,000 900600 300 0 900 0.45 0.67 Steamer (bun) 5,100 700600 100 0 700 0.14 0.86 Toaster: 4-slice pop up (large): cooking 6,100 3,000 200 1,400 1,000 2,600 0.49 0.07 contact (vertical) 11,300 5,300 2,700 2,6000 5,3000.47 0.51 conveyor (large) 32,800 10,3003,000 7,300 0 10,300 0.31 0.29 small conveyor 5,800 3,700400 3,300 0 3,7000.64 0.11 Waffle iron 3,100 1,200800 400 0 1,2000.39 0.67 *Items with an asterisk appear only in Swierczyna et al. (2009); all others appear in both Swierczyna et al. (2008) and (2009).

Table 5B Recommended Rates of Radiant Heat Gain from Hooded Electric Appliances During Idle (Ready-to-Cook) Conditions Energy Rate, Btu/h Rate of Heat Gain, Btu/h Usage Radiation Appliance Rated Standby Sensible Radiant Factor FU Factor FR Broiler: underfired 3 ft 36,900 30,900 10,800 0.84 0.35 Cheesemelter* 12,300 11,900 4,600 0.97 0.39 Fryer: kettle 99,000 1,800 500 0.02 0.28 Fryer: open deep-fat, 1-vat 47,800 2,800 1,000 0.06 0.36 Fryer: pressure 46,100 2,700 500 0.06 0.19 Griddle: double sided 3 ft (clamshell down)* 72,400 6,900 1,400 0.10 0.20 Griddle: double sided 3 ft (clamshell up)* 72,400 11,500 3,600 0.16 0.31 Griddle: flat 3 ft 58,400 11,500 4,500 0.20 0.39 Griddle-small 3 ft* 30,700 6,100 2,700 0.20 0.44 Induction cooktop* 71,700 0 0 0.00 0.00 Induction wok* 11,900 0 0 0.00 0.00 Oven: combi: combi-mode* 56,000 5,500 800 0.10 0.15 Oven: combi: convection mode 56,000 5,500 1,400 0.10 0.25 Oven: convection full-size 41,300 6,700 1,500 0.16 0.22 Oven: convection half-size* 18,800 3,700 500 0.20 0.14 Pasta cooker* 75,100 8,500 0 0.11 0.00 Range top: top off/oven on* 16,600 4,000 1,000 0.24 0.25 Range top: 3 elements on/oven off 51,200 15,400 6,300 0.30 0.41 Range top: 6 elements on/oven off 51,200 33,200 13,900 0.65 0.42 Range top: 6 elements on/oven on 67,800 36,400 14,500 0.54 0.40 Range: hot-top 54,000 51,300 11,800 0.95 0.23 Rotisserie* 37,900 13,800 4,500 0.36 0.33 Salamander* 23,900 23,300 7,000 0.97 0.30 Steam kettle: large (60 gal) simmer lid down* 110,600 2,600 100 0.02 0.04 Steam kettle: small (40 gal) simmer lid down* 73,700 1,800 300 0.02 0.17 Steamer: compartment: atmospheric* 33,400 15,300 200 0.46 0.01 Tilting skillet/braising pan 32,900 5,300 0 0.16 0.00 *Items with an asterisk appear only in Swierczyna et al. (2009); all others appear in both Swierczyna et al. (2008) and (2009). Nonresidential Cooling and Heating Load Calculations 18.9

Table 5C Recommended Rates of Radiant Heat Gain from Hooded Gas Appliances During Idle (Ready-to-Cook) Conditions Energy Rate, Btu/h Rate of Heat Gain, Btu/h Usage Radiation Appliance Rated Standby Sensible Radiant Factor FU Factor FR Broiler: batch* 95,000 69,200 8,100 0.73 0.12 Broiler: chain (conveyor) 132,000 96,700 13,200 0.73 0.14 Broiler: overfired (upright)* 100,000 87,900 2,500 0.88 0.03 Broiler: underfired 3 ft 96,000 73,900 9,000 0.77 0.12 Fryer: doughnut 44,000 12,400 2,900 0.28 0.23 Fryer: open deep-fat, 1 vat 80,000 4,700 1,100 0.06 0.23 Fryer: pressure 80,000 9,000 800 0.11 0.09 Griddle: double sided 3 ft (clamshell down)* 108,200 8,000 1,800 0.07 0.23 Griddle: double sided 3 ft (clamshell up)* 108,200 14,700 4,900 0.14 0.33 Griddle: flat 3 ft 90,000 20,400 3,700 0.23 0.18 Oven: combi: combi-mode* 75,700 6,000 400 0.08 0.07 Oven: combi: convection mode 75,700 5,800 1,000 0.08 0.17 Oven: convection full-size 44,000 11,900 1,000 0.27 0.08 Oven: conveyor (pizza) 170,000 68,300 7,800 0.40 0.11 Oven: deck 105,000 20,500 3,500 0.20 0.17 Oven: rack mini-rotating* 56,300 4,500 1,100 0.08 0.24 Pasta cooker* 80,000 23,700 0 0.30 0.00 Range top: top off/oven on* 25,000 7,400 2,000 0.30 0.27 Range top: 3 burners on/oven off 120,000 60,100 7,100 0.50 0.12 Range top: 6 burners on/oven off 120,000 120,800 11,500 1.01 0.10 Range top: 6 burners on/oven on 145,000 122,900 13,600 0.85 0.11 Range: wok* 99,000 87,400 5,200 0.88 0.06 Rethermalizer* 90,000 23,300 11,500 0.26 0.49 Rice cooker* 35,000 500 300 0.01 0.60 Salamander* 35,000 33,300 5,300 0.95 0.16 Steam kettle: large (60 gal) simmer lid down* 145,000 5,400 0 0.04 0.00 Steam kettle: small (10 gal) simmer lid down* 52,000 3,300 300 0.06 0.09 Steam kettle: small (40 gal) simmer lid down 100,000 4,300 0 0.04 0.00 Steamer: compartment: atmospheric* 26,000 8,300 0 0.32 0.00 Tilting skillet/braising pan 104,000 10,400 400 0.10 0.04 *Items with an asterisk appear only in Swierczyna et al. (2009); all others appear in both Swierczyna et al. (2008) and (2009).

Table 5D Recommended Rates of Radiant Heat Gain from Hooded Solid Fuel Appliances During Idle (Ready-to-Cook) Conditions Energy Rate, Btu/h Rate of Heat Gain, Btu/h Usage Radiation Appliance Rated Standby Sensible Factor FU Factor FR Broiler: solid fuel: charcoal 40 lb 42,0006200 N/A0.15 Broiler: solid fuel: wood (mesquite)* 40 lb 49,600 7000 N/A 0.14 *Items with an asterisk appear only in Swierczyna et al. (2009); all others appear in both Swierczyna et al. (2008) and (2009).

Table 5E Recommended Rates of Radiant and Convective Heat Gain from Warewashing Equipment During Idle (Standby) or Washing Conditions Rate of Heat Gain, Btu/h Energy Rate, Btu/h Unhooded Hooded Usage Radiation Standby/ Sensible Sensible Sensible Factor Factor Appliance Rated Washing Radiant Convective Latent Total Radiant FU FR Dishwasher (conveyor type, chemical sanitizing) 46,800 5700/43,600 0 4450 13490 17940 0 0.36 0 Dishwasher (conveyor type, hot-water sanitizing) standby 46,800 5700/N/A 0 4750 16970 21720 0 N/A 0 Dishwasher (door-type, chemical sanitizing) washing 18,400 1200/13,300 0 1980 2790 4770 0 0.26 0 Dishwasher (door-type, hot-water sanitizing) washing 18,400 1200/13,300 0 1980 2790 4770 0 0.26 0 Dishwasher* (under-counter type, chemical sanitizing) standby 26,600 1200/18,700 0 2280 4170 6450 0 0.35 0.00 Dishwasher* (under-counter type, hot-water sanitizing) standby 26,600 1700/19,700 800 1040 3010 4850 800 0.27 0.34 Booster heater* 130,000 0 500 0 0 0 500 0 N/A *Items with an asterisk appear only in Swierczyna et al. (2009); all others appear in both Swierczyna Note: Heat load values are prorated for 30% washing and 70% et al. (2008) and (2009). standby. space. Chapter 16 of the 2011 ASHRAE Handbook—HVAC Appli- Office Equipment cations discusses heat gain from equipment, which may range from Computers, printers, copiers, etc., can generate very signifi- 5 to 25 W/ftW/fft2 in highly automated laboratories. Table 7 lists some ccantant heatheat gains,gains, sometimessometimes greatgreaterer tthanhan aallll ototherher ggainsains combined.combined. values for laboratory equipment, but, as with medical equipment, it ASHRAE research projectt RP-822 developed a method to measure is for general guidance only. Wilkins and Cook (1999) also exam- ththee actuaactuall heatheat gaingain fromfrom equipmentequipment inin buildingsbuildings andand thethe radiant/radiant/ ined laboratory equipment heat gains. convective percentages (Hosni( et al. 1998; Jones et al. 1998). This 18.10 2013 ASHRAE Handbook—Fundamentals

Table 6 Recommended Heat Gain from Actual power consumption is assumedassumed to equal total (radiant plus Typical Medical Equipment cconvective)onvective) heatheat gain,gain, bbutut iitsts ratratioio to tthehe namepnameplatelate valuevalue variesvaries widwidely.ely. ASHRAE researcresearchh proprojectject RP-1055 ((HosniHosni et aal.l. 19991999)) Equipment Nameplate, W Peak, W Average, W ffoundound tthat,hat, fforor ggeneraleneral oofficeffice equequipmentipment wwithith namenameplateplate ppowerower concon-- Anesthesia system 250 177 166 ssumptionumption of less than 1000 W, the acactualtual raratiotio of total heat gain to Blanket warmer 500 504 221 nameplate ranged from 25% to 50%, but when all tested equipmenequipmentt Blood pressure meter 180 33 29 iiss considered, the range is broader.broader. Generally, if the nameplate value Blood warmer 360 204 114 iiss the only information known and no actual heat gain data are availavail-- ECG/RESP 1440 54 50 Electrosurgery 1000 147 109 aableble for similar equipment, it is conservativeconservative to use 50% of name- Endoscope 1688 605 596 pplatelate as heat gain and more nearnearlyly correct if 25% of nameplate iiss Harmonical scalpel 230 60 59 uused.sed. Much better results can be obtained,obtained, however, byby consideringconsidering Hysteroscopic pump 180 35 34 hheateat gaingain to bebe predictablepredictable bbasedased on thethe typetype ooff equequipment.ipment. HowHow-- Laser sonics 1200 256 229 eever,ver, if the device has a mainly resistive internal electric load (e.g., Optical microscope 330 65 63 a space heater),heater), thethe nameplatenameplate ratingrating may bebe a goodgood estimateestimate ofof itsits Pulse oximeter 72 21 20 ppeakeak energy dissipation. Stress treadmill N/A 198 173 Computers. Based on tests by Hosni et al. (1999) and Wilkins Ultrasound system 1800 1063 1050 Vacuum suction 621 337 302 and McGaffin (1994), nameplate values on computers should be X-ray system 968 82 igignorednored when performingperforming coolingcooling loadload calculations. Table 8 pres-pres- 1725 534 480 ents typical heat gain values for computers with varying degrees of 2070 18 ssafetyafety factor. Source: Hosni et al. (1999). Monitors. Based on monitors tested by Hosni et al. (1999), heat ggainain for cathode rarayy tube ((CRT)CRT) monitors correlates approximatelapproximatelyy Table 7 Recommended Heat Gain from wiwithth screen sizesize as Typical Laboratory Equipment qmon = 5S – 20 (7) Equipment Nameplate, W Peak, W Average, W wwherehere

Analytical balance 7 7 7 qmon = sensiblesensible heatheat gaingain fromfrom monitor,monitor, W Centrifuge 138 89 87 S=nnominalominal screen ssize,ize, in.in. 288 136 132 Table 8 shows typical values. 5500 1176 730 Flat-panel monitors have replaced CRT monitors in many work- Electrochemical analyzer 50 45 44 places. Power consumption, and thus heat gain, for flat-panel dis- 100 85 84 plays aree significantly lower thann for CCRTs.RTs. CConsultonsult manufacturersmanufacturers’’ Flame photometer 180 107 105 literatureliterature forfor average power consumptionconsumption datadata forfor use iinn hheateat gagainin Fluorescent microscope 150 144 143 calculations.calculations. 200 205 178 Laser Printers. Hosni et al. (1999) found that power consump- Function generator 58 29 29 tion, and therefore the heat ggain,ain, ofof laser printers depended largelylargely Incubator 515 461 451 on thethe levellevel ooff tthroughputhroughput fforor wwhichhich tthehe prprinterinter was ddesigned.esigned. 600 479 264 SmallerSmaller printersprinters tendtend to bebe usedused more intermittently,intermittently, andand largerlarger 3125 1335 1222 printersprinters may run contcontinuouslyinuously forfor longerlonger periods.periods. Orbital shaker 100 16 16 Table 9 presents data on laser printers. These data can bee applied Oscilloscope 72 38 38 byby tatakingking thethe valuevalue forfor contcontinuousinuous operatoperationion anandd tthenhen appapplyinglying aann 345 99 97 appropriate diversitydiversity factor. This would likelylikely be most appropriate Rotary evaporator 75 74 73 forfor llargerarger open officeoffice areas. AnotherAnother approach,approach, whichwhich may be 94 29 28 appropriate for a singlesingle room or small area, is to take the value that Spectronics 36 31 31 most closely matches the expecteexpectedd ooperatioperationn of the printer with no Spectrophotometer 575 106 104 diversity.diversity. 200 122 121 Copiers. Hosni et al. (1999) also tested five photocopy N/A 127 125 machines, including desktop and oofficeffice ((freestandingfreestanding hihigh-volumegh-volume Spectro fluorometer 340 405 395 copiers)copiers) models. LargerLarger machines used in productionproduction environmentsenvironments Thermocycler 1840 965 641 werewere notnot addressed.addressed. TableTable 9 summarizessummarizes the results. DesktopDesktop copi-copi- N/A 233 198 ers rarelyrarely operate continuouslcontinuously,y, but office copiers frequentlyfrequently operateoperate Tissue culture 475 132 46 continuouslycontinuously forfor periodsperiods ofof an hourhour or more. Large, high-volumehigh-volume 2346 1178 1146 photocopiersphotocopiers often include pprovisionsrovisions for exhausting air outdoors; if Source: Hosni et al. (1999). so equipped,equipped, thethe direct-to-spacedirect-to-space oror systemsystem makeupmakeup airair heatheat gaingain needsneeds to bbee iincludedncluded iinn tthehe lloadoad cacalclcuulation.lation. Also,Also, whenwhen thethe airair isis methodology wasw then incorporated into ASHRAE research project dry,dry, humidifiers are often operated near copiers to limit static elecelec-- RP-1055 and applied to a wide rarangenge of equipment ((HosniHosni et alal.. tricity;tricity; if this occurs durinduringg ccoolingooling mode, their load on HVAC ssys-ys- 1999) as a follow-up to independent research by Wilkins and tems shouldshould bebe consconsidered.idered. McGaffin (1994)(1994) and Wilkins et al. (1991).(1991). Komor (1997)(1997) founfoundd Miscellaneous Office Equipment. Table 10 presents data on ssimilarimilar results.results. AnaAnalysislysis ofof measmeasureuredd datadata showedshowed thatthat resuresultslts fforor miscellaneous office equipment such as vending machines and office equipment could be generalized,generalized, but results from laboratory mailingmailing equipment.equipment. anandd hhospitalospital equequipmentipment proveprovedd too diverse. The following general Diversity. The ratio of measured peak electrical load at equip- guidelines for office equipment are a result of these studies. ment panels to the sum of the maximum electrical load of each Nameplate Versus Measured Energy Use. Nameplate data individual item of equipment is the usage diversity. A small, one- or rarerarelyly rereflectflect tthehe actuaactuall powepowerr consumconsumptionption ooff oofficeffice eequipment.quipment. two-person office containing equipment listed in Tables 8 to 10 Nonresidential Cooling and Heating Load Calculations 18.11

Table 8 Recommended Heat Gain from Typical Computer Equipment Equipment Description Nameplate Power, W Average Power, W Radiant Fraction Desktop computera Manufacturer A (model A); 2.8 GHz processor, 1 GB RAM 480 73 0.10a Manufacturer A (model B); 2.6 GHz processor, 2 GB RAM 480 49 0.10a Manufacturer B (model A); 3.0 GHz processor, 2 GB RAM 690 77 0.10a Manufacturer B (model B); 3.0 GHz processor, 2 GB RAM 690 48 0.10a Manufacturer A (model C); 2.3 GHz processor, 3 GB RAM 1200 97 0.10a Laptop computerb Manufacturer 1; 2.0 GHz processor, 2 GB RAM, 17 in. screen 130 36 0.25b Manufacturer 1; 1.8 GHz processor, 1 GB RAM, 17 in. screen 90 23 0.25b Manufacturer 1; 2.0 GHz processor, 2 GB RAM, 14 in. screen 90 31 0.25b Manufacturer 2; 2.13 GHz processor, 1 GB RAM, 14 in. screen, tablet 90 29 0.25b PC Manufacturer 2; 366 MHz processor, 130 MB RAM (4 in. screen) 70 22 0.25b Manufacturer 3; 900 MHz processor, 256 MB RAM (10.5 in. screen) 50 12 0.25b Flat-panel monitorc Manufacturer X (model A); 30 in. screen 383 90 0.40c Manufacturer X (model B); 22 in. screen 360 36 0.40c Manufacturer Y (model A); 19 in. screen 288 28 0.40c Manufacturer Y (model B); 17 in. screen 240 27 0.40c Manufacturer Z (model A); 17 in. screen 240 29 0.40c Manufacturer Z (model C); 15 in. screen 240 19 0.40c Source: Hosni and Beck (2008). aPower consumption forr newer desktop computers in operationaloperational modemode variesvaries fromfrom 50 to 100 W, butbut a cFlat-panelFlat--panel monitors have replacereplacedd catcathodehode rarayy tutubebe ((CRT)CRT) monmonitorsitors conservatconservativeive valuevalue ofof aboutabout 65 W maymay bebe used.used. PowerPower consumptionconsumption inin sleepsleep modemode isis negligible.negligible. iinn manmanyy worworkplaces,kplaces, provprovidingiding bbetteretter resoresolutionlution anandd bbeingeing mucmuchh BBecauseecause ooff coocoolingling ffan,an, aapproximatelypproximately 90% ofof loadload isis by convectionconvection andand 10% isis by radiation.radiation. ActualActual lighlighter.ter. Power consumptconsumptionion ddependsepends on ssizeize anandd resoresolution,lution, anandd ppowerower consumptconsumptionion iiss aaboutbout 10 to 15% ooff namepnameplatelate vavalue.lue. ranges ffromrom aaboutbout 20 W (for(for 15 in.in. size)size) to 90 W (for(for 30 in.).in.). TheThe bPower consumption off laptop computcomputersers iiss rerelativelylatively smasmall:ll: ddependingepending on processor speespeedd anandd screen most common ssizesizes iinn worworkplaceskplaces are 19 anandd 22 in.,in., fforor wwhichhich aann size, it varies from about 15 to 40 W. Thus, diffdifferentiatingferentiating between radiative and convective parts of averaaveragege 30 W power consumptconsumptionion vavaluelue mamayy bbee useused.d. Use 6060/40%/40% tthehe coolingcooling load is unnecessaryunnecessary andand the entire load maymay be classified as convective. Otherwise, a 7575// ssplitplit bbetweenetween convectconvectiveive anandd raradidiatativeive components. In idlidlee momode,de, 225%5% splitsplit betweenbetween convectiveconvective andand radiativeradiative componentscomponents maymay bebe used.used. ActualActual power consumptionconsumption forfor monitors have nenegligiblegligible power consumption. Nameplate valuevaluess llaptopsaptops is about 25% of nameplatenameplate values.values. shshouldould not bbee used.used.

Table 9 Recommended Heat Gain from Typical Laser Printers and Copiers Equipment Description Nameplate Power, W Average Power, W Radiant Fraction Laser printer, typical desktop, Printing speed up to 10 pages per minute 430 137 0.30a small-office typea Printing speed up to 35 pages per minute 890 74 0.30a Printing speed up to 19 pages per minute 508 88 0.30a Printing speed up to 17 pages per minute 508 98 0.30a Printing speed up to 19 pages per minute 635 110 0.30a Printing speed up to 24 page per minute 1344 130 0.30a Multifunction (copy, print, scan)b Small, desktop type 600 30 d 40 15 d Medium, desktop type 700 135 d Scannerb Small, desktop type 19 16 d Copy machinec Large, multiuser, office type 1750 800 (idle 260 W) d (idle 0.00c) 1440 550 (idle 135 W) d (idle 0.00c) 1850 1060 (idle 305 W) d (idle 0.00c) Fax machine Medium 936 90 d Small 40 20 d Plotter Manufacturer A 400 250 d Manufacturer B 456 140 d Source: Hosni and Beck (2008). bSmall multifunction (copy, scan, print) systems use aboutabout 15 to 30 W;W; medium-sizedmedium-sized ones use aboutabout 135 W.W. Power consumptionconsumption inin idleidle modemode iiss nenegligible.gligible. NamepNameplatelate vavalueslues ddoo not represent actuaactuall power consumptionconsumption aVarious laser printers commerciallycommercially availableavailable andand commoncommonlyly andand shouldshould not bebe used.used. Small,Small, single-sheetsingle-sheet scanners consumeconsume lessless thanthan 20 W andand dodo not contributecontribute signifi-signifi- useusedd iinn personapersonall oofficesffices were testetestedd fforor power consumptconsumptionion iinn cantlycantly to bbuildinguilding coocoolingling load.load. pprintrint mode, which varied from 75 to 140 W, dependingdepending onon cPower consumption forr large copy machines in large offices and copy centers ranges from about 550 to 1100 W momodel,del, prprintint capaccapacity,ity, anandd spspeed.eed. AveraAveragege power consumptconsumptionion iinn copy mode.mode. ConsumptionConsumption inin idleidle modemode variesvaries fromfrom aaboutbout 130 to 300 W. Count idlidle-modee-mode power consumptconsumptionion of 110 W maymay bebe used.used. SplitSplit betweenbetween convectionconvection andand radiationradiation as mostly convective in cooling load calculations. iiss approximatelyapproximately 70/30%.70/30%. dSplit between convective and radiant heat gain waswas not determineddetermined forfor thesethese typestypes ofof equipment.equipment.

usually contributes heat gain to thethe spacespace at the sum of the appro-appro- (normalized based on area) being 46%. Figure 4 illustrates the prpriateiate listedlisted values.values. ProgressivelyProgressively largerlarger areas wwithith many equequipmentipment relationship between nameplate, sumsum ofof peaks,peaks, andand actualactual electri-electri- itemsitems aalwayslways experexperienceience some dedegreegree ooff usausagege didiversityversity resuresultinglting ccalal lloadoad wwithith didiversityversity accounteaccountedd fofor,r, bbasedased on tthehe average ofof thethe from whatever percentapercentagege of such equipment is not in operation aatt totatotall area tested.tested. Data on actualactual diversitydiversity can bebe usedused as a guide,guide, ananyy gigivenven ttime.ime. bbutut diversitydiversity variesvaries significantlysignificantly withwith occupancy. TheThe properproper Wilkins and McGaffin (1994) measured diversity in 23 areas ddiversityiversity factor for an office of mail-order catalogcatalog telephone operoper-- within five different buildings totaling over 275,000 ft2. Diversity aatorstors is differentdifferent fromfrom thatthat forfor an officeoffice ooff sasalesles representatrepresentativesives was found to range between 37 and 78%, with the average who travel reregularly.gularly. 18.12 2013 ASHRAE Handbook—Fundamentals

Table 11 Recommended Load Factors for Various Types of Offices Load Factor, Type of Use W/ft2 Description 100% Laptop, 0.25 167 ft2/workstation, all laptop use, 1 printer per light 10, speakers, misc. medium 0.33 125 ft2/workstation, all laptop use, 1 printer per 10, speakers, misc. 50% Laptop, 0.40 167 ft2/workstation, 50% laptop / 50% desk- light top, 1 printer per 10, speakers, misc. medium 0.50 125 ft2/workstation, 50% laptop / 50% desk- top, 1 printer per 10, speakers, misc. 100% Desktop, 0.60 167 ft2/workstation, all desktop use, 1 printer light per 10, speakers, misc. Fig. 4 Office Equipment Load Factor Comparison medium 0.80 125 ft2/workstation, all desktop use, 1 printer (Wilkins and McGaffin 1994) per 10, speakers, misc. 100% Desktop, 1.00 125 ft2/workstation, all desktop use, 2 moni- Table 10 Recommended Heat Gain from two monitors tors, 1 printer per 10, speakers, misc. 2 Miscellaneous Office Equipment 100% Desktop, 1.50 85 ft /workstation, all desktop use, 2 monitors, heavy 1 printer per 8, speakers, misc. Maximum Input Recommended Rate 100% Desktop, 2.00 85 ft2/workstation, all desktop use, 2 monitors, Equipment Rating, W of Heat Gain, W full on 1 printer per 8, speakers, misc., no diversity. Mail-processing equipment Source: Wilkins and Hosni (2011). Folding machine 125 80 Inserting machine, 600 to 3300 390 to 2150 Table 12 Recommended Diversity Factors for 3600 to 6800 pieces/h Office Equipment Labeling machine, 600 to 6600 390 to 4300 1500 to 30,000 pieces/h Device Recommended Diversity Factor Postage meter 230 150 Vending machines Desktop computer 75% Cigarette 72 72 LCD monitor 60% Cold food/beverage 1150 to 1920 575 to 960 Notebook computer 75% Hot beverage 1725 862 Snack 240 to 275 240 to 275 eestimatesstimates even forfor denselydensely populatedpopulated andand highly automatedautomated spaces.spaces. Other Table 12 indicates applicableapplicable diversity factors. Bar code printer 440 370 Radiant/Convective Split. ASHRAE research projectt RP-1482 Cash registers 60 48 Check processing workstation, 4800 2470 (Hosni and Beck 2008)) is examiningexamining the radiant/convective split foforr 12 pockets ccommonommon oofficeffice equequipment;ipment; tthehe most iimportantmportant diffdifferentiatingerentiating Coffee maker, 10 cups 1500 1050 W sens., ffeatureeature iiss wwhetherhether tthehe equequipmentipment hhadad a coocoolingling ffan.an. Footnotes iinn 1540 Btu/h latent Tables 8 and 9 summarizes those results. Microfiche reader 85 85 Microfilm reader 520 520 Microfilm reader/printer 1150 1150 INFILTRATION AND MOISTURE Microwave oven, 1 ft3 600 400 MIGRATION HEAT GAINS Paper shredder 250 to 3000 200 to 2420 Water cooler, 32 qt/h 700 350 Two other load components contribute to space cooling load directly without time delay from building mass: (1) infiltration, and ASHRAE research project RP-1RP-1093093 dderivederived didiversityversity proprofilesfiles (2) moisture migration through the building envelope. for use in energy calculations (Abushakra( et al. 2004; Claridge et al. 2004). Those profiles were derivedderived fromfrom availableavailable measuredmeasured dadatata INFILTRATION setssets forfor a varietyvariety ofof officeoffice buildings,buildings, andand indicatedindicated a range ofof peakpeak Principles of estimating infiltration in buildings, with emphasis weekdayweekday diversitydiversity factorsfactors forfor lightinglighting rangingranging fromfrom 70 to 85% andand on the heating season, are discussed in Chapterr 16. When econom- forfor receptacreceptaclesles ((applianceappliance lload)oad) bbetweenetween 42 anandd 89%. ically feasible, somewhat more outoutdoordoor airair may bebe introducedintroduced to a Heat Gain per Unit Area. Wilkins and Hosni (2000, 2011) and bbuildinguilding thanthan thethe totaltotal ofof thatthat exhausted,exhausted, to create a slightslight overalloverall Wilkins and McGaffin (1994) summarizedsummarized researchresearch on a heatheat gaingain positive pressure in the buildingbuilding relative to the outdoors. UnderUnder per unit area basis. Diversity testing showed that the actual heat tthesehese conconditions,ditions, aairir usuausuallylly exexfiltrates,filtrates, ratratherher tthanhan iinfiltrates,nfiltrates, gain per unit area, or load factor, ranged from 0.44 to 1.08 W/ftW/fft2, throuthroughgh the buildingbuilding envelope and thusthus effectivelyeffectively eeliminatesliminates infilinfil-- with an averageaverage ((normalizednormalized based on area) of 0.81 W/fW/ftft2. Spaces ttrationration sesensiblensible aandnd llatentatent heat gains. However, there is concern, testetestedd were fullyfully occupoccupiedied aandnd hihighlyghly automateautomated,d, comprcomprisingising 2211 especially in some climates, that water may condense within the ununiqueique areas inin fivefive buildings,buildings, withwith a computer andand monitormonitor at every buildinbuildingg envelope; activelyactively managingmanaging space air pressures to reduce workstation. Table 11 presents a range of load factors with a tthishis condensation problem,problem, as well as infiltration,infiltration, maymay be needed. subjective description of the type of space to which they would When positive air pressure is assumed, most designers do not apply. The medium load density is likely to be appropriate for most include infiltration in cooling load calculations for commercial sstandardtandard oofficeffice spaces. MeMedium/heavydium/heavy or hheavyeavy lloadoad ddensitiesensities may buildings. However, including some infiltration for spaces such bbee encountereencounteredd bbutut can bbee conconsideredsidered extremeextremelyly conservativeconservative eentryntry areas or loadinloadingg docks mamayy bbee appropriate, especiallespeciallyy whenwhen Nonresidential Cooling and Heating Load Calculations 18.13

thosethose sspacespaces are on tthehe wwindwardindward ssideide ooff bbuildings.uildings. But tthehe ddown-own- qs = Cs Qs t warwardd stackstack effect,effect, as occurs wwhenhen iindoorndoor aairir iiss ddenserenser tthanhan tthehe out- ddoor,oor, mightmight eliminateeliminate infiltrationinfiltration to thesethese entriesentries onon lowerlower floorsfloors of wherewhere Cs = 1.1 is the air sensible heheatat ffactor,actor, iinn BtuBtu/h·cfm·°F./h·cfm·°F. tatallll buildings;buildings; infiltrationinfiltration mmayay occur on tthehe upper flfloorsoors dduringuring 3. Latent heat cooling conditions if makemakeupup air is not sufficient. Latent heat gain ql corresponding to the change of humidity ratio Infiltration also depends on windwind direction and magnitude, temtem-- W (in( n lb /lb/lb ) for given airflow (standard conditions) Q is perature differences,differences, constructionconstruction type andand quality,quality, andand occupantoccupant m,w m,m,ddaa s   use of exterior doors and operabloperablee windows. As such, it is impossiimpossi-- ql = 60 0.075 1076Qs W = 4840Qs W (11) ble to accurately predict ininfiltratiofiltrationn rates. DDesigners usually predict overall rates of infiltration using the number of air changes per where 1076 Btu/lb is the approximate heat content of 50% rh vapor hour (ACH). A common guideline for climates and buildings typ- at 75°F less the heat content off water at 50°F. A common design ical of at least the central UnitedUnited StatesStates is to estimate the ACHsACHs forfor conditioncondition for the space is 50% rh at 75°F, and 50°F is normal con-con- winter heating conditions, and then use half that value for the cool- densatedensate temperature from coocoolingling and dehumidifying coils.coils. inging load calculations.calculations. This latent heat equation can also be expressed as

Standard Air Volumes ql = Cl Qs W Because the specific volume of air varies appreciably, calcula- wheree Cl = 4840 is the air latent heat factor, in Btu/h·cfm. When W tions are more accurate when made on the basis of air mass instead is inn gr /lb/lb , C = 0.69 Btu/h·cfm. ooff vovolume.lume. However, vovolumetriclumetric flflowow rates are ooftenften requiredrequired forfor w m,m,dada l selectinselectingg coils, fans, ducts, etcetc.;.; basinbasingg volumes on measurement aatt 4. Elevation correction for total, sensible, and latent heat equations standard conditions may be used forfor accurate results.results. One standard The constants 4.5, 1.10, and 4840 are useful in air-conditioninair-conditioningg 3 3 value is 0.075 lbda/ft/fft (13.33 ft /lb)./ This density corresponds to calculationscalculations at sea levellevel (14.696(14.696 psia)psia) andand forfor normalnormal temperaturestemperatures about 60°F at saturation and 69°F drydrry air (at 14.696 psia). Because andand moisturemoisture ratios.ratios. For otherother conditions,conditions, more preciseprecise vavalueslues airair usuausuallylly passes tthrohrougughh thethe equipmentequipment at a densitydensity closeclose to stan- should be used. For an elevation off 5000 ft (12.2 psia), appropriate dard for locations below about 1000 ft, the accuracyaccuracy desired nornor-- valuesvalues are 3.74, 0.92, anandd 4027. EquationsEquations (9)(9) to (11)(11) can bebe mally requires no correction. When airflow is to be measured at a correctedcorrected fforor elevationselevations ototherher tthahann sea llevelevel by mumultiplyingltiplying themthem by particular condition or point, such as at a coil entrance or exit, the the ratio of ppressureressure at sea level divideddivided byby the pressure at actual altialti-- corresponding specific volume can bbee reareadd ffromrom tthehe sea-sea-levellevel tude.tude. ThisThis can bebe derivedderived fromfrom EquationEquation (3)(3) inin ChapterChapter 1 as psychrometricpsychrometric cchart.hart. For highhigherer eelevations,levations, the mass flow rates of C = C P/P airair must bebe adjustedadjusted andand higher-elevationhigher-elevation psychrometricpsychrometric cchartsharts oorr x,altt x,0 0 algorithmsalgorithms must bebe used.used. wheree Cx,0, is any of the sea-level C values and P/P0 = [1 – (elevation   –6–6 5.25595 Heat Gain Calculations Using Standard Air Values 66.8754.8754 10 )])] , where elevation is in feet. Air-conditioning design often requires the following infor- Elevation Correction Examples mation: To correct the C values for El Paso, Texas, the elevation listed in 1. Total heat the appendix of Chapter 14 is 3917 ft. C values for Equations (8) to Total heat gain qt corresponding to the change of a given standard (11) can be corrected using Equation (3) in Chapter 1 as follows: flow rate Q through an enthalpy difference h is s C = 4.5 × [1 – (3917 × 6.8754 × 10–6)]5.2559 = 3.90  t,3917 qt = 60 0.075Qs h = 4.5Qs h (8) C = 1.10 × [1 – (3917 × 6.8754 × 10–6)]5.2559 = 0.95 3 s,3917 where 60 = min/h, 0.075 = lbdada/ft/fft . –6 5.2559 This total heat equation can also be expressed as Cl,3917 = 4840 × [1 – (3917 × 6.8754 × 10 )] = 4192

qt = Ct Qs h To correct the C values for Albuquerque, New Mexico, the ele- vation listed in the appendix of Chapter 14 is 5315 ft. C values for where Ct = 4.5 is the air total heat factor, in Btu/h·cfm per Btu/lb enthalpy h. Equations (8) to (11) can be corrected as follows: –6 5.2559 2. Sensible heat Ct,5315 = 4.5 × [1 – (5315 × 6.8754 × 10 )] Ct,531 = 3.70 Sensible heat gain qs corresponding to the change of dry-bulb –6 5.2559 temperature t for given airflow (standard conditions) Qs is Cs,5315 = 1.10 × [1 – (5315 × 6.8754 × 10 )] Cs,5315 = 0.90  qs = 60 0.075(0.24 + 0.45W )Qs t (9)(9) –6 5.2559 Cl,5315 = 4840 × [1 – (5315 × 6.8754 × 10 )] Cl,5315 = 3979 wherewhere 0.24 = specspecificific heatheat ofof drydry air,air, BtuBtu/lb·°F/lb·°F LATENT HEAT GAIN FROM W = humidity ratio, lbw/lbda MOISTURE DIFFUSION 0.45 = specspecificific heatheat ofof water vapor, Btu/lb·°FBtu/lb·°F Diffusion of moisture through building materials is a natural phe- The specific heats are for a range from about –100 to 200°F.200°F. nomenon that is always present. Chapters 25 to 27 cover principles, WWhenhen W = 0, the value of 60  0.075 ((0.240.24 + 0.45W) = 1.08; when materials, and specific methods used to control moisture. Moisture W = 0.01, tthehe vavaluelue iiss 1.10; wwhenhen W = 0.02, the value is 1.12; and transfer through walls and roofs is often neglected in comfort air wwhenhen W = 0.03, the value is 1.14. Because a value of W = 0.01 conditioning because the actual rate is quite small and the corre- approxapproximatesimates conconditionsditions ffoundound iinn many aair-conditioningir-conditioning proproblems,blems, sponding latent heat gain is insignificant. Permeability and per- ththee senssensibleible hheateat cchangehange (i(inn BtBtu/h)u/h) hashas traditionallytraditionally beenbeen foundfound asas meance values for various building materials are given in Chapter q = 1.10Q t (10) 26. Vapor retarders should be specified and ininstalledstalled iinn tthehe pproperroper s s llocationocation to keepkeep moisturemoisture transfertransfer to a minimum,minimum, andand to minimizeminimize This sensible heat equation can also be expressed as ccondensationondensation within the envelope.envelope. Moisture migration up through 18.14 2013 ASHRAE Handbook—Fundamentals slabs-on-gradeslabs-on-grade andand basementbasement floorsfloors hashas beenbeen foundfound to bebe signifi-signifi- DDiffuseiffuse sosolarlar hheateat ggainain qd: cant, but has historically not beenn addressed in cooling load calcu- > N lations. Under-slab continuous moisture retarders and drainage can qd = A(Et,d + Et,r) SHGCSHGC D IACD (14)(14) rereduceduce upwarupwardd momoistureisture flflow.ow. ConductiveConductive heatheat gaingain q : Some industrial applications require low moisture to be main- c tained in a conditioned space. In these cases, the latent heat gain qc = UUAA(Toutt – Tin) (15) accompanying moisture transfer through walls and roofs may be greater than any other latent heat gain. This gain is computed by TotalTotal fenestration heat gain Q: Q = q + q + q (16)(16) q = (M/7000))A p (h –h ) (12) b d c l m v g f wherewhere wherwheree A = window area, ft2 q ==l latentatent heatheat gaingain fromfrom moisturemoisture transfer,transfer, Btu/hBtu/h Et,b, Et,d, l m M = permeance of wall or roof assembly, perms or anandd Et,r = beam,beam, sskyky diffuse,diffuse, anandd grounground-reflectedd-reflected diffdiffuseuse irradiance,irradiance, grains/(ftgrains/(fft2·h·in.·h·in. HgHg)) cacalculatedlculated usingusing equationsequations inin ChapterChapter 1414

