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CHAPTER 18. NONRESIDENTIAL COOLING AND HEATING LOAD CALCULATIONS

 

Heating and cooling load calculations are the primary design basis for most heating and air-conditioning systems and components. These calculations affect the size of piping, ductwork, diffusers, air handlers, boilers, chillers, coils, compressors, fans, and every other component of systems that condition indoor environments. Cooling and heating load calculations can significantly affect first cost of building construction, comfort and productivity of occupants, and operating cost and energy consumption.

Simply put, heating and cooling loads are the rates of energy input (heating) or removal (cooling) required to maintain an indoor environment at a desired temperature and humidity condition. Heating and air conditioning systems are designed, sized, and controlled to accomplish that energy transfer. The amount of heating or cooling required at any particular time varies widely, depending on external (e.g., outdoor temperature) and internal (e.g., number of people occupying a space) factors.

Peak design heating and cooling load calculations, which are this chapter’s focus, seek to determine the maximum rate of heating and cooling energy transfer needed to maintain the space conditions at the desired level (set point). Similar principles, but with different assumptions, data, and application, can be used to estimate building energy consumption, as described in Chapter 19.

This chapter discusses common elements of cooling and heating load calculation (e.g., internal heat gain, ventilation and infiltration, moisture migration, fenestration heat gain) and two methods of heating and cooling load estimation: heat balance (HB) and radiant time series (RTS).

1. COOLING LOAD CALCULATION PRINCIPLES

Cooling loads result from many conduction, convection, and radiation heat transfer processes through the building envelope and from internal sources and system components. Building components or contents that may affect cooling loads include the following:

  • External: Walls, roofs, windows, skylights, doors, partitions, ceilings, and floors

  • Internal: Lights, people, appliances, and equipment

  • Infiltration: Air leakage and moisture migration

  • System: Outdoor air, duct leakage and heat gain, reheat, fan and pump energy, and energy recovery

1.1 TERMINOLOGY

The variables affecting cooling load calculations are numerous, often difficult to define precisely, and always intricately interrelated. Many cooling load components vary widely in magnitude, and possibly direction, during a 24 h period. Because these cyclic changes in load components often are not in phase with each other, each component must be analyzed to establish the maximum cooling load for a building or zone. A zoned system (i.e., one serving several independent areas, each with its own temperature control) needs to provide no greater total cooling load capacity than the largest hourly sum of simultaneous zone loads throughout a design day; however, it must handle the peak cooling load for each zone at its individual peak hour. At some times of day during heating or intermediate seasons, some zones may require heating while others require cooling. The zones’ ventilation, humidification, or dehumidification needs must also be considered.

The current terminology presented here has been developed over time based on the assumption that heat will be removed from a space through a convective- (air system) based cooling process. ASHRAE research project RP-1729 (Moftakhari et al. 2020) shows that when cooling is provided through a predominantly radiant-based cooling system, conversion of heat gain to cooling load can differ from convective-based systems. It is always important to distinguish between room load and HVAC system load. This is true for both convective-based and radiant cooling systems. This chapter deals with calculation of the room cooling load. For radiant cooling systems, those room loads should be applied to calculation of HVAC system loads using principles described in Chapter 6 of the 2024 ASHRAE Handbook—HVAC Systems and Equipment. This current chapter is largely based on convective or air-system-based cooling, but some key differences that would exist with radiant systems will be pointed out.

 Heat Flow Rates

In air-conditioning design, the following four related heat flow rates, each of which varies with time, must be differentiated.

Space Heat Gain. This instantaneous rate of heat gain is the rate at which heat enters into and/or is generated within a space. Heat gain is classified by its mode of entry into the space and whether it is sensible or latent. Entry modes include (1) solar radiation through transparent surfaces; (2) heat conduction through exterior walls and roofs; (3) heat conduction through ceilings, floors, and interior partitions; (4) heat generated in the space by occupants, lights, and appliances; (5) heat transfer through direct-with-space ventilation and infiltration of outdoor air; and (6) miscellaneous heat gains. Sensible heat is added directly to the conditioned space by conduction, convection, and/or radiation. Latent heat gain occurs when moisture is added to the space (e.g., from vapor emitted by occupants and equipment). To maintain a constant humidity ratio, water vapor must condense on the cooling apparatus and be removed at the same rate it is added to the space. The amount of energy required to offset latent heat gain essentially equals the product of the condensation rate and latent heat of condensation. In selecting cooling equipment, distinguish between sensible and latent heat gain: every cooling apparatus has different maximum removal capacities for sensible versus latent heat for particular operating conditions. In extremely dry climates, humidification may be required, rather than dehumidification, to maintain thermal comfort.

Radiant Heat Gain. Radiant heat gain will first be absorbed by surfaces that enclose the space (walls, floor, and ceiling) and objects in the space (furniture, etc.). With convective or air-based cooling systems, these surfaces and objects become warmer than the surrounding air and some of their heat transfers to the air by convection. The composite heat storage capacity of these surfaces and objects determines the rate at which their respective surface temperatures increase for a given radiant input, and thus governs the relationship between the radiant portion of heat gain and its corresponding conversion to space cooling load (Figure 1). The thermal storage effect is critical in differentiating between instantaneous heat gain for a given space and its cooling load at that moment. Predicting 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 on the subject.

With radiant-based cooling systems, radiant gains are still absorbed by surfaces in the space but the process of conversion from radiant heat gains to cooling load can be very different than would occur with convective or air-based cooling systems. The first difference occurs if the radiant gain strikes the radiant cooling surface directly. In this case, the radiant gain is converted to cooling load immediately as the heat is absorbed directly by the active radiant cooling system. Other radiant gains are absorbed by nonactive surfaces in the space. In these cases, though, the heat gain could be converted to cooling load either by convection to the space air or through radiation exchange with the active radiant cooling surface. ASHRAE research project RP-1729 (Moftakhari et al. 2020) found that in general, the radiant system maintains nonactive surfaces at a temperature below the room air and that most absorbed radiant gains are converted to cooling load by exchange with the radiant cooling system. This resulted in less stored heat and less time lag between the heat gain and its conversion to cooling load as compared to conventional air based systems.

Origin of Difference Between Magnitude of Instantaneous Heat Gain and Instantaneous Cooling Load

Figure 1. Origin of Difference Between Magnitude of Instantaneous Heat Gain and Instantaneous Cooling Load


The heat transfer mechanics of the conversion of radiant heat gains to cooling load does not depend on the mass of the radiant cooling device. All radiant exchange between the cooling device and the space is through the exposed surface of the device. The position, configuration, and surface area of the device can result in different heat transfer dynamics. For example, a radiant cooling floor interacts differently with direct solar gain than a radiant ceiling would for a given space. The same might be true for radiant gain from ceiling-mounted lighting, though RP-1729 performed experiments only for the case of radiant ceiling panels. Computer modeling was done to explore the differences between ceiling- and floor-mounted radiant cooling devices, verifying these conclusions.

Space Cooling Load. This is the rate at which sensible and latent heat must be removed from the space to maintain a constant space air temperature and humidity. The sum of all space instantaneous heat gains at any given time does not necessarily (or even frequently) equal the cooling load for the space at that same time because of the effect of radiant gains being stored in the building mass, as described previously.

Space Heat Extraction Rate. The rates at which sensible and latent heat are removed from the conditioned space equal the space cooling load when the room air temperature and humidity are constant. Along with the intermittent operation of cooling equipment, control systems usually allow a minor cyclic variation or swing in room temperature; humidity is often allowed to float, but it can be controlled. Therefore, proper simulation of the control system gives a more realistic value of energy removal over a fixed period than using values of the space cooling load. However, this is primarily important for estimating energy use over time; it is not needed to calculate design peak cooling load for equipment selection.

Cooling Coil Load. The rate at which energy is removed at a cooling coil serving one or more conditioned spaces equals the sum of instantaneous space cooling loads (or space heat extraction rate, if it is assumed that space temperature and humidity vary) for all spaces served by the coil, plus any system loads. System loads include fan heat gain, duct heat gain, and outdoor air heat and moisture brought into the cooling equipment to satisfy the ventilation air requirement.

 Time Delay Effect

Heat gain absorbed by walls, floor, furniture, etc., contributes to space cooling load only after it has been converted to cooling load, as described previously. Some of this stored heat gain can still be present and converting to cooling load even after the heat gain sources have been switched off or removed, as shown in Figure 2.

For other than purely convective heat gains, there is some delay between the time a heat source is activated and the point when the rate of conversion to cooling load equals the rate of heat gain (steady-state). This time lag must be considered when calculating cooling load, because the load required for the space can be much lower than the instantaneous heat gain being generated, and the space’s peak load may be significantly affected.

Thermal Storage Effect in Cooling Load from Lights

Figure 2. Thermal Storage Effect in Cooling Load from Lights


Accounting for the time delay effect is the major challenge in cooling load calculations. Several methods, including the two presented in this chapter, have been developed to take the time delay effect into consideration.

1.2 COOLING LOAD CALCULATION METHODS

This chapter presents two load calculation methods that vary significantly from previous methods. The technology involved, however (the principle of calculating a heat balance for a given space) is not new. The first of the two methods is the heat balance (HB) method; the second is radiant time series (RTS), which is a simplification of the HB procedure. Both methods are explained in their respective sections.

Cooling load calculation of an actual, multiple-room building requires a complex computer program implementing the principles of either method.

 Cooling Load Calculations in Practice

Load calculations should accurately describe the building. All load calculation inputs should be as accurate as reasonable, without using safety factors. Introducing compounding safety factors at multiple levels in the load calculation results in an unrealistic and oversized load.

Variation in heat transmission coefficients of typical building materials and composite assemblies, differing motivations and skills of those who construct the building, unknown infiltration rates, and the manner in which the building is actually operated are some of the variables that make precise calculation impossible. Even if the designer uses reasonable procedures to account for these factors, the calculation can never be more than a good estimate of the actual load. Frequently, a cooling load must be calculated before every parameter in the conditioned space can be properly or completely defined. An example is a cooling load estimate for a new building with many floors of unleased spaces for which detailed partition requirements, furnishings, lighting, and layout cannot be predefined. Potential tenant modifications once the building is occupied also must be considered. Load estimating requires proper engineering judgment that includes a thorough understanding of heat balance fundamentals.

Perimeter spaces exposed to high solar heat gain often need cooling during sunlit portions of traditional heating months, as do completely interior spaces with significant internal heat gain. These spaces can also have significant heating loads during nonsunlit hours or after periods of nonoccupancy, when adjacent spaces have cooled below interior design temperatures. The heating loads involved can be estimated conventionally to offset or to compensate for them and prevent overheating, but they have no direct relationship to the spaces’ design heating loads.

Correct design and sizing of air-conditioning systems require more than calculation of the cooling load in the space to be conditioned. The type of air-conditioning system, ventilation rate, reheat, fan energy, fan location, duct heat loss and gain, duct leakage, heat extraction lighting systems, type of return air system, and any sensible or latent heat recovery all affect system load and component sizing. Adequate system design and component sizing require that system performance be analyzed as a series of psychrometric processes.

System design could be driven by either sensible or latent load, and both need to be checked. In a sensible-load-driven space (the most common case), the cooling supply air has surplus capacity to dehumidify, but this is usually permissible. For a space driven by latent load (e.g., an auditorium), supply airflow based on sensible load is likely not to have enough dehumidifying capability, so subcooling and reheating or some other dehumidification process is needed.

This chapter is primarily concerned with a given space or zone in a building. When estimating loads for a group of spaces (e.g., for an air-handling system that serves multiple zones), the assembled zones must be analyzed to consider (1) the simultaneous effects taking place; (2) any diversification of heat gains for occupants, lighting, or other internal load sources; (3) ventilation; and/or (4) any other unique circumstances. With large buildings that involve more than a single HVAC system, simultaneous loads and any additional diversity also must be considered when designing the central equipment that serves the systems. Methods presented in this chapter are expressed as hourly load summaries, reflecting 24 h input schedules and profiles of the individual load variables. Specific systems and applications may require different profiles.

1.3 DATA ASSEMBLY

Calculating space cooling loads requires detailed building design information and weather data at design conditions. Generally, the following information should be compiled.

Building Characteristics. Building materials, component size, external surface colors, and shape are usually determined from building plans and specifications.

Configuration. Determine building location, orientation, and external shading from building plans and specifications. Shading from adjacent buildings can be determined from a site plan or by visiting the proposed site, but its probable permanence should be carefully evaluated before it is included in the calculation. The possibility of abnormally high ground-reflected solar radiation (e.g., from adjacent water, sand, or parking lots) or solar load from adjacent reflective buildings should not be overlooked.

Outdoor Design Conditions. Obtain appropriate weather data, and select outdoor design conditions. Chapter 14 provides information for many weather stations; note, however, that these design 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. Also, consider prevailing wind velocity and the relationship of a project site to the selected weather station.

Recent research projects have greatly expanded the amount of available weather data (e.g., ASHRAE 2012). In addition to the conventional dry bulb with mean coincident wet bulb, data are now available for wet bulb and dew point with mean coincident dry bulb. Peak space load generally coincides with peak solar or peak dry bulb, but peak system load often occurs at peak wet-bulb temperature. The relationship between space and system loads is discussed further in following sections of the chapter.

To estimate conductive heat gain through exterior surfaces and infiltration and outdoor air loads at any time, applicable outdoor dry- and wet-bulb temperatures must be used. Chapter 14 gives monthly cooling load design values of outdoor conditions for many locations. These are generally midafternoon conditions; for other times of day, the daily range profile method described in Chapter 14 can be used to estimate dry- and wet-bulb temperatures. Peak cooling load is often determined by solar heat gain through fenestration; this peak may occur in winter months and/or at a time of day when outdoor air temperature is not at its maximum.

Understanding Annual Design Conditions. Heating and cooling loads are often calculated based on ASHRAE annual design conditions, which are available in

Heating design temperatures are presented as 99% and 99.6% conditions and cooling design temperatures are presented as 0.4%, 1%, and 2%. These statistical thresholds represent the percentage of hours in a typical year where the design condition will be exceeded, either warmer or colder, depending on the season, as shown in Table 1.

Table 1 Hours Annual Conditions Are Exceeded for Typical Year

Annual Condition

Hours Exceeded per Year

Summer 0.4%

35 hrs

Summer 1%

88 hrs

Summer 2%

175 hrs

Winter 99%

88 hrs

Winter 99.6%

35 hrs


Table 2 Comparison of Annual Design and Extreme Dry-Bulb Conditions

Chicago, O’Hare, IL, USA (WMO: 725300, Elev 662 ft)

Heating Dry-Bulb

Δ from 99%

Cooling Dry-Bulb

Δ from 1%

99% heating/1% cooling

–15.3°C

0.0 K

31.4°C

0.0 K

99.6% heating/0.4% cooling

–18.1°C

–2.8 K

32.9°C

+1.4 K

5 year extreme

–24.2°C

–8.9 K

36.8°C

+5.3 K

10 year extreme

–26.2°C

–10.9 K

37.9°C

+6.4 K

20 year extreme

–28.1°C

–12.8 K

38.9°C

+7.5 K

50 year extreme

–30.6°C

–15.3 K

40.4°C

+8.9 K


Extreme Outdoor Temperature Conditions. ASHRAE now also publishes data for extreme annual temperatures presented as 5, 10, 20, and 50 year extreme temperatures. Extreme temperatures can exceed the annual design conditions by a significant amount, particularly in the winter. Table 2 is a comparison of heating and cooling annual design dry bulb temperature conditions and annual extreme dry bulb temperature conditions for Chicago O’Hare, Illinois (WMO: 725300).

Outdoor Temperature Impact on Peak Space Load. Outdoor air dry-bulb temperature typically does not have a significant impact on space peak cooling load. Solar and internal gains have far more influence on the peak cooling load of a space. Cooling design temperature can be exceeded for a few hours on a given day, and it will likely have little or no effect on peak cooling load for a given space. It is generally not necessary to consider extreme temperature for space cooling loads.

Peak space heating loads generally occur in the early morning hours when there are no solar gains or internal gains. Traditionally, peak space heating loads are determined with an instantaneous U × A × ΔT calculation. The dominant drivers of the peak space heating loads are transmission and infiltration, both of which vary linearly with outside air dry-bulb temperature. If a building is using night setback, these extreme winter temperature conditions can be expected to occur at the time the building will need to be “warmed up.” In many applications, it is prudent to consider extreme conditions for the calculation of peak space heating loads.

Outdoor Temperature Impact on System Loads. Outdoor dry bulb temperature can affect system loads, capacity, and efficiency for coils, air-cooled refrigeration, and air-to-air and air-to-water heat pumps. Extreme summer temperature conditions can be used as the design basis when sizing air-cooled chillers or other DX systems for certain applications, where the loss of capacity and efficiency that air-cooled refrigeration equipment would experience during periods of extreme temperatures would impact comfort or critical operations within a building. This is particularly true for air-cooled equipment mounted on rooftops or in constricted spaces.

Extreme winter temperature conditions can impact heating coil performance and can also have a significant effect on the capacity and efficiency of air-source heat pumps when sized on heating conditions. It is customary practice to use comparable design conditions for air-handling unit (AHU) heating coils as would be used for space heating loads. If use of extreme conditions is warranted for space heating loads, then comparable values should be used for sizing AHU coils. Where heat pumps are part of the primary heating plant for a building, it may be necessary to account for the loss of capacity that could occur during periods of extreme cold temperatures.

Extreme Outdoor Latent Conditions. Temperature or sensible load is only one aspect of design or extreme conditions. ASHRAE weather data (see Chapter 14) also includes design and extreme conditions for moisture or latent components of these conditions. These are presented as evaporation (wet-bulb), dehumidification (dewpoint/humidity ratio), and enthalpy design conditions. These conditions result in similar air properties, but each is intended to provide the design condition for different systems or equipment. The evaporation design condition is for evaporative cooling apparatus such as cooling towers and is based on peak wet-bulb temperature with associated coincident conditions. The dehumidification design condition is based on peak dew point temperature and can represent the peak dehumidification load on a cooling coil or standalone dehumidifier. The enthalpy condition is the point of highest overall energy content of outside air.

Extreme conditions are presented for wet-bulb temperature, but there is not a specific coincident condition included. (Note: The corresponding extreme dry-bulb temperatures included in ASHRAE weather data are not intended to be a coincident condition.) Table 3 indicates the extreme wet-bulb temperature with the other coincident properties calculated based on an assumed 65% RH, to allow comparison to 1.0% and 0.4% summer design conditions. Extreme wet-bulb temperatures are also included in ASHRAE weather data for winter conditions.

Latent Conditions Impact on Peak Space Load. In most cases, space cooling loads are defined based on peak sensible loads. In cases where dehumidification is the driver of peak space load, the 1% or 0.4% dehumidification design condition should be considered over the cooling dry-bulb design conditions. Extreme wet-bulb conditions will result in even higher space dehumidification loads than the traditional design conditions and could be considered where appropriate for the application.

Latent Conditions Impact on System Loads. Design and extreme latent conditions will have a significant impact on peak loads for cooling systems and cooling equipment. In most climates, cooling coils in AHUs must provide both sensible cooling and dehumidification at peak conditions. Both temperature and humidity of the outside air will impact the load on an AHU cooling coil. Table 3 illustrates that any of the latent design conditions will result in higher coil loads relative to dry-bulb design conditions. It is generally necessary to consider a peak latent load condition when sizing cooling coils or other cooling system components.

Table 3 indicates that extreme wet bulb conditions may result in significantly higher moisture and enthalpy levels in outside air than traditional design conditions, especially in humid climates. These extreme conditions may be appropriate to consider as the design basis for facilities where high outdoor air quantities exist or tight humidity control is a critical operational parameter.

Application of Extreme Weather Conditions. The degree to which extreme conditions should be the design basis for space load calculations or system/equipment sizing depends on the application. A noncritical office space may tolerate periods of time where the temperature is maintained but not the relative humidity. For advanced manufacturing, research, health care, or other critical spaces that require strict humidity control, it may be prudent to base the design of cooling coils and chilled water systems on one of the extreme conditions. At a minimum, even for strictly comfort applications, it is advisable to consider the dehumidification design conditions as well as the temperature design conditions. In all cases though, it is important to understand the impact of weather data on design decisions and apply appropriate engineering judgment.

Table 3 Comparison of Annual Design and Extreme Conditions Involving Humidity

Chicago, O’Hare, IL, USA (WMO: 725300, Elev 189.6 m)

Dry-Bulb (DB), °C

Wet-Bulb (WB), °C

Dew Point (DP), °C

Humidity Ratio (HR), g/kgA

Enthalpy (Enth), kJ/kgA

Relative Humidity (RH), %

1% cooling dry-bulb

31.4

22.5

18.7

13.9

67.3

47

1% evaporation

29.2

24.1

22.2

17.3

73.5

66

1% dehumidification

27.2

23.7

22.4

17.6

72.4

75

1% enthalpy

29.3

24.0

22.1

17.2

73.3

65

0.4% cooling dry-bulb

32.9

23.2

19.3

14.4

70.0

45

0.4% evaporation

30.7

25.1

23.2

18.4

78.0

64

0.4% dehumidification

28.3

24.7

23.4

18.7

76.1

75

0.4% enthalpy

30.8

25.0

23.0

18.2

77.5

63

5 yr extreme wet-bulb

32.9

27.2

25.4

21.2

87.3

65

10 yr extreme wet-bulb

33.5

27.8

26.0

22.0

90.0

65

20 yr extreme wet-bulb

34.2

28.3

26.6

22.8

92.8

65

50 yr extreme wet-bulb

34.9

29.1

27.4

23.9

96.3

65

Bold values are from published data points. Italics data were derived.


Indoor Design Conditions. Select indoor dry-bulb temperature, indoor relative humidity, and ventilation rate. Include permissible variations and control limits. Consult ASHRAE Standard 90.1 for energy-savings conditions, and Standard 55 for ranges of indoor conditions needed for thermal comfort.

Table 4 Representative Rates at Which Heat and Moisture Are Given Off by Human Beings in Different States of Activity

Degree of Activity

Location

Total Heat, W

Sensible Heat, W

Latent Heat, W

% Sensible Heat that is Radiantb

Adult Male

Adjusted, M/Fa

Low V

High V

Seated at theater

Theater

114

103

72

31

60

27

Seated, very light work

Offices, hotels, apartments

132

117

72

45

   

Moderately active office work

Offices, hotels, apartments

139

132

73

59

   

Standing, light work; walking

Department store; retail store

161

132

73

59

58

38

Walking, standing

Drug store, bank

161

147

73

73

   

Sedentary work

Restaurantc

144

161

81

81

   

Light bench work

Factory

235

220

81

139

   

Moderate dancing

Dance hall

264

249

89

160

49

35

Walking 3 mph; light machine work

Factory

293

293

110

183

   

Bowlingd

Bowling alley

440

425

170

255

   

Heavy work

Factory

440

425

170

255

54

19

Heavy machine work; lifting

Factory

469

469

186

283

   

Athletics

Gymnasium

587

528

208

320

   

Notes:

1. Tabulated values are based on 23.9°C room dry-bulb temperature. For 26.7°C room dry bulb, total heat remains the same, but sensible heat values should be decreased by approximately 20%, and latent heat values increased accordingly.

2. Also see Table 4, Chapter 9, for additional rates of metabolic heat generation.

3. All values are rounded to nearest watt.

a Adjusted heat gain is based on normal percentage of men, women, and children for the application listed, and assumes that gain from an adult female is 85% of that for an adult male, and gain from a child is 75% of that for an adult male.

b Values approximated from data in Table 6, Chapter 9, where V is air velocity with limits shown in that table.

c Adjusted heat gain includes 18 W for food per individual (9 W sensible and 9 W latent).

d Figure one person per alley actually bowling, and all others as sitting (117 W) or standing or walking slowly (161 W).


Internal Heat Gains and Operating Schedules. Obtain planned density and a proposed schedule of lighting, occupancy, internal equipment, appliances, and processes that contribute to the internal thermal load.

Areas. Use consistent methods for calculation of building areas. For fenestration, the definition of a component’s area must be consistent with associated ratings.

Gross surface area. It is efficient and conservative to derive gross surface areas from outer building dimensions, ignoring wall and floor thicknesses and avoiding separate accounting of floor edge and wall corner conditions. Measure floor areas to the outside of adjacent exterior walls or to the centerline of adjacent partitions. When apportioning to rooms, façade area should be divided at partition centerlines. Wall height should be taken as floor-to-floor height.

The outer-dimension procedure is expedient for load calculations, but it is not consistent with rigorous definitions used in building-related standards. The resulting differences do not introduce significant errors in this chapter’s procedures.

Fenestration area. As discussed in Chapter 15, fenestration ratings [U-factor and solar heat gain coefficient (SHGC)] are based on the entire product area, including frames. Thus, for load calculations, fenestration area is the area of the rough opening in the wall or roof.

Net surface area. Net surface area is the gross surface area less any enclosed fenestration area.

2. INTERNAL HEAT GAINS

Internal heat gains from people, lights, motors, appliances, and equipment can contribute the majority of the cooling load in a modern building. As building envelopes have improved in response to more restrictive energy codes, internal loads have increased because of factors such as increased use of computers and the advent of dense-occupancy spaces (e.g., call centers). Internal heat gain calculation techniques are identical for both heat balance (HB) and radiant time series (RTS) cooling-load calculation methods, so internal heat gain data are presented here independent of calculation methods.

2.1 PEOPLE

Table 4 gives representative rates at which sensible heat and moisture are emitted by humans in different states of activity. In high-density spaces, such as auditoriums, these sensible and latent heat gains comprise a large fraction of the total load. Even for short-term occupancy, the extra sensible heat and moisture introduced by people may be significant. See Chapter 9 for detailed information; however, Table 4 summarizes design data for common conditions.

The conversion of sensible heat gain from people to space cooling load is affected by the thermal storage characteristics of that space because some percentage of the sensible load is radiant energy. Latent heat gains are usually considered instantaneous, but research is yielding practical models and data for the latent heat storage of and release from common building materials.

2.2 LIGHTING

Because lighting is often a major space cooling load component, an accurate estimate of the space heat gain it imposes is needed. Calculation of this load component is not straightforward; the rate of cooling load from lighting at any given moment can be quite different from the heat equivalent of power supplied instantaneously to those lights, because of heat storage.

 Instantaneous Heat Gain from Lighting

The primary source of heat from lighting comes from light-emitting elements, or lamps, although significant additional heat may be generated from ballasts and other appurtenances in the luminaires. Generally, the instantaneous rate of sensible heat gain from electric lighting may be calculated from

(1)

where

qel = heat gain, W
W = total light wattage, W
Ful = lighting use factor
Fsa = lighting special allowance factor

The total light wattage is obtained from the ratings of all lamps installed, both for general illumination and for display use. Ballasts are not included, but are addressed by a separate factor. Wattages of magnetic ballasts are significant; the energy consumption of high-efficiency electronic ballasts might be insignificant compared to that of the lamps.

The lighting use factor is the ratio of wattage in use, for the conditions under which the load estimate is being made, to total installed wattage. For commercial applications such as stores, the use factor is generally 1.0.

The special allowance factor is the ratio of the lighting fixtures’ power consumption, including lamps and ballast, to the nominal power consumption of the lamps. For incandescent lights, this factor is 1. For fluorescent lights, it accounts for power consumed by the ballast as well as the ballast’s effect on lamp power consumption. The special allowance factor can be less than 1 for electronic ballasts that lower electricity consumption below the lamp’s rated power consumption. Use manufacturers’ values for system (lamps + ballast) power, when available.

For high-intensity-discharge lamps (e.g. metal halide, mercury vapor, high- and low-pressure sodium vapor lamps), the actual lighting system power consumption should be available from the manufacturer of the fixture or ballast. Ballasts available for metal halide and high-pressure sodium vapor lamps may have special allowance factors from about 1.3 (for low-wattage lamps) down to 1.1 (for high-wattage lamps).

An alternative procedure is to estimate the lighting heat gain on a per-square-metre basis. Such an approach may be required when final lighting plans are not available. Table 5 shows the maximum lighting power density (LPD) (lighting heat gain per square metre) allowed by ASHRAE Standard 90.1-2019 for a range of space types.

In addition to determining the lighting heat gain, the fraction of lighting heat gain that enters the conditioned space may need to be distinguished from the fraction that enters an unconditioned space; of the former category, the distribution between radiative and convective heat gain must be established.

Fisher and Chantrasrisalai (2006) and Zhou et al. (2016) experimentally studied 12 luminaire types and recommended several categories of luminaires, as shown in Table 6. The table provides a range of design data for the conditioned space fraction, short-wave radiative fraction, and long-wave radiative fraction under typical operating conditions: airflow rate of 5 L/(s·m2), supply air temperature between 15 and 16.7°C, and room air temperature between 22 and 24°C. The recommended fractions in Table 6 are based on lighting heat input rates range of 9.7 to 28 W/m2. For higher design power input, the lower bounds of the space and short-wave fractions should be used; for design power input below this range, the upper bounds of the space and short-wave fractions should be used. The space fraction in the table is the fraction of lighting heat gain that goes to the room; the fraction going to the plenum can be computed as 1 – the space fraction. The radiative fraction is the radiative part of the lighting heat gain that goes to the room. The convective fraction of the lighting heat gain that goes to the room is 1 – the radiative fraction. Using values in the middle of the range yields sufficiently accurate results. However, values that better suit a specific situation may be determined according to the notes for Table 6.

Table 6’s data apply to both ducted and non-ducted returns. However, application of the data, particularly the ceiling plenum fraction, may vary for different return configurations. For instance, for a room with a ducted return, although a portion of the lighting energy initially dissipated to the ceiling plenum is quantitatively equal to the plenum fraction, a large portion of this energy would likely end up as the conditioned space cooling load and a small portion would end up as the cooling load to the return air.

If the space airflow rate is different from the typical condition [i.e., about 5 L/(s·m2)], Figure 3 can be used to estimate the lighting heat gain parameters. Design data shown in Figure 3 are only applicable for the recessed fluorescent luminaire without lens.

Although design data presented in Table 6 and Figure 3 can be used for a vented luminaire with side-slot returns, they are likely not applicable for a vented luminaire with lamp compartment returns, because in the latter case, all heat convected in the vented luminaire is likely to go directly to the ceiling plenum, resulting in zero convective fraction and a much lower space fraction. Therefore, the design data should only be used for a configuration where conditioned air is returned through the ceiling grille or luminaire side slots.

Lighting Heat Gain Parameters for Recessed Fluorescent Luminaire Without Lens (Fisher and Chantrasrisalai 2006)

Figure 3. Lighting Heat Gain Parameters for Recessed Fluorescent Luminaire Without Lens (Fisher and Chantrasrisalai 2006)


For other luminaire types, it may be necessary to estimate the heat gain for each component as a fraction of the total lighting heat gain by using judgment to estimate heat-to-space and heat-to-return percentages.

Because of the directional nature of downlight luminaires, a large portion of the short-wave radiation typically falls on the floor. When converting heat gains to cooling loads in the RTS method, the solar radiant time factors (RTFs) may be more appropriate than nonsolar RTFs. (Solar RTFs are calculated assuming most solar radiation is intercepted by the floor; nonsolar RTFs assume uniform distribution by area over all interior surfaces.) This effect may be significant for rooms where lighting heat gain is high and for which solar RTFs are significantly different from nonsolar RTFs.

2.3 ELECTRIC MOTORS

Instantaneous sensible heat gain from equipment operated by electric motors in a conditioned space is calculated as

(2)

where

qem = heat equivalent of equipment operation, W
P = motor power rating, W
EM = motor efficiency, decimal fraction <1.0
FUM = motor use factor, 1.0 or decimal fraction <1.0
FLM = motor load factor, 1.0 or decimal fraction <1.0

The motor use factor may be applied when motor use is known to be intermittent, with significant nonuse during all hours of operation (e.g., overhead door operator). For conventional applications, its value is 1.0.

The motor load factor is the fraction of the rated load delivered under the conditions of the cooling load estimate. Equation (2) assumes that both the motor and driven equipment are in the conditioned space. If the motor is outside the space or airstream,

(3)

When the motor is inside the conditioned space or airstream but the driven machine is outside,

(4)

Equation (4) also applies to a fan or pump in the conditioned space that exhausts air or pumps fluid outside that space.

Table 7A and 7B gives minimum efficiencies and related data representative of typical electric motors from ASHRAE Standard 90.1-2019. If electric motor load is an appreciable portion of cooling load, the motor efficiency should be obtained from the manufacturer. Also, 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.

 Overloading or Underloading

Heat output of a motor is generally proportional to motor load, within rated overload limits. Because of typically high no-load motor current, fixed losses, and other reasons, FLM is generally assumed to be unity, and no adjustment should be made for underloading or overloading unless the situation is fixed and can be accurately established, and reduced-load efficiency data can be obtained from the motor manufacturer.

 Radiation and Convection

Unless the manufacturer’s technical literature indicates otherwise, motor heat gain normally should be equally divided between radiant and convective components for the subsequent cooling load calculations.

2.4 APPLIANCES

A cooling load estimate should take into account heat gain from all appliances (electrical, gas, or steam). Because of the variety of appliances, applications, schedules, use, and installations, estimates can be very subjective. Often, the only information available about heat gain from equipment is that on its nameplate, which can overestimate actual heat gain for many types of appliances, as discussed in the section on Office Equipment.

 Cooking Appliances

These appliances include common heat-producing cooking equipment found in conditioned commercial kitchens.


Fundamental Principles. In commercial kitchens, appliances are typically turned on at the beginning of each operating period and are not turned off until closing time. Although the appliances are “up to temperature” all of the time, they may be used to cook food less than 25% of the time. The “up to temperature” condition is referred to as the “idle (ready to cook)” condition, while “cooking” condition is when the appliance is being used to cook food. Due to this operation, idle (ready to cook) heat gain measurements provide a good estimate of heat gain for calculating cooling load (Swierczyna et al. 2008). In estimating appliance heat gains, probabilities of simultaneous use and operation for different appliances located in the same space should be considered.

Cooking appliances generate three types of heat gain to the kitchen space: sensible radiant, sensible convective, and latent heat gain. For unhooded appliances, all three types of heat gain contribute to cooling load in the kitchen space. For hooded appliances, Marn (1962) determined that, where appliances are installed under an effective hood, only sensible radiant gain adds to the cooling load of the kitchen space. Convective and latent heat from cooking and combustion products are exhausted and do not enter the kitchen space. Gordon et al. (1994) and Smith et al. (1995) substantiated these findings. Chapter 34 of the 2023 ASHRAE Handbook—HVAC Applications has more information on kitchen ventilation. Marn (1962) also concluded that appliance surfaces contributed most of the heat to commercial kitchens and that when appliances were installed under an effective hood, the cooling load was independent of the fuel or energy used for similar unhooded equipment performing the same operations.

Radiant heat gain from hooded cooking equipment can range from 15 to 45% of the actual appliance energy consumption (Gordon et al. 1994; Smith et al. 1995; Swierczyna et al. 2008; Talbert et al. 1973). This ratio of heat gain to appliance energy consumption may be expressed as a radiation factor, FR, and it is a function of both appliance type and fuel source. The radiation factor is applied to the average rate of appliance energy consumption, determined by applying usage factor FU to the nameplate or rated energy input:

(5)

or

(6)

Table 5 Lighting Power Densities Using Space-by-Space Method

Common Space Types*

LPD, W/m2

   

Common Space Typesa

LPD, W/m2

   

Building-Specific Space Types*

LPD, W/m2

Atrium

   

  Daylight transition zone

11.4

   

  Operating room

24.9

  <6.1 m in height

3.5

   

  All other parking and drive areas

1.2

   

  Patient room

8.4

  ≥6.1 and ≤12.2 m in height

4.4

   

Pharmacy Area

17.9

   

  Physical therapy room

8.8

  >12.2 m in height

5.5

   

Restroom

8.0

   

  Recovery room

12.7

Audience Seating Area

   

Sales Areab

9.1

   

  Telemedicine

15.4

  Auditorium

6.1

   

Seating Area, General

2.2

   

Library

 

  Gymnasium

2.5

   

Security Screening

     

  Reading area

9.3

  Motion picture theater

2.9

   

  Airport/bus/ship/train/transportation screening

10.0

   

  Stacks

12.7

  Performing arts theater

11.8

   

  Airport/bus/ship/train/transportation screening queue

6.0

   

Manufacturing Facility

 

  Sports arena

2.9

   

  General security screening

6.9

   

  Detailed manufacturing area

8.1

  All other audience seating areas

2.5

   

Stairway

     

  Extra-high-bay area (>15.2 m floor-to-ceiling height)

14.6

Banking Activity Area

6.0

   

  Space containing stairway determines LPD and control requirements for stairway.

