Lender Deleveraging/ Acquisition Profile HEP Acquisitions Doug Spitler John Pierce.
PRF Spitler Fisher 99
Transcript of PRF Spitler Fisher 99
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ABSTRACT
Harris and McQuiston (1988) developed conductiontransfer function (CTF) coefficients corresponding to 41 repre-sentative wall assemblies and 42 representative roof assem-blies for use with the transfer function method (TFM). Theyalso developed a grouping procedure that allows design engi-neers to determine the correct representative wall or roofassembly that most closely matches a specific wall or roofassembly. The CTF coefficients and the grouping procedurehave been summarized in the ASHRAE Handbook —Funmentals (1989, 1993, 1997) and the ASHRAE Cooling aHeating Load Calculation Manual, second edition (McQuiton and Spitler 1992).
More recently, a new, simplified design cooling loacalculation procedure, the radiant time series method (RTShas been developed (Spitler et al. 1997). The RTSM uses odic response factors to model transient conductive heat trafer. While not a true manual load calculation procedure, it quite feasible to implement the RTSM in a spreadsheet. Tuseful in such an environment, it would be desirable to havpre-calculated set of periodic response factors. Accordinglyset of periodic response factors has been calculated anpresented in this paper.
INTRODUCTION
The transfer function method (TFM) for design coolingload calculations has been in use for a number of years. Thismethod uses conduction transfer functions (CTFs) to calculatethe transient, one-dimensional conduction through the build-ing wall and roof elements. Conduction transfer functions area closed form representation of a conduction response factorseries. Conduction response factors, as derived by Mitalas and
ASHRAE Transactions: Symposia
da-nd
s-
dM),peri-ns-iso bee a, a
d is
Stephenson (1967) and Hittle (1981), are an exact solution tothe transient conductive heat transfer problem for a multi-layer wall or roof with boundary conditions that can be repre-sented by a piecewise linear profile. The response factor seriesis infinite, so in practice it must be truncated, resulting in someminor, but controllable, loss of accuracy. Stephenson andMitalas (1967) compared a response factor method to ananalog computer simulation and showed that for the one-hourtime steps commonly used in building energy and thermal loadcalculations, the expected error due to truncation of the infi-nite response factor series is small. Procedures for developingconduction transfer functions from response factors aredescribed by Peavy (1978) and Hittle (1981). The methods arenecessarily inexact but have been compared to both analyticaland numerical solutions with excellent results. Maloney(1985) showed that for a one-dimensional, transient slab withlinearly varying surface temperatures, the differences betweena CTF solution and an analytical solution based on Duhammethod are negligible.
ASHRAE research project RP-472 provided a set conduction transfer function coefficients (Harris and McQuiton 1988) corresponding to 41 representative roof types 42 representative wall types. In addition, a grouping procdure was developed so that, theoretically, any wall or rocould be mapped into one of the representative wall types. walls are mapped using four parameters: primary wall marial (the most thermally massive element), secondary wmaterial, R-value, and the thermal mass location (in, out,integral). Roofs are also mapped using four parameteprimary roof material, thermal mass location, R-value, apresence or absence of a suspended ceiling. Once the resentative wall or roof type has been identified, the CTF coficients may be “unnormalized” so that the U-factor of th
Development of Periodic Response Factors for Use with the Radiant Time Series Method
Jeffrey D. Spitler, Ph.D., P.E. Daniel E. Fisher, Ph.D. Member ASHRAE Member ASHRAE
Jeffrey D. Spitler is associate professor at Oklahoma State University, Stillwater. Daniel E. Fisher is senior research engineer at the Universityof Illinois at Urbana-Champaign.
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actual wall or roof is preserved in the CTF coefficients. Oncethe coefficients have been determined, they are applied usingthe conduction transfer function:
(1)
Since originally appearing in the 1989 ASHRAE Hand-book—Fundamentals, the tabulated CTF coefficients haveproved to be useful to designers. The radiant time seriesmethod (RTSM) uses periodic response factors to model tran-sient conductive heat transfer:
(2)
Since the RTSM is amenable to spreadsheet-level imple-mentation, a tabulated set of periodic response factors is auseful addition to the literature. The objective of this paper isto present a set of periodic response factors that correspondexactly to the CTFs previously published. If desired, they canbe used with exactly the same grouping procedure and aslightly different “unnormalization” procedure.
METHODOLOGY
Periodic response factors can be derived directly fromset of CTF coefficients. The procedure is discussed in gredetail in another paper (Spitler and Fisher 1999), butpresented here to document the method to generate the odic response factors directly from the tabulated CTF coecients. The periodic response factors developed with tprocedure yield exactly the same results as the conductransfer functions, if the boundary conditions (sol-air tempatures) are steady periodic. Table 1 defines the terms usethe discussion.