7000 = grains/lbgrains/lb SSHGC(HGC( ) = b beameam sosolarlar hheateat ggainain coecoefficientfficient as a fufunctionnction of iincidentncident

A = area of wall or roof surface, ft2 anganglele ; may bbee iinterpolatednterpolated betweenbetween valuesvalues inin TableTable 10 ofof CChapterhapter 15 pv = vapor pressure difference,difference, in.in. HgHg > N SSHGCHGC D = diffuse solar heat gain coefficientcoeffficient (also referred to as hg =ent enthalpyhalpy at room conditions,conditions, Btu/lbBtu/lb h =ent enthalpyhalpy ooff water concondenseddensed at coocoolingling coil,coil, Btu/lbBtu/lb hhemisphericalemispherical SHGCSHGC);); ffromrom TaTableble 10 ooff CChapterhapter 15 f T = indoorindoor temperature, °°FF h – h = 1076 Btu/lb when room temperature is 75°F and condensate off in g f T ==out outdoordoor temperature, °F coil is 50°F50°F out U = overall U-factor, including frame and mounting orientation from Table 4 of Chapter 15, Btu/h·fBtu/h·ftft2·°F·°F OTHER LATENT LOADS IAC(IAC( . ) = indoorindoor solarsolar attenuationattenuation coefficientcoefficient forfor beambeam solarsolar heatheat gaingain

Moisture sources within a building (e.g., shower areas, swim- coefficient;coefficient; = 1.0 if no iindoorndoor sshadinghading ddevice.evice. IACIAC(( . ) iiss a ming pools or natatoriums, arboretums) can also contribute to latent ffunctionunction ooff shadeshade typetype and,and, ddependingepending on ttype,ype, mamayy aalsolso bbee a ffunctionunction ooff bbeameam sosolarlar angleangle ofof incidenceincidence anandd shadeshade load. Unlike sensible loads, which correcorrelatelate to suppsupplyly aairir quantquantitiesities ggeometryeometry rerequiredquired inin a space,space, latentlatent loadsloads usuallyusually onlyonly affectaffect coolingcooling coilscoils siz-siz- IACD =i indoorndoor sosolarlar attenuationattenuation coefficientcoefficient forfor diffusediffuse solarsolar hheateat gaingain iingng or rerefrigerationfrigeration lload.oad. Because aairir fromfrom showersshowers andand some otherother coecoefficient;fficient; = 1.0 if not iindoorndoor shading device. IACD is a momoisture-generatingisture-generating areas isis exhaustedexhausted completely,completely, tthosehose airborneairborne functionfunction ofof shadeshade typetype and,and, ddependingepending on ttype,ype, mamayy alsoalso bebe a latentlatent lloadsoads ddoo not reacreachh tthehe coocoolingling cocoilil anandd tthushus ddoo not contrcontributeibute functionfunction ooff shadeshade geometrygeometry to cooling load. However, system loads associated with ventilation If specific window manufacturer’s SHGC and U-factor data are airair requiredrequired to makemake up exexhausthaust aairir must bebe recognized,recognized, andand anyany available, those should be used. For fenestration equipped with recirculated air’s moisture mustmust be considered when sizingsizing ththee indoor shading (blinds, drapes, or shades), the indoor solar attenu- dehumidificationdehumidification eequipment.quipment. ation coefficients IAC( . ) and IACD are listed in Tables 13A to For natatoriums, occupant comfort and humidity control aree crit- 13G of Chapterr 15. ical.ical. In manmanyy iinstances,nstances, ssize,ize, lolocation,cation, anandd envenvironmentalironmental require-require- Note that, as discussed in Chapter 15, fenestration ratings (U- ments makemake completecomplete exhaustexhaust ssystemsystems exexpensivepensive anandd iineffective.neffective. factor and SHGC) are based on the entire product area, including WhereWhere recirculatingrecirculating memechanicalchanical coolingcooling systesystemsms are used, evapora-evapora- frames. Thus, for load calculations, fenestration area is the area of tion (latent) loads are significant. Chapter 5 of the 2011 ASASHRAEHRAE thethe ententireire openopeninging iinn tthehe wawallll or roof.roof. HHandbook—HVACandbook—HVAC AApplicationspplications pprovidesrovides gguidanceuidance on natatornatatoriumium lloadoad cacalculations.lculations. EXTERIOR SHADING Nonuniform exterior shading, caused by roof overhangs, side FENESTRATION HEAT GAIN fins, or building projections, requiresrequires separate hourly calculations For spaces with neutral or positive air pressurization, the primary fforor tthehe externaexternallylly sshadedhaded anandd unsunshadedhaded areas ooff thethe wwindowindow iinn ques- weather-related variable affecting cooling load is solar radiation. tion, with the indoor shadinshadingg SHGCSHGC still used to account for anyany The effect of solar radiation is more pronounced and immediate on internal shading devices. The areas, shaded and unshaded, depend exposed, nonopaque surfaces. Chapter 14 includes procedures for on the location of the shadow line on a surface in the plane of the calculatincalculatingg clear-skclear-skyy ssolarolar rradiationadiation intintensityensity and incidence ananglesgles glass. Sun (1968) developedd fundamentalfundamental algorithms for analysis of for weather conditions encountered att specific locations. That chap- shade patterns. McQuiston and Spitler (1992) provide graphical ter aalsolso iincludesncludes some useusefulful sosolarlar equatequations.ions. CaCalculationlculation ooff sosolarlar dadatata toto facilitatefacilitate shadowshadow lineline calculation.calculation. heat ggainain and conductive heat transfer throughthrough various glazingglazing Equations for calculating shade angles [Chapter 15, Equations mmaterialsaterials aandnd assoassociatedciated mountingmounting frames, withwith oror withoutwithout interiorinterior (34) to (37)] can be used to determine the shape and area of a mov- anand/ord/or exterexteriorior sshadinghading ddevices,evices, is discussed in Chapter 15. This iingng shadow falling across a given window from external shadingshading chapter covers application of such data to overall heat gaingain evalua-evalua- elelementsements duringduring thethe course ofof a design day. Thus, a subprofile of ttion,ion, anandd conversconversionion ooff cacalculatedlculated hheateat gagainin iintonto a composcompositeite coocool-l- hheateat gaingain forfor thatthat windowwindow can bebe createdcreated by separatingseparating itsits sunsunlitlit anandd ing load for the conditioned space. sshadedhaded areasareas forfor eacheach hour.hour. FENESTRATION DIRECT SOLAR, DIFFUSE HEAT BALANCE METHOD SOLAR, AND CONDUCTIVE HEAT GAINS Cooling load estimation involves calculating a surface-by- For fenestration heat gain, use the following equations: surface conductive, convective, and radiative heat balance for each room surface and a convective heat balance for the room air. These DirectDirect bbeameam sosolarlar hheateat gagainin qb: principles form the foundation for all methods described in this

qb = AEAEt,b SHGC(SHGC( )IAC()IAC( , ) (13) chapter. The heat balance (HB) method solves the problem directly Nonresidential Cooling and Heating Load Calculations 18.15 instead of introducing transformation-based procedures. The ad- vantages are that it contains no arbitrarilyarbitrarily set parameters, and nono processes are hiddenhidden fromfrom view.view. Some computations required by this rigorous approach require the use of computers. The heat balance procedure is not new. Many energy calculation programs have used it in some form for many years. The first implementation that incorporated all the elements to form a complete method was NBSLD (Kusuda 1967). The heat balance procedure is also implemented in both the BLAST and TARP energy analysis programs (Walton 1983). Before ASHRAE research projectt RP-875, the methodmethod hadhad never beenbeen ddescribedescribed comcom-- pletelpletelyy or in a form applicable to coolincoolingg load calculations. The papers resultingresulting from RP-875 descrdescribeibe the heat balance procedurproceduree iinn ddetailetail ((LiesenLiesen aandnd PePedersendersen 19971997;; McCMcClellanlellan anandd PePedersendersen 19971997;; Pedersen et al. 1997). The HB method is codified in the software called Hbfort that accompanies Cooling and Heating Load Calculation PrinciplePrincipless (Pedersen(Pedersen et al. 1998).1998). ASHRAE research project RPRP-1117-1117 constructed two modemodell rooms for which coolingcooling loads werewere physicallyphysically measured usingusing extensive instrumentation (Chantrasrisalai(Chantrasrisalai etet al.al. 2003; EldridgeEldridge et al.al. 2003; Iu et al.al. 2003).2003). HB calculations clcloselyosely approxapproximatedimated measuremeasuredd coocoolingling lloadsoads wwhenhen proprovidedvided wwiitthh detaileddetailed ddataata fforor tthehe test rooms.rooms.

ASSUMPTIONS All calculation procedures involve some kind of model; all mod- els require simplifying assumptions and, therefore, are approxi- mate. The most fundamental assumption is that air in the thermal zone can be modeled as well mixedmixed, meanmeaninging iitsts temperature is uniform throughout the zone. ASHRAE research project RP-664 ((FisherFisher and Pedersen 1997)1997) established that this assumption is valid Fig. 5 Schematic of Heat Balance Processes in Zone over a wide range of conditions. The next majormajor assumption is that the surfaces of the rooroomm     ((walls,walls, windows,windows, floor,floor, etc.)etc.) can bebe treatedtreated as hhavingaving qssolol + qLWRLWR + qconv – qkoko = 0 (17) •Un• Uniformiform surfacesurface temperaturestemperatures whwhereere  2 •Un• Uniformiform long-wavelong-wave (LW)(LW) andand short-waveshort-wave ((SW)SW) irradiationirradiation qsoll = absorbed direct and diffuse solar radiation flux (q/Aq/A), Btu/h·ftBtu/h·fft  •D• Diffuseiffuse raradiatingdiating sursurfacesfaces qLWR = net long-wave radiation flux exchange with air and 2 • One-dimensional heat conduction withinwithin surroundings, Btu/h·ftBtu/h·fft  2 qconvv = convective exchange flux with outdoor air, Btu/h·fBtu/h·ftft  2 The resulting formulation is called the heat balance (HB)(HB) qkoko =con conductiveductive fluxflux (q/q/AA) into wall, Btu/h·ftBtu/h·fft mmodelodel. Note that the assumptions, although common, are quite All terms are positive for net flux to the face except q , which is restrictive and set certain limits on the information that can be ko ttraditionallyraditionally takentaken to bebe positivepositive fromfrom outdoorsoutdoors to insideinside thethe wall.wall. obtained from the model. Each term in Equation (17) has been modeled in several ways, and in simplified methods the first three terms are combined by ELEMENTS uusingsing the sol-air temperature. Within the framework of the assumptions, the HB can be viewed as four distinct pprocesses: Wall Conduction Process The wall conduction process has been formulated in more ways 1. OutOutdoor-facedoor-face heatheat balancebalance than any of the other processes. Techniques include 2. WaWallll conconductionduction procesprocesss 3. Indoor-faceIndoor-face heatheat balancebalance • Numerical finite difference 44.. Air heatheat balancebalance •N• Numericalumerical finitefinite elementelement •Tr• Transformansform mmethodsethods Figure 5 shows the relationship between these processes for a •Tim• Timee seriesseries methodsmethods single opaque surface. The top part of the figure, inside the shaded box, is repeated for each surface enclosing the zone. The process for This process introduces part off the time dependence inherent in transparent surfaces is similar, but the absorbed solar component load calculation. FigureF 6 shows surface temperatures on the indooindoorr aappearsppears in the conduction pprocessrocess bblocklock ininsteadstead ooff aatt ththee ououtdoortdoor aandnd outoutdoordoor ffacesaces ooff tthehe wawallll eelement,lement, anandd corresponcorrespondingding conduc-conduc- face, and the absorbed component splits into inward- and outwardoutward-- ttiveive heat fluxes awayaway from the outer face and toward the indoor face.face. flflowingowing ffractions.ractions. TThesehese components partparticipateicipate iinn tthehe sursurfaceface hheateat All four qquantitiesuantities are fufunctionsnctions ooff ttime.ime. Direct formulation of the babalances.lances. process uses temperature functions as iinputnput or knownknown quantquantities,ities, aandnd heatheat flfluxesuxes aass outputs or resresultantultant quantitiesquantities.. Outdoor-Face Heat Balance In some models, surface heat transfer coefficients are included as The heat balance on the outdoor face of each surface is part of the wall element, makinmakingg the temperatures in question ththee 18.16 2013 ASHRAE Handbook—Fundamentals

thermalthermal mass to thethe zone. TheseThese two cchangeshanges can aaffectffect tthehe ttimeime responseresponse ofof thethe zone coolingcooling load.load. SW Radiation from Lights. The short-wavelength radiation fromfrom lightslights isis usuallyusually assumedassumed to bebe distributeddistributed over thethe surfacessurfaces in the zone in some manner. The HB pprocedurerocedure retains this aapproachpproach but allows the distributiondistribution function to be changed.changed. LW Radiation from Internal Sources. TheThe traditionaltraditional modelmodel forfor thisthis source definesdefines a raradiative/convectivediative/convective splitsplit forfor heatheat intro-intro- ducedduced into a zone from equipment. TheThe radiative part is then distrib-distrib- uteduted over the zone’s surfaces in some manner. This model is notnot completelycompletely realistic, and it departs from HB principles. In a true HB model,model, equipment surfaces are treatedtreated just as other LW radiant sourcessources within the zone. However, because information about the surfacesurface temperature of equipment is rarely known, it is reasonable ttoo keepkeep the radiative/convective splitsplit concept even thoughthough it ignoresignores the true nature of the radiant exchange.exchange. ASHRAE research project RP-1055RP-1055 (Hosni(Hosni et al. 1999)1999) determined radiative/convective splits Fig. 6 Schematic of Wall Conduction Process forfor manymany additional equipment types,types, as listed in footnotes for TablesTables 8 and 9. indoorindoor and outdoor air temperatures.temperatures. This is not a desirable formu- llation,ation, because it hides the heat transfer coefficients and prohibits Transmitted Solar Heat Gain. Chapterr 15’s calculation proce- cchanginghanging themthem as aairflowirflow conditionsconditions change.change. It alsoalso prohibitsprohibits treattreat-- dure for determining transmitted solar energy through fenestration ing the internal long-wave radiradiationation exchanexchangege appropriatelappropriately.y. uses the solar heat gain coefficicoefficientent (SHGC) directly rather than Because heat balances on both sides of the element induce both relatingrelating itit to double-strengthdouble-strength glass,glass, asas isis donedone whenwhen usingusing a shadingshading the temtemperatureperature and heat flux, tthehe sosolutionlution mmustust deadeall wwithith thithiss coefficientcoefficient (SC).(SC). TThehe diffidifficultyculty wwithith tthishis pplanlan iiss tthathat tthehe SHGC ssimultaneousimultaneous condition.condition. Two computationalcomputational methodsmethods tthathat hhaveave beenbeen includesincludes both transmitted solar and inward-flowinginward-flowing fraction of the useusedd widelywidely are finitefinite differencedifference andand conductionconduction transfertransfer functionfunction solarsolar raradiationdiation aabsorbedbsorbed iinn tthehe wwindow.indow. WWithith tthehe HB metmethod,hod, tthishis metmethods.hods. Because ofof thethe computationalcomputational timetime advantage,advantage, thethe conduc-conduc- latterlatter part shouldshould bebe addedadded toto thethe coconductionnduction cocomponentmponent so iitt can be ttionion transfertransfer functionfunction formulationformulation hashas beenbeen seselectedlected forfor presentationpresentation includedincluded inin thethe indoor-faceindoor-face heatheat balance.balance. hehere.re. Transmitted solar radiation iss also didistributedstributed over sursurfacesfaces iinn tthehe zone inin a prescribedprescribed manner. It iiss ppossibleossible to cacalculatelculate tthehe actuaactuall Indoor-Face Heat Balance positionposition ofof beambeam solarsolar radiation,radiation, butbut thisthis involvesinvolves partialpartial sursurfaceface The heart of the HB method is the intinternaernall hheateat baballanceance involvinginvolving irradiation,irradiation, wwhichhich iiss iinconsistentnconsistent withwith thethe rest ofof thethe zone model,model, tthehe innerinner facesfaces ofof thethe zone surfaces.surfaces. ThisThis heatheat balancebalance hashas many hheateat which assumesassumes uuniformniform coconditionsnditions oveoverr aann entireentire surface.surface. transtransferfer components, anandd ttheyhey are aallll coupcoupled.led. BotBothh llong-waveong-wave Using SHGC to Calculate Solar Heat Gain ((LW)LW) andand short-waveshort-wave (SW)(SW) radiationradiation are important,important, as wellwell as wallwall conconductionduction andand convectionconvection to thethe air.air. The indoor-face heat balance The total solar heat gain through fenestration consists off directly for each surface can be written as follows: transmtransmitteditted sosolarlar raradiationdiation ppluslus tthehe iinward-flowingnward-flowing ffractionraction ooff sosolarlar rradiationadiation thatthat isis absorbedabsorbed iinn tthehe glglazingazing ssystem.ystem. BotBothh parts contacontainin       qLWX + qSWSW + qLWSLWS + qki + qsolsol + qconv = 0 (18) bbeameam anandd diffdiffuseuse contrcontributions.ibutions. TrTransmittedansmitted raradiationdiation goes didirectlyrectly oontonto surfaces in the zone and is accounted for in the surface indoor whewherere hheateat balance.balance. TheThe zone heatheat balancebalance momodeldel accommoaccommodatesdates tthehe  qLWXLWX = net long-waveg radiant flux exexchangechange betweenbetween zone surfaces,surfaces, resulting heat fluxes without difficulty.diffficulty. The second part, the inward- Btu/h·ftBtu/h·fft2 flflowingowing ffractionraction ooff tthehe aabsorbedbsorbed sosolarlar raradiation,diation, iinteractsnteracts wwithith ototherher  2 qSW = net short-waveshort-wave raradiationdiation fluxflux to surface from lights, Btu/h·ftBtu/h·fft ssurfacesurfaces ooff tthehe enclosureenclosure throughthrough llong-waveong-wave radiantradiant exchangeexchange andand  2 qLWSLWS = long-wave radiation flux from equipment in zone, Btu/h·ftBtu/h·fft with zone air through convective heat transfer. As such, it depends  2 qki = conductive flux through wall, Btu/h·ftBtu/h·fft bbothoth on geometrgeometricic anandd raradiativediative proppropertieserties ooff thethe zone enclosureenclosure andand  2 qsol = transmittedtransmitted sosolarlar raradiativediative flfluxux absorbed at surface, Btu/h·ftBtu/h·fft coconvectionnvection ccharacteristicsharacteristics ininsideside aandnd ououtsidetside ththee zzone.one. ThThee sosolarlar  2 qconv = convective heat flux to zone air, Btu/h·ftBtu/h·fft hheateat gaingain coecoefficientfficient ((SHGC)SHGC) comcombinesbines tthehe transmtransmitteditted sosolarlar raradia-dia- These terms are explained in the following paragraphs. ttionion anandd tthehe iinward-flowingnward-flowing ffractionraction ooff tthehe aabsorbedbsorbed raradiation.diation. TThehe LW Radiation Exchange Among Zone Surfaces. The limiting SHGC is defined as cases for modeling internal LW radiation exchange are n SHGC =  + B N  (19) • Zone air is completely transparent to LW radiatioradiationn k k k=1 •Zone airair completelycompletely absorbsabsorbs LW radiationradiation fromfrom surfacessurfaces inin thethe zonezone wherewhere  = solar transmittance of glazing Most HB momodelsdels treat aairir as complcompletelyetely transparent andand not par-par-  k = solar absorptance of the kthth layerlayer ofof tthehe gglazinglazing systesystemm ticipatingticipating iinn LW raradiationdiation exchangeexchange among surfacessurfaces inin thethe zone.zone. n ==num numberber ofof layerslayers TheThe secondsecond modelmodel is attractiveattractive becausebecause itit can bebe formulatedformulated simplysimply N ==i inward-flowingnward-flowing ffractionraction ooff aabsorbedbsorbed raradiationdiation iinn tthehe kth layer usingusing a combined radiative and convective heat transfer coefficiencoefficientt k ffromrom eaceachh sursurfaceface to tthehe zone aairir anandd tthushus ddecouplesecouples raradiantdiant Note that Equation (19) is written genergenerically.ically. It ccanan be wwrittenritten for exchangeexchange among surfacessurfaces inin thethe zone.zone. However, because the trans- a specific incidence angle and/orr radiation wavelength and inte- parent air model allows radiant exchangeexchange and is more realistic, ththee ggratedrated over tthehe wavelengthwavelength and/orand/or angle,angle, butbut thethe principleprinciple isis thethe secondsecond modelmodel is iinferior.nferior. ssameame inin eacheach case. ReferRefer to CChapthapterer 15 fforor tthehe specspecificific expressexpressions.ions. FurnitureFurniture iinn a zone iincreasesncreases tthehe amount ooff sursurfaceface area tthathat cacann Unfortunately,Unfortunately, thethe inward-flowinginward-flowing fractionfraction N interacts with the participateparticipate inin radiativeradiative andand convectivconvectivee heatheat exchanges.exchanges. It alsoalso addsadds zone inin manymany ways.ways. ThisThis interactioninteraction can bbee exexpressedpressed aass Nonresidential Cooling and Heating Load Calculations 18.17

Table 13 Single-Layer Glazing Data Produced by WINDOW 5.2

Incident Angle Diffuse Parameter 0 102030405060708090(Hemis.)

Vtc 0.899 0.899 0.898 0.896 0.889 0.870 0.822 0.705 0.441 0 0.822 Rfv 0.083 0.083 0.083 0.085 0.091 0.109 0.156 0.272 0.536 1 0.148 Rbv 0.083 0.083 0.083 0.085 0.091 0.109 0.156 0.272 0.536 1 0.148 Tsol 0.834 0.833 0.831 0.827 0.818 0.797 0.749 0.637 0.389 0 0.753

Rf 0.075 0.075 0.075 0.077 0.082 0.099 0.143 0.253 0.506 1 0.136 Rb 0.075 0.075 0.075 0.077 0.082 0.099 0.143 0.253 0.506 1 0.136 Abs1 0.091 0.092 0.094 0.096 0.100 0.104 0.108 0.110 0.105 0 0.101 SHGC 0.859 0.859 0.857 0.854 0.845 0.825 0.779 0.667 0.418 0 0.781 Source: LBL (2003).

N = f (indoor(indoor convectionconvection coefficient,coefficient, outdooroutdoor convectionconvection coefficient,coefficient, If there is more than one layer, the appropriate summation of glazing system overall heat transfertransffer coefficient, zone geometry, absorptancesabsorptances must be done.done. zone raradiationdiation properties)properties) There is some potential inaccuracy in using the WINDOW 5.2 The only way to model these interactions correctly is to combine SHGC values because the inward-flowinginward-flowing fraction part was deterdeter-- the window model with the zone heat balance model and solve botbothh minedmined under specific conditions foforr ththee inindoordoor aandnd ououtdoortdoor hheateat ssimultaneously.imultaneously. TThishis hhasas bbeeneen ddoneone recentlyrecently inin some energyenergy analysisanalysis transfertransfer coefficients. However, the program can be run with indoorindoor pprograms,rograms, but is not generallygenerally available in load calculation proce-proce- andand outdooroutdoor coefficientscoefficients of one’sone’s own choosing.choosing. Normally,Normally, however,however, ddures.ures. In aaddition,ddition, tthehe SHGC useusedd fforor ratratinging gglazinglazing systems iiss bbasedased thisthis effecteffect isis not large,large, andand onlyonly inin highly absorptiveabsorptive glazingglazing ssystemsystems on sspecificpecific vavalueslues ooff tthehe iindoor,ndoor, outoutdoor,door, anandd overaoverallll hheateat transtransferfer mightmight cause significantsignificant error.error. coecoefficientsfficients anandd doesdoes not iincludenclude ananyy zonazonall llong-wavelengthong-wavelength radia-radia- ForFor sosolarlar heatheat gaingain calculations,calculations, then,then, itit seemsseems reasonareasonableble to useuse ttionion considerations.considerations. So, thethe challengechallenge isis to devisedevise a way to use SHGCSHGC the generic window property dataa thatthat comes fromfrom WINDOW 5.2.5.2. vavalueslues withinwithin thethe frameworkframework ofof heatheat balancebalance calculationcalculation in thethe mostmost ConsideringConsidering Table 13, the procedure is as followsfollows:: accurate way possible, as discussed in the following paragraphs. Using SHGC Data. The normal incidence SHGC used to rate 1.1. DetermineDetermine angleangle ofof incidenceincidence forfor thethe glazing.glazing. and characterize glazing systems is not sufficient for determining 2.2. DetermineDetermine correspondingcorresponding SHGC.SHGC.  solar heat gain for load calculations. These calculations require 3. Evaluate Nk k using Equation (19). solar heat gain as a function of the incident solar angle in order to 44..Mu Multiplyltiply Tsoll by incident beam radiatiradiationon iintensityntensity to ggetet trans-trans- determine the hour-by-hour gain profile. Thus, it is necessary to use mmitteditted bbeameam sosolarlar raradiation.diation.  angular SHGC values and also diffuse SHGC values. These can be 55..Mu Multiplyltiply Nk k by incident beam radiradiationation iintensityntensity to get obtained from the WINDOW 5.2 program (LBL 2003). This pro- inward-flowininward-flowingg absorbed heatheat.. gram does a detailed optical and thermal simulation of a glazing sys- 66..Re Repeatpeat stepssteps 2 to 5 with diffusediffuse parametersparameters anandd ddiffuseiffuse rradiation.adiation. tem and, when applied to a single clear layer, produces the 77.. Add beam and diffuse components of transmitted and inwardinward-- information shown in Table 13. flflowingowing aabsorbedbsorbed hheat.eat. Table 13 shows the parameters as a function of incident solar angle and also the diffuse values. The specific parameters shown are This procedure is incorporated into the HB method so the solar gain is calculated accurately for each hour. V = transmittance in visible spectrum tc Table 10 in Chapter 15 contains SHGC information for many Rfvand Rbv = front and back surface visible reflectances additional glazing systems. That table is similar to Table 13 but is  Tsol = solar transmittance [ in Equations (19), (20), and (21)] sslightlylightly abbreviated. Again, the information needed for heat gain Rf and Rb = front and back surface solar reflectances cacalculationslculations isis Tsol, SHGC, and Abs. Abs1 = solar absorptance for layer 1, which is the only layer in this ThThee same cautcautionion aaboutbout tthehe iindoorndoor andand outdooroutdoor heatheat transfertransfer case [ in Equations (19), (20), and (21)] ccoefficientsoefficients appliesapplies to thethe informationinformation iinn TableTable 10 inin ChapterChapter 15.15. SHGC = solar heat gain coefficient at the center of the glazing ThThoseose valuesvalues were alsoalso obtainedobtained withwith specificspecific indoorindoor andand outdooroutdoor hheateat transfertransfer coefficients,coefficients, andand thethe inward-flowinginward-flowing fractionfraction N is The parameters used for heat gain calculations are Tsol , Abs, ddependentependent upon those valuesvalues.. and SHGC. For the specific convective conditions assumed in Convection to Zone Air. Indoor convection coefficients pre- WINDOW 5.2 program, the inward-flowing fraction of the ab- sented in past editions of this chapter and used in most load calcu- sorbed solar can be obtained by rearranging Equation (19) to give lation procedures and energy programs are based on very old, N  = SHGC –  (20) natural convection experiments and do not accurately describe heat k k transfer coefficients in a mechanically ventilated zone. In previous This quantity, when multiplied by the appropriate incident solar load calculation procedures, these coefficients were buried in the intensity, provides the amount of absorbed solar radiation that flows procedures and could not be changed. A heat balance formulation ininward.ward. In thethe heatheat balancebalance formulationformulation for zone loads,loads, this heat fluxflux keeps them as working parameters. In this way, research results such iiss comcombinedbined wwithith tthathat causecausedd by conconductionduction tthroughhrough glglazingazing anandd as those from ASHRAE research projectt RP-664 (Fisher 1998) can iincludedncluded iinn tthehe susurfacerface heaheatt balabalance.nce. be incorporated into the procedureprocedures.s. It also allows determinindeterminingg ththee TThehe outwaroutward-flowingd-flowing ffractionraction ofof absorbedabsorbed solarsolar radiationradiation isis usedused sensitivitysensitivity ooff tthehe lloadoad cacalclculationulation to thesethese parametersparameters.. iinn tthehe heaheatt balabalancence oonn tthehe ououtdoortdoor fafacece ooff tthehe glglazingazing anandd iiss ddeter-eter- minmineded frfromom Air Heat Balance In HB formulations aimed at determining cooling loads, the      ((11 – Nk) k = k – Nk k = k – (SHGC – ) (21) capacitance of air in the zone is neneglecglectetedd anandd thethe airair heaheatt balabalancence is 18.18 2013 ASHRAE Handbook—Fundamentals done as a quasisteadyquasisteady balance in eacheach time pperiod.eriod. Four factors concon-- tthehe case ooff tthehe rooroof).f). TThishis mamakeskes a totatotall ooff 12 sursurfaces,faces, ananyy ooff wwhichhich trtributeibute toto thethe aiairr heaheatt balabalance:nce: may have zero area if it is not present in the zone to be modeled. q + q + q + q = 0 (22) The heat balance processes for this general zone are formulated conv CEE IVV sys for a 24 h steady-periodic condition.condition. TheThe variablesvariables are thethe indoorindoor wwherehere aandnd outdoor temperatures of the 12 surfaces plus either the HVAC qconv =convect convectiveive hheateat transfertransfer fromfrom surfaces,surfaces, BtuBtu/h/h ssystemystem energy requrequiredired to mamaintainintain a specspecifiedified airair temperature or qCECE =convect convectiveive parts ofof internalinternal loads,loads, Btu/hBtu/h the air temperature, if system capacity is specified. This makes a qIV = sensiblesensible loadload causedcaused by infiltrationinfiltration andand ventilationventilation air,air, Btu/hBtu/h totatotall ooff 25  24 = 600 variables. Although it is possible to set up the qsys ==h heateat transfertransfer to/fromto/from HVAC system, Btu/hBtu/h problem for a simultaneous solution of these variables, the relatively Convection from zone surfaces qconv is the sum of all the con-con- weak coupling of the problem from one hour to the next allows a vective heat transfer quantities from the indoor-surface heat bal-bal- ddoubleouble iterative approach. One iterationiteration is throughthrough all the surfaces in ance. This comes to the air through the convective heat transfer eeachach hour, and the other is through the 24 h of a day. This procedurproceduree coefficient on the surfaces.surfaces. aautomaticallyutomatically reconcilesreconciles nonlinear aspects of surface radiativeradiative The convective parts of the internal loads qCE is the compancompan-- eexchangexchange and other hheateat flfluxux tterms.erms.  ioionn ttoo q LWS, the radiant contribution from internal loads [Equation (18)]. It is added directly to the air heat balance. This also violates MATHEMATICAL DESCRIPTION the tenets of the HB approach, because surfaces producing internal loads exchangeexchange heat with zone air throughthrough normal convective pro-pro- Conduction Process cesses. However, once again,again, this level of detail is ggenerallyenerally not Because it links the outdoor and indoor heat balances, the wall included in the heat balance, so it is included directlydirectly into the airair conduction process regulates the cooling load’s time dependence. heatheat balancebalance instead.instead. For the HB procedure presented here, wall conduction is formulated In keeping with the well-mixed model for zone air, any air that uusingsing conductionconduction transfertransfer functionsfunctions (CTFs)(CTFs), whichwhich relaterelate conduc-conduc- titiveve heatheat fluxesfluxes toto currentcurrent andand pastpast surface temperaturestemperatures and ppastast enters directly to a space throughh infiltrationinfiltration or ventventilationilation qIVV is iimmediatelymmediately mmixedixed wwithith tthehe zone’s air. TThe amount of infiltrationi or hheateat flfluxes.uxes. TThehe ggeneraleneral fformorm fforor tthehe iindoorndoor heatheat fluxflux is natural ventilation air is uncertainuncertain. Sometimes it is related to the nz iindoor/outdoorndoor/outdoor temperature differencedifference andand windwind speed;speed; howeverhowever it q t = – Z T – Z T iiss ddetermined,etermined, iitt iiss aaddeddded didirectlyrectly to tthehe aairir hheateat bbalance.alance. ki o si, B j si, – j Conditioned air that enters the zone from the HVAC system and j=1 (23) nz nq provides qsys is also mixed directly with ththee zzoneone air.air. FForor cocommer-mmer-   cialcial HVAC systems,systems, ventventilationilation airair isis most oftenoften providedprovided usingusing out-out- ++YoTso, BYjTso, – j +B j q ki, –j doordoor aairir as part ooff tthishis mmixed-inixed-in conconditionedditioned aair;ir; ventventilationilation aairir is j=1 j=1 thus normally a system load ratherr than a direct-to-spacedirect-to-space load. AnAn exceptionexception iiss wwherehere iinfiltrationnfiltration or naturanaturall ventventilationilation isis usedused to pro-pro- For outdoor heat flux, the form is videvide allall or part ofof the ventilation air, as discussed in Chapterr 16. nz   qko t = – YoTsi, – BYjTsi, – j GENERAL ZONE FOR LOAD CALCULATION j=1 (24) The HB procedure is tailored to a single thermal zone, shown in nz nq   Figure 7. The definition of a thermal zone depends onn how the fixed ++XoTso, BXjTso, – j +B j q ko, –j temperature iiss controcontrolled.lled. IIff aairir ccirculatedirculated tthroughhrough an ententireire bbuildinguilding j=1 j=1 or an entireentire flflooroor iiss ununiformlyiformly wellwell stirred,stirred, thethe entireentire bbuildinguilding or floorfloor coucouldld bebe consideredconsidered a thermalthermal zone. On thethe ototherher hhand,and, if eacheach roomroom where hhasas a differentdifferent controlcontrol scheme,scheme, eacheach room maymay needneed to bebe consideredconsidered Xj ==out outdoordoor CTF, j = 0,1,…nz as a separate tthermalhermal zone. TheThe frameworkframework needsneeds to bebe flexibleflexible Yj = cross CCTF,TF, j = 0,1,…nznz Zj = indoorindoor CTF, j = 0,1,…nz enough to accommodate any zone arrangement,arrangement, but the heat balance  j =flux= flux CTF, j = 1,2,…nq aspect ofof thethe procedureprocedure alsoalso requiresrequires thatthat a completecomplete zone bebe de-de- = time scscribed.ribed. TThishis zzoneone coconsistsnsists ooff ffourour wawalls,lls, a roorooff or ceceiling,iling, a flfloor,oor, anandd  = timetime stepstep a “thermal mass surface” (described(described in the section on Input Re-Re- Tsi = indoor-faceindoor-face temperature, °F ququired).ired). EacEachh wawallll andand tthehe roorooff can iincludenclude a wwindowindow ((oror sskylightkylight in Tso ==out outdoor-facedoor-face temperature, °F  2 q ki = conductive heat flux on indoor face, Btu/h·ftBtu/h·fft  2 qkoko = conductive heat flux on outdoor face, Btu/h·ftBtu/h·fft The subscript following the comma indicates the time period for the quantity in terms of time step . Also, the first terms in the series have beenn separated from the rerestst to facilitate solving for the current temperaturetemperature iinn tthehe sosolutionlution scscheme.heme. TheThe two summatsummationion lilimitsmits nz andand nq dependdepend on wallwall constructionconstruction andand alsoalso sosomewhatmewhat oonn ththee scschemeheme used for calculating the CTFs. If nq = 0, the CTFs are generally referred to as responseresponse ffactorsactors, but thenthen theoreticallytheoretically nzz is infinite. Values for nznz andand nq are generallygenerally setset to minimizeminimize thethe amount ofof computation.computation. A ddevelopmentevelopment ooff CTFs cancan be found in Hittle and Pedersen (1981).(1981). Heat Balance Equations The primary variables in the heat balance for the general zone are the 12 indoor face temperatures and the 12 outdoor face tempera- Fig. 7 Schematic View of General Heat Balance Zone tures at eaceachh ofof tthehe 24 h,h, assigningassigning i as thethe susurfacerface indexindex andand j as thethe Nonresidential Cooling and Heating Load Calculations 18.19 hourhour index,index, or, inin thethe case ooff CTFs, thethe sequencesequence index.index. Thus,Thus, thethe 55..D Distributeistribute LW, SW, andand convectiveconvective energy ffromrom internalinternal lloadsoads ttoo prprimaryimary variablesvariables are all surfacessurfaces forfor allall hours.hours. 66.. C Calculatealculate infiltrationinfiltration anandd didirect-to-spacerect-to-space ventventilationilation lloadsoads fforor allall T = outdoor face temperature, i = 11,2,…,12;,2,…,12; j = 1,2,…, 24 soi,j,jj hours.hours. T = indoor face temperature, i = 1,2,…,12; j = 1,2,…, 24 77.. Iterate the heat balance according to the following schemescheme:: sii,j,jj For Day = 1 to Maxdays In additionn, qsyssj = cooling load, j = 1,2,…, 2244 For j = 1 to 24 {hours in the day} Equations (17(17) and (24) are combined and solved for Tso to pro- For SurfaceIter = 1 to MaxIter duce 12 equations aapplicablepplicable in each time step: For i = 1 to 12 {The twelve zone surfaces} C Evaluate Equations (34) and (35) D nz nz nq Next i T = T Y  – T Z –   q soiji DB siiji – k iki B soiji – k ik, B iki k kok iji – k Next SurfaceIter Ek=1=1 k==11 k=1=1 Evaluate Equation (36) (25) Next j S If not converged, Next Day   T
Z  + h  + q  +++q + T Y  + To hco i 0 coiji soliji LWRiji siiji j i 0 j ij jU 8. Display results. where Generally, four or six surface iterationsiterations are sufficient to provide To = outdoor air temperature cconvergence.onvergence. TThehe converconvergencegence ccheckheck on tthehe ddayay iiterationteration sshouldhould bbee  hco = outdoor convection coefficient, introduced by using q conv = bbasedased on the difference between the indoor and outdoor conductivconductivee h (T – T ) co o so heat flux termss qk. A limit, such as requiringrequiring the difference betweebetweenn Equation (25) shows the need to separate Zi,0, because the con- all indoorindoor andand outdooroutdoor flfluxux ttermserms to bbee llessess thanthan 1% ooff eithereither flux,flux, ttributionribution ooff current sursurfaceface temperature to conconductiveductive flfluxux can be worksworks well.well. collected with the other tetermsrms involvininvolvingg that temperature.temperature. Equations (18) and (23) are combined and solved for Tsi toto propro-- INPUT REQUIRED dduceuce thethe next 12 equations:equations: Previous methods for calculating cooling loads attempted to sim- nz C plify the procedure by precalculating representative cases and Tsi = + B Tso Yiki, k ij, j E Tsi Yi, 0, 0 iji, – k grouping the results with various correlating parameters. This gen- iji, k––11 erally tended to reduce the amount of information required to apply nz nq (26) the procedure. With heat balance, no precalculations are made, so –B T Z ++++ B  q + T h + q the procedure requires a fairly complete description of the zone. siiji, – k iki, k iki, k kik ij, j – k aj ciij LWS k=1 k=1=1 Global Information. Because the procedure incorporatess a solar S ccalculation,alculation, some ggloballobal informationinformation is required,required, iincludingncluding latitudelatitude,, ++++ q + q + q e
Z + h  llongitude,ongitude, timetime zone,zone, montmonth,h, dayday ofof month,month, directionaldirectional orientationorientation LWXLWWX SWW solso U i, 0, 0 ciij, j of the zone, and zone height (floorr to floor). Additionally, to take where full advantage of the flexibility of the method to incorporate, for Ta = zone air temperature example, variable outdoor heat transfer coefficients, things such as hci = convective heat transfer coefficient indoors, obtained from  wind speed, wind direction, and terrain roughness may be specified. qconv = hci(Ta – Tsi) Normally,Normally, tthesehese variablesvariables anandd otothershers ddefaultefault to some reasonareasonableble set Note that in Equations (25) and (26), the opposite surface tempera- of values,values, bbutut tthehe flflexibilityexibility remains.remains. ture at tthehe current timetime appearappearss on thethe right-handright-hand sside.ide. TThehe two Wall Information (Each Wall). Because the walls are involved equationsequations couldcould bebe solvedsolved simultaneouslysimultaneously to eliminateeliminate thosethose varvari-i- inn three ofo the fundamental processess (external and internal heat bal- ables. Depending on the order of updating the other terms in thethe anceance and wall conductionconduction),), each wawallll of the zone requires a fairlfairlyy equations, this can have a benefbeneficialicial effect on solution stability. large set of variables. TheyT include The remaining equation comes from the air heat balance, Equa- The remaining equation comes from the air heat balance, Equa- • FacingFacing angleangle with respect to solar exposure ttionion (22).(22). ThisThis providesprovides thethe coolingcooling loadload q aatt each time step:step: sys ••T Tiltilt (degrees(degrees fromfrom horizontal)horizontal) 12 •Area•Area q = A h T – T  +++ q + q (27) ••So Solarlar absorptivityabsorptivity outoutdoorsdoors syssj B i cii siiji, aj CE IV i=1=1 • Long-wave emissivity outdoors • Short-wave absorptivitabsorptivityy indoors In Equation (27), the convective heatheat transfer term is expandedexpanded toto ••Lon Long-waveg-wave emissivityemissivity indoors showshow ththee intinterconnectionerconnection bebetweentween tthehe surface temperatures and the • ExteriorExterior boundaryboundary temperature conconditiondition ((solarsolar versus nonsononsolar)lar) coolingcooling load.load. • External roughnessroughness Overall HB Iterative Solution • Layer-by-layerLayer-by-layer constructionconstruction informationinformation The iterative HB procedure consists of a series of initial calcula- Again, some of these parameters can be defaulted, but they are ttionsions tthathat proceedproceed sequentially,sequentially, followedfollowed by a doubledouble iterationiteration loop,loop, changeable, and they indicate the more fundamental character of the as shown in the followinfollowingg stepssteps:: HB method because they are related ttoo true heatheat transfertransfer processesprocesses.. Window Information (Each Window). The situation for win- 1. Initialize areas, properties,properties, and face tempetemperaturesratures for all surfacessurfaces,, dows is similar to that for walls, but the windows requiree some addi- 24 h.h. tionaltional informationinformation because ooff ththeireir role in the solar load. NecessarNecessaryy 2. CalculateCalculate iincidentncident anandd transmtransmitteditted sosolarlar fluxflux forfor allall sursurfacesfaces anandd parametersparameters includeinclude hours.hours. 3. DDistributeistribute transmtransmitteditted sosolarlar eenergynergy to aallll iindoorndoor ffaces,aces, 24 hh.. •Area• Area 4. Calculate internal loadd quantities for all 24 h. • Normal solar transmissivity 18.20 2013 ASHRAE Handbook—Fundamentals