   

Classroom/Lecture Hall/Training Room

       

  High-bay area (7.6 to 15.2 m floor-to-ceiling height)

13.3

  Shop classroom

12.6

   

Stairwell

5.0

   

  Low bay area (<7.6 m floor-to-ceiling height)

9.2

  All other classrooms/lecture halls/training rooms

7.7

   

Storage Room

     
     

  <4.6 m2

5.2

   

Museum

 

Computer Room

8.0

   

  ≥4.6 m2

3.8

   

  General exhibition area

3.3

Conference/Meeting/Multipurpose Room

9.5

   

Vehicular Maintenance Area

6.4

   

  Restoration room

13.4

   

Workshop (including classrooms)

12.6

   

Performing Arts Theater, Dressing Room

4.2

Control/Editing Booth or Room

7.9

   

Building-Specific Space Types*

LPD, W/m2

   

Copy/Print Room

6.0

       

Post Office, Sorting Area

7.6

Corridorb

0.48

   

Casino: Gaming Area

     

Religious Buildings

 

Courtroom

11.6

   

  Betting/sportsbook/keno/bingo area

8.8

   

  Audience seating area

7.8

Dining Area

     

  High-limit game area

18.0

   

  Fellowship hall

5.4

  Bar/lounge or leisure dining

8.2

   

  Slot machine/digital gaming area

5.9

   

  Worship/pulpit/choir area

8.1

  Cafeteria or fast food dining

3.9

   

  Table games area

11.7

   

Retail Facilities

 

  Family dining

5.6

   

Convention Center, Exhibit Space

5.4

   

  Dressing/fitting room

4.9

  All other dining areas

4.5

   

Correctional Facilities

     

  Hair care

7.0

Electrical/Mechanical Roomf

7.6

   

  Audience seating area

6.1

   

  Mall concourse

6.1

Emergency Vehicle Garage

5.5

   

  Classroom/lecture hall/training room

8.0

   

  Massage

8.7

Equipment Room

7.9

   

  Confinement cells

6.5

   

  Nail care

8.1

Food Preparation Area

10.4

   

  Dining area

3.8

   

Sports Arena, Playing Aread

 

Guest Room

4.4

   

Dormitory/Living Quarters

5.2

   

  Class I facility

30.8

Laboratory

     

Facility for Visually Impairedc

     

  Class II facility

21.3

  In or as classroom

11.3

   

  Chapel (primarily used by residents)

7.1

   

  Class III facility

13.8

  All other laboratories

13.0

   

  Corridor (primarily used by residents)

6.5

   

  Class IV facility

9.2

Laundry/Washing Area

5.5

   

  Dining (primarily used by residents)

13.1

   

Natatoriumd

 

Loading Dock, Interior

9.4

   

  Lobby

15.5

   

  Class I facility

23.7

Lobby

     

  Recreation room/common living room (primarily used by residents)

12.9

   

  Class II facility

15.8

  Elevator

6.3

   

  Restroom (primarily used by residents)

10.3

   

  Class III facility

10.7

  Hotel

5.2

   

Fire Station, Sleeping Quarters

2.4

   

  Class IV facility

6.4

  Motion picture theater

2.1

   

Gymnasium/Fitness Center

     

Transportation Facility

 

  Performing arts theater

13.0

   

  Exercise area

8.8

   

  Airport hangar

14.6

  All other lobbies

8.6

   

  Playing area

8.8

   

  Baggage/carousel area

3.0

Locker Room

4.6

   

Health Care Facility

     

  Concourse

5.3

Lounge/Breakroom

     

  Control room (MRI/CT/radiology/PET)

8.4

   

  Passenger loading area

7.7

  Mother’s/wellness room

7.3

 

  Exam/treatment room

14.3

 

  Ticket counter

4.3

  All other lounges/breakrooms

5.4

   

  Hospital corridor

6.5

   

Warehouse—Storage Area

 

Office

     

  Imaging room

10.1

   

  Medium to bulky, palletized items

3.6

  Office ≤13.9 m2

7.9

   

  Lounge

8.3

   

  Smaller, hand-carried itemse

7.4

  Office >13.9 and ≤27.9 m2

7.1

   

  Medical supply room

6.0

       

  Office >27.9 m2

6.0

   

  Nursery

9.4

       

Parking Area, Interior

     

  Nurses’ station

11.5

       

Source: ASHRAE Standard 90.1-2022, Table 9.5.2.1-1.

a When both a common space type and a building-specific type are listed, the building-specific space type applies.

b For accent lighting, see Section 9.5.2.2[b] in Standard 90.1-2022.

c A facility for the visually impaired is a facility that can be documented as being designed to comply with light levels in ANSI/IES RP-28 and is (or will be) licensed by local/state authorities for either senior long-term care, adult daycare, senior support, and/or people with special visual needs.

d Class of play as defined by ANSI/IES RP-6.


Table 6 Lighting Heat Gain Parameters for Typical Operating Conditions

Luminaire Category

 

Space Fraction

 

Radiative Fraction

 

Notes

Recessed fluorescent luminaire without lens

 

0.64 to 0.74

 

0.48 to 0.68

 

Use middle values in most situations

May use higher space fraction, and lower radiative fraction for luminaire with side-slot returns

May use lower values of both fractions for direct/indirect luminaire

May use higher values of both fractions for ducted returns

Recessed fluorescent luminaire with lens

 

0.40 to 0.50

 

0.61 to 0.73

 

May adjust values in the same way as for recessed fluorescent luminaire without lens

Downlight compact fluorescent luminaire

 

0.12 to 0.24

 

0.95 to 1.0

 

Use middle or high values if detailed features are unknown

Use low value for space fraction and high value for radiative fraction if there are large holes in luminaire’s reflector

Downlight incandescent luminaire

 

0.70 to 0.80

 

0.95 to 1.0

 

Use middle values if lamp type is unknown

Use low value for space fraction if standard lamp (i.e. A-lamp) is used

Use high value for space fraction if reflector lamp (i.e. BR-lamp) is used

Non-in-ceiling fluorescent luminaire

 

1.0

 

0.5 to 0.57

 

Use lower value for radiative fraction for surface-mounted luminaire

Use higher value for radiative fraction for pendant luminaire

Recessed LED troffer partial aperture diffuser

 

0.49 to 0.64

 

0.37 to 0.47

 

Use middle value in most cases

May use higher space fraction for ducted return configuration and lower space fraction for high supply air temperature

May use higher radiant value for ducted return configuration and lower value for large supply airflow rate

Recessed LED troffer uniform diffuser

 

0.44 to 0.66

 

0.32 to 0.41

 

Use middle value in most cases.

May use higher space fraction for smaller supply airflow rate and lower value for larger supply airflow rate.

May use higher radiant value for ducted return configuration and lower value for larger supply airflow rate.

Recessed high-efficacy LED troffer

 

0.59

 

0.51

   

Recessed LED downlight

 

0.40 to 0.56

 

0.15 to 0.18

 

Use middle value in most cases.

May use higher space fraction value for high supply air temperature and lower value for smaller air flowrate.

May use higher radiant value for dimming control and lower value for large supply air flowrate.

Recessed LED retrofit kit 2×4

 

0.41 to 0.53

 

0.31 to 0.42

 

Use middle value in most cases.

May use higher space fraction value for large supply air flowrate and lower value for ducted return configuration.

May use higher radiant value for ducted return configuration and lower value for larger supply airflow rate.

Recessed LED color tuning fixture

 

0.53 to 0.56

 

0.40 to 0.42

 

Use middle value in most cases.

High-bay LED fixture

 

1.0

 

0.42 to 0.51

 

Use middle value in most cases.

Linear pendant LED fixture

 

1.0

 

0.55 to 0.60

 

Use middle value in most cases.

Sources: Fisher and Chantrasrisalai (2006); Zhou et al. (2016).


where FL is the ratio of sensible heat gain to the manufacturer’s rated energy input.

ASHRAE research (Swierczyna et al. 2008, 2009) showed the design value for heat gain from a hooded appliance at idle (ready-to-cook) conditions based on its energy consumption rate is, at best, a rough estimate. When appliance heat gain measurements during idle conditions were regressed against energy consumption rates for gas and electric appliances, the appliances’ emissivity, insulation, and surface cooling (e.g., through ventilation rates) scattered the data points widely, with large deviations from the average values. Because large errors could occur in the heat gain calculation for specific appliance types by using a general non-appliance-specific radiation factor, the appliance-specific radiation factors or heat gain values in Tables 8C through 8E should be applied in HVAC design rather than calculating heat gain using a non-appliance-specific radiation factor.

Gordon et al. (1994) and Smith et al. (1995) found that gas appliances may exhibit slightly higher heat gains than their electric counterparts under wall-canopy hoods operated at typical ventilation rates. This is because heat contained in combustion products exhausted from a gas appliance may increase the temperatures of the appliance and surrounding surfaces, as well as the hood above the appliance, more so than the heat produced by its electric counterpart. These higher-temperature surfaces radiate heat to the kitchen, adding moderately to the radiant gain directly associated with the appliance cooking surface.

Marn (1962) found that radiant heat temperature rise can be substantially reduced by shielding the fronts of cooking appliances. Although this approach may not always be practical in a commercial kitchen, radiant gains can also be reduced by adding side panels or partial enclosures that are integrated with the exhaust hood.

Heat Gain from Unhooded Cooking Appliances. Use the sensible radiant, sensible convective, and latent heat gains tabulated for unhooded appliances at idle (ready to cook) conditions in Table 8A, or at cooking conditions tabulated in Table 8B.

Heat Gain from Hooded Cooking Appliances. For specified or existing appliances where the actual nameplate rating is available, sensible radiant heat gain can be estimated using Equation (5) and the appliance-specific radiation and usage factors in Tables 8C, 8D, and 8E. When the appliance is not yet specified or the nameplate rating is not available, use the appliance-specific sensible radiant heat gains tabulated in Tables 8C, 8D, and 8E.

Table 7A Minimum Nominal Full-Load Efficiency for NEMA Design A, NEMA Design B, and IEC Design N Motors (excluding Fire Pump Electric Motors) at 60 Hza,b

Number of Poles ⇒

2

2

4

4

6

6

8

8

 

Motor Type

Enclosed

Open

Enclosed

Open

Enclosed

Open

Enclosed

Open

 

Motor Kilowatts

           

0.75

77.0

77.0

85.5

85.5

82.5

82.5

75.5

75.5

 

1.1

84.0

84.0

86.5

86.5

87.5

86.5

78.5

77.0

 

1.5

85.5

85.5

86.5

86.5

88.5

87.5

84.0

86.5

 

2.2

86.5

85.5

89.5

89.5

89.5

88.5

85.5

87.5

 

3.7

88.5

86.5

89.5

89.5

89.5

89.5

86.5

88.5

 

5.5

89.5

88.5

91.7

91.0

91.0

90.2

86.5

89.5

 

7.5

90.2

89.5

91.7

91.7

91.0

91.7

89.5

90.2

 

11

91.0

90.2

92.4

93.0

91.7

91.7

89.5

90.2

 

15

91.0

91.0

93.0

93.0

91.7

92.4

90.2

91.0

 

18.5

91.7

91.7

93.6

93.6

93.0

93.0

90.2

91.0

 

22

91.7

91.7

93.6

94.1

93.0

93.6

91.7

91.7

 

30

92.4

92.4

94.1

94.1

94.1

94.1

91.7

91.7

 

37

93.0

93.0

94.5

94.5

94.1

94.1

92.4

92.4

 

45

93.6

93.6

95.0

95.0

94.5

94.5

92.4

93.0

 

55

93.6

93.6

95.4

95.0

94.5

94.5

93.6

94.1

 

75

94.1

93.6

95.4

95.4

95.0

95.0

93.6

94.1

 

90

95.0

94.1

95.4

95.4

95.0

95.0

94.1

94.1

 

110

95.0

94.1

95.8

95.8

95.8

95.4

94.1

94.1

 

150

95.4

95.0

96.2

95.8

95.8

95.4

94.5

94.1

 

186

95.8

95.0

96.2

95.8

95.8

95.8

95.0

95.0

 

224

95.8

95.4

96.2

95.8

95.8

95.8

NR

NR

 

261

95.8

95.4

96.2

95.8

95.8

95.8

NR

NR

 

298

95.8

95.8

96.2

95.8

NR

NR

NR

NR

 

336

95.8

96.2

96.2

96.2

NR

NR

NR

NR

 

373

95.8

96.2

96.2

96.2

NR

NR

NR

NR

 

Source: ASHRAE Standard 90.1-2022, Table 10.8-1

NR = no requirement.

a Nominal efficiencies shall be established in accordance with 10 CFR 431.

b For purposes of determining the required minimum nominal full-load efficiency of an electric motor that has a horsepower or kilowatt rating between two horsepower or two kilowatt ratings listed in this table, each such motor shall be deemed to have a listed horsepower or kilowatt rating, determined as follows:

  1. A horsepower at or above the midpoint between the two consecutive horsepowers shall be rounded up to the higher of the two horsepowers.

  2. A horsepower below the midpoint between the two consecutive horsepowers shall be rounded down to the lower of the two horsepowers.

  3. A kilowatt rating shall be directly converted from kilowatts to horsepower using the formula 1 kilowatt = (1/0.746) horsepower. The conversion should be calculated to three significant decimal places, and the resulting horsepower shall be rounded in accordance with paragraph (1) or (2), whichever applies.

Table 7B Minimum Average Full-Load Efficiency for Polyphase Small Electric Motorsa

Full-Load Efficiency, %

Number of Poles ⇒

Open Motors

2

4

6

Synchronous Speed (RPM) ⇒

3600

1800

1200

Motor Kilowatts

0.19

65.6

69.5

67.5

0.25

69.5

73.4

71.4

0.37

73.4

78.2

75.3

0.56

76.8

81.1

81.7

0.75

77.0

83.5

82.5

1.1

84.0

86.5

83.8

1.5

85.5

86.5

N/A

2.2

85.5

86.9

N/A

Source: ASHRAE Standard 90.1-2022, Table 10.8-3.

a Average full-load efficiencies shall be established in accordance with 10 CFR 431.


Warewashing Applications. Typically, hot-water sanitizing and conveyor-type dish machines have either a dishwasher/condensing hood or direct-connected ductwork. If the ventilation is not operating properly, there are significant sensible and latent gains to the space. Chemical sanitizing and vapor reduction models are typically unhooded; consequently, the dish machines produce internal gains that must be accounted for and managed by the building HVAC system.

Sensible radiant and convective gains are affected by dishwasher insulation, and latent convective gains are affected by door seals. Heat loads may vary.

Recirculating Systems. Cooking appliances ventilated by recirculating systems or “ductless” hoods should be treated as unhooded appliances when estimating heat gain. In other words, all energy consumed by the appliance and all moisture produced by cooking is introduced to the kitchen as a sensible or latent cooling load.

Recommended Heat Gain Values. Table 8 lists recommended rates of heat gain from typical commercial cooking appliances. Data in the “hooded” columns assume installation under a properly designed exhaust hood connected to a mechanical fan exhaust system operating at an exhaust rate for complete capture and containment of the thermal and effluent plume. Improperly operating hood systems load the space with a significant convective component of the heat gain.

 Hospital and Laboratory Equipment

Hospital and laboratory equipment items are major sources of sensible and latent heat gains in conditioned spaces. Care is needed in evaluating the probability and duration of simultaneous usage when many components are concentrated in one area, such as a laboratory, an operating room, etc. Commonly, heat gain from equipment in a laboratory ranges from 50 to 220 W/m2 or, in laboratories with outdoor exposure, as much as four times the heat gain from all other sources combined.

Table 8A Recommended Rates of Radiant and Convective Heat Gain from Unhooded Electric Appliances During Idle (Ready-to-Cook) Conditions

Appliance

Energy Rate, W

 

Rate of Heat Gain, W

Usage Factor FU

Radiation Factor FR

Rated

Standby

Sensible Radiant

Sensible Convective

Latent

Total

Cabinet: hot serving (large), insulateda

1993

352

 

117

234

0

352

0.18

0.33

  hot serving (large), uninsulated

1993

1026

 

205

821

0

1026

0.51

0.20

  proofing (large)a

5099

410

 

352

0

59

410

0.08

0.86

  proofing (small-15 shelf)

4191

1143

 

0

264

879

1143

0.27

0.00

Cheesemelterb

2400

976

 

443

533

0

976

0.41

0.45

Coffee brewing urn

3810

352

 

59

88

205

352

0.08

0.17

Drawer warmers, 2-drawer (moist holding)a

1202

147

 

0

0

59

59

0.12

0.00

Egg cookerb

2380

249

 

65

184

0

249

0.10

0.26

Espresso machinea

2403

352

 

117

234

0

352

0.15

0.33

Food warmer: steam table (2-well-type)

1495

1026

 

88

176

762

1026

0.69

0.08

Freezer (small)

791

322

 

147

176

0

322

0.41

0.45

Fryer, countertop, open deep fatb

4600

431

 

202

229

0

431

0.09

0.47

Griddle, countertopb

8000

1771

 

848

923

0

1771

0.22

0.48

Hot dog rollerb

1600

1240

 

267

973

0

1240

0.77

0.22

Hot plate: single element, high speedb

1100

982

 

314

668

0

982

0.89

0.32

Hot-food case (dry holding)a

9115

733

 

264

469

0

733

0.08

0.36

Hot-food case (moist holding)a

9115

967

 

264

528

176

967

0.11

0.27

Induction hob, countertopb

5000

0

 

0

0

0

0

0.00

0.00

Microwave oven: commercialb

1700

0

 

0

0

0

0

0

0.00

Oven: countertop conveyorized bake/finishingb

5000

3932

 

718

3214

0

3932

0.79

0.18

Paninib

1800

673

 

195

478

0

673

0.37

0.29

Popcorn popperb

850

115

28

87

0

115

0.14

0.24

Rapid-cook oven (quartz-halogen)a

12 016

0

0

0

0

0

0

0.00

Rapid-cook oven (microwave/convection)b

5700

1141

96

1045

0

1141

0.20

0.08

Reach-in refrigeratora

1407

352

88

264

0

352

0.25

0.25

Refrigerated prep tablea

586

264

176

88

0

264

0.45

0.67

Rice cookerb

1550

82

14

68

0

82

0.05

0.17

Soup warmerb

800

390

0

53

337

390

0.49

0.00

Steamer (bun)b

1500

200

32

168

0

200

0.13

0.16

Steamer, countertopb

8300

344

0

248

96

344

0.04

0.00

Toaster: 4-slice pop up (large): cooking

1788

879

59

410

293

762

0.49

0.07

  contact (vertical)b

2600

759

180

579

0

759

0.29

0.24

  conveyor (large)

9613

3019

879

2139

0

3019

0.31

0.29

  small conveyorb

1745

1702

358

1344

0

1702

0.98

0.21

Tortilla grillb

2200

1034

254

780

0

1034

0.47

0.25

Waffle ironb

2700

267

60

207

0

267

0.10

0.22

Sources: Swierczyna et al. (2008, 2009), with the following exceptions as noted.

a Swierczyna et al. (2009) only.

b Additions and updates from ASHRAE research project RP-1631 (Kong and Zhang 2016; Zhang et al. 2016).


Table 8B Recommended Rates of Radiant and Convective Heat Gain from Unhooded Electric Appliances during Cooking Conditions

Appliance

Energy Rate, W

 

Rate of Heat Gain, W

Usage Factor FU

Radiation Factor FR

Rated

Cooking

Sensible Radiant

Sensible Convective

Latent

Total

Cheesemelter

2400

2714

 

443

1094

599

2136

1.13

0.16

Egg cooker

2380

1191

 

65

369

630

1065

0.50

0.05

Fryer, countertop, open deep fryer

4600

3818

 

202

492

1629

2323

0.83

0.05

Griddle, countertop

8000

3280

 

848

631

1277

2757

0.41

0.26

Hot dog roller

1600

1577

 

267

611

679

1556

0.99

0.17

Hot plate, single burner

1100

985

 

313

627

44

985

0.90

0.32

Induction hob, countertop

5000

653

 

0

318

335

653

0.13

0.00

Oven, conveyor

5000

4292

 

718

2454

193

3365

0.86

0.17

  Microwave

1700

2363

 

0

934

995

1929

1.39

0.00

  Rapid cook

5700

2310

 

96

1234

771

2102

0.41

0.04

Panini grill

1800

1374

 

195

718

150

1062

0.76

0.14

Popcorn popper

850

576

 

28

236

192

457

0.68

0.05

Rice cooker

1550

1159

 

14

95

44

153

0.75

0.01

Soup warmer

800

842

 

0

85

716

801

1.05

0.00

Steamer (bun)

1500

791

 

32

240

511

783

0.53

0.04

Steamer, countertop

8300

7731

 

0

499

6934

7433

0.93

0.00

Toaster, conveyor

1745

1705

 

358

974

373

1705

0.98

0.21

  Vertical

2600

1841

 

180

715

322

1218

0.71

0.10

Tortilla grill

2200

2194

 

254

1267

673

2194

1.00

0.12

Waffle maker

2700

1180

 

60

357

559

975

0.44

0.05

Source: ASHRAE research project RP-1631 (Zhang et al. 2015).


Table 8C Recommended Rates of Radiant Heat Gain from Hooded Electric Appliances During Idle (Ready-to-Cook) Conditions

Appliance

Energy Rate, W

 

Rate of Heat Gain, W

Usage Factor FU

Radiation Factor FR

Rated

Standby

Sensible Radiant

Broiler: underfired 900 mm

10 814

9 056

 

3165

0.84

0.35

Cheesemelter*

3 605

3 488

 

1348

0.97

0.39

Fryer, kettle

29 014

528

 

147

0.02

0.28

  Open deep-fat, 1-vat

14 008

821

 

293

0.06

0.36

  Pressure

13 511

791

 

147

0.06

0.19

Griddle, double-sided 900 mm (clamshell down)*

21 218

2 022

 

410

0.10

0.20

  (Clamshell up)*

21 218

3 370

 

1055

0.16

0.31

  Flat 900 mm

17 115

3 370

 

1319

0.20

0.39

  Small 900 mm*

8 997

1 788

 

791

0.20

0.44

Induction cooktop*

21 013

0

 

0

0.00

0.00

Induction wok*

3 488

0

 

0

0.00

0.00

Oven, combi: combi-mode*

16 411

1 612

 

234

0.10

0.15

  Combi: convection mode

16 412

1 612

 

410

0.10

0.25

Oven, convection full-size

12 103

1 964

 

440

0.16

0.22

  Convection half-size*

5 510

1 084

 

147

0.20

0.14

Pasta cooker*

22 010

2 491

 

0

0.11

0.00

Range top, top off/oven on*

4 865

1 172

 

293

0.24

0.25

  3 elements on/oven off

15 005

4 513

 

1846

0.30

0.41

  6 elements on/oven off

15 005

9 730

 

4074

0.65

0.42

  6 elements on/oven on

19 870

10 668

 

4250

0.54

0.40

Range, hot-top

15 826

15 035

 

3458

0.95

0.23

Rotisserie*

11 107

4 044

 

1319

0.36

0.33

Salamander*

7 004

6 829

 

2051

0.97

0.30

Steam kettle, large (225 L), simmer lid down*

32 414

762

 

29

0.02

0.04

  small (150 L), simmer lid down*

21 599

528

 

88

0.02

0.17

Steamer, compartment, atmospheric*

9 789

4 484

 

59

0.46

0.01

Tilting skillet/braising pan

9 642

1 553

 

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).


Table 8D Recommended Rates of Radiant Heat Gain from Hooded Gas Appliances during Idle (Ready-to-Cook) Conditions

Appliance

Standby Energy Rate, W

 

Rate of Heat Sensible Gain, W

 

Usage Factor FU

Radiation Factor FR

Broiler: batch*

27 842

20 280

 

2374

 

0.73

0.12

  Chain (conveyor)

38 685

28 340

 

3869

 

0.73

0.14

  Overfired (upright)*

29 307

25 761

 

733

 

0.88

0.03

  Underfired 900 mm

28 135

21 658

 

2638

 

0.77

0.12

Fryer: doughnut

12 895

3634

 

850

 

0.28

0.23

  Open deep-fat, 1 vat

23 446

1377

 

322

 

0.06

0.23

  Pressure

23 446

2638

 

234

 

0.11

0.09

Griddle: double sided 900 mm, clamshell down*

31 710

2345

 

528

 

0.07

0.23

  Clamshell up*

31 710

4308

 

1436

 

0.14

0.33

  Flat 900 mm

26 376

5979

 

1084

 

0.23

0.18

Oven: combi: combi-mode*

22 185

1758

 

117

 

0.08

0.07

  Convection mode

22 185

1700

 

293

 

0.08

0.17

  Convection, full-size

12 895

3488

 

293

 

0.27

0.08

  Conveyor (pizza)

49 822

20 017

 

2286

 

0.40

0.11

  Deck

30 772

6008

 

1026

 

0.20

0.17

  Rack mini-rotating*

16 500

1319

 

322

 

0.08

0.24

Pasta cooker*

23 446

6946

 

0

 

0.30

0.00

Range top: top off/oven on*

7327

2169

 

586

 

0.30

0.27

  3 burners on/oven off

35 169

17 614

 

2081

 

0.50

0.12

  6 burners on/oven off

35 169

35 403

 

3370

 

1.01

0.10

  6 burners on/oven on

42 495

36 018

 

3986

 

0.85

0.11

Range: wok*

29 014

25 614

 

1524

 

0.88

0.06

Rethermalizer*

26 376

6829

 

3370

 

0.26

0.49

Rice cooker*

10 257

147

 

88

 

0.01

0.60

Salamander*

10 257

9759

 

1553

 

0.95

0.16

Steam kettle: large (225 L) simmer lid down*

42 495

1583

 

0

 

0.04

0.00

  Small (38 L) simmer lid down*

15 240

967

 

88

 

0.06

0.09

  Medium (150 L) simmer lid down

29 307

1260

 

0

 

0.04

0.00

Steamer: compartment: atmospheric*

7620

2432

 

0

 

0.32

0.00

Tilting skillet/braising pan

30 479

3048

 

117

 

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 8E Recommended Rates of Radiant Heat Gain from Hooded Solid-Fuel Appliances during Idle (Ready-to-Cook) Conditions

Appliance

Rated

Standby Energy Rate, W

Rate of Sensible Heat Gain, W

Usage Factor FU

Radiation Factor FR

Broiler: solid fuel: charcoal

18 kg

12 309

 

1817

 

N/A

0.15

Broiler: solid fuel: wood (mesquite)

18 kg

14 536

 

2051

 

N/A

0.14

Source: Swierczyna et al. (2008).


Table 8F Recommended Rates of Sensible and Latent Heat Gain to Space from Warewashing Equipment

Equipment Type

Supply Water Flow Rate, L/s

Operating Water Temperature, C

Rate of Heat Gain to Space, Wa

Usage Factor FUc

Sensible Radiant b

Sensible Convective

Latent

Total

Pre-Rinse Equipment

             

  Pre-rinse spray valve

0.04

49

0

59

2403

2462

1

  Pre-rinse spray valve

0.08

49

0

88

3429

3517

1

  Pre-rinse spray valve

0.25

49

0

322

4044

4367

1

  3-Compartment sink, rinsing

NA

49

0

264

1436

1700

1

    Idle

NA

NA

0

205

586

791

NA

  Power wash sink, rinsing

NA

49

0

586

909

1495

1

    Idle

NA

NA

0

440

469

909

NA

  Scrapper

1.14d

49

0

352

3224

3575

1

  Scrapper with trough

4.42d

49

0

821

4074

4894

1

Unhooded Dishwashers

             

  Under-counter dishwasher, low temperature

0.05

60

0

645

1436

2081

1

  Under-counter dishwasher, high temperature

0.05

82

0

1172

1348

2520

1

  Under-counter dishwasher, high temperature with heat recovery

0.04

82

0

645

322

967

1

  Upright door type, low temperature dump and fill

0.06

49

0

938

1026

1964

1

  Upright door type, low temperature with tank

0.04

60

0

1143

3869

5012

1

  Upright door type, high temperature

0.06

82

0

2345

6272

8616

1

  Upright door type, high temperature with heat recovery

0.06

82

0

1407

3810

5217

1

  Pot and pan washer

0.15

82

0

1758

6887

8646

1

  Pot and pan washer with heat recovery

0.15

82

0

1612

5568

7180

1

  1120 mm Conveyor dishwasher, unvented

0.11

82

0

2931

17379

20310

1

  1680 mm Conveyor dishwasher, unvented

0.11

82

0

4718

13188

17907

1

Hooded or Ducted High-Temperature Dishwashers

             

  Upright door type, high temperature under a 0.9 × 0.9 m hood at 142 L/s

NA

82

0

1026

3810

4836

1

  Upright door type, high temperature under a 1.5 × 1.2 m hood at 236 L/s

NA

82

0

469

2315

2784

1

  1120 mm conveyor, high temperature under a 0.9 m hood at 472 L/s

0.11

88

0

293

5861

6154

1

Ducted Conveyor Dishwashers

             

  Ducted 1680 mm conveyor dishwasher

0.11

82

0

3107

1846

4953

1

  Ducted flight type conveyor dishwasher

0.06

88

0

3927

2608

6535

1

  Ducted flight type conveyor dishwasher with heat recovery

0.06

88

0

3605

1055

4660

1

  Ducted flight type conveyor dishwasher with blow dryer

0.06

88

0

6213

4601

10814

1

Source: Livchak and Swierczyna (2020)

a Heat gain rates for pre-rinse equipment and unhooded dishwashers are for unhooded appliances only. For these equipment items the total appliance heat gain affects the space directly. If an appliance is hooded or vented, the heat gain rates in the hooded and ducted sections of the table must be used. Hooded and ducted line items account for the heat gain captured by the hood or duct and therefore only list the portion of heat gain affecting the space.

b Average surface temperature of pre-rinse equipment does not exceed 49°C which is the maximum temperature of water flowing through these devices. Average surface temperatures of the dishwashers are less than the wash tank temperature of 75°C. The surfaces are stainless steel and produce negligible radiant heat gain.

c Values given are for continuous rinsing or washing and are peak values. Rinse and wash times usually extend 1 to 3 hours after each meal period served by the food service facility. Duration of heat gains will vary based on the operating schedule of the food service.

d For scrapper equipment the recirculation flow rate is listed.


Medical Equipment. It is more difficult to provide generalized heat gain recommendations for medical equipment than for general office equipment because medical equipment is much more varied in type and in application. Some heat gain testing has been done, but the equipment included represents only a small sample of the type of equipment that may be encountered.

Data presented for medical equipment in Table 9 are relevant for portable and bench-top equipment. Medical equipment is very specific and can vary greatly from application to application. The data are presented to provide guidance in only the most general sense. For large equipment, such as MRI, heat gain must be obtained from the manufacturer.

Laboratory Equipment. Equipment in laboratories is similar to medical equipment in that it varies significantly from space to space. Chapter 17 of the 2023 ASHRAE Handbook—HVAC Applications discusses heat gain from equipment, which may range from 50 to 270 W/m2 in highly automated laboratories. Table 10 lists some values for laboratory equipment, but, as with medical equipment, it is for general guidance only. Wilkins and Cook (1999) also examined laboratory equipment heat gains.

 Office Equipment

Computers, printers, copiers, etc., can generate very significant heat gains, sometimes greater than all other gains combined. ASHRAE research project RP-822 developed a method to measure the actual heat gain from equipment in buildings and the radiant/convective percentages (Hosni et al. 1998; Jones et al. 1998). This methodology was then incorporated into ASHRAE research project RP-1055 and applied to a wide range of equipment (Hosni et al. 1999) as a follow-up to independent research by Wilkins and McGaffin (1994) and Wilkins et al. (1991). Komor (1997) found similar results. Analysis of measured data showed that results for office equipment could be generalized, but results from laboratory and hospital equipment proved too diverse. The following general guidelines for office equipment are a result of these studies.

Table 9 Recommended Heat Gain from Typical Medical Equipment

Equipment

Nameplate, W

Peak, W

Average, W

Anesthesia system

250

177

166

Blanket warmer

500

504

221

Blood pressure meter

180

33

29

Blood warmer

360

204

114

ECG/RESP

1440

54

50

Electrosurgery

1000

147

109

Endoscope

1688

605

596

Harmonical scalpel

230

60

59

Hysteroscopic pump

180

35

34

Laser sonics

1200

256

229

Optical microscope

330

65

63

Pulse oximeter

72

21

20

Stress treadmill

N/A

198

173

Ultrasound system

1800

1063

1050

Vacuum suction

621

337

302

X-ray system

968

 

82

 

1725

534

480

 

2070

 

18

Source: Hosni et al. (1999).


Nameplate Versus Measured Energy Use. Nameplate data rarely reflect the actual power consumption of office equipment. Actual power consumption is assumed to equal total (radiant plus convective) heat gain, but its ratio to the nameplate value varies widely. ASHRAE research project RP-1055 (Hosni et al. 1999) found that, for general office equipment with nameplate power consumption of less than 1000 W, the actual ratio of total heat gain to nameplate ranged from 25 to 50%, but when all tested equipment is considered, the range is broader. Generally, if the nameplate value is the only information known and no actual heat gain data are available for similar equipment, it is conservative to use 50% of nameplate as heat gain and more nearly correct if 25% of nameplate is used. Much better results can be obtained, however, by considering heat gain to be predictable based on the type of equipment. However, if the device has a mainly resistive internal electric load (e.g., a space heater), the nameplate rating may be a good estimate of its peak energy dissipation.

Table 10 Recommended Heat Gain from Typical Laboratory Equipment

Equipment

Nameplate, W

Peak, W

Average, W

Analytical balance

7

7

7

Centrifuge

138

89

87

288

136

132

5500

1176

730

Electrochemical analyzer

50

45

44

100

85

84

Flame photometer

180

107

105

Fluorescent microscope

150

144

143

200

205

178

Function generator

58

29

29

Incubator

515

461

451

 

600

479

264

 

3125

1335

1222

Orbital shaker

100

16

16

Oscilloscope

72

38

38

345

99

97

Rotary evaporator

75

74

73

94

29

28

Spectronics

36

31

31

Spectrophotometer

575

106

104

200

122

121

N/A

127

125

Spectro fluorometer

340

405

395

Thermocycler

1840

965

641

N/A

233

198

Tissue culture

475

132

46

 

2346

1178

1146

Source: Hosni et al. (1999).


Computers. Based on tests by Hosni et al. (1999) and Wilkins and McGaffin (1994), nameplate values on computers should be ignored when performing cooling load calculations. Tables 11A, 11B, and 11C (Bach and Sarfraz 2018) present typical heat gain values for computers of varying types and models.

Monitors. Table 11D shows typical values for various sizes and types.

Flat-panel monitors have replaced CRT monitors in almost all workplaces. Power consumption, and thus heat gain, for flat-panel displays are significantly lower than for CRTs.

Table 11A Recommended Heat Gain for Typical Desktop Computers

Description

Nameplate Power,aW

Peak Heat Gain,b, d W

Manufacturer 1

3.0 GHz processor, 4 GB RAM, n = 1

NA

83

3.3 GHz processor, 8 GB RAM, n = 8

NA

50

3.5 GHz processor, 8 GB RAM, n = 2

NA

42

3.6 GHz processor, 16 GB RAM, n = 2

NA

66

3.3 GHz processor, 16 GB RAM, n = 2

NA

52

4.0 GHz processor, 16 GB RAM, n = 1

NA

83

3.3 GHz processor, 8 GB RAM, n = 1

NA

84

3.7 GHz processor, 32 GB RAM, n = 1

750

116

3.5 GHz processor, 16 GB RAM, n = 3c

NA

102

550

144

NA

93

Manufacturer 2

3.6 GHz processor, 32 GB RAM, n = 8

NA

80

3.6 GHz processor, 16 GB RAM, n = 1

NA

78

3.4 GHz processor, 32 GB RAM, n = 1

NA

72

3.4 GHz processor, 24 GB RAM, n = 1

NA

86

3.50 GHz processor, 4 GB RAM, n = 1

NA

26

3.3 GHz processor, 8 GB RAM, n = 1

NA

78

3.20 GHz processor, 8 GB RAM, n = 1

NA

61

3.20 GHz processor, 4 GB RAM, n = 1

NA

44

2.93 GHz processor, 16 GB RAM, n = 1

NA

151

2.67 GHz processor, 8 GB RAM, n = 1

NA

137

Average 15-min peak power consumption (range)

82 (26-151)

Source: Bach and Sarfraz (2018)

n = number of tested equipment of same configuration.

a Nameplate for desktop computer is present on its power supply, which is mounted inside desktop, hence not accessible for most computers, where NA = not available.

b For equipment peak heat gain value, highest 15-min interval of recorded data is listed in tables.

c For tested equipment with same configuration, increasing power supply size does not increase average power consumption.

d Approximately 90% convective heat gain and 10% radiative heat gain.