Noting that a fundamental property of conduction tranfer functions is that Σbn = Σcn, the general CTF equation (1can be written out for each hour to form a set of 24 houequations, as follows:
(3a)
(3b)
(3c)
The 24 hourly equations can be rearranged and writtea matrix form, as shown in Equation 4.
qθ″
bnTe θ nδ–, dnqθ nδ–″
Trc–n 1=
6
∑ cn
n 0=
6
∑–n 0=
6
∑=
qθ″
YPjTe θ jδ–, Trc– YPj
j 0=
23
∑j 0=
23
∑=
q1″
bnTe 1 nδ–, dnq1 nδ–″
Trc–n 1=
6
∑ bn
n 0=
6
∑–n 0=
6
∑=
q2″
bnTe 2 nδ–, dnq2 nδ–″
Trc–n 1=
6
∑ bnn 0=
6
∑–n 0=
6
∑=
q24″
bnTe 24 nδ–, dnq24 nδ–″
Trc–n 1=
6
∑ bn
n 0=
6
∑–n 0=
6
∑=
492
aater isperi-ffi-histioner-d in
s-)rly
n in
(4)
Equation 4 can be rearranged and represented msimply as:
q´´ = D-1 B Te − D-1 B Trc = D-1 B (Te − Trc) (5)
TABLE 1 Nomenclature
Subscripts
q´´ heat flux, (Btu/h)/ft2 (W/m2) P periodic
T temperature, ºF (°C) j index
b, d, c conduction transfer function coefficients
n index
Y periodic response factors δ timeinterval, h
Matrices e sol-air
q´´ column vector containing conductive heat fluxes
rc constant room air
Te column vector containing sol-air temperatures
θ current hour
B, D b and d CTF coefficient matrices
Y periodic response factor matrix
Trc column vector containing Trc in every row
1 0 0 … d3 d2 d1
d1 1 0 0 … d2
d2 d1 1 0 0 …
…
… d3 d2 d1 1
q1″
q2″
q3″
…
q1
″
•
b0 0 0 … b2 b1
b1 b0 0 0 … b2
b2 b1 b0 0 0 …
…
b4 b3 b2 b1 b0
Te 1,
Te 2,
Te 3,
…
Te 24,
TrcΣbn
…
TrcΣbn
–•=
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E
41 42ers 11,
reheal
F
orel
ri-singreith
ne
ighl or
cy,wallE
where
D = the left-hand side coefficient matrix,
q´´ = the column vector containing the conductive heat fluxes,
B = the right-hand side coefficient matrix,
Te = the column vector containing the sol-air temperatures,
Trc = a column vector containing Trc in every row.
Similarly, the response factor equations can be writtena matrix formulation, as in Equation 6.
(6)
Equation 6 can be represented as:
q´´ = Y Te − Y Trc = Y(Te − Trc) (7)
where
q´´ = the column vector containing the conductive heat fluxes,
Y = the periodic response factor matrix,
Te = the column vector containing the sol-air temperatures,
Trc = a column vector containing Trc in every row.
Together, Equations 5 and 7 yield the following relatioship between the conduction transfer functions and the podic response factors:
Y = D-1 B. (8)
Consequently, the periodic response factors can be demined from the matrix, D-1 B. In fact, the first column of D-1
B is a column vector containing YP0,YP1,YP2, …, YP23.
q1″
q2″
q3″
…
q24″
YP0 YP23 YP22 …
YP2 YP1
YP1 YP0 YP23 YP22 … YP2
YP2 YP1 YP0 YP23 YP22 …
…
YP2 YP1 YP0
=
•
Te 1,
Te 2,
Te 3,
…
Te 24,
TrcΣYPn
…
TrcΣYPn
–
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In order to generate the periodic response factors, following algorithm was implemented in a FORTRANprogram: • Read wall and roof CTF coefficients from the ASHRA
RP-626 database. (Falconer et al. 1993).• Fill D and B matrices.• Calculate D-1 and D-1 B.• Extract periodic response factors from D-1 B.• Output results in tabular form.
RESULTS AND DISCUSSION
Periodic response factors were calculated for the representative wall types summarized in Table 2 and therepresentative roof types summarized in Table 3. The layare described using the code numbers detailed in Tablechapter 28, 1997 ASHRAE Handbook—Fundamentals.
The periodic response factors are given in Tables 4through 9. They are given to accuracy of six decimal places,which should be more than sufficient for any practical appli-cation. SI versions of the periodic response factors are tabu-lated in the appendix in Tables A-1 through A-6.
APPLICATION
The representative wall types and roof types may beselected using exactly the same procedure as originally givenby Harris and McQuiston (1988) and later described inASHRAE Fundamentals (ASHRAE 1989, 1993, 1997) andCooling and Heating Load Calculation Manual, secondedition (McQuiston and Spitler 1992). However, if this proce-dure is used, a slightly different “unnormalization” proceduis necessary. (The “unnormalization” procedure modifies tCTF coefficients so that they reflect the U-factor of the actuwall rather than the U-factor of the typical wall.) The CTcoefficients are “unnormalized” by multiplying the b coeffi-cients by the ratio of the actual U-factor to the typical wall roof’s U-factor. To “unnormalize” the periodic responsfactor, each Y coefficient is multiplied by the ratio of the actuaU-factor to the typical wall or roof’s U-factor.
Finally, the error associated with using the tabulated peodic response factors is the same as that associated with uthe tabulated CTF coefficients. The grouping procedudeveloped by Harris and McQuiston (1988) was designed wtwo criteria:
1. The typical wall or roof has a peak heat gain within ± ohour of the actual wall or roof.
2. The typical wall or roof has a peak heat gain at least as has, but no more than 20% higher than, the actual walroof.
If users of the RTSM desire a higher degree of accuraperiodic response factors may be calculated for the actual or roof type using software developed as part of ASHRA875-RP. (Pedersen et al. 1998).