• NormaNormall SSHGCHGC RADIANT TIME SERIES (RTS) • Normal total absorptivitabsorptivityy METHOD •Lon• Long-waveg-wave emissivityemissivity outdoors The radiant time series (RTS) method is a simplified method for •Lon• Long-waveg-wave emissivitemissivityy indoor perperformingforming designdesign coolingcooling loadload calculationscalculations thatt is derived from the • Surface-to-surface thermal conductancconductancee heat balance (HB) method. It effeeffectivelyctively replaces all other simpli- • Reveal ((forfor solar shadinshading)g) ffiedied (non-heat-balance) methods, such as the transfer function •Over• Overhanghang widthwidth (for(for solarsolar shading)shading) method (TFM), the cooling load temperature difference/cooling • Distance from overhanoverhangg to window (for(for solar shading)shading) load factor (CLTD/CLF) method, and the total equivalent tempera- ture difference/time averaging (TETD/TA) method. Roof and Floor Details. The roof and floor surfaces are speci- TThishis method was developed to offofferer a method that is rigorous, yeyett fied similarly to walls. The main difference is that the ground out- ddoesoes not rerequirequire iterative calculatcalculations,ions, and that quantifiesquantifies each com- ddooroor bboundaryoundary conconditiondition wwillill proprobablybably bbee specspecifiedified more ooftenften fforor ponent’s contribution to the total cooling load. In addition, it isis a floor. ddesirableesirable for the user to be able to inspect and compare the coeffi- Thermal Mass Surface Details. An “extra” surface, called a ther- ccientsients for different construction andand zone ttypesypes in a form illustratinillustratingg mal mass surface, can serve several functions. It is included in radiant their relative effect on the result. These characteristics of the RTRTSS heat exchange with the other surfaces in the space but is only exposed method make it easierr to apply engineeringengineering judgment during cool- to the indoor air convective boundary condition. As an example, this iingng load calculationcalculation.. surface would be used to account for movable partitions in a space. The RTS method is suitable for ppeakeak desidesigngn load calculationscalculations,, Partition construction is specified layer by layer, similar to specifica- bubutt itit should notnot be used forfor annualannual energy simulations because of tion for walls, and those layers store and release heat by the same con- iitsts inherent limlimitingiting assumptions. AAlthough simple in concept, RTS duction mechanism as walls. As a general definition, the extra involves too many calculations for practical use as a manual thermal mass surface should be sized to represent all surfaces in the method, although it can easily be implementedimplemented in a simsimpleple comcomput-put- space thatthat are exposeexposedd to tthehe airair mass,mass, except thethe walls,walls, roof,roof, floor,floor, erized spreadsheet, as illustrated in the examples. For a manual and windows. In the formulation, bothboth sidessides ooff tthehe thermalthermal mass par- cooling load calculation method, refer to the CLTD/CLF method in ticipateticipate inin thethe exchange.exchange. Chapterr 28 of the 1997 ASHRAE Handbook—Fundamentals. Internal Heat Gain Details. The space can be subjected to sev- eral internal heat sources: people, lights, electrical equipment, and ASSUMPTIONS AND PRINCIPLES infiltration. Infiltration energy is assumed too go immediately into Design cooling loads are based on the assumption of steady- thethe airair heatheat balance,balance, so itit isis thethe leastleast complicatedcomplicated ofof thethe heatheat gains.gains. periodic conditions (i.e., the design day’s weather, occupancy, and For thethe others,others, severalseveral parameters must be specified. These include hheateat ggainain conconditionsditions are ididenticalentical ttoo tthosehose fforor preceprecedingding ddaysays sucsuchh the following fractions: tthathat thethe lloadsoads repeat on an identicalidentical 24 h ccyclicalyclical bbasis).asis). TThus,hus, tthehe heat gain for a particular componentt at a partparticularicular hhourour iiss tthehe samsamee • SensibleSensible heatheat gaingain as 24 h prior, which is the same as 48 h prior, etc. This assumption • Latent heat gaingain is the basis for the RTS derivation from the HB method. ••S Short-wavehort-wave radiationradiation Cooling load calculations must address two timtime-delaye-delay effectseffects ••Lon Long-waveg-wave radiationradiation iinherentnherent iinn bbuildinguilding heatheat transfertransfer processes:processes: ••Ener Energygy thatthat enters thethe airair iimmediatelymmediately as convectionconvection • DelayDelay ofof conductiveconductive hheateat ggainain tthroughhrough opaque massmassiveive exterexteriorior ••Act Activityivity levellevel ofof peoplepeople surfaces ((walls,walls, roofs, or floorsfloors)) ••Li Lightingghting heat gaingain that ggoesoes directlydirectly to the return air • Dela Delayy of radiative heat ggainain conversion to coolincoolingg loads.loads. Radiant Distribution Functions. As mentioned previously, the Exterior walls and roofs conduct heat because of temperature dif- generally accepted assumptions for the HB method includee specify- ferences between outdoor and indoor air. In addition, solar energy inging the distribution of radiant energy from several sources to sur-sur- on exterior surfaces is absorbed, then transferred by conduction to faces that enclose the space. This requires a distribution functionfunction the building interior. Because of the mass and thermal capacity of thatthat specifiesspecifies tthehe ffractionraction ooff totatotall raradiantdiant inputinput absorbedabsorbed byby eacheach sursur-- the wall or roof construction materials, there is a substantial time face.face. TThehe typestypes ofof radiationradiation thatthat requirerequire didistributionstribution ffunctionsunctions araree delay in heat input at the exterior surface becoming heat gain at the interior surface. ••Lon Long-wave,g-wave, from equipment and lightslights As described in the section on Cooling Load Principles, most • Short-wave, from lightslights heat sources transfer energy to a room by a combination of convec- tion and radiation. The convective part of heat gain immediately ••Tr Transmittedansmitted sosolarlar becomes cooling load. The radiative part must first be absorbed by Other Required Information. Additional flexibility is included tthehe finifinishesshes andand massmass ooff thethe intinteriorerior room surfacessurfaces,, and becomes in the model so that results of research can be incorporated easily. ccoolingooling loadload onlyonly whenwhen itit isis laterlater transferredtransferred byby convectionconvection fromfrom This includes the capability to specify such things as those surfaces to the room air. Thus,T , radiant heat gains become cool- iingng lloadsoads over a ddelayedelayed perperiodiod ofof time.time. ••H Heateat transfertransfer coefficients/convectioncoefficients/convection modelsmodels ••So Solarlar coecoefficientsfficients OVERVIEW • Sky modelsmodels Figure 8 gives an overview of the RTS method. When calculating solar radiation, transmitted solar heat gain through windows, sol-air The amount of input information required may seem extensive, temperature, and infiltration, RTS is exactly the same as previous but many parameters can be set to default values in most routine simplified methods (TFM and TETD/TA). Important areas that applications. However, all parameters listed can be changed when differ from previous simplified methods include necessary to fit unusual circumstances or when additional informa- tion is obtained. • ComputationComputation ofof conductiveconductive heatheat gaingain Nonresidential Cooling and Heating Load Calculations 18.21

Fig. 8 Overview of Radiant Time Series Method

• Splitting of all heat gains into radiant and convectiveconvective portions • ConversionConversion ofof radiantradiant heatheat gainsgains intointo coolingcooling lloadsoads The RTS method accounts for both conduction time delay and radiant time deladelayy effects bbyy multmultiplyingiplying hourlhourlyy heat ggainsains bbyy 24 h time series. The time series multimultiplication,plication, in effect, distributes heatheat gagainsins over time.time. SeriesSeries coefficients,coefficients, wwhichhich are cacalledlled radiantradiant timetime factorsfactors andand conductconductionion ttimeime factorsfactors, are dderivederived ususinging tthehe HB method.method. RadiantRadiant timetime factorsfactors reflectreflect the percentagepercentage of an earlier radiantradiant heatheat gaingain tthathat bbecomesecomes coocoolingling lloadoad dduringuring tthehe current hhour.our. Likewise,Likewise, conconductionduction ttimeime ffactorsactors rereflectflect tthehe percentage ooff an ear- lier heat gaingain at the exterior of a wall or roof that becomes heat gaingain indoorsindoors dduringuring tthehe current hhour.our. BByy ddefinition,efinition, eaceachh raradiantdiant or con-con- ductionduction timetime seriesseries must totaltotal 100%.100%. These series can be used to easily compare the time-delay effect ofof one constructconstructionion versus anotanother.her. TThishis abilityability to compare cchoiceshoices isis ooff partparticularicular bbenefitenefit dduringuring dedesign,sign, wwhenhen aallll constructconstructionion detailsdetails maymay not have been decided. CComparisonomparison can illustrate the magnitudemagnitude ooff diffdifferenceerence bbetweenetween tthehe cchoices,hoices, aallowingllowing tthehe engengineerineer Fig. 9 CTS for Light to Heavy Walls to applyapply jjudgmentudgment anandd mamakeke more iinformednformed assumptassumptionsions inin estimat-estimat- inging the load.load. Figure 9 illustrates conduction time series (CTS) values for three 2. Split heat gainsgains into radiant andand convective parts (see(see Table 14 walls with similar U-factors but with light to heavy construction. for radiant and convective fractionsfractions).). Figure 10 illustrates CTS for three walls with similar construction 3. ApplyApply appropriate radiant time series to radiant part of heat gainsgains but with different amounts of insulation, thus with significantly dif- to account for time delay in conversion to cooling load. ferentt U-factors. Figure 11 illustrates RTS values for zones varying 4.4. Sum convectconvectiveive part ooff hheateat gagainin anandd ddelayedelayed radiantradiant part ofof heatheat from light to heavy construction. gaingain to determinedetermine coolingcooling loadload forfor eacheach hourhour forfor eacheach coolingcooling loadload component.component. RTS PROCEDURE After calculating cooling loads for each component for each The general procedure for calculating cooling load for each load hour,hour, sum thosethose to determinedetermine thethe totaltotal coolingcooling loadload forfor eacheach hourhour andand component (lights, people, walls, roofs, windows, appliances, etc.) select the hour with the peak loadload for designdesign of the air-conditioninair-conditioningg with RTS is as follows: system.system. Repeat this process for mumultipleltiple desidesigngn monmonthsths ttoo determinedetermine thethe montmonthh wwhenhen tthehe peapeakk lloadoad ococcurs,curs, especespeciallyially wwithith wwindowsindows oonn 1. Calculate 24 h profile of componentcommponent heat gains for design day southern exposures ((northernnorthern exposexposureure in southern latitudeslatitudes),), whicwhichh (for(for conconduction,duction, fifirstrst accounaccountt fforor conconductionduction ttimeime ddelayelay by cancan resultresult iinn hihighergher peapeakk room ccoolingooling lloadsoads iinn wwinterinter monthsmonths thanthan applyingapplying conductionconduction ttimeime serseries).ies). inin summer.summer. 18.22 2013 ASHRAE Handbook—Fundamentals

Table 14 Recommended Radiative/Convective Splits for Internal Heat Gains Recommended Recommended Heat Gain Type Radiative Fraction Convective Fraction Comments Occupants, typical office conditions 0.60 0.40 See Table 1 for other conditions. Equipment 0.1 to 0.8 0.9 to 0.2 See Tables 6 to 12 for details of equipment heat gain and recommended Office, with fan 0.10 0.90 radiative/convective splits for motors, cooking appliances, laboratory Without fan 0.30 0.70 equipment, medical equipment, office equipment, etc. Lighting Varies; see Table 3. Conduction heat gain Through walls and floors 0.46 0.54 Through roof 0.60 0.40 Through windows 0.33 (SHGC > 0.5) 0.67 (SHGC > 0.5) 0.46 (SHGC < 0.5) 0.54 (SHGC < 0.5) Solar heat gain through fenestration Without interior shading 1.00 0.00 With interior shading Varies; see Tables 13A to 13G in Chapter 15. Infiltration 0.00 1.00 Source: Nigusse (2007).

iintonto ththee susurfacerface as wouwouldld ththee cocombinationmbination ooff inincidentcident sosolarlar rradia-adia- ttion,ion, radiant enerenergygy exchangeexchange with the skskyy and other outdoor sur-sur- roundinroundings,gs, and convective heat exchangeexchange with outdoor air. Heat Flux into Exterior Sunlit Surfaces. The heat balance at a sunlit surface gives the heat flux into the surface q/A as

q --- = E + h (t – t ) –   R (28) A t o o s

wherewhere  = absorptance of surface for solar radiation 2 Et = total solar radiation incident on surface, Btu/h·ftBtu/h·fft ho = coefficient of heat transfer by long-wave radiation and convection at outer surface, Btu/h·ftBtu/h·fft2·°F to =out outdoordoor airair temperature, °F°F ts =sur surfaceface temperature, °F =hemispherical emittance of surface R = differencedifference bbetweenetween llong-waveong-wave raradiationdiation iincidentncident oonn surfacesurface fromfrom sky andand surroundingssurroundings andand radiationradiation emitted by blackbody at Fig. 10 CTS for Walls with Similar Mass and outdoor air temperature, Btu/h·ftBtu/h·fft2 Increasing Insulation Assuming the rate of heat transfer can be expressed in terms of the sol-air temperature te,

q --- = h (t – t ) (29) A o e s

and from Equations (28) and (29),  Et  R te = to + ------– ------(30) ho ho

For horizontal surfaces that receive long-wave radiation from the sky only,, an appropriate value of R is about 20 Btu/h·ftBtu/h·fft2, so that if  = 1 and h = 3.0 Btu/h·ftBtu/h·fft2·°F, thethe long-wavelong-wave correctioncorrection term is Fig. 11 RTS for Light to Heavy Construction o aboutabout 7°F (Bliss(Bliss 1961).1961). Because vertical surfaces receive long-wave radiation from the HEAT GAIN THROUGH EXTERIOR SURFACES ground and surrounding buildings as well as from the sky, accurate Heat gain through exterior opaque surfaces is derived from the R values are difficult to determine. When solar radiation intensity same elements of solar radiation and thermal gradient as that for is high, surfaces of terrestrial objects usually have a higher temper- fenestrationfenestration areas. It diffdiffersers primarilyprimarily as a ffunctionunction ooff tthehe mass andand ature than the outdoor air; thus, their long-wave radiation compen- nnatureature ooff ththee wawallll oorr rroofoof cconstruction,onstruction, because those elementselements sates to some extent for the sky’s low emittance. Therefore, it is aaffectffect ththee rrateate ooff coconductivenductive hheateat transfer through the compositcompositee common practice to assume  R = 0 for vertical surfaces. assemassemblybly to tthehe interiorinterior surface.surface. Tabulated Temperature Values. The sol-air temperatures in Example Cooling and Heating Load Calculations section have been Sol-Air Temperature  calculated based on R/ho values of 7°F for horizontal surfaces Sol-air temperature is the outdoor air temperature that, in the andand 0°F forfor verticalvertical surfaces;surfaces; totaltotal solarsolar intensityintensity valuesvalues usedused fforor tthehe absence of all radiation changes givesgives thethe same rate ofof heatheat entryentry calculations were calculated using equations in Chapter 14. Nonresidential Cooling and Heating Load Calculations 18.23

Table 15 Solar Absorptance Values of Various Surfaces rrespectiveespective overaoverallll wawallll or roorooff U-U-factorfactor to formform thethe conductionconduction timetime seseries.ries. TheThe conductionconduction timetime factorsfactors cancan thenthen be used in Equation Surface Absorptance (32) and provide a way to comparecompare timetime delaydelay chcharacteraracteristicsistics Brick, red (Purdue) a 0.63 bbetweenetween diffdifferenterent wawallll anandd roorooff constructconstructions.ions. ConstructConstructionion mate- Paint b ririalal datadata useusedd iinn thethe calculcalculationsations for walls and roofs in TTables 16 and Red 0.63 17 are listed in Table 18. Black, matteb 0.94 Sandstoneb 0.50 Heat gains calculated for walls or roofs using periodic response White acrylica 0.26 factors (and thus CTS) are identiidenticalcal to tthosehose cacalculatedlculated ususinging con- Sheet metal, galvanized ducductiontion trtransferansfer ffunctionsunctions fforor ththee steadsteadyy periodic conditions assumeassumedd Newa 0.65 iinn desidesigngn coolingcooling load calculcalculations.ations. The methodology for calculating Weathereda 0.80 periodic response factors from conduction transfer functions was Shingles 0.82 originally developed as part of ASHRAE research project RP-875 Grayb b (Spitler and Fisher 1999b; Spitler et al. 1997). For walls and roofs Brown 0.91 that are not reasonably close to the representative constructions inin Blackb 0.97 Whiteb 0.75 TTablesables 16 and 17, CTS coefficients may be computed with a com- Concretea,c 0.60 to 0.83 puter program such as that described by Iu and Fisher (2004). For aIncropera and DeWitt (1990). walls and roofs with thermal bridges, the procedure described by bParker et al. (2000). Karambakkam et al. (2005) may be uusedsed to determine an equivalentequivalent cMiller (1971). wwallall construction,construction, which can then be used as the basis for findingfinding the CCTSTS coefficients. When considerinconsideringg the level of detail needed to Surface Colors. Sol-air temperature values are given in the mmakeake an aadequatedequate approxapproximation,imation, rememrememberber tthat,hat, fforor bbuildingsuildings wwithith Example Cooling and Heating Load Calculations section for two wiwindowsndows anandd iinternalnternal hheateat gagains,ins, tthehe conconductionduction hheateat gagainsins mamakeke upup  values of the parameter /ho; the value of 0.15 is appropriate for a a rerelativelylatively smallsmall part ofof thethe coolingcooling load.load. For heatingheating loadload calcula-calcula- lilight-coloredght-colored surface, whereas 0.300.30 represents the usual maximummaximum titions,ons, thethe conductionconduction heatheat lossloss maymay bebe more significant.significant. vavaluelue forfor thisthis parameter (i.e.,(i.e., foforr a ddark-coloredark-colored sursurfaceface or ananyy The tedious calculations involved make a simple computer sursurfaceface fforor wwhichhich tthehe permanent lilightnessghtness cannot rereliablyliably bbee antantic-ic- spreadsheet or other computer software a useful labor saver. ipated). Solar absorptance values of various surfaces are included in Table 15. HEAT GAIN THROUGH INTERIOR SURFACES This procedure was used to calculate the sol-air temperatures included in the Examples section. Because of the tedious solar angle Whenever a conditioned space is adjacent to a space with a dif- and intensity calculations, using a simple computer spreadsheet or ferent temperature, heat transfer through the separating physical other software for these calculations can reduce the effort involved. section must be considered. The heat transfer rate is given by

Calculating Conductive Heat Gain Using Conduction q = UA(tb – ti) (33) Time Series where In the RTS method, conduction through exterior walls and roofs q = heat transfer rate, Btu/h is calculated usingg CTS values. Wall and roof conductive heat input U = coefficient of overall heat transfer between adjacent and at the exterior is defined by the familiar conduction equation as conditioned space, Btu/h·ft2·°F A = area of separating section concerned, ft2 qi,, -n = UAUA(te, -n – trc) (31) tb = average air temperature in adjacent space, °F t = air temperature in conditioned space, °F wherewhere i qi,, n ==con conductiveductive heatheat inputinput forfor surfacesurface n hours ago, Btu/h U-values can be obtained from Chapter 27. Temperature tb may 2 U = overall heat transfer coefficient for surface, Btu/h·ftBtu/h·fft ·°F·°F differ greatlygreatly from ti. The temperature in a kitchen or boiler room, A = surface area, ft2 fforor example, mamayy be as much as 15 to 50°F above the outdoor air te, -n = sol-air temperature n hourshours aago,go, °F ttemperature.emperature. ActuaActuall temperaturetemperaturess iinn aadjoiningdjoining spaces shouldshould bebe trc = presumed constant room air temperature, °F measured, when possible. Where nothingnotthing is known except that the Conductive heat gain through walls or roofs can be calculated adjadjacentacent space iiss ofof conventionalconventional construction,construction, containscontains no hheateat using conductive heat inputs for the current hours and past 23 h and ssources,ources, andand itselfitself receives no significant solar heat gain, tb – ti may conduction time series: be consideredconsidered thethe differencedifference betweenbetween thethe outdooroutdoor airair andand condi-condi- titionedoned space ddesignesign ddry-bulbry-bulb temperatures mminusinus 5°F. In somsomee … q = c0qi,, + c1qi,, --1 + c2qi,, --2 + c3qi,, --3 + + c2323qi,, --23 (32) ccases,ases, airair temperature inin thethe adjacentadjacent space correspondscorresponds to thethe out- ddooroor air temperature or higher.higher. wherewhere q =h hourlyourly conductiveconductive heatheat gaingain forfor surface,surface, Btu/hBtu/h Floors qi,, = heat input for current hour For floors directly in contact with the ground or over an under- qi,, -n = heatheat inputinput n hhoursours ago ground basement thatt is neither ventilatedventilated nornor conditioned,conditioned, senssensibleible c0, c1, etc. = conduction time factors heatheat transfertransfer may bebe neglectedneglected foforr coocoolingling loadload estimatesestimates becausebecause Conduction time factors for representative wall and roof types usuallyusually therethere isis a heatheat llossoss ratratherher ththanan a gagain.in. An exceptexceptionion iiss iinn hhotot are included in Tables 16 and 17. Those values were derived by first climatesclimates ((i.e.,i.e., where averageaverage outdoor air temperature exceedexceedss cacalculatinglculating conconductionduction transtransferfer ffunctionsunctions fforor eaceachh examexampleple wawallll anandd indoorindoor designdesign condition),condition), wherewhere thethe positivepositive soil-to-indoorsoil-to-indoor temtemper-per- roorooff construction.construction. AssumAssuminging stesteady-periodicady-periodic heatheat inputinput conditionsconditions atureature differencedifference causescauses sensiblesensible heatheat gainsgains (Rock(Rock 20052005).). In manmanyy for desidesigngn load calculacalculationstions aallowsllows coconductionnduction trtransferansfer ffunctionsunctions ttoo climatesclimates aandnd fforor vavariousrious temperatures and local soil conditionsconditions,, bbee reformulatedreformulated intointo periodicperiodic responseresponse factors,factors, as demonstrated by moisturemoisture transport up tthroughhrough sslabs-on-gradelabs-on-grade andand basementbasement floorsfloors is Spitler and Fisher (1999a). The periodic response factors were fur- alsoalso significant,significant, anandd ccontributesontributes to thethe latentlatent heatheat portionportion ofof thethe ther simplified by dividing the 24 periodic response factors bbyy ththee coolingcooling load.load. 18.24 2013 ASHRAE Handbook—Fundamentals

Table 16 Wall Conduction Time Series (CTS) Curtain Walls Stud Walls EIFS Brick Walls Wall Number = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 U-Factor, Btu/h·fBtu/h·ftft2·°F·°F 00.075.075 0 0.076.0760 0.075.075 0 0.074.0740 0.074.0740 0.071.0710 0.073.073 0 0.118.118 0.0540.0540 0.092.092 0.1010.101 0.0660.066 0.0500.0500 0.102.102 0.0610.061 0.1110.111 0.1240.124 0.0910.091 0.1020.102 0.0680.068 TTotalotal R 13.3 13.2 13.3 13.6 13.6 14.0 13.8 8.58.518.610.8 18.6 10.8 9.9 15.1 20.1 9.8 16.3 9.08.1 11.0 9.8 14.6 Mass, lb/flb/ftft2 6.34.3 16.4 5.2 17.3 5.2 13.7 7.5 7.8 26.8 42 42.9.944 44.0.044 44.2.2 5 59.69.662 62.3.3 7 76.26.280 80.2.296 96.2.2182 182.8.8 136136.3.3 Thermal Capacity,p 1.5 1.0 3.3 1.2 3.6 1.6 3.0 1.8 1.9 5.9 8.7 8.7 8.7 11.7 12.4 15.7 15.3 19.0 38.4 28.4 Btu/ftBtu/fft2·°F·°F Hour Conduction Time Factors, % 0018258196751121000122134318 25 8 19 6 7 5 11 2 1 0 0 0 1 2 2 1 3 4 3 1 58 585745594244415025257 45 59 42 44 41 50 25 2 5 4 1 1 2 2 1 3 4 3 2 20 20153218333234263161413715 32 18 33 32 34 26 31 6 14 13 7 2 2 2 3 3 4 3 3 4 3 11 3 13 12 13 9 20 9 17 17 12 5 3 4 6 3 4 4 4 0 0 3 31444311915151385573441 4 4 4 3 11 9 15 15 13 8 5 5 7 3 4 4 5 0 0 1 1011215912121396684440 1 1 2 1 5 9 12 12 13 9 6 6 8 4 4 4 6 0 0 0 00101038991197684450 1 0 1 0 3 8 9 9 11 9 7 6 8 4 4 5 7 0 0 0 0000002777997785450 0 0 0 0 2 7 7 7 9 9 7 7 8 5 4 5 8 0 0 0 0000001655787785450 0 0 0 0 1 6 5 5 7 8 7 7 8 5 4 5 9 0 0 0 0000000644677675450 0 0 0 0 0 6 4 4 6 7 7 6 7 5 4 5 101000 0 0 0000000533576665450 0 0 0 0 0 5 3 3 5 7 6 6 6 5 4 5 111100 0 0 0000000522466665550 0 0 0 0 0 5 2 2 4 6 6 6 6 5 5 5 121200 0 0 0000000422355555550 0 0 0 0 0 4 2 2 3 5 5 5 5 5 5 5 131300 0 0 0000000412245545550 0 0 0 0 0 4 1 2 2 4 5 5 4 5 5 5 141400 0 0 0000000312245545550 0 0 0 0 0 3 1 2 2 4 5 5 4 5 5 5 151500 0 0 0000000311134435440 0 0 0 0 0 3 1 1 1 3 4 4 3 5 4 4 161600 0 0 0000000311134435440 0 0 0 0 0 3 1 1 1 3 4 4 3 5 4 4 171700 0 0 0000000211123434440 0 0 0 0 0 2 1 1 1 2 3 4 3 4 4 4 181800 0 0 0000000200123324440 0 0 0 0 0 2 0 0 1 2 3 3 2 4 4 4 191900 0 0 0000000200123324440 0 0 0 0 0 2 0 0 1 2 3 3 2 4 4 4 202000 0 0 0000000200013324440 0 0 0 0 0 2 0 0 0 1 3 3 2 4 4 4 212100 0 0 0000000100012214440 0 0 0 0 0 1 0 0 0 1 2 2 1 4 4 4 222200 0 0 0000000100012214430 0 0 0 0 0 1 0 0 0 1 2 2 1 4 4 3 232300 0 0 0000000000001113430 0 0 0 0 0 0 0 0 0 0 1 1 1 3 4 3 Total Percentage 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Layer ID from F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 outdoors to indoors F09 F08 F10 F08F10 F11 F07 F06 F06 F06M01M01M01M01M01M01M01M01M01M01 F06 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 (see Table 18) F04 F04 F04 G03G03 G02 G03I01 I01 I01 F04 F04 F04 F04 F04 F04 F04 F04 F04 F04 I02 I02 I02 I04 I04 I04 I04 G03 G03 G03 I01 G03 I01 I01 M03 I01 I01 I01 I01 M15 F04 F04 F04 G01 G01 G04 G01 F04 I04 M03 G03 I04 G03 M03 I04 M05 M01 M13 M16 I04 G01 G01 G01 F02 F02 F02 F02 G01 G01 F04 F04 G01 I04 F02 G01 G01 F02 F04 F04 G01 F02 F02F02 — — — — F02 F02 G01 G01F02 G01— F02 F02 — G01 G01 F02 — — — ———————F02F02—F02————F02F02—— — — — — — F02 F02 — F02 — — — — F02 F02 — Wall Number Descriptions 1. Spandrel glass, R-10 insulation board, gyp board 11. Brick, R-5 insulation board, sheathing, gyp board 2. Metal wall panel, R-10 insulation board, gyp board 12. Brick, sheathing, R-11 batt insulation, gyp board 3. 1 in. stone, R-10 insulation board, gyp board 13. Brick, R-5 insulation board, sheathing, R-11 batt insulation, gyp board 4. Metal wall panel, sheathing, R-11 batt insulation, gyp board 14. Brick, R-5 insulation board, 8 in. LW CMU 5. 1 in. stone, sheathing, R-11 batt insulation, gyp board 15. Brick, 8 in. LW CMU, R-11 batt insulation, gyp board 6. Wood siding, sheathing, R-11 batt insulation, 1/2 in. wood 16. Brick, R-5 insulation board, 8 in. HW CMU, gyp board 7. 1 in. stucco, sheathing, R-11 batt insulation, gyp board 17. Brick, R-5 insulation board, brick 8. EIFS finish, R-5 insulation board, sheathing, gyp board 18. Brick, R-5 insulation board, 8 in. LW concrete, gyp board 9. EIFS finish, R-5 insulation board, sheathing, R-11 batt insulation, gyp board 19. Brick, R-5 insulation board, 12 in. HW concrete, gyp board 10. EIFS finish, R-5 insulation board, sheathing, 8 in. LW CMU, gyp board 20. Brick, 8 in. HW concrete, R-11 batt insulation, gyp board