Table 11B Recommended Heat Gain for Typical Laptops and Laptop Docking Station

Equipment

Description

Nameplate Power,a W

Peak Heat Gain,b, c W

Laptop computer

Manufacturer 1, 2.6 GHz processor, 8 GB RAM, n = 1

NA

46

Manufacturer 2, 2.4 GHz processor, 4 GB RAM, n = 1

NA

59

Average 15-min peak power consumption (range)

53 (46-59)

Laptop with docking station

Manufacturer 1, 2.7 GHz processor, 8 GB RAM, n = 1

NA

38

1.6 GHz processor, 8 GB RAM, n = 2

NA

45

2.0 GHz processor, 8 GB RAM, n = 1

NA

50

2.6 GHz processor, 4 GB RAM, n = 1

NA

51

2.4 GHz processor, 8 GB RAM, n = 1

NA

40

2.6 GHz processor, 8 GB RAM, n = 1

NA

35

2.7 GHz processor, 8 GB RAM, n = 1

NA

59

3.0 GHz processor, 8 GB RAM, n = 3

NA

70

2.9 GHz processor, 32 GB RAM, n = 3

NA

58

3.0 GHz processor, 32 GB RAM, n = 1

NA

128

3.7 GHz processor, 32 GB RAM, n = 1

NA

63

3.1 GHz processor, 32 GB RAM, n = 1

NA

89

Average 15-min peak power consumption (range)

61 (26-151)

Source: Bach and Sarfraz (2018)

n = number of tested equipment of same configuration.

a Voltage and amperage information for laptop computer and laptop docking station is available on power supply nameplates; however, nameplate does not provide information on power consumption, where NA = not available.

b For equipment peak heat gain value, the highest 15-min interval of recorded data is listed in tables.

c Approximately 75% convective heat gain and 25% radiative heat gain.


Laser Printers. Hosni et al. (1999) found that power consumption, and therefore the heat gain, of laser printers depended largely on the level of throughput for which the printer was designed. Smaller printers tend to be used more intermittently, and larger printers may run continuously for longer periods.

Table 11C Recommended Heat Gain for Typical Tablet PC

Description

Nameplate Power,a W

Peak Heat Gain,b W

1.7 GHz processor, 4 GB RAM, n = 1

NA

42

2.2 GHz processor, 16 GB RAM, n = 1

NA

40

2.3 GHz processor, 8 GB RAM, n = 1

NA

30

2.5 GHz processor, 8 GB RAM, n = 1

NA

31

Average 15-min peak power consumption (range)

36 (31-42)

Source: Bach and Sarfraz (2018)

n = number of tested equipment of same configuration.

a Voltage and amperage information for tablet PC is available on power supply nameplate; however, nameplate does not provide information on power consumption, where NA = not available.

b For equipment peak heat gain value, highest 15-min interval of recorded data is listed in tables.


Table 12 presents data on typical printers. These data can be applied by taking the value for continuous operation and then applying an appropriate diversity factor. This would likely be most appropriate for larger open office areas. Another approach, which may be appropriate for a single room or small area, is to take the value that most closely matches the expected operation of the printer with no diversity.

Table 11D Recommended Heat Gain for Typical Monitors

Descriptiona

Nameplate Power, W

Peak Heat Gain,b, c W

Manufacturer 1

1397 mm LED flat screen, n = 1 (excluded from average because atypical size)

240

50

686 mm LED flat screen, n = 2

40

26

546 mm LED flat screen, n = 2

29

25

Manufacturer 2

1270 mm 3D LED flat screen, n = 1 (excluded from average because atypical size)

94

49

Manufacturer 3

864 mm LCD curved screen, n = 1 (excluded from average because atypical size and curved)

130

48

584 mm LED flat screen, n = 3

50

17

584 mm LED flat screen, n = 1

38

21

584 mm LED flat screen, n = 1

38

14

Manufacturer 4

610 mm LED flat screen, n = 1

42

25

Manufacturer 5

   

600 mm LED flat screen, n = 1

26

17

546 mm LED flat screen, n = 1

29

22

Manufacturer 6

   

546 mm LED flat screen, n = 1

28

24

Average 15-min peak power consumption (range)

21 (14-26)

Source: Bach and Sarfraz (2018)

n = number of tested equipment of same configuration.

a Screens with atypical size and shape are excluded for calculating average 15-min peak power consumption.

b For equipment peak heat gain value, highest 15-min interval of recorded data is listed in tables.

c Approximately 60% convective heat gain and 40% radiative heat gain.


Office Equipment Load Factor Comparison (Wilkins and McGaffin 1994)

Figure 4. Office Equipment Load Factor Comparison (Wilkins and McGaffin 1994)


Copiers. Bach and Sarfraz (2018) also tested photocopy machines, including desktop and office (freestanding high-volume copiers) models. Larger machines used in production environments were not addressed. Table 12 summarizes the results. Desktop copiers rarely operate continuously, but office copiers frequently operate continuously for periods of an hour or more. Large, high-volume photocopiers often include provisions for exhausting air outdoors; if so equipped, the direct-to-space or system makeup air heat gain needs to be included in the load calculation. Also, when the air is dry, humidifiers are often operated near copiers to limit static electricity; if this occurs during cooling mode, their load on HVAC systems should be considered.

Miscellaneous Office Equipment. Table 13 presents data on miscellaneous office equipment such as vending machines and other equipment tested by Bach and Sarfraz (2018).

Table 12 Recommended Heat Gain for Typical Printers

Equipment

 

Description

Max. Printing Speed, Pages per Minute

Nameplate Power, W

Peak Heat Gain,a W

Multifunction printer (copy, print, scan)

 

Large, multiuser, office type

40

1010

540 (Idle 29 W)

30

1300

303 (Idle 116 W)

28

1500

433 (Idle 28 W)

Average 15-min peak power consumption (range)

425 (303-540)

   

Multiuser, medium-office type

35

900

732 (Idle 18 W)

 

Desktop, small-office type

25

470

56 (Idle 3 W)

Monochrome printer

 

Desktop, medium-office type

55

1000

222

 

45

680

61

Average 15-min peak power consumption (range)

142 (61-222)

Color printer

 

Desktop, medium-office type

40

620

120

Laser printer

 

Desktop, small-office type

14

310

89

 

24

495

67

 

26

1090

65

Average 15-min peak power consumption (range)

74 (65-89)

Plotter

 

Manufacturer 1

 

1600

571

 

Manufacturer 2

 

270

173

Average 15-min peak power consumption (range)

372 (173-571)

Fax machine

 

Medium

 

1090

92

   

Small

 

600

46

Average 15-min peak power consumption (range)

69 (46-92)

Source: Bach and Sarfraz (2018)

a Approximately 70% convective heat gain and 30% radiative heat gain.


Diversity. The ratio of measured peak electrical load at equipment panels to the sum of the maximum electrical load of each individual item of equipment is the usage diversity. A small, one- or two-person office containing equipment listed in Tables 8 to 10 usually contributes heat gain to the space at the sum of the appropriate listed values. Progressively larger areas with many equipment items always experience some degree of usage diversity resulting from whatever percentage of such equipment is not in operation at any given time.

Wilkins and McGaffin (1994) measured diversity in 23 areas within five different buildings totaling over 25 600 m2. Diversity was found to range between 37 and 78%, with the average (normalized based on area) being 46%. Figure 4 shows the relationship between nameplate, sum of peaks, and actual electrical load with diversity accounted for, based on the average of the total area tested. Data on actual diversity can be used as a guide, but diversity varies significantly with occupancy. The proper diversity factor for an office of call center operators is different from that for an office of sales representatives who travel regularly.

ASHRAE research project RP-1093 derived diversity profiles for use in energy calculations (Abushakra et al. 2004; Claridge et al. 2004). Those profiles were derived from available measured data sets for a variety of office buildings, and indicated a range of peak weekday diversity factors for lighting ranging from 70 to 85% and for receptacles (appliance load) between 42 and 89%.

Table 13 Recommended Heat Gain for Miscellaneous Equipment

Equipment

Nameplate Power,a W

Peak Heat Gain,b W

Vending machine

Drinks, 280 to 400 items

NA

940

Snacks

NA

54

Food (e.g., for sandwiches)

NA

465

Thermal binding machine, 2 single documents up to 340 pages

350

28.5

Projector, resolution 1024 ′ 768

340

308

Paper shredder, up to 28 sheets

1415

265

Electric stapler, up to 45 sheets

NA

1.5

Speakers

220

15

Temperature-controlled electronics soldering station

95

16

Cell phone charger

NA

5

Battery charger

  40 V

NA

19

  AA

NA

5.5

Microwave oven, 25 to 34 L

1000 to 1550

713 to 822

Coffee maker

  Single cup

1400

385

  Up to 12 cups

950

780

  With grinder

1350

376

Coffee grinder, up to 12 cups

NA

73

Tea kettle, up to 6 cups

1200

1200

Dorm fridge, 88 L

NA

57

Freezer, 510 L

130

125

Fridge, 510 L

NA

387 to 430

Ice maker and dispenser, 9 kg bin capacity

NA

658

Top mounted bottled water cooler

NA

114 to 350

Cash register

25

9

Touch screen computer, 380 mm standard LCD and 2.2 GHz processor

NA

58

Self-checkout machine

NA

15

Source: Bach and Sarfraz (2018)

a For some equipment, nameplate power consumption is not available, where NA = not available.

b For equipment peak heat gain value, highest 15-min interval of recorded data is listed in tables.


Heat Gain per Unit Area. Bach and Sarfraz (2018), Wilkins and Hosni (2000, 2011) and Wilkins and McGaffin (1994) summarized research on a heat gain per unit area basis. Early diversity testing by Wilkins and McGaffin showed that the actual heat gain per unit area, or load factor, ranged from 4.7 to 11.6 W/m2, with an average (normalized based on area) of 8.7 W/m2. Spaces tested were fully occupied and highly automated, comprising 21 unique areas in five buildings, with a computer and monitor at every workstation. These data are from a time when equipment was primarily desktop computers with cathode ray tube (CRT) monitors, but the relative values for nameplate, sum of peaks, and actual are still applicable today. Table 11 presents more recent data from Bach and Sarfraz indicating a range of load factors with a subjective description of the type of space to which they would apply. This represents more current laptop equipment with LED or LCD monitors. The medium load density is likely to be appropriate for most standard office spaces. Medium/heavy or heavy load densities may be encountered but can be considered extremely conservative estimates even for densely populated and highly automated spaces. Table 12 indicates applicable diversity factors.

Table 14 Recommended Load Factors for Various Types of Offices

Type of Use

Load Factor*, W/m2

 

Description

100% laptop, docking station

  light

3.67

 

15.5 m2/workstation, all laptop docking station use, 1 printer per 10

  medium

4.91

 

11.6 m2/workstation, all laptop docking station use, 1 printer per 10

50% laptop, docking station

  light

4.75

 

15.5 m2/workstation, 50% laptop docking station/50% desktop, 1 printer per 10

  medium

6.35

 

11.6 m2/workstation, 50% laptop docking station/50% desktop, 1 printer per 10

100% desktop

  light

5.83

 

15.5 m2/workstation, all desktop use, 1 printer per 10

  medium

7.79

 

11.6 m2/workstation, all desktop use, 1 printer per 10

100% laptop, docking station

  2 screens

7.44

 

11.6 m2/workstation, all laptop docking station use, 2 screens, 1 printer per 10

100% desktop

  2 screens

9.06

 

11.6 m2/workstation, all laptop use, 2 screens, 1 printer per 10

  3 screens

10.33

 

11.6 m2/workstation, all desktop use, 3 screens, 1 printer per 10

100% desktop

  heavy, 2 screens

11.00

 

7.9 m2/workstation, all desktop use, 2 screens, 1 printer per 8

  heavy, 3 screens

12.49

 

7.9 m2/workstation, all desktop use, 3 screens, 1 printer per 8

100% laptop, docking station

  full on, 2 screens

12.23

 

7.9 m2/workstation, all laptop docking use, 2 screens, 1 printer per 8, no diversity

100% desktop

  full on, 2 screens

14.35

 

7.9 m2/workstation, all desktop use, 2 screens, 1 printer per 8, no diversity

  full on, 3 screens

16.48

 

7.9 m2/workstation, all desktop use, 3 screens, 1 printer per 8, no diversity

Source: Bach and Sarfraz (2018)

* Medium office type monochrome printer is used for load factor calculator with 15-min peak power consumption of 142 W.


Table 15 Diversity Factor for Different Equipment

Equipment

Diversity Factor, %

Diversity Factor,a %

Desktop PC

75

75

Laptop docking station

70

NA

Notebook computer

75b

75

Screen

70

60

Printer

45

NA

Source: Bach and Sarfraz (2017)

a 2013 ASHRAE Handbook—Fundamentals

b Insufficient data from RP-1742; values based on previous data from 2013 ASHRAE Handbook—Fundamentals and judgment of Bach and Sarfraz (2017).


Radiant/Convective Split. ASHRAE research project RP-1482 (Hosni and Beck 2008) examined the radiant/convective split for common office equipment; the most important differentiating feature is whether the equipment had a cooling fan. Footnotes in Tables 11 and 12 summarize those results.

3. INFILTRATION AND MOISTURE MIGRATION HEAT GAINS

Two other load components contribute to space cooling load directly without time delay from building mass: (1) infiltration, and (2) moisture migration through the building envelope.

3.1 INFILTRATION

Principles of estimating infiltration in buildings, with emphasis on the heating season, are discussed in Chapter 16. When economically feasible, somewhat more outdoor air may be introduced to a building than the total of that exhausted, to create a slight overall positive pressure in the building relative to the outdoors. Under these conditions, air usually exfiltrates, rather than infiltrates, through the building envelope and thus effectively eliminates infiltration sensible and latent heat gains. However, there is concern, especially in some climates, that water may condense within the building envelope; actively managing space air pressures to reduce this condensation problem, as well as infiltration, may be needed. When positive air pressure is assumed, most designers do not include infiltration in cooling load calculations for commercial buildings. However, including some infiltration for spaces such entry areas or loading docks may be appropriate, especially when those spaces are on the windward side of buildings. But the downward stack effect, as occurs when indoor air is denser than the outdoor, might eliminate infiltration to these entries on lower floors of tall buildings; infiltration may occur on the upper floors during cooling conditions if makeup air is not sufficient.

Infiltration also depends on wind direction and magnitude, temperature differences, construction type and quality, and occupant use of exterior doors and operable windows. As such, it is impossible to accurately predict infiltration rates. Designers usually predict overall rates of infiltration using the number of air changes per hour (ACH). A common guideline for climates and buildings typical of at least the central United States is to estimate the ACHs for winter heating conditions, and then use half that value for the cooling load calculations.

 Standard Air Volumes

Because the specific volume of air varies appreciably, calculations are more accurate when made on the basis of air mass instead of volume. However, volumetric flow rates are often required for selecting coils, fans, ducts, etc.; basing volumes on measurement at standard conditions may be used for accurate results. One standard value is 1.2 kgda/m3 (0.833 m3/kg). This density corresponds to about 16°C at saturation and 21°C dry air (at 101.325 kPa). Because air usually passes through the equipment at a density close to standard for locations below about 300 m, the accuracy desired normally requires no correction. When airflow is to be measured at a particular condition or point, such as at a coil entrance or exit, the corresponding specific volume can be read from the sea-level psychrometric chart. For higher elevations, the mass flow rates of air must be adjusted and higher-elevation psychrometric charts or algorithms must be used.

 Heat Gain Calculations Using Standard Air Values

Air-conditioning design often requires the following information:

  1. Total heat

    Total heat gain qt corresponding to the change of a given standard flow rate Qs through an enthalpy difference Δh is

    (7)

    where 60 = min/h, 1.2 = kgda/m3.

    This total heat equation can also be expressed as

    where Ct = 1.2 is the air total heat factor, in kgda/m3.

  2. Sensible heat

    Sensible heat gain qs corresponding to the change of dry-bulb temperature Δt for given airflow (standard conditions) Qs is

    (8)

    where

    1005 = specific heat of dry air, J/(kg·K)
    W = humidity ratio, kgw/kgda
    1884 = specific heat of water vapor, J/(kg·K)

    The specific heats are for a range from about –75 to 90°C. When W = 0, the value of 1.20(1005 + 1884W) = 1210; when W = 0.01, the value is 1230; when W = 0.02, the value is 1250; and when W = 0.03, the value is 1270. Because a value of W = 0.01 approximates conditions found in many air-conditioning problems, the sensible heat change (in watts) has traditionally been found as

    (9)

    This sensible heat equation can also be expressed as

    where Cs = 1230 is the air sensible heat factor, in (W·s)/(m3·K).

  3. Latent heat

    Latent heat gain ql corresponding to the change of humidity ratio ΔW (in kgw/kgda) for given airflow (standard conditions) Qs is

    (10)

    where 2500 is the approximate heat content of 50% rh vapor at 24°C less the heat content of water at 10°C. A common design condition for the space is 50% rh at 24°C, and 10°C is normal condensate temperature from cooling and dehumidifying coils.

    This latent heat equation can also be expressed as

    where Cl = 3000 is the air latent heat factor, in (W·s)/m3. When ΔW is in grw/lbm,da, Cl = 0.69 Btu/h·cfm.

  4. Elevation correction for total, sensible, and latent heat equations

    The constants 1200, 1230, and 3000 are useful in air-conditioning calculations at sea level (101.325 kPa) and for normal temperatures and moisture ratios. For other conditions, more precise values should be used. For an elevation of 1525 m (84.1 kPa), appropriate values are 998, 1023, and 2496. Equations (8) to (10) can be corrected for elevations other than sea level by multiplying them by the ratio of pressure at sea level divided by the pressure at actual altitude. This can be derived from Equation (3) in Chapter 1 as

    where Cx,0 is any sea-level C value and P/P0 = [1 – (elevation × 2.25577 × 10–5]5.2559, where elevation is in metres.

 Elevation Correction Examples

To correct the C values for El Paso, Texas, the elevation listed in the appendix of Chapter 14 is 1194 m. C values for Equations (7) to (10) can be corrected using Equation (3) in Chapter 1 as follows:

To correct the C values for Albuquerque, New Mexico, the elevation listed in the appendix of Chapter 14 is 1619 m. C values for Equations (7) to (10) can be corrected as follows:

3.2 LATENT HEAT GAIN FROM MOISTURE DIFFUSION

Diffusion of moisture through building materials is a natural phenomenon that is always present. Chapters 25 to 27 cover principles, materials, and specific methods used to control moisture. Moisture transfer through walls and roofs is often neglected in comfort air conditioning because the actual rate is quite small and the corresponding latent heat gain is insignificant. Permeability and permeance values for various building materials are given in Chapter 26. Vapor retarders should be specified and installed in the proper location to keep moisture transfer to a minimum, and to minimize condensation within the envelope. Moisture migration up through slabs-on-grade and basement floors has been found to be significant, but has historically not been addressed in cooling load calculations. Under-slab continuous moisture retarders and drainage can reduce upward moisture flow.

Some industrial applications require low moisture to be maintained in a conditioned space. In these cases, the latent heat gain accompanying moisture transfer through walls and roofs may be greater than any other latent heat gain. This gain is computed by

(11)

where

= latent heat gain from moisture transfer, W
M = permeance of wall or roof assembly, ng/(s·m2·Pa)
A = area of wall or roof surface, m2
Δpv = vapor pressure difference, Pa
hg = enthalpy at room conditions, kJ/kg
hf = enthalpy of water condensed at cooling coil, kJ/kg
hghf = 2500 kJ/kg when room temperature is 24°C and condensate off coil is 10°C

3.3 OTHER LATENT LOADS

Moisture sources within a building (e.g., shower areas, swimming pools or natatoriums, arboretums) can also contribute to latent load. Unlike sensible loads, which correlate to supply air quantities required in a space, latent loads usually only affect cooling coils sizing or refrigeration load. Because air from showers and some other moisture-generating areas is exhausted completely, those airborne latent loads do not reach the cooling coil and thus do not contribute to cooling load. However, system loads associated with ventilation air required to make up exhaust air must be recognized, and any recirculated air’s moisture must be considered when sizing the dehumidification equipment.

For natatoriums, occupant comfort and humidity control are critical. In many instances, size, location, and environmental requirements make complete exhaust systems expensive and ineffective. Where recirculating mechanical cooling systems are used, evaporation (latent) loads are significant. Chapter 6 of the 2023 ASHRAE Handbook—HVAC Applications provides guidance on natatorium load calculations.

4. FENESTRATION HEAT GAIN

For spaces with neutral or positive air pressurization, the primary weather-related variable affecting cooling load is solar radiation. The effect of solar radiation is more pronounced and immediate on exposed, nonopaque surfaces. Chapter 14 includes procedures for calculating clear-sky solar radiation intensity and incidence angles for weather conditions encountered at specific locations. That chapter also includes some useful solar equations. Calculation of solar heat gain and conductive heat transfer through various glazing materials and associated mounting frames, with or without interior and/or exterior shading devices, is discussed in Chapter 15. This chapter covers application of such data to overall heat gain evaluation, and conversion of calculated heat gain into a composite cooling load for the conditioned space.

4.1 FENESTRATION DIRECT SOLAR, DIFFUSE SOLAR, AND CONDUCTIVE HEAT GAINS

For fenestration heat gain, use the following equations:

Direct beam solar heat gain qb:

(12)

Diffuse solar heat gain qd:

(13)

Conductive heat gain qc:

(14)

Total fenestration heat gain Q:

(15)

where

A = window area, m2
Et,b, Et,d, and Et,r = beam, sky diffuse, and ground-reflected diffuse irradiance, calculated using equations in Chapter 14
SHGC(θ) = beam solar heat gain coefficient as a function of incident angle θ; may be interpolated between values in Table 10 of Chapter 15
⟨SHGC⟩D = diffuse solar heat gain coefficient (also referred to as hemispherical SHGC); from Table 10 of Chapter 15
Tin = indoor temperature, °C
Tout = outdoor temperature, °C
U = overall U-factor, including frame and mounting orientation from Table 4 of Chapter 15, W/(m2·K)
IAC(θ.Ω) = indoor solar attenuation coefficient for beam solar heat gain coefficient; = 1.0 if no indoor shading device. IAC(θ.Ω) is a function of shade type and, depending on type, may also be a function of beam solar angle of incidence θ and shade geometry
IACD = indoor solar attenuation coefficient for diffuse solar heat gain coefficient; = 1.0 if not indoor shading device. IACD is a function of shade type and, depending on type, may also be a function of shade geometry

If specific window manufacturer’s SHGC and U-factor data are available, those should be used. For fenestration equipped with indoor shading (blinds, drapes, or shades), the indoor solar attenuation coefficients IAC(θ.Ω) and IACD are listed in Tables 14A to 14G of Chapter 15.

Note that, as discussed in Chapter 15, fenestration ratings (U-factor and SHGC) are based on the entire product area, including frames. Thus, for load calculations, fenestration area is the area of the entire opening in the wall or roof.

4.2 EXTERIOR SHADING

Nonuniform exterior shading, caused by roof overhangs, side fins, or building projections, requires separate hourly calculations for the externally shaded and unshaded areas of the window in question, with the indoor shading SHGC still used to account for any internal shading devices. The areas, shaded and unshaded, depend on the location of the shadow line on a surface in the plane of the glass. Sun (1968) developed fundamental algorithms for analysis of shade patterns. McQuiston and Spitler (1992) provide graphical data to facilitate shadow line calculation.

Equations for calculating shade angles [Chapter 15, Equations (34) to (37)] can be used to determine the shape and area of a moving shadow falling across a given window from external shading elements during the course of a design day. Thus, a subprofile of heat gain for that window can be created by separating its sunlit and shaded areas for each hour.

5. HEAT BALANCE METHOD

Cooling load estimation involves calculating a surface-by-surface conductive, convective, and radiative heat balance for each room surface and a convective heat balance for the room air. These principles form the foundation for all methods described in this chapter. The heat balance (HB) method solves the problem using the most fundamental principles and the fewest simplifications. The advantages are that it contains the fewest parameters and general assumptions.

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 project RP-875, the method had never been described completely or in a form applicable to cooling load calculations. The papers resulting from RP-875 describe the heat balance procedure in detail (Liesen and Pedersen 1997; McClellan and Pedersen 1997; Pedersen et al. 1997).

The HB method is codified in the software called Hbfort that accompanies Cooling and Heating Load Calculation Principles (Pedersen et al. 1998).

ASHRAE research project RP-1117 constructed two model rooms for which cooling loads were physically measured using extensive instrumentation (Chantrasrisalai et al. 2003; Eldridge et al. 2003; Iu et al. 2003). HB calculations closely approximated measured cooling loads when provided with detailed data for the test rooms.

5.1 ASSUMPTIONS

All calculation procedures involve some kind of model; all models require simplifying assumptions and, therefore, are approximate. The most fundamental assumption inherent in the traditional heat balance solution is that air in the thermal zone can be modeled as well mixed, meaning its temperature is uniform throughout the zone. ASHRAE research project RP-664 (Fisher and Pedersen 1997) established that this assumption is valid over a wide range of conditions. This assumption remains the same for both convective air system-based cooling systems and radiant cooling systems.

The next major assumption is that the surfaces of the room (walls, windows, floor, etc.) can be treated as having

  1. Uniform surface temperatures

  2. Uniform long-wave (LW) and short-wave (SW) irradiation

  3. Diffuse radiating surfaces

  4. One-dimensional heat conduction within

The resulting formulation is called the heat balance (HB) model. Note that the assumptions, although common, set certain limits on the information that can be obtained from the model. When using heat balance to solve for the cooling load in a space with radiant cooling, not all of the assumptions 1-4 above will apply. In particular, not all surfaces will have uniform surface temperatures.

ASHRAE research project RP-1729 (Moftakhari et al. 2020) developed modifications to the current implementation of heat balance to allow for solution when radiant cooling is the primary cooling system. The principles of heat balance still apply. Radiant and convective exchanges of heat are all modeled based on the same fundamental principles. Similar considerations are required when using heat balance for load calculation with under-floor air distribution (UFAD) systems. With UFAD, the floor is maintained at a lower temperature due to the below-floor air supply, so the resulting heat exchange interactions mimic radiant systems more than convective systems. The discussion that follows is primarily focused on the use of heat balance with convective air system based cooling systems.

5.2 ELEMENTS

Within the framework of the assumptions, the HB can be viewed as four distinct processes:

  1. Outdoor-face heat balance

  2. Wall conduction process

  3. Indoor-face heat balance

  4. Air heat balance

Figure 5 shows the relationship between these processes for a single opaque surface. The top part of the figure, inside the shaded box, is repeated for each surface enclosing the zone. The process for transparent surfaces is similar, but the absorbed solar component appears in the conduction process block instead of at the outdoor face, and the absorbed component splits into inward- and outward-flowing fractions. These components participate in the surface heat balances.

 Outdoor-Face Heat Balance

The heat balance on the outdoor face of each surface is

(16)

where

qαsol = absorbed direct and diffuse solar radiation flux (q/A), W/m2
qLWR = net long-wave radiation flux exchange with air and surroundings, W/m2
qconv = convective exchange flux with outdoor air, W/m2
qko = conductive flux (q/A) into wall, W/m2

Schematic of Heat Balance Processes in Zone

Figure 5. Schematic of Heat Balance Processes in Zone


All terms are positive for net flux to the face except qko, which is traditionally taken to be positive from outdoors to inside the wall.

Each term in Equation (16) has been modeled in several ways, and in simplified methods the first three terms are combined by using the sol-air temperature.

 Wall Conduction Process

The wall conduction process has been formulated in more ways than any of the other processes. Techniques include

  • Numerical finite difference

  • Numerical finite element

  • Transform methods

  • Time series methods

This process introduces part of the time dependence inherent in load calculation. Figure 6 shows surface temperatures on the indoor and outdoor faces of the wall element, and corresponding conductive heat fluxes away from the outer face and toward the indoor face. All four quantities are functions of time. Direct formulation of the process uses temperature functions as input or known quantities, and heat fluxes as outputs or resultant quantities.

In some models, surface heat transfer coefficients are included as part of the wall element, making the temperatures in question the indoor and outdoor air temperatures. This is not a desirable formulation, because it hides the heat transfer coefficients and prohibits changing them as airflow conditions change. It also prohibits treating the internal long-wave radiation exchange appropriately.

Schematic of Wall Conduction Process

Figure 6. Schematic of Wall Conduction Process


Because heat balances on both sides of the element induce both the temperature and heat flux, the solution must deal with this simultaneous condition. Two computational methods that have been used widely are finite difference and conduction transfer function methods. Because of the computational time advantage, the conduction transfer function formulation has been selected for presentation here.

 Indoor-Face Heat Balance

The heart of the HB method is the internal heat balance involving the inner faces of the zone surfaces. This heat balance has many heat transfer components, and they are all coupled. Both long-wave (LW) and short-wave (SW) radiation are important, as well as wall conduction and convection to the air. The indoor-face heat balance for each surface can be written as follows:

(17)

where

qLWX = net long-wave radiant flux exchange between zone surfaces, W/m2
qSW = net short-wave radiation flux to surface from lights, W/m2
qLWS = long-wave radiation flux from equipment in zone, W/m2
qki = conductive flux through wall, W/m2
qsol = transmitted solar radiative flux absorbed at surface, W/m2
qconv = convective heat flux to zone air, W/m2

These terms are explained in the following paragraphs.

LW Radiation Exchange Among Zone Surfaces. The limiting cases for modeling internal LW radiation exchange are

  • Zone air is completely transparent to LW radiation

  • Zone air completely absorbs LW radiation from surfaces in the zone

Most HB models treat air as completely transparent and not participating in LW radiation exchange among surfaces in the zone. The second model is attractive because it can be formulated simply using a combined radiative and convective heat transfer coefficient from each surface to the zone air and thus decouples radiant exchange among surfaces in the zone. However, because the transparent air model allows radiant exchange and is more realistic, the second model is inferior.

Furniture in a zone increases the amount of surface area that can participate in radiative and convective heat exchanges. It also adds thermal mass to the zone. These two changes can affect the time response of the zone cooling load.

SW Radiation from Lights. The short-wavelength radiation from lights is usually assumed to be distributed over the surfaces in the zone in some manner. The HB procedure retains this approach but allows the distribution function to be changed.

LW Radiation from Internal Sources. The traditional model for this source defines a radiative/convective split for heat introduced into a zone from equipment. The radiative part is then distributed over the zone’s surfaces in some manner. This model is not completely realistic, and it departs from HB principles. In a true HB model, equipment surfaces are treated just as other LW radiant sources in the zone. However, because information about the surface temperature of equipment is rarely known, it is reasonable to keep the radiative/convective split concept even though it ignores the true nature of the radiant exchange. ASHRAE research project RP-1055 (Hosni et al. 1999) determined radiative/convective splits for many additional equipment types, as listed in footnotes for Tables 11 and 12.

Transmitted Solar Heat Gain. Chapter 15’s calculation procedure for determining transmitted solar energy through fenestration uses the solar heat gain coefficient (SHGC) directly rather than relating it to double-strength glass, as is done when using a shading coefficient (SC). The difficulty with this plan is that the SHGC includes both transmitted solar and inward-flowing fraction of the solar radiation absorbed in the window. With the HB method, this latter part should be added to the conduction component so it can be included in the indoor-face heat balance.

Transmitted solar radiation is also distributed over surfaces in the zone in a prescribed manner. It is possible to calculate the actual position of beam solar radiation, but this involves partial surface irradiation, which is inconsistent with the rest of the zone model, which assumes uniform conditions over an entire surface.

 Using SHGC to Calculate Solar Heat Gain

The total solar heat gain through fenestration consists of directly transmitted solar radiation plus the inward-flowing fraction of solar radiation that is absorbed in the glazing system. Both parts contain beam and diffuse contributions. Transmitted radiation goes directly onto surfaces in the zone and is accounted for in the surface indoor heat balance. The zone heat balance model accommodates the resulting heat fluxes without difficulty. The second part, the inward-flowing fraction of the absorbed solar radiation, interacts with other surfaces of the enclosure through long-wave radiant exchange and with zone air through convective heat transfer. As such, it depends both on geometric and radiative properties of the zone enclosure and convection characteristics inside and outside the zone. The solar heat gain coefficient (SHGC) combines the transmitted solar radiation and the inward-flowing fraction of the absorbed radiation. The SHGC is defined as

(18)

where

τ = solar transmittance of glazing
αk = solar absorptance of the kth layer of the glazing system
n = number of layers
Nk = inward-flowing fraction of absorbed radiation in the kth layer

Note that Equation (18) is written generically. It can be written for a specific incidence angle and/or radiation wavelength and integrated over the wavelength and/or angle, but the principle is the same in each case. Refer to Chapter 15 for the specific expressions.

Unfortunately, the inward-flowing fraction N interacts with the zone in many ways. This interaction can be expressed as

N = f (indoor convection coefficient, outdoor convection coefficient, glazing system overall heat transfer coefficient, zone geometry, zone radiation properties)

The only way to model these interactions correctly is to combine the window model with the zone heat balance model and solve both simultaneously. This has been done recently in some energy analysis programs, but is not generally available in load calculation procedures. In addition, the SHGC used for rating glazing systems is based on specific values of the indoor, outdoor, and overall heat transfer coefficients and does not include any zonal long-wavelength radiation considerations. So, the challenge is to devise a way to use SHGC values within the framework of heat balance calculation in the most accurate way possible, as discussed in the following paragraphs.

Table 16 Single-Layer Glazing Data Produced by WINDOW 7.8.74

Parameter

Incident Angle

Diffuse (Hemis.)

0

10

20

30

40

50

60

70

80

90

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

0.861

0.860

0.859

0.855

0.847

0.827

0.781

0.669

0.424

0

0.783

Source: LBNL (2023).


Using SHGC Data. The normal incidence SHGC used to rate and characterize glazing systems is not sufficient for determining solar heat gain for load calculations. These calculations require solar heat gain as a function of the incident solar angle to determine the hour-by-hour gain profile. Thus, it is necessary to use angular SHGC values and also diffuse SHGC values. These can be obtained from the WINDOW 7.8.74 program (LBNL 2023). This program does a detailed optical and thermal simulation of a glazing system and, when applied to a single clear layer, produces the information shown in Table 16.

Table 16 shows the parameters as a function of incident solar angle and also the diffuse values. The specific parameters shown are

Vtc = transmittance in visible spectrum
Rfvand Rbv = front and back surface visible reflectances
Tsol = solar transmittance [τ in Equations (18), (19), and (20)]
Rf and Rb = front and back surface solar reflectances
Abs1 = solar absorptance for layer 1, which is the only layer in this case [α in Equations (18), (19), and (20)]
SHGC = solar heat gain coefficient at center of glazing

The parameters used for heat gain calculations are Tsol, Abs, and SHGC. For the specific convective conditions assumed in WINDOW 7.8.74 program, the inward-flowing fraction of the absorbed solar can be obtained by rearranging Equation (18) to give

(19)

This quantity, when multiplied by the appropriate incident solar intensity, provides the amount of absorbed solar radiation that flows inward. In the heat balance formulation for zone loads, this heat flux is combined with that caused by conduction through glazing and included in the surface heat balance.

The outward-flowing fraction of absorbed solar radiation is used in the heat balance on the outdoor face of the glazing and is determined from

(20)

If there is more than one layer, the appropriate summation of absorptances must be done.

There is some potential inaccuracy in using the WINDOW 7.8.74 SHGC values because the inward-flowing fraction part was determined under specific conditions for the indoor and outdoor heat transfer coefficients. However, the program can be run with indoor and outdoor coefficients of one’s own choosing. Normally, however, this effect is not large, and only in highly absorptive glazing systems might cause significant error.

For solar heat gain calculations, then, it seems reasonable to use the generic window property data that comes from WINDOW 7.8.74. Considering Table 16, the procedure is as follows:

  1. Determine angle of incidence for the glazing.

  2. Determine corresponding SHGC.

  3. Evaluate Nkαk using Equation (18).

  4. Multiply Tsol by incident beam radiation intensity to get transmitted beam solar radiation.

  5. Multiply Nkαk by incident beam radiation intensity to get inward-flowing absorbed heat.

  6. Repeat steps 2 to 5 with diffuse parameters and diffuse radiation.

  7. Add beam and diffuse components of transmitted and inward-flowing absorbed heat.

This procedure is incorporated into the HB method so the solar gain is calculated accurately for each hour.

Table 10 in Chapter 15 contains SHGC information for many additional glazing systems. That table is similar to Table 16 but is slightly abbreviated. Again, the information needed for heat gain calculations is Tsol, SHGC, and Abs.

The same caution about the indoor and outdoor heat transfer coefficients applies to the information in Table 10 in Chapter 15. Those values were also obtained with specific indoor and outdoor heat transfer coefficients, and the inward-flowing fraction N is dependent upon those values.

Convection to Zone Air. Indoor convection coefficients presented in past editions of this chapter and used in most load calculation procedures and energy programs are based on very old, natural convection experiments and do not accurately describe heat transfer coefficients in a mechanically ventilated zone. In previous load calculation procedures, these coefficients were buried in the procedures and could not be changed. A heat balance formulation keeps them as working parameters. In this way, research results such as those from ASHRAE research project RP-664 (Fisher 1998) can be incorporated into the procedures. It also allows determining the sensitivity of the load calculation to these parameters.

 Air Heat Balance

In HB formulations aimed at determining cooling loads, the capacitance of air in the zone is neglected and the air heat balance is done as a quasisteady balance in each time period. Four factors contribute to the air heat balance:

(21)

where

qconv = convective heat transfer from surfaces, W
qCE = convective parts of internal loads, W
qIV = sensible load caused by infiltration and ventilation air, W
qsys = heat transfer to/from HVAC system, W

Convection from zone surfaces qconv is the sum of all the convective heat transfer quantities from the indoor-surface heat balance. This comes to the air through the convective heat transfer coefficient on the surfaces.