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TABLE 2 Wall Types
Layers (Inside to Outside) Description U (Btu/h⋅ft2 °F) U (W/m2 K)
1 E0 A3 B1 B13 A3 A0 Steel siding with 4 in. (100 mm) insulation 0.066 0.375
2 E0 E1 B14 A1 A0 Frame wall with 5 in. (125 mm) insulation 0.055 0.312
3 E0 C3 B5 A6 A0 4 in. (100 mm) h.w. concrete block with 1 in. (25 mm) insulation 0.191 1.084
4 E0 E1 B6 C12 A0 2 in. (50 mm) insulation with 2 in. (50 mm) h.w. concrete 0.047 0.267
5 E0 A6 B21 C7 A0 1.36 in. (35 mm) insulation with 8 in. (200 mm) l.w. concrete block 0.129 0.732
6 E0 E1 B2 C5 A1 A0 1 in. (25 mm) insulation with 4 in. (100 mm) h.w. concrete 0.199 1.130
7 E0 A6 C5 B3 A3 A0 4 in. (100 mm) h.w. concrete with 2 in. (50 mm) insulation 0.122 0.693
8 E0 A2 C12 B5 A6 A0 Face brick and 2 in. (50 mm) h.w. concrete with 1 in. (25 mm) insul. 0.195 1.107
9 E0 A6 B15 B10 A0 6 in. (150 mm) insulation with 2 in. (50 mm) wood 0.042 0.238
10 E0 E1 C2 B5 A2 A0 4 in. (100 mm) l.w. conc. block with 1 in. (25 mm) insul. and face brick 0.155 0.880
11 E0 E1 C8 B6 A1 A0 8 in. (200 mm) h.w. concrete block with 2 in. (50 mm) insulation 0.109 0.619
12 E0 E1 B1 C10 A1 A0 8 in. (200 mm) h.w. concrete 0.339 1.925
13 E0 A2 C5 B19 A6 A0 Face brick and 4 in. (100 mm) h.w. concrete with 0.61 in. (16 mm) ins. 0.251 1.425
14 E0 A2 A2 B6 A6 A0 Face brick and face brick with 2 in. (50 mm) insulation 0.114 0.647
15 E0 A6 C17 B1 A7 A0 8 in. (200 mm) l.w. concrete block (filled) and face brick 0.092 0.522
16 E0 A6 C18 B1 A7 A0 8 in. (200 mm) h.w. concrete block (filled) and face brick 0.222 1.261
17 E0 A2 C2 B15 A0 Face brick and 4 in. (100 mm) l.w. conc. block with 6 in. (150 mm) ins. 0.043 0.244
18 E0 A6 B25 C9 A0 3.33 in. (85 mm) insulation with 8 in. (200 mm) common brick 0.072 0.409
19 E0 C9 B6 A6 A0 8 in. (200 mm) common brick with 2 in. (50 mm) insulation 0.106 0.602
20 E0 C11 B19 A6 A0 12 in. (300 mm) h.w. concrete with 0.61 in. (15 mm) insulation 0.237 1.346
21 E0 C11 B6 A1 A0 12 in. (300 mm) h.w. concrete with 2 in. (50 mm) insulation 0.112 0.636
22 E0 C14 B15 A2 A0 4 in. (100 mm) l.w. concrete with 6 in. (150 mm) insul. and face brick 0.040 0.227
23 E0 E1 B15 C7 A2 A0 6 in. (150 mm) insulation with 8 in. (200 mm) l.w. concrete block 0.042 0.238
24 E0 A6 C20 B1 A7 A0 12 in. (300 mm) h.w. concrete block (filled) and face brick 0.196 1.113
25 E0 A2 C15 B12 A6 A0 Face brick and 6 in. (150 mm) l.w. conc. blk. with 3 in. (75 mm) insul. 0.060 0.341
26 E0 A2 C6 B6 A6 A0 Face brick and 8 in. (200 mm) clay tile with 2 in. (50 mm) insulation 0.097 0.551
27 E0 E1 B14 C11 A1 A0 5 in. (125 mm) insulation with 12 in. (300 mm) h.w. concrete 0.052 0.295
28 E0 E1 C11 B13 A1 A0 12 in. (300 mm) h.w. concrete with 4 in. (100 mm) insulation 0.064 0.363
29 E0 A2 C11 B5 A6 A0 Face brick and 12 in. (300 mm) h.w. concrete with 1 in. (25 mm) insul. 0.168 0.954
30 E0 El B19 C19 A2 A0 0.61 in. (15 mm) ins. with 12 in. (300 mm) l.w. blk. (fld.) and face brick 0.062 0.352
31 E0 E1 BI5 C15 A2 A0 6 in. (150 mm) insul. with 6 in. (150 mm) l.w. conc. and face brick 0.038 0.216
32 E0 E1 B23 B9 A2 A0 2.42 in. (60 mm) insulation with face brick 0.069 0.392
33 E0 A2 C6 BI5 A6 A0 Face brick and 8 in. (200 mm) clay tile with 6 in. (150 mm) insulation 0.042 0.238
34 E0 C11 B21 A2 A0 12 in. (300 mm) h.w. conc. with 1.36 in. (35 mm) insul. and face brick 0.143 0.812