CALCULATING COOLING LOAD HeatHeat balance proceduresprocedures calculatecalculate the radiant exchangeexchange be- tweentween surfacessurfaces based onon theirtheir surfacesurface temperatures and emissivi-emissivi- The instantaneous cooling load is the rate at which heat energy ties,ties, butbut theythey typicallytypically relyrely onon estimatedestimated “radiative/convective“radiative/convective is coconvectednvected ttoo thethe zonezone airair aatt a given point in time. Computation of splits”splits” to determine the contributicontributionon of internal loads, includinincludingg cooling load is complicated by thethe radiantradiant exchangeexchange betweenbetween people, lighting, appliances, and equipment,equipment, to the radiant ex-ex- surfaces,surfaces, furniture,furniture, partitions,partitions, andand otherother massmass inin thethe zone.zone. MostMost heat change. RTS further simplifies thethe HB procedureprocedure by alsoalso relyingrelying gaingain sources transfer energyenergy byby bothboth coconvectionnvection aandnd rradiation.adiation. RRadi-adi- onon anan estimatedestimated rradiative/convectiveadiative/convective ssplitplit of wall and roof conduc- ativeative heatheat transfertransfer introducesintroduces a timetime dependencydependency to thethe process thatthat tivetive heatheat gagainin iinsteadnstead ooff ssimultaneouslyimultaneously sosolvinglving fforor tthehe iinstanta-nstanta- isis not easilyeasily quantified.quantified. RadiationRadiation isis absorbedabsorbed byby thermalthermal masses in neous convectiveconvective andand rradiativeadiative hheateat transfer from each surface, asas thethe zonezone aandnd thenthen laterlater transferredtransferred bbyy convection into the space. ThiThiss inin thethe HB procedure.procedure. processprocess creates a time laglag and dadampeninmpeningg effect. The convectiveconvective Thus, the cooling load for each load component (lights, people, portion, on the other hand, is assumedassuumed toto immediatelyimmediately becomebecome cool-cool- walls, roofs, windows, appliances, etc.) for a particular hour is the inging load in the hour in which that heat ggainain occursoccurs.. sumsum ofof thethe convectiveconvective portionportion ofof thethe heatheat gaingain forfor thatthat hourhour plusplus thethe Nonresidential Cooling and Heating Load Calculations 18.25

Table 16 Wall Conduction Time Series (CTS) (Concluded) Concrete Block Wall Precast and Cast-in-Place Concrete Walls Wall Number = 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 U-Factor, Btu/h·fBtu/h·ftft2·°F·°F 0.067 0.059 0.073 0.186 0.147 0.121 0.118 0.074 0.076 0.115 0.068 0.082 0.076 0.047 0.550 TotalTotal R 14.8 16.9 13.7 5.4 6.8 8.2 8.4 13.6 13.1 8.7 14.7 12.2 13.1 21.4 1.8 Mass, lb/ftlb/fft2 22.3 22.3 46.0 19.3 21.9 34.6 29.5 29.6 53.8 59.8 56.3 100.0 96.3 143.2 140.0 Thermal Capacity,p 4.8 4.8 10.0 4.1 4.77.4 6.1 6.1 10.812.1 11.4 21.6 20.8 30.9 30.1 Btu/fBtu/ftft2·°F·°F Hour Conduction Time Factors, % 000101011012131210 1 0 1 0 1 1 0 1 2 1 3 1 2 1 11412113110812232224 1 2 11 3 1 10 8 1 2 2 3 2 2 2 221358211222018333453413 5 8 21 12 2 20 18 3 3 3 4 5 3 4 3316912201651818656583716 9 12 20 16 5 18 18 6 5 6 5 8 3 7 44141112151571414867695814 11 12 15 15 7 14 14 8 6 7 6 9 5 8 55111011101291011968695811 10 11 10 12 9 10 11 9 6 8 6 9 5 8 6699971097896868689 9 9 7 10 9 7 8 9 6 8 6 8 6 8 777885885696757687 8 8 5 8 8 5 6 9 6 7 5 7 6 8 886773684486756676 7 7 3 6 8 4 4 8 6 7 5 6 6 7 994662473376656664 6 6 2 4 7 3 3 7 6 6 5 6 6 6 10103552362275655663 5 5 2 3 6 2 2 7 5 6 5 5 6 6 11113441362265555553 4 4 1 3 6 2 2 6 5 5 5 5 5 5 12122431251255544542 4 3 1 2 5 1 2 5 5 5 4 4 5 4 13132321241145444542 3 2 1 2 4 1 1 4 5 4 4 4 5 4 14142320141144443442 3 2 0 1 4 1 1 4 4 4 4 3 4 4 15151320131134343431 3 2 0 1 3 1 1 3 4 3 4 3 4 3 16161210130124343431 2 1 0 1 3 0 1 2 4 3 4 3 4 3 17171210120023342431 2 1 0 1 2 0 0 2 3 3 4 2 4 3 18181210020013242421 2 1 0 0 2 0 0 1 3 2 4 2 4 2 19190110020013232320 1 1 0 0 2 0 0 1 3 2 3 2 3 2 20200110020013232320 1 1 0 0 2 0 0 1 3 2 3 2 3 2 21210110020013232310 1 1 0 0 2 0 0 1 3 2 3 2 3 1 22220110010013231310 1 1 0 0 1 0 0 1 3 2 3 1 3 1 23230100010012221310 1 0 0 0 1 0 0 1 2 2 2 1 3 1 Total Percentage 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Layer ID from F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 outdoors to indoors M03M08F07M08M08M09M11M11M11F06M13F06M15M16M16M03 M08 F07 M08 M08 M09 M11 M11 M11 F06 M13 F06 M15 M16 M16 (see Table 18) I04I04M05F02F04F04I01I04I02I01I04I02I04I05F02I04 I04 M05 F02 F04 F04 I01 I04 I02 I01 I04 I02 I04 I05 F02 G01 G01 I04 — G01 G01 F04 G01 M11 M13 G01 M15 G01 G01 — F02 F02 G01 — F02 F02 G01 F02 F02 G01 F02 G01 F02 F02 — ——F02———F02——F02—F02———— — F02 — — — F02 — — F02 — F02 — — — Wall Number Descriptions 21. 8 in. LW CMU, R-11 batt insulation, gyp board 29. 4 in. LW concrete, R-10 board insulation, 4 in. LW concrete 22. 8 in. LW CMU with fill insulation, R-11 batt insulation, gyp board 30. EIFS finish, R-5 insulation board, 8 in. LW concrete, gyp board 23. 1 in. stucco, 8 in. HW CMU, R-11 batt insulation, gyp board 31. 8 in. LW concrete, R-11 batt insulation, gyp board 24. 8 in. LW CMU with fill insulation 32. EIFS finish, R-10 insulation board, 8 in. HW concrete, gyp board 25. 8 in. LW CMU with fill insulation, gyp board 33. 8 in. HW concrete, R-11 batt insulation, gyp board 26. 12 in. LW CMU with fill insulation, gyp board 34. 12 in. HW concrete, R-19 batt insulation, gyp board 27. 4 in. LW concrete, R-5 board insulation, gyp board 35. 12 in. HW concrete 28. 4 in. LW concrete, R-11 batt insulation, gyp board time-delayedtime-delayed portion of radiant heat ggainsains for that hour and the prepre-- … Qr, = r0qr, + r1qr, –1– + r2qr, –2– + r3qr, –3– + + r2323qr, –23– (34)(34) vviousious 23 h.h. TableTable 14 containscontains recommendationsrecommendations for splitting each of the heat gaingain components into convective and radiant portions.portions. wherewhere

RTS converts the radiant portion of hourly heat gains to hourly Qr,, = radiant cooling load Qr for current hour , Btu/hBtu/h ccoolingooling loads using radiant time factors,factors, the coefficients of the radi- qr, = radiant heat gain for current hour, Btu/h aantnt time series. Radiant time factors are used to calculate the coolingcooling qr,, n ==ra radiantdiant heatheat gaingain n hourshours ago,ago, Btu/hBtu/h r , r , etc.=radiant time factors lloadoad forfor tthehe current hourhour on thethe basisbasis ofof current andand past heatheat gains.gains. 0 1 TThehe radiantradiant timetime seriesseries forfor a particularparticular zone gigivesves tthehe ttime-ime- The radiant cooling load for the current hour, which is calculated ddependentependent response of the zone to a sinsinglegle pulse of radiant energy.energy. using RTS and Equation (34), is aaddeddded to the convective portion toto TThehe seriesseries showsshows thethe portionportion ofof thethe radiantradiant pulsepulse thatthat isis convectedconvected to determine the total cooling load for that component for that hour. zone air for each hour. Thus, r0 represents the fraction of the radiant Radiant time factors are generated by a heat-balance-based pro- ppulseulse convecteconvectedd to tthehe zonzonee air in the current hourr r1 in the previous cedure. A separate series of radiant time factors is theoretically hourhour,, and so on. The radiant time series thus generatedgenerated is used toto rrequiredequired for each unique zone and for each unique radiant energenergyy convert tthehe raradiantdiant portportionion ooff hourlyhourly heatheat gainsgains to hourlyhourly coolingcooling didistributionstribution ffunctionunction assumptassumption.ion. For most common ddesignesign appapplica-lica- lloadsoads accoraccordingding to thethe ffollowingollowing equatequation:ion: titions,ons, RTS varvariationiation ddependsepends pprimarilyrimarily on tthehe overaoverallll massmassivenessiveness 18.26 2013 ASHRAE Handbook—Fundamentals

Table 17 Roof Conduction Time Series (CTS) Sloped Frame Roofs Wood Deck Metal Deck Roofs Concrete Roofs Roof Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 U-Factor, 0.044 0.040 0.045 0.041 0.042 0.041 0.069 0.058 0.080 0.065 0.057 0.036 0.052 0.054 0.052 0.051 0.056 0.055 0.042 Btu/h·ftBtu/h·fft2·°F·°F Total R 22.8 25.0 22.2 24.1 23.7 24.6 14.5 17.2 12.6 15.4 17.6 27.6 19.1 18.6 19.2 19.7 18.0 18.2 23.7 Mass, lb/ftlb/fft2 5.54.3 2.9 7.1 11.4 7.1 10.0 11.5 4.9 6.3 5.1 5.6 11.8 30.6 43.9 57.2 73.997.2 74.2 Thermal Capacity,p 1.30.8 0.6 2.3 3.6 2.3 3.7 3.9 1.4 1.6 1.4 1.6 2.8 6.6 9.3 12.0 16.321.4 16.2 Btu/fBtu/ftft2·°F·°F Hour Conduction Time Factors, % 0 6 61027111010 27 1 1 1 0 1 118481018 4 8 1 0 11222312 2 2 3 1 11455762171712745 57 62 17 17 12 7 361415323102222323 61 41 53 23 10 2 2 2 2 3 2 22332710313425188183530382283353633 27 10 31 34 25 18 8 18 35 30 38 22 8 3 3 5 3 6 331151242522181031472220116465811 5 1 24 25 22 18 10 3 14 7 22 20 11 6 4 6 5 8 4 3101413151510042101411757683 1 0 14 13 15 15 10 0 4 2 10 14 11 7 5 7 6 8 5 1 100761011901041010 0 7 6 10 11 9 0 1 0 4 10 100867688 6 7 6 8 6 1 1004360 0 4 3 6 8 8010278 0 1 0 2 7 99866678 6 6 6 7 7 0 0002140 0 2 1 4 6 7000057 0 0 0 0 5 77766677 6 6 6 7 8 0 0000020 0 0 0 2 5 6000046 0 0 0 0 4 66766667 6 6 6 6 9 0 0000010 0 0 0 1 3 5000035 0 0 0 0 3 55665556 6 5 5 5 1000000110 0 0 0 0 0 1 3 5000025 0 0 0 0 2 55565555 6 5 5 5 1100000111 0 0 0 0 0 1 2 4000014 0 0 0 0 1 44555555 5 5 5 5 1200000012 0 0 0 0 0 0 1 4000014 0 0 0 0 1 33554545 5 4 5 4 1300000013 0 0 0 0 0 0 1 3000013 0 0 0 0 1 33454444 5 4 4 4 1400000014 0 0 0 0 0 0 1 3000003 0 0 0 0 0 33444434 4 4 4 3 1500000015 0 0 0 0 0 0 1 3000003 0 0 0 0 0 22344433 4 4 4 3 1600000016 0 0 0 0 0 0 0 2000002 0 0 0 0 0 22343433 4 3 4 3 1700000017 0 0 0 0 0 0 0 2000002 0 0 0 0 0 22343433 4 3 4 3 1800000018 0 0 0 0 0 0 0 2000002 0 0 0 0 0 11333323 3 3 3 2 1900000019 0 0 0 0 0 0 0 2000002 0 0 0 0 0 11233322 3 3 3 2 2000000020 0 0 0 0 0 0 0 1000001 0 0 0 0 0 11233322 3 3 3 2 2100000021 0 0 0 0 0 0 0 1000001 0 0 0 0 0 11233322 3 3 3 2 2200000022 0 0 0 0 0 0 0 1000001 0 0 0 0 0 11232222 3 2 2 2 2300000023 0 0 0 0 0 0 0 0000000 0 0 0 0 0 11122221 2 2 2 2 Total Percentage 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Layer ID F01 F01 F01 F01 F01 F01F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 F01 from outdoors to F08 F08 F08 F12 F14 F15 F13 F13 F13 F13 F13 F13M17 F13F13 F13F13 F13 F13 indoors G03 G03 G03 G05G05 G05 G03 G03 G03 G03 G03 G03 F13 G03 G03 G03 G03 G03 M14 (see Table 18) F05 F05 F05 F05 F05 F05 I02 I02 I02 I02 I03 I02 G03 I03 I03 I03 I03 I03 F05 I05 I05 I05 I05 I05 I05 G06 G06F08 F08 F08 I03 I03 M11 M12 M13 M14 M15 I05 G01 F05 F03 F05 F05 F05F03 F05 F03 F05F03 F08F08 F03F03 F03 F03 F03F16 F03 F16 — G01 G01 G01 — F16 — F16 — — F03 — — — — — F03 ——F03—F03F03F03—F03—F03—————————F03 — F03 F03 F03 — F03 — F03 — — — — — — — — — Roof Number Descriptions 1. Metal roof, R-19 batt insulation, gyp board 11. Membrane, sheathing, R-15 insulation board, metal deck 2. Metal roof, R-19 batt insulation, suspended acoustical ceiling 12. Membrane, sheathing, R-10 plus R-15 insulation boards, metal deck 3. Metal roof, R-19 batt insulation 13. 2 in. concrete roof ballast, membrane, sheathing, R-15 insulation board, metal 4. Asphalt shingles, wood sheathing, R-19 batt insulation, gyp board deck 5. Slate or tile, wood sheathing, R-19 batt insulation, gyp board 14. Membrane, sheathing, R-15 insulation board, 4 in. LW concrete 6. Wood shingles, wood sheathing, R-19 batt insulation, gyp board 15. Membrane, sheathing, R-15 insulation board, 6 in. LW concrete 7. Membrane, sheathing, R-10 insulation board, wood deck 16. Membrane, sheathing, R-15 insulation board, 8 in. LW concrete 8. Membrane, sheathing, R-10 insulation board, wood deck, suspended acoustical ceiling 17. Membrane, sheathing, R-15 insulation board, 6 in. HW concrete 9. Membrane, sheathing, R-10 insulation board, metal deck 18. Membrane, sheathing, R-15 insulation board, 8 in. HW concrete 10. Membrane, sheathing, R-10 insulation board, metal deck, suspended acoustical ceiling 19. Membrane, 6-in HW concrete, R-19 batt insulation, suspended acoustical ceiling

of tthehe coconstructionnstruction aandnd thethe thermalthermal responsresponsivenessiveness ooff tthehe sursurfacesfaces valuesvalues of the transfer function method weightingweighting factors to mostmost the radiant heat gains strikestrike.. closelyclosely matcmatchh tthehe lloadoad proprofile.file. In tthehe proceproceduredure ddescribedescribed hhere,ere, a One goal in developing RTS was to provide a simplified method unitunit periodic heat gain pulse is used to generate loads for a 24 h based directly on the HB method; thus, it was deemed desirable to period. As longlong as the heat gaingain pulsepulse is a unit pulse, the resultingresulting generate RTS coefficients directlyy from a heat balance. A heat bal- loads are equivalent to the RTS coefficients. ance computer program was developed to do this: Hbfort, which is Two different radiant time series are used: solar, for direct trans- included as part off CoolingCooling andand HeatingHeating LoadLoad CCalculationalculation Princi- mitted solar heat gain (radiant energyenergy assumedassumed to bbee didistributedstributed ttoo ples (Pedersen et al. 1998). The RTS procedure is described by the floor and furnishings only) and nonsolar, for all other types of Spitler et al. (1997). The procedure for generating RTS coefficients heat gains (radiant energy assumed to bebe uniformlyuniformly distributeddistributed onon may be thought of as analogous to the custom weightingweighting factorfactor all internal surfaces). NonsolarN RTS apply too radiant heat gains from generatgenerationion procedureprocedure usedused byby DOE 2.12.1 (Kerrisk(Kerrisk et al.al. 1981; SowellSowell people,people, lights,lights, appliances,appliances, walls,walls, roofs,roofs, andand floors.floors. Also,Also, forfor diffusediffuse 1988a, 19881988b).b). In bbothoth cases, a zzoneone modelmodel isis pulsedpulsed withwith a heatheat solarsolar hheateat ggainain anandd didirectrect sosolarlar hheateat ggainain ffromrom ffenestrationenestration withwith ggain.ain. With DOE 2.1, the resultingresulting loads are used to estimate the besbestt indoorindoor shadingshading (blinds,(blinds, drapes, etc.),etc.), the nonsolar RTS should bbee Nonresidential Cooling and Heating Load Calculations 18.27

Table 18 Thermal Properties and Code Numbers of Layers Used in Wall and Roof Descriptions for Tables 16 and 17 Specific Thermal Layer Thickness, Conductivity, Density, Heat, Resistance, Mass, Capacity, ID Description in. Btu·in/h·ft2·°F lb/ft3 Btu/lb·°F ft2·°F·h/Btu R lb/ft2 Btu/ft2·°F Notes F01 Outdoor surface resistance — — — — 0.25 0.25 — — 1 F02 Indoor vertical surface resistance — — — — 0.68 0.68 — — 2 FF0303 In Indoordoor hhorizontalorizontal susurfacerface resistance — — — — 0.92 0.92 — — 3 F04 Wall air space resistance — — — — 0.87 0.87 — — 4 F05 Ceiling air space resistance — — — — 1.00 1.00 — — 5 F06 EIFS finish 0.375 5.00 116.0 0.20 — 0.08 3.63 0.73 6 F07 1 in. stucco 1.000 5.00 116.0 0.20 — 0.20 9.67 1.93 6 F08 Metal surface 0.030 314.00 489.0 0.12 — 0.00 1.22 0.15 7 F09 Opaque spandrel glass 0.250 6.90 158.0 0.21 — 0.04 3.29 0.698 F10 1 in. stone 1.000 22.00 160.0 0.19 — 0.05 13.33 2.53 9 F11 Wood siding 0.500 0.62 37.0 0.28 — 0.81 1.54 0.43 10 F12 Asphalt shingles 0.125 0.28 70.0 0.30 — 0.44 0.730.22 F13 Built-up roofing 0.375 1.131.13 70.0 0.35 — 0.33 2.19 0.77 F14 Slate or tile 0.500 11.00 120.0 0.30 — 0.05 5.00 1.50 F15 Wood shingles 0.250 0.27 37.0 0.31 — 0.94 0.770.24 F16 Acoustic tile 0.750 0.42 23.00.14 — 1.79 1.44 0.20 11 F17 Carpet0.500 0.41 18.0 0.33 — 1.23 0.75 0.25 12 F18 Terrazzo 1.000 1 12.502.50 160.0 0.19 — 0.08 13.33 2.53 13 G01 5/8 in. gyp board 0.625 1.11 50.0 0.26 — 0.56 2.60 0.68 G02 5/8 in. plywood 0.6250.80 34.0 0.29 — 0.78 1.77 0.51 G03 1/2 in. fiberboard sheathing 0.500 0.47 25.0 0.31 — 1.06 1.04 0.3214 G04 1/2 in. wood 0.500 1.06 38.0 0.39 — 0.47 1.58 0.62 15 G05 1 in. wood 1.000 1.06 38.0 0.39 — 0.94 3.17 1.24 15 G06 2 in. wood 2.000 1.06 38.0 0.39 — 1.89 6.33 2.47 15 G07 4 in. wood 4.000 1.06 38.00.39 — 3.77 12.67 4.94 15 I01 R-5, 1 in. insulation board 1.000 0.20 2.7 0.29 — 5.00 0.23 0.07 16 I02 R-10, 2 in. insulation board 2.000 0.20 2.7 0.29 — 10.00 0.45 0.13 16 I03 R-15, 3 in. insulation board 3.000 0.20 2.7 0.29 — 15.00 0.68 0.20 16 I04 R-11, 3-1/2 in. batt insulation 3.520 0.32 1.2 0.23 — 11.00 0.35 0.08 17 I05 R-19, 6-1/4 in. batt insulation 6.080 0.32 1.2 0.23 — 19.00 0.61 0.14 17 I06 R-30, 9-1/2 in. batt insulation 9.600 0.32 1.2 0.23 — 30.00 0.96 0.22 17 M01 4 in. brick 4.000 6.20120.0 0.19 — 0.65 40.00 7.60 18 M02 6 in. LW concrete block 6.000 3.39 32.0 0.21— 1.77 16.00 3.36 19 M03 8 in. LW concrete block 8.008.00003.44 29.0 0.21 — 2.33 19.33 4.06 20 M04 12 in. LW concrete block 12.000 4.92 32.0 0.21 — 2.44 32.00 6.72 21 M05 8 in. concrete block 8.000 7.72 50.0 0.22 — 1.04 33.33 7.33 22 M06 12 in. concrete block 12.000 9.72 50.0 0.22 — 1.23 50.00 11.00 23 M07 6 iin.n. LW concrete blblockock (fill(filled)ed) 6.000 1.98 32.0 0.21 — 3.03 16.00 3.36 24 M08 8 iin.n. LW concrete blblockock (fill(filled)ed) 8.000 1.80 29.0 0.21 — 4.44 19.33 4.06 25 M09 12 in. LW concrete block (filled) 12.000 2.04 32.0 0.21 — 5.88 32.00 6.72 26 M10 8 iin.n. concrete blockblock (fill(filled)ed) 8.000 5.00 50.00.22 — 1.60 33.33 7.33 27 M11 4 in. lightweight concrete 4.000 3.70 80.0 0.20 — 1.08 26.675.33 M12 6 in. lightweight concrete 6.000 3.70 80.0 0.20 — 1.62 40.008.00 M13 8 in. lightweight concrete 8.000 3.70 80.0 0.20 — 2.1653.33 10.67 M14 6 in. heavyweight concrete 6.000 13.50 140.0 0.22 — 0.44 70.00 15.05 M15 8 in. heavyweight concrete 8.000 13.50 140.0 0.22 — 0.48 93.33 20.07 M16 12 in. heavyweight concrete 12.000 113.503.50140.0 0.22 — 0.89 140.0 30.10 M17 2 in. LW concrete roof ballast2.000 1.30 40 0.20 — 1.54 6.7 1.33 28 Notes: The following notes give sources for the data in this table. 14. Chapter 26, Table 4 for nail-base sheathing 1. Chapter 26, Table 1 for 7.5 mph wind 15. Chapter 26, Table 4 for Southern pine 2. Chapter 26, Table 1 for still air, horizontal heat flow 16. Chapter 26, Table 4 for expanded polystyrene 3. Chapter 26, Table 1 for still air, downward heat flow 17. Chapter 26, Table 4 for glass fiber batt, specific heat per glass fiber board 4. Chapter 26, Table 3 for 1.5 in. space, 90°F, horizontal heat flow, 0.82 emittance 18. Chapter 26, Table 4 for clay fired brick 5. Chapter 26, Table 3 for 3.5 in. space, 90°F, downward heat flow, 0.82 emittance 19. Chapter 26, Table 4, 16 lb block, 8 16 in. face 6. EIFS finish layers approximated by Chapter 26, Table 4 for 3/8 in. cement plaster, 20. Chapter 26, Table 4, 19 lb block, 8 16 in. face sand aggregate 21. Chapter 26, Table 4, 32 lb block, 8 16 in. face 7. Chapter 33, Table 3 for steel (mild) 22. Chapter 26, Table 4, 33 lb normal weight block, 8  16 in. face 8. Chapter 26, Table 4 for architectural glass 23. Chapter 26, Table 4, 50 lb normal weight block, 8 16 in. face 9. Chapter 26, Table 4 for marble and granite 24. Chapter 26, Table 4, 16 lb block, vermiculite fill 10. Chapter 26, Table 4, density assumed same as Southern pine 25. Chapter 26, Table 4, 19 lb block, 8 16 in. face, vermiculite fill 11. Chapter 26, Table 4 for mineral fiberboard, wet molded, acoustical tile 26. Chapter 26, Table 4, 32 lb block, 8 16 in. face, vermiculite fill 12. Chapter 26, Table 4 for carpet and rubber pad, density assumed same as fiberboard 27. Chapter 26, Table 4, 33 lb normal weight block, 8 16 in. face, vermiculite fill 13. Chapter 26, Table 4, density assumed same as stone 28. Chapter 26, Table 4 for 40 lb/ft3 LW concrete 18.28 2013 ASHRAE Handbook—Fundamentals used. RRadiationadiation ffromrom tthosehose sousourcesrces isis assumedassumed to bebe more uniformlyuniformly instrumentation. The results agreedagreed with previous simulations disdistributedtributed ontoonto all roomroom surfaces.surfaces. EEffectffect of beabeamm solasolarr radiationradiation (Chantrasrisalai et al. 2003; Eldridge et al. 2003; Iu et al. 2003). HB didistributionstribution assumptionsassumptions isis addressed by Hittle (1999). calculations closely approximatedapproximated measuredmeasured coolingcooling lloadsoads wwhenhen Representative solar and nonsolar RTS data for light, medium, provided with detailed data for the test rooms. RTS overpredicteoverpredictedd and heavyweight constructions are provided in Tables 19 and 20. mmeasuredeasured cooling loads in tests witwithh large, clear, single-glazed win- Those were calculated using the Hbfort computer program (Peder- ddowow areas with bare concrete flflooroor and no furnishings or internal sen et al. 1998) with zone characteristics listed in Table 21. Custom- lloads.oads. Tests under more typical conditionsconditions (venetian blinds, car-car- ized RTS values may be calculated using the HB method where the peted floor, office-type furnishings, and normal internal loads) pro- zone is not reasonably ssimilarimilar to these typical zones or where mormoree vidvideded googoodd agreement bbetweenetween HB, RTS, anandd measuremeasuredd lloads.oads. pprecisionrecision is desired.desired. ASHRAE research project RPRP-942-942 compared HB and RTRTSS results over a wide rangerange of zone types and input variables (Rees HEATING LOAD CALCULATIONS et al. 2000; Spitler et al. 1998). In general, total cooling loads cal- culated using RTS closely agreed wiwithth or were slislightlyghtly hihighergher thathann Techniques for estimating design heating load for commercial, those of the HB method with the same inputs. TThe project examined institutional, and industrial applications are essentially the same aass more than 5000 test cases of varying zone parameters. The domi- for those estimatinestimatingg desdesignign coolincoolingg loads for such uses, with the fol-fol- natinnatingg variable was overall thermalthermal mass, and resultsresults were groupedgrouped lowing exceptions:exceptions: into lightweight, U.SU.S.. medium-weight, U.K. medium-weight, anandd heavyweight construcconstruction.tion. Best agreementagreement between RTS and HHBB • Temperatures outdoor conditionedconditioned spaces are generally lowelowerr results was obtained for light- and medium-weight constructionconstruction.. than maintained space temperatures.temperatures. Greater differences occurred in hheavyweighteavyweight cases, with RTS gen-gen- ••Cre Creditdit forfor solarsolar or internalinternal heatheat gainsgains isis not includedincluded erallyerally predictingpredicting slightlyslightly higherhigher peapeakk coocoolingling lloadsoads tthanhan HBHB.. ••T Thermalhermal storastoragege eeffectffect ooff bbuildinguilding structure or content isis ignored.ignored. Greater differencesdifferences alsoalso were observedobserved iinn zones wwithith extremeextremelyly ••T Thermalhermal bridgingbridging effectseffects on wallwall andand roofroof conductionconduction are greatergreater high internal radiant loads and lalargerge glazing areas or with a very forfor hheatingeating lloadsoads tthanhan fforor coocoolingling lloads,oads, anandd ggreaterreater care must bbee lightweightlightweight exterior envelope. In thisthis case,case, heat balancebalance calculationscalculations takentaken to account forfor bridgingbridging effectseffects on U-factorsU-factors usedused iinn hheatingeating predictpredict tthathat some ooff tthehe iinternalnternal radiantradiant loadload willwill bebe transmittedtransmitted toto load calculations.calculations. thethe outdooroutdoor environmentenvironment andand never bbecomesecomes coocoolingling lloadoad wwithinithin tthehe space. RTS ddoesoes not account fforor eenergynergy transtransferfer out ooff tthehe space ttoo Heat losses (negative heat gains) are thuss considered to be instan- thethe environment,environment, andand thusthus predictedpredicted higherhigher coolingcooling loads.loads. taneous,taneous, heat transfertransfer essentiallyessentially conductive, andand llatentatent heatheat treatedtreated ASHRAE research project RP-1117 built two model rooms for onlyonly as a ffunctionunction ooff repreplacinglacing sspacepace hhumidityumidity llostost to tthehe exterexteriorior whichwhich coolingcooling loadsloads were physicallyphysically measuredmeasured ususinging extensextensiveive environment.environment.

Table 19 Representative Nonsolar RTS Values for Light to Heavy Construction Interior Zones Light Medium Heavy Light Medium Heavy With Carpet No Carpet With Carpet No Carpet With Carpet No Carpet % No No No With With With

Glass 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% Carpet Carpet Carpet Carpet Carpet Carpet Hour Radiant Time Factor, % 0 47 47505341434646495231333534384222252846404631332150 53 41 43 46 46 49 52 31 33 35 34 38 42 22 25 28 46 40 46 31 33 21 1 19 191817201919181716171615918 17 20 19 19 18 17 16 17 16 15 9 9 91099 10 9 9 19201817919 20 18 17 9 9 2 111091211111098111010665666111210116611 10 9 12 11 11 10 9 8 11 10 10 6 6 5 6 6 6 11 12 10 11 6 6 3 6 6658776 5 8 7 7 6558776 5 5 8 7 7 4445554 4 4 5 5 5 6868556 8 6 8 5 5 4 4 4435554 3 5 5 5 4336554 3 3 6 5 5 4445544 4 4 5 5 4 4536454 5 3 6 4 5 5 3 3324333 2 4 3 3 2224442 2 2 4 4 4 4334444 3 3 4 4 4 3424443 4 2 4 4 4 6 2 2223322 2 3 3 2 2224332 2 2 4 3 3 3334443 3 3 4 4 4 2324342 3 2 4 3 4 7 2 2112221 1 2 2 2 1113331 1 1 3 3 3 3334443 3 3 4 4 4 2213342 2 1 3 3 4 8 1 1111111 1 1 1 1 1113221 1 1 3 2 2 3334333 3 3 4 3 3 1113341 1 1 3 3 4 9 1 1111111 1 1 1 1 1112221 1 1 2 2 2 3323333 3 2 3 3 3 1112331 1 1 2 3 3 10101111111 1 1 1 1 1 1112221 1 1 2 2 2 3223333 2 2 3 3 3 1112331 1 1 2 3 3 11111111111 1 1 1 1 1 1112221 1 1 2 2 2 2223332 2 2 3 3 3 1112231 1 1 2 2 3 12121111111 1 1 1 1 1 1111111 1 1 1 1 1 2223332 2 2 3 3 3 1111231 1 1 1 2 3 13131110101 1 1 0 1 0 1111111 1 1 1 1 1 2223322 2 2 3 3 2 1111231 1 1 1 2 3 14140010100 0 1 0 1 0 1111111 1 1 1 1 1 2223222 2 2 3 2 2 1011231 0 1 1 2 3 15150010000 0 1 0 0 0 1111111 1 1 1 1 1 2222222 2 2 2 2 2 0011230 0 1 1 2 3 16160000000 0 0 0 0 0 1111111 1 1 1 1 1 2222222 2 2 2 2 2 0011230 0 1 1 2 3 17170000000 0 0 0 0 0 1111111 1 1 1 1 1 2222222 2 2 2 2 2 0011220 0 1 1 2 2 18180000000 0 0 0 0 0 1111111 1 1 1 1 1 2212222 2 1 2 2 2 0011220 0 1 1 2 2 19190000000 0 0 0 0 0 0100110 1 0 0 1 1 2212222 2 1 2 2 2 0010220 0 1 0 2 2 20200000000 0 0 0 0 0 0000110 0 0 0 1 1 2112222 1 1 2 2 2 0000220 0 0 0 2 2 21210000000 0 0 0 0 0 0000110 0 0 0 1 1 2112222 1 1 2 2 2 0000220 0 0 0 2 2 22220000000 0 0 0 0 0 0000100 0 0 0 1 0 1112221 1 1 2 2 2 0000120 0 0 0 1 2 23230000000 0 0 0 0 0 0000000 0 0 0 0 0 1112211 1 1 2 2 1 0000120 0 0 0 1 2 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Nonresidential Cooling and Heating Load Calculations 18.29

Table 20 Representative Solar RTS Values for Light to Heavy Construction Light Medium Heavy With Carpet No Carpet With Carpet No Carpet With Carpet No Carpet % Glass 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% 10% 50% 90% Hour Radiant Time Factor, % 0 53 53555644454652545528292947495126272855 56 44 45 46 52 54 55 28 29 29 47 49 51 26 27 28 1 17 17171719202016161515151511121212131317 17 19 20 20 16 16 15 15 15 15 11 12 12 12 13 13 2 9 9991111118881010106667779 9 11 11 11 8 8 8 10 10 10 6 6 6 7 7 7 3 5 5557775 5 7 7 7 5 5447774 4 7 7 7 4435554 4 3 5 5 5 4 3 3335553 3 5 5 5 3 3336663 3 6 6 6 3334443 3 3 4 4 4 5 2 2223332 2 3 3 3 2 2225552 2 5 5 5 2224442 2 2 4 4 4 6 2 2223222 2 3 2 2 2 2114441 1 4 4 4 2223332 2 2 3 3 3 7 1 1112221 1 2 2 2 1 1114331 1 4 3 3 2223332 2 2 3 3 3 8 1 1111111 1 1 1 1 1 1113331 1 3 3 3 2223332 2 2 3 3 3 9 1 1111111 1 1 1 1 1 1113331 1 3 3 3 2223332 2 2 3 3 3 10101111111 1 1 1 1 1 1 1112221 1 2 2 2 2 2223332 2 3 3 3 11111111111 1 1 1 1 1 1 1112221 1 2 2 2 2 2213322 1 3 3 2 12121111101 1 1 1 1 0 1 1112221 1 2 2 2 2 2112221 1 2 2 2 13131101001 1 0 1 0 0 1 1112221 1 2 2 2 2 2112221 1 2 2 2 14141000001 0 0 0 0 0 1 1111111 1 1 1 1 2 2112221 1 2 2 2 15151000001 0 0 0 0 0 1 1111111 1 1 1 1 1 1112221 1 2 2 2 16160000000 0 0 0 0 0 1 1111111 1 1 1 1 1 1112221 1 2 2 2 17170000000 0 0 0 0 0 1 1111111 1 1 1 1 1 1112221 1 2 2 2 18180000000 0 0 0 0 0 1 1111111 1 1 1 1 1 1112221 1 2 2 2 19190000000 0 0 0 0 0 0 0001110 0 1 1 1 1 1112221 1 2 2 2 20200000000 0 0 0 0 0 0 0001110 0 1 1 1 1 1112221 1 2 2 2 21210000000 0 0 0 0 0 0 0000000 0 0 0 0 1 1112221 1 2 2 2 22220000000 0 0 0 0 0 0 0000000 0 0 0 0 1 1112111 1 2 1 1 23230000000 0 0 0 0 0 0 0000000 0 0 0 0 1 1112111 1 2 1 1 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

Table 21 RTS Representative Zone Construction for Tables 19 and 20 Construction Class Exterior Wall Roof/Ceiling Partitions Floor Furnishings Light Steel siding, 2 in. insulation, 4 in. LW concrete, ceiling 3/4 in. gyp, air space, Acoustic tile, ceiling air 1 in. wood @ 50% air space, 3/4 in. gyp air space, acoustic tile 3/4 in. gyp space, 4 in. LW concrete of floor area Medium 4 in. face brick, 2 in. insulation, 4 in. HW concrete, ceiling 3/4 in. gyp, air space, Acoustic tile, ceiling air 1 in. wood @ 50% air space, 3/4 in. gyp air space, acoustic tile 3/4 in. gyp space, 4 in. HW concrete of floor area Heavy 4 in. face brick, 8 in. HW 8 in. HW concrete, ceiling 3/4 in. gyp, 8 in. HW Acoustic tile, ceiling air 1 in. wood @ 50% concrete air space, air space, acoustic tile concrete block, space, 8 in. HW concrete of floor area 2 in. insulation, 3/4 in. gyp 3/4 in. gyp