The convective parts of the internal loads qCE is the companion to qLWS, the radiant contribution from internal loads [Equation (17)]. It is added directly to the air heat balance. This also violates the tenets of the HB approach, because surfaces producing internal loads exchange heat with zone air through normal convective processes. However, once again, this level of detail is generally not included in the heat balance, so it is included directly into the air heat balance instead.

In keeping with the well-mixed model for zone air, any air that enters directly to a space through infiltration or ventilation qIV is immediately mixed with the zone’s air. The amount of infiltration or natural ventilation air is uncertain. Sometimes it is related to the indoor/outdoor temperature difference and wind speed; however it is determined, it is added directly to the air heat balance.

Conditioned air that enters the zone from the HVAC system and provides qsys is also mixed directly with the zone air. For commercial HVAC systems, ventilation air is most often provided using outdoor air as part of this mixed-in conditioned air; ventilation air is thus normally a system load rather than a direct-to-space load. An exception is where infiltration or natural ventilation is used to provide all or part of the ventilation air, as discussed in Chapter 16.

5.3 GENERAL ZONE FOR LOAD CALCULATION

The HB procedure is tailored to a single thermal zone, shown in Figure 7. The definition of a thermal zone depends on how the fixed temperature is controlled. If air circulated through an entire building or an entire floor is uniformly well stirred, the entire building or floor could be considered a thermal zone. On the other hand, if each room has a different control scheme, each room may need to be considered as a separate thermal zone. The framework needs to be flexible enough to accommodate any zone arrangement, but the heat balance aspect of the procedure also requires that a complete zone be described. This zone consists of four walls, a roof or ceiling, a floor, and a “thermal mass surface” (described in the section on Input Required). Each wall and the roof can include a window (or skylight in the case of the roof). This makes a total of 12 surfaces, any of which may have zero area if it is not present in the zone to be modeled.

The heat balance processes for this general zone are formulated for a 24 h steady-periodic condition. The variables are the indoor and outdoor temperatures of the 12 surfaces plus either the HVAC system energy required to maintain a specified air temperature or the air temperature, if system capacity is specified. This makes a total of 25 × 24 = 600 variables. Although it is possible to set up the problem for a simultaneous solution of these variables, the relatively weak coupling of the problem from one hour to the next allows a double iterative approach. One iteration is through all the surfaces in each hour, and the other is through the 24 h of a day. This procedure automatically reconciles nonlinear aspects of surface radiative exchange and other heat flux terms.

5.4 MATHEMATICAL DESCRIPTION

 Conduction Process

Because it links the outdoor and indoor heat balances, the wall conduction process regulates the cooling load’s time dependence. For the HB procedure presented here, wall conduction is formulated using conduction transfer functions (CTFs), which relate conductive heat fluxes to current and past surface temperatures and past heat fluxes. The general form for the indoor heat flux is

(22)

For outdoor heat flux, the form is

(23)

where

Xj = outdoor CTF, j = 0,1,…nz
Yj = cross CTF, j = 0,1,…nz
Zj = indoor CTF, j = 0,1,…nz
Φj = flux CTF, j = 1,2,…nq
θ = time
δ = time step
Tsi = indoor-face temperature, °C
Tso = outdoor-face temperature, °C
qki = conductive heat flux on indoor face, W/m2
qko = conductive heat flux on outdoor face, W/m2

The subscript following the comma indicates the time period for the quantity in terms of time step δ. Also, the first terms in the series have been separated from the rest to facilitate solving for the current temperature in the solution scheme.

The two summation limits nz and nq depend on wall construction and also somewhat on the scheme used for calculating the CTFs. If nq = 0, the CTFs are generally referred to as response factors, but then theoretically nz is infinite. Values for nz and nq are generally set to minimize the amount of computation. A development of CTFs can be found in Hittle and Pedersen (1981).

Schematic View of General Heat Balance Zone

Figure 7. Schematic View of General Heat Balance Zone


 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 temperatures at each of the 24 h, assigning i as the surface index and j as the hour index, or, in the case of CTFs, the sequence index. Thus, the primary variables are

In addition, qsysj = cooling load, j = 1,2,…, 24.

Equations (16) and (23) are combined and solved for Tso to produce 12 equations applicable in each time step:

(24)

where

To = outdoor air temperature
hco = outdoor convection coefficient, introduced by using qconv = hco(ToTso)

Equation (24) shows the need to separate Xi,0, because the contribution of current surface temperature to conductive flux cannot be collected with the other historical terms involving that temperature.

Equations (17) and (22) are combined and solved for Tsi to produce the next 12 equations:

(25)

where

Ta = zone air temperature
hci = convective heat transfer coefficient indoors, obtained from qconv = hci(TaTsi)

Note that in Equations (24) and (25), the opposite surface temperature at the current time appears on the right-hand side. The two equations could be solved simultaneously to eliminate those variables. Depending on the order of updating the other terms in the equations, this can have a beneficial effect on solution stability.

The remaining equation comes from the air heat balance, Equation (21). This provides the cooling load qsys at each time step:

(26)

In Equation (26), the convective heat transfer term is expanded to show the interconnection between the surface temperatures and the cooling load.

 Overall HB Iterative Solution

The iterative HB procedure consists of a series of initial calculations that proceed sequentially, followed by a double iteration loop, as shown in the following steps:

  1. Initialize areas, properties, and face temperatures for all surfaces, 24 h.

  2. Calculate incident and transmitted solar flux for all surfaces and hours.

  3. Distribute transmitted solar energy to all indoor faces, 24 h.

  4. Calculate internal load quantities for all 24 h.

  5. Distribute LW, SW, and convective energy from internal loads to all surfaces for all hours.

  6. Calculate infiltration and direct-to-space ventilation loads for all hours.

  7. Iterate the heat balance according to the following scheme:

  8. Display results.

Generally, four or six surface iterations are sufficient to provide convergence. The convergence check on the day iteration should be based on the difference between the indoor and outdoor conductive heat flux terms qk. A limit, such as requiring the difference between all indoor and outdoor flux terms to be less than 1% of either flux, works well.

5.5 INPUT REQUIRED

Previous methods for calculating cooling loads attempted to simplify the procedure by precalculating representative cases and grouping the results with various correlating parameters. This generally tended to reduce the amount of information required to apply the procedure. With heat balance, no precalculations are made, so the procedure requires a fairly complete description of the zone.

Global Information. Because the procedure incorporates a solar calculation, some global information is required, including latitude, longitude, time zone, month, day of month, directional orientation of the zone, and zone height (floor to floor). Additionally, to take full advantage of the flexibility of the method to incorporate, for example, variable outdoor heat transfer coefficients, things such as wind speed, wind direction, and terrain roughness may be specified. Normally, these variables and others default to some reasonable set of values, but the flexibility remains.

Wall Information (Each Wall). Because the walls are involved in three of the fundamental processes (external and internal heat balance and wall conduction), each wall of the zone requires a fairly large set of variables. They include

  • Facing angle with respect to solar exposure

  • Tilt (degrees from horizontal)

  • Area

  • Solar absorptivity outdoors

  • Long-wave emissivity outdoors

  • Short-wave absorptivity indoors

  • Long-wave emissivity indoors

  • Exterior boundary temperature condition (solar versus nonsolar)

  • External roughness

  • Layer-by-layer construction information

Again, some of these parameters can be defaulted, but they are changeable, and they indicate the more fundamental character of the HB method because they are related to true heat transfer processes.

Window Information (Each Window). The situation for windows is similar to that for walls, but the windows require some additional information because of their role in the solar load. Necessary parameters include

  • Area

  • Normal solar transmissivity

  • Normal SHGC

  • Normal total absorptivity

  • Long-wave emissivity outdoors

  • Long-wave emissivity indoor

  • Surface-to-surface thermal conductance

  • Reveal (for solar shading)

  • Overhang width (for solar shading)

  • Distance from overhang to window (for solar shading)

Roof and Floor Details. The roof and floor surfaces are specified similarly to walls. The main difference is that the ground outdoor boundary condition will probably be specified more often for a floor.

Thermal Mass Surface Details. An “extra” surface, called a thermal mass surface, can serve several functions. It is included in radiant heat exchange with the other surfaces in the space but is only exposed to the indoor air convective boundary condition. As an example, this surface would be used to account for movable partitions in a space. Partition construction is specified layer by layer, similar to specification for walls, and those layers store and release heat by the same conduction mechanism as walls. As a general definition, the extra thermal mass surface should be sized to represent all surfaces in the space that are exposed to the air mass, except the walls, roof, floor, and windows. In the formulation, both sides of the thermal mass participate in the exchange.

Internal Heat Gain Details. The space can be subjected to several internal heat sources: people, lights, electrical equipment, and infiltration. Infiltration energy is assumed to go immediately into the air heat balance, so it is the least complicated of the heat gains. For the others, several parameters must be specified. These include the following fractions:

  • Sensible heat gain

  • Latent heat gain

  • Short-wave radiation

  • Long-wave radiation

  • Energy that enters the air immediately as convection

  • Activity level of people

  • Lighting heat gain that goes directly to the return air

Radiant Distribution Functions. As mentioned previously, the generally accepted assumptions for the HB method include specifying the distribution of radiant energy from several sources to surfaces that enclose the space. This requires a distribution function that specifies the fraction of total radiant input absorbed by each surface. The types of radiation that require distribution functions are

  • Long-wave, from equipment and lights

  • Short-wave, from lights

  • Transmitted solar

Other Required Information. Additional flexibility is included in the model so that results of research can be incorporated easily. This includes the capability to specify such things as

  • Heat transfer coefficients/convection models

  • Solar coefficients

  • Sky models

The amount of input information required may seem extensive, but many parameters can be set to default values in most routine applications. However, all parameters listed can be changed when necessary to fit unusual circumstances or when additional information is obtained.

6. RADIANT TIME SERIES (RTS) METHOD

The radiant time series (RTS) method is a simplified method for performing design cooling load calculations that is derived from the heat balance (HB) method. It is intended as a more up-to-date alternative to other simplified (non-heat-balance) methods, such as the transfer function method (TFM), the cooling load temperature difference/cooling load factor (CLTD/CLF) method, and the total equivalent temperature difference/time averaging (TETD/TA) method.

This method was developed to offer an approach that is rigorous, yet does not require iterative calculations, and that quantifies each component’s contribution to the total cooling load. In addition, it is desirable for the user to be able to inspect and compare the coefficients for different construction and zone types in a form showing their relative effect on the result. These characteristics of the RTS method make it easier to apply engineering judgment during cooling load calculation.

The RTS method is suitable for peak design load calculations, but it should not be used for annual energy simulations because of its inherent limiting assumptions. Although simple in concept, RTS involves too many calculations for practical use as a manual method, although it can easily be implemented in a simple computerized spreadsheet, as shown in the examples. For a manual cooling load calculation method, refer to the CLTD/CLF method in Chapter 28 of the 1997 ASHRAE Handbook—Fundamentals.

6.1 ASSUMPTIONS AND PRINCIPLES

Design cooling loads are based on the assumption of steady-periodic conditions (i.e., the design day’s weather, occupancy, and heat gain conditions are identical to those for preceding days such that the loads repeat on an identical 24 h cyclical basis). Thus, the heat gain for a particular component at a particular hour is the same as 24 h prior, which is the same as 48 h prior, etc. This assumption is the basis for the RTS derivation from the HB method.

Cooling load calculations must address two time-delay effects inherent in building heat transfer processes:

  • Delay of conductive heat gain through opaque massive exterior surfaces (walls, roofs, or floors)

  • Delay of radiative heat gain conversion to cooling loads.

Exterior walls and roofs conduct heat because of temperature differences between outdoor and indoor air. In addition, solar energy on exterior surfaces is absorbed, then transferred by conduction to the building interior. Because of the mass and thermal capacity of the wall or roof construction materials, there is a substantial time delay in heat input at the exterior surface becoming heat gain at the interior surface.

As described in the section on Cooling Load Principles, most heat sources transfer energy to a room by a combination of convection and radiation. The convective part of heat gain immediately becomes cooling load. The radiative part must first be absorbed by the finishes and mass of the interior room surfaces, and becomes cooling load only when it is later transferred by convection from those surfaces to the room air. Thus, radiant heat gains become cooling loads over a delayed period of time.

Overview of Radiant Time Series Method

Figure 8. Overview of Radiant Time Series Method


6.2 OVERVIEW

Figure 8 gives an overview of the RTS method. When calculating solar radiation, transmitted solar heat gain through windows, sol-air temperature, and infiltration, RTS is exactly the same as previous simplified methods (TFM and TETD/TA). Important areas that differ from previous simplified methods include

  • Computation of conductive heat gain

  • Splitting of all heat gains into radiant and convective portions

  • Conversion of radiant heat gains into cooling loads

The RTS method accounts for both conduction time delay and radiant time delay effects by multiplying hourly heat gains by 24 h time series. The time series multiplication, in effect, distributes heat gains over time. Series coefficients, which are called radiant time factors and conduction time factors, are derived using the HB method. Radiant time factors reflect the percentage of an earlier radiant heat gain that becomes cooling load during the current hour. Likewise, conduction time factors reflect the percentage of an earlier heat gain at the exterior of a wall or roof that becomes heat gain indoors during the current hour. By definition, each radiant or conduction time series must total 100%.

These series can be used to easily compare the time-delay effect of one construction versus another. This ability to compare choices is of particular benefit during design, when all construction details may not have been decided. Comparison can show the magnitude of difference between the choices, allowing the engineer to apply judgment and make more informed assumptions in estimating the load.

Figure 9 shows conduction time series (CTS) values for three walls with similar U-factors but with light to heavy construction. Figure 10 shows CTS for three walls with similar construction but with different amounts of insulation, thus with significantly different U-factors. Figure 11 shows RTS values for zones varying from light to heavy construction.

CTS for Light to Heavy Walls

Figure 9. CTS for Light to Heavy Walls


CTS for Walls with Similar Mass and Increasing Insulation

Figure 10. CTS for Walls with Similar Mass and Increasing Insulation


Note that the RTS and CTS factors presented in this section were derived using heat balance method solutions with an air-based system assumed. Specific values have not been developed that would take into account radiant cooling systems. In the case of the CTS factors, conduction through an exterior opaque wall is not expected to be meaningfully different whether a radiant or convective cooling system is used. In reality, the radiant cooling system alters inside surface temperature of the exterior wall, so there will be differences in the resulting heat exchange mechanics. However, based on modeling and testing completed as part of ASHRAE RP-1729 (Moftakhari et al. 2020), the impact on the timing and magnitude of conduction heat gains is small (5 to 10%) in relation to the overall space load.

RTS factors are used to model the conversion of stored radiant heat gains to cooling loads. There is a difference in the conversion of these heat gains for radiant systems compared to convective or air-based systems. RP-1729 found that the radiant time series method could be used with radiant cooling systems but only if RTS factors for radiantly cooled spaces were derived. To date, RTS factors based on radiant cooling systems have not been developed beyond the pilot examples developed for RP-1729.

6.3 RTS PROCEDURE

The general procedure for calculating cooling load for each load component (lights, people, walls, roofs, windows, appliances, etc.) with RTS is as follows:

  1. Calculate 24 h profile of component heat gains for design day (for conduction, first account for conduction time delay by applying conduction time series).

  2. Split heat gains into radiant and convective parts (see Table 17 for radiant and convective fractions).

  3. Apply appropriate radiant time series to radiant part of heat gains to account for time delay in conversion to cooling load.

  4. Sum convective part of heat gain and delayed radiant part of heat gain to determine cooling load for each hour for each cooling load component.

After calculating cooling loads for each component for each hour, sum those to determine the total cooling load for each hour and select the hour with the peak load for design of the air-conditioning system. Repeat this process for multiple design months to determine the month when the peak load occurs, especially with windows on southern exposures (northern exposure in southern latitudes), which can result in higher peak room cooling loads in winter months than in summer.

RTS for Light to Heavy Construction

Figure 11. RTS for Light to Heavy Construction


6.4 HEAT GAIN THROUGH EXTERIOR SURFACES

Heat gain through exterior opaque surfaces is derived from the same elements of solar radiation and thermal gradient as that for fenestration areas. It differs primarily as a function of the mass and nature of the wall or roof construction, because those elements affect the rate of conductive heat transfer through the composite assembly to the interior surface.

 Sol-Air Temperature

Sol-air temperature is the outdoor air temperature that, in the absence of all radiation changes gives the same rate of heat entry into the surface as would the combination of incident solar radiation, radiant energy exchange with the sky and other outdoor surroundings, and convective heat exchange 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

(27)

where

α = absorptance of surface for solar radiation
Et = total solar radiation incident on surface, W/m2
ho = coefficient of heat transfer by long-wave radiation and convection at outer surface, W/(m2·K)
to = outdoor air temperature, °C
ts = surface temperature, °C
ε = hemispherical emittance of surface
ΔR = difference between long-wave radiation incident on surface from sky and surroundings and radiation emitted by blackbody at outdoor air temperature, W/m2

Assuming the rate of heat transfer can be expressed in terms of the sol-air temperature te,

(28)

and from Equations (27) and (28),

(29)

For horizontal surfaces that receive long-wave radiation from the sky only, an appropriate value of ΔR is about 63 W/m2, so that if ε = 1 and ho = 17 W/(m2·K), the long-wave correction term is about 4 K (Bliss 1961).

Because vertical surfaces receive long-wave radiation from the ground and surrounding buildings as well as from the sky, accurate ΔR values are difficult to determine. When solar radiation intensity is high, surfaces of terrestrial objects usually have a higher temperature than the outdoor air; thus, their long-wave radiation compensates to some extent for the sky’s low emittance. Therefore, it is common practice to assume εΔR = 0 for vertical surfaces.

Tabulated Temperature Values. The sol-air temperatures in Example Cooling and Heating Load Calculations section have been calculated based on εΔR/ho values of 4 K for horizontal surfaces and 0 K for vertical surfaces; total solar intensity values used for the calculations were calculated using equations in Chapter 14.

Surface Colors. Sol-air temperature values are given in the Example Cooling and Heating Load Calculations section for two values of the parameter α/ho; the value of 0.026 is appropriate for a light-colored surface, whereas 0.052 represents the usual maximum value for this parameter (i.e., for a dark-colored surface or any surface for which the permanent lightness cannot reliably be anticipated). Solar absorptance values of various surfaces are included in Table 18.

Table 17 Recommended Radiative/Convective Splits for Internal Heat Gains

Heat Gain Type

Recommended Radiative Fraction

Recommended Convective Fraction

Comments

Occupants, typical office conditions

0.60

0.40

See Table 4 for other conditions.

Equipment

0.1 to 0.8

0.9 to 0.2

See Tables 9 to 15 for details of equipment heat gain and recommended radiative/convective splits for motors, cooking appliances, laboratory equipment, medical equipment, office equipment, etc.

Office, with fan

0.10

0.90

    Without fan

0.30

0.70

Lighting

   

Varies; see Table 6.

Conduction heat gain

     

  Through walls and floors

0.46

0.54

 

  Through roof

0.60

0.40

 

  Through windows

0.33 (SHGC > 0.5) 0.46 (SHGC < 0.5)

0.67 (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 14A to 14G in Chapter 15.

Infiltration

0.00

1.00

 

Source: Spitler and Nigusse (2010).


Table 18 Solar Absorptance Values of Various Surfaces

Surface

Absorptance

Brick, red (Purdue)a

0.63

Paint

  Redb

0.63

  Black, matteb

0.94

  Sandstoneb

0.50

  White acrylica

0.26

Sheet metal, galvanized

  Newa

0.65

  Weathereda

0.80

Shingles

  Grayb

0.82

  Brownb

0.91

  Blackb

0.97

  Whiteb

0.75

Concretea,c

0.60 to 0.83

a Incropera and DeWitt (1990).

b Parker et al. (2000).

c Miller (1971).


This procedure was used to calculate the sol-air temperatures included in the Examples section. Because of the tedious solar angle and intensity calculations, using a simple computer spreadsheet or other software for these calculations can reduce the effort involved.

 Calculating Conductive Heat Gain Using Conduction Time Series

In the RTS method, conduction through exterior walls and roofs is calculated using CTS values. Wall and roof conductive heat input at the exterior is defined by the familiar conduction equation as

(30)

where

qi,θ–n = conductive heat input for surface n hours ago, W
U = overall heat transfer coefficient for surface, W/(m2·K)
A = surface area, m2
te,θ−n = sol-air temperature n hours ago, °C
trc = presumed constant room air temperature, °C

Conductive heat gain through walls or roofs can be calculated using conductive heat inputs for the current hours and past 23 h and conduction time series:

(31)

where

qθ = hourly conductive heat gain for surface, W
qi,θ = heat input for current hour
qi,θ−n = heat input n hours ago
c0, c1, etc. = conduction time factors

Conduction time factors for representative wall and roof types are included in Tables 19 and 20. Those values were derived by first calculating conduction transfer functions for each example wall and roof construction. Assuming steady-periodic heat input conditions for design load calculations allows conduction transfer functions to be reformulated into periodic response factors, as demonstrated by Spitler and Fisher (1999a). The periodic response factors were further simplified by dividing the 24 periodic response factors by the respective overall wall or roof U-factor to form the conduction time series. The conduction time factors can then be used in Equation (31) and provide a way to compare time delay characteristics between different wall and roof constructions. Construction material data used in the calculations for walls and roofs in Tables 19 and 20 are listed in Table 21.

Heat gains calculated for walls or roofs using periodic response factors (and thus CTS) are identical to those calculated using conduction transfer functions for the steady periodic conditions assumed in design cooling load calculations. The methodology for calculating periodic response factors from conduction transfer functions was originally developed as part of ASHRAE research project RP-875 (Spitler and Fisher 1999b; Spitler et al. 1997). For walls and roofs that are not reasonably close to the representative constructions in Tables 19 and 20, CTS coefficients may be computed with a computer program such as that described by Iu and Fisher (2004). For walls and roofs with thermal bridges, the procedure described by Karambakkam et al. (2005) may be used to determine an equivalent wall construction, which can then be used as the basis for finding the CTS coefficients. When considering the level of detail needed to make an adequate approximation, remember that, for buildings with windows and internal heat gains, the conduction heat gains make up a relatively small part of the cooling load. For heating load calculations, the conduction heat loss may be more significant.

The tedious calculations involved make a simple computer spreadsheet or other computer software a useful labor saver.

6.5 HEAT GAIN THROUGH INTERIOR SURFACES

Whenever a conditioned space is adjacent to a space with a different temperature, heat transfer through the separating physical section must be considered. The heat transfer rate is given by

(32)

where

q = heat transfer rate, W
U = coefficient of overall heat transfer between adjacent and conditioned space, W/(m2·K)
A = area of separating section concerned, m2
tb = average air temperature in adjacent space, °C
ti = air temperature in conditioned space, °C

U-values can be obtained from Chapter 27. Temperature tb may differ greatly from ti. The temperature in a kitchen or boiler room, for example, may be as much as 8 to 28 K above the outdoor air temperature. Actual temperatures in adjoining spaces should be measured, when possible. Where nothing is known except that the adjacent space is of conventional construction, contains no heat sources, and itself receives no significant solar heat gain, tbti may be considered the difference between the outdoor air and conditioned space design dry-bulb temperatures minus 3 K. In some cases, air temperature in the adjacent space corresponds to the outdoor air temperature or higher.

 Floors

For floors directly in contact with the ground or over an underground basement that is neither ventilated nor conditioned, sensible heat transfer may be neglected for cooling load estimates because usually there is a heat loss rather than a gain. An exception is in hot climates (i.e., where average outdoor air temperature exceeds indoor design condition), where the positive soil-to-indoor temperature difference causes sensible heat gains (Rock 2005). In many climates and for various temperatures and local soil conditions, moisture transport up through slabs-on-grade and basement floors is also significant, and contributes to the latent heat portion of the cooling load.

6.6 CALCULATING COOLING LOAD

The instantaneous cooling load is the rate at which heat energy is convected to the zone air at a given point in time. Computation of cooling load is complicated by the radiant exchange between surfaces, furniture, partitions, and other mass in the zone. Most heat gain sources transfer energy by both convection and radiation. Radiative heat transfer introduces a time dependency to the process that is not easily quantified. Radiation is absorbed by thermal masses in the zone and then later transferred by convection into the space. This process creates a time lag and dampening effect. The convective portion, on the other hand, is assumed to immediately become cooling load in the hour in which that heat gain occurs.

Heat balance procedures calculate the radiant exchange between surfaces based on their surface temperatures and emissivities, but they typically rely on estimated “radiative/convective splits” to determine the contribution of internal loads, including people, lighting, appliances, and equipment, to the radiant exchange. RTS further simplifies the HB procedure by also relying on an estimated radiative/convective split of wall and roof conductive heat gain instead of simultaneously solving for the instantaneous convective and radiative heat transfer from each surface, as in the HB procedure.

Thus, the cooling load for each load component (lights, people, walls, roofs, windows, appliances, etc.) for a particular hour is the sum of the convective portion of the heat gain for that hour plus the time-delayed portion of radiant heat gains for that hour and the previous 23 h. Table 17 contains recommendations for splitting each of the heat gain components into convective and radiant portions.

RTS converts the radiant portion of hourly heat gains to hourly cooling loads using radiant time factors, the coefficients of the radiant time series. Radiant time factors are used to calculate the cooling load for the current hour on the basis of current and past heat gains. The radiant time series for a particular zone gives the time-dependent response of the zone to a single pulse of radiant energy. The series shows the portion of the radiant pulse that is convected to zone air for each hour. Thus, r0 represents the fraction of the radiant pulse convected to the zone air in the current hour r1 in the previous hour, and so on. The radiant time series thus generated is used to convert the radiant portion of hourly heat gains to hourly cooling loads according to the following equation:

Table 19 Wall Conduction Time Series (CTS)

 

Curtainwalls

Studwalls

Spandrel Glass, R-1.8 Insulation Board, Gyp. Board

Spandrel Glass, R-3.5 Insulation Board, Gyp. Board

Metal Wall Panel, R-1.8 Insulation Board, Gyp. Board

Metal Wall Panel, R-3.5 Insulation Board, Gyp. Board

25 mm Stone, R-1.8 Insulation Board, Gyp. Board

25 mm Stone, R-3.5 Insulation Board, Gyp. Board

Metal Wall Panel, Sheathing, R-.9 Batt Insulation, Gyp. Board

Metal Wall Panel, Sheathing, R-3.9 Batt Insulation, Gyp. Board

25 mm Stone, Sheathing, R-1.9 Batt Insulation, Gyp. Board

25 mm Stone, Sheathing, R-3.9 Batt Insulation, Gyp. Board

Wall Number

1

2

3

4

5

6

7

8

9

10

U, W/(m2·K)

0.428

0.244

0.429

0.244

0.427

0.244

0.419

0.231

0.417

0.231

Total R

2.34

4.10

2.33

4.09

2.34

4.10

2.39

4.33

2.40

4.34

Hour

Conduction Time Factors, %

Conduction Time Factors, %

0

22.4

3.7

30.8

5.8

10.4

1.5

35.0

22.6

13.1

7.6

1

61.0

38.1

58.0

43.2

49.0

23.7

56.7

62.1

49.9

45.7

2

14.7

36.5

9.9

33.1

28.9

36.5

7.6

13.7

25.9

31.4

3

1.7

14.6

1.1

12.2

8.8

22.4

0.6

1.4

8.0

10.8

4

0.2

4.8

0.1

3.9

2.3

9.9

0.0

0.1

2.2

3.2

5

0.0

1.5

0.0

1.2

0.6

3.8

0.0

0.0

0.6

0.9

6

0.0

0.5

0.0

0.4

0.1

1.4

0.0

0.0

0.2

0.3

7

0.0

0.2

0.0

0.1

0.0

0.5

0.0

0.0

0.0

0.1

8

0.0

0.0

0.0

0.0

0.0

0.2

0.0

0.0

0.0

0.0

9

0.0

0.0

0.0

0.0

0.0

0.1

0.0

0.0

0.0

0.0

10

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

11

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

12

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

13

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

14

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

15

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

16

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

17

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

18

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

19

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

20

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

21

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

22

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

23

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Total Percentage

100

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

F01

F09

F09

F08

F08

F10

F10

F08

F08

F10

F10

F04

F04

F04

F04

F04

F04

G03

G03

G03

G03

I02

I02

I02

I02

I02

I02

I04

I04

I04

I04

F04

I02

F04

I02

F04

I02

G01

I04

G01

I04

G01

F04

G01

F04

I02

F04

F02

G01

F02

G01

F02

G01

F02

G01

F02

G01

0

F02

0

F02

0

F02

0

F02

0

F02

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

 

Studwalls

EIFS

Wood Siding, Sheathing, R-1.9 Batt Insulation, 12.5 mm Wood

Wood Siding, Sheathing, R-3.9 Batt Insulation, 12.5 mm Wood

25 mm Stucco, Sheathing, R-1.9 Batt Insulation, Gyp. Board

25 mm Stucco, Sheathing, R-3.9 Batt Insulation, Gyp. Board

EIFS, R-0.9 Insulation Board, Sheathing, Gyp. Board

EIFS, R-1.8 Insulation Board, Sheathing, Gyp. Board

EIFS, R-0.9 Insulation Board, Sheathing, R-1.9 Batt Insulation, Gyp. Board

EIFS, R-0.9 Insulation Board, Sheathing, R-3.9 Batt Insulation, Gyp. Board

EIFS, R0.9 Insulation Board, Sheathing, 200 mm LW CMU, Gyp. Board

EIFS, R-1.8 Insulation Board, Sheathing, 200 mm LW CMU, Gyp. Board

Wall Number

11

12

13

14

15

16

17

18

19

20

U, W/(m2·K)

0.401

0.226

0.412

0.229

0.667

0.420

0.305

0.192

0.514

0.354

Total R

2.49

4.43

2.42

4.36

1.50

2.38

3.28

5.22

1.95

2.83

Hour

Conduction Time Factors, %

Conduction Time Factors, %

0

7.2

3.9

11.7

6.6

15.4

7.4

5.3

2.5

1.0

1.4

1

39.0

33.0

50.0

45.1

53.1

45.1

33.6

25.4

2.0

1.8

2

29.5

32.3

27.0

32.6

22.9

30.4

29.7

29.9

5.7

4.4

3

13.7

16.6

8.2

11.2

6.3

11.1

15.8

18.6

8.5

7.1

4

6.0

7.7

2.3

3.3

1.7

3.9

7.9

10.5

9.1

8.1

5

2.6

3.5

0.6

0.9

0.5

1.3

3.9

5.8

8.7

8.1

6

1.1

1.6

0.2

0.3

0.1

0.5

1.9

3.2

8.0

7.6

7

0.5

0.7

0.0

0.1

0.0

0.2

0.9

1.8

7.2

7.0

8

0.2

0.3

0.0

0.0

0.0

0.1

0.5

1.0

6.4

6.4

9

0.1

0.2

0.0

0.0

0.0

0.0

0.2

0.5

5.7

5.8

10

0.0

0.1

0.0

0.0

0.0

0.0

0.1

0.3

5.1

5.3

11

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.2

4.6

4.8

12

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.1

4.1

4.3

13

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.1

3.6

3.9

14

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

3.2

3.6

15

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

2.9

3.2

16

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

2.6

2.9

17

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

2.3

2.7

18

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

2.0

2.4

19

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.8

2.2

20

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.6

2.0

21

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.4

1.8

22

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.3

1.6

23

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.1

1.5

Total Percentage

100

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

F01

F11

F11

F07

F07

F06

F06

F06

F06

F06

F06

G02

G02

G03

G03

I01

I01

I01

I01

I01

I01

I04

I04

I04

I04

G03

I01

G03

G03

G03

I01

G01

I04

G01

I04

F04

G03

I04

I04

M03

G03

F02

G01

F02

G01

G01

F04

G01

I04

F04

M03

0

F02

0

F02

F02

G01

F02

G01

G01

F04

0

0

0

0

0

F02

0

F02

F02

G01

0

0

0

0

0

0

0

0

0

F02

0

0

0

0

0

0

0

0

0

0

 

Brick Walls

Brick, R-0.9 Insulation Board, Sheathing, Gyp. Board

Brick, R-1.8 Insulation Board, Sheathing, Gyp. Board

Brick, Sheathing, R-1.9 Batt Insulation, Gyp. Board

Brick, Sheathing, R-3.9 Batt Insulation, Gyp. Board

Brick, R-0.9 Insulation Board, Sheathing, R-1.9 Batt Insulation, Gyp. Board

Brick, R-0.9 Insulation Board, Sheathing, R-3.9 Batt Insulation, Gyp. Board

Brick, R-0.9 Insulation Board, 200 mm LW CMU

Brick, R-1.8 Insulation Board, 200 mm LW CMU

Brick, 200 mm LW CMU, R-1.9 Batt Insulation, Gyp. Board

Wall Number

21

22

23

24

25

26

27

28

29

U, W/(m2·K)

0.571

0.380

0.376

0.218

0.283

0.157

0.568

0.378

0.343

Total R

1.75

2.63

2.66

4.59

3.54

6.36

1.76

2.64

2.92

Hour

Conduction Time Factors, %

0

0.3

0.1

0.3

0.2

0.2

0.3

0.7

0.9

1.6

1

5.9

3.5

6.6

4.5

2.4

0.8

0.8

0.9

1.6

2

15.3

12.2

16.2

14.2

8.9

3.8

2.4

1.9

2.1

3

17.1

16.1

17.0

16.8

13.2

7.7

5.0

4.0

3.6

4

14.6

15.0

13.9

14.4

13.8

9.9

7.1

6.1

5.2

5

11.5

12.4

10.8

11.4

12.4

10.6

8.3

7.4

6.3

6

8.8

9.7

8.3

8.8

10.5

10.3

8.7

8.0

6.9

7

6.6

7.5

6.4

6.8

8.5

9.4

8.6

8.1

7.0

8

5.0

5.7

4.9

5.3

6.8

8.3

8.1

7.9

6.9

9

3.8

4.4

3.7

4.1

5.4

7.2

7.4

7.4

6.6

10

2.8

3.3

2.9

3.1

4.2

6.1

6.7

6.8

6.2

11

2.1

2.5

2.2

2.4

3.2

5.1

5.9

6.1

5.8

12

1.6

1.9

1.7

1.9

2.5

4.2

5.2

5.5

5.3

13

1.2

1.4

1.3

1.4

1.9

3.5

4.5

4.9

4.9

14

0.9

1.1

1.0

1.1

1.5

2.8

3.9

4.3

4.5

15

0.7

0.8

0.8

0.9

1.2

2.3

3.3

3.7

4.1

16

0.5

0.6

0.6

0.7

0.9

1.9

2.8

3.2

3.7

17

0.4

0.5

0.4

0.5

0.7

1.5

2.4

2.8

3.3

18

0.3

0.4

0.3

0.4

0.5

1.2

2.0

2.4

3.0

19

0.2

0.3

0.3

0.3

0.4

1.0

1.7

2.1

2.7

20

0.2

0.2

0.2

0.2

0.3

0.8

1.4

1.8

2.5

21

0.1

0.2

0.2

0.2

0.2

0.6

1.2

1.5

2.2

22

0.1

0.1

0.1

0.1

0.2

0.5

1.0

1.3

2.0

23

0.1

0.1

0.1

0.1

0.1

0.4

0.8

1.1

1.8

Total Percentage

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

M01

M01

M01

M01

M01

M01

M01

M01

M01

F04

F04

F04

F04

F04

F04

F04

F04

F04

I01

I01

G03

G03

I01

I01

I01

I01

M03

G03

I01

I04

I04

G03

I01

M03

I01

I04

F04

G03

G01

I04

I04

G03

F02

M03

G01

G01

F04

F02

G01

G01

I04

0

F02

F02

F02

G01

0

F02

F02

I04

0

0

0

0

F02

0

0

0

G01

0

0

0

0

0

0

0

0

F02

0

0

0

 

Brick Walls

Brick, 200 mm LW CMU, R-3.9 Batt Insulation, Gyp. Board

Brick, R-0.9 Insulation Board, 200 mm HW CMU, Gyp. Board

Brick, R-1.8 Insulation Board, 200 mm HW CMU, Gyp. Board

Brick, R-0.9 Insulation Board, Brick

Brick, R-1.8 Insulation Board, Brick

Brick, R-0.9 Insulation Board, 200 mm LW Concrete, Gyp. Board

Brick, R-1.8 Insulation Board, 200 mm LW Concrete, Gyp. Board

Brick, R-0.9 Insulation Board, 300 mm HW Concrete, Gyp. Board

Brick, R-1.8 Insulation Board, 300 mm HW Concrete, Gyp. Board

Wall Number

30

31

32

33

34

35

36

37

38

U, W/(m2·K)