35 E0 E1 B14 C11 A2 A0 5 in. (125 mm) insul. with 12 in. (300 mm) h.w. conc. and face brick 0.052 0.295
36 E0 A2 C11 B25 A6 A0 Face brick and 12 in. (300 mm) h.w. conc. with 3.33 in. (85 mm) insul. 0.073 0.414
37 E0 E1 B25 C19 A2 A0 3.33 in. (85 mm) ins. with 12 in. (300 mm) l.w. blk. (fld.) and face brick 0.040 0.227
38 E0 E1 B15 C20 A2 A0 6 in. (150 mm) ins. with 12 in. (300 mm) h.w. block (fld.) and face brick 0.041 0.233
39 E0 A2 C16 B14 A6 A0 Face brick and 8 in. (200 mm) l.w. concrete with 5 in. (125 mm) insul. 0.040 0.227
40 E0 A2 C20 B15 A6 A0 Face brick, 12 in. (300 mm) h.w. block (fld.), 6 in. (150 mm) insul. 0.041 0.233
41 E0 E1 C11 B14 A2 A0 12 in. (300 mm) h.w. conc. with 5 in. (125 mm) insul. and face brick 0.052 0.295
ASHRAE Transactions: Symposia 495
TABLE 3 Roof Types
Layers (Inside to Outside) DescriptionU
(Btu/h⋅ft2 °F)U
(W/m2 K)
1 E0 A3 B25 E3 E2 A0 Steel deck with 3.33 in. (85 mm) insulation 0.080 0.454
2 E0 A3 BI4 E3 E2 A0 Steel deck with 5 in. (125 mm) insulation 0.055 0.312
3 E0 E5 E4 C12 E3 E2 A0 2 in. (50 mm) h.w. concrete deck with suspended ceiling 0.232 1.317
4 E0 E1 BI5 E4 B7 A0 Attic roof with 6 in. (150 mm) insulation 0.043 0.244
5 E0 BI4 C12 E3 E2 A0 5 in. (125 mm) insulation with 2 in. (50 mm) h.w. concrete deck 0.055 0.312
6 E0 C5 BI7 E3 E2 A0 4 in. (100 mm) h.w. concrete deck with 0.3 in. (8 mm) insulation 0.371 2.107
7 E0 B22 C12 E3 E2 C12 A0 1.67 in. (40 mm) insulation with 2 in. (50 mm) h.w. concrete RTS 0.138 0.784
8 E0 B16 C13 E3 E2 A0 0.15 in. (4 mm) insul. with 6 in. (150 mm) h.w. concrete deck 0.424 2.407
9 E0 E5 E4 B12 C14 E3 E2 A0 3 in. (75 mm) insul. with 4 in. (100 mm) l.w. conc. deck and susp. clg. 0.057 0.324
10 E0 E5 E4 C15 B16 E3 E2 A0 6 in. (150 mm) l.w. conc. dk with 0.15 in. (4 mm) ins. and susp. clg. 0.104 0.591
11 E0 C5 BI5 E3 E2 A0 4 in. (100 mm) h.w. concrete deck with 6 in. (150 mm) insulation 0.046 0.261
12 E0 C13 B16 E3 E2 CI2 A0 6 in. (150 mm) h.w. deck with 0.15 in. (4 mm) ins. and 2 in. (50 mm) h.w. RTS 0.396 2.248
13 E0 C13 B6 E3 E2 A0 6 in. (150 mm) h.w. concrete deck with 2 in. (50 mm) insulation 0.117 0.664
14 E0 E5 E4 C12 B13 E3 E2 A0 2 in. (50 mm) 1 w. conc. deck with 4 in. (100 mm) ins. and susp. clg. 0.057 0.324
15 E0 E5 E4 C5 B6 E3 E2 A0 1 in. (25 mm) insul. with 4 in. (100 mm) h.w. conc. deck and susp. clg. 0.090 0.511
16 E0 E5 E4 CI3 B2O E3 E2 A0 6 in. (150 mm) h.w. deck with 0.76 in. (20 mm) insul. and susp. clg. 0.140 0.795
17 E0 E5 E4 B15 C14 E3 E2 A0 6 in. (150 mm) insul. with 4 in. (100 mm) l.w. conc. deck and susp. clg. 0.036 0.204
18 E0 CI2 B15 E3 E2 C5 A0 2 in. (50 mm) h.w. conc. dk with 6 in. (150 mm) ins. and 2 in. (50 mm) h.w. RTS 0.046 0.261
19 E0 C5 B27 E3 E2 C12 A0 4 in. (100 mm) h.w. deck with 4.54 in. (115 mm) ins. and 2 in. (50 mm) h.w. RTS 0.059 0.335
20 E0 B21 C16 E3 E2 A0 1.36 in. (35 mm) insulation with 8 in. (200 mm) l.w. concrete deck 0.080 0.454
21 E0 CI3 B12 E3 E2 C12 A0 6 in. (150 mm) h.w. deck with 3 in. (75 mm) insul. and 2 in. (50 mm) h.w. RTS 0.083 0.471
22 E0 B22 C5 E3 E2 C13 A0 1.67 in. (40 mm) ins. with 4 in. (100 mm) h.w. deck and 6 in. (150 mm) h.w. RTS 0.129 0.732
23 E0 E5 E4 C12 B14 E3 E2 C12 A0 Susp. clg, 2 in. (50 mm) h.w. dk, 5 in. (125 mm) ins, 2 in. (50 mm) h.w. RTS 0.047 0.267
24 E0 E5 E4 C5 E3 E2 B6 B1 C12 A0 Susp. clg, 4 in. (100 mm) h.w. dk, 2 in. (50 mm) ins, 2 in. (50 mm) h.w. RTS 0.082 0.466
25 E0 E5 E4 C13 B13 E3 E2 A0 6 in. (150 mm) h.w. conc. deck with 4 in. (100 mm) ins. and susp. clg. 0.056 0.318