ThisThis ssimplifiedimplified approacapproachh iiss jjustifiedustified bbecauseecause iitt evaevaluatesluates worstworst-- HEAT LOSS CALCULATIONS case coconditionsnditions thatthat cacann rreasonablyeasonably occur during a heating seasonseason.. The general procedure for calculation of design heat losses of a Therefore, the near-worst-case load is based on the followinfollowing:g: structure is as follows: • DesiDesigngn interior and exterior conditions 11.. Select outdoor desidesigngn conditionconditions:s: temperature, humidithumidity,y, anandd • IncludinIncludingg infiltration aand/ornd/or veventilationntilation wind direction and speed.speed. • No solar effect (at nightt or on cloudy winter days) 22..Se Selectlect indoorindoor ddesignesign conconditionsditions to bebe maintained.maintained. •Be• Beforefore thethe periodicperiodic presence ofof people,people, lights,lights, andand appliancesappliances hashas an ooffsettingffsetting effecteffect 3. Estimate temperattemperatureture in any adjacentadjacent unheatedunheated spaces. 44.. Select transmission coefficients and comcomputepute heat losses for Typical commercial and retail spaces have nighttime unoccupied walls,walls, flfloors,oors, ceceilings,ilings, wwindows,indows, ddoors,oors, anandd ffoundationoundation eelements.lements. periods at a setback temperature where little to no ventilation is required, building lights and equipment are off, and heat loss is pri- 55.. Compute heatheat loadload throughthrough infiltrationinfiltration anandd any ototherher outoutdoordoor aairir marily through conduction and infiltration. Before being occupied, introduced directlydirectly to the spacespace.. buildings are warmed to the occupied temperature (see the follow- 66.. Sum the losses caused bbyy ttransmissionransmission aandnd infiltration.infiltration. ing discussion). During occupied time, building lights, equipment, and people cooling loads can offsoffsetet conduction heatt loss, although Outdoor Design Conditions some perperimeterimeter heatheat mmayay bbee required,required, leavingleaving iinfiltrationnfiltration anandd ven- The ideal heating system provides enough heat to match the struc- tilation as the primary heating loads. Ventilation heat load may be ture’s heat loss. However, weather conditions vary considerably offset with heat recoveryrecovery equipment.equipment. These loads ((conductionconduction lossloss,, from year to year, and heating systems designed for the worst warm-upwarm-up load,load, andand ventilationventilation load)load) may not bebe additiveadditive whenwhen siz-siz- weather conditions on record would have a great excess of capacity inging buildingbuilding heatingheating equipment,equipment, and it is prudentprrudent to analyze each most of the time. A system’s failure to maintain design conditions load and their interactions to ararriverrive at final equipment sizing for during brief periods of severe weather usually is not critical. How- heating.heating. ever, close regulation of indoor temperature may be critical for some 18.30 2013 ASHRAE Handbook—Fundamentals occupancies or industrial processes. Design temperature data and HF = Uavgg (tin – tgr) (37) discussion of their application are given in Chapter 14. Generally, the wherewhere 99% temperature values given in the tabulated weather data are used. However, caution is needed, and local conditions should always be Uavg = average U-factor for below-grade surface from Equation (39) or (40), Btu/h·ftBtu/h·fft2·°F·°F investigated. In some locations, outdoor temperatures are commonly tin ==b below-gradeelow-grade space aairir temperature, °F°F much lower and wind velocities higher than those given in the tabu- t ==d designesign groundground surfacesurface temperature ffromrom EquatEquationion (38),(38), °°FF lated weather data. gr The effect of soil heat capacity means that none of the usual Indoor Design Conditions eexternalxternal design air temperatures are suitable values forfor tgr. Ground surfacesurface temperature fluctuates about an annual mean value byby The main purpose of the heating system is to maintain indoor amplitudeamplitude A, which varies with geographic location and surface conditions that make most of the occupants comfortable. It should cover. The minimum ground surface temperature, suitable for heat be kept in mind, however, that the purpose of heating load calcula- loss estimates, is therefore tions is to obtain data for sizing the heating system components. In many cases, the system will rarely be called upon to operate at the tgrr =t gr – A (38) design conditions. Therefore, the use and occupancy of the space wwherehere are general considerations from the design temperature point of t gr = mean groungroundd temperature, °F, eestimatedstimated fromfrom thethe annualannual average view. Later, when the building’s energy requirements are computed, airair temperature or fromfrom well-waterwell-water temperatures, shownshown inin the actual conditions in the space and outdoor environment, includ- FigureFigure 17 ooff CChapterhapter 34 iinn tthehe 2011 ASHRAEASHRAE Handbook—HVACHandbook—HVAC ing internal heat gains, must be considered. Applications The indoor design temperature should be selected at the lower end A ==g groundround surface temperature amplitude,amplitude, °F, from FigureFigure 13 for of the acceptable temperature range, so that the heating equipment NorthNorth AmerAmericaica will not be oversized. Even properly sized equipment operates under Figure 14 shows depth parameters used in determining Uavg. For partial load, at reduced efficiency, most of the time; therefore, any walls, the region definedd by z1 and z2 may be the entire wall or any oversizing aggravates this condition and lowers overall system effi- portportionion ofof it,it, allowingallowing partiallypartially insulatedinsulated configurationsconfigurations to bebe ana-ana- ciency. A maximum design dry-bulb temperature off 70°F is recom- llyzedyzed ppiecewise.iecewise. mended for most occupancies. The indoor design value of relative ThThee below-gradebelow-grade wallwall averageaverage U-factorU-factor isis givengiven by humidity should be compatible with a healthful environment and the 2ksoil thermal and moisture integrity of the building envelope. A minimum U = ------avg,bw z – z  relative humidity off 30% is recommended for most situations. 2 1 ((39)39) CCS2ksoilRotherrS CSC 2ksoilRotherS Calculation of Transmission Heat Losses ×ln× lnDDTz + ------T – llnnDTDz + ------T EEU2  U EEU1  U Exterior Surface Above Grade. All above-grade surfaces ex- posed to outdoor conditions (walls, doors, ceilings, fenestration, whewherere and raised floors) are treated identically, as follows: Uavg,bwavg,g,bw = averageg U-factor for wall region defined by z1 and z2, Btu/h·ftBtu/h·fft2·°F·°F  q = A HF (35) ksoil = soilsoil tthermalhermal conconductivity,ductivity, Btu/h·ft·°FBtu/h·ft·°F HF = U t (36) Rotherother = totaltotal resistanceresistance ofof wall,wall, insulation,insulation, andand indoorindoor surfacesurface resistance,resistance, h·fth·fft2·°F/Btu·°F/Btu 2 where HF is the heating load factor inn BBtu/Btu/h·ft/h·fft . z1, z2 ==d depthsepths ofof top andand bottombottom ofof wallwall segment underunder consideration,consideration, ftft Below-Grade Surfaces. An approximate method for estimating (Figure(Figure 1414)) below-grade heat loss [based on the work of Latta and Boileau The value of soil thermal conductivity k varies widely with soil (1969)] assumes that the heat flow paths shown in Figure 12 can be ttypeype and moisture content. A ttypicalypical value of 0.8 Btu/h·ft·°F hashas used to find the steady-state heat loss to the ground surface, as been used previously to tabulatetabulate U-factors,U-factors, andand Rotherr is approxi- follows: mately 1.47 h·fh·ftft2 ·°F/Btu·°F/Btu fforor uuninsulatedninsulated coconcretencrete wawalls.lls. FForor

Fig. 12 Heat Flow from Below-Grade Surface Fig. 13 Ground Temperature Amplitude Nonresidential Cooling and Heating Load Calculations 18.31

Table 24 Heat Loss Coefficient Fp of Slab Floor Construction

Construction Insulation Fp , Btu/h·ft·°F 8 in. block wall, brick facing Uninsulated 0.68 R-5.4 from edge to footer0.50 4 in. block wall, brick facing Uninsulated 0.84 R-5.4 from edge to footer0.49 Metal stud wall, stucco Uninsulated 1.20 R-5.4 from edge to footer0.53 PPouredoured concrete wallwall withwith Uninsulated 2.12 Fig. 14 Below-Grade Parameters dductuct near perimeter*perimeter* R-5.4 from edge to footer0.72 *Weighted average temperature of heating duct was assumed at 110ºF during heating Table 22 Average U-Factor for Basement Walls season (outdoor air temperature less than 65ºF). with Uniform Insulation q = p  HF (41) U from Grade to Depth, Btu/h·ftBtu/h·fft2·°F·°F Depth, avg,bwavg,g,bw HF = F t (42) ft Uninsulated R-5 R-10 R-15 p 10.432 0.135 0.080 0.057 wherewhere 2.6 0.331 0.121 0.075 0.054 q ==h heateat lossloss throughthrough perperimeter,imeter, BtuBtu/h/h 30.273 0.110 0.070 0.052 Fp ==h heateat lossloss coefficientcoefficient per footfoot ofof perimeter,perimeter, Btu/h·ft·°F,Btu/h·ft·°F, TableTable 2424 40.235 0.101 0.066 0.050 p =per perimeterimeter (exposed(exposed edge)edge) ofof floor,floor, ftft 50.208 0.094 0.063 0.048 60.187 0.088 0.060 0.046 Surfaces Adjacent to Buffer Space. Heat loss to adjacent 70.170 0.083 0.057 0.044 unconditioned or semiconditioned spaces can be calculated using a 80.157 0.078 0.055 0.043 heating factor based on the partition temperature difference: Soil conductivity = 0.8 Btu/h·ft·°F; insulation is over entire depth. For other soil con- HFHF = U (tin – tb) (43) ductivities and partial insulation, use Equation (39). Infiltration Table 23 Average U-Factor for Basement Floors Infiltration of outdoor air through openings into a structure is 2 Uavg,bfavg,g,bff , Btu/h·ftBtu/h·fft ·°F·°F caused by thermal forces, wind pressure, and negative pressure zf wb (Shortest Width of Basement), ft (planned or unplanned) with respect to the outdoors created by (Depth of Floor mechanical systems. Typically, in building design, if the mechani- Below Grade), ft 20 24 28 32 cal systems are designed to maintain positive building pressure, 1 0.064 0.057 0.052 0.047 infiltration need not be considered except in ancillary spaces such 2 0.054 0.048 0.044 0.040 as entryways and loading areas. 3 0.047 0.042 0.039 0.036 4 0.042 0.038 0.035 0.033 Infiltration is treated as a room load and has both sensible and 5 0.038 0.035 0.032 0.030 latent components. During winter, this means heat and humidity 6 0.035 0.032 0.030 0.028 loss because cold, dry air must be heated to design temperature and 7 0.032 0.030 0.028 0.026 moisture must be added to increase the humidity to design condi- Soil conductivity is 0.8 Btu/h·ft·°F; floor is uninsulated. For other soil conductivities tion. Typically, during winter, controlling indoor humidity is not a and insulation, use Equation (39). factor and infiltration is reduced to a simple sensible component. Under cooling conditions, both sensible and latent components are thesethese parameters, representativerepresentative vavalueslues forfor Uavg,bwavg,g,bw are shown in added to the space load to be treated by the air conditioning system. Table 22. Procedures for estimating the infiltration rate are discussed in The average below-grade floor U-factor (where the entire base- Chapterr 16. TThe infiltration rate is reduced to a volumetric flow rate ment floor is uninsulated or has uniform insulation) is given by at a known dry bulb/wet bulb condition. Along with indoor air con- dition, the following equations define the infiltration sensible and 2ksoil latent loads. U = ------= - (40) avg,bf w b q (Btu/h) = 60(cfm/v) c (t – t ) (44) CCSz k R S z k R s p in o wb f soil otherr CCSf soil otherrS × lnDDT------+ --- + ------T – lnnEEU---- + ------U EEU2 2  U 2  whewherere cfmcfm = volumevolume flowflow rate ooff infiltratinginfiltrating airair wwherehere cp = specific heat capacity of air, Btu/lbBtu//lbm·ºF·ºF 3 wb = basementbasement widthwidth (shortest(shortest dimension),dimension), ft v = specific volume of infiltrating air, ft /lb/ m z = floorfloor ddepthepth bbelowelow ggrade,rade, fftt ((seesee FFigureigure 1414)) f Assuming standard air conditions (59°F and sea-level condi- Representative values of U for uninsulated basement floors avg,bf ttions)ions) for v aandnd cp, Equation (44) may be written as are shown in Table 23. At-Grade Surfaces. Concrete slab floors may be (1) unheated, qs (Btu/h) = 1.10(cfm)((tin – to) (45) relying for warmth on heat delivered above floor level by the heating system, or (2) heated, containing heated pipes or ducts that consti- The infiltrating air also introduces a latent heating load given by tute a radiant slab or portion of it for complete or partial heating of q = 60(cfm/v)((W – W )D (46) the house. l in o h The simplified approach that treats heat loss as proportional to wherewhere

slab perimeter allows slab heat loss to be estimated for both Win = humidity ratio for indoor space air, lbw/lba unheated and heated slab floors: Wo = humidity ratio for outdoor air, lbw/lba 18.32 2013 ASHRAE Handbook—Fundamentals

Dh ==c changehange iinn ententhalpyhalpy to convert 1 lb water fromfrom vapor to liquid,liquid, Table 25 Common Sizing Calculations in Other Chapters Btu/lbBtu//lb w Subject Volume/Chapter Equation(s) For standard air and nominal indoor comfort conditions, the Duct heat transfer ASTM Standardd C680 latent load may be expressed as Piping heat transfer Fundamentals Ch. 3 (35) Fan heat transfer Fundamentals Ch. 19(22) ql = 4840(cfm)((Win – Wo) (47) Pump heat transfer Systems Ch. 44 (3), (4), (5) The coefficients 1.10 in Equation (45) andd 4840 ini Equation (47) MMoist-airoist-air senssensibleible hheatingeating anandd cooling Fundamentals Ch. 1 (43) are given for standard conditions. They depend onn temperature and Moist-air cooling and dehumidification Fundamentals Ch. 1 (45) altitude (and, consequently,consequently, pressure).pressure). Air mixing Fundamentals Ch. 1 (46) SSpacepace hheateat aabsorptionbsorption anandd momoist-airist-air Fundamentals Ch. 1 (48) HEATING SAFETY FACTORS AND mmoistureoisture ggainsains AAdiabaticdiabatic mixingmixing ofof water injectedinjected intointo Fundamentals Ch. 1 (47) LOAD ALLOWANCES mmoistoist aairir Before mechanical cooling became common in the second half of the 1900s, and when energy was less expensive, buildings included loads. However, specific grouping and ungrouping of rooms into much less insulation; large, operable windows; and generally more zones may cause peak system loads to occur at different times infiltration-prone assemblies than the energy-efficient and much during the day or year and may significantly affected heat removal tighter buildings typical of today. Allowances of 10 to 20% of the net equipment sizes. calculated heating load for piping losses to unheated spaces, and 10 For example, if each room is cooled by a separate heat removal to 20% more for a warm-up load, were common practice, along with system, the total capacity of the heat transport systems equals the other occasional safety factors reflecting the experience and/or con- sum of peak room loads. Conditioning all rooms by a single heat cern of the individual designer. Such measures are less conserva- transport system (e.g., a variable-volume air handler) requires less tively applied today with newer construction. A combined warm-up/ capacity (equal to the simultaneous peak of the combined rooms safety allowance off 20 to 25% isi fairly common butt varies depending load, which includes some rooms at off-peak loads). This may sig- on the particular climate, building use, and type of construction. nificantly reduce equipment capacity, depending on the configura- Engineering judgment must be applied for the particular project. tion of the building. Armstrong et al. (1992a, 1992b) provide a design method to deal with warm-up and cooldown load. VENTILATION OTHER HEATING CONSIDERATIONS Consult ASHRAE Standard 62.1 and building codes to deter- mine the required quantity of ventilation air for an application, and Calculation of design heating load estimates has essentially the various methods of achieving acceptable indoor air quality. The become a subset of the more involved and complex estimation of following discussion is confined to the effect of mechanical venti- cooling loads for such spaces. Chapter 19 discusses using the heat- lation on sizing heat removal equipment. Where natural ventilation ing load estimate to predict or analyze energy consumption over is used, through operable windows or other means, it is considered time. Special provisions to deal with particular applications are cov- aass iinfiltrationnfiltration anandd iiss part ooff tthehe direct-to-room heat gain. Where ered in the 2011 ASHRAE Handbook—HVAC Applications and the ventilation air is conditioned and supplied through the mechanical 2012 ASHRAE Handbook—HVAC Systems and Equipment. system, its sensible and latent loads are applied directly to heat The 1989 ASHRAE Handbook—Fundamentals was the last edi- transport andand centralcentral equipment,equipment, andand ddoo not affectaffect room hheatingeating anandd tion to contain a chapter dedicated only to heating load. Its contents cooling loads. IfI the mechanical ventilation rate sufficiently exceeds were incorporated into this volume’s Chapter 17, which describes exhaust airflows,, air pressure maymay bebe positivepositive andand infiltrationinfiltration ffromrom steady-state conduction and convection heat transfer and provides, eenvelopenvelope openingsopenings andand outdooroutdoor windwind maymay not bebe includedincluded inin thethe among other data, information on losses through basement floors load calculations. Chapter 16 includes more information on venti- and slabs. lating commercial buildings. SYSTEM HEATING AND COOLING AIR HEAT TRANSPORT SYSTEMS LOAD EFFECTS Heat transport equipment is usually selected to provide adequate heating or cooling for the peak load condition. However, selection The heat balance (HB) or radiant time series (RTS) methods are must also consider maintaining desired indoor conditions during all used too determine cooling loads off rooms within a building, but they occupied hours, which requires matchingmatching the rate of heat transportransportt ddoo not addressaddress thethe plantplant sizesize necessanecessary to reject the heat. Principal to room peak heating and cooling loads. Automatic control systems factors to consider in determining the plant size aree ventilation, heat normally vary the heating and cooling system capacity during these transport equequipment,ipment, anandd aairir didistributionstribution systems. Some ooff tthesehese off-peak hours of operation. factors varvaryy as a function of rooroomm load,load, ambient temperature,temperature, anandd controcontroll strategstrategies,ies, so iitt iiss ooftenften nnecessaryecessary to evaevaluateluate tthehe ffactorsactors andand On/Off Control Systems strategstrategiesies ddynamicallyynamically aandnd ssimultaneouslyimultaneously wwithith tthehe hheateat llossoss or gagainin On/off control systems, common in residential and light com- cacalculations.lculations. mercial applications, cycle equipment on and off to match room Detailed analysis of system components and methods calculating load. They are adaptable to heating or cooling because they can their contribution to equipment sizing are beyond the scope of this cycle both heating and cooling equipment. In their purest form,, their chapter, which is general in nature. Table 25 lists the most fre- hheateat transport matches the combined room and ventilation load oveoverr quently used calculations in other chapters and volumes. a series of ccycles.ycles. ZONING Variable-Air-Volume Systems The organization of building rooms as defined for load calcula- Variable-air-volumeVariable-air-volume ((VAV)VAV ) systemsystemss hhaveave aairflowirflow controcontrolsls thatthat tions into zones and air-handling units has no effect on room cooling adjadjustust coocoolingling aairflowirflow to matmatchch tthehe room coolingcooling load.load. Damper Nonresidential Cooling and Heating Load Calculations 18.33 leakageleakage or mminimuminimum aairflowirflow settingssettings maymay cause overcooling,overcooling, so The power required to provide airflow and static pressure can be most VAV ssystemsystems are used in cconjunctiononjunction with separate heatinheatingg determined from the first law of thermodynamics with the following ssystems.ystems. TheseThese maymay bebe duct-mountedduct-mounted heating coils, orr separate radi-radi- equation: ant or convectconvectiveive hheatingeating systems.systems. P = 0.0001570.000157VVpp TheThe amount ofof heatheat addedadded byby thethe heatingheating systems duringduring coolingcooling A becomesbecomes ppartart of the room coolingcooling load. CalculationsCalculations mustmust deter-deter- wherwheree mine the minimum airflow relative to off-peak cooling loads. The PA ==a airir power, hp quantity of heat added to the coolcoolinging load can be determined for V =fl flowow raterate,, cfmcfm each terminal by Equation (9) uusingsing the minimum required supplysupply p = pressure,pressure, in.in. ofof waterwater airflow rate and the difference between supply air temperature andand atat standard air conditions withwith air density = 0.075 lb/ftlb/fft3 built into the tthehe room indoorindoor hheatingeating ddesignesign temperaturetemperature.. mmultiplierultiplier 0.000157. The power necessarnecessaryy at the fan shaft must aaccountccount fforor ffanan inefficiencies,inefficiencies, whichwhich may vary fromfrom 50 to 70%. ThisThis Constant-Air-Volume Reheat Systems mmayay be determined frofromm In constant-air-volume (CAV)(CAV) reheatreheat systems,systems, all supplysupply air isis P = P / coocooledled to remove momoistureisture andand thenthen hheatedeated to avoavoidid overcooovercoolingling F A F rooms. Reheatt refers to the amount of heat added to cooling supply wherewhere air to raise the supplsupplyy air temperature to the temperature necessarnecessaryy PF = power requrequiredired at fanfan shaft,shaft, hp  fforor ppickingicking up tthehe senssensibleible lload.oad. TThehe quantquantityity ooff hheateat aaddeddded can bbee F =fan efficiency, dimensionless determined bbyy Equation (9).(9). The power necessary at the input to the fan motor must account for WithWith a constant-volumeconstant-volume reheatreheat system,system, heatheat transport system fan motor inefficiencies and drive losses. Fan motor efficiencies load does not varyvary with changeschanges in room load, unless the coolingcooling generally vary from 80 to 95%, and drive losses for a belt drive are coil dischardischargege temperaturetemperature is allowed to varvary.y. Where a minimumminimum 3% of the fan power. This may be determined from ccirculationirculation rate requrequiresires a suppsupplyly aairir temperature ggreaterreater tthanhan tthehe available design supply air temperature,temperatture, reheat adds to the cooling PM = (1 + DL) PF /EM ED lloadoad on thethe heatheat transport system.system. ThisThis makesmakes thethe coolingcooling loadload on tthehe heatheat transport ssystemystem llargerarger tthanhan tthehe room peapeakk lload.oad. where P = power required at input to motor, hp Mixed Air Systems M ED = belt drive efficiency, dimensionless MixedMixed airair systems cchangehange tthehe ssupplyupply aairir temperature to matcmatchh EM = fan motor efficiency, dimensionless P = power required at fan shaft, hp the coolincoolingg capacitcapacityy bbyy mixinmixingg airstairstreamsreams of different temtemperatures;peratures; F DL = drive loss, dimensionless exampexamplesles iincludenclude mumultizoneltizone anandd ddual-ductual-duct systems. Systems tthathat cool tthehe eentirentire aiairstreamrstream ttoo rremoveemove mmoistureoisture aandnd ttoo rreheateheat sosomeme of Almost all the energy required to generate airflow and static pressure tthehe aairir bbeforeefore mmixingixing wwithith tthehe ccoolingooling aairstreamirstream influenceinfluence lloadoad on is ultimately dissipated as heat within the building and HVAC sys- tthehe hheateat transport system iinn tthehe same way a rereheatheat system ddoes.oes. tem; a small portion is discharged with any exhaust air. Generally, it OtOtherher systemssystems separate thethe airair pathspaths so thatthat mixingmixing ooff hhot-ot- anandd cocold-ld- is assumed that all the heat is released at the fan rather than dispersed ddeckeck airstreamsairstreams doesdoes not occur. ForFor systemssystems thatthat mixmix hothot andand coldcold to the remainder of the system. The portion of fan heat released to the aairstreams,irstreams, tthehe contrcontributionibution to thethe hheateat transport system lloadoad is airstream depends on the location of the fan motor and drive: if they determined as follows. are within the airstream, all the energy input to the fan motor is released to the airstream. If the fan motor and drive are outdoor the 1. Determine the ratio of cold-deck flow to hot-deck flow from airstream, the energy is split between the airstream and the room housing the motor and drive. Therefore, the following equations may Qh ------= (Tc – Tr)/(Tr – Th) be used to calculate heat generated by fans and motors: Qc If motor and drive are outside the airstream, 2. From Equation (10), the hot-deck contribution to room load dur- q = 2545P ing off-peak cooling is fs F q = 2545(P – P ) qrh = 1.1Qh(Th – Tr) fr M F wherewhere If motor and drive are inside the airstream, Q ==h heatingeating airflow,airflow, cfmcfm h qfs = 2545PM Qc = coolingcooling airflow,airflow, cfmcfm qfr = 0.0 Tc =coo coolingling airair temperature, °F°F Th ==h heatingeating airair temperature, °F°F where T =room or return aairir temperature, °°FF r PF = power required at fan shaft, hp qrhrh ==h heatingeating aairflowirflow contrcontributionibution to room lloadoad at ooff-peakff-peak hhours,ours, Btu/hBtu/h PM = power required at input to motor, hp qfs = heat release to airstream, Btu/h Heat Gain from Fans qfr = heat release to room housing motor and drive, Btu/h 2545 = conversion factor, Btu/h·hp Fans that circulate air through HVAC systems add energy to the system through the following processes: Supply airstream temperature rise may be determined from psy- chrometric formulas or Equation (9). • IncreasinIncreasingg velocitvelocityy aandnd static pressure addaddss kinetic and potentiapotentiall Variable- or adjustable-frequency drives (VFDs or AFDs) often energyenergy drive fan motors in VAV air-handling units. These devices release • Fan iinefficiencynefficiency inin producingproducing aairflowirflow anandd statstaticic pressure addsadds heat to the surrounding space. Refer to manufacturers’ data for heat sensible heat (fan(fan heat)heat) to the airfloairfloww released or efficiencies. The disposition of heat released is deter- • InefficiencyInefficiency of motor and drivedrive dissipates sensible heat mined by the drive’s location: in the conditioned space, in the return 18.34 2013 ASHRAE Handbook—Fundamentals air path, or in a nonconditioned equipment room. These drives, and iiss lleakageeakage iintonto tthehe pplenumlenum ffromrom ssupplyupply aairir dducts,ucts, anand,d, if exposeexposedd ttoo other electronic equipment such as building control, data process- tthehe rooroof,f, iincreasingncreasing llevelsevels ooff iinsulation.nsulation. ing, and communications devices, are temperature sensitive, so the Where the ceiling space is used as a return air plenum, energy rooms in which they are housed require cooling, frequently year- balance requires that heat picked up from the lights into the return round. airr (1) become part of the cooling load to the return air (represente(representedd by a temperature rise of return aiairr as it passes through the ceilingceiling Duct Surface Heat Transfer sspace),pace), (2) be partially transferretransferredd back into the conditioned space Heat transfer across the duct surface is one mechanism for tthroughhrough tthehe ceceilingiling matermaterialial bbelow,elow, aand/ornd/or ((3)3) bbee partpartiallyially llostost fromfrom energy transfer to or from air inside a duct. It involves conduction the space throuthroughgh floor surfaces above the plenum. If the plenuplenumm through the duct wall and insulation, convection at inner and outer hhasas one or more exterior surfaces,surfaces, heat gains through them must be surfaces, and radiation between the duct and its surroundings. cconsidered;onsidered; if adjacentadjacent to spaces withwith differentdifferent indoorindoor temperatures, Chapter 4 presents a rigorous analysis of duct heat loss and gain, partition loads must be considered, too. In a multistory building, ththee and Chapter 23 addresses application of analysis to insulated duct cconditionedonditioned space frequently gains heat through its floor from a systems. sisimilarmilar plenumplenum below,below, offsettingoffsetting thethe floorfloor loss.loss. TheThe radiantradiant compocompo-- The effect of duct heat loss or gain depends on the duct routing, nent of heat leaving the ceiling orr floor surface of a plenum is nornor-- dductuct iinsulation,nsulation, andand itsits surroundingsurrounding environment.environment. ConsiderConsider thethe fol-fol- mmallyally so smasmall,ll, bbecauseecause ooff rerelativelylatively smasmallll temperaturetemperature diffdifferences,erences, lowing conditions: ththatat allall suchsuch heatheat transfertransfer isis connsideredsidered convectiveconvective fforor cacalculationlculation purposes (Rock and Wolfe 1997). • For duct run within the area cooledcooled or heated by air in the duct,duct, Figure 15 shows a schematic of a typical return air plenum. The heat transfer from the space to the duct has no effect on heatinheatingg oorr following equations, using the heat flow directions shown in Figure coolingcooling load, but beware of the potentialpotential for condensation on coldcold 15, represent the heat balance of a return air plenum design for a typ- ducts.ducts. ical interior room in a multifloor building: • For ductduct run throughthrough unconditionedunconditioned spaces or outdoors,outdoors, heatheat transfer adds to the coolingcooling or heatingheating load for the air transport q1 = Uc Ac(tp – tr) (48) systemsystem butbut not forfor thethe conditionedconditioned sspace.pace. • For duct run throughthrough conditioned space not served byby the duct, q2 = Uf Af (tp – tfa) (49) heatheat transtransferfer aaffectsffects tthehe conconditioneditioned spacespace as wellwell as tthehe aairir transtrans-- port system servingserving thethe duct.duct. q3 = 1.1Q(tp – tr) (50) • For an extensextensiveive ductduct ssystem,ystem, hheateat transtransferfer rereducesduces tthehe eeffectiveffective q – q – q – q = 0 (51) supplysupply aairir diffdifferentialerential temperatemperature,ture, requrequiringiring adjustmentadjustment tthroughhrough lp 2 1 3 air balancingbalancing to increase airflow to extremities of the distribution system.system. qr + q1 Q =------(52) 1.1t – t Duct Leakage r s Air leakage from supply ducts can considerably affect HVAC whewherere sysystemstem enerenergygy use. LeaLeakagekage rereducesduces coocoolingling anand/ord/or ddehumidifyingehumidifying q1 = heatheat gaingain to space fromfrom plenumplenum throughthrough ceiling,ceiling, Btu/hBtu/h capacitcapacityy for the conditioned space, and must be offset bbyy increased q2 = heatheat llossoss fromfrom plenumplenum throughthrough floorfloor above,above, Btu/hBtu/h aairflowirflow (sometimes(sometimes rereducedduced suppsupplyly aairir temperaturestemperatures),), unlessunless leakedleaked q3 = heatheat gaingain “pickup”“pickup” byby return air,air, Btu/hBtu/h aairir enters tthehe conconditionedditioned sspacepace didirectly.rectly. SuppSupplyly aairir lleakageeakage iintonto a Q = return airflow,airflow, ccfmfm ceilinceilingg return plenum or leakleakageage from unconditioned spaces intintoo qlpp =li lightght hheateat gagainin to pplenumlenum vviaia return aair,ir, BtuBtu/h/h return ducts also affects returnn air temperature and/or humidity. qlrlr = lightlight heatheat gaingain to space, Btu/hBtu/h Determining leakage from a duct system is complex because of qf = heatheat gaingain fromfrom pplenumlenum below,below, throughthrough floor,floor, Btu/hBtu/h q = heatheat gaingain fromfrom exteriorexterior wall,wall, Btu/hBtu/h the variables in paths, fabrication, and installation methods. Refer to w q = space coolingcooling load,load, includingincluding appropriate treatment off q , q , Chapter 21 and publications from the Sheet Metal and Air Condi- r lr f aand/ornd/or qw, Btu/h tioning Contractors’ National Association (SMACNA) for methods t ==p plenumlenum aairir temperature, °F of determining leakage. In general, good-quality ducts and post- p tr = space aairir temperature, °F installation duct sealing provide highly cost-effective energy sav- tfaf = space air temperature of floor above, °F ings, with improved thermal comfort and delivery of ventilation air. ts ==supp supplyly airair temperature, °F°F Ceiling Return Air Plenum Temperatures The space above a ceiling, when used as a return air path, is a ceiling return air plenum, or simply a return plenum. Unlike a tra- ditional ducted return, the plenum may have multiple heat sources in the air path. These heat sources may be radiant and convective loads from lighting and transformers; conduction loads from adja- cent walls, roofs, or glazing; or duct and piping systems within the plenum. As heat from these sources is picked up by the unducted return air, the temperature differential between the ceiling cavity and con- ditioned space is small. Most return plenum temperatures do not rise more than 1 to 3°F above space temperature, thus generating only a relativelrelativelyy small thermal ggradientradient for heat transfer throughthrough plenumplenum ssurfaces,urfaces, exceptexcept to thethe outdoors.outdoors. ThisThis yieldsyields a relativelyrelatively large-large- ppercentageercentage rereductionduction iinn space coocoolingling lloadoad by shiftingshifting plenumplenum loadsloads to the ssystem.ystem. Another reason plenuplenumm temperatures do not rise more Fig. 15 Schematic Diagram of Typical Return Air Plenum Nonresidential Cooling and Heating Load Calculations 18.35

By substituting Equations (48), (49), (50), and (52) into heat bal- greater mass of a structural floor slab. Schiavon et al. (2010b) ance Equation (51), tp cancan be foundfound as thethe resultantresultant returnreturn airair tem-tem- showed that the presence of the raised floor reduces the slab’s ability perature or plenum temperature. The results, although rigorous and to store heat, thereby producing higher peak cooling loads for a best solved by computer, are important in determining the cooling raised-floor system than for one without a raised floor. A second load, which affects equipment size selection, future energy con-con- contributing factor is that the raised-floor surface above the under- sumptsumption,ion, andand otherother ffactors.actors. floor plenum tends to be cooler (except when illuminated by the Equations (48) to (52) are simplified to illustrate the heat balance sun) than most other room surfaces, producing a room surface tem- relationship. Heat gain into a return air plenum is nott limited to heat perature distribution resembling a chilled radiant floor system, from lights. Exterior wallswalls directly exposed toto the ceiling space cacann which has a different peak cooling load than an all-air system (Feng transfer heat directly to or from return air. For single-story buildingbuildingss et al. 2012). The precise magnitude of difference in design cooling or the top floor of a multistory buibuilding,lding, roof heat gain or loss enters loads between OH and UFAD systems is still under investigation, or leaves the ceiling plenum rather than the conditioned space but mainly depends on zone orientation and floor level, and possibly directly. TheT supply air quantity calculated by Equation (52) is only the effects of furniture. Methods for determining UFAD cooling for the conditioned space under consideration, and is assumed to loads will be updated as additional research results become availa- equal the return air quantity. ble. For more information about simplified approaches to UFAD The amount of airflow through a return plenum above a condi- cooling load calculations, see Bauman et al. (2010), Schiavon et al. tioned space may not be limited to that supplied intintoo the space; iitt (2010c), and the updated ASHRAE Underfloor Air Distribution will, however, have no noticeable effect on plenum temperature if (UFAD) Design Guide (Bauman and Daly 2013). tthehe surpsurpluslus comes ffromrom an aadjacentdjacent pplenumlenum operatoperatinging ununderder ssimilarimilar conditions. WWhere special conditions exist, Equations (48) to (52) Plenums in Load Calculations must be modified appropriately. Finally, although the building’s Currently, most designers include ceiling and floor plenums thermal storage has some effect, the amount of heat entering the within neighboring occupied spaces when thermally zoning a build- return air iss small and may be considereconsideredd as convective for calcula- ing. However, temperatures in these plenums, and the way that they ttionion ppurposes.urposes. behave, are significantly different from those of occupied spaces. Thus, they should be defined as a separate thermal zone. However, Ceiling Plenums with Ducted Returns most hand and computer-based load calculation routines currently Compared to those in unducted plenum returns, temperatures in do not allow floating air temperatures or humidities; assuming a ceiling plenums that have well-sealed return or exhaust air ducts constant air temperature in plenums, attics, and other unconditioned float considerably. In cooling mode, heat from lights and other spaces is a poor, but often necessary, assumption. The heat balance equipment raises the ceilinceilingg plplenum’senum’s temperature considerablconsiderably.y. method does allow floating space conditions, and when fully imple- SoSolarlar heatheat gaingain throughthrough a poorlypoorly insulatedinsulated roofroof can drivedrive tthehe ceceilingiling mented in design load software, should allow more accurate mod- plplenumenum temtemperatureperature to extreme levels,levels, so muchmuch so thatthat heatheat gainsgains eling of plenums and other complex spaces. to ununinsulatedinsulated suppsupplyly aairir dductuctss inin thethe pplenumlenum ccanan dramaticallydramatically decrease available coocoolingling capacitycapacity to the rooms below. In colcoldd CENTRAL PLANT weatweather,her, mucmuchh hheateat iiss llostost ffromrom warm suppsupplyly dducts.ucts. TThus,hus, iinsulatingnsulating Piping suppsupplyly airair ductsducts andand sealingsealing themthem well toto minimizeminimize airair leaks areare hihighlyghly desirable, if not essentialessential.. AppropriatelyAppropriately insulatininsulatingg roofs anandd Losses must be considered for piping systems that transport heat. plplenums’enums’ exterexteriorior wawallslls anandd mminimizinginimizing infiltrationinfiltration are alsoalso keykey toto For water or hydronic piping systems, heat iss transferred through the lowerinloweringg total buildinbuildingg loads and improvinimprovingg HVAC ssystemystem perforperfor-- piping and insulation (see(s Chapter 23 for ways to determine this mmance.ance. transfer). However, distribution of this transferred heat depends on ththee flfluiduid iinn tthehe ppipeipe anandd tthehe surrounsurroundingding envenvironment.ironment. Underfloor Air Distribution Systems Consider a heating hot-water pipe. If the pipe serves a room Room cooling loads determined by methods in this chapter can- heater and is routed through the heated space, any heat loss from the not model two distinguishing aspects of the thermal performance of pipe adds heat to the room. Heat transfer to the heated space and underfloor air distribution (UFAD) systems under cooling opera- heat loss from the piping system is null. If the piping is exposed to tion: ambient conditions en route to the heater, the loss must be consid- eeredred wwhenhen seselectinglecting tthehe hheatingeating equequipment;ipment; if tthehe ppipeipe iiss routeroutedd • Room air stratification: UFAD systems supply cool air at the floor tthroughhrough a space requiringrequiring cooling,cooling, heat loss from the pipinpipingg alsalsoo and extract warmer air at the ceiling, thus creating vertical ther- bbecomesecomes a lloadoad on tthehe coocoolingling system. mal stratification. Cooling load models assume a well-mixed uni- In summary, the designer must evaluate both the magnitude of form space temperature. tthehe pipe heat transfer and the routinroutingg of the pipinpiping.g. • Underfloor air supply plenums: cool supply air flowing through the underfloor plenum is exposed to heat gain from both the con- Pumps crete slab (conducted from the warm return air on the adjacent Calculating heat gain from pumps is addressed in the section on floor below in a multistory building) and the raised floor panels Electric Motors. For pumps serving hydronic systems, disposition (conducted from the warmer room above). of heat from the pumps depends on the service. For chilled-water Extensive simulation and experimental research led to the devel- systems, energy applied to the fluid to generate flow and pressure opment of a whole-building energy simulation program capable of becomes a chiller load. For condenser water pumps, pumping en- modeling energy performance and load calculations for UFAD sys- ergy must be rejected through the cooling tower. The magnitude of tems (Bauman et al. 2007; Webster et al. 2008). Previously, it was pumping energy relative to cooling load is generally small. thought that cooling loads for UFAD and overhead (OH) mixing systems were nearly identical. However, energy modeling studies EXAMPLE COOLING AND HEATING show that the UFAD cooling load is generally higher than that LOAD CALCULATIONS calculated in the same building for a well-mixed system (Schiavon et al. 2010a). The difference is primarily caused by the thermal stor- To illustrate the cooling and heating load calculation procedures age effect of the lighter-weight raised-floor panels compared to the discussed in this chapter, an example problem has been developed 18.36 2013 ASHRAE Handbook—Fundamentals