0.206

0.627

0.404

0.701

0.433

0.514

0.353

0.545

0.351

Total R

4.86

1.59

2.48

1.43

2.31

1.95

2.83

1.83

2.85

Hour

Conduction Time Factors, %

0

1.9

1.7

2.0

0.9

1.0

3.2

3.4

3.8

3.9

1

1.7

1.7

1.9

1.3

1.2

3.1

3.3

3.8

3.8

2

2.1

2.4

2.3

3.3

2.7

3.0

3.2

3.7

3.8

3

3.3

3.9

3.4

5.7

4.9

3.1

3.2

3.7

3.8

4

4.7

5.2

4.7

7.3

6.6

3.4

3.4

3.8

3.8

5

5.9

6.0

5.5

8.0

7.5

3.9

3.8

3.9

3.9

6

6.5

6.5

6.1

8.2

7.8

4.3

4.1

4.1

4.0

7

6.7

6.7

6.3

7.9

7.7

4.6

4.4

4.2

4.2

8

6.7

6.6

6.3

7.5

7.4

4.9

4.7

4.3

4.3

9

6.5

6.4

6.2

6.9

6.9

5.0

4.8

4.4

4.4

10

6.1

6.1

6.0

6.3

6.4

5.1

4.9

4.5

4.5

11

5.8

5.7

5.7

5.6

5.8

5.1

5.0

4.5

4.5

12

5.4

5.3

5.4

5.0

5.2

5.1

4.9

4.6

4.5

13

5.0

4.9

5.0

4.4

4.6

5.0

4.9

4.5

4.5

14

4.6

4.5

4.7

3.8

4.1

4.8

4.8

4.5

4.5

15

4.2

4.2

4.3

3.3

3.6

4.7

4.7

4.5

4.5

16

3.9

3.8

4.0

2.9

3.2

4.5

4.6

4.3

4.3

17

3.5

3.5

3.7

2.5

2.8

4.4

4.4

4.3

4.3

18

3.2

3.2

3.4

2.2

2.4

4.2

4.3

4.2

4.2

19

3.0

2.9

3.1

1.9

2.1

4.0

4.1

4.2

4.2

20

2.7

2.6

2.8

1.6

1.8

3.9

4.0

4.1

4.1

21

2.5

2.4

2.6

1.4

1.6

3.7

3.8

4.0

4.1

22

2.2

2.1

2.4

1.2

1.4

3.5

3.7

4.0

4.0

23

2.0

1.9

2.2

1.0

1.2

3.4

3.6

3.9

3.9

Total Percentage

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

M01

M01

M01

M01

M01

M01

M01

M01

M01

F04

F04

F04

F04

F04

F04

F04

F04

F04

M03

I01

I01

I01

I01

I01

I01

I01

I01

I04

M05

I01

M01

I01

M13

I01

M16

I01

I04

G01

M05

F02

M01

F04

M13

F04

M16

G01

F02

G01

0

F02

G01

F04

G01

F04

F02

0

F02

0

0

F02

G01

F02

G01

0

0

0

0

0

0

F02

0

F02

0

0

0

0

0

0

0

0

0

 

Brick Walls

Concrete Block Walls

Brick, 200 mm HW Concrete, R-1.9 Batt Insulation, Gyp. Board

Brick, 200 mm HW Concrete, R-3.9 Batt Insulation, Gyp. Board

200 mm LW CMU, R-1.9 Batt Insulation, Gyp. Board

200 mm LW CMU, R-3.9 Batt Insulation, Gyp. Board

200 mm LW CMU w/Fill Insulation, R-1.9 Batt Insulation, Gyp. Board

200 mm LW CMU w/Fill Insulation, R-3.9 Batt Insulation, Gyp. Board

25 mm Stucco, 200 mm HW CMU, R-1.9 Batt Insulation, Gyp. Board

25 mm Stucco, 200 mm HW CMU, R-3.9 Batt Insulation, Gyp. Board

200 mm LW CMU w/Fill Insulation

Wall Number

39

40

41

42

43

44

45

46

47

U, W/(m2·K)

0.383

0.218

0.377

0.218

0.332

0.202

0.413

0.229

1.027

Total R

2.61

4.60

2.65

4.59

3.01

4.95

2.42

4.37

0.97

Hour

Conduction Time Factors, %

Conduction Time Factors, %

0

3.4

3.4

0.4

0.3

0.6

0.8

0.5

0.5

0.6

1

3.3

3.4

5.9

4.1

2.1

1.6

3.4

2.5

9.3

2

3.3

3.4

14.2

12.2

6.7

5.4

9.8

8.4

19.5

3

3.7

3.6

15.3

14.6

10.0

8.8

12.2

11.6

19.2

4

4.1

4.0

13.1

13.1

10.7

9.9

11.5

11.4

15.0

5

4.5

4.4

10.6

10.8

10.0

9.6

10.1

10.2

10.9

6

4.7

4.6

8.5

8.8

8.9

8.7

8.6

8.8

7.7

7

4.9

4.8

6.7

7.1

7.7

7.7

7.3

7.5

5.4

8

4.9

4.9

5.3

5.8

6.7

6.8

6.1

6.4

3.8

9

4.9

4.9

4.2

4.7

5.7

5.9

5.2

5.4

2.6

10

4.9

4.8

3.4

3.8

4.9

5.2

4.4

4.6

1.8

11

4.8

4.8

2.7

3.0

4.2

4.5

3.7

3.9

1.3

12

4.7

4.7

2.1

2.5

3.6

4.0

3.1

3.3

0.9

13

4.6

4.6

1.7

2.0

3.1

3.5

2.6

2.8

0.6

14

4.5

4.5

1.3

1.6

2.7

3.0

2.2

2.4

0.4

15

4.4

4.4

1.1

1.3

2.3

2.6

1.9

2.0

0.3

16

4.2

4.2

0.9

1.0

2.0

2.3

1.6

1.7

0.2

17

4.1

4.1

0.7

0.8

1.7

2.0

1.3

1.5

0.1

18

4.0

4.0

0.5

0.7

1.5

1.8

1.1

1.2

0.1

19

3.9

3.9

0.4

0.6

1.3

1.5

0.9

1.1

0.1

20

3.8

3.8

0.3

0.4

1.1

1.3

0.8

0.9

0.0

21

3.7

3.7

0.3

0.4

0.9

1.2

0.7

0.8

0.0

22

3.6

3.6

0.2

0.3

0.8

1.0

0.6

0.6

0.0

23

3.5

3.5

0.2

0.2

0.7

0.9

0.5

0.6

0.0

Total Percentage

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

M01

M01

M03

M03

M08

M08

F07

F07

M08

F04

F04

I04

I04

I04

I04

M05

M05

F02

M15

M15

G01

I04

G01

I04

I04

I04

0

I04

I04

F02

G01

F02

G01

G01

I04

0

G01

I04

0

F02

0

F02

F02

G01

0

F02

G01

0

0

0

0

0

F02

0

0

F02

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

 

Concrete Block Walls

Precast and Cast-In-Place Block Walls

200 mm LW CMU w/Fill Insulation, Gyp. Board

300 mm LW CMU w/Fill Insulation, Gyp. Board

100 mm LW Concrete. R-0.9 Board Insulation, Gyp. Board

100 mm LW Concrete. R-1.8 Board Insulation, Gyp. Board

100 mm LW Concrete. R-1.9 Batt Insulation, Gyp. Board

100 mm LW Concrete. R-3.9 Batt Insulation, Gyp. Board

100 mm LW Concrete. R-1.8 Board Insulation, 100 mm LW Concrete

100 mm LW Concrete. R-3.5 Board Insulation, 100 mm LW Concrete

EIFS, R-0.9 Insulation Board, 200 mm LW Concrete, Gyp. Board

EIFS, R-1.8 Insulation Board, 200 mm LW Concrete, Gyp. Board

Wall Number

48

49

50

51

52

53

54

55

56

57

U, W/(m2·K)

0.815

0.695

0.672

0.422

0.418

0.231

0.433

0.246

0.650

0.413

Total R

1.23

1.44

1.49

2.37

2.39

4.33

2.31

4.07

1.54

2.42

Hour

Conduction Time Factors, %

Conduction Time Factors, %

0

0.2

0.9

0.9

0.4

1.0

0.5

0.7

0.9

2.1

2.4

1

4.0

1.2

12.5

8.5

12.3

9.3

0.9

0.8

2.3

2.4

2

12.1

2.9

20.9

18.9

20.2

19.0

2.7

1.5

3.3

3.1

3

15.4

5.5

17.7

18.1

17.3

17.6

5.5

3.4

4.8

4.3

4

14.3

7.6

13.1

14.1

13.0

13.6

7.6

5.6

5.8

5.3

5

11.9

8.5

9.6

10.5

9.6

10.2

8.6

7.2

6.2

5.8

6

9.5

8.7

6.9

7.8

7.1

7.6

8.8

8.1

6.3

6.0

7

7.4

8.3

5.0

5.7

5.2

5.7

8.6

8.3

6.2

5.9

8

5.8

7.6

3.7

4.2

3.8

4.2

8.0

8.1

6.0

5.8

9

4.5

6.9

2.7

3.1

2.8

3.2

7.3

7.6

5.7

5.6

10

3.5

6.1

1.9

2.3

2.1

2.4

6.5

7.0

5.4

5.3

11

2.7

5.4

1.4

1.7

1.5

1.8

5.7

6.3

5.1

5.1

12

2.1

4.8

1.0

1.3

1.1

1.3

5.0

5.7

4.8

4.8

13

1.6

4.2

0.7

0.9

0.8

1.0

4.3

5.0

4.5

4.5

14

1.3

3.7

0.5

0.7

0.6

0.7

3.7

4.4

4.2

4.3

15

1.0

3.2

0.4

0.5

0.4

0.5

3.2

3.8

3.9

4.1

16

0.8

2.8

0.3

0.4

0.3

0.4

2.7

3.3

3.7

3.8

17

0.6

2.4

0.2

0.3

0.2

0.3

2.3

2.8

3.4

3.6

18

0.5

2.1

0.1

0.2

0.2

0.2

1.9

2.4

3.2

3.4

19

0.3

1.9

0.1

0.2

0.1

0.2

1.6

2.1

3.0

3.2

20

0.3

1.6

0.1

0.1

0.1

0.1

1.4

1.8

2.8

3.1

21

0.2

1.4

0.1

0.1

0.1

0.1

1.1

1.5

2.6

2.9

22

0.2

1.2

0.0

0.1

0.1

0.1

1.0

1.3

2.5

2.7

23

0.1

1.1

0.0

0.0

0.0

0.1

0.8

1.1

2.3

2.6

Total Percentage

100

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

F01

M08

M09

M11

M11

M11

M11

M11

M11

F06

F06

F04

F04

I01

I01

I04

I04

I02

I02

I01

I01

G01

G01

F04

I01

G01

I04

M11

I02

M13

I01

F02

F02

G01

F04

F02

G01

F02

M11

G01

M13

0

0

F02

G01

0

F02

0

F02

F02

G01

0

0

0

F02

0

0

0

0

0

F02

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

 

Precast and Cast-In-Place Block Walls

200 mm LW Concrete. R-11 Batt Insulation, Gyp. Board

200 mm LW Concrete. R-22 Batt Insulation, Gyp. Board

EIFS Finish, R-1.8 Insulation Board, 200 mm HW Concrete, Gyp. Board

EIFS Finish, R-3.5 Insulation Board, 200 mm HW Concrete, Gyp. Board

200 mm HW Concrete, R-11 Batt Insulation, Gyp. Board

200 mm HW Concrete, R-22 Batt Insulation, Gyp. Board

300 mm HW Concrete, R-3.3 Batt Insulation, Gyp. Board

300 mm HW Concrete, R-6.7 Batt Insulation, Gyp. Board

300 mm HW Concrete

Wall Number

58

59

60

61

62

63

64

65

66

U, W/(m2·K)

0.387

0.221

0.465

0.255

0.434

0.236

0.265

0.140

3.120

Total R

2.58

4.52

2.15

3.92

2.31

4.24

3.77

7.12

0.32

Hour

Conduction Time Factors, %

0

1.4

1.5

2.8

2.9

1.1

1.2

2.4

2.5

1.2

1

1.8

1.7

3.0

2.9

2.7

2.2

2.4

2.4

1.9

2

3.9

3.4

4.2

3.5

6.5

5.7

3.0

2.7

4.1

3

6.3

5.7

5.2

4.4

8.6

8.2

4.2

3.6

6.4

4

7.6

7.1

5.5

5.1

8.9

8.7

5.1

4.6

7.6

5

7.9

7.6

5.6

5.4

8.4

8.4

5.7

5.4

8.0

6

7.6

7.5

5.5

5.4

7.6

7.7

6.0

5.8

7.8

7

7.1

7.1

5.3

5.3

6.9

7.0

6.0

5.9

7.4

8

6.6

6.6

5.1

5.2

6.2

6.3

5.8

5.8

6.8

9

6.0

6.0

5.0

5.0

5.5

5.7

5.6

5.7

6.2

10

5.5

5.5

4.8

4.9

5.0

5.1

5.4

5.5

5.6

11

5.0

5.1

4.6

4.7

4.5

4.6

5.1

5.2

5.0

12

4.5

4.6

4.4

4.5

4.0

4.1

4.8

5.0

4.5

13

4.1

4.2

4.3

4.4

3.6

3.7

4.6

4.7

4.1

14

3.7

3.8

4.1

4.2

3.2

3.3

4.3

4.5

3.6

15

3.4

3.5

3.9

4.1

2.9

3.0

4.1

4.2

3.3

16

3.0

3.2

3.8

3.9

2.6

2.7

3.9

4.0

2.9

17

2.8

2.9

3.6

3.8

2.3

2.4

3.6

3.8

2.6

18

2.5

2.7

3.5

3.7

2.1

2.2

3.4

3.6

2.3

19

2.3

2.4

3.4

3.5

1.9

1.9

3.3

3.4

2.1

20

2.1

2.2

3.2

3.4

1.7

1.7

3.1

3.2

1.9

21

1.9

2.0

3.1

3.3

1.5

1.6

2.9

3.0

1.7

22

1.7

1.8

3.0

3.2

1.3

1.4

2.7

2.8

1.5

23

1.5

1.7

2.9

3.1

1.2

1.3

2.6

2.7

1.3

Total Percentage

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

M13

M13

F06

F06

M15

M15

M16

M16

M16

I04

I04

I02

I02

I04

I04

I05

I05

F02

G01

I04

M15

I02

G01

I04

G01

I05

0

F02

G01

G01

M15

F02

G01

F02

G01

0

0

F02

F02

G01

0

F02

0

F02

0

0

0

0

F02

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0


(33)

where

Qr,θ = radiant cooling load Qr for current hour θ, W
qr,θ = radiant heat gain for current hour, W
qr,θ–n = radiant heat gain n hours ago, W
r0, r1, etc. = radiant time factors

The radiant cooling load for the current hour, which is calculated using RTS and Equation (33), is added to the convective portion to determine the total cooling load for that component for that hour.

Radiant time factors are generated by a heat-balance-based procedure. A separate series of radiant time factors is theoretically required for each unique zone and for each unique radiant energy distribution function assumption. For most common design applications, RTS variation depends primarily on the overall massiveness of the construction and the thermal responsiveness of the surfaces the radiant heat gains strike.

One goal in developing RTS was to provide a simplified method based directly on the HB method; thus, it was deemed desirable to generate RTS coefficients directly from a heat balance. A heat balance computer program was developed to do this: Hbfort, which is included as part of Cooling and Heating Load Calculation Principles (Pedersen et al. 1998). The RTS procedure is described by Spitler et al. (1997). The procedure for generating RTS coefficients may be thought of as analogous to the custom weighting factor generation procedure used by DOE 2.1 (Kerrisk et al. 1981; Sowell 1988a, 1988b). In both cases, a zone model is pulsed with a heat gain. With DOE 2.1, the resulting loads are used to estimate the best values of the transfer function method weighting factors to most closely match the load profile. In the procedure described here, a unit periodic heat gain pulse is used to generate loads for a 24 h period. As long as the heat gain pulse is a unit pulse, the resulting loads are equivalent to the RTS coefficients.

Two different radiant time series are used: solar, for direct transmitted solar heat gain (radiant energy assumed to be distributed to the floor and furnishings only) and nonsolar, for all other types of heat gains (radiant energy assumed to be uniformly distributed on all internal surfaces). Nonsolar RTS apply to radiant heat gains from people, lights, appliances, walls, roofs, and floors. Also, for diffuse solar heat gain and direct solar heat gain from fenestration with indoor shading (blinds, drapes, etc.), the nonsolar RTS should be used. Radiation from those sources is assumed to be more uniformly distributed onto all room surfaces. Effect of beam solar radiation distribution assumptions is addressed by Hittle (1999).

Representative solar and nonsolar RTS data for light, medium, and heavyweight constructions are provided in Tables 22 and 23. Those were calculated using the Hbfort computer program (Pedersen et al. 1998) with zone characteristics listed in Table 24. Customized RTS values may be calculated using the HB method where the zone is not reasonably similar to these typical zones or where more precision is desired.

Table 20 Roof Conduction Time Series (CTS)

 

Sloped Frame Roofs

Metal Roof, R-3.3 Batt Insulation, Gyp. Board

Metal Roof, R-6.7 Batt Insulation, Gyp. Board

Metal Roof, R-3.3 Batt Insulation, Suspended Acoustical Ceiling

Metal Roof, R-6.7 Batt Insulation, Suspended Acoustical Ceiling

Metal Roof, R-3.3 Batt Insulation

Metal Roof, R-6.7 Batt Insulation

Asphalt Shingles, Wood Sheathing, R-3.3 Batt Insulation, Gyp. Board

Asphalt Shingles, Wood Sheathing, R-6.7 Batt Insulation, Gyp. Board

Slate or Tile, Wood Sheathing, R-3.3 Batt Insulation, Gyp. Board

Roof Number

1

2

3

4

5

6

7

8

9

U, W/(m2·K)

0.249

0.136

0.221

0.129

0.255

0.138

0.235

0.132

0.239

Total R

4.02

7.37

4.46

7.80

3.94

7.27

4.25

7.60

4.18

Hour

Conduction Time Factors, %

0

21.8

6.2

22.9

6.1

52.6

19.7

4.1

0.9

3.6

1

59.8

48.0

62.5

49.3

46.0

61.5

31.9

17.6

33.3

2

15.7

33.8

13.2

33.5

1.4

16.3

31.6

32.0

34.8

3

2.3

9.4

1.3

8.8

0.0

2.2

17.1

23.6

17.1

4

0.3

2.1

0.1

1.9

0.0

0.3

8.2

13.1

6.9

5

0.0

0.4

0.0

0.4

0.0

0.0

3.8

6.6

2.7

6

0.0

0.1

0.0

0.1

0.0

0.0

1.8

3.2

1.0

7

0.0

0.0

0.0

0.0

0.0

0.0

0.8

1.6

0.4

8

0.0

0.0

0.0

0.0

0.0

0.0

0.4

0.8

0.1

9

0.0

0.0

0.0

0.0

0.0

0.0

0.2

0.4

0.1

10

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.2

0.0

11

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.0

12

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

13

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

14

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

15

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

16

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

17

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

18

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

19

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

20

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

21

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

22

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

23

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Total Percentage

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

F08

F08

F08

F08

F08

F08

F12

F12

F14

G03

G03

G03

G03

G03

G03

G05

G05

G05

F05

F05

F05

F05

F05

F05

F05

F05

F05

I05

I05

I05

I05

I05

I05

I05

I05

I05

G01

I05

F05

I05

F03

I05

F05

I05

F05

F03

G01

F16

F05

0

F03

G01

F05

G01

0

F03

F03

F16

0

0

F03

G01

F03

0

0

0

F03

0

0

0

F03

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

 

Sloped Frame Roofs

Wood Deck

Metal Deck Roofs

Slate or Tile, Wood Sheathing, R-6.7 Batt Insulation, Gyp. Board

Wood Shingles, Wood Sheathing, R-3.3 Batt Insulation, Gyp. Board

Wood Shingles, Wood Sheathing, R-6.7 Batt Insulation, Gyp. Board

Membrane, Sheathing, R-1.8 Insulation Board, Wood Deck

Membrane, Sheathing, R-3.5 Insulation Board, Wood Deck

Membrane, Sheathing, R-1.8 Insulation Board, Wood Deck, Suspended Acoustical Ceiling

Membrane, Sheathing, R-3.5 Insulation Board, Wood Deck, Suspended Acoustical Ceiling

Membrane, Sheathing, R-1.8 Insulation Board, Metal Deck

Membrane, Sheathing, R-3.5 Insulation Board, Metal Deck

Roof Number

10

11

12

13

14

15

16

17

18

U, W/(m2·K)

0.133

0.231

0.130

0.393

0.232

0.324

0.204

0.452

0.251

Total R

7.53

4.34

7.68

2.55

4.31

3.08

4.84

2.21

3.98

Hour

Conduction Time Factors, %

Conduction Time Factors, %

Conduction Time Factors, %

0

0.7

2.6

0.5

0.2

0.1

0.9

1.3

16.6

2.5

1

17.6

23.9

12.5

6.5

1.7

2.5

1.5

59.6

33.7

2

35.1

28.0

26.1

17.0

9.1

7.3

3.8

19.8

38.2

3

25.1

18.6

22.5

17.8

14.9

9.7

6.9

3.4

16.9

4

12.4

11.1

15.0

14.4

15.2

9.6

8.3

0.5

5.9

5

5.4

6.5

9.3

11.0

13.0

8.7

8.4

0.1

1.9

6

2.2

3.8

5.6

8.3

10.4

7.8

7.9

0.0

0.6

7

0.9

2.2

3.4

6.2

8.2

6.9

7.2

0.0

0.2

8

0.3

1.3

2.0

4.7

6.4

6.1

6.5

0.0

0.1

9

0.1

0.8

1.2

3.5

4.9

5.5

5.9

0.0

0.0

10

0.1

0.4

0.7

2.6

3.8

4.8

5.4

0.0

0.0

11

0.0

0.3

0.4

2.0

2.9

4.3

4.8

0.0

0.0

12

0.0

0.1

0.3

1.5

2.3

3.8

4.4

0.0

0.0

13

0.0

0.1

0.2

1.1

1.7

3.4

4.0

0.0

0.0

14

0.0

0.1

0.1

0.8

1.3

3.0

3.6

0.0

0.0

15

0.0

0.0

0.1

0.6

1.0

2.7

3.2

0.0

0.0

16

0.0

0.0

0.0

0.5

0.8

2.4

2.9

0.0

0.0

17

0.0

0.0

0.0

0.3

0.6

2.1

2.6

0.0

0.0

18

0.0

0.0

0.0

0.3

0.5

1.9

2.4

0.0

0.0

19

0.0

0.0

0.0

0.2

0.4

1.7

2.2

0.0

0.0

20

0.0

0.0

0.0

0.1

0.3

1.5

2.0

0.0

0.0

21

0.0

0.0

0.0

0.1

0.2

1.3

1.8

0.0

0.0

22

0.0

0.0

0.0

0.1

0.2

1.2

1.6

0.0

0.0

23

0.0

0.0

0.0

0.1

0.1

1.0

1.4

0.0

0.0

Total Percentage

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

F14

F15

F15

F13

F13

F13

F13

F13

F13

G05

G05

G05

G03

G03

G03

G03

G03

G03

F05

F05

F05

I02

I02

I02

I02

I02

I02

I05

I05

I05

G06

I02

G06

I02

F08

I02

I05

F05

I05

F03

G06

F05

G06

F03

F08

F05

G01

F05

0

F03

F16

F05

0

F03

G01

F03

G01

0

0

F03

F16

0

0

F03

0

F03

0

0

0

F03

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

 

Metal Deck Roofs

Concrete Roofs

Membrane, Sheathing, R-1.8 Insulation Board, Metal Deck, Suspended Acoustical Ceiling

Membrane, Sheathing, R-3.5 Insulation Board, Metal Deck, Suspended Acoustical Ceiling

Membrane, Sheathing, R-2.6 Insulation Board, Metal Deck

Membrane, Sheathing, R-5.3 Insulation Board, Metal Deck

Membrane, Sheathing, R-4.4 Insulation Board, Metal Deck

50 mm Concrete Roof Ballast, Membrane, Sheathing, R-2.6 Insulation Board, Metal Deck

50 mm Concrete Roof Ballast, Membrane, Sheathing, R-5.3 Insulation Board, Metal Deck

Membrane, Sheathing, R-2.6 Insulation Board, 100 mm LW Concrete

Membrane, Sheathing, R-5.3 Insulation Board, 100 mm LW Concrete

Roof Number

19

20

21

22

23

24

25

26

27

U, W/(m2·K)

0.363

0.224

0.323

0.174

0.249

0.297

0.166

0.304

0.169

Total R

2.76

4.47

3.10

5.74

4.02

3.37

6.01

3.29

5.93

Hour

Conduction Time Factors, %

Conduction Time Factors, %

0

3.7

0.4

7.2

0.2

21.8

0.3

0.1

0.6

0.8

1

36.4

12.8

49.6

9.6

59.8

9.0

0.9

2.0

0.8

2

35.6

30.8

31.9

27.5

15.7

21.2

6.6

7.4

2.1

3

15.7

25.7

8.7

25.6

2.3

19.6

13.1

11.0

5.1

4

5.7

15.0

2.0

16.4

0.3

14.6

15.1

11.2

7.8

5

1.9

7.8

0.4

9.4

0.0

10.4

14.0

10.1

9.1

6

0.7

3.9

0.1

5.2

0.0

7.3

11.8

8.8

9.3

7

0.2

1.9

0.0

2.8

0.0

5.2

9.4

7.6

8.8

8

0.1

0.9

0.0

1.5

0.0

3.7

7.3

6.5

8.0

9

0.0

0.4

0.0

0.8

0.0

2.6

5.6

5.6

7.1

10

0.0

0.2

0.0

0.5

0.0

1.8

4.2

4.8

6.3

11

0.0

0.1

0.0

0.2

0.0

1.3

3.1

4.1

5.5

12

0.0

0.0

0.0

0.1

0.0

0.9

2.3

3.5

4.8

13

0.0

0.0

0.0

0.1

0.0

0.6

1.7

3.0

4.1

14

0.0

0.0

0.0

0.0

0.0

0.5

1.3

2.6

3.6

15

0.0

0.0

0.0

0.0

0.0

0.3

1.0

2.2

3.1

16

0.0

0.0

0.0

0.0

0.0

0.2

0.7

1.9

2.7

17

0.0

0.0

0.0

0.0

0.0

0.2

0.5

1.6

2.3

18

0.0

0.0

0.0

0.0

0.0

0.1

0.4

1.4

2.0

19

0.0

0.0

0.0

0.0

0.0

0.1

0.3

1.2

1.7

20

0.0

0.0

0.0

0.0

0.0

0.1

0.2

1.0

1.5

21

0.0

0.0

0.0

0.0

0.0

0.0

0.2

0.9

1.3

22

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.7

1.1

23

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.6

1.0

Total Percentage

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

F13

F13

F13

F13

F08

M17

M17

F13

F13

G03

G03

G03

G03

G03

F13

F13

G03

G03

I02

I02

I03

I03

F05

G03

G03

I03

I03

F08

I02

F08

I03

I05

I03

I03

M11

I03

F05

F08

F03

F08

G01

F08

I03

F03

M11

F16

F05

0

F03

F03

F03

F08

0

F03

F03

F16

0

0

0

0

F03

0

0

0

F03

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

 

Concrete Roofs

Membrane, Sheathing, R-2.6 Insulation Board, 150 mm LW Concrete

Membrane, Sheathing, R-5.3 Insulation Board, 150 mm LW Concrete

Membrane, Sheathing, R-2.6 Insulation Board, 200 mm LW Concrete

Membrane, Sheathing, R-5.3 Insulation Board, 200 mm LW Concrete

Membrane, Sheathing, R-2.6 Insulation Board, 150 mm HW Concrete

Membrane, Sheathing, R-5.3 Insulation Board, 150 mm HW Concrete

Membrane, Sheathing, R-2.6 Insulation Board, 200 mm HW Concrete

Membrane, Sheathing, R-5.3 Insulation Board, 200 mm HW Concrete

Membrane, 150 mm HW Concrete, R-3.3 Batt Insulation, Suspended Acoustical Ceiling

Membrane, 150 mm HW Concrete, R-6.7 Batt Insulation, Suspended Acoustical Ceiling

Roof Number

28

29

30

31

32

33

34

35

36

37

U, W/(m2·K)

0.296

0.166

0.288

0.163

0.315

0.172

0.312

0.171

0.239

0.133

Total R

3.38

6.02

3.48

6.12

3.17

5.82

3.20

5.85

4.23

7.59

Hour

Conduction Time Factors, %

0

1.5

1.9

2.4

2.8

2.0

2.4

2.6

2.9

1.4

1.5

1

1.6

1.8

2.3

2.6

2.4

2.2

2.6

2.8

3.0

2.0

2

3.2

1.9

2.6

2.5

4.4

2.6

3.4

2.8

6.7

4.8

3

5.7

2.9

3.6

2.7

6.2

3.7

4.7

3.3

8.2

7.4

4

7.3

4.4

4.8

3.3

6.9

5.0

5.5

4.1

8.1

8.0

5

7.8

5.8

5.6

4.1

6.8

5.8

5.8

4.8

7.6

7.8

6

7.6

6.6

6.1

4.9

6.4

6.2

5.8

5.3

6.9

7.2

7

7.1

6.9

6.1

5.4

6.1

6.2

5.7

5.5

6.4

6.6

8

6.6

6.8

6.0

5.7

5.7

6.1

5.5

5.5

5.8

6.1

9

6.0

6.6

5.8

5.7

5.3

5.8

5.3

5.5

5.3

5.6

10

5.5

6.2

5.6

5.7

5.0

5.5

5.0

5.3

4.9

5.1

11

5.0

5.8

5.3

5.5

4.7

5.2

4.8

5.1

4.4

4.7

12

4.6

5.4

5.0

5.3

4.4

4.9

4.6

4.9

4.1

4.3

13

4.2

4.9

4.7

5.1

4.1

4.6

4.4

4.7

3.7

3.9

14

3.8

4.6

4.4

4.9

3.9

4.4

4.2

4.5

3.4

3.6

15

3.5

4.2

4.2

4.6

3.6

4.1

4.0

4.3

3.1

3.3

16

3.2

3.8

3.9

4.4

3.4

3.9

3.8

4.2

2.8

3.0

17

2.9

3.5

3.7

4.1

3.2

3.6

3.6

4.0

2.6

2.8

18

2.7

3.2

3.5

3.9

3.0

3.4

3.5

3.8

2.4

2.5

19

2.4

3.0

3.3

3.7

2.8

3.2

3.3

3.6

2.2

2.3

20

2.2

2.7

3.1

3.5

2.6

3.0

3.2

3.5

2.0

2.1

21

2.0

2.5

2.9

3.3

2.5

2.8

3.0

3.3

1.8

1.9

22

1.8

2.3

2.7

3.1

2.3

2.7

2.9

3.2

1.7

1.8

23

1.7

2.1

2.5

2.9

2.2

2.5

2.8

3.0

1.5

1.6

Total Percentage

100

100

100

100

100

100

100

100

100

100

Layer ID from outdoors to indoors (See Table 21)

F01

F01

F01

F01

F01

F01

F01

F01

F01

F01

F13

F13

F13

F13

F13

F13

F13

F13

F13

F13

G03

G03

G03

G03

G03

G03

G03

G03

M14

M14

I03

I03

I03

I03

I03

I03

I03

I03

F05

F05

M12

I03

M13

I03

M14

I03

M15

I03

I05

I05

F03

M12

F03

M13

F03

M14

F03

M15

F16

I05

0

F03

0

F03

0

F03

0

F03

F03

F16

0

0

0

0

0

0

0

0

0

F03

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0


Table 21 Thermal Properties and Code Numbers of Layers Used in Wall and Roof Descriptions for Tables 19 and 20

Layer ID

Description

Thickness, mm

Conductivity, W/(m·K)

Density, kg/m3

Specific Heat, kJ/(kg·K)

Resistance R, (m2·K)/W

Mass, kg/m2

Thermal Capacity, kJ/(m2·K)

Notes

F01

Outdoor surface resistance

0.04

1

F02

Indoor vertical surface resistance

0.12

2

F03

Indoor horizontal surface resistance

0.16

3

F04

Wall air space resistance

0.15

4

F05

Ceiling air space resistance

0.18

5

F06

EIFS finish

9.5

0.72

1858

0.84

0.01

17.7

14.83

6

F07

25 mm stucco

25.4

0.72

1858

0.84

0.04

47.2

39.55

6

F08

Metal surface

0.8

45.35

7833

0.50

2 × 10–5

6.0

3.00

7

F09

Opaque spandrel glass

6.4

0.99

2531

0.88

0.01

16.1

14.14

8

F10

25 mm stone

25.4

3.17

2563

0.80

0.01

65.1

51.82

9

F11

Wood siding

12.7

0.09

593

1.63

0.14

7.5

12.30

10

F12

Asphalt shingles

3.2

0.04

1121

1.26

0.08

3.6

4.47

 

F13

Built-up roofing

9.5

0.16

1121

1.47

0.06

10.7

15.66

 

F14

Slate or tile

12.7

1.44

1922

1.26

0.01

24.4

30.68

 

F15

Wood shingles

6.4

0.04

593

1.30

0.17

3.8

4.89

10

F16

Acoustic tile

19.1

0.05

352

0.67

0.37

6.7

4.50

11

F17

Carpet

9.5

0.08

320

1.38

0.12

3.1

4.22

12

F18

Terrazzo

25.4

1.80

2563

0.80

0.01

65.1

51.82

13

G01

16 mm gypsum board

15.9

0.16

641

0.88

0.10

10.2

8.95

 

G02

16 mm plywood

15.9

0.11

545

1.88

0.15

8.6

16.30

 

G03

13 mm fiberboard sheathing

12.7

0.07

400

1.30

0.19

5.1

6.61

14

G04

13 mm wood

12.7

0.15

609

1.63

0.08

7.7

12.63

15

G05

25 mm wood

25.4

0.15

609

1.63

0.17

15.5

25.26

15

G06

50 mm wood

50.8

0.15

609

1.63

0.33

30.9

50.52

15

G07

100 mm wood

101.6

0.15

609

1.63

0.66

61.8

101.25

15

I01

25 mm insulation board

25.4

0.03

40

1.47

0.88

1.0

1.49

16

I02

50 mm insulation board

50.8

0.03

40

1.47

1.76

2.0

2.98

16

I03

75 mm insulation board

76.2

0.05

40

1.47

2.64

3.1

4.47

16

I04

89 mm batt insulation

89.4

0.05

8

0.84

1.94

0.7

0.59

17

I05

154 mm batt insulation

154.4

0.05

8

0.84

3.35

1.2

1.02

17

I06

244 mm batt insulation

243.8

0.05

8

0.84

5.28

1.9

1.60

17

M01

100 mm brick

101.6

0.89

1922

0.80

0.11

195.3

155.45

18

M02

150 mm LW concrete block

152.4

0.49

513

0.88

0.31

78.1

68.73

19

M03

200 mm LW concrete block

203.2

0.45

465

0.88

0.45

94.4

83.05

20

M04

300 mm LW concrete block

304.8

0.71

513

0.88

0.43

156.2

137.45

21

M05

200 mm concrete block

203.2

1.11

801

0.92

0.18

162.7

150.00

22

M06

300 mm concrete block

304.8

1.41

801

0.92

0.22

244.1

225.00

23

M07

150 mm LW concrete block (filled)

152.4

0.29

513

0.88

0.53

78.1

68.73

24

M08

200 mm LW concrete block (filled)

203.2

0.25

465

0.88

0.81

94.4

83.05

25

M09

300 mm LW concrete block (filled)

304.8

0.30

513

0.88

1.02

156.2

137.45

26

M10

200 mm concrete block (filled)

203.2

0.70

801

0.92

0.29

162.7

150.00

27

M11

100 mm lightweight concrete

101.6

0.53

1281

0.84

0.19

130.2

109.09

 

M12

150 mm lightweight concrete

152.4

0.53

1281

0.84

0.29

195.3

163.64

 

M13

200 mm lightweight concrete

203.2

0.53

1281

0.84

0.38

260.4

218.18

 

M14

150 mm heavyweight concrete

152.4

1.95

2243

0.92

0.08

341.8

315.00

 

M15

200 mm heavyweight concrete

203.2

1.95

2243

0.92

0.10

455.7

420.00

 

M16

300 mm heavyweight concrete

304.8

1.95

2243

0.92

0.16

683.5

630.00

 

M17

50 mm LW concrete roof ballast

50.8

0.19

641

0.84

0.27

32.5

27.27

28

Notes: The following notes give sources for the data in this table.