26 E0 E5 E4 B15 C15 E3 E2 A0 6 in. (150 mm) insul. with 6 in. (150 mm) l.w. conc. deck and susp. clg. 0.034 0.193
27 E0 C13 B15 E3 E2 C12 A0 6 in. (150 mm) h.w. deck with 6 in. (150 mm) ins. and 2 in. (50 mm) h.w. RTS 0.045 0.256
28 E0 B9 B14 E3 E2 A0 4 in. (100 mm) wood deck with 5 in. (125 mm) insulation 0.044 0.250
29 E0 E5 E4 C12 B13 E3 E2 C5 A0 Susp. clg, 2 in. (50 mm) h.w. dk, 4 in. (100 mm) ins, 4 in. (100 mm) h.w. RTS 0.056 0.318
30 E0 E5 E4 B9 B6 E3 E2 A0 4 in. (100 mm) wood deck with 2 in. (50 mm) insul. and susp. ceiling 0.064 0.363
31 E0 B27 C13 E3 E2 C13 A0 4.54 in. (115 mm) ins. with 6 in. (150 mm) h.w. deck and 6 in. (150 mm) h.w. RTS 0.057 0.324
32 E0 E5 E4 C5 B20 E3 E2 C13 A0 Susp. clg, 4 in. (100 mm) h.w. dk, 0.76 in. (20 mm) ins, 6 in. (150 mm) h.w. RTS 0.133 0.755
33 E0 E5 E4 C5 B13 E3 E2 C5 A0 Susp. clg, 4 in. (100 mm) h.w. dk, 4 in. (100 mm) ins, 4 in. (100 mm) h.w. RTS 0.055 0.312
34 E0 E5 E4 C13 B23 E3 E2 C5 A0 Susp. clg, 6 in. (150 mm) h.w. dk, 2.42 in. (60 mm) ins, 4 in. (100 mm) h.w. RTS 0.077 0.437
35 E0 C5 B15 E3 E2 C13 A0 4 in. (100 mm) h.w. deck with 6 in. (150 mm) ins and 6 in. (150 mm) h.w. RTS 0.045 0.256
36 E0 C13 B27 E3 E2 CI3 A0 6 in. (150 mm) h.w. deck with 4.54 in. (115 mm) ins. and 6 in. (150 mm) h.w. RTS 0.057 0.324
37 E0 E5 E4 B15 C13 E3 E2 C13 A0 Susp. clg, 6 in. (150 mm) ins, 6 in. (150 mm) h.w. dk, 6 in. (150 mm) h.w. RTS 0.040 0.227
38 E0 E5 E4 B9 B15 E3 E2 A0 4 in. (100 mm) wood deck with 6 in. (150 mm) insul. and susp. ceiling 0.035 0.199
39 E0 E5 E4 C13 B20 E3 E2 C13 A0 Susp. clg, 6 in. (150 mm) h.w. dk, 0.76 in. (20 mm) ins, 6 in. (150 mm) h.w. RTS 0.131 0.744
40 E0 E5 E4 C5 B26 E3 E2 C13 A0 Susp. clg, 4 in. (100 mm) h.w. dk, 3.64in. (90 mm) ins, 6 in. (150 mm) h.w. RTS 0.059 0.335
41 E0 E5 E4 C13 B6 E3 E2 C13 A0 Susp. clg, 6 in. (150 mm) h.w. deck, 2 in. (50 mm) ins, 6 in. (150 mm) h.w. RTS 0.085 0.483
42 E0 E5 E4 C13 B14 E3 E2 C13 A0 Susp. clg, 6 in. (150 mm) h.w. deck, 5 in. (125 mm) ins, 6 in. (150 mm) h.w. RTS 0.046 0.261
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12 13 14
202 0.004482 0.004202 0.002413
690 0.006047 0.005920 0.002563
788 0.014850 0.012471 0.004252
109 0.023672 0.017213 0.006297
497 0.027289 0.018574 0.007307
506 0.027407 0.018271 0.007538
905 0.025970 0.017328 0.007388
110 0.023992 0.016183 0.007075
301 0.021916 0.015014 0.006701
540 0.019918 0.013889 0.006314
847 0.018060 0.012831 0.005934
224 0.016357 0.011847 0.005570
665 0.014808 0.010936 0.005226
166 0.013403 0.010094 0.004901
720 0.012129 0.009316 0.004595
322 0.010976 0.008597 0.004309
966 0.009933 0.007935 0.004040
649 0.008989 0.007323 0.003788
365 0.008134 0.006758 0.003551
112 0.007361 0.006237 0.003330
886 0.006661 0.005756 0.003122
684 0.006027 0.005312 0.002927
504 0.005454 0.004903 0.002744
343 0.004936 0.004525 0.002573
TABLE 4 Periodic Response Factors (Btu/h⋅ft2°F) for Representative Wall Types 1-14
Wall Type
PRF 1 2 3 4 5 6 7 8 9 10 11
YP0 0.007679 0.000156 0.004133 0.000012 0.000265 0.001215 0.001949 0.002401 0.000129 0.000520 0.001
YP1 0.036827 0.005600 0.035484 0.001094 0.004675 0.010571 0.010142 0.006811 0.000168 0.001441 0.001
YP2 0.016043 0.014795 0.041888 0.005339 0.015527 0.022649 0.013054 0.014860 0.001047 0.006448 0.004
YP3 0.003856 0.014441 0.031281 0.008544 0.019464 0.024744 0.011863 0.017308 0.003050 0.012194 0.008