Table 26 Summary of RTS Load Calculation Procedures Equation Equation No. in No. in Equation Chapter Equation Chapter ExternalExternal Heat GaiGainn IAC(IAC( . ) = indoor solar attenuation coefcoefficientfficient foforr beabeamm solarsolar heatheat gaingain coefficient;coefficient; = 1.0 if no indoorindoor shadingshading device.device. Sol-AirSol-Air TemperaturTemperaturee IAC(IAC( . ) iiss a ffunctionunction ooff sshadehade ttypeype anand,d, ddependingepending on  type, may also be a function of beam solar angle of Et  R te = to + ------– ------(30) incidenceincidence and shade geometry ho ho wwherehere IACIACD = indoorindoor solarsolar attenuationattenuation coefficientcoefficient forfor diffusediffuse solarsolar heatheat te ==so sol-airl-air temperature, °F gaingain coecoefficient;fficient; = 1.0 if nonott indoor shading device. IACD iiss a functionfunction ofof shadeshade typetype and,and, dependingdepending on type,type, maymay to ==out outdoordoor aairir temperature, °F°F a ==a absorptancebsorptance ooff sursurfaceface fforor solarsolar radiationradiation aalsolso bebe a functionfunction ofof sshadehade ggeometryeometry E = total solar radiation incident on surface, Btu/h·ftBtu/h·fft2 t PPartitions,artitions, CeiCeilings,lings, FFloorsloors Transmission ho = coefficient of heat transfer by long-wave radiation and convection at outer surface, Btu/h·ftBtu/h·fft2·°F q = UA(t – t ) (33)(33)  = hemispherical emittance of surface b i R = differencedifference betweenbetween long-wavelong-wave radiationradiation incidentincident on wherewhere surface from sky and surroundings and radiation emitted q = heatheat transfertransfer rate,rate, Btu/hBtu/h 2 by blackbody at outdoor air temperature, Btu/h·ftBtu/h·fft ; 20 for U = coefficient of overall heat transfer between adjacent and horizontalhorizontal surfaces;surfaces; 0 forfor verticalvertical sursurfacesfaces conditioned space, Btu/h·ftBtu/h·fft2·°F·°F 2 WWallall andand RoofRoof TransmissionTransmission A = area of separating section concerned, ft tb ==average average aairir temperature inin adjacentadjacent space, °F ti ==a airir temperature iinn conconditionedditioned space, °F q = c0qi, + c1qi, --1 + c2qi, -2- + … + c2323qi, -23- (32)(32) IInternalnternal Heat GainGain qi, -n = UA(te, -n – trc) (31)(31) wherewhere OOccupantsccupants q =h hourlyourly conductiveconductive hheateat ggainain fforor sursurface,face, Btu/hBtu/h q = q N qi, =h heateat inputinput forfor current hourhour s s,pers,p,per

qi, -n ==con conductiveductive heatheat inputinput forfor surfacesurface n hourshours ago, Btu/hBtu/h ql = ql,perl,p N c0, c1, etc. = conduction time factors wherewhere U = overall heat transfer coefficient for surface, Btu/h·ftBtu/h·fft2·°F qs = occupant sensiblesensible heatheat gain,gain, Btu/hBtu/h A = surface area, ft2 ql = occupant latentlatent heatheat gagain,in, BtuBtu/h/h t ==so sol-airl-air temperature n hhoursours ago, °F e, -n qs,pers,p,perp = sensiblesensible hheateat gaingain per person, BtuBtu/h·person;/h·person; see TaTableble 1 t = presumedpresumed constant room aairir temperature, °F rc ql,perl,pp =l latentatent heatheat gaingain per person, BtuBtu/h·person;/h·person; see TableTable 1 N ==num numberber ooff occuoccupantspants FFenestrationenestration TransmissionTransmission LLightingighting q = UAUA(T – T ) ((15)15) c outt in qell = 3.41WFFul Fsa (1)(1) wwherehere whewherere q = f fenestrationenestration transmtransmissionission hheateat gagain,in, BtuBtu/h/h qelel =h heateat gagain,in, Btu/hBtu/h U = overaoverallll U-U-factor,factor, iincludingncluding fframerame and mounting orientation W = totatotall lighlightt wattawattage,ge, W 2 from Table 4 of Chapter 15, Btu/h·fBtu/h·ftft ·°F·°F Ful = lightinglighting use factorfactor 2 A =window area, ft Fsa =ligh lightingting specspecialial aallowancellowance factorfactor Tin =i indoorndoor temperature, °F 3.3.4141 = co conversionnversion facfactortor T ==out outdoordoor temperature, °F°F out ElectElectricric MotorsMotors

Fenestration SoSolarlar qem = 2545((P/EM)FUM FLM (2)(2) whwhereere q = AAEE SHGC(( )IAC() ( , ) b t,b ((13)13) qem = heatheat equivalentequivalent ofof equipmentequipment operation,operation, Btu/hBtu/h P = motor power rating,rating, hp E = motor efficiency,efficiency, decimaldecimal fractionfraction <1.0 qd = A(Et,d + Et,r)>SHGCCND IACD (14)(14) M FUMUM = motor use ffactor,actor, 1.0 or ddecimalecimal ffractionraction <1.<1.00 wherewhere FLM ==motor motor lloadoad factor,factor, 1.0 or ddecimalecimal fractionfraction <1.0<1.0 qb = beambeam solarsolar heatheat gagain,in, BtuBtu/h/h 2545 = conversconversionion ffactor,actor, BtuBtu/h·hp/h·hp q = diffusediffuse solarsolar heatheat gain,gain, Btu/hBtu/h d HHoodedooded CooCookingking AppAppliancesliances A =window area, ft2 Et,b, Et,d , = beam,beam, skysky diffdiffuse,use, anandd grounground-d-rereflectedflected diffdiffuseuse irradiance,irradiance, qs = qinput FU FR andd Et,r calculatedcalculated usingusing equationsequations inin ChapterChapter 14 SHGCSHGC(( ) = beambeam solarsolar heatheat gaingain coefficientcoefficient as a functionfunction ofof incidentincident wherewhere

angleangle ; may be interpolated between values in Table 10 of qs = sensiblesensible heatheat gain,gain, Btu/hBtu/h ChapterChapter 1515 qinputp = namepnameplatelate or rateratedd energy input,input, Btu/hBtu/h > N SSHGCHGC D = diffusediffuse solarsolar heatheat gaingain coefficientcoefficient (also(also referredreferred to as FU ==usage usage factor;factor; see TaTablesbles 5B, 5C, 5D hemisphericalhemispherical SHGC);SHGC); fromfrom TableTable 10 ofof ChapterChapter 1515 FR ==ra radiationdiation factor;factor; see TablesTables 5B,5B, 5C,5C, 55DD Nonresidential Cooling and Heating Load Calculations 18.37

Table 26 Summary of RTS Load Calculation Procedures (Concluded) Equation Equation No. in No. in Equation Chapter Equation Chapter

ForFor ototherher appappliancesliances andand equipment,equipment, findfind qs for Radiant Portion of Sensible Cooling Load UUnhoodednhooded cookingcooking appliances:appliances: TableTable 55AA Qi,r = Qr, ((34)34) OtOtherher kitchenkitchen equipment:equipment: TableTable 5E5E … HospHospitalital andand laboratorylaboratory equequipment:ipment: TaTablesbles 6 anandd 7 Qr, = r0qr, + r1qr, ––1 + r2qr, –2– + r3qr, –3– + + r23qr, –23– Computers, printers,printers, scanners, etc.: TablesTables 8 andand 9 wherewhere

MMiscellaneousiscellaneous officeoffice equipment:equipment: TableTable 10 Qr, ==ra radiantdiant coolingcooling loadload Qr for current hour , BtuBtu/h/h qr, ==ra radiantdiant hheateat gaingain forfor current hour,hour, Btu/hBtu/h FiFindnd ql forfor qr, n ==ra radiantdiant heatheat gaingain n hourshours ago, Btu/hBtu/h UnhoodedUnhooded cookingcooking appliances:appliances: TableTable 55AA r0, r1, etc. = radiant time factors; see Table 19 for radiant time factors for OtherOther kitchenkitchen equipment:equipment: TableTable 5E5E nnonsolaronsolar hheateat gains:gains: wall,wall, roof,roof, partition,partition, ceiling,ceiling, floor,floor, ffenestrationenestration transmtransmissionission hheateat ggains,ains, anandd occupant, lighlighting,ting, mmotor,otor, appapplianceliance heatheat gain.gain. AlsoAlso usedused forfor fenestrationfenestration diffdiffuseuse VentVentilationilation andand InfiltrationInfiltration AirAir Heat GainGain ssolarolar hheateat gain;gain; see TableTable 20 forfor radiantradiant timetime factorsfactors forfor ffenestrationenestration bbeameam sosolarlar hheateat gagain.in.

qs = 1.10Qs t (10)(10) qr, = qi,ssFr wherewhere

ql = 60 × 0.075 × 1076Qs W = 4840Qs W (11)(11) qi,si,,s = senssensibleible hheateat gagainin frfromom hheateat gagainin eelementlement i, Btu/hBtu/h F =f fractionraction ofof heatheat gaingain thatthat isis radiant.radiant. wherewhere r DDataata Sources:Sources: qs =sens sensibleible heatheat gaingain duedue to infiltration,infiltration, Btu/hBtu/h ql ==l latentatent heatheat gaingain duedue to infiltration,infiltration, Btu/hBtu/h WallWall transmission:transmission: see TableTable 1414 Qs ==i infiltrationnfiltration airflowairflow at standardstandard aairir conconditions,ditions, ccfmfm RoofRoof transmtransmission:ission: see TaTableble 1144 to = outdooroutdoor aairir temperature, °F°F FloorFloor transmtransmission:ission: see TableTable 14 ti ==i indoorndoor airair temperature, °F°F FenestrationFenestration transmission:transmission: see TableTable 14 Wo =out outdoordoor airair humidityhumidity ratio,ratio, lb/lb FenestrationFenestration sosolarlar hheateat gagain:in: see TableTable 14, ChapterChapter 18 Wi ==i indoorndoor aairir hhumidityumidity ratratio,io, lb/lb andand TablesTables 13A to 13G, ChapterChapter 1515 11.10.10 = ai airr sesensiblensible heaheatt facfactortor at stanstandarddard aairir conconditions,ditions, BtuBtu/h·cfm/h·cfm Lighting:Lighting: see TaTableble 3 44840840 = ai airr lalatenttent heaheatt facfactortor at sstandardtandard aairir conconditions,ditions, Btu/h·cfmBtu/h·cfm Occupants:Occupants: see TaTablesbles 1 andand 14 HoodedHooded cookingcooking appliances:appliances: see TablesTables 5B, 5C, anandd 5D5D UnhoodedUnhooded coocookingking appappliances:liances: see TaTableble 5A5A Instantaneous Room Cooling Load OtherOther appliancesappliances andand equipment:equipment: see TablesTables 5E, 8, 9, 10,10, andand 14   Infiltration:Infiltration: see TaTableble 1414 Qs = Qi,r + Qi,c  Convective Portion of Sensible Cooling Load Ql = qi,l Q = q wherewhere i,ci,,c i,c where qi,c is convective portion of heat gaingain fromfrom heatheat gaingain elementelement i, BtuBtu/h./h. Qs =room sensiblesensible coolingcooling load,load, BtuBtu/h/h q = q (1( – F ) Qi,ri,,r = radiantradiant portportionion ooff senssensibleible coocoolingling lloadoad fforor current hhour,our, i,c i,s r resultingresulting fromfrom heatheat gaingain elementelement i, Btu/hBtu/h wherewhere Qi,ci,,c = convectiveconvective portionportion ofof sensiblesensible coocoolingling load,load, resultingresulting fromfrom qi,si,,s = senssensibleible hheateat gagainin frfromom hheateat gagainin eelementlement i, Btu/hBtu/h heatheat gaingain elementelement i, Btu/hBtu/h Fr =f fractionraction ooff hheateat ggainain tthathat iiss rradiant;adiant; see row fforor radiantradiant portionportion Ql =room latentlatent coolingcooling load,load, Btu/hBtu/h forfor sources ooff raradiantdiant ffractionraction ddataata fforor iindividualndividual heatheat gaingain qi,li,,l ==l latentatent heatheat gaingain forfor heatheat gaingain elementelement i, BtuBtu/h/h elementselements

based on the ASHRAE headquarters building located in Atlanta, Room Characteristics Georgia. This example is a two-story office building of approxi- Area: 130 ft2. mately 35,000 ft2, including a variety of common office functions Floor: Carpeted 5 in. concrete slab on metal deck above a con- and occupancies. In addition to demonstrating calculation proce- ditioned space. dures, a hypothetical design/construction process is discussed to Roof: Flat metal deck topped with rigid closed-cell polyisocyan- illustrate (1) application of load calculations and (2) the need to urate foam core insulation (R = 30), and light-colored membrane develop reasonable assumptions when specific data is not yet avail- roofing. Space above 9 ft suspended acoustical tile ceiling is used as able, as often occurs in everyday design processes. a return air plenum. Assume 30% of the cooling load from the roof Table 26 provides a summary of RTS load calculation procedures. is directly absorbed in the return airstream without becoming room load. Use roof U = 0.032 Btu/h·ft2·°F. SINGLE-ROOM EXAMPLE Spandrel wall: Spandrel bronze-tinted glass, opaque, backed with air space, rigid mineral fiber insulation (R = 5.0), mineral fiber Calculate the peak heating and cooling loads for the office room batt insulation (R = 13), and 5/8 in. gypsum wall board. Use span- shown in Figure 16, for Atlanta, Georgia. The room is on the second drel wall U = 0.077 Btu/h·ft2·°F. floor of a two-story building and has two vertical exterior exposures, Brick wall: Light-brown-colored face brick (4 in.), lightweight with a flat roof above. concrete block (6 in.), rigid continuous insulation (R = 5), mineral 18.38 2013 ASHRAE Handbook—Fundamentals

fiber batt insulation (R = 13), and gypsum wall board (5/8 in.). Use profile calculated per Chapter 14. See Table 27 for temperature pro- brick wall U = 0.08 Btu/h·ft2·°F. files used in these examples. Windows: Double glazed, 1/4 in. bronze-tinted outdoor pane, Indoor design conditions: 72°F for heating; 75°F with 50% rh for 1/2 in. air space and 1/4 in. clear indoor pane with light-colored inte- cooling. rior miniblinds. Window normal solar heat gain coefficient (SHGC) = 0.49. Windows are nonoperable and mounted in aluminum frames Cooling Loads Using RTS Method with thermal breaks having overall combined U = 0.56 Btu/h·ft2·°F Traditionally, simplified cooling load calculation methods have (based on Type 5d from Tables 4 and 10 of Chapter 15). Indoor atten- estimated the total cooling load at a particular design condition by uation coefficients (IACs) for indoor miniblinds are based on light independently calculating and then summing the load from each venetian blinds (assumed louver reflectance = 0.8 and louvers posi- component (walls, windows, people, lights, etc). Although the actual tioned at 45° angle) with heat-absorbing double glazing (Type 5d heat transfer processes for each component do affect each other, this from Table 13B of Chapter 15), IAC(0) = 0.74, IAC(60) = 0.65, simplification is appropriate for design load calculations and useful IAD(diff) = 0.79, and radiant fraction = 0.54. Each window is to the designer in understanding the relative contribution of each 6.25 ft1.91 m wide by 6.4 ft tall for an area per window = 40 ft2. component to the total cooling load. South exposure: Orientation = 30° east of true south Cooling loads are calculated with the RTS method on a compo- Window area = 40 ft2 nent basis similar to previous methods. The following example parts Spandrel wall area = 60 ft2 illustrate cooling load calculations for individual components of Brick wall area = 60 ft2 this single room for a particular hour and month. Equations used are West exposure: Orientation = 60° west of south summarized in Table 26. 2 Window area = 40 ft Part 1. Internal cooling load using radiant time series. Calculate the 2 Spandrel wall area = 60 ft cooling load from lighting at 3:00 PM for the previously described office. 2 Brick wall area = 40 ft Solution: First calculate the 24 h heat gain profile for lighting, then Occupancy: 1 person from 8:00 AM to 5:00 PM. split those heat gains into radiant and convective portions, apply the Lighting: One 4-lamp pendant fluorescent 8 ft type. The fixture appropriate RTS to the radiant portion, and sum the convective and has four 32 W T-8 lamps plus electronic ballasts (special allowance radiant cooling load components to determine total cooling load at the factor 0.85 per manufacturer’s data), for a total of 110 W for the designated time. Using Equation (1), the lighting heat gain profile, based on the occupancy schedule indicated is room. Operation is from 7:00 AM to 7:00 PM. Assume 0% of the cooling load from lighting is directly absorbed in the return air- q1 = (110 W)3.41(0%) = 0 q13 = (110 W)3.41(100%) = 375 stream without becoming room load, per Table 3. q2 = (110 W)3.41(0%) = 0 q1414 = (110 W)3.41(100%) = 375 Equipment: One computer and a personal printer are used, for q3 = (110 W)3.41(0%) = 0 q15 = (110 W)3.41(100%) = 375 2 which an allowance of 1 W/ft is to be accommodated by the q = (110 W)3.41(0%) = 0 q = (110 W)3.41(100%) = 375 cooling system, for a total of 130 W for the room. Operation is from 4 16 q = (110 W)3.41(0%) = 0 q = (110 W)3.41(100%) = 375 8:00 AM to 5:00 PM. 5 17 Infiltration: For purposes of this example, assume the building is q6 = (110 W)3.41(0%) = 0 q18 = (110 W)3.41(100%) = 375 maintained under positive pressure during peak cooling conditions q7 = (110 W)3.41(100%) = 375 q19 = (110 W)3.41(0%) = 0 and therefore has no infiltration. Assume that infiltration during q8 = (110 W)3.41(100%) = 375 q2020 = (110 W)3.41(0%) = 0 peak heating conditions is equivalent to one air change per hour. q9 = (110 W)3.41(100%) = 375 q21 = (110 W)3.41(0%) = 0 Weather data: Per Chapter 14, for Atlanta, Georgia, latitude = q = (110 W)3.41(100%) = 375 q = (110 W)3.41(0%) = 0 33.64, longitude = 84.43, elevation = 1027 ft above sea level, 99.6% 10 2222 heating design dry-bulb temperature = 21.5°F. For cooling load cal- q1111 = (110 W)3.41(100%) = 375 q23 = (110 W)3.41(0%) = 0 culations, use 5% dry-bulb/coincident wet-bulb monthly design day q1212 = (110 W)3.41(100%) = 375 q24 = (110 W)3.41(0%) = 0 The convective portion is simply the lighting heat gain for the hour being calculated times the convective fraction for non-in-ceiling fluo- rescent luminaire (pendant), from Table 3:

Qc,15, = (375)(43%) = 161.3 Btu/h The radiant portion of the cooling load is calculated using lighting heat gains for the current hour and past 23 h, the radiant fraction from Table 3 (57%), and radiant time series from Table 19, in accordance with Equation (34). From Table 19, select the RTS for medium-weight construction, assuming 50% glass and carpeted floors as representative of the described construction. Thus, the radiant cooling load for light- ing is … Qr,,15 = r0(0.48)( )q1515 + r1(0.48)( )q1414 + r2(0.48)( )q13 + r3(0.48)( )q12 + + r23(0.48)( )q1616 = (0.49)(0.57)(375)(0.49)(0.57)(375) + (0.17)(0.57)(375)(0.17)(0.57)(375) + ((0.09)(0.57)(375)0.09)(0.57)(375) + (0.05)(0.57)(375)(0.05)(0.57)(375) + (0.03)(0.57)(375)(0.03)(0.57)(375) + ((0.02)(0.57)(375)0.02)(0.57)(375) + (0.02)(0.57)(375)(0.02)(0.57)(375) + (0.01)(0.57)(375)(0.01)(0.57)(375) + ((0.01)(0.57)(375)0.01)(0.57)(375) + ((0.01)(0.57)0.01)(0.57) ((0)0) + ((0.01)(0.57)(0)0.01)(0.57)(0) + ((0.01)(0.57)(0)0.01)(0.57)(0) + (0.01)(0.57)(0)(0.01)(0.57)(0) + (0.01)(0.57)(0)(0.01)(0.57)(0) + ((0.01)(0.5748)(0)0.01)(0.5748)(0) + (0.01)(0.57)(0)(0.01)(0.57)(0) + (0.01)(0.57)(0)(0.01)(0.57)(0) + ((0.01)(0.57)(0)0.01)(0.57)(0) + ((0.01)(0.57)(0)0.01)(0.57)(0) + (0.01)(0.57)(0)(0.01)(0.57)(0) + (0.00)(0.57)(0)(0.00)(0.57)(0) + ((0.00)(0.57)(375)0.00)(0.57)(375) + (0.00)(0.57)(375)(0.00)(0.57)(375) Fig. 16 Single-Room Example Office + ((0.00)(0.57)(375)0.00)(0.57)(375) = 190.3 BtuBtu/h/h Nonresidential Cooling and Heating Load Calculations 18.39

Table 27 Monthly/Hourly Design Temperatures (5% Conditions) for Atlanta, GA, °F January February March April May June July August September October November December Hour db wb db wb db wb db wb db wb db wb db wb db wb db wb db wb db wb db wb 1 44.8 44.0 47.4 45.7 53.1 48.7 59.4 54.3 66.4 61.9 72.2 66.7 73.9 68.9 73.8 69.3 69.5 64.9 60.1 56.8 52.5 50.8 46.4 46.3 2 44.0 43.4 46.6 45.1 52.1 48.2 58.5 53.9 65.6 61.6 71.4 66.4 73.0 68.7 73.1 69.1 68.7 64.6 59.3 56.4 51.7 50.3 45.6 45.6 3 43.4 43.0 46.0 44.8 51.5 47.9 57.8 53.6 65.0 61.4 70.8 66.2 72.4 68.5 72.5 68.9 68.2 64.4 58.7 56.2 51.0 50.0 45.0 45.0 4 42.8 42.6 45.3 44.4 50.8 47.5 57.2 53.3 64.4 61.2 70.2 66.0 71.8 68.3 71.9 68.7 67.6 64.2 58.1 55.9 50.4 49.6 44.4 44.4 5 42.4 42.3 44.9 44.1 50.3 47.3 56.7 53.1 64.0 61.0 69.8 65.9 71.4 68.2 71.5 68.6 67.2 64.1 57.7 55.7 50.0 49.4 44.0 44.0 6 42.8 42.6 45.3 44.4 50.8 47.5 57.2 53.3 64.4 61.2 70.2 66.0 71.8 68.3 71.9 68.7 67.6 64.2 58.1 55.9 50.4 49.6 44.4 44.4 7 44.2 43.6 46.8 45.3 52.4 48.3 58.8 54.0 65.8 61.7 71.6 66.5 73.2 68.8 73.2 69.1 68.9 64.7 59.5 56.5 51.9 50.4 45.8 45.8 8 47.7 46.0 50.4 47.5 56.3 50.3 62.6 55.6 69.3 63.0 75.1 67.6 76.7 69.8 76.5 70.2 72.2 65.9 63.0 58.1 55.4 52.4 49.1 48.2 9 51.6 48.7 54.4 50.0 60.7 52.4 67.0 57.5 73.1 64.5 78.9 68.8 80.6 71.0 80.2 71.3 75.8 67.2 66.8 59.8 59.4 54.6 52.9 50.9 10 55.0 51.1 57.9 52.2 64.6 54.4 70.8 59.1 76.6 65.8 82.3 69.9 84.1 72.0 83.5 72.3 79.0 68.3 70.3 61.3 62.9 56.6 56.3 53.2 11 58.1 53.2 61.1 54.1 68.0 56.1 74.3 60.6 79.6 66.9 85.4 70.9 87.2 73.0 86.4 73.2 81.9 69.3 73.3 62.7 66.0 58.3 59.2 55.3 12 60.1 54.7 63.2 55.4 70.3 57.2 76.5 61.5 81.7 67.7 87.4 71.6 89.2 73.6 88.4 73.8 83.8 70.0 75.4 63.6 68.1 59.5 61.2 56.7 13 61.8 55.8 64.9 56.5 72.2 58.1 78.4 62.3 83.3 68.3 89.0 72.1 90.9 74.1 89.9 74.3 85.3 70.6 77.0 64.3 69.8 60.4 62.8 57.8 14 62.8 56.5 65.9 57.1 73.3 58.7 79.5 62.8 84.3 68.7 90.0 72.4 91.9 74.4 90.9 74.6 86.3 70.9 78.0 64.8 70.8 61.0 63.8 58.5 15 62.8 56.5 65.9 57.1 73.3 58.7 79.5 62.8 84.3 68.7 90.0 72.4 91.9 74.4 90.9 74.6 86.3 70.9 78.0 64.8 70.8 61.0 63.8 58.5 16 61.6 55.6 64.6 56.3 71.9 58.0 78.1 62.2 83.1 68.2 88.8 72.0 90.7 74.0 89.7 74.2 85.2 70.5 76.8 64.3 69.6 60.3 62.6 57.7 17 59.9 54.5 63.0 55.3 70.1 57.1 76.3 61.4 81.5 67.6 87.2 71.5 89.0 73.5 88.2 73.8 83.6 69.9 75.2 63.5 67.9 59.4 61.0 56.6 18 57.9 53.1 60.9 54.0 67.8 56.0 74.0 60.5 79.4 66.9 85.2 70.8 87.0 72.9 86.2 73.2 81.7 69.3 73.1 62.6 65.8 58.2 59.0 55.2 19 54.8 51.0 57.7 52.0 64.3 54.3 70.6 59.0 76.4 65.7 82.1 69.9 83.9 72.0 83.3 72.3 78.9 68.2 70.1 61.3 62.7 56.5 56.1 53.1 20 52.6 49.4 55.4 50.6 61.8 53.0 68.1 58.0 74.2 64.9 79.9 69.2 81.7 71.3 81.2 71.6 76.8 67.5 67.9 60.3 60.4 55.2 53.9 51.6 21 50.8 48.1 53.5 49.4 59.7 52.0 66.0 57.1 72.3 64.2 78.1 68.6 79.8 70.7 79.5 71.1 75.0 66.9 66.0 59.4 58.5 54.2 52.1 50.3 22 48.9 46.8 51.6 48.3 57.7 50.9 64.0 56.2 70.5 63.5 76.3 68.0 78.0 70.2 77.7 70.5 73.3 66.3 64.2 58.6 56.7 53.1 50.3 49.0 23 47.5 45.9 50.2 47.4 56.1 50.2 62.4 55.5 69.1 62.9 74.9 67.5 76.5 69.8 76.4 70.1 72.0 65.8 62.8 58.0 55.2 52.3 49.0 48.1 24 46.1 44.9 48.7 46.4 54.4 49.4 60.8 54.8 67.7 62.4 73.4 67.1 75.1 69.3 75.0 69.7 70.6 65.3 61.4 57.3 53.7 51.5 47.6 47.1

Table 28 Cooling Load Component: Lighting, Btu/h Heat Gain, Btu/h Nonsolar Total Room Usage RTS Zone Radiant Sensible % Lighting Sensible Convective Radiant Profile, Type 8, Cooling Cooling to Return Cooling Hour % Total 43% 57% % Load Load 26% Load 1 0 — — — 49 26 26 — 26 2 0 — — — 17 26 26 — 26 330———90 — — — 9 24 242244—2— 244 440———50 — — — 5 21 212211—2— 211 550———30 — — — 3 19 191199—1— 199 660———20 — — — 2 17 171177—1— 177 7 100 375 161 214 2 120 281 — 281 8 100 375 161 214 1 154 315 — 315 9 100 375 161 214 1 171 332 — 332 10 100 375 161 214 1 180 341 — 341 11 100 375 161 214 1 184 345 — 345 12 100 375 161 214 1 186 347 — 347 13 100 375 161 214 1 188 349 — 349 14 100 375 161 214 1 188 349 — 349 15 100 375 161 214 1 190 352 — 352 16 100 375 161 214 1 192 354 — 354 17 100 375 161 214 1 195 356 — 356 18 100 375 161 214 1 197 358 — 358 11990———10 — — — 1 99449944—9— 944 22000———10 — — — 1 66006600—6— 600 22110———00 — — — 0 44334433—4— 433 22220———00 — — — 0 33443344—3— 344 22330———00 — — — 0 33003300—3— 300 22440———00 — — — 0 22882288—2— 288 Total 4,501 1,936 2,566 1 2,566 4,501 — 4,501 18.40 2013 ASHRAE Handbook—Fundamentals

The total lighting cooling load at the designated hour is thus BeamBeam normanormall iirradiancerradiance Eb  ab Qlight = Qc,15 + Qr,15 = 161.3 + 190.3 = 351.6 Btu/h Eb = Eo exp(–– b m ) See Table 28 for the office’s lighting usage, heat gain, and cooling m = relativerelative airair mass ! ! –1.6364–1.6364 ! load profiles. =1/[sin= 1/[sin +0.50572(6.07995 + ) ],], expressedd in degrees = 1.189051.18905 Part 2. Wall cooling load using sol-air temperature, conduction time ab ==b beameam airair mass exexponentponent     series and radiant time series. Calculate the cooling load contribution ==1 1.454.454 – 00.406.406 b – 0.268 d + 0.021 b d from the spandrel wall section facing 60° west of south at 3:00 PM local =0.705570 0.70557055 0.70557050.7055705 standard time in July for the previously described office. Eb = 419.8 exp[–0.556(1.8905exp[–0.556(11.8905 )])] = 255.3 Btu/h·fBtu/h·ftft2 Solution: Determine the wall cooling load by calculating (1) sol-air temperaturestemperatures at thethe exteriorexterior surface,surface, (2)(2) heatheat inputinput basedbased on sol-airsol-air tem- SurfaceSurface bbeameam iirradiancerradiance Et,bt,

perature,perature, (3)(3) delayeddelayed heatheat gaingain thrthrougoughh thethe mass ofof thethe wallwall to thethe inte-inte- Et,bt, = Eb cos riorrior surfacesurface usingusing conductionconduction timetime series,series, andand (4)(4) delayeddelayed space coolingcooling = (255.3) cos (58.5) loadload ffromrom hheateat gagainin ususinging raradiantdiant ttimeime serseries.ies. = 133.6 Btu/h·fBtu/h·ftft2 First,First, calculatecalculate thethe sol-airsol-air temperaturetemperature at 3:00 PM local standard RatioRatio Y of sky diffuse radiation on vertical surface to sky diffuse radia- timetime (LST)(LST) (4:00(4:00 PM daylight saving time) on July 21 for a vertical, tiontion onon horizontalhorizontal surfacesurface ddark-coloredark-colored wallwall surface,surface, facingfacing 60° west ofof south,south, locatedlocated inin Atlanta,Atlanta, GeorGeorgiagia (l(latitudeatitude = 33.64, longitudelongitude = 84.4384.43),), solarsolar taubtaub = 0.440 andand Y = 0.55 + 0.0.437437 cos + 0.313 cos2 tautaudd = 2.202 ffromrom montmonthlyhly AtAtlantalanta weatherweather ddataata forfor JuJulyly ((TableTable 1 in = 0.55 + 0.437 cos (58.45) + 0.313 cos2(58.45)( CChapterhapter 14).14). From TaTableble 26, thethe calculatedcalculated outdooroutdoor designdesign temperaturetemperature =0.8644= 0.8644 fforor tthathat montmonthh anandd timetime isis 92°F. TheThe groundground reflectivityreflectivity isis assumedassumed DiffuseDiffuse irradianceirradiance Ed – Horizontal surfaces = 0.2. g E = E exp(–– madd) Sol-airSol-air temperature iiss cacalculatedlculated uusingsing EquatEquationion (30).(30). For tthehe ddark-ark- d o d adad ==diff diffuseuse airair mass exponentexponent coloredcolored wall,wall, /h = 0.30, and for vertical surfaces,  R/h = 0. The o o = 0.507 + 0.0.205205 – 0.080  – 0.190   solarsolar irradianceirradiance E on the wall must be determined using the equations b d b d t ==0 0.2369528.2369528 inin ChapterChapter 14:14:  add Ed = Eo exp(–– d m ) SolarSolar AnglesAngles: = 419.8 exp[–2.202(1.8905exp[–2.202(11.89050.23695280.2369528)])] = southwest orientation = +60° = 42.3 Btu/h·ftBtu/h·fft2  = surface tilt from horizontal (where horizontal = 0°) = 90° for DiffuseDiffuse irradianceirradiance Ed – Vertical surfaces verticalvertical wallwall surfacesurface E = E Y 3:003:00 PM LST = hour 15 t,dt, d = (42.3)(0.864)) CaCalculatelculate sosolarlar altitude,altitude, solarsolar azimuth,azimuth, surfacesurface solarsolar azimuth,azimuth, andand = 36.6 Btu/h·fBtu/h·ftft2 iincidentncident angleangle as follows:follows: GroundGround reflectedreflected irradianceirradiance Et,rt, From TableTable 2 inin ChapterChapter 14, solarsolar positionposition datadata andand constants forfor ! $% JuJulyly 21 areare Et,rt,r =(= (Eb sinsin + Ed) g(l( – cos =[%&&'(% sinn (57.2) + 42.3](0.2)[1 – cos (90)]/2 ET = –6.4 mminin = 25.7 Btu/h·ftBtu/h·fft2  = 20.4° 2 TotalTotal sursurfaceface iirradiancerradiance Et Eo = 419.8 Btu/h·ftBtu/h·fft LocalLocal standardstandard meridianmeridian (LSM)(LSM) forfor Eastern TimeTime Zone = 75°.75°. Et = ED + Ed + Er = 133.6 + 36.6 + 25.7 Apparent solarsolar timetime ASTAST = 195.9 Btu/h·ftBtu/h·fft2 AST = LST + ETET/60/60 + (LSM(LSM – LON)/15LON)/15 Sol-airSol-air temperature [from[from EquationEquation (30)]:(30)]: = 15 + (–6.4/60) + [(75 – 84.43)/15]   = 14 14.2647.2647 Te = to + Et /ho – R/ho = 91.9 + (0.30)(195.9) – 0 Hour anganglele H, degrees = 150.7°F H =15= 15(AST(AST – 1212)) This procedure is used to calculate the sol-air temperatures for each = 15(14.2647 – 12) hour on each surface. Because of the tedious solar angle and intensity = 33.97° calculations, using a simple computer spreadsheet or other computer SSolarolar aaltitudeltitude ! software can reduce the effort involved. A spreadsheet was used to cal- ssinin ! =cos L cos  cos H + sin L ssinin  culate a 24 h sol-air temperature profile for the data of this example. =cos= cos (33.64)(33.64) cos (20.4)(20.4) cos (33.97)(33.97) + sinsin (33.64)(33.64) sinsin (20.4)(20.4) See Table 29A for the solar angle and intensity calculations and Table = 0 0.841.841 29B for the sol-air temperatures for this wall surface and orientation. !! ==sinsinn–1(0.841)( = 57.2° Conductive heat gain is calculated using Equations (31) and (32). First, calculate the 24 h heat input profile using Equation (31) and the " SolarSolar azimuthazimuth sol-air temperatures for a southwest-facing wall with dark exterior cos " ==(sin(sin ! sin L – sinsin )/(cos)/(cos ! cos L) color: ==[ [(sin(sin (57.2)sin(57.2)sin (33.64)(33.64) – sinsin (20.4)]/[cos(20.4)]/[cos (57.2)(57.2) cos (33.64)](33.64)] qi,1, = (0.077)(60)(73.9 – 75) = –5 Btu/h = 0.2580.258 qi,2, = (0.077)(60)(73 – 75)= –9 " =cos= cos–1–1(0.253)( = 75.05° qi,3, = (0.077)(60)(72.4 – 75)= –12 # Surface-solarSurface-solar azimuthazimuth qi,4, = (0.077)(60)(71.8 – 75)= –15 # = " – qi,5, = (0.077)(60)(71.4 – 75)= –17 = 75.05 – 60 qi,6, = (0.077)(60)(72.8 – 75)= –10 = 15.05° qi,7, = (0.077)(60)(77.4 – 75)= 11 q = (0.077)(60)(84.1 – 75)= 42 IncidentIncident angleangle i,8, qi,9, = (0.077)(60)(90.8 – 75)= 73 !  !  cos =cos cos g sin + sin cos qi,10, = (0.077)(60)(96.7 – 75)= 100 ==cos cos (57.2)(57.2) cos ((15.05)15.05) ssinin ((90)90) + ssinin ((57.2)57.2) cos (90)(90) qi,11, = (0.077)(60)(101.5 – 75)= 122 = 0.5230.523 qi,12, = (0.077)(60)(105.5 – 75)= 141 –1 ==coscos (0.523)( = 58.45° qi,13, = (0.077)(60)(122.4 – 75)= 219 Nonresidential Cooling and Heating Load Calculations 18.41

