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.
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):
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
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.
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)]:
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:
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.
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.