YP4 0.000901 0.009628 0.022408 0.008706 0.017766 0.022457 0.010539 0.016716 0.004607 0.015366 0.009
YP5 0.000211 0.005414 0.016008 0.007219 0.014707 0.019318 0.009350 0.015380 0.005098 0.016223 0.009
YP6 0.000049 0.002786 0.011434 0.005364 0.011815 0.016347 0.008295 0.013967 0.004859 0.015652 0.008
YP7 0.000011 0.001363 0.008167 0.003735 0.009408 0.013762 0.007359 0.012638 0.004295 0.014326 0.008
YP8 0.000003 0.000647 0.005833 0.002496 0.007472 0.011567 0.006528 0.011424 0.003648 0.012675 0.007
YP9 0.000001 0.000301 0.004166 0.001623 0.005930 0.009717 0.005791 0.010324 0.003032 0.010957 0.006
YP10 0.000000 0.000139 0.002976 0.001036 0.004705 0.008162 0.005138 0.009329 0.002489 0.009313 0.005
YP11 0.000000 0.000063 0.002125 0.000652 0.003733 0.006855 0.004558 0.008430 0.002030 0.007816 0.005
YP12 0.000000 0.000029 0.001518 0.000407 0.002962 0.005757 0.004043 0.007618 0.001649 0.006497 0.004
YP13 0.000000 0.000013 0.001084 0.000252 0.002350 0.004836 0.003587 0.006883 0.001337 0.005360 0.004
YP14 0.000000 0.000006 0.000774 0.000155 0.001865 0.004061 0.003182 0.006220 0.001082 0.004395 0.003
YP15 0.000000 0.000003 0.000553 0.000095 0.001480 0.003411 0.002823 0.005620 0.000876 0.003587 0.003
YP16 0.000000 0.000001 0.000395 0.000058 0.001174 0.002865 0.002504 0.005079 0.000708 0.002915 0.002
YP17 0.000000 0.000001 0.000282 0.000035 0.000931 0.002406 0.002222 0.004589 0.000572 0.002362 0.002
YP18 0.000000 0.000000 0.000202 0.000022 0.000739 0.002021 0.001971 0.004147 0.000463 0.001909 0.002
YP19 0.000000 0.000000 0.000144 0.000013 0.000586 0.001697 0.001748 0.003747 0.000374 0.001539 0.002
YP20 0.000000 0.000000 0.000103 0.000008 0.000465 0.001425 0.001551 0.003386 0.000302 0.001239 0.001
YP21 0.000000 0.000000 0.000073 0.000005 0.000369 0.001197 0.001376 0.003059 0.000244 0.000996 0.001
YP22 0.000000 0.000000 0.000052 0.000003 0.000293 0.001006 0.001221 0.002765 0.000197 0.000799 0.001
YP23 0.000000 0.000000 0.000037 0.000002 0.000232 0.000845 0.001083 0.002498 0.000159 0.000641 0.001
AS
HR
AE
Transactions: Sym
posia497
26 27 28
75 0.002758 0.001690 0.002150
60 0.002609 0.001622 0.002082
89 0.002568 0.001564 0.002034
27 0.002909 0.001576 0.002099
37 0.003569 0.001735 0.002326
38 0.004237 0.002003 0.002620
72 0.004747 0.002283 0.002878
83 0.005074 0.002506 0.003055
71 0.005245 0.002651 0.003154
58 0.005294 0.002722 0.003190
66 0.005256 0.002737 0.003182
15 0.005154 0.002711 0.003143
21 0.005010 0.002658 0.003085
99 0.004837 0.002588 0.003014
56 0.004646 0.002508 0.002937
02 0.004445 0.002422 0.002855
42 0.004240 0.002335 0.002772
81 0.004036 0.002247 0.002689
20 0.003834 0.002160 0.002607
64 0.003637 0.002075 0.002526
12 0.003446 0.001992 0.002447
67 0.003262 0.001913 0.002369
29 0.003086 0.001836 0.002294
99 0.002918 0.001761 0.002221
TABLE 5 Periodic Response Factors (Btu/h⋅ft2°F) for Representative Wall Types 15-28
Wall Type
PRF 15 16 17 18 19 20 21 22 23 24 25
YP0 0.000604 0.002439 0.000735 0.001511 0.002488 0.006271 0.003403 0.000530 0.000860 0.004478 0.0015
YP1 0.000530 0.002253 0.000671 0.001414 0.002392 0.006081 0.003278 0.000454 0.000776 0.004085 0.0014
YP2 0.001077 0.003798 0.000747 0.001589 0.002933 0.007083 0.003347 0.000446 0.000716 0.003877 0.0013
YP3 0.003078 0.008042 0.001265 0.002454 0.004311 0.009430 0.003889 0.000727 0.000787 0.004434 0.0015
YP4 0.005595 0.012598 0.002043 0.003569 0.005546 0.011549 0.004658 0.001332 0.001117 0.005947 0.0019