qi,14, = (0.077)(60)(139.6 – 75)= 298 Solution: First, calculate the 24 h heat gain profile for the window, qi,15, = (0.077)(60)(150.7 – 75)= 350 then split those heat gains into radiant and convective portions, apply qi,16, = (0.077)(60)(153.7 – 75)= 363 the appropriate RTS to the radiant portion, then sum the convective and qi,17, = (0.077)(60)(147.7 – 75)= 336 radiant cooling load components to determine total window cooling qi,18, = (0.077)(60)(131.7 – 75)= 262 load for the time. The window heat gain components are calculated PM qi,19, = (0.077)(60)(103.1 – 75)= 130 using Equations (13) to (15). From Part 2, at hour 15 LST (3:00 ): q = (0.077)(60)(81.7 – 75) = 31 2 i,20, Et,bt,, = 133.6 Btu/h·ftBtu/h·fft q = (0.077)(60)(79.8 – 75) = 22 2 i,21, Et,d = 36.6 Btu/h·ftBtu/h·fft q = (0.077)(60)(78.0 – 75) = 14 2 i,22, Er = 25.7 Btu/h·ftBtu/h·fft q = (0.077)(60)(76.5 – 75) = 7 i,23, = 58.45° qi,24, = (0.077)(60)(75.1 – 75) = 0 From Chapter 15, Table 10, for glass type 5d, Next, calculate wall heat gain using conduction time series. The preceding heat input profile is used with conduction time series to SHGC(SHGC( ) = SHGCSHGC(58.45)(58.45) = 0.3978 (i(interpolated)nterpolated) calculate the wall heat gain. From Table 16, the most similar wall >SHGCSHGCN =0.41= 0.41 construction is wall number 1. This is a spandrel glass wall that has D similar mass and thermal capacity. Using Equation (32), the conduction From Chapter 15, Table 13B, for light-colored blinds (assumed lou- time factors for wall 1 can be used in conjunction with the 24 h heat ver reflectance = 0.8 and louvers positioned at 45° angle) on double- input profile to determine the wall heat gain at 3:00 PM LST: glazed, heat-absorbing windows (Type 5d from Table 13B of Chapter 15), IAC(0) = 0.74, IAC(60) = 0.65, IAC(diff) = 0.79, and radiant frac- … q1515 = c0 qi,15, + c1qi,14, + c2qi,13, + c3qi,12, + + c2323qi,14, tion = 0.54. Without blinds, IAC = 1.0. Therefore, window heat gain = ((0.18)(350)0.18)(350) + (0.58)(298)(0.58)(298) + ((0.20)(219)0.20)(219) + ((0.04)(141)0.04)(141) components for hour 15, without blinds, are + (0.00)(122)(0.00)(122) + ((0.00)(100)0.00)(100) + ((0.00)(73)0.00)(73) + ((0.00)(42)0.00)(42) q = AE SHGC(SHGC( )()(IAC)IAC) = ((40)(133.6)(0.3978)(1.00)40)(133.6)(0.3978)(1.00) = 2126 BtuBtu/h/h + ((0.00)(11)0.00)(11) + ((0.00)(–10)0.00)(–10) + ((0.00)(–17)0.00)(–17) + ((0.00)(–15)0.00)(–15) b1515 t,bt, + ((0.00)(–12)0.00)(–12) + ((0.00)(–9)0.00)(–9) + ((0.00)(–5)0.00)(–5) + ((0.00)(0)0.00)(0) > N qd15 = A(Et,d + Er) SHGCSHGC D(IAC)( = (40)(36.6 + 25.7)(0.41)(1.00) + ((0.00)(7)0.00)(7) + ((0.00)(14)0.00)(14) + ((0.00)(22)0.00)(22) + ((0.00)(31)0.00)(31) + ((0.00)(130)0.00)(130) + ((0.00)(262)0.00)(262) + ((0.00)(336)0.00)(336) + ((0.00)(363)0.00)(363) = 1021 Btu/hBtu/h = 285 Btu/hBtu/h qc1515 = UA(toutt – tin) = (0.56)(40)(91.9 – 75) = 379 Btu/h Because of the tedious calculations involved, a spreadsheet is used This procedure is repeated to determine these values for a 24 h heat to calculate the remainder of a 24 h heat gain profile indicated in Table gain profile, shown in Table 30. 29B for the data of this example. Total cooling load for the window is calculated by summing the con- Finally, calculate wall cooling load using radiant time series. Total vective and radiant portions. For windows with indoor shading (blinds, cooling load for the wall is calculated by summing the convective and drapes, etc.), the direct beam, diffuse, and conductive heat gains may be radiant portions. The convective portion is simply the wall heat gain for summed and treated together in calculating cooling loads. However, in the hour being calculated times the convective fraction for walls from this example, the window does not have indoor shading, and the direct Table 14 (54%): beam solar heat gain should be treated separately from the diffuse and conductive heat gains. The direct beam heat gain, without indoor shad- Qc = (285)(0.54) = 154 Btu/h ing, is treated as 100% radiant, and solar RTS factors from Table 20 are The radiant portion of the cooling load is calculated using conduc- used to convert the beam heat gains to cooling loads. The diffuse and tive heat gains for the current and past 23 h, the radiant fraction for conductive heat gains can be totaled and split into radiant and convective walls from Table 14 (46%), and radiant time series from Table 19, in portions according to Table 14, and nonsolar RTS factors from Table 19 accordance with Equation (34). From Table 19, select the RTS for are used to convert the radiant portion to cooling load. medium-weight construction, assuming 50% glass and carpeted floors The solar beam cooling load is calculated using heat gains for the as representative for the described construction. Use the wall heat gains current hour and past 23 h and radiant time series from Table 20, in from Table 29B for 24 h design conditions in July. Thus, the radiant accordance with Equation (39). From Table 20, select the solar RTS for cooling load for the wall at 3:00 PM is medium-weight construction, assuming 50% glass and carpeted floors for this example. Using Table 30 values for direct solar heat gain, the Q = r (0.46)( )q + r (0.46)( q + r (0.46)( q + r (0.46)( q r,15, 0 i,15, 1 i,14, 2 i,13, 3 i,,12 radiant cooling load for the window direct beam solar component is + … + r (0.46)( q 23 i,,16 … ==( (0.49)(0.46)(285)0.49)(0.46)(285) + ((0.17)(0.46)(214)0.17)(0.46)(214) + ((0.09)(0.46)(150)0.09)(0.46)(150) Qb,15, = r0qb,15, + r1qb,14, + r2qb,13, + r3qb,12, + + r23qb,16, + (0.05)(0.46)(119)(0.05)(0.46)(119) + ((0.03)(0.46)(96)0.03)(0.46)(96) + ((0.02)(0.46)(69)0.02)(0.46)(69) = (0.54)(2126)(0.54)(2126) + (0.16)(1234)(0.16)(1234) + (0.08)(302)(0.08)(302) + (0.04)(0)(0.04)(0) + (0.02)(0.46)(39)(0.02)(0.46)(39) + (0.01)(0.46)(11)(0.01)(0.46)(11) + (0.01)(0.46)(–8)(0.01)(0.46)(–8) + (0.03)(0)(0.03)(0) + (0.02)(0)(0.02)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0.46)(–15)(0.01)(0.46)(–15) + (0.01)(0.46)(–14)(0.01)(0.46)(–14) + (0.01)(0.46)(–12)(0.01)(0.46)(–12) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0.46)(–9)(0.01)(0.46)(–9) + (0.01)(0.46)(–4)(0.01)(0.46)(–4) + (0.01)(0.46)(1)(0.01)(0.46)(1) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0)(0.01)(0) + (0.01)(0.46)(8)(0.01)(0.46)(8) + ((0.01)(0.46)(15)0.01)(0.46)(15) + (0.01)(0.46)(27)(0.01)(0.46)(27) + (0.00)(0)(0.00)(0) + (0.00)(865)(0.00)(865) + ((0.00)(2080)0.00)(2080) + ((0.00)(2656)0.00)(2656) + (0.01)(0.46)(58)(0.01)(0.46)(58) + (0.01)(0.46)(147)(0.01)(0.46)(147) + (0.00)(0.46)(257)(0.00)(0.46)(257) + ((0.00)(2670)0.00)(2670) = 1370 BtuBtu/h/h + (0.00)(0.46)(329)(0.00)(0.46)(329) + (0.00)(0.00) (0.46)(353)(0.46)(353) + (0.00)(0.46)(337)(0.00)(0.46)(337) = 93 Btu/hBtu/h This process is repeated for other hours; results are listed in Table 31. The total wall cooling load at the designated hour is thus For diffuse and conductive heat gains, the radiant fraction accord- Qwalll = Qc + Qr1515 = 154 + 93 = 247 Btu/h ing to Table 14 is 46%. The radiant portion is processed using nonsolar RTS coefficients from Table 19. The results are listed in Tables 30 and Again, a simple computer spreadsheet or other software is neces- 31. For 3:00 PM, the diffuse and conductive cooling load is 1297 Btu/h. sary to reduce the effort involved. A spreadsheet was used with the heat The total window cooling load at the designated hour is thus gain profile to split the heat gain into convective and radiant portions, apply RTS to the radiant portion, and total the convective and radiant Qwindowwindow = Qb + Qdifff + condd = 1370 + 1297 = 2667 Btu/h loads to determine a 24 h cooling load profile for this example, with results in Table 29B. Again, a computer spreadsheet or other software is commonly used to reduce the effort involved in calculations. The spreadsheet illustrated Part 3. Window cooling load using radiant time series. Calculate the in Table 30 is expanded in Table 31 to include splitting the heat gain cooling load contribution, with and without indoor shading (venetian into convective and radiant portions, applying RTS to the radiant por- blinds) for the window area facing 60° west of south at 3:00 PM in July tion, and totaling the convective and radiant loads to determine a 24 h for the conference room example. cooling load profile for a window without indoor shading. 18.42 2013 ASHRAE Handbook—Fundamentals

Table 29A Wall Component of Solar Irradiance Direct Beam Solar Diffuse Solar Heat Gain Total Local Apparent Hour Solar Solar Air Eb, Direct Surface Surface Ed, Diffuse Ground Sky Subtotal Surface Standard Solar Angle Altitude Azimuth Solar Normal Incident Direct Horizontal, Diffuse Y Diffuse Diffuse Irradiance Hour Time H ! ) Mass m Btu/h·ft2 Angle Btu/h·ft2 Btu/h·ft2 Btu/h·ft2 Ratio Btu/h·ft2Btu/h·ft2 Btu/h·ft2 1 0.26 –176–36 –175 0.00.0 117.4 0.0 0.0 0.0 0.4500 0.0 0.0 0.0 2 1.26 –161–33 –159 0.00.0 130.9 0.0 0.0 0.0 0.4500 0.0 0.0 0.0 3 2.26 –146–27 –144 0.00.0 144.5 0.0 0.0 0.0 0.4500 0.0 0.0 0.0 4 3.26 –131–19 –132 0.00.0 158.1 0.0 0.0 0.0 0.4500 0.0 0.0 0.0 5 4.26 –116 –9–122 0.00.0 171.3 0.0 0.0 0.0 0.4500 0.0 0.0 0.0 6 5.26 –101 3 –113 16.91455 16.5 172.5 0.0 5.7 0.6 0.4500 2.6 3.2 3.2 76.26 –86 14 –105 3.98235 130.7 159.5 0.0 19.8 5.2 0.4500 8.9 14.1 14.1 87.26 –71 27 –98 2.22845 193.5 145.9 0.0 29.3 11.6 0.4500 13.224.8 24.8 98.26 –56 39 –90 1.58641 228.3 132.3 0.0 36.0 18.0 0.4500 16.234.2 34.2 10 9.26 –4151 –81 1.27776 248.8 118.8 0.0 40.7 23.5 0.4500 18.3 41.8 41.8 11 10.26 –2663 –67 1.11740 260.9 105.6 0.0 43.8 27.7 0.4553 19.9 47.6 47.6 12 11.26 –1174 –39 1.04214 266.9 92.6 0.0 45.4 30.1 0.5306 24.1 54.2 54.2 13 12.26 4 76 16 1.02872 268.0 80.2 45.5 45.7 30.6 0.6332 29.0 59.6 105.1 14 13.26 19 6957 1.07337 264.3 68.7 96.2 44.7 29.1 0.7505 33.6 62.7 158.8 15 14.26 34 5775 1.18905 255.3 58.45 133.6 42.3 25.7 0.8644 36.6 62.3 195.9 16 15.26 4945 86 1.41566 239.2 50.4 152.4 38.4 20.7 0.9555 36.757.4 209.9 17 16.26 6432 94 1.86186 212.2 45.8 148.1 32.7 14.6 1.0073 33.047.6 195.7 18 17.26 79 20 102 2.89735 165.3 45.5 115.8 24.7 8.1 1.0100 24.9 33.1 148.9 19 18.2694 8 109 6.84406 76.0 49.7 49.1 13.0 2.4 0.9631 12.5 14.9 64.0 20 19.26 109 –3 117 0.0 0.0 57.5 0.0 0.0 0.0 0.8755 0.0 0.0 0.0 21 20.26 124 –14 127 0.0 0.067.5 0.0 0.0 0.0 0.7630 0.0 0.0 0.0 22 21.26 139 –23 138 0.0 0.079.0 0.0 0.0 0.0 0.6452 0.0 0.0 0.0 23 22.26 154 –30 151 0.0 0.091.3 0.0 0.0 0.0 0.5403 0.0 0.0 0.0 24 23.26 169 –35 167 0.0 0.0 104.2 0.0 0.0 0.0 0.4618 0.0 0.0 0.0

Table 29B Wall Component of Sol-Air Temperatures, Heat Input, Heat Gain, Cooling Load Total Heat Gain, Btu/h Nonsolar Radiant Total Local Surface Outdoor Sol-Air Indoor Heat CTS RTS Zone Cooling Cooling Convective Radiant Standard Irradiance Temp., Temp., Temp., Input, Type 1, Type 8, Load, Load, Hour Btu/h·ft2 °F °F °F Btu/h % Total 54% 46% % Btu/h Btu/h 110.073.973.975–5181114916160.0 73.9 73.9 75 –5 18 1 1 1 49 16 16 220.073.073.075–958–4–2–21712100.0 73.0 73.0 75 –9 58 –4 –2 –2 17 12 10 3 0.0 72.4 72.4 75 –12 20 –9 –5 –4 9 10 5 4 0.0 71.8 71.8 75 –15 4 –12 –6 –5 5 8 2 5 0.0 71.4 71.4 75 –17 0 –14 –8 –7 3 7 –1 6 3.2 71.8 72.8 75 –10 0 –15 –8 –7 2 6 –2 7 14.1 73.2 77.4 75 110 –8 –4 –4 2 7 2 8 24.8 76.7 84.1 75 420 11 6 5 1 11 17 9 34.2 80.6 90.8 75 730 39 21 18 1 18 39 10 41.8 84.1 96.7 75 100 0 69 37 32 1 27 64 11 47.6 87.2 101.5 75 122 0 96 52 44 1 36 88 12 54.2 89.2 105.5 75 141 0 119 64 55 1 43 108 13 105.1 90.9 122.4 75 219 0 150 81 69 1 53 134 14 158.8 91.9 139.6 75 298 0 214 115 98 1 71 186 15 195.9 91.9 150.7 75 350 0 285 154 131 1 93 247 16 209.9 90.7 153.7 75 363 0 337 182 155 1 114 296 17 195.7 89.0 147.7 75 336 0 353 191 162 1 127 318 18 148.9 87.0 131.7 75 262 0 329 177 151 1 128 306 19 64.0 83.9 103.1 75 130 0 257 139 118 1 115 253 20 0.0 81.7 81.7 75 310 147 79 67 1 86 165 21 0.0 79.8 79.8 75 220 58 32 27 0 56 88 22 0.0 78.0 78.0 75 140 27 14 12 0 38 52 23 0.0 76.5 76.5 75 7 0 15 8 7 0 27 35 24240.075.175.17500844020250.0 75.1 75.1 75 0 0 8 4 4 0 20 25 Nonresidential Cooling and Heating Load Calculations 18.43

Table 30 Window Component of Heat Gain (No Blinds or Overhang) Beam Solar Heat Gain Diffuse Solar Heat Gain Conduction Beam Diffuse Diff. Con- Total Beam Surface Surface Solar Horiz. Ground Sky Subtotal Solar Out- duction Window Local Normal, Inci- Beam, Adjusted Heat Ed, Diffuse, Diffuse, Diffuse, Heat side Heat Heat Std. Btu/ dent Btu/ Beam Beam Gain, Btu/ Btu/ Y Btu/ Btu/ Hemis. Gain, Temp., Gain, Gain, Hour h·ft2 Angle h·ft2 SHGC IAC Btu/h h·ft2 h·ft2 Ratio h·ft2 h·ft2 SHGC Btu/h °F Btu/h Btu/h 10.0 117.40.0 0.000 1.000 0 0.0 0.0 0.4500 0.0 0.0 0.410 0 73.9 –25 –25 20.0 130.90.0 0.000 1.000 0 0.0 0.0 0.4500 0.0 0.0 0.410 0 73.0 –45 –45 30.0 144.50.0 0.000 1.000 0 0.0 0.0 0.4500 0.0 0.0 0.410 0 72.4 –58 –58 40.0 158.10.0 0.000 1.000 0 0.0 0.0 0.4500 0.0 0.0 0.410 0 71.8 –72 –72 50.0 171.30.0 0.000 1.000 0 0.0 0.0 0.4500 0.0 0.0 0.410 0 71.4 –81 –81 6 16.5 172.5 0.0 0.000 0.000 0 5.7 0.6 0.4500 2.6 3.2 0.410 52 71.8 –72 –19 7130.7 159.5 0.0 0.000 0.000 0 19.8 5.2 0.4500 8.9 14.1 0.410 231 73.2 –40 191 8 193.5145.9 0.0 0.000 0.000 0 29.3 11.6 0.4500 13.2 24.8 0.410 406 76.7 38 444 9 228.3132.3 0.0 0.000 0.000 0 36.0 18.0 0.4500 16.2 34.2 0.410 560 80.6 125 686 10 248.8 118.8 0.0 0.000 0.000 0 40.7 23.5 0.4500 18.3 41.8 0.410 686 84.1 204 890 11 260.9 105.6 0.0 0.000 0.000 0 43.8 27.7 0.4553 19.9 47.6 0.410 781 87.2 273 1055 12 266.9 92.6 0.0 0.000 0.000 0 45.4 30.1 0.5306 24.1 54.2 0.410 890 89.2 318 1208 13 268.0 80.2 45.5 0.166 1.000 302 45.7 30.6 0.6332 29.0 59.6 0.410 977 90.9 356 1635 14 264.3 68.7 96.2 0.321 1.000 1234 44.7 29.1 0.7505 33.6 62.7 0.410 1028 91.9 379 2640 15 255.3 58.4133.6 0.3981.000 2126 42.3 25.7 0.8644 36.6 62.3 0.410 1021 91.9 379 3526 16 239.2 50.4152.4 0.4381.000 2670 38.4 20.7 0.9555 36.7 57.4 0.410 942 90.7 352 3964 17 212.2 45.8148.1 0.4481.000 2656 32.7 14.6 1.0073 33.0 47.6 0.410 781 89.0 314 3751 18 165.3 45.5 115.8 0.449 1.000 2080 24.7 8.1 1.0100 24.9 33.1 0.410 542 87.0 269 2892 19 76.0 49.7 49.1 0.441 1.000865 13.0 2.4 0.963112.5 14.9 0.410 244 83.9 199 1309 20 0.057.5 0.0 0.403 0.000 0 0.0 0.0 0.8755 0.0 0.0 0.410 0 81.7 150 150 21 0.067.5 0.0 0.330 0.000 0 0.0 0.0 0.7630 0.0 0.0 0.410 0 79.8 108 108 22 0.0 79.00.0 0.185 0.000 0 0.0 0.0 0.6452 0.0 0.0 0.410 0 78.0 67 67 23 0.0 91.30.0 0.000 1.000 0 0.0 0.0 0.5403 0.0 0.0 0.410 0 76.5 34 34 24 0.0 104.2 0.0 0.000 1.000 0 0.0 0.0 0.4618 0.0 0.0 0.4100 75.1 2 2

Table 31 Window Component of Cooling Load (No Blinds or Overhang) Unshaded Direct Beam Solar (if AC = 1) Shaded Direct Beam (AC < 1.0) + Diffuse + Conduction Solar Con- Non- Local Beam Con- RTS, Beam Diffuse duction Total Con- Radi- solar Window Stan- Heat vective Radiant Zone Radi- Cooling Heat Heat Heat Heat vective ant RTS, Radi- Cooling Cooling dard Gain, 0%, 100%, Type 8, ant Load, Gain, Gain, Gain, Gain, 54%, 46%, Zone ant Load, Load, Hour Btu/h Btu/h Btu/h % Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h Type 8 Btu/h Btu/h Btu/h 1 0 0 0 54 119 119 0 0 –25 –25 –13 –11 49% 59 45 165 2 0 0 0 16 119 119 0 0 –45 –45 –24 –21 17% 49 24 144 3 0 0 0 8 119 119 0 0 –58 –58 –31 –27 9% 41 9 129 4 0 0 0 4 119 119 0 0 –72 –72 –39 –33 5% 32 –6 113 5 0 0 0 3 119 119 0 0 –81 –81 –44 –37 3% 25 –19 100 6 0 0 0 2 119 119 0 52 –72 –19 –10 –9 2% 32 22 141 7 0 0 0 1 119 119 0 231 –40 191 103 88 2% 78 181 301 8 0 0 0 1 116 116 0 406 38 444 240 204 1% 148 388 504 9 0 0 0 1 104 104 0 560 125 686 370 315 1% 225 596 700 10 0 0 0 1 83 83 0 686 204 890 481 409 1% 300 780 863 11 0 0 0 1 56 56 0 781 273 1055 569 485 1% 365 935 991 12 0 0 0 1 29 29 0 890 318 1208 652 556 1% 426 1078 1108 13 302 0 302 1 172 172 0 977 356 1333 720 613 1% 480 1200 1372 14 1234 0 1234 1715 715 0 1028 379 1406 759 647 1% 521 1281 1995 15 2126 0 2126 1 1370 1370 0 1021 379 1400 756 644 1% 541 1297 2666 16 2670 0 2670 1 1893 1893 0 942 352 1294 699 595 1% 530 1229 3122 17 2656 0 2656 1 2090 2090 0 781 314 1094 591 503 1% 487 1078 3168 18 2080 0 2080 1 1890 1890 0 542 269 811 438 373 1% 411 849 2739 19 865 0 865 1 1211 1211 0 244 199 444 240 204 1% 302 542 1753 20 0 0 0 0 549 549 0 0 150 150 81 69 1% 196 277 826 21 0 0 0 0 322 322 0 0 108 108 58 49 0% 145 203 525 22 0 0 0 0 213 213 0 0 67 67 36 31 0% 112 148 361 23 0 0 0 0 157 157 0 0 34 34 18 15 0% 89 107 265 24 0 0 0 0 128 128 0 0 2 2 1 1 0% 7273 201 18.44 2013 ASHRAE Handbook—Fundamentals

Table 32 Window Component of Cooling Load (With Blinds, No Overhang) Unshaded Direct Beam Solar (if AC = 1) Shaded Direct Beam (AC < 1.0) + Diffuse + Conduction Solar Con- Non- Beam Con- RTS, Beam Diffuse duction Total Con- solar Window Local Heat vective Radiant Zone Cooling Heat Heat Heat Heat vective Radiant RTS, Cooling Cooling Standard Gain, 0%, 100%, Type 8, Radiant Load, Gain, Gain, Gain, Gain, 54%, 46%, Zone Radiant, Load, Load, Hour Btu/h Btu/h Btu/h % Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h Type 8 Btu/h Btu/h Btu/h 1 0 0 0 1 0 0 0 0 –25 –25 –11 –13 49% 105 94 94 2 0 0 0 0 0 0 0 0 –45 –45 –21 –24 17%90 70 70 3 0 0 0 0 0 0 0 0 –58 –58 –27 –31 9% 81 54 54 4 0 0 0 0 0 0 0 0 –72 –72 –33 –39 5% 72 39 39 5 0 0 0 0 0 0 0 0 –81 –81 –37 –44 3% 63 26 26 6 0 0 0 0 0 0 0 41 –72 –30 –14 –16 2%70 56 56 7 0 0 0 0 0 0 0 183 –40 143 66 77 2% 114 180 180 8 0 0 0 0 0 0 0 321 38 359 165 194 1% 183 348 348 9 0 0 0 0 0 0 0 443 125 568 261 307 1% 260 522 522 10 0 0 0 0 0 0 0 542 204 746 343 403 1% 331 674 674 11 0 0 0 0 0 0 0 617 273 891 410 481 1% 391 801 801 12 0 0 0 0 0 0 0 703 318 1021 470 551 1% 443 913 913 13 0 0 0 0 0 0 196 772 356 1325 609 715 1% 540 1149 1149 14 0 0 0 0 0 0 802 812 379 1992 916 1076 1% 751 1668 1668 15 0 0 0 0 0 0 1388 807 379 2574 1184 1390 1% 987 2171 2171 16 0 0 0 0 0 0 1784 744 352 2880 1325 1555 1% 1170 2495 2495 17 0 0 0 0 0 0 1816 617 314 2747 1263 1483 1% 1221 2484 2484 18 0 0 0 0 0 0 1458 428 269 2156 992 1164 1% 1103 2094 2094 19 0 0 0 0 0 0 624 193 199 1017 468 549 1% 774 1242 1242 20 0 0 0 0 0 0 0 0 150 150 69 81 1% 434 503 503 21 0 0 0 0 0 0 0 0 108 108 49 58 0% 290 339 339 22 0 0 0 0 0 0 0 0 67 67 31 36 0% 209 240 240 23 0 0 0 0 0 0 0 0 34 34 15 18 0% 160 176 176 24240000000 0 0 0 0 0 0 0022110%1281291290 2 2 1 1 0% 128 129 129

Table 33 Window Component of Cooling Load (With Blinds and Overhang) Overhang and Fins Shading Shaded Direct Beam (AC < 1.0) + Diffuse + Conduction Con- Non- Direct Beam Diffuse duction Total Con- solar Window Local Surface Shadow Shadow Sunlit Heat Heat Heat Heat vective Radiant RTS, Cooling Cooling Standard Solar Profile Width, Height, Area, Gain, Gain, Gain, Gain, 54%, 46%, Zone Radiant, Load, Load, Hour Azimuth Angle ft ft ft2 Btu/h Btu/h Btu/h Btu/h Btu/h Btu/h Type 8 Btu/h Btu/h Btu/h 1 –235 52 0.0 0.0 0.0 0 0 –25 –25 –13 –11 49% 55 42 42 2 –219 40 0.0 0.0 0.0 0 0 –45 –45 –24 –21 17% 43 19 19 3 –204 29 0.0 0.0 0.0 0 0 –58 –58 –31 –27 9% 36 4 4 4 –192 19 0.0 0.0 0.0 0 0 –72 –72 –39 –33 5% 28 –11 –11 5 –182 9 0.0 0.0 0.0 0 0 –81 –81 –44 –37 3% 20 –23 –23 6 –173 –3 0.0 0.0 0.0 0 41 –72 –30 –16 –14 2% 26 10 10 7 –165 –15 0.0 0.0 0.0 0 183 –40 143 77 66 2% 64 141 141 8 –158 –28 0.0 0.0 0.0 0 321 38 359 194 165 1% 122 316 316 9 –150 –43 0.0 0.0 0.0 0 443 125 568 307 261 1% 189 496 496 10–141 –58 0.0 0.0 0.0 0 542 204 746 403 343 1% 253 656 656 11–127 –73 0.0 0.0 0.0 0 617 273 891 481 410 1% 310 791 791 12 –99–87 0.0 0.0 0.0 0 703 318 1021 551 470 1% 363 914 914 13 –44 80 0.0 6.4 0.0 0 772 356 1128 609 519 1% 409 1018 1018 14–3 69 0.0 6.4 0.0 0 812 379 1190 643 548 1% 443 1085 1085 1515 58 0.0 6.4 0.0 0 807 379 1186 640 545 1% 457 1098 1098 1626 48 0.0 6.4 0.0 0 744 352 1096 592 504 1% 449 1040 1040 1734 380.0 6.4 0.00 617 314 930 502 428 1% 412 915 915 18 42 26 0.0 4.9 18.9 344428 269 1041 562 479 1% 427 990 990 19 49 12 0.0 2.2 53.0 414 193 199 806 435 371 1% 380 816 816 20 57 –6 0.0 0.0 0.0 0 0 150 150 81 69 1% 219 300 300 21 67 –32 0.0 0.0 0.0 0 0 108 108 58 49 0% 154 212 212 22 78 –64 0.0 0.0 0.0 0 0 67 67 36 31 0%113 150 150 23 91 87 0.0 0.0 0.0 0 0 34 34 18 15 0% 87 106 106 24107 67 0.0 0.0 0.00 0 2 2 1 1 0% 7071 71 Nonresidential Cooling and Heating Load Calculations 18.45

If the window has an indoor shading device, it is accounted for with Table 34 Single-Room Example Cooling Load (July 3:00 PM) the indoor attenuation coefficients (IAC), the radiant fraction, and the for ASHRAE Example Office Building, Atlanta, GA RTS type used. If a window has no indoor shading, 100% of the direct beam energy is assumed to be radiant and solar RTS factors are used. However, if an indoor shading device is present, the direct beam is assumed to be interrupted by the shading device, and a portion immedi- ately becomes cooling load by convection. Also, the energy is assumed to be radiated to all surfaces of the room, therefore nonsolar RTS values are used to convert the radiant load into cooling load. IAC values depend on several factors: (1) type of shading device, (2) position of shading device relative to window, (3) reflectivity of shading device, (4) angular adjustment of shading device, as well as (5) solar position relative to the shading device. These factors are discussed in detail in Chapter 15. For this example with venetian blinds, the IAC for beam radiation is treated separately from the diffuse solar gain. The direct beam IAC must be adjusted based on the profile angle of the sun. At 3:00 PM in July, the profile angle of the sun relative to the window surface is 58°. Calculated using Equation (45) from Chapter 15, the beam IAC = 0.653. The diffuse IAC is 0.79. Thus, the window heat gains, with light-colored blinds, at 3:00 PM are

qb1515 = AEED SHGC(SHGC( )()(IAC)IAC) = ((40)(133.6)(0.3978)(0.653)40)(133.6)(0.3978)(0.653) = 1388 Btu/hBtu/h > N qd1515 = A(Ed + Er) SSHGCHGC D(IAC)( )D= (40)(36.6 + 25.7)(0.41)(0.79) = 807 Btu/h

qc1515 = UA (toutt – tin) = (0.56)(40)(91.9 – 75) = 379 Btu/h Because the same radiant fraction and nonsolar RTS are applied to all parts of the window heat gain when indoor shading is present, those loads can be totaled and the cooling load calculated after splitting the radiant portion for processing with nonsolar RTS. This is illustrated by the spreadsheet results in Table 32. The total window cooling load with venetian blinds at 3:00 PM = 2171 Btu/h.