1 . Chapter 26, Table 10 for 3.4 m/s wind

2 . Chapter 26, Table 10 for still air, horizontal heat flow, 0.9 emittance

3 . Chapter 26, Table 10 for still air, downward heat flow, 0.2 emittance

4 . Chapter 26, Table 3 for 40 mm space, 32.2°C, horizontal heat flow, 0.82 emittance

5 . Chapter 26, Table 3 for 90 mm space, 32.2°C, downward heat flow, 0.82 emittance

6 . EIFS finish layers approximated by Chapter 26, Table 1 for cement plaster, sand aggregate

7 . Chapter 33, Table 3 for steel (mild)

8 . Chapter 26, Table 1 for architectural (soda-lime float) glass

9 . Chapter 26, Table 1 for calcitic, dolomitic, limestone, marble, and granite

10 . Chapter 26, Table 1, density assumed same as Southern pine

11 . Chapter 26, Table 1 for acoustical tile

12 . Chapter 26, Table 1 for carpet and rubber pad

13 . Chapter 26, Table 1, density assumed same as stone

14 . Chapter 26, Table 1 for nail-based sheathing

15 . Chapter 26, Table 1 for Southern pine

16 . Chapter 26, Table 1 for extruded polystyrene, smooth skin

17 . Chapter 26, Table 1 for glass fiber batt

18 . Chapter 26, Table 1 for clay fired brick

19 . Chapter 26, Table 1, lightweight aggregate, 152 mm, 7.3 to 7.7 kg, 2 or 3 cores

20 . Chapter 26, Table 1, lightweight aggregate, 203 mm, 8.6 to 10 kg

21 . Chapter 26, Table 1, lightweight aggregate, 14.5 to 16.3 kg, 2 or 3 cores

22 . Chapter 26, Table 1, normal weight aggregate, 203 mm, 14.5 to 16.3 kg, 2 or 3 cores

23 . Chapter 26, Table 1, normal weight aggregate, 305 mm, 22.7 kg, 2 cores

24 . Chapter 26, Table 1, same as note 19, plus vermiculite fill

25 . Chapter 26, Table 1, same as note, 20 plus vermiculite fill

26 . Chapter 26, Table 1, same as note 21, plus vermiculite fill

27 . Chapter 26, Table 1, same as note 22, plus vermiculite fill

28 . Chapter 26, Table 1 for 640 kg/m3 lightweight or limestone concrete


Table 22 Representative Nonsolar RTS Values for Light to Heavy Construction

% Glass

     

Interior Zones

Light

 

Medium

 

Heavy

Light

Medium

Heavy

With Carpet

No Carpet

 

With Carpet

No Carpet

 

With Carpet

No Carpet

With Carpet

No Carpet

With Carpet

No Carpet

With Carpet

No Carpet

10%

50%

90%

10%

50%

90%

 

10%

50%

90%

10%

50%

90%

 

10%

50%

90%

10%

50%

90%

Hour

 

Radiant Time Factor, %

0

 

47

50

53

41

43

46

 

46

49

52

31

33

35

 

34

38

42

22

25

28

 

46

40

46

31

33

21

1

 

19

18

17

20

19

19

 

18

17

16

17

16

15

 

9

9

9

10

9

9

 

19

20

18

17

9

9

2

 

11

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

6

5

8

7

7

 

6

5

5

8

7

7

 

4

4

4

5

5

5

 

6

8

6

8

5

5

4

 

4

4

3

5

5

5

 

4

3

3

6

5

5

 

4

4

4

5

5

4

 

4

5

3

6

4

5

5

 

3

3

2

4

3

3

 

2

2

2

4

4

4

 

4

3

3

4

4

4

 

3

4

2

4

4

4

6

 

2

2

2

3

3

2

 

2

2

2

4

3

3

 

3

3

3

4

4

4

 

2

3

2

4

3

4

7

 

2

1

1

2

2

2

 

1

1

1

3

3

3

 

3

3

3

4

4

4

 

2

2

1

3

3

4

8

 

1

1

1

1

1

1

 

1

1

1

3

2

2

 

3

3

3

4

3

3

 

1

1

1

3

3

4

9

 

1

1

1

1

1

1

 

1

1

1

2

2

2

 

3

3

2

3

3

3

 

1

1

1

2

3

3

10

 

1

1

1

1

1

1

 

1

1

1

2

2

2

 

3

2

2

3

3

3

 

1

1

1

2

3

3

11

 

1

1

1

1

1

1

 

1

1

1

2

2

2

 

2

2

2

3

3

3

 

1

1

1

2

2

3

12

 

1

1

1

1

1

1

 

1

1

1

1

1

1

 

2

2

2

3

3

3

 

1

1

1

1

2

3

13

 

1

1

1

0

1

0

 

1

1

1

1

1

1

 

2

2

2

3

3

2

 

1

1

1

1

2

3

14

 

0

0

1

0

1

0

 

1

1

1

1

1

1

 

2

2

2

3

2

2

 

1

0

1

1

2

3

15

 

0

0

1

0

0

0

 

1

1

1

1

1

1

 

2

2

2

2

2

2

 

0

0

1

1

2

3

16

 

0

0

0

0

0

0

 

1

1

1

1

1

1

 

2

2

2

2

2

2

 

0

0

1

1

2

3

17

 

0

0

0

0

0

0

 

1

1

1

1

1

1

 

2

2

2

2

2

2

 

0

0

1

1

2

2

18

 

0

0

0

0

0

0

 

1

1

1

1

1

1

 

2

2

1

2

2

2

 

0

0

1

1

2

2

19

 

0

0

0

0

0

0

 

0

1

0

0

1

1

 

2

2

1

2

2

2

 

0

0

1

0

2

2

20

 

0

0

0

0

0

0

 

0

0

0

0

1

1

 

2

1

1

2

2

2

 

0

0

0

0

2

2

21

 

0

0

0

0

0

0

 

0

0

0

0

1

1

 

2

1

1

2

2

2

 

0

0

0

0

2

2

22

 

0

0

0

0

0

0

 

0

0

0

0

1

0

 

1

1

1

2

2

2

 

0

0

0

0

1

2

23

 

0

0

0

0

0

0

 

0

0

0

0

0

0

 

1

1

1

2

2

1

 

0

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


Table 23 Representative Solar RTS Values for Light to Heavy Construction

% Glass

 

Light

 

Medium

 

Heavy

With Carpet

No Carpet

With Carpet

No Carpet

With Carpet

No Carpet

10%

50%

90%

10%

50%

90%

10%

50%

90%

10%

50%

90%

10%

50%

90%

10%

50%

90%

Hour

 

Radiant Time Factor, %

0

 

53

55

56

44

45

46

 

52

54

55

28

29

29

 

47

49

51

26

27

28

1

 

17

17

17

19

20

20

 

16

16

15

15

15

15

 

11

12

12

12

13

13

2

 

9

9

9

11

11

11

 

8

8

8

10

10

10

 

6

6

6

7

7

7

3

 

5

5

5

7

7

7

 

5

4

4

7

7

7

 

4

4

3

5

5

5

4

 

3

3

3

5

5

5

 

3

3

3

6

6

6

 

3

3

3

4

4

4

5

 

2

2

2

3

3

3

 

2

2

2

5

5

5

 

2

2

2

4

4

4

6

 

2

2

2

3

2

2

 

2

1

1

4

4

4

 

2

2

2

3

3

3

7

 

1

1

1

2

2

2

 

1

1

1

4

3

3

 

2

2

2

3

3

3

8

 

1

1

1

1

1

1

 

1

1

1

3

3

3

 

2

2

2

3

3

3

9

 

1

1

1

1

1

1

 

1

1

1

3

3

3

 

2

2

2

3

3

3

10

 

1

1

1

1

1

1

 

1

1

1

2

2

2

 

2

2

2

3

3

3

11

 

1

1

1

1

1

1

 

1

1

1

2

2

2

 

2

2

1

3

3

2

12

 

1

1

1

1

1

0

 

1

1

1

2

2

2

 

2

1

1

2

2

2

13

 

1

1

0

1

0

0

 

1

1

1

2

2

2

 

2

1

1

2

2

2

14

 

1

0

0

0

0

0

 

1

1

1

1

1

1

 

2

1

1

2

2

2

15

 

1

0

0

0

0

0

 

1

1

1

1

1

1

 

1

1

1

2

2

2

16

 

0

0

0

0

0

0

 

1

1

1

1

1

1

 

1

1

1

2

2

2

17

 

0

0

0

0

0

0

 

1

1

1

1

1

1

 

1

1

1

2

2

2

18

 

0

0

0

0

0

0

 

1

1

1

1

1

1

 

1

1

1

2

2

2

19

 

0

0

0

0

0

0

 

0

0

0

1

1

1

 

1

1

1

2

2

2

20

 

0

0

0

0

0

0

 

0

0

0

1

1

1

 

1

1

1

2

2

2

21

 

0

0

0

0

0

0

 

0

0

0

0

0

0

 

1

1

1

2

2

2

22

 

0

0

0

0

0

0

 

0

0

0

0

0

0

 

1

1

1

2

1

1

23

 

0

0

0

0

0

0

 

0

0

0

0

0

0

 

1

1

1

2

1

1

   

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100


Table 24 RTS Representative Zone Construction for Tables 22 and 23

Construction Class

 

Exterior Wall

 

Roof/Ceiling

 

Partitions

 

Floor

 

Furnishings

Light

 

Steel siding, 50 mm insulation, air space, 19 mm gyp.

 

100 mm LW concrete, ceiling air space, acoustic tile

 

19 mm gyp., air space, 19 mm gyp.

 

Acoustic tile, ceiling air space, 100 mm LW concrete

 

25 mm wood @ 50% of floor area

Medium

 

100 mm face brick, 50 mm insulation, air space, 19 mm gyp.

 

100 mm HW concrete, ceiling air space, acoustic tile

 

19 mm gyp., air space, 19 mm gyp.

 

Acoustic tile, ceiling air space, 100 mm HW concrete

 

25 mm wood @ 50% of floor area

Heavy

 

100 mm face brick, 200 mm HW concrete air space, 50 mm insulation, 19 mm gyp.

 

200 mm HW concrete, ceiling air space, acoustic tile

 

19 mm gyp., 200 mm HW concrete block, 19 mm gyp.

 

Acoustic tile, ceiling air space, 200 mm HW concrete

 

25 mm wood @ 50% of floor area


ASHRAE research project RP-942 compared HB and RTS results over a wide range of zone types and input variables (Rees et al. 2000; Spitler et al. 1998). In general, total cooling loads calculated using RTS closely agreed with or were slightly higher than those of the HB method with the same inputs. The project examined more than 5000 test cases of varying zone parameters. The dominating variable was overall thermal mass, and results were grouped into lightweight, U.S. medium-weight, U.K. medium-weight, and heavyweight construction. Best agreement between RTS and HB results was obtained for light- and medium-weight construction. Greater differences occurred in heavyweight cases, with RTS generally predicting slightly higher peak cooling loads than HB. Greater differences also were observed in zones with extremely high internal radiant loads and large glazing areas or with a very lightweight exterior envelope. In this case, heat balance calculations predict that some of the internal radiant load will be transmitted to the outdoor environment and never becomes cooling load in the space. RTS does not account for energy transfer out of the space to the environment, and thus predicted higher cooling loads.

ASHRAE research project RP-1117 built two model rooms for which cooling loads were physically measured using extensive instrumentation. The results agreed with previous simulations (Chantrasrisalai et al. 2003; Eldridge et al. 2003; Iu et al. 2003). HB calculations closely approximated measured cooling loads when provided with detailed data for the test rooms. RTS overpredicted measured cooling loads in tests with large, clear, single-glazed window areas with bare concrete floor and no furnishings or internal loads. Tests under more typical conditions (venetian blinds, carpeted floor, office-type furnishings, and normal internal loads) provided good agreement between HB, RTS, and measured loads.

7. HEATING LOAD CALCULATIONS

Techniques for estimating design heating load for commercial, institutional, and industrial applications are essentially the same as for those estimating design cooling loads for such uses, with the following exceptions:

  • Temperatures outdoor conditioned spaces are generally lower than maintained space temperatures.

  • Credit for solar or internal heat gains is not included

  • Thermal storage effect of building structure or content is ignored.

Thermal bridging effects on wall and roof conduction are greater for heating loads than for cooling loads, and greater care must be taken to account for bridging effects on U-factors used in heating load calculations.

Heat losses (negative heat gains) are thus considered to be instantaneous, heat transfer essentially conductive, and latent heat treated only as a function of replacing space humidity lost to the exterior environment.

This simplified approach is justified because it evaluates worst-case conditions that can reasonably occur during a heating season. Therefore, the near-worst-case load is based on the following:

  • Design interior and exterior conditions

  • Including infiltration and/or ventilation

  • No solar effect (at night or on cloudy winter days)

  • Before the periodic presence of people, lights, and appliances has an offsetting effect

Typical commercial and retail spaces have nighttime unoccupied periods at a setback temperature where little to no ventilation is required, building lights and equipment are off, and heat loss is primarily through conduction and infiltration. Before being occupied, buildings are warmed to the occupied temperature (see the following discussion). During occupied time, building lights, equipment, and people cooling loads can offset conduction heat loss, although some perimeter heat may be required, leaving infiltration and ventilation as the primary heating loads. Ventilation heat load may be offset with heat recovery equipment. These loads (conduction loss, warm-up load, and ventilation load) may not be additive when sizing building heating equipment, and it is prudent to analyze each load and their interactions to arrive at final equipment sizing for heating.

The traditional approach to design heating load calculation, described in the previous paragraphs and in sections 7.1 and 7.2 below, is widely applicable. For special applications dealing with decarbonization, high-performance buildings, or passive design, there are other methods that can be applied.

7.1 HEAT LOSS CALCULATIONS

The general procedure for calculation of design heat losses of a structure is as follows:

  1. Select outdoor design conditions: temperature, humidity, and wind direction and speed.

  2. Select indoor design conditions to be maintained.

  3. Estimate temperature in any adjacent unheated spaces.

  4. Select transmission coefficients and compute heat losses for walls, floors, ceilings, windows, doors, and foundation elements.

  5. Compute heat load through infiltration and any other outdoor air introduced directly to the space.

  6. Sum the losses caused by transmission and infiltration.

 Outdoor Design Conditions

The ideal heating system provides enough heat to match the structure’s heat loss. However, weather conditions vary considerably from year to year, and heating systems designed for the worst weather conditions on record would have a great excess of capacity most of the time. A system’s failure to maintain design conditions during brief periods of severe weather usually is not critical. However, close regulation of indoor temperature may be critical for some occupancies or industrial processes. Design temperature data and discussion of their application are given in Chapter 14. Generally, the 99% temperature values given in the tabulated weather data are used. However, caution is needed, and local conditions should always be investigated. In some locations, outdoor temperatures are commonly much lower and wind velocities higher than those given in the tabulated weather data.

 Indoor Design Conditions

The main purpose of the heating system is to maintain indoor conditions that make most of the occupants comfortable. Keep in mind, however, that the purpose of heating load calculations is to obtain data for sizing the heating system components. In many cases, the system will rarely be called upon to operate at the design conditions. Therefore, the use and occupancy of the space are general considerations from the design temperature point of view. Later, when the building’s energy requirements are computed, the actual conditions in the space and outdoor environment, including internal heat gains, must be considered.

The indoor design temperature should be selected at the lower end of the acceptable temperature range, so that the heating equipment will not be oversized. Even properly sized equipment operates under partial load, at reduced efficiency, most of the time; therefore, any oversizing aggravates this condition and lowers overall system efficiency. A maximum design dry-bulb temperature of 21°C is recommended for most occupancies. The indoor design value of relative humidity should be compatible with a healthful environment and the thermal and moisture integrity of the building envelope. A minimum relative humidity of 30% is recommended for most situations.

 Calculation of Transmission Heat Losses

Exterior Surface Above Grade. All above-grade surfaces exposed to outdoor conditions (walls, doors, ceilings, fenestration, and raised floors) are treated identically, as follows:

(34)

(35)

where HF is the heating load factor in W/m2.

Below-Grade Surfaces. An approximate method for estimating below-grade heat loss [based on the work of Latta and Boileau (1969)] assumes that the heat flow paths shown in Figure 12 can be used to find the steady-state heat loss to the ground surface, as follows:

(36)

where

Uavg = average U-factor for below-grade surface from Equation (38) or (39), W/(m2 · K)
tin = below-grade space air temperature, °C
tgr = design ground surface temperature from Equation (37), °C

Heat Flow from Below-Grade Surface

Figure 12. Heat Flow from Below-Grade Surface


The effect of soil heat capacity means that none of the usual external design air temperatures are suitable values for tgr. Ground surface temperature fluctuates about an annual mean value by amplitude A, which varies with geographic location and surface cover. The minimum ground surface temperature, suitable for heat loss estimates, is therefore

(37)

where

= mean ground temperature, °C, estimated from the annual average air temperature or from well-water temperatures, shown in Figure 14 of Chapter 35 in the 2023 ASHRAE Handbook—HVAC Applications
A = ground surface temperature amplitude, K, from Figure 13 for North America

Ground Temperature Amplitude

Figure 13. Ground Temperature Amplitude


Figure 14 shows depth parameters used in determining Uavg. For walls, the region defined by z1 and z2 may be the entire wall or any portion of it, allowing partially insulated configurations to be analyzed piecewise.

Below-Grade Parameters

Figure 14. Below-Grade Parameters


Table 25 Average U-Factor for Basement Walls with Uniform Insulation

Depth, m

Uavg,bw from Grade to Depth, W/(m2·K)

Uninsulated

R-0.88

R-1.76

R-2.64

0.3

2.468

0.769

0.458

0.326

0.6

1.898

0.689

0.427

0.310

0.9

1.571

0.628

0.401

0.296

1.2

1.353

0.579

0.379

0.283

1.5

1.195

0.539

0.360

0.272

1.8

1.075

0.505

0.343

0.262

2.1

0.980

0.476

0.328

0.252

2.4

0.902

0.450

0.315

0.244

Soil conductivity = 1.4 W/(m · K); insulation is over entire depth. For other soil conductivities and partial insulation, use Equation (39).


The below-grade wall average U-factor is given by

(38)

where

Uavg,bw = average U-factor for wall region defined by z1 and z2, W/(m2 · K)
ksoil = soil thermal conductivity, W/(m · K)
Rother = total resistance of wall, insulation, and indoor surface resistance, (m2 · K)/W
z1, z2 = depths of top and bottom of wall segment under consideration, m (Figure 14)

The value of soil thermal conductivity k varies widely with soil type and moisture content. A typical value of 1.4 W/(m · K) has been used previously to tabulate U-factors, and Rother is approximately 0.259 (m2 · K)/W for uninsulated concrete walls. For these parameters, representative values for Uavg,bw are shown in Table 25.

The average below-grade floor U-factor (where the entire basement floor is uninsulated or has uniform insulation) is given by

(39)

where

wb = basement width (shortest dimension), m
zf = floor depth below grade, m (see Figure 14)

Representative values of Uavg,bf for uninsulated basement floors are shown in Table 26.

At-Grade Surfaces. Concrete slab floors may be (1) unheated, relying for warmth on heat delivered above floor level by the heating system, or (2) heated, containing heated pipes or ducts that constitute a radiant slab or portion of it for complete or partial heating of the house.

The simplified approach that treats heat loss as proportional to slab perimeter allows slab heat loss to be estimated for both unheated and heated slab floors (Wang 1979):

(40)

(41)

where

q = heat loss through perimeter, W
Fp = heat loss coefficient per metre of perimeter, W/(m · K), Table 27
p = perimeter (exposed edge) of floor, m

Table 26 Average U-Factor for Basement Floors

zf(Depth of Floor Below Grade), m

Uavg,bf, W/(m2·K)

wb (Shortest Width of Basement), m

6

7

8

9

0.3

0.370

0.335

0.307

0.283

0.6

0.310

0.283

0.261

0.242

0.9

0.271

0.249

0.230

0.215

1.2

0.242

0.224

0.208

0.195

1.5

0.220

0.204

0.190

0.179

1.8

0.202

0.188

0.176

0.166

2.1

0.187

0.175

0.164

0.155

Soil conductivity is 1.4 W/(m · K); floor is uninsulated so that Rother = 0.25 (m2·K)/W. For other soil conductivities and insulation, use Equation (39).


Table 27 Heat Loss Coefficient Fp of Slab Floor Construction

Construction

Insulation

Fp, W/(m · K)

200 mm block wall, brick facing

Uninsulated

 

1.17

R-0.95 (m2 · K)/W from edge to footer

0.86

100 mm block wall, brick facing

Uninsulated

 

1.45

R-0.95 (m2 · K)/W from edge to footer

0.85

Metal stud wall, stucco

Uninsulated

 

2.07

R-0.95 (m2 · K)/W from edge to footer

0.92

Poured concrete wall with duct near perimeter*

Uninsulated

 

3.67

R-0.95 (m2 · K)/W from edge to footer

1.24

Source: Wang (1979)

* Weighted average temperature of heating duct was assumed at 43°C during heating season (outdoor air temperature less than 18°C).


Surfaces Adjacent to Buffer Space. Heat loss to adjacent unconditioned or semiconditioned spaces can be calculated using a heating factor based on the partition temperature difference:

(42)

 Infiltration

Infiltration of outdoor air through openings into a structure is caused by thermal forces, wind pressure, and negative pressure (planned or unplanned) with respect to the outdoors created by mechanical systems. Typically, in building design, if the mechanical systems are designed to maintain positive building pressure, infiltration need not be considered except in ancillary spaces such as entryways and loading areas.

Infiltration is treated as a room load and has both sensible and latent components. During winter, this means heat and humidity loss because cold, dry air must be heated to design temperature and moisture must be added to increase the humidity to design condition. Typically, during winter, controlling indoor humidity is not a factor and infiltration is reduced to a simple sensible component. Under cooling conditions, both sensible and latent components are added to the space load to be treated by the air conditioning system.Procedures for estimating the infiltration rate are discussed in Chapter 16. The infiltration rate is reduced to a volumetric flow rate at a known dry bulb/wet bulb condition. Along with indoor air condition, the following equations define the infiltration sensible and latent loads.

(43)

where

m3/s = volume flow rate of infiltrating air
cp = specific heat capacity of air, kJ/(kg · K)
v = specific volume of infiltrating air, m3/kg

Table 28 Common Sizing Calculations in Other Chapters

Subject

Volume/Chapter

Equation(s)

Duct heat transfer

ASTM Standard C680

 

Piping heat transfer

Fundamentals Ch. 4

Table 5

Pump power

Systems Ch. 44

(3), (4)

Moist-air sensible heating and cooling

Fundamentals Ch. 1

(43)

Moist-air cooling and dehumidification

Fundamentals Ch. 1

(45)

Air mixing

Fundamentals Ch. 1

(46)

Space heat absorption and moist-air moisture gains

Fundamentals Ch. 1

(48)

Adiabatic mixing of water injected into moist air

Fundamentals Ch. 1

(47)


Assuming standard air conditions (15°C and sea-level conditions) for v and cp, Equation (43) may be written as

(44)

The infiltrating air also introduces a latent heating load given by

(45)

where

Win = humidity ratio for indoor space air, kgw/kga
Wo = humidity ratio for outdoor air, kgw/kga
Dh = change in enthalpy to convert 1 kg water from vapor to liquid, kJ/kg

For standard air and nominal indoor comfort conditions, the latent load may be expressed as

(46)

The coefficients 1.23 in Equation (44) and 3010 in Equation (46) are given for standard conditions. They depend on temperature and altitude (and, consequently, pressure).

7.2 HEATING SAFETY FACTORS AND LOAD ALLOWANCES

Before mechanical cooling became common in the second half of the 1900s, and when energy was less expensive, buildings included much less insulation; large, operable windows; and generally more infiltration-prone assemblies than the energy-efficient and much tighter buildings typical of today. In the past, allowances of 10 to 20% of the net calculated heating load for piping losses to unheated spaces, and 10 to 20% more for a warm-up load, were common practice, along with other occasional safety factors reflecting the experience and/or concern of the individual designer. Today such safety allowances are more conservatively applied with modern construction practices. A combined warm-up/safety allowance of 20 to 25% is common but varies depending on the particular climate, building use, and type of construction. Engineering judgment must be applied for the particular project.

Today’s more efficient buildings have smaller overall heating loads at peak design conditions. The spare capacity in absolute terms needed for warm-up may not be any less in the highly efficient building than a more traditional building, assuming building mass is the same in both cases. Simply adding the same percentage factor to a lower peak load value may not result in enough spare capacity for timely warm up of the building. Transient models can be used to calculate both the quasi-steady state peak heating load and the spare capacity needed for building warm-up, but this level of analytical rigor may not be possible for a typical building design process. Experience and judgment must be applied, especially in cases where the base heating system capacity has been reduced through enhanced insulation and infiltration reduction.

7.3 OTHER HEATING CONSIDERATIONS

Calculation of design heating load estimates has essentially become a subset of the more involved and complex estimation of cooling loads for such spaces. Chapter 19 discusses using the heating load estimate to predict or analyze energy consumption over time. Special provisions to deal with particular applications are covered in the 2023 ASHRAE Handbook—HVAC Applications and the 2024 ASHRAE Handbook—HVAC Systems and Equipment.

8. SYSTEM HEATING AND COOLING LOAD EFFECTS

The heat balance (HB) or radiant time series (RTS) methods are used to determine cooling loads of rooms within a building, but they do not address the plant size necessary to reject the heat. Principal factors to consider in determining the plant size are ventilation, heat transport equipment, and air distribution systems. Some of these factors vary as a function of room load, ambient temperature, and control strategies, so it is often necessary to evaluate the factors and strategies dynamically and simultaneously with the heat loss or gain calculations.

Detailed analysis of system components and methods calculating their contribution to equipment sizing are beyond the scope of this chapter, which is general in nature. Table 28 lists the most frequently used calculations in other chapters and volumes.

8.1 ZONING

Organization of building rooms into zones as defined for load calculations and air-handling units has no effect on room cooling loads. However, specific grouping and ungrouping of rooms into zones may cause peak system loads to occur at different times during the day or year, and may significantly affect heat removal equipment sizes.

For example, if each room is cooled by a separate heat removal system, the total capacity of the heat transport systems equals the sum of peak room loads. Conditioning all rooms by a single heat transport system (e.g., a variable-volume air handler) requires less capacity (equal to the simultaneous peak of the combined rooms load, which includes some rooms at off-peak loads). This may significantly reduce equipment capacity, depending on the configuration of the building.

Grouping rooms together to reduce the number of HVAC systems or zones is called thermal zoning. Zoning choices can affect the HVAC system peak load as well as system energy performance. A detailed introduction to thermal zoning, including examples, is given in Rock (2018).

8.2 VENTILATION

Consult ASHRAE Standard 62.1 and building codes to determine the required quantity of ventilation air for an application, and the various methods of achieving acceptable indoor air quality. The following discussion is confined to the effect of mechanical ventilation on sizing heat removal equipment. Where natural ventilation is used, through operable windows or other means, it is considered as infiltration and is part of the direct-to-room heat gain. Where ventilation air is conditioned and supplied through the mechanical system, its sensible and latent loads are applied directly to heat transport and central equipment, and do not affect room heating and cooling loads. If the mechanical ventilation rate sufficiently exceeds exhaust airflows, air pressure may be positive and infiltration from envelope openings and outdoor wind may not be included in the load calculations. Chapter 16 includes more information on ventilating commercial buildings.

Depending on ventilation requirements and local climate conditions, peak cooling coil loads may occur at peak dehumidification or enthalpy conditions instead of design dry-bulb conditions. Coil loads should be checked against all those peak conditions.

8.3 AIR HEAT TRANSPORT SYSTEMS

Heat transport equipment is usually selected to provide adequate heating or cooling for the peak load condition. However, selection must also consider maintaining desired indoor conditions during all occupied hours, which requires matching the rate of heat transport to room peak heating and cooling loads. Automatic control systems normally vary the heating and cooling system capacity during these off-peak hours of operation.

 On/Off Control Systems

On/off control systems, common in residential and light commercial applications, cycle equipment on and off to match room load. They are adaptable to heating or cooling because they can cycle both heating and cooling equipment. In their purest form, their heat transport matches the combined room and ventilation load over a series of cycles.

 Variable-Air-Volume Systems

Variable-air-volume (VAV) systems have airflow controls that adjust cooling airflow to match the room cooling load. Damper leakage or minimum airflow settings may cause overcooling, so most VAV systems are used in conjunction with separate heating systems. These may be duct-mounted heating coils, or separate radiant or convective heating systems.

The amount of heat added by the heating systems during cooling becomes part of the room cooling load. Calculations must determine the minimum airflow relative to off-peak cooling loads. The quantity of heat added to the cooling load can be determined for each terminal by Equation (8) using the minimum required supply airflow rate and the difference between supply air temperature and the room indoor heating design temperature.

 Constant-Air-Volume Reheat Systems

In constant-air-volume (CAV) reheat systems, all supply air is cooled to remove moisture and then heated to avoid overcooling rooms. Reheat refers to the amount of heat added to cooling supply air to raise the supply air temperature to the temperature necessary for picking up the sensible load. The quantity of heat added can be determined by Equation (8).

With a constant-volume reheat system, heat transport system load does not vary with changes in room load, unless the cooling coil discharge temperature is allowed to vary. Where a minimum circulation rate requires a supply air temperature greater than the available design supply air temperature, reheat adds to the cooling load on the heat transport system. This makes the cooling load on the heat transport system larger than the room peak load.

 Mixed Air Systems

Mixed air systems change the supply air temperature to match the cooling capacity by mixing airstreams of different temperatures; examples include multizone and dual-duct systems. Systems that cool the entire airstream to remove moisture and to reheat some of the air before mixing with the cooling airstream influence load on the heat transport system in the same way a reheat system does. Other systems separate the air paths so that mixing of hot- and cold-deck airstreams does not occur. For systems that mix hot and cold airstreams, the contribution to the heat transport system load is determined as follows.

  1. Determine the ratio of cold-deck flow to hot-deck flow from

  2. From Equation (9), the hot-deck contribution to room load during off-peak cooling is

    where

    Qh = heating airflow, L/s
    Qc = cooling airflow, L/s
    Tc = cooling air temperature, °C
    Th = heating air temperature, °C
    Tr = room or return air temperature, °C
    qrh = heating airflow contribution to room load at off-peak hours, W

 Heat Gain from Fans

Fans that circulate air through HVAC systems add energy to the system through the following processes:

  • Increasing velocity and static pressure adds kinetic and potential energy

  • Fan inefficiency in producing airflow and static pressure adds sensible heat (fan heat) to the airflow

  • Inefficiency of motor and drive dissipates sensible heat

The power required to provide airflow and static pressure can be determined from the first law of thermodynamics with the following equation:

where

Pa = air power, kW
V = flow rate, m3/s
p = pressure, kPa

at standard air conditions with air density = 1.2 kg/m3 built into the multiplier 0.009804. The power necessary at the fan shaft must account for fan inefficiencies, which may vary from 50 to 70%. This may be determined from

where

Pf = power required at fan shaft, kW
ηf = fan efficiency, dimensionless

The power necessary at the input to the fan motor must account for fan motor inefficiencies and drive losses. Fan motor efficiencies generally vary from 80 to 95%, and drive losses for a belt drive are 3% of the fan power. This may be determined from

where

Pm = power required at input to motor, kW
Ed = belt drive efficiency, dimensionless
Em = fan motor efficiency, dimensionless
Pf = power required at fan shaft, kW
DL = drive loss, dimensionless

Almost all the energy required to generate airflow and static pressure is ultimately dissipated as heat in the building and HVAC system; a small portion is discharged with any exhaust air. Generally, it is assumed that all the heat is released at the fan rather than dispersed to the remainder of the system. The portion of fan heat released to the airstream depends on the location of the fan motor and drive: if they 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 airstream, the energy is split between the airstream and the room housing the motor and drive. Therefore, the following equations may be used to calculate heat generated by fans and motors:

If motor and drive are outside the airstream,

If motor and drive are inside the airstream,

where

PF = power required at fan shaft, kW
Pm = power required at input to motor, kW
qfs = heat release to airstream, kW
qfr = heat release to room housing motor and drive, kW

Supply airstream temperature rise may be determined from psychrometric formulas or Equation (8).

Variable- or adjustable-frequency drives (VFDs or AFDs) often drive fan motors in VAV air-handling units. These devices release heat to the surrounding space. Refer to manufacturers’ data for heat released or efficiencies. The disposition of heat released is determined by the drive’s location: in the conditioned space, in the return air path, or in a nonconditioned equipment room. These drives, and other electronic equipment such as building control, data processing, and communications devices, are temperature sensitive, so the rooms in which they are housed require cooling, frequently year round.

 Duct Surface Heat Transfer

Heat transfer across the duct surface is one mechanism for energy transfer to or from air inside a duct. It involves conduction through the duct wall and insulation, convection at inner and outer surfaces, and radiation between the duct and its surroundings. Chapter 4 presents a rigorous analysis of duct heat loss and gain, and Chapter 23 addresses application of analysis to insulated duct systems.

The effect of duct heat loss or gain depends on the duct routing, duct insulation, and its surrounding environment. Consider the following conditions:

  • For duct run within the area cooled or heated by air in the duct, heat transfer from the space to the duct has no effect on heating or cooling load, but beware of the potential for condensation on cold ducts.

  • For duct run through unconditioned spaces or outdoors, heat transfer adds to the cooling or heating load for the air transport system but not for the conditioned space.

  • For duct run through conditioned space not served by the duct, heat transfer affects the conditioned space as well as the air transport system serving the duct.

  • For an extensive duct system, heat transfer reduces the effective supply air differential temperature, requiring adjustment through air balancing to increase airflow to extremities of the distribution system.

 Duct Leakage

Air leakage from supply ducts can considerably affect HVAC system energy use. Leakage reduces cooling and/or dehumidifying capacity for the conditioned space, and must be offset by increased airflow (sometimes reduced supply air temperatures), unless leaked air enters the conditioned space directly. Supply air leakage into a ceiling return plenum or leakage from unconditioned spaces into return ducts also affects return air temperature and/or humidity.

Determining leakage from a duct system is complex because of the variables in paths, fabrication, and installation methods. Refer to Chapter 21 and publications from the Sheet Metal and Air Conditioning Contractors’ National Association (SMACNA) for methods of determining leakage. In general, good-quality ducts and post-installation duct sealing provide highly cost-effective energy savings, with improved thermal comfort and delivery of ventilation air.

 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 traditional 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 adjacent 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 conditioned space is small. Most return plenum temperatures do not rise more than 0.6 to 1.7 K above space temperature, thus generating only a relatively small thermal gradient for heat transfer through plenum surfaces, except to the outdoors. This yields a relatively large-percentage reduction in space cooling load by shifting plenum loads to the system. Another reason plenum temperatures do not rise more is leakage into the plenum from supply air ducts, and, if exposed to the roof, increasing levels of insulation.

Where the ceiling space is used as a return air plenum, energy balance requires that heat picked up from the lights into the return air (1) become part of the cooling load to the return air (represented by a temperature rise of return air as it passes through the ceiling space), (2) be partially transferred back into the conditioned space through the ceiling material below, and/or (3) be partially lost from the space through floor surfaces above the plenum. If the plenum has one or more exterior surfaces, heat gains through them must be considered; if adjacent to spaces with different indoor temperatures, partition loads must be considered, too. In a multistory building, the conditioned space frequently gains heat through its floor from a similar plenum below, offsetting the floor loss. The radiant component of heat leaving the ceiling or floor surface of a plenum is normally so small, because of relatively small temperature differences, that all such heat transfer is considered convective for calculation purposes (Rock and Wolfe 1997).

Figure 15 shows a schematic of a typical return air plenum. The following equations, using the heat flow directions shown in Figure 15, represent the heat balance of a return air plenum design for a typical interior room in a multifloor building:

(47)

(48)

(49)

(50)

(51)

where

q1 = heat gain to space from plenum through ceiling, kW
q2 = heat loss from plenum through floor above, kW
q3 = heat gain “pickup” by return air, kW
Q = return airflow, L/s
qlp = light heat gain to plenum via return air, kW
qlr = light heat gain to space, kW
qf = heat gain from plenum below, through floor, kW
qw = heat gain from exterior wall, kW
qr = space cooling load, including appropriate treatment of qlr, qf, and/or qw, kW
tp = plenum air temperature, °C
tr = space air temperature, °C
tfa = space air temperature of floor above, °C
ts = supply air temperature, °C

Schematic Diagram of Typical Return Air Plenum

Figure 15. Schematic Diagram of Typical Return Air Plenum


By substituting Equations (47), (48), (49), and (51) into heat balance Equation (50), tp can be found as the resultant return air temperature or plenum temperature. The results, although rigorous and best solved by computer, are important in determining the cooling load, which affects equipment size selection, future energy consumption, and other factors.

Equations (47) to (51) are simplified to illustrate the heat balance relationship. Heat gain into a return air plenum is not limited to heat from lights. Exterior walls directly exposed to the ceiling space can transfer heat directly to or from return air. For single-story buildings or the top floor of a multistory building, roof heat gain or loss enters or leaves the ceiling plenum rather than the conditioned space directly. The supply air quantity calculated by Equation (51) is only for the conditioned space under consideration, and is assumed to equal the return air quantity.

The amount of airflow through a return plenum above a conditioned space may not be limited to that supplied into the space; it will, however, have no noticeable effect on plenum temperature if the surplus comes from an adjacent plenum operating under similar conditions. Where special conditions exist, Equations (47) to (51) must be modified appropriately. Finally, although the building’s thermal storage has some effect, the amount of heat entering the return air is small and may be considered as convective for calculation purposes.