YP5 0.007450 0.015779 0.002679 0.004362 0.006233 0.012837 0.005304 0.002005 0.001625 0.007865 0.0024
YP6 0.008357 0.017383 0.003032 0.004730 0.006482 0.013417 0.005714 0.002544 0.002136 0.009623 0.0028
YP7 0.008496 0.017747 0.003144 0.004788 0.006460 0.013521 0.005912 0.002884 0.002527 0.010946 0.0031
YP8 0.008131 0.017273 0.003093 0.004666 0.006287 0.013332 0.005957 0.003039 0.002764 0.011773 0.0033
YP9 0.007482 0.016288 0.002949 0.004452 0.006036 0.012970 0.005901 0.003046 0.002858 0.012152 0.0034
YP10 0.006702 0.015027 0.002758 0.004197 0.005748 0.012512 0.005782 0.002949 0.002842 0.012172 0.0034
YP11 0.005890 0.013650 0.002549 0.003930 0.005447 0.012005 0.005626 0.002783 0.002749 0.011923 0.0034
YP12 0.005104 0.012259 0.002339 0.003667 0.005147 0.011478 0.005449 0.002576 0.002608 0.011485 0.0033
YP13 0.004377 0.010917 0.002136 0.003413 0.004855 0.010949 0.005263 0.002349 0.002440 0.010924 0.0031
YP14 0.003724 0.009659 0.001946 0.003174 0.004575 0.010430 0.005072 0.002116 0.002260 0.010290 0.0030
YP15 0.003148 0.008504 0.001769 0.002949 0.004308 0.009926 0.004882 0.001889 0.002078 0.009620 0.0029
YP16 0.002648 0.007459 0.001607 0.002739 0.004055 0.009440 0.004696 0.001672 0.001900 0.008941 0.0027
YP17 0.002218 0.006522 0.001458 0.002543 0.003816 0.008974 0.004514 0.001471 0.001731 0.008272 0.0025
YP18 0.001853 0.005690 0.001323 0.002361 0.003590 0.008529 0.004337 0.001286 0.001573 0.007625 0.0024
YP19 0.001544 0.004955 0.001200 0.002192 0.003377 0.008104 0.004167 0.001119 0.001426 0.007008 0.0022
YP20 0.001283 0.004308 0.001088 0.002034 0.003177 0.007700 0.004002 0.000970 0.001291 0.006427 0.0021
YP21 0.001065 0.003741 0.000987 0.001889 0.002989 0.007315 0.003843 0.000838 0.001168 0.005883 0.0019
YP22 0.000883 0.003246 0.000894 0.001753 0.002812 0.006949 0.003691 0.000721 0.001055 0.005377 0.0018
YP23 0.000731 0.002815 0.000811 0.001627 0.002645 0.006601 0.003544 0.000619 0.000953 0.004909 0.0016
498A
SH
RA
E Transactions: S
ymp
osia
dix B)
39 40 41
0.001242 0.001297 0.001730
0.001178 0.001242 0.001675
0.001115 0.001189 0.001621
0.001059 0.001143 0.001573
0.001037 0.001127 0.001554
0.001073 0.001167 0.001582
0.001167 0.001257 0.001652
0.001290 0.001373 0.001745
0.001417 0.001487 0.001844
0.001529 0.001586 0.001934
0.001618 0.001661 0.002008
0.001681 0.001713 0.002065
0.001721 0.001741 0.002102
0.001739 0.001751 0.002122
0.001738 0.001744 0.002127
0.001721 0.001724 0.002117
0.001692 0.001695 0.002097
0.001653 0.001657 0.002068
0.001605 0.001613 0.002031
0.001552 0.001565 0.001988
0.001494 0.001514 0.001942
0.001433 0.001461 0.001891
0.001370 0.001406 0.001839
0.001306 0.001351 0.001785
TABLE 6 Periodic Response Factors (Btu/h⋅ft2°F) for Representative Wall Types 29-41 (*See Appen
Wall Type
PRF 29 30* 31* 32 33 34 35* 36 37* 38*
YP0 0.005932 0.001472 0.000959 0.002108 0.001386 0.004948 0.001577 0.002683 0.000894 0.000941
YP1 0.005759 0.001320 0.000873 0.001975 0.001322 0.004754 0.001519 0.002620 0.000806 0.000869
YP2 0.005634 0.001186 0.000795 0.001853 0.001261 0.004599 0.001463 0.002561 0.000722 0.000800
YP3 0.005737 0.001131 0.000747 0.001789 0.001229 0.004616 0.001419 0.002543 0.000648 0.000739
YP4 0.006141 0.001288 0.000795 0.001884 0.001280 0.004882 0.001421 0.002618 0.000610 0.000713
YP5 0.006676 0.001696 0.000977 0.002162 0.001426 0.005306 0.001495 0.002771 0.000646 0.000755
YP6 0.007176 0.002246 0.001254 0.002545 0.001619 0.005770 0.001627 0.002948 0.000763 0.000870