Part 4. Window cooling load using radiant time series for window with overhang shading. Calculate the cooling load contribution for the pre- vious example with the addition of a 10 ft overhang shading the window. Solution: In Chapter 15, methods are described and examples provided for calculating the area of a window shaded by attached vertical or horizontal projections. For 3:00 PM LST IN July, the solar position cal- culated in previous examples is SolarSolar altitudealtitude ! = 57.2° SSolarolar azazimuthimuth ""** 75.75.1°1° Surface-solarSurface-solar azimuthazimuth # = 15.1°15.1° From CChapterhapter 15, EquationEquation (106),(106), proprofilefile anganglele isis calculatedcalculated by cooling load actually occurs in July at hour 14 (2:00 PM solar time) at tantan =tan= tan !/cos/cos # ==tan tan(57.2)/cos(15.1)(57.2)/cos(15.1) = 1.60871.6087 3675 Btu/h as indicated in Table 35. = 58.1° Although simple in concept, these steps involved in calculating cooling loads are tedious and repetitive, even using the “simplified” From Chapter 15, Equation (40), shadow height S is H RTS method; practically, they should be performed using a com-

SH = PH tantan = 10 10(1.6087)(1.6087) = 16.1 ftft puter spreadsheet or other program. The calculations should be repeated for multiple design conditions (i.e., times of day, other Because the window is 6.4 ft tall, at 3:00 PM the window is com- months) to determine the maximum cooling load for mechanical pletely shaded by the 10 ft deep overhang. Thus, the shaded window equipment sizing. Example spreadsheets for computing each cool- heat gain includes only diffuse solar and conduction gains. This is con- verted to cooling load by separating the radiant portion, applying RTS, ing load component using conduction and radiant time series have and adding the resulting radiant cooling load to the convective portion been compiled and are available from ASHRAE. To illustrate the to determine total cooling load. Those results are in Table 33. The total full building example discussed previously, those individual com- window cooling load = 1098 Btu/h. ponent spreadsheets have been compiled to allow calculation of cooling and heating loads on a room by room basis as well as for a Part 5. Room cooling load total. Calculate the sensible cooling loads for “block” calculation for analysis of overall areas or buildings where the previously described office at 3:00 PM in July. detailed room-by-room data are not available. Solution: The steps in the previous example parts are repeated for each of the internal and external loads components, including the southeast SINGLE-ROOM EXAMPLE PEAK HEATING LOAD facing window, spandrel and brick walls, the southwest facing brick wall, the roof, people, and equipment loads. The results are tabulated in Table Although the physics of heat transfer that creates a heating load 34. The total room sensible cooling load for the office is 3674 Btu/h at is identical to that for cooling loads, a number of traditionally used 3:00 PM in July. When this calculation process is repeated for a 24 h simplifying assumptions facilitate a much simpler calculation pro- design day for each month, it is found that the peak room sensible cedure. As described in the Heating Load Calculations section, 18.46 2013 ASHRAE Handbook—Fundamentals

Table 35 Single-Room Example Peak Cooling Load (Sept. Windows: 0.56800((72 – 21.5)) = 2262 Btu/h   5:00 PM) for ASHRAE Example Office Building, Atlanta, GA Spandrelp Wall: 0.077 1200 ((72() – 21.5) = 467 Brick Wall: 0.081000 ((72 – 21.5)) = 404 Roof: 0.032 1300 ((72 – 21.5) = 210 Infiltration: 19.5 1.11((72 – 21.5) = 1083 Total Room Heating Load: 4426 Btu/h WHOLE-BUILDING EXAMPLE Because a single-room example does not illustrate the full appli- cation of load calculations, a multistory, multiple-room example building has been developed to show a more realistic case. A hypo- thetical project development process is described to illustrate its effect on the application of load calculations. Design Process and Shell Building Definition A development company has acquired a piece of property in Atlanta, GA, to construct an office building. Although no tenant or end user has yet been identified, the owner/developer has decided to proceed with the project on a speculative basis. They select an archi- tectural design firm, who retains an engineering firm for the mechanical and electrical design. At the first meeting, the developer indicates the project is to pro- ceed on a fast-track basis to take advantage of market conditions; he is negotiating with several potential tenants who will need to occupy the new building within a year. This requires preparing shell-and- core construction documents to obtain a building permit, order equipment, and begin construction to meet the schedule. The shell-and-core design documents will include finished design of the building exterior (the shell), as well as permanent inte- rior elements such as stairs, restrooms, elevator, electrical rooms and mechanical spaces (the core). The primary mechanical equip- ment must be sized and installed as part of the shell-and-core pack- age in order for the project to meet the schedule, even though the building occupant is not yet known. The architect selects a two-story design with an exterior skin of tinted, double-glazed vision glass; opaque, insulated spandrel glass, and brick pilasters. The roof area extends beyond the building edge to form a substantial overhang, shading the second floor windows. Architectural drawings for the shell-and-core package (see Figures 17 to 22) include plans, elevations, and skin construction details, and are furnished to the engineer for use in “block” heating and cooling load calculations. Mechanical systems and equipment must be specified and installed based on those calculations. (Note: Full- size, scalable electronic versions of the drawings in Figures 17 to design heating load calculations typically assume a single outdoor 22, as well as detailed lighting plans, are available from ASHRAE temperature, with no heat gain from solar or internal sources, under at www.ashrae.org.) steady-state conditions. Thus, space heating load is determined by The HVAC design engineer meets with the developer’s opera- computing the heat transfer rate through building envelope elements tions staff to agree on the basic HVAC systems for the project. Based (UA T) plus heat required because of outdoor air infiltration. on their experience operating other buildings and the lack of specific information on the tenant(s), the team decides on two variable- Part 6. Room heating load. Calculate the room heating load for the pre- volume air-handling units (AHUs), one per floor, to provide operat- vious described office, including infiltration airflow at one air change ing flexibility if one floor is leased to one tenant and the other floor per hour. to someone else. Cooling will be provided by an air-cooled chiller Solution: Because solar heat gain is not considered in calculating located on grade across the parking lot. Heating will be provided by design heating loads, orientation of similar envelope elements may be electric resistance heaters in parallel-type fan-powered variable-air- ignored and total areas of each wall or window type combined. Thus, volume (VAV) terminal units. The AHUs must be sized quickly to the total spandrel wall area = 60 + 60 = 120 ft2, total brick wall area = confirm the size of the mechanical rooms on the architectural plans. 60 + 40 = 100 ft2, and total window area = 40 + 40 = 80 ft2. For this The AHUs and chiller must be ordered by the mechanical subcon- example, use the U-factors that were used for cooling load conditions. tractor within 10 days to meet the construction schedule. Likewise, In some climates, higher prevalent winds in winter should be consid- the electric heating loads must be provided to the electrical engi- ered in calculating U-factors (see Chapter 25 for information on calcu- neers to size the electrical service and for the utility company to lating U-factors and surface heat transfer coefficients appropriate for extend services to the site. local wind conditions). The 99.6% heating design dry-bulb temperature for Atlanta is 21.5°F and the indoor design temperature is 72°F. The The mechanical engineer must determine the (1) peak airflow room volume with a 9 ft ceiling = 9130 = 1170 ft3. At one air change and cooling coil capacity for each AHU, (2) peak cooling capacity per hour, the infiltration airflow = 11170/60 = 19.5 cfm. Thus, the required for the chiller, and (3) total heating capacity for sizing the heating load is electrical service. Nonresidential Cooling and Heating Load Calculations 18.47

Table 36 Block Load Example: Envelope Area Summary, ft2 Brick Areas Spandrel/Soffit Areas Window Areas Floor Area North South East West North South East West North South East West First Floor 19,000 680 560 400 400 1400 1350 1040 360 600 1000 120 360 Second Floor 15,700 510 390 300 300 1040 920 540 540 560 840 360 360 Building Total 34,700 1190 950 700 700 2440 2270 1580 900 1160 1840 480 720

Solution: First, calculate “block” heating and cooling loads for Table 37 Block Load Example—First Floor Loads for each floor to size the AHUs, then calculate a block load for the ASHRAE Example Office Building, Atlanta, GA whole building determine chiller and electric heating capacity. Based on the architectural drawings, the HVAC engineer assem- bles basic data on the building as follows: Location: Atlanta, GA. Per Chapter 14, latitude = 33.64, longi- tude = 84.43, elevation = 1027 ft above sea level, 99.6% heating design dry-bulb temperature = 21.5°F. For cooling load calculations, use 5% dry-bulb/coincident wet-bulb monthly design day profile from Chapter 14 (on CD-ROM). See Table 27 for temperature pro- files used in these examples. Indoor design conditions: 72°F for heating; 75°F with 50% rh for cooling. Building orientation: Plan north is 30° west of true north. Gross area per floor: 19,000 ft2 first floor and 15,700 ft2 second floor Total building gross area: 34,700 ft2 Windows: Bronze-tinted, double-glazed. Solar heat gain coeffi- cients, U-factors are as in the single-room example. Walls: Part insulated spandrel glass and part brick-and-block clad columns. The insulation barrier in the soffit at the second floor is similar to that of the spandrel glass and is of lightweight construc- tion; for simplicity, that surface is assumed to have similar thermal heat gain/loss to the spandrel glass. Construction and insulation val- ues are as in single-room example. Roof: Metal deck, topped with board insulation and membrane roofing. Construction and insulation values are as in the single- room example. Floor: 5 in. lightweight concrete slab on grade for first floor and 5 in. lightweight concrete on metal deck for second floor Total areas of building exterior skin, as measured from the archi- tectural plans, are listed in Table 36. The engineer needs additional data to estimate the building loads. Thus far, no tenant has yet been signed, so no interior layouts for population counts, lighting layouts or equipment loads are avail- able. To meet the schedule, assumptions must be made on these load components. The owner requires that the system design must be flexible enough to provide for a variety of tenants over the life of the building. Based on similar office buildings, the team agrees to base the block load calculations on the following assumptions: Occupancy: 7 people per 1000 ft2 = 143 ft2/person To maintain indoor air quality, outdoutdoooorr aiairr mmustust be iintroducedntroduced Lighting:1.1 W/ft2 intointo the building.building. Air will be ductedducted fromfrom roofroof intakeintake hoodshoods toto thethe Tenant’s office equipment:1 W/ft2 AHUs where it will be mixed with returnreturn airair beforebefore beingbeing cooled andand Normal use schedule is assumed at 100% from 7:00 AM to dehumidified by the AHU’s cooling coil. ASHRAEA Standardd 62.1 isi 7:00 PM and unoccupied/off during other hours. the design basis for ventilation rates; however, no interior tenant lay- With interior finishes not finalized, the owner commits to using out is available for application of Standard 62.1 procedures. Based light-colored interior blinds on all windows. The tenant interior oonn past experexperience,ience, tthehe enengineergineer decides ttoo use 2200cf cfmm of ououtdoortdoor air design could include carpeted flooring or acoustical tile ceilings in per person for sizingsizing the ccoolingooling coils and chiller. all areas, but the more conservative assumption, from a peak load Block load calculations were performed using the RTS method, standpoint, is chosen: carpeted flooring and no acoustical tile ceil- and results for the first and second floors and the entire building are ings (no ceiling return plenum). summarized in Tables 37, 38, and 39. Based on these results, the For block loads, the engineer assumes that the building is main- engineer performs psychrometric coil analysis, checks capacities tained under positive pressure during peak cooling conditions and versus vendor catalog data, and prepares specifications and sched- that infiltration during peak heating conditions is equivalent to ules for the equipment. This information is released to the contrac- one air change per hour in a 12 ft deep perimeter zone around the tor with the shell-and-core design documents. The air-handling building. units and chiller are purchased, and construction proceeds. 18.48 2013 ASHRAE Handbook—Fundamentals

Table 38 Block Load Example—Second Floor Loads for Table 39 Block Load Example—Overall Building Loads for ASHRAE Example Office Building, Atlanta, GA ASHRAE Example Office Building, Atlanta, GA

Tenant Fit Design Process and Definition About halfway through construction, a tenant agrees to lease the roof will be extracted via the ceiling return air plenum. From expe- entire building. The tenant will require a combination of open and rience, the engineer understands that return air plenum paths are enclosed office space with a few common areas, such as conference/ not always predictable, and decides to credit only 30% of the roof training rooms, and a small computer room that will operate on a heat gain to the return air, with the balance included in the room 24 h basis. Based on the tenant’s space program, the architect pre- cooling load. pares interior floor plans and furniture layout plans (Figures 23 and For the open office areas, some areas along the building perime- 24), and the electrical engineer prepares lighting design plans. ter will have different load characteristics from purely interior Those drawings are furnished to the HVAC engineer to prepare spaces because of heat gains and losses through the building skin. detailed design documents. The first step in this process is to pre- Although those perimeter areas are not separated from other open pare room-by-room peak heating and cooling load calculations, office spaces by walls, the engineer knows from experience that which will then be used for design of the air distribution systems they must be served by separate control zones to maintain comfort from each of the VAV air handlers already installed. conditions. The HVAC engineer must perform a room-by-room “takeoff” of the architect’s drawings. For each room, this effort identifies the Room-by-Room Cooling and Heating Loads floor area, room function, exterior envelope elements and areas, The room-by-room results of RTS method calculations, includ- number of occupants, and lighting and equipment loads. ing the month and time of day of each room’s peak cooling load, as The tenant layout calls for a dropped acoustical tile ceiling well as peak heating loads for each room and all input data, are throughout, which will be used as a return air plenum. Typical 2 by available at www.ashrae.org in spreadsheet format similar to Table 4 ft fluorescent, recessed, return-air-type lighting fixtures are 39. These results are used by the HVAC engineer to select and selected. Based on this, the engineer assumes that 20% of the heat design room air distribution devices and to schedule airflow rates gain from lighting will be to the return air plenum and not enter for each space. That information is incorporated into the tenant fit rooms directly. Likewise, some portion of the heat gain from the drawings and specifications issued to the contractor. Nonresidential Cooling and Heating Load Calculations 18.49

Conclusions aassumptionsssumptions usedused inin thethe originaloriginal workwork to derivederive tthosehose ffactorsactors lilimitmit The example results illustrate issues which should be understood thithiss metmethod’shod’s appapplicabilitylicability to ththoseose bbuildinguilding ttypesypes anandd conconditionsditions and accounted for in calculating heating and cooling loads: fforor wwhichhich thethe CLTD/CLFCLTD/CLF factorsfactors werewere derived;derived; thethe methodmethod shouldshould nnotot bbee useusedd bbeyondeyond tthehe range ooff appapplicability.licability. • First, pgpeak room cooling loads occur at different months and AAlthoughlthough the TFM, TETD/TA, aandnd CLTD/CLF procedures araree times dependingdeppgending on the exteriorexterior exposureexposure of the room. Calcula-Calcula- nnotot rerepublishedpublished in this chachapter,pter, those methods are not invalidated oror tion of coolingcoolinggg loads for a singlesingle pointp in time may miss the peak ddiscredited.iscredited. ExperiencedExperienced engineers have successfully used them in and result in inadequate cooling for that room.room. mmillionsillions of buildings around the woworld.rld. The accuracy of cooling • Often, in real designgp processes, aallll data is not known. ReasonablReasonablee assumptions based on pastpast experience must be mademade.. lloadoad cacalculationslculations inin practicepractice dependsdepends primarily on the availability of aaccurateccurate informationinformation andand thethe designdesign engineer’sengineer’s judgmentjudgment inin thethe • Heatingg and air-conditioningair-conditioninggy systemssystems often serveserve sspacespaces whose ususee changeschanges over the life of a buildbuildiing.nggp. AssumAssumptionsptions used in heatingheatin gaassumptionsssumptions made in interpretininterpretingg the available data. Those factorfactorss and coolincoolingg load calculcalculationsations sshouldhould coconsidernsider reasonable ppossibleossible hhaveave much greater influence onon a project’s success than does ththee uses over the life of the building, not just the first use of the space. cchoicehoice of a particular coolingcooling load calculation methodmethod.. • The relative importancep of eachh coolincoolinggggp and heatinheatingg load comcompo-po- TThehe primary benefit of HB and RTS calculations is their somesome-- nent varies dependingdeppgending on the portion portion of the buildingbuildinggg beingbeing con- wwhathat reduced dependencydependency on purelypurely subjectivesubjective input ((e.g.,e.g., deter- sidered. Characteristics of a ppyparticulararticular window mamayy have littllittlee miminingning a proper ttime-averagingime-averaging perperiodiod fforor TTETD/TA;ETD/TA; ascertaascertainingining effect on the entire buildinggg load, but could have a significant aappropriateppropriate safety factors to aadddd to the rounded-off TFM results; effect on the supplypp y airflow to the room where the window is ddeterminingetermining whetherwhether CLTDCLTD/CLF/CLF factorsfactors are appapplicablelicable to a specspecificific located and thus on the comfort off the occupants of that space. uuniquenique applicationapplication).). However, ususinging the most up-to-date techniques iinn real-world desidesigngn still requires jjudgmentudgment on the part of the designdesign PREVIOUS COOLING LOAD eengineerngineer and care in choosingchoosing appropriateappropriate assumptions, jjustust as iinn CALCULATION METHODS aapplyingpplying older ccalculationalculation methods. Procedures described in this chapter are the most current and sci- REFERENCES entifically derived means for estimating cooling load for a defined Abushakra, B., J.S. Haberl, and D.E. Claridge. 2004. Overview of literature building space, but methods in earlier editions of the ASHRAE on diversity factors and schedules for energy and cooling load calcula- Handbook are valid for many applications. These earlier procedures tions (1093-RP). ASHRAE Transactions 110(1):164-176. are simplifications of the heat balancebalance principles,principles, andand theirtheir useuse Armstrong, P.R., C.E. Hancock, III, and J.E. Seem. 1992a. Commercial requrequiresires experexperienceience to deal with atypical orr uunusualnusual cicircumstances.rcumstances. building temperature recovery—Part I: Design procedure based on a step In fact, any cooling or heating loadd estestimateimate iiss no bbetteretter tthanhan tthehe response model. ASHRAE Transactions 98(1):381-396. assumptassumptionsions useusedd to ddefineefine conditionsconditions andand parameters suchsuch as phys-phys- Armstrong, P.R., C.E. Hancock, III, and J.E. Seem. 1992b. Commercial iicalcal mamakeupkeup ooff tthehe varvariousious enveenvelopelope sursurfaces,faces, conconditionsditions ooff occu- building temperature recovery—Part II: Experiments to verify the step pancpancyy andand use, anandd amambientbient weatweatherher conconditions.ditions. ExExperienceperience ooff tthehe response model. ASHRAE Transactions 98(1):397-410. practpractitioneritioner can never bbee iignored.gnored. ASHRAE. 2010. Thermal environmental conditions for human occupancy. The primaryprimary difference betweenbetween the HB and RTS methods and ANSI/ASHRAE Standard 55-2010. tthehe olderolder methodsmethods is thethe newernewer methods’methods’ directdirect approach,approach, comparedcompared ASHRAE. 2010. Ventilation for acceptable indoor air quality. ANSI/ to tthehe ssimplificationsimplifications necessnecessitateditated bbyy tthehe lilimitedmited computer capacapabil-bil- ASHRAE Standard 62.1-2010. itityy available previouslpreviously.y. ASHRAE. 2010. Energy standard for building except low-rise residential TThehe transfertransfer function method (TFM)(TFM), forfor example,example, requiredrequired buildings. ANSI/ASHRAE/IESNA Standard 90.1-2010. manmanyy cacalculationlculation steps. It was ororiginallyiginally ddesignedesigned forfor energyenergy anal-anal- ASHRAE. 2012. Updating the climatic design conditions in the ASHRAE Handbook—Fundamentals (RP-1613). ASHRAE Research Project, yysissis withwith emphasisemphasis on daily,daily, monthly,monthly, andand annualannual energyenergy use, anandd Final Report. tthushus was more orientedoriented to average hourlyhourly coolingcooling loadsloads thanthan peakpeak ASTM. 2008. Practice for estimate of the heat gain or loss and the surface ddesignesign loads.loads. temperatures of insulated flat, cylindrical, and spherical systems by use TheThe totaltotal equivalent temperature differential method withwith of computer programs. Standard C680-08. American Society for Testing time averaging (TETD/TA(TETD/TA)) hashas beenbeen a highlyhighly reliablereliable (if subjec-subjec- and Materials, West Conshohocken, PA. ttive)ive) metmethodhod ooff lloadoad estestimatingimating ssinceince iitsts iinitialnitial presentatpresentationion iinn tthehe Bauman, F.S., and A. Daly. 2013. Underfloor air distribution (UFAD) 11967967 HHandbookandbook ooff FundamentalFundamentalss. OriginallyOriginally intended as a manualmanual design guide, 2nd ed. ASHRAE. metmethodhod ofof calculation,calculation, itit provedproved suitablesuitable onlyonly as a computer appli-appli- Bauman, F., T. Webster, P. Linden, and F. Buhl. 2007. Energy performance cacationtion because ofof thethe needneed toto calculatecalculate an extended profile of hourlyhourly of UFAD systems. CEC-500-2007-050, Final Report to CEC PIER hheateat gaingain values,values, fromfrom whichwhich radiantradiant components hadhad to bebe averagedaveraged Buildings Program. Center for the Built Environment, University of over a timetime representativerepresentative ofof thethe generalgeneral mass ofof thethe buildingbuilding California, Berkeley. http://www.energy.ca.gov/2007publications/CEC involved. Because perceptionperception of thermal storagestorage characteristics of a -500-2007-050/index.html gigivenven buildingbuilding iiss aalmostlmost ententirelyirely susubjective,bjective, wwithith lilittlettle specspecificific iinfor-nfor- Bauman, F., S. Schiavon, T. Webster, and K.H. Lee. 2010. Cooling load matmationion fforor tthehe user to jjudgeudge variations,variations, thethe TETD/TATETD/TA method’smethod’s prpri-i- design tool for UFAD systems. ASHRAE Journal (September):62-71. marmaryy usefulness has alwaalwaysys beebeenn to the experienced enengineer.gineer. http://escholarship.org/uc/item/9d8430v3. TheThe coolincoolingg load temperature diffedifferentialrential mmethodethod wwithith sosolarlar Bliss, R.J.V. 1961. Atmospheric radiation near the surface of the ground. Solar Energy 5(3):103. cooling load factors (CLTD/CLF(CLTD/CLF)) attempteattemptedd to simplifysimplify thethe two- Chantrasrisalai, C., D.E. Fisher, I. Iu, and D. Eldridge. 2003. Experimental step TFM and TETD/TA methods inintoto a sinsingle-stepgle-step technique that validation of design cooling load procedures: The heat balance method. proceeded directly from raw dataa to cooling load without inter- ASHRAE Transactions 109(2):160-173. mediate conversion of radiant heat gain to cooling load. A series of Claridge, D.E., B. Abushakra, J.S. Haberl, and A. Sreshthaputra. 2004. factors were taken from coolingcooling loadload calculation results (produced(produced Electricity diversity profiles for energy simulation of office buildings bbyy more sophisticatedsophisticated methods)methods) as “cooling“cooling loadload temperature dif- (RP-1093). ASHRAE Transactions 110(1):365-377. fferences”erences” andand “coo“coolingling loadload factors”factors” foforr use inin traditionaltraditional conduc-conduc- Eldridge, D., D.E. Fisher, I. Iu, and C. Chantrasrisalai. 2003. Experimental tion (q = UUAA t) equations. The results are approximate cooling load validation of design cooling load procedures: Facility design (RP-1117). vavalueslues ratratherher tthanhan ssimpleimple hheateat ggainain vavalues.lues. TThehe ssimplificationsimplifications anandd ASHRAE Transactions 109(2):151-159. 18.50 2013 ASHRAE Handbook—Fundamentals

Feng, J., S. Schiavon, and F. Bauman. 2012. Comparison of zone cooling Parker, D.S., J.E.R. McIlvaine, S.F. Barkaszi, D.J. Beal, and M.T. Anello. load for radiant and air conditioning systems. Proceedings of the Inter- 2000. Laboratory testing of the reflectance properties of roofing mate- national Conference on Building Energy and Environment. Boulder, CO. rial. FSEC-CR670-00. Florida Solar Energy Center, Cocoa. http://escholarship.org/uc/item/9g24f38j. Pedersen, C.O., D.E. Fisher, and R.J. Liesen. 1997. Development of a heat Fisher, D.R. 1998. New recommended heat gains for commercial cooking balance procedure for calculating cooling loads. ASHRAE Transactions equipment. ASHRAE Transactions 104(2):953-960. 103(2):459-468. Fisher, D.E., and C. Chantrasrisalai. 2006. Lighting heat gain distribution in Pedersen, C.O., D.E. Fisher, J.D. Spitler, and R.J. Liesen. 1998. Cooling and buildings (RP-1282). ASHRAE Research Project, Final Report. heating load calculation principles. ASHRAE. Fisher, D.E., and C.O. Pedersen. 1997. Convective heat transfer in building Rees, S.J., J.D. Spitler, M.G. Davies, and P. Haves. 2000. Qualitative com- energy and thermal load calculations. ASHRAE Transactions 103(2): parison of North American and U.K. cooling load calculation methods. 137-148. International Journal of Heating, Ventilating, Air-Conditioning and Gordon, E.B., D.J. Horton, and F.A. Parvin. 1994. Development and appli- Refrigerating Research 6(1):75-99. cation of a standard test method for the performance of exhaust hoods Rock, B.A. 2005. A user-friendly model and coefficients for slab-on-grade with commercial cooking appliances. ASHRAE Transactions 100(2). load and energy calculation. ASHRAE Transactions 111(2):122-136. Hittle, D.C. 1999. The effect of beam solar radiation on peak cooling loads. Rock, B.A., and D.J. Wolfe. 1997. A sensitivity study of floor and ceiling ASHRAE Transactions 105(2):510-513. plenum energy model parameters. ASHRAE Transactions 103(1):16-30. Hittle, D.C., and C.O. Pedersen. 1981. Calculating building heating loads Schiavon, S., F. Bauman, K.H. Lee, and T. Webster. 2010a. Simplified using the frequency of multi-layered slabs. ASHRAE Transactions calculation method for design cooling loads in underfloor air distribu- 87(2):545-568. tion (UFAD) systems. Energy and Buildings 43(1-2):517-528. http:// Hosni, M.H., and B.T. Beck. 2008. Update to measurements of office equip- escholarship.org/uc/item/5w53c7kr. ment heat gain data (RP-1482). ASHRAE Research Project, Progress Schiavon, S., K.H. Lee, F. Bauman, and T. Webster. 2010b. Influence of Report. raised floor on zone design cooling load in commercial buildings. En- Hosni, M.H., B.W. Jones, J.M. Sipes, and Y. Xu. 1998. Total heat gain and ergy and Buildings 42(5):1182-1191. http://escholarship.org/uc/item the split between radiant and convective heat gain from office and labo- /2bv611dt. ratory equipment in buildings. ASHRAE Transactions 104(1A):356-365. Schiavon, S., F. Bauman, K.H. Lee, and T. Webster. 2010c. Development of Hosni, M.H., B.W. Jones, and H. Xu. 1999. Experimental results for heat a simplified cooling load design tool for underfloor air distribution sys- gain and radiant/convective split from equipment in buildings. ASHRAE tems. Final Report to CEC PIER Program, July. http://escholarship.org Transactions 105(2):527-539. /uc/item/6278m12z. Smith, V.A., R.T. Swierczyna, and C.N. Claar. 1995. Application and Incropera, F.P., and D.P DeWitt. 1990. Fundamentals of heat and mass enhancement of the standard test method for the performance of com- transfer, 3rd ed. Wiley, New York. mercial kitchen ventilation systems. ASHRAE Transactions 101(2). Iu, I., and D.E. Fisher. 2004. Application of conduction transfer functions Sowell, E.F. 1988a. Cross-check and modification of the DOE-2 program for and periodic response factors in cooling load calculation procedures. calculation of zone weighting factors. ASHRAE Transactions 94(2). ASHRAE Transactions 110(2):829-841. Sowell, E.F. 1988b. Load calculations for 200,640 zones. ASHRAE Trans- Iu, I., C. Chantrasrisalai, D.S. Eldridge, and D.E. Fisher. 2003. experimental actions 94(2):716-736. validation of design cooling load procedures: The radiant time series Spitler, J.D., and D.E. Fisher. 1999a. Development of periodic response fac- method (RP-1117). ASHRAE Transactions 109(2):139-150. tors for use with the radiant time series method. ASHRAE Transactions Jones, B.W., M.H. Hosni, and J.M. Sipes. 1998. Measurement of radiant 105(2):491-509. heat gain from office equipment using a scanning radiometer. ASHRAE Spitler, J.D., and D.E. Fisher. 1999b. On the relationship between the radiant Transactions 104(1B):1775-1783. time series and transfer function methods for design cooling load calcu- Karambakkam, B.K., B. Nigusse, and J.D. Spitler. 2005. A one-dimensional lations. International Journal of Heating, Ventilating, Air-Conditioning approximation for transient multi-dimensional conduction heat transfer and Refrigerating Research (now HVAC&R Research) 5(2):125-138. in building envelopes. Proceedings of the 7th Symposium on Building Spitler, J.D., D.E. Fisher, and C.O. Pedersen. 1997. The radiant time series Physics in the Nordic Countries, The Icelandic Building Research Insti- cooling load calculation procedure. ASHRAE Transactions 103(2). tute, Reykjavik, vol. 1, pp. 340-347. Spitler, J.D., S.J. Rees, and P. Haves. 1998. Quantitive comparison of North Kerrisk, J.F., N.M. Schnurr, J.E. Moore, and B.D. Hunn. 1981. The custom American and U.K. cooling load calculation procedures—Part 1: Meth- weighting-factor method for thermal load calculations in the DOE-2 odology, Part II: Results. ASHRAE Transactions 104(2):36-46, 47-61. computer program. ASHRAE Transactions 87(2):569-584. Sun, T.-Y. 1968. Shadow area equations for window overhangs and side-fins Komor, P. 1997. Space cooling demands from office plug loads. ASHRAE and their application in computer calculation. ASHRAE Transactions Journal 39(12):41-44. 74(1):I-1.1 to I-1.9. Kusuda, T. 1967. NBSLD, the computer program for heating and cooling Swierczyna, R., P. Sobiski, and D. Fisher. 2008. Revised heat gain and cap- loads for buildings. BSS 69 and NBSIR 74-574. National Bureau of ture and containment exhaust rates from typical commercial cooking Standards. appliances (RP-1362). ASHRAE Research Project, Final Report. Latta, J.K., and G.G. Boileau. 1969. Heat losses from house basements. Swierczyna, R., P.A. Sobiski, and D.R. Fisher. 2009 (forthcoming). Revised Canadian Building 19(10):39. heat gain rates from typical commercial cooking appliances from RP- LBL. 2003. WINDOW 5.2: A PC program for analyzing window thermal 1362. ASHRAE Transactions 115(2). performance for fenestration products. LBL-44789. Windows and Day- Talbert, S.G., L.J. Canigan, and J.A. Eibling. 1973. An experimental study of lighting Group. Lawrence Berkeley Laboratory, Berkeley. ventilation requirements of commercial electric kitchens. ASHRAE Liesen, R.J., and C.O. Pedersen. 1997. An evaluation of inside surface heat Transactions 79(1):34. balance models for cooling load calculations. ASHRAE Transactions Walton, G. 1983. Thermal analysis research program reference manual. 103(2):485-502. National Bureau of Standards. Marn, W.L. 1962. Commercial gas kitchen ventilation studies. Research Webster, T., F. Bauman, F. Buhl, and A. Daly. 2008. Modeling of underfloor Bulletin 90(March). Gas Association Laboratories, Cleveland, OH. air distribution (UFAD) systems. SimBuild 2008, University of Califor- McClellan, T.M., and C.O. Pedersen. 1997. Investigation of outdoor heat nia, Berkeley. balance models for use in a heat balance cooling load calculation proce- Wilkins, C.K., and M.R. Cook. 1999. Cooling loads in laboratories. dure. ASHRAE Transactions 103(2):469-484. ASHRAE Transactions 105(1):744-749. McQuiston, F.C., and J.D. Spitler. 1992. Cooling and heating load calcula- Wilkins, C.K., and M.H. Hosni. 2000. Heat gain from office equipment. tion manual, 2nd ed. ASHRAE. ASHRAE Journal 42(6):33-44. Miller, A. 1971. Meteorology, 2nd ed. Charles E. Merrill, Columbus. Wilkins, C.K., and M. Hosni. 2011. Plug load design factors. ASHRAE Jour- Nigusse, B.A. 2007. Improvements to the radiant time series method cooling nal 53(5):30-34. load calculation procedure. Ph.D. dissertation, Oklahoma State Univer- Wilkins, C.K., and N. McGaffin. 1994. Measuring computer equipment sity. loads in office buildings. ASHRAE Journal 36(8):21-24. Nonresidential Cooling and Heating Load Calculations 18.51

Wilkins, C.K., R. Kosonen, and T. Laine. 1991. An analysis of office equip- Mitalas, G.P., and K. Kimura. 1971. A calorimeter to determine cooling load ment load factors. ASHRAE Journal 33(9):38-44. caused by lights. ASHRAE Transactions 77(2):65. Mitalas, G.P., and D.G. Stephenson. 1967. Room thermal response factors. BIBLIOGRAPHY ASHRAE Transactions 73(2): III.2.1. Alereza, T., and J.P. Breen, III. 1984. Estimates of recommended heat gain Nevins, R.G., H.E. Straub, and H.D. Ball. 1971. Thermal analysis of heat due to commercial appliances and equipment. ASHRAE Transactions removal troffers. ASHRAE Transactions 77(2):58-72. 90(2A):25-58. NFPA. 2012. Health care facilities code. Standard 99-2012. National Fire ASHRAE. 1975. Procedure for determining heating and cooling loads for Protection Association, Quincy, MA. computerized energy calculations, algorithms for building heat transfer Ouyang, K., and F. Haghighat. 1991. A procedure for calculating thermal subroutines. response factors of multi-layer walls—State space method. Building and ASHRAE. 1979. Cooling and heating load calculation manual. Environment 26(2):173-177. BLAST Support Office. 1991. BLAST user reference. University of Illinois, Peavy, B.A. 1978. A note on response factors and conduction transfer func- Urbana–Champaign. tions. ASHRAE Transactions 84(1):688-690. Buffington, D.E. 1975. Heat gain by conduction through exterior walls and Peavy, B.A., F.J. Powell, and D.M. Burch. 1975. Dynamic thermal perfor- roofs—Transmission matrix method. ASHRAE Transactions 81(2):89. mance of an experimental masonry building. NBS Building Science Burch, D.M., B.A. Peavy, and F.J. Powell. 1974. Experimental validation of Series 45 (July). the NBS load and indoor temperature prediction model. ASHRAE Trans- Romine, T.B., Jr. 1992. Cooling load calculation: Art or science? ASHRAE actions 80(2):291. Journal, 34(1):14. Burch, D.M., J.E. Seem, G.N. Walton, and B.A. Licitra. 1992. Dynamic evaluation of thermal bridges in a typical office building. ASHRAE Rudoy, W. 1979. Don’t turn the tables. ASHRAE Journal 21(7):62. Transactions 98:291-304. Rudoy, W., and F. Duran. 1975. Development of an improved cooling load Butler, R. 1984. The computation of heat flows through multi-layer slabs. calculation method. ASHRAE Transactions 81(2):19-69. Building and Environment 19(3):197-206. Seem, J.E., S.A. Klein, W.A. Beckman, and J.W. Mitchell. 1989. Transfer Ceylan, H.T., and G.E. Myers. 1985. Application of response-coefficient functions for efficient calculation of multidimensional transient heat method to heat-conduction transients. ASHRAE Transactions 91:30-39. transfer. Journal of Heat Transfer 111:5-12. Chiles, D.C., and E.F. Sowell. 1984. A counter-intuitive effect of mass on Sowell, E.F., and D.C. Chiles. 1984a. Characterization of zone dynamic zone cooling load response. ASHRAE Transactions 91(2A):201-208. response for CLF/CLTD tables. ASHRAE Transactions 91(2A):162-178. Chorpening, B.T. 1997. The sensitivity of cooling load calculations to win- Sowell, E.F., and D.C. Chiles. 1984b. Zone descriptions and response char- dow solar transmission models. ASHRAE Transactions 103(1). acterization for CLF/CLTD calculations. ASHRAE Transactions 91(2A): Clarke, J.A. 1985. Energy simulation in building design. Adam Hilger Ltd., 179-200. Boston. Spitler, J.D. 1996. Annotated guide to load calculation models and algo- Davies, M.G. 1996. A time-domain estimation of wall conduction transfer rithms. ASHRAE. function coefficients. ASHRAE Transactions 102(1):328-208. Falconer, D.R., E.F. Sowell, J.D. Spitler, and B.B. Todorovich. 1993. Elec- Spitler, J.D., F.C. McQuiston, and K.L. Lindsey. 1993. The CLTD/SCL/ tronic tables for the ASHRAE load calculation manual. ASHRAE Trans- CLF cooling load calculation method. ASHRAE Transactions 99(1): actions 99(1):193-200. 183-192. Harris, S.M., and F.C. McQuiston. 1988. A study to categorize walls and Spitler, J.D., and F.C. McQuiston. 1993. Development of a revised cooling roofs on the basis of thermal response. ASHRAE Transactions 94(2): and heating calculation manual. ASHRAE Transactions 99(1):175-182. 688-714. Stephenson, D.G. 1962. Method of determining non-steady-state heat flow Hittle, D.C. 1981. Calculating building heating and cooling loads using the through walls and roofs at buildings. Journal of the Institution of Heating frequency response of multilayered slabs, Ph.D. dissertation, Depart- and Ventilating Engineers 30:5. ment of Mechanical and Industrial Engineering, University of Illinois, Stephenson, D.G., and G.P. Mitalas. 1967. Cooling load calculation by ther- Urbana-Champaign. mal response factor method. ASHRAE Transactions 73(2):III.1.1. Hittle, D.C., and R. Bishop. 1983. An improved root-finding procedure for Stephenson, D.G., and G.P. Mitalas. 1971. Calculation of heat transfer func- use in calculating transient heat flow through multilayered slabs. Inter- tions for multi-layer slabs. ASHRAE Transactions 77(2):117-126. national Journal of Heat and Mass Transfer 26:1685-1693. Kimura and Stephenson. 1968. Theoretical study of cooling loads caused by Sun, T.-Y. 1968. Computer evaluation of the shadow area on a window cast lights. ASHRAE Transactions 74(2):189-197. by the adjacent building. ASHRAE Journal (September). Kusuda, T. 1969. Thermal response factors for multilayer structures of var- Todorovic, B. 1982. Cooling load from solar radiation through partially ious heat conduction systems. ASHRAE Transactions 75(1):246. shaded windows, taking heat storage effect into account. ASHRAE Mast, W.D. 1972. Comparison between measured and calculated hour heat- Transactions 88(2):924-937. ing and cooling loads for an instrumented building. ASHRAE Sympo- Todorovic, B. 1984. Distribution of solar energy following its transmittal sium Bulletin 72(2). through window panes. ASHRAE Transactions 90(1B):806-815. McBridge, M.F., C.D. Jones, W.D. Mast, and C.F. Sepsey. 1975. Field vali- Todorovic, B. 1987. The effect of the changing shade line on the cooling load dation test of the hourly load program developed from the ASHRAE calculations. In ASHRAE videotape, Practical applications for cooling algorithms. ASHRAE Transactions 1(1):291. load calculations. Mitalas, G.P. 1968. Calculations of transient heat flow through walls and Todorovic, B. 1989. Heat storage in building structure and its effect on cool- roofs. ASHRAE Transactions 74(2):182-188. ing load; Heat and mass transfer in building materials and structure. Mitalas, G.P. 1969. An experimental check on the weighting factor method Hemisphere Publishing, New York. of calculating room cooling load. ASHRAE Transactions 75(2):22. Todorovic, B., and D. Curcija. 1984. Calculative procedure for estimating Mitalas, G.P. 1972. Transfer function method of calculating cooling loads, cooling loads influenced by window shading, using negative cooling heat extraction rate, and space temperature. ASHRAE Journal 14(12):52. load method. ASHRAE Transactions 2:662. Mitalas, G.P. 1973. Calculating cooling load caused by lights. ASHRAE Transactions 75(6):7. Todorovic, B., L. Marjanovic, and D. Kovacevic. 1993. Comparison of dif- Mitalas, G.P. 1978. Comments on the Z-transfer function method for calcu- ferent calculation procedures for cooling load from solar radiation lating heat transfer in buildings. ASHRAE Transactions 84(1):667-674. through a window. ASHRAE Transactions 99(2):559-564. Mitalas, G.P., and J.G. Arsenault. 1970. Fortran IV program to calculate Z- Wilkins, C.K. 1998. Electronic equipment heat gains in buildings. ASHRAE transfer functions for the calculation of transient heat transfer through Transactions 104(1B):1784-1789. walls and roofs. Use of Computers for Environmental Engineering York, D.A., and C.C. Cappiello. 1981. DOE-2 engineers manual (Version Related to Buildings, pp. 633-668. National Bureau of Standards, Gaith- 2.1A). Lawrence Berkeley Laboratory and Los Alamos National Labo- ersburg, MD. ratory. Thank You

To find out more about how ASHRAE Research impacts your work, your daily life and the world as a whole, please visit the Research Promotion page online: www.ashrae.org/researchpromotion.

Make your own investment in the future and help continue this important resource to ASHRAE Members. Please contact your Chapter RP Chair, ASHRAE Research Promotion Staff or donate online at: www.ashrae.org/contribute.

Reader comments, suggestions, or requests for additional copies of this document are welcome. Please contact ASHRAE RP Fundraising staff at 404/636-8400 or email [email protected] .