 Ceiling Plenums with Ducted Returns

Compared to those in unducted plenum returns, temperatures in ceiling plenums that have well-sealed return or exhaust air ducts float considerably. In cooling mode, heat from lights and other equipment raises the ceiling plenum’s temperature considerably. Solar heat gain through a poorly insulated roof can drive the ceiling plenum temperature to extreme levels, so much so that heat gains to uninsulated supply air ducts in the plenum can dramatically decrease available cooling capacity to the rooms below. In cold weather, much heat is lost from warm supply ducts. Thus, insulating supply air ducts and sealing them well to minimize air leaks are highly desirable, if not essential. Appropriately insulating roofs and plenums’ exterior walls and minimizing infiltration are also key to lowering total building loads and improving HVAC system performance.

 Underfloor Air Distribution Systems

Room cooling loads determined by methods in this chapter cannot model two distinguishing aspects of the thermal performance of underfloor air distribution (UFAD) systems under cooling operation:

  • Room air stratification: UFAD systems supply cool air at the floor and extract warmer air at the ceiling, thus creating vertical thermal stratification. Cooling load models assume a well-mixed uniform space temperature.

  • Underfloor air supply plenums: cool supply air flowing through the underfloor plenum is exposed to heat gain from both the concrete slab (conducted from the warm return air on the adjacent floor below in a multistory building) and the raised floor panels (conducted from the warmer room above).

Extensive simulation and experimental research led to the development of a whole-building energy simulation program capable of modeling energy performance and load calculations for UFAD systems (Bauman et al. 2007; Webster et al. 2008). Previously, it was thought that cooling loads for UFAD and overhead (OH) mixing systems were nearly identical. However, energy modeling studies show that the UFAD cooling load is generally higher than that calculated in the same building for a well-mixed system (Schiavon et al. 2010a). The difference is primarily caused by the thermal storage effect of the lower-mass} raised-floor panels compared to the greater mass of a structural floor slab. Schiavon et al. (2010b) showed that the presence of the raised floor reduces the slab’s ability to store heat, thereby producing higher peak cooling loads for a raised-floor system than for one without a raised floor. A second contributing factor is that the raised-floor surface above the underfloor plenum tends to be cooler (except when illuminated by the sun) than most other room surfaces, producing a room surface temperature distribution resembling a chilled radiant floor system, which has a different peak cooling load than an all-air system (Feng et al. 2012). The precise magnitude of difference in design cooling loads between OH and UFAD systems is still under investigation, but mainly depends on zone orientation and floor level, and possibly the effects of furniture. Methods for determining UFAD cooling loads will be updated as additional research results become available. For more information about simplified approaches to UFAD cooling load calculations, see the ASHRAE Underfloor Air Distribution (UFAD) Design Guide (ASHRAE 2013), Bauman et al. (2010), and Schiavon et al. (2010c).

 Plenums in Load Calculations

Currently, most designers include ceiling and floor plenums within neighboring occupied spaces when thermally zoning a building. However, temperatures in these plenums, and the way that they behave, are significantly different from those of occupied spaces. Thus, they should be defined as a separate thermal zone. Most hand and computer-based load calculation routines, though, currently do not allow floating air temperatures or humidities; assuming a constant air temperature in plenums, attics, and other unconditioned spaces is a poor, but often necessary, assumption. The heat balance method does allow floating space conditions, and when fully implemented in design load software, should allow more accurate modeling of plenums and other complex spaces.

8.4 CENTRAL PLANT

 Piping

Losses must be considered for piping systems that transport heat. For water or hydronic piping systems, heat is transferred through the piping and insulation (see Chapter 23 for ways to determine this transfer). However, distribution of this transferred heat depends on the fluid in the pipe and the surrounding environment.

Consider a heating hot-water pipe. If the pipe serves a room heater and is routed through the heated space, any heat loss from the pipe adds heat to the room. Heat transfer to the heated space and heat loss from the piping system is null. If the piping is exposed to ambient conditions en route to the heater, the loss must be considered when selecting the heating equipment; if the pipe is routed through a space requiring cooling, heat loss from the piping also becomes a load on the cooling system.

In summary, the designer must evaluate both the magnitude of the pipe heat transfer and the routing of the piping.

 Pumps

Calculating heat gain from pumps is addressed in the section on Electric Motors. For pumps serving hydronic systems, disposition of heat from the pumps depends on the service. For chilled-water systems, energy applied to the fluid to generate flow and pressure becomes a chiller load. For condenser water pumps, pumping energy must be rejected through the cooling tower. The magnitude of pumping energy relative to cooling load is generally small.

9. EXAMPLE COOLING AND HEATING LOAD CALCULATIONS

To illustrate the cooling and heating load calculation procedures discussed in this chapter, an example problem has been developed. The objectives of this example are to demonstrate (1) the component cooling load calculation procedures for a room using the radiant time series (RTS) method, (2) how orientation of opaque envelope and fenestration affects the magnitude and timing of peak room loads, (3) how a block load accounts for load diversity among rooms, and (4) the component heating load calculations for a room.

Table 29 summarizes RTS cooling load calculation procedures.

Single-Room Example Office

Figure 16. Single-Room Example Office


Table 29 Summary of RTS Load Calculation Procedures

Equation

Equation No. in Chapter

 

Equation

Equation No. in Chapter

External Heat Gain

     

  Partitions, Ceilings, Floors Transmission

 
 

  Sol-Air Temperature

   

32

 

29    

where

     

q

=

q = heat transfer rate, W

 

where

   

U

=

coefficient of overall heat transfer between adjacent and conditioned space, W/(m2·K)
 

te

=

sol-air temperature, °C

         
 

to

=

outdoor air temperature, °C

     

A

=

area of separating section concerned, ft2

 

a

=

absorptance of surface for solar radiation

     

tb

=

average air temperature in adjacent space, °C

 

Et

=

total solar radiation incident on surface, W/m2

   

ti

=

air temperature in conditioned space, °C

 

ho

=

coefficient of heat transfer by long-wave radiation and convection at outer surface, W/(m2·K)

 

Internal Heat Gain

 
     

Occupants

 
 

ε

=

hemispherical emittance of surface

     

 
 

ΔR

=

difference between long-wave radiation incident on surface from sky and surroundings and radiation emitted by blackbody at outdoor air temperature, W/m2; 20 for horizontal surfaces; 0 for vertical surfaces

     

 
     

where

     

qs

=

occupant sensible heat gain, W

 
     

ql

=

occupant latent heat gain, W

 
 

Wall and Roof Transmission

   

ql,per

=

latent heat gain per person, W · person; see Table 4

 

(31)    
 

(30)  

N

=

number of occupants

 
 

where

     

Lighting

 

qθ

=

hourly conductive heat gain for surface, W

     

(1)
 

qi,θ

=

heat input for current hour

     

where

 

qi,θ-n

=

conductive heat input for surface n hours ago, W

   

qel

=

heat gain, W

 

c0, c1, etc.

=

conduction time factors

     

W

=

total light wattage, W

 
 

U

=

overall heat transfer coefficient for surface, W/(m2·K)

     

Ful

=

lighting use factor

 
 

A

=

surface area, m2

     

Fsa

=

lighting special allowance factor

 
 

Fenestration Transmission

     
 

(14)    

Electric Motors

 

where

   

(2)
 

q

=

fenestration transmission heat gain, W

     

where

 

U

=

overall U-factor, including frame and mounting orientation from Table 4 of Chapter 15, W/(m2·K)

     

qem

=

heat equivalent of equipment operation, W

             

P

=

motor power rating, W

 
 

A

=

window area, m2

     

EM

=

motor efficiency, decimal fraction <1.0

 
 

Tin

=

indoor temperature, °C

     

FUM

=

motor use factor, 1.0 or decimal fraction <1.0

 
 

Tout

=

outdoor temperature, °C

     

FLM

=

motor load factor, 1.0 or decimal fraction <1.0

 
 

Fenestration Solar

     
 

Tout

=

outdoor temperature, °C

     

Hooded Cooking Appliances

 

(12)    

 
 

(13)      

where

 

where

   

qs

=

sensible heat gain, W

 
 

qb

=

beam solar heat gain, W

     

qinput

=

nameplate or rated energy input, W

 
 

qd

=

diffuse solar heat gain, W

     

FU

=

usage factor; see Tables 8B, 8C, 8D

 
 

A

=

window area, m2

     

FR

=

radiation factor; see Tables 8B, 8C, 8D

 
 

Et,b, Et,d, and Et,r

=

beam, sky diffuse, and ground-reflected diffuse irradiance, calculated using equations in Chapter 14

   

For other appliances and equipment, find qs for

         

    Unhooded cooking appliances: Table 8A

 
 

SHGC(θ)

=

beam solar heat gain coefficient as a function of incident angle θ; may be interpolated between values in Table 10 of Chapter 15

       

    Other kitchen equipment: Table 8E

 
         

    Hospital and laboratory equipment: Tables 9 and 10

         

    Computers, printers, scanners, etc.: Tables 11 and 12

 
 

IAC(θ.Ω)

=

IAC(θ.Ω) = indoor solar attenuation coefficient for beam solar heat gain coefficient; = 1.0 if no indoor shading device. IAC(θ.Ω) is a function of shade type and, depending on type, may also be a function of beam solar angle of incidence θ and shade geometry

       

    Miscellaneous office equipment: Table 13

 
     

Find ql for

         

    Unhooded cooking appliances: Table 8A

 
         

    Other kitchen equipment: Table 8E

 
   

Ventilation and Infiltration Air Heat Gain

 

IACD

=

indoor solar attenuation coefficient for diffuse solar heat gain coefficient; = 1.0 if not indoor shading device. IACD is a function of shade type and, depending on type, may also be a function of shade geometry

   

(9)

     

(10)

     

where

     

qs

=

sensible heat gain due to infiltration, W

 

Table 30 Room Characteristics – Opaque Envelope and Fenestration

Element

Net Surface Area, m2

Surface Orientation

Assembly Details

Performance / Other Details

Floor

12.1

Horizontal

(top to bottom)

Carpet

127 mm concrete slab on metal deck

(above conditioned space)

Roof

12.1

Horizontal

(top to bottom)

Light-colored membrane roofing

Rigid closed-cell polyisocynurate foam core insulation (RSI-5.3)

Flat metal deck

Ceiling space

Acoustic tile

U = 0.165 W/(m2·K)

Ceiling used as a return plenum.

Assume 30% of roof cooling load directly absorbed by return air stream without becoming room load.

Spandrel Wall

5.6

30° east of true south

(outside to inside)

Spandrel bronze-tinted glass, opaque, backed with air space

Rigid mineral fiber insulation (RSI=0.9)

Mineral fiber batt insulation (RSI=2.3)

16 mm gypsum wall board

U = 0.278 W/(m2·K)

Spandrel Wall

5.6

60° west of true south

Same as above

Same as above

Brick Wall

5.6

30° east of true south

(outside to inside)

102 mm light brown colored face brick

152 mm low-mass concrete block

Rigid continuous insulation (RSI = 0.9)

Mineral fiber batt insulation (RSI = 2.3)

16 mm gypsum board

U = 0.261 W/(m2·K)

Brick Wall

3.7

60° west of true south

Same as above

Same as above

Window

3.7

30° east of true south

(outside to inside)

6 mm bronze-tinted outdoor pane

13 mm air space

6 mm clear indoor pane

Light-colored mini blinds

Window dimensions: 1.91 m W × 1.95 m H.

Normal incidence solar heat gain coefficient (SHGC) = 0.49

Window non-operable mounted in aluminum frame with thermal breaks.

Overall U-value = 3.18 W/(m2·K)

(Reference: Chapter 15, Tables 4 and 10, glazing type 5d)

Indoor attenuation coefficients (IAC):

IAC(0) = 0.74

IAC(60) = 0.65

IAC(diff) = 0.79

Radiant Fraction = 0.54

(Reference: Chapter 15, Table 14B, glazing type 5d, louver location = inside, louver reflectance = 0.8, louvers positioned at 45° angle.)

Window

3.7

60° west of true south

Same as above

Same as above

Table 31 Room Characteristics – Internal Heat Gains

Heat Gain Source

Heat Gain

Schedule

Details

Overhead Lighting

110 W total

7:00 am to 7:00 pm

One 4-lamp pendant fluorescent 2.4 m type fixture

Fixture has four 32 W T-8 lamps plus electronic ballasts with special allowance factor = 0.85 per manufacturer’s data.

Assume all cooling load from lighting is directly absorbed in the room, per Table 3.

Equipment

130 W total

8:00 am to 5:00 pm

One computer and one personal printer for total 10.8 W/m2 heat gain.

Occupants

73 W sensible

59 W latent

8:00 am to 5:00 pm

1 occupant

Activity level: Moderately active office work.

Heat gains per Table 1.



9.1 SINGLE-ROOM DETAILED COOLING LOAD EXAMPLE

The objective of this example is to calculate the cooling load for the office shown in Figure 16 for July 3:00 pm local standard time. This corner office is on the second floor of a two-story office building.

 Room and Weather Characteristics

Opaque envelope: See Table 30 for surface areas, orientations and construction assembly details for floor, roof, and wall elements of the space.

Fenestration: See Table 30 for surface areas, orientations, window construction, and performance data.

Internal heat gain: See Table 31 for heat gain and schedule data.


Infiltration: For purposes of this example, assume the building is maintained under positive pressure during peak cooling conditions and therefore has no infiltration. Assume that infiltration during peak heating conditions is equivalent to one air change per hour.

Indoor design conditions: 23.9°C with 50% rh for cooling; 22.2°C for heating.

Weather data: This example uses the Example City weather data found in Chapter 14, Table 1: Latitude = 33.64° North, Longitude = 84.43° West, elevation = 313 m above sea level. For heating load calculation, the heating design dry-bulb temperature is –5.6°C. For cooling load calculations the 5% monthly design dry-bulb and coincident wet-bulb temperature data from Chapter 14 Table 1 is used. This is statistically equivalent to a 2% annual cooling design condition. See Table 32 for the 24 h temperature profiles calculated per Chapter 14.

Table 32 Monthly/Hourly 5% Design Temperatures for Example City, °C

Hour

January

 

February

 

March

 

April

 

May

 

June

 

July

 

August

 

September

 

October

 

November

 

December

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

7.7

7.3

 

8.6

7.3

 

12.1

9.7

 

15.4

12.8

 

19.4

16.8

 

22.3

19.3

 

23.2

20.5

 

23.2

20.5

 

20.9

18.2

 

15.7

13.8

 

11.1

10.2

 

8.6

8.6

2

7.3

7.1

 

8.2

7.1

 

11.6

9.4

 

15.0

12.6

 

18.9

16.6

 

21.8

19.1

 

22.8

20.4

 

22.8

20.4

 

20.4

18.0

 

15.2

13.6

 

10.6

9.9

 

8.2

8.2

3

6.9

6.8

 

7.8

6.8

 

11.2

9.3

 

14.6

12.4

 

18.6

16.5

 

21.5

19.0

 

22.4

20.3

 

22.4

20.3

 

20.2

17.9

 

14.9

13.4

 

10.2

9.7

 

7.8

7.8

4

6.6

6.6

 

7.4

6.6

 

10.8

9.1

 

14.2

12.3

 

18.3

16.4

 

21.2

18.9

 

22.1

20.2

 

22.1

20.2

 

19.8

17.8

 

14.6

13.3

 

9.9

9.5

 

7.5

7.5

5

6.4

6.4

 

7.2

6.4

 

10.6

8.9

 

14.0

12.2

 

18.1

16.3

 

20.9

18.8

 

21.9

20.1

 

21.9

20.1

 

19.6

17.7

 

14.3

13.2

 

9.7

9.4

 

7.3

7.3

6

6.6

6.6

 

7.4

6.6

 

10.8

9.1

 

14.2

12.3

 

18.3

16.4

 

21.2

18.9

 

22.1

20.2

 

22.1

20.2

 

19.8

17.8

 

14.6

13.3

 

9.9

9.5

 

7.5

7.5

7

7.4

7.1

 

8.3

7.1

 

11.7

9.5

 

15.1

12.7

 

19.1

16.7

 

21.9

19.2

 

22.9

20.4

 

22.9

20.4

 

20.6

18.1

 

15.3

13.7

 

10.7

10.0

 

8.3

8.3

8

9.2

8.4

 

10.2

8.4

 

13.8

10.6

 

17.2

13.6

 

20.9

17.4

 

23.8

19.8

 

24.8

21.0

 

24.7

21.0

 

22.4

18.7

 

17.3

14.5

 

12.7

11.1

 

10.1

9.6

9

11.3

9.8

 

12.4

9.8

 

16.2

11.7

 

19.5

14.6

 

23.1

18.2

 

25.9

20.5

 

26.9

21.6

 

26.8

21.6

 

24.4

19.4

 

19.4

15.4

 

14.9

12.3

 

12.2

10.9

10

13.1

11.1

 

14.4

11.0

 

18.3

12.7

 

21.6

15.4

 

25.0

18.9

 

27.9

21.1

 

28.8

22.2

 

28.6

22.2

 

26.2

20.1

 

21.3

16.3

 

16.9

13.4

 

14.0

12.2

11

14.7

12.3

 

16.2

12.1

 

20.2

13.7

 

23.4

16.2

 

26.7

19.5

 

29.6

21.7

 

30.6

22.7

 

30.2

22.7

 

27.8

20.6

 

23.1

17.1

 

18.6

14.4

 

15.6

13.3

12

15.8

13.0

 

17.3

12.9

 

21.4

14.3

 

24.6

16.8

 

27.8

19.9

 

30.7

22.0

 

31.7

23.1

 

31.3

23.0

 

28.8

21.0

 

24.2

17.5

 

19.8

15.1

 

16.7

14.1

13

16.7

13.6

 

18.3

13.4

 

22.4

14.8

 

25.6

17.2

 

28.7

20.2

 

31.6

22.3

 

32.6

23.3

 

32.2

23.3

 

29.7

21.3

 

25.1

17.9

 

20.7

15.6

 

17.6

14.6

14

17.2

14.0

 

18.8

13.8

 

23.1

15.1

 

26.2

17.4

 

29.2

20.4

 

32.1

22.5

 

33.1

23.5

 

32.7

23.4

 

30.2

21.5

 

25.7

18.2

 

21.3

15.9

 

18.1

15.0

15

17.2

14.0

 

18.8

13.8

 

23.1

15.1

 

26.2

17.4

 

29.2

20.4

 

32.1

22.5

 

33.1

23.5

 

32.7

23.4

 

30.2

21.5

 

25.7

18.2

 

21.3

15.9

 

18.1

15.0

16

16.6

13.6

 

18.1

13.4

 

22.3

14.7

 

25.5

17.1

 

28.6

20.2

 

31.4

22.3

 

32.4

23.3

 

32.1

23.2

 

29.6

21.3

 

25.0

17.9

 

20.6

15.5

 

17.4

14.6

17

15.7

12.9

 

17.2

12.8

 

21.3

14.2

 

24.5

16.7

 

27.7

19.9

 

30.6

22.0

 

31.6

23.0

 

31.2

23.0

 

28.7

20.9

 

24.1

17.5

 

19.7

15.0

 

16.6

14.0

18

14.6

12.2

 

16.1

12.1

 

20.1

13.6

 

23.3

16.2

 

26.6

19.4

 

29.4

21.6

 

30.4

22.7

 

30.1

22.7

 

27.7

20.6

 

22.9

17.0

 

18.5

14.3

 

15.5

13.2

19

13.0

11.1

 

14.3

10.9

 

18.2

12.7

 

21.4

15.4

 

24.9

18.8

 

27.8

21.1

 

28.7

22.2

 

28.5

22.2

 

26.1

20.0

 

21.2

16.2

 

16.7

13.3

 

13.9

12.2

20

11.8

10.2

 

13.1

10.2

 

16.8

12.0

 

20.1

14.8

 

23.7

18.4

 

26.6

20.7

 

27.5

21.8

 

27.3

21.8

 

24.9

19.6

 

20.0

15.7

 

15.5

12.7

 

12.7

11.3

21

10.8

9.6

 

12.0

9.5

 

15.7

11.4

 

19.0

14.3

 

22.6

18.0

 

25.5

20.3

 

26.5

21.5

 

26.3

21.5

 

23.9

19.3

 

19.0

15.2

 

14.4

12.1

 

11.7

10.7

22

9.8

8.9

 

10.9

8.8

 

14.6

10.9

 

17.9

13.8

 

21.6

17.6

 

24.5

20.0

 

25.5

21.2

 

25.3

21.2

 

23.0

18.9

 

17.9

14.8

 

13.4

11.4

 

10.7

10.0

23

9.1

8.3

 

10.1

8.3

 

13.7

10.5

 

17.1

13.5

 

20.8

17.3

 

23.7

19.8

 

24.7

20.9

 

24.6

20.9

 

22.3

18.7

 

17.2

14.4

 

12.6

11.0

 

10.0

9.5

24

8.3

7.8

 

9.3

7.8

 

12.8

10.1

 

16.2

13.1

 

20.1

17.1

 

22.9

19.5

 

23.9

20.7

 

23.8

20.7

 

21.5

18.4

 

16.4

14.1

 

11.8

10.6

 

9.2

9.0


 Cooling Loads Using RTS Method

Traditionally, simplified cooling load calculation methods such as the radiant time series (RTS) Method have estimated the total cooling load at a particular design condition by independently calculating each component load (wall, windows, occupants, lighting, etc.) and then summing the component loads. Although the actual heat transfer processes for each component do affect each other, this simplification, known as the principle of superposition, is appropriate for design load calculations and useful to the designer in understanding the relative contribution of each component to the total cooling load.

On the following pages RTS procedures will be demonstrated for calculating (1) load due to internal heat gain, (2) exterior wall load, (3) load for windows with no shading, (4) load for windows with internal shading, (5) load for windows with internal and external shading, and (6) the total room load. All loads will be calculated for July 3:00 pm local standard time. Equations used in these calculations are summarized in Table 29.

Part 1. Cooling load due to internal heat gain.

Objective: Calculate the cooling load due to overhead lighting heat gain at 3:00 pm local standard time.

Solution: Calculation of the lighting load involves the following steps: (a) calculate the 24 h heat gain profile, (b) split those heat gains into convective and radiant components, (c) determine the radiant portion of the load by applying appropriate RTS factors, and (d) sum the convective and radiant load components to determine the total lighting load.

The heat gain profile is calculated using Equation (1) for each hour of the day. Calculations are shown in columns b through e in Table 33. Each heat gain is designated as qi. For example, for 3:00 pm (hour 15):

Table 33 Lighting Load

Hour

Lighting Wattage

Conversion Factor

Usage Factor, %

Lighting Heat Gain, Btu/h

Heat Gain, W

Cooling Load, W

Convective 43%

Radiant 57%

Convective

Radiant

Total

a

b

c

d

e

f

g

h

i

j

1

110

1.00

0

0

0

0

0

8

8

2

110

1.00

0

0

0

0

0

7

7

3

110

1.00

0

0

0

0

0

6

6

4

110

1.00

0

0

0

0

0

6

6

5

110

1.00

0

0

0

0

0

5

5

6

110

1.00

0

0

0

0

0

4

4

7

110

1.00

100

110

47

63

47

38

85

8

110

1.00

100

110

47

63

47

47

94

9

110

1.00

100

110

47

63

47

51

99

10

110

1.00

100

110

47

63

47

53

101

11

110

1.00

100

110

47

63

47

55

102

12

110

1.00

100

110

47

63

47

55

102

13

110

1.00

100

110

47

63

47

55

102

14

110

1.00

100

110

47

63

47

56

103

15

110

1.00

100

110

47

63

47

56

103

16

110

1.00

100

110

47

63

47

57

104

17

110

1.00

100

110

47

63

47

58

105

18

110

1.00

100

110

47

63

47

58

106

19

110

1.00

0

0

0

0

0

25

25

20

110

1.00

0

0

0

0

0

16

16

21

110

1.00

0

0

0

0

0

11

11

22

110

1.00

0

0

0

0

0

9

9

23

110

1.00

0

0

0

0

0

8

8

24

110

1.00

0

0

0

0

0

7

7

Totals:

1,320

568

752

568

751

1319


Next, the lighting heat gain is divided into convective and radiant portions. Table 6 shows that a “Non-in-ceiling fluorescent luminaire” has a radiant factor between 0.5 and 0.57. We will use the higher value of 0.57 or 57%. Therefore 57% of the heat gain is radiant and the remaining 43% is convective. Columns f and g in Table 33 show the results of this calculation: convective heat gain is 47 W while radiant heat gain is 63 W.

The convective portion of the heat gain immediately becomes a cooling load. The radiant portion undergoes a conversion process from heat gain to cooling load which is modeled using the appropriate RTS factors. Those factors are obtained from Table 22 using the data for medium weight construction, carpeted floor, and 50% glass. The factors are reproduced in Table 34 in the “non-solar RTS factors, zone type 8” column. The radiant load is calculated using Equation (33). Results are shown in column i of Table 33. For 3:00 PM, for example, the calculation is

Table 34 Radiant Time Series and Conduction Time Series Factors for Example Problem

Hour

Non-Solar RTS Factors, Zone Type 8, %

Solar RTS Factors, Zone Type 8, %

Conduction Time Series (CTS) Factors, Wall Type 2, %

0

49

54

3.7

1

17

16

38.1

2

9

8

36.5

3

5

4

14.6

4

3

3

4.8

5

2

2

1.5

6

2

1

0.5

7

1

1

0.2

8

1

1

0.0

9

1

1

0.0

10

1

1

0.0

11

1

1

0.0

12

1

1

0.0

13

1

1

0.0

14

1

1

0.0

15

1

1

0.0

16

1

1

0.0

17

1

1

0.0

18

1

1

0.0

19

1

0

0.0

20

0

0

0.0

21

0

0

0.0

22

0

0

0.0

23

0

0

0.0


Finally, the total lighting cooling load at the designated hour is the sum of convective and radiant portions. Table 33 shows the results in column j. For 3:00 pm the calculation is as follows:

Part 2. Wall cooling load.

Objective: Calculate the cooling load for the spandrel wall section facing 60° west of south for July 3:00 pm local standard time.

Solution: Determining the wall cooling load requires calculation of: (a) the sol-air temperature at the exterior surface (b) the heat input at the exterior surface based on sol-air temperature, (c) the delayed heat gain through the mass of the wall to the interior surface using conduction time series factors, (d) convective and radiant portions of the heat gain, (e) the delayed space cooling load from interior surface radiant heat gain using radiant time series factors, and (f) the total wall load as the sum of convective and radiant load components.

First, calculate the sol-air temperature at 3:00 pm local standard time (LST) on July 21 for a vertical, spandrel glass wall assembly, facing 60° west of south. Key input data for the calculation is shown in Table 35.

Table 35 Input Data for Calculation of Sol-Air Temperature

Item

Value

Notes

Local Standard Time

3:00 pm

 

Month and Day

July 21

 

Orientation

60° west of true south

 

Latitude

33.64° N

 

Longitude

84.43° W

 

τb

0.515

Chapter 14, Table 1, July. τb = solar clear sky optical depth for beam irradiance

τd

2.066

Chapter 14, Table 1, July. τd = solar clear sky optical depth for diffuse irradiance.

Outdoor air dry-bulb temperature

33.1°C

Table 29, July 3:00 pm

Ground reflectivity, ρg

0.2

Assumed


Sol-air temperature is calculated using Equation (29). For the dark-colored wall, α/ho = 0.053, and for vertical surfaces, εΔR/ho = 0. The solar irradiance Et on the wall must be determined using the equations in Chapter 14:

Solar Angles:

.

ψ = surface azimuth = +60°

Σ = surface tilt from horizontal (where horizontal = 0°) = 90° for vertical wall surface

3:00 pm LST = hour 15

Calculate solar altitude, solar azimuth, surface solar azimuth, and incident angle as follows:

From Table 2 in Chapter 14, solar position data and constants for July 21 are

ET = –6.3536 min

δ = 20.44°

Eo = 1319 W/m2

Local standard meridian (LSM) for Eastern Time Zone = –75°.

Apparent solar time AST

Hour angle H, degrees

Solar altitude β

Solar azimuth ϕ

Surface-solar azimuth γ

Incident angle θ

Beam normal irradiance Eb

Surface beam irradiance Et,b

Diffuse irradiance Ed – Horizontal surfaces

Diffuse irradiance Ed – Vertical surface with surface azimuth +60°

Ground reflected irradiance Et,r

Total surface irradiance Et

Sol-air temperature [from Equation (29)]:


Table 36A Wall Component of Solar Irradiance for July

           

Beam Solar Irradiance

Diffuse Solar Irradiance

 

Local Standard Hour

Apparent Solar Time

Hour Angle H

Solar Altitude β

Solar Azimuth ϕ

Solar Air Mass m

Beam Normal Eb, W/m2

Surface Incident Angle θ

Surface Direct Beam Et,b, W/m2

Diffuse Horizontal Ed, W/m2

Sky Diffuse Et,d, W/m2

Ground Diffuse Et,r, W/m2

Diffuse Subtotal, W/m2

Total Surface Irradiance Et, W/m2

a

b

c

d

e

f

g

h

i

j

k

l

m

n

1

0.24

–176

–36

–176

0.0

0.0

0.0

0.0

0.0

0.0

0.0

2

1.24

–161

–33

–159

0.0

0.0

0.0

0.0

0.0

0.0

0.0

3

2.24

–146

–27

–144

0.0

0.0

0.0

0.0

0.0

0.0

0.0

4

3.24

–131

–19

–132

0.0

0.0

0.0

0.0

0.0

0.0

0.0

5

4.24

–116

–9

–122

0.0

0.0

0.0

0.0

0.0

0.0

0.0

6

5.24

–101

2

–113

18.23816

22.1

172.8

0.0

19.6

9.6

2.0

11.7

11.7

7

6.24

–86

14

–105

4.06606

324.7

159.9

0.0

71.5

27.0

15.0

42.0

42.0

8

7.24

–71

26

–98

2.25339

525.5

146.3

0.0

105.9

31.8

33.8

65.7

65.7

9

8.24

–56

39

–90

1.59750

642.0

132.7

0.0

129.9

33.3

53.1

86.4

86.4

10

9.24

–41

51

–81

1.28345

712.4

119.2

0.0

146.6

33.7

70.1

103.8

103.8

11

10.24

–26

63

–67

1.12031

754.1

105.9

0.0

157.5

33.7

83.0

116.7

116.7

12

11.24

–11

73

–40

1.04326

775.2

93.0

0.0

163.4

33.7

90.6

124.3

124.3

13

12.24

4

76

14

1.02835

779.4

80.5

128.1

164.6

50.1

92.2

142.3

270.4

14

13.24

19

69

56

1.07141

767.4

68.9

275.7

161.2

69.8

87.8

157.5

433.2

15

14.2388

33.58

57.5

74.71

1.18490

737.1

58.69

383.1

153.0

86.4

77.5

163.9

546.9

16

15.24

49

45

86

1.40773

683.1

50.6

433.7

139.4

98.2

62.4

160.6

594.3

17

16.24

64

33

94

1.84558

593.8

45.8

413.8

119.5

102.2

44.0

146.2

560.0

18

17.24

79

20

102

2.85472

443.8

45.5

311.3

91.1

92.1

24.6

116.6

429.7

19

18.24

94

8

109

6.61488

181.5

49.6

117.6

49.4

51.8

7.6

59.4

177.0

20

19.26

109

–3

117

0.0

0.0

0.0

0.0

0.0

0.0

0.0

21

20.24

124

–14

127

0.0

0.0

0.0

0.0

0.0

0.0

0.0

22

21.24

139

–23

138

0.0

0.0

0.0

0.0

0.0

0.0

0.0

23

22.24

154

–30

151

0.0

0.0

0.0

0.0

0.0

0.0

0.0

24

23.24

169

–35

167

0.0

0.0

0.0

0.0

0.0

0.0

0.0


Table 36B Wall Sol-Air Temperatures, Heat Input, Heat Gain, and Cooling Load for July

           

Heat Gain, W

Cooling Load, W

Local Standard Hour

Total Surface Irradiance Et W/m2

Outdoor Dry-Bulb, °C

Sol-Air Temp., °C

Indoor Dry-Bulb, °C

Heat Input W

Total

Convective (54%)

Radiant (46%)

Convective

Radiant

Total

a

b

c

d

e

f

g

h

i

j

k

l

1

0.0

23.2

23.2

24

–1

1

1

1

1

3

4

2

0.0

22.8

22.8

24

–2

0

0

0

0

2

2

3

0.0

22.4

22.4

24

–2

–1

–1

0

–1

2

1

4

0.0

22.1

22.1

24

–3

–2

–1

–1

–1

1

1

5

0.0

21.9

21.9

24

–3

–2

–1

–1

–1

1

0

6

11.7

22.1

22.7

24

–2

–3

–1

–1

–1

1

–1

7

42.0

22.9

25.1

24

2

–2

–1

–1

–1

1

0

8

65.7

24.8

28.3

24

7

0

0

0

0

1

1

9

86.4

26.9

31.5

24

12

3

2

2

2

2

4

10

103.8

28.8

34.3

24

16

8

4

4

4

3

8

11

116.7

30.6

36.7

24

20

12

7

6

7

5

11

12

124.3

31.7

38.2

24

22

16

9

8

9

6

15

13

270.4

32.6

46.8

24

36

20

11

9

11

7

18

14

433.1

33.1

56.0

24

50

27

15

13

15

10

24

15

546.9

33.1

62.0

24

59

39

21

18

21

13

34

16

594.2

32.4

63.8

24

62

50

27

23

27

17

44

17

560.0

31.6

61.1

24

58

57

31

26

31

20

51

18

427.9

30.4

53.0

24

45

58

31

27

31

22

53

19

177.0

28.7

38.1

24

22

52

28

24

28

21

49

20

0.0

27.5

27.5

24

6

38

20

17

20

18

38

21

0.0

26.5

26.5

24

4

21

11

10

11

13

24

22

0.0

25.5

25.5

24

3

10

6

5

6

9

14

23

0.0

24.7

24.7

24

1

5

3

3

3

6

9

24

0.0

23.9

23.9

24

0

3

2

1

2

4

6


This procedure is used to calculate the sol-air temperatures for each hour. Because of the tedious solar angle and intensity calculations, using a simple computer spreadsheet or other computer software can reduce the effort involved. A spreadsheet was used to calculate a 24 h sol-air temperature profile for the data of this example. See Table 36A for the solar angle and intensity calculations and Table 36B for the sol-air temperatures for this wall surface and orientation.

Next, use the sol-air temperature to calculate the heat input at the exterior surface of the wall using Equation (30). Table 36B shows the results of this calculation in column f. The calculation for 3:00 pm is

With the heat input at the exterior surface known, the conduction heat gain at the interior surface of the wall can be calculated using Equation (31). This involves applying the conduction time series to calculate the delay as heat flows through the wall. In Table 19, the most similar wall construction is wall number 2. This is a spandrel glass wall that has similar mass and thermal resistance. Conduction time series factors for this wall are also shown in Table 33. Results of this calculation are shown in Table 36B in column g. For example, the calculation for 3:00 pm is:

Next, split the conduction heat gain into convective and radiant portions. Table 17 shows that for conduction heat gain through walls and floors the convective fraction is 54% and the radiant fraction is 46%. Table 36B shows the division of the total heat gain into convective and radiant portions for all hours of the July design day in columns h and i. For 3:00 pm the calculation is:

The convective heat gain will immediately become a cooling load. The radiant portion of the heat gain will undergo a conversion process to cooling load that is modeled using the RTS factors for the room. The same RTS factors used in Part 1 for lighting load calculation will be applied to the wall calculation since the room conditions are the same. Table 34 lists these factors in the “non-solar RTS factors, zone type 8” column. Table 36B shows the result of this calculation in column k. The calculation for 3:00 pm is as follows:

Finally, the total wall cooling load is the sum of the convective and radiant loads. Table 36B shows these results in column l. For July 3:00 pm the calculation is as follows:

Part 3. Window cooling load without internal or external shading

Objective: Calculate the cooling load for the 3.72 m2 window facing 60° west of south for July 3:00 pm local standard time, without considering internal or external shading. Internal and external shading will be considered in Parts 4 and 5, respectively.

Solution: Determining the window cooling load requires calculation of: (a) the 24 h window heat gain profile, (b) the convective and radiant portions of the heat gain, (c) the conversion of the radiant heat gain into cooling load using RTS factors, and (d) the total window load as the sum of convective and radiant loads.

First calculate the window heat gain profile using Equations (12) to (15). Respectively, these equations calculate the direct beam solar heat gain qb, the diffuse solar heat gain qd, the conduction heat gain qc, and the total fenestration heat gain. The calculation uses solar irradiance and solar angle values calculated in Part 2. The solar irradiance and solar angle values along with the window heat gain results are shown in Table 37 in columns b through d and h through k. For July 3:00 pm (hour 15), for example, Part 2 calculated:

Table 37 Window Heat Gain for July (No Blinds or Overhang)

 

Beam Solar Heat Gain

 

Diffuse Solar Heat Gain

 

Conduction Heat Gain

 

Local Std Hour

Beam Normal Eb, W/m2

Surface Incident Angle θ

Surface Direct Beam Et,b, W/m2

Beam SHGC

Adjusted Beam IAC

Beam Solar Heat Gain, qb W

 

Diffuse Hor. Ed, W/m2

 

Sky Diffuse Et,d W/m2

 

Ground Diffuse Et,r W/m2

Subtotal Diffuse, W/m2

Hemis. SHGC

Diffuse Solar Heat Gain qd W

 

Outdoor Dry-Bulb, °C

Conduction Heat Gain, qc W

Total Window Heat Gain Q W

a

b

c

d

e

f

g

 

h

i

j

 

k

l

m

 

n

o

p

1

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

23.2

–8

–8

2

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

22.8

–13

–13

3

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

22.4

–17

–17

4

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

22.1

–21

–21

5

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

21.9

–24

–24

6

22.1

172.8

0.0

0

 

19.6

 

9.6

2.0

 

11.7

0.410

18

 

22.1

–21

–3

7

324.6

159.9

0.0

0

 

71.5

 

27.0

15.0

 

452.0

0.410

64

 

22.9

–12

52

8

525.5

146.3

0.0

0

 

105.9

 

31.8

33.8

 

65.7

0.410

100

 

24.8

11

111

9

641.9

132.7

0.0

0

 

129.9

 

33.3

53.1

 

86.4

0.410

132

 

26.9

36

168

10

712.3

119.2

0.0

0

 

146.6

 

33.7

70.1

 

103.8

0.410

158

 

28.8

58

217

11

754.0

105.9

0.0

0

 

157.5

 

33.7

83.0

 

116.7

0.410

178

 

30.6

79

257

12

775.2

93.0

0.0

0

 

163.4

 

33.7

80.6

 

124.3

0.410

189

 

31.7

92

281

13

779.4

80.5

128.1

0.170

1.000

81

 

164.6

 

50.1

82.2

 

142.3

0.410

217

 

32.6

102

400

14

767.3

68.9

275.6

0.320

1.000

328

 

161.2

 

69.8

87.7

 

157.5

0.410

240

 

33.1

109

677

15

737.0

58.69

383.0

0.400

1.000

570

 

153.0

 

86.4

77.5

 

163.9

0.410

250

 

33.1

109

929

16

683.0

50.6

433.6

0.436

1.000

703

 

139.4

 

98.2

62.4

 

160.6

0.410

245

 

32.4

101

1049

17

593.7

45.8

413.7

0.450

1.000

692

 

119.5

 

102.2

44.0

 

146.2

0.410

223

 

31.6

91

1005

18

443.7

45.5

311.2

0.451

1.000

521

 

91.1

 

92.1

24.5

 

116.6

0.410

178

 

30.4

78

777

19

181.4

49.6

117.6

0.439

1.000

192

 

49.4

 

51.8

7.6

 

59.4

0.410

91

 

28.7

57

340

20

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

27.5

43

43

21

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

26.5

31

31

22

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

25.5

19

19

23

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

24.7

10

10

24

0.0

0.0

0

 

0.0

 

0.0

0.0

 

0.0

0

 

23.9

0

0


From Chapter 15, Table 10, for glass type 5d,

The indoor attenuation coefficient (IAC) is 1.0 because internal shades are not considered in this calculation.

Then, applying Equations (12) to (15) for July 3:00 pm:

Next, divide the window heat gain into convective and radiant components. Because loads for windows without internal shading (blinds, drapes, etc.) are being calculated, the direct beam solar gain must be treated separately from the diffuse and conduction heat gains. The direct beam heat gain is treated as 100% radiant, and the conversion from heat gain to load uses special solar RTS factors different from those used to convert other types of radiant heat gain to load. Therefore, the total window heat gain must be divided into three parts: (1) the direct beam heat gain, (2) the radiant part of the conduction plus diffuse solar heat gain, and (3) the convective part of the conduction plus diffuse solar heat gain. In Table 38, columns b to d show the direct beam component of heat gain. For conduction and diffuse solar heat gains, Table 17 shows that for conduction heat gains through windows where the SHGC is less than 0.5, the convective fraction of the heat gain is 54% and the radiative fraction is 46%. Columns f to j in Table 38 show how the sum of diffuse solar and conduction heat gain is split into convective and radiant portions.

Table 38 Window Cooling Loads for July (No Blinds or Overhang)

Local Standard Hour

Unshaded Direct Beam Solar Cooling Load

 

Diffuse Solar + Conduction Cooling Load

Window Cooling Load, W

Beam Solar Heat Gain W

Convective Heat Gain 0%, W

Radiant Heat Gain 100%, W

 

Radiant Cooling Load, W

   

Diffuse Solar Heat Gain, W

Conduction Heat Gain, W

Total Heat Gain, W

Convective Heat Gain 54%, W

Radiant Heat Gain 46%, W

Convective Load W

Radiant, Cooling Load W

Total Cooling Load, W

a

b

c

d

 

e

     

f

g

h

i

j

k

l

m

n

1

0

0

0

 

31

     

0

–8

–8

–4

–4

–4

14

10

41

2

0

0

0

 

31

     

0

–13

–13

–7

–6

–7

11

4

35

3

0

0

0

 

31

     

0

–17

–17

–9

–8

–9

9

0

31

4

0

0

0

 

31

     

0

–21

–21

–11

–10

–11

6

–5

26

5

0

0

0

 

31

     

0

–24

–24

–13

–11

–13

4

–9

22

6

0

0

0

 

31

     

18

–21

–3

–2

–1

–2

7

6

37

7

0

0

0

 

31

     

64

–12

52

28

24

28

21

49

80

8

0

0

0

 

30

     

100

11

111

60

51

60

39

99

129

9

0

0

0

 

27

     

132

36

168

91

77

91

58

149

175

10

0

0

0

 

21

     

158

58

217

117

100

117

76

193

214

11

0

0

0

 

14

     

178

79

257

139

118

139

92

231

245

12

0

0

0

 

7

     

189

92

281

152

129

152

104

256

263

13

81

0

81

 

46

     

217

102

319

173

147

173

118

290

336

14

328

0

328

 

190

     

240

109

349

189

161

189

131

319

509

15

570

0

570

 

367

     

250

109

359

194

165

194

139

333

699

16

703

0

703

 

500

     

245

101

346

187

159

187

140

326

827

17

692

0

692

 

547

     

223

91

314

169

144

169

133

303

850

18

521

0

521

 

483

     

178

78

255

138

117

138

118

256

739

19

192

0

192

 

295

     

91

57

148

80

68

80

88

167

463

20

0

0

0

 

137

     

0

43

43

23

20

23

52

75

212

21

0

0

0

 

81

     

0

31

31

17

14

17

38

55

135

22

0

0

0

 

54

     

0

19

19

10

9

10

29

39

93

23

0

0

0

 

40

     

0

10

10

5

5

5

23

28

68

24

0

0

0

 

33

     

0

0

0

0

0

0

17

17

50


With the heat gains split into three categories, the conversion of heat gain to cooling load can be calculated for each radiant gain. First, for the load due to the direct beam solar heat gain is calculated using Equation (33). The solar RTS factors from Table 23 for medium weight construction, carpeted floor, and 50% window area will be used. These factors are also shown in Table 34 in the column titled “Solar RTS Factors, Room Type 8.” Cooling load results appear in column e of Table 38. For July 3:00 pm the calculation is as follows:

The cooling load due to the radiant portion of the diffuse solar and conduction window heat gain is also calculated with Equation (33). This time the non-solar RTS factors are used. These are the same factors used for conversion of lighting and wall conduction heat gains to load in Parts 1 and 2. The non-solar RTS factors are shown in Table 34 in the column titled “Non-Solar RTS Factors, Room Type 8.” Results appear in column l of Table 38.

The convective portion of the diffuse solar and conduction window heat gains immediately converts to load and is shown Table 38 column k. The total diffuse solar and conduction load is the sum of radiant and convective components and is shown in column m.

Finally, the total window load is the sum of the direct beam solar load, and the diffuse solar plus convective load. These loads are shown in Table 38 column n. For July 3:00 pm the calculation is

Part 4. Window cooling load with internal shading

Objective: Building on the window load calculation in Part 3, calculate the window load considering internal shading due to light-colored mini-blinds. Consider the same 3.72 m2 window facing 60° west of south for July 3:00 pm local standard time.

Solution: Calculation of the window cooling load requires the same four steps used in Part 3, but with different application data. Calculate: (a) the 24 h window heat gain profile, (b) the convective and radiant portions of the heat gain, (c) the conversion of the radiant heat gain into cooling load using RTS factors, and (d) the total window load as the sum of convective and radiant loads.

Calculation of the 24 h heat gain profiles requires consideration of the effect of the mini-blinds. This effect is calculated with indoor attenuation coefficients (IAC), and different radiant and convective fractions than an unshaded window.

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 mini-blinds, the IAC for beam radiation is treated separately from the IAC for diffuse solar gain. The direct beam IAC must be adjusted based on the profile angle of the sun.

The mini-blinds are assumed to be light colored with louver reflectance = 0.8 and louvers positioned at a 45° angle on double-glazed heat absorbing windows. Chapter 15 Table 14B lists IAC factors for window type 5d plus this shading type as IAC(0) = 0.74, IAC(60) = 0.65, IAC(diff) = 0.79, and radiant fraction = 0.54.

At 3:00 pm in July, the profile angle of the sun relative to the window surface is 58.4°. Using interpolation, the beam IAC is 0.652. The diffuse IAC is 0.79. As calculated in Part 3, SHGC(θ) = 0.400 and ⟨SHGC⟩D = 0.41. Thus, the window heat gains at 3:00 pm are

Calculation of beam solar heat gain is shown in Table 39 columns b through e. Calculation of the diffuse solar heat gain is shown in columns f through i. The conduction heat gain is found in column j.

Because internal shades are used, the direct beam solar heat gain is assumed to be absorbed by the shading device, and a portion immediately becomes a cooling load by convection. The remaining solar heat absorbed by the blind is assumed to be radiated to all surfaces of the room just as the diffuse and conduction heat gains are. As a result, the beam direct solar heat gain is combined with diffuse and conduction heat gains to obtain the total heat gain shown in column k of Table 39.

Next, the total heat gain is divided into convective and radiant portions. For window type 5d with mini-blinds, Chapter 15 Table 14B lists a radiant fraction as 0.54. Thus 54% of the heat gain is radiant and 46% is convective. These convective and radiant heat gains are shown in columns l and m in Table 39.

The radiant portion of the heat gain is converted to cooling load using Equation (33). In this equation the “Non-Solar RTS Factors, Zone Type 8” factors from Table 34 are used. Results appear in Table 39 in column o. The convective part of the heat gain immediately becomes a load and is shown in column n.

The total window load is then calculated combining the radiant and convective loads. Results are shown in Table 39 column p. For July 3:00 pm the calculation is

Part 5. Window cooling load with internal and external shading

Objective: Calculate the cooling load for the window in Part 4 with the addition of a 1.5 m overhang shading the window.

Solution: As in Parts 3 and 4, determining the window cooling load requires calculation of (a) the 24 h window heat gain profile, (b) the convective and radiant portions of the heat gain, (c) the conversion of the radiant heat gain into cooling load using RTS factors, and (d) the total window load as the sum of convective and radiant loads.

The diffuse solar and conduction heat gain profiles are the same as in Part 4 and are shown in columns h and i of Table 40. The direct beam solar heat gain profile must be recalculated accounting for the shading effect of the overhang. In Chapter 15, methods are described and examples provided for calculating the area of a window shaded by attached vertical or horizontal projections. For July 3:00 pm, the solar position calculated in previous parts of this example is:

From Chapter 15, Equation (33), profile angle Ω is calculated by

From Chapter 15, Equation (35), shadow height SH is

Because the window is 1.95 m tall, at July 3:00 pm the window is completely shaded by the 1.5 m deep overhang. Thus, the shaded window heat gain includes only diffuse solar and conduction gains for this hour. When the shadow height is less than 1.95 m then part of the window is exposed to direct beam solar. The sunlit area is calculated as A = 1.91(1.95 – Sh) where 1.91 is the window width in metres. The direct beam heat gain is then Sunlit Area × Et,b. Table 39 shows the profile angle, shadow height, sunlit area and direct beam heat gain in columns d through g. Note that the overhang shades the window completely for all hours except hours 16 through 19 when the solar altitude angle is low enough that part of the window is sunlit.

As in Part 4, due to the use of internal shading, direct beam solar heat gain is combined with diffuse solar and conduction heat gains to obtain the total heat gain shown in Table 40, column j. The total heat gain is divided using the 46% convective fraction and 54% radiative fraction used in Part 4 for a window with internal shades. These heat gain components are shown in Table 40, columns k and l.

The radiant heat gain is converted to cooling load using the “Non-Solar RTS Factors, Zone Type 8” from Table 34 as before. The radiant cooling load is shown in Table 40, column n. Combining with the convective load yields the total cooling load listed in Table 40, column o. For July 3:00 pm the total window cooling load is 280 W.

Part 6. Total room sensible cooling load.

Objective: Calculate the total sensible cooling load for the example office for July 3:00 pm local standard time.

Solution: To calculate the total sensible cooling load for the office, cooling loads for all ten heat gain components must be calculated and then summed.

Part 1 demonstrated the calculation of the lighting load. The same general procedure can be applied to calculating the occupant and equipment cooling loads using those component heat gains.

Part 2 demonstrated the calculation of the cooling load for the spandrel glass wall facing 60° west of true south. The same procedures can be used to calculate wall cooling loads for the other spandrel wall section and the two sections of brick wall. In addition, the same procedures can be used to calculate the roof load. Note that because the ceiling space is used as a return air plenum, we are assuming 30% of the roof load is directly absorbed by the return air and only the remaining 70% reaches the room.

Part 5 demonstrated the calculation of the cooling load for the window facing west of true south, with internal shading and external overhang shading. The same procedures can be used for the window facing east of true south.

Finally the 10 load components are summed to obtain the total sensible load for the room. Table 41 shows the 24 h component and total room load profiles for July. The total room load is in column l. The 3:00 pm load is 925 W.

9.2 EFFECT OF ORIENTATION ON PEAK COOLING LOAD MAGNITUDE AND TIME

A room cooling load is the combination of multiple load components, each driven by separate, independently varying heat gains. The peak room load occurs when the sum of all component loads is largest. This is often at a time when many of the individual component loads are not at their largest value. Among the heat gains driving loads in a room,

  • There are multiple different internal sources of heat gain whose intensity varies with time.

  • Opaque envelope heat gains are a function of the thermal properties of the assembly, surface area, outdoor and indoor dry-bulb temperature, and the orientation of the surface. Orientation affects when the surface is exposed to solar irradiance of varying intensities.

  • Fenestration heat gains are a function of the thermal and optical performance of the fenestration assembly, surface area, outdoor and indoor dry-bulb temperature, and orientation of the surface. Like opaque envelope components, orientation affects when the fenestration is exposed to solar irradiance of different intensities.

Orientation can significantly affect the peak time of individual opaque envelope and fenestration component loads. For example, driven by solar irradiance, an east-facing room will have peak opaque envelope and fenestration loads earlier in the day than a west-facing room. Orientation can also affect the time of year when peak loads occur. In the northern hemisphere, a south-facing window will experience a peak load during a fall month due to the solar altitude angle being lower so solar irradiance on the window is more intense than during summer months. Because of the effect of orientation, the time of peak load for individual envelope load components and for the room itself can be difficult to predict from intuition or experience for a specific building project. As a result the common practice is to calculate loads for a range of times of day and times of year, and then examine the results to identify the true peak load and time of load for individual rooms. Room load calculations are tedious by hand, but a multiple-hour calculation is feasible using a spreadsheet or software application for load calculation. When software is used, this typically involves calculating room loads for 24 h design cooling days corresponding to the 21st of each month. This section will demonstrate the importance of calculating loads for a wide range of times of day and times of year to determine the true peak load for rooms. If the range of times is too constrained, the engineer risks missing the true peak load and therefore under sizing airflow and thermal cooling capacity for the room.

Table 39 Window Cooling Loads for July (Blinds and no Overhang)

Local Standard Time

Surface Beam Irradiance Et,b, Btu/h-ft2

Beam SHGC

Beam IAC

Beam Solar Heat Gain, W

Total Diffuse Irradiance W/m2

Diffuse SHGC

Diffuse IAC

Diffuse Solar Heat Gain, W

Conduction Heat Gain, W

Total Heat Gain, W

Conv. Heat Gain (46%), W

Radiant Heat Gain (54%), W

Conv. Cooling Load, W

Radiant Cooling Load W

Total Window Cooling Load, W

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

1

0

0

0

0

–8

–8

–4

–4

–4

25

22

2

0

0

0

0

–13

–13

–6

–7

–6

22

16

3

0

0

0

0

–17

–17

–8

–9

–8

19

12

4

0

0

0

0

–21

–21

–10

–11

–10

17

7

5

0

0

0

0

–24

–24

–11

–13

–11

14

3

6

0

0

12

0.41

0.79

14

–21

–7

–3

–4

–3

17

14

7

0

0

42

0.41

0.79

51

–12

39

18

21

18

30

48

8

0

0

66

0.41

0.79

79

11

90

42

49

42

48

89

9

0

0

86

0.41

0.79

104

36

140

64

76

64

66

131

10

0

0

104

0.41

0.79

125

58

183

84

99

84

83

167

11

0

0

117

0.41

0.79

141

79

219

101

118

101

97

198

12

0

0

124

0.41

0.79

150

92

242

111

130

111

107

218

13

128

0.170

0.650

53

142

0.41

0.79

171

102

327

150

176

150

134

285

14

276

0.320

0.650

213

158

0.41

0.79

190

109

512

235

276

235

198

433

15

383

0.400

0.652

372

164

0.41

0.79

197

109

678

312

366

312

268

580

16

434

0.436

0.668

470

161

0.41

0.79

193

101

764

352

413

352

319

671

17

414

0.450

0.683

473

146

0.41

0.79

176

91

739

340

399

340

333

673

18

311

0.451

0.700

365

117

0.41

0.79

140

78

583

268

315

268

298

566

19

118

0.439

0.721

139

59

0.41

0.79

72

57

267

123

144

123

200

322

20

0

0

0

0

43

43

20

23

20

105

125

21

0

0

0

0

31

31

14

17

14

70

84

22

0

0

0

0

19

19

9

10

9

50

59

23

0

0

0

0

10

10

5

5

5

38

43

24

0

0

0

0

0

0

0

0

0

30

30


In section 9.1, a detailed cooling load calculation was presented for the example office for July 3:00 pm. This time was chosen because it is the time of peak outdoor air dry-bulb temperature in design-day weather profiles and historically has been assumed to be the time of peak room load. However, July 3:00 pm is not the time of true peak load for this room. It is not the largest load in July, and in fact, the true peak load occurs at September 5:00 pm. Tables 41 and 42 show the detailed load profiles for July and September, respectively. Comparing Tables 41 and 42, the July peak is at 5:00 pm and is 1022 W while the September peak in Table 42 is 1146 W at 5:00 pm (hour 17). The true peak is 12% larger than the July peak, and 24% larger than the July 3:00 pm load. Note that the internal load components are the same in July and September. The wall loads are smaller due to the cooler design-day outdoor temperatures in September and in spite of the higher solar irradiance on the walls. The roof load is also lower, due both to the cooler outdoor temperatures and lower intensity of solar irradiance on the horizontal roof surface. But the window loads are much larger due to the more intense solar irradiance, and this overcomes the reduction in wall and roof loads to result in a higher total room load than in July.


To illustrate the effect of orientation further, examine four copies of the example office, each rotated 90 from the other, as shown in Table 43. In the four cases, all room characteristics are the same except orientation. As the table shows the peak load times vary.

  • Case 1: With walls facing southeasterly and southwesterly, the peak time of September 5:00 pm is driven by the window loads due to more intense solar irradiance in fall months. This peak load is 24% larger than the July 3:00 pm load.

  • Case 2: Walls face northwesterly and southwesterly. This office also has a peak time of September 5:00 pm, driven by the same factors as Case 1. While the northwest-facing window will be less strongly affected by fall solar irradiance, the effect for the southwest-facing window is strong enough to drive the room peak to September. In this case the peak load is also 24% larger than the July 3:00 pm load for this room.

  • Case 3: Walls and windows face northerly directions and as a result window loads and wall loads are smaller. This reduces the effect of orientation and the peak time occurs at July 3:00 pm when outdoor dry-bulb is at its maximum value.

  • Case 4: Walls and windows face north-easterly and south-easterly. The southeasterly facing window has higher load during the fall months, but the northeasterly facing window does not. As a result this case behaves like Case 3, peaking in a summer month. Note the time of peak load is at 1:00 pm, earlier in the day than the other cases because its exterior surfaces face eastward. In this case the true peak is 3% larger than the July 3:00 pm load.

Finally, note that three of the four cases do not peak at July 3:00 pm. If loads were only calculated for July 3:00 pm due to intuition about when peak loads were likely to occur, much larger loads for two of the cases would be missed and supply airflow and thermal cooling capacity would be significantly undersized for these rooms.

Table 40 Window Cooling Loads for July (with Blinds and Overhang)

Local Standard Hour

Overhang and Fins Shading Calculations

 

Shaded Direct Beam + Diffuse + Conduction Cooling Load

Beam Solar Irradiance, W/m2

Surface Incident Angle θ

Profile Angle Ω

Shadow Height, m

Direct Sunlit Area, m2

Beam Solar Heat Gain, W

Diffuse Heat Gain, W

Conduction Heat Gain, W

Total Heat Gain, W

Conv. Heat Gain 46%, W

Radiant Heat Gain 54%, W

Conv. Cooling Load, W

Radiant, Cooling Load W

Total Cooling Load, W

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

1

0

 

0

0

–8

–8

–4

–4

–4

17

14

2

0

 

0

0

–13

–13

–6

–7

–6

14

8

3

0

 

0

0

–17

–17

–8

–9

–8

11

3

4

0

 

0

0

–21

–21

–10

–11

–10

9

–1

5

0

 

0

0

–24

–24

–11

–13

–11

6

–5

6

0

172.8

 

0

14

–21

–7

–3

–4

–3

9

6

7

0

159.9

 

0

51

–12

39

18

21

18

22

40

8

0

146.3

 

0

79

11

90

42

49

42

40

82

9

0

132.7

 

0

104

36

140

64

76

64

60

124

10

0

119.2

 

0

125

58

183

84

99

84

78

163

11

0

105.9

 

0

141

79

219

101

118

101

95

196

12

0

93.0

 

0

150

92

242

111

130

111

106

217

13

128

80.5

80.4

9.02

0.0

 

0

171

102

274

126

148

126

119

245

14

276

68.9

68.9

4.00

0.0

 

0

190

109

299

137

161

137

131

269

15

383

58.69

58.4

2.45

0.0

 

0

197

109

306

141

165

141

139

280

16

434

50.6

48.2

1.70

0.6

 

60

193

101

354

163

191

163

157

320

17

414

45.8

37.8

1.18

1.8

 

186

176

91

453

208

245

208

193

401

18

311

45.5

26.4

0.76

2.8

 

224

140

78

442

203

238

203

202

405

19

118

49.6

12.6

0.34

3.8

 

114

72

57

243

112

131

112

150

262

20

0

 

0

0

43

43

20

23

20

79

99

21

0

 

0

0

31

31

14

17

14

53

67

22

0

 

0

0

19

19

9

10

9

39

47

23

0

 

0

0

10

10

5

5

5

29

34

24

0

 

0

0

0

0

0

0

0

21

21


Table 41 Example Office Cooling Loads, July Design Day

 

Sensible Cooling Load, W

Local Standard Hour

Spandrel Wall – ψ = –30°

Spandrel Wall – ψ = +60°

Brick Wall – ψ = –30°

Brick Wall – ψ = +60°

Window ψ = –30°

Window ψ = +60°

Roof (70% to Room)

Overhead Lighting

Equipment

Occupants

Room Total

a

b

c

d

e

f

g

h

i

j

k

l

1

3

4

15

16

10

14

3

8

4

4

80

2

2

2

14

14

4

8

1

7

4

4

61

3

1

1

13

13

–1

3

–1

6

4

4

44

4

0

1

11

11

–6

–1

–2

6

3

4

27

5

0

0

10

10

–10

–5

–3

5

3

3

13

6

–1

–1

9

9

2

6

–4

4

2

3

30

7

–1

0

8

8

59

40

–5

85

2

2

197

8

3

1

7

7

108

82

–5

94

114

55

465

9

12

4

6

6

159

124

–4

99

119

61

586

10

21

8

6

5

201

163

–1

101

122

65

690

11

30

11

7

5

232

196

4

102

123

66

776

12

36

15

8

5

248

217

10

102

124

67

833

13

39

18

11

5

252

245

16

102

125

68

881

14

37

24

14

6

242

269

22

103

125

68

910

15

32

34

16

7

231

280

27

104

126

68

925

16

27

44

18

8

211

320

31

104

126

69

958

17

24

51

20

10

184

401

32

105

126

69

1022

18

21

53

20

12

151

405

32

106

15

17

832

19

18

49

21

14

108

262

29

25

9

10

546

20

15

38

21

16

65

99

25

16

6

7

307

21

11

24

20

18

49

67

20

11

5

6

231

22

8

14

19

18

36

47

14

9

4

5

177

23

6

9

18

18

27

34

10

8

4

4

138

24

4

6

16

17

16

21

6

7

4

4

100


Table 42 Example Office Cooling Loads, September Design Day

 

Sensible Cooling Load, W

Local Standard Hour

Spandrel Wall – ψ = –30°

Spandrel Wall – ψ = +60°

Brick Wall – ψ = –30°

Brick Wall – ψ = +60°

Window ψ = –30°

Window ψ = +60°

Roof (70% to room)

Overhead Lighting

Equipment

Occupants

Room Total

a

b

c

d

e

f

g

h

i

j

k

l

1

0

0

16

14

–15

–13

–2

8

4

4

16

2

–1

–1

14

13

–21

–18

–3

7

4

4

–4

3

–2

–2

12

11

–27

–22

–5

6

4

4

–21

4

–3

–3

10

10

–33

–26

–6

6

3

4

–39

5

–4

–3

9

8

–38

–30

–7

5

3

3

–54

6

–4

–4

7

7

–38

–29

–8

4

2

3

–60

7

–4

–4

6

6

84

–8

–8

85

2

2

159

8

0

–3

5

5

271

32

–9

94

114

55

564

9

13

–1

4

4

336

74

–8

99

119

61

701

10

29

2

4

3

322

111

–6

101

122

65

753

11

41

6

5

3

261

141

–2

102

123

66

747

12

50

10

8

2

237

173

4

102

124

67

776

13

53

16

12

3

230

204

10

102

125

68

823

14

51

28

16

3

215

227

16

103

125

68

851

15

44

41

20

4

187

387

20

104

126

68

1001

16

35

52

23

6

154

533

23

104

126

69

1127

17

25

59

25

9

123

580

24

105

126

69

1146

18

18

58

26

12

86

377

23

106

15

17

737

19

13

46

26

15

48

107

20

25

9

10

319

20

9

28

25

17

32

61

15

16

6

7

217

21

6

15

23

18

19

35

11

11

5

6

148

22

4

8

22

18

9

17

6

9

4

5

102

23

2

4

20

17

0

4

3

8

4

4

67

24

1

2

17

16

–11

–6

0

7

4

4

33

Table 43 Room Peak Cooling Loads for Different Room Orientations

Case

Surface Azimuth, Exposure 1

Surface Azimuth, Exposure 2

Time of True Peak Load

True Peak Room Load, W

Room Load at July 3:00 pm, W

1 (SE,SW)

–30°

+60°

Sept 5:00 pm

1146

925

2 (SW,NW)

+60°

+150°

Sept 5:00 pm

1138

916

3 (NW, NE)

+150°

–120°

July 3:00 pm

869

869

4 (NE,SE)

–120°

–30°

July 1:00 pm

902

880

Total

4055


Table 44 Peak Heating Load Calculation

Opaque Envelope Component

U-factor, W/(m2·K)

 

Area, m2

 

(Indoor DB – Outdoor DB), K

 

Heating Load, W

Windows

3.180

×

(3.72 + 3.72)

×

(22.2 – (–5.6))

=

658

Spandrel Walls

0.278

×

(5.57 + 5.57)

×

(22.2 – (–5.6))

=

86

Brick Walls

0.261

×

(5.57 + 3.72)

×

(22.2 – (–5.6))

=

67

Roof

0.165

×

12.08

×

(22.2 – (–5.6))

=

55

Infiltration Component

Infiltration Cs, J/°K

 

Infiltration Flow Rate Qs, L/s

 

(Indoor DB – Outdoor DB), K

 

Heating Load, W

Infiltration

1.206

×

9.2

×

(22.2 – (–5.6))

=

308

Total

           

Heating Load, W

Total Room Load

 

 

 

1174


9.3 EFFECT OF COOLING LOAD DIVERSITY ON PEAK COINCIDENT LOAD

Previous sections of this example focused on calculation of peak cooling loads for individual rooms. Room loads are important for sizing supply airflow rates and cooling capacities for individual rooms when using room by room equipment such as water source heat pumps or fan coil units. However, the calculation of the peak coincident load also has relevance for building projects. The peak coincident load is the largest simultaneous load among all rooms in a building, or in a portion of a building such as a floor. This is also sometimes referred to as the “peak block load.” The peak coincident load can be used for a preliminary assessment of airflow capacity or thermal capacity for the project. For example, a central VAV AHU only needs sufficient airflow capacity to meet the simultaneous peak of rooms it serves, rather than the sum of individual room peak airflow rates. A central chiller plant only needs enough capacity to meet the simultaneous peak load of AHUs or fan-coil units it serves rather than the sum of individual AHU or fan-coil peak loads.

When determining the peak coincident load it is important not to sum the individual peak room loads. Rather, room loads should be calculated for a wide range of times of day and times of year. Then for each hour, sum the room loads to obtain an hourly coincident load. Review the resulting hourly coincident loads across all hours calculated to identify the peak value. This section will illustrate the concept of calculating the peak coincident load.

Instead of calculating the peak coincident load for a full-scale building, this example will consider a simplified case where a building contains only the four corner offices described in section 9.2 First, loads for the four offices were calculated for a 24 h design day for the 21st of each month. For each hour the resulting loads were summed to obtain an hourly coincident load. Then the largest coincident load was identified. The peak coincident load is 3782 W at July 5:00 pm.

In this example, the peak coincident load was at a different time than all four individual room peaks shown in Table 43. Further the peak coincident load is 7% less than the sum of individual room peak loads shown at the bottom of Table 43. This difference between the peak coincident load and the “sum of the peaks” load is known as load diversity. Although the diversity of 7% is relatively small in this simple example, it can be much larger in a full scale building. The ultimate effect of load diversity is that central HVAC equipment serving multiple rooms can be sized for a peak load that is often considerably less than the sum of the individual peaks of those rooms.

9.4 SINGLE-ROOM DETAILED HEATING LOAD EXAMPLE

Although the physics of heat transfer that creates heating loads is identical to that for cooling loads, a number of traditionally used simplifying assumptions facilitate a much simpler procedure for peak heating load calculation. As described in the section 7.1, Heat Loss Calculations, design heating load calculations typically assume a single outdoor temperature with no heat gain from solar or internal sources, under steady-state conditions. Thus, space heating load is determined by computing the instantaneous heat transfer rate through building envelope elements (UA ΔT) plus heat required because of outdoor air infiltration.

Room heating load.

Objective: Calculate the peak heating load for the example office.

Solution: Calculation of the individual component heating loads and the total room heating load is shown in Table 44.

For the opaque envelope components, the calculation is UA ΔT. For the Example City location the 99.6% heating design dry-bulb is –5.6°C. The indoor design temperature is 22.2°C. Because solar heat gain is not considered in calculating peak heating loads, similar envelope elements can be combined without regard to orientation. For example the two spandrel wall sections can be combined in a single component load calculation. For this example the U-factors used for cooling calculations were also used for the heating load calculation. In some climates, higher prevalent winds in winter should be considered in calculating U-factors. Chapter 25 provides information on calculating U-factors and surface heat transfer coefficients appropriate for local wind conditions.

For heating conditions an infiltration rate of 1 air change per hour was assumed. The room volume with a 2.74 m floor to ceiling height is 2.74 × 12.1 = 33.2 m3 = 33 200 L. Therefore, the infiltration flow rate at one air change per hour is (33 200 L/h)/(3600 s/h) = 9.2 L/s. With these airflows, infiltration load can be computed using Equation (9) as shown in Table 44.

The total heating load, shown in the last row of Table 44, is 1174 W.

9.5 CONCLUSION

The example problem illustrates key issues that should be understood and accounted for in calculating peak room cooling and heating loads:

  • Room peak cooling and heating loads result from many independently varying sources of heat gain or loss.

  • For cooling loads, the sensible heat gain profile must be determined first and then divided into convective and radiant components. The load due to the radiant component of heat gain is calculated considering the dynamic conversion of radiant heat gain to load using RTS factors. Finally, the sensible room load is computed as convective load plus radiant load.

  • Peak room cooling loads occur at different times of day and times of year depending on the orientation of exterior walls and fenestration. Calculating loads for a single point in time may miss the true peak load and therefore risks under sizing supply airflow and thermal cooling capacity for the room. Instead, peak room loads should be calculated for a range of times of day and times of year to identify the true peak cooling load.

  • The relative importance of each cooling and heating load component varies, depending on the portion of the building being considered. Characteristics of a particular window may have little effect on the entire building load, but could have a significant effect on the supply airflow to the room where the window is located and thus on the comfort of the occupants of that space.

  • The peak block load is valuable for preliminary assessments of airflow or thermal capacity for an entire building or a portion of the building such as a floor. To accurately identify the peak block load, room loads must first be computed over a range of times of day and times of year and then summed for each hour to obtain the block load for each hour. The peak block load is identified from the profile of hourly block loads.

10. PREVIOUS COOLING LOAD CALCULATION METHODS

Procedures described in this chapter are the most current and scientifically derived means for estimating cooling load for a defined building space, but methods in earlier editions of the ASHRAE Handbook are valid for many applications. These earlier procedures are simplifications of the heat balance principles, and their use requires experience to deal with atypical or unusual circumstances. In fact, any cooling or heating load estimate is no better than the assumptions used to define conditions and parameters such as physical makeup of the various envelope surfaces, conditions of occupancy and use, and ambient weather conditions. Experience of the practitioner can never be ignored.

The primary difference between the HB and RTS methods and the older methods is the newer methods’ direct approach, compared to the simplifications necessitated by the limited computer capability available previously.

The transfer function method (TFM), for example, required many calculation steps. It was originally designed for energy analysis with emphasis on daily, monthly, and annual energy use, and thus was more oriented to average hourly cooling loads than peak design loads.

The total equivalent temperature differential method with time averaging (TETD/TA) has been a highly reliable (if subjective) method of load estimating since its initial presentation in the 1967 Handbook of Fundamentals. Originally intended as a manual method of calculation, it proved suitable only as a computer application because of the need to calculate an extended profile of hourly heat gain values, from which radiant components had to be averaged over a time representative of the general mass of the building involved. Because perception of thermal storage characteristics of a given building is almost entirely subjective, with little specific information for the user to judge variations, the TETD/TA method’s primary usefulness has always been to the experienced engineer.

The cooling load temperature differential method with solar cooling load factors (CLTD/CLF) attempted to simplify the two-step TFM and TETD/TA methods into a single-step technique that proceeded directly from raw data to cooling load without intermediate conversion of radiant heat gain to cooling load. A series of factors were taken from cooling load calculation results (produced by more sophisticated methods) as “cooling load temperature differences” and “cooling load factors” for use in traditional conduction (q = UAΔt) equations. The results are approximate cooling load values rather than simple heat gain values. The simplifications and assumptions used in the original work to derive those factors limit this method’s applicability to those building types and conditions for which the CLTD/CLF factors were derived; the method should not be used beyond the range of applicability.

Although the TFM, TETD/TA, and CLTD/CLF procedures are not republished in this chapter, those methods are not invalidated or discredited. Experienced engineers have successfully used them in millions of buildings around the world. The accuracy of cooling load calculations in practice depends primarily on the availability of accurate information and the design engineer’s judgment in the assumptions made in interpreting the available data. Those factors have much greater influence on a project’s success than does the choice of a particular cooling load calculation method.

The primary benefit of HB and RTS calculations is their somewhat reduced dependency on purely subjective input (e.g., determining a proper time-averaging period for TETD/TA; ascertaining appropriate safety factors to add to the rounded-off TFM results; determining whether CLTD/CLF factors are applicable to a specific unique application). However, using the most up-to-date techniques in real-world design still requires judgment on the part of the design engineer and care in choosing appropriate assumptions, just as in applying older calculation methods.

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Kusuda, T. 1969. Thermal response factors for multilayer structures of various heat conduction systems. ASHRAE Transactions 75(1):246.

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Todorovic, B. 1982. Cooling load from solar radiation through partially shaded windows, taking heat storage effect into account. ASHRAE Transactions 88(2):924-937.

Todorovic, B. 1984. Distribution of solar energy following its transmittal through window panes. ASHRAE Transactions 90(1B):806-815.

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The preparation of this chapter is assigned to TC 4.1, Load Calculation Data and Procedures.