YP7 0.007565 0.002797 0.001549 0.002931 0.001806 0.006191 0.001780 0.003104 0.000933 0.001028
YP8 0.007828 0.003254 0.001806 0.003257 0.001957 0.006530 0.001920 0.003222 0.001117 0.001194
YP9 0.007980 0.003577 0.001995 0.003495 0.002062 0.006774 0.002030 0.003301 0.001287 0.001340
YP10 0.008039 0.003763 0.002111 0.003643 0.002124 0.006926 0.002104 0.003344 0.001426 0.001453
YP11 0.008027 0.003827 0.002161 0.003711 0.002149 0.006995 0.002146 0.003360 0.001527 0.001530
YP12 0.007961 0.003793 0.002157 0.003712 0.002144 0.006995 0.002160 0.003353 0.001591 0.001573
YP13 0.007855 0.003685 0.002111 0.003661 0.002116 0.006938 0.002152 0.003328 0.001620 0.001586
YP14 0.007720 0.003525 0.002035 0.003572 0.002072 0.006836 0.002127 0.003291 0.001620 0.001575
YP15 0.007565 0.003329 0.001939 0.003454 0.002017 0.006699 0.002090 0.003245 0.001595 0.001545
YP16 0.007395 0.003113 0.001830 0.003318 0.001953 0.006538 0.002044 0.003191 0.001551 0.001500
YP17 0.007217 0.002886 0.001715 0.003169 0.001884 0.006357 0.001992 0.003133 0.001491 0.001445
YP18 0.007033 0.002658 0.001597 0.003014 0.001813 0.006165 0.001936 0.003072 0.001420 0.001382
YP19 0.006847 0.002433 0.001479 0.002856 0.001740 0.005964 0.001877 0.003008 0.001340 0.001313
YP20 0.006660 0.002217 0.001365 0.002699 0.001666 0.005760 0.001817 0.002943 0.001255 0.001240
YP21 0.006474 0.002011 0.001255 0.002544 0.001594 0.005554 0.001757 0.002878 0.001165 0.001165
YP22 0.006291 0.001818 0.001150 0.002393 0.001523 0.005349 0.001696 0.002813 0.001075 0.001090
YP23 0.006110 0.001638 0.001052 0.002248 0.001454 0.005146 0.001636 0.002748 0.000984 0.001015
AS
HR
AE
Transactions: Sym
posia499
12 13 14
97 0.003593 0.001590 0.001027
72 0.006741 0.002817 0.001417
79 0.019054 0.006883 0.002939
82 0.029822 0.009367 0.003944
64 0.034493 0.009723 0.004133
22 0.034992 0.009224 0.003991
62 0.033303 0.008501 0.003756
19 0.030635 0.007766 0.003505
21 0.027647 0.007076 0.003264
26 0.024671 0.006443 0.003036
59 0.021868 0.005865 0.002824
29 0.019305 0.005338 0.002626
36 0.017000 0.004859 0.002442
78 0.014947 0.004422 0.002271
52 0.013130 0.004025 0.002112
55 0.011527 0.003664 0.001964
82 0.010116 0.003335 0.001826
32 0.008875 0.003035 0.001698
00 0.007786 0.002763 0.001580
85 0.006830 0.002515 0.001469
85 0.005991 0.002289 0.001366
98 0.005255 0.002083 0.001270
22 0.004609 0.001896 0.001181
55 0.004042 0.001726 0.001099
TABLE 7 Periodic Response Factors (Btu/h⋅ft2°F) for Representative Roof Types 1-14
Roof Type
PRF 1 2 3 4 5 6 7 8 9 10 11
YP0 0.004870 0.000556 0.006192 0.000004 0.000105 0.003675 0.001003 0.003468 0.000145 0.000621 0.0003
YP1 0.036463 0.012356 0.044510 0.000658 0.002655 0.034908 0.009678 0.022622 0.000362 0.000777 0.0004
YP2 0.026468 0.020191 0.047321 0.004270 0.007678 0.054823 0.017455 0.045052 0.002612 0.003246 0.0014
YP3 0.008915 0.012498 0.035390 0.007757 0.008783 0.050193 0.017588 0.047168 0.005981 0.007589 0.0030
YP4 0.002562 0.005800 0.026082 0.008259 0.007720 0.041867 0.015516 0.042727 0.007459 0.010269 0.0040
YP5 0.000708 0.002436 0.019215 0.006915 0.006261 0.034391 0.013169 0.037442 0.007228 0.010854 0.0043
YP6 0.000193 0.000981 0.014156 0.005116 0.004933 0.028178 0.011038 0.032544 0.006305 0.010265 0.0041
YP7 0.000053 0.000388 0.010429 0.003527 0.003844 0.023078 0.009213 0.028228 0.005261 0.009210 0.0038
YP8 0.000014 0.000152 0.007684 0.002330 0.002982 0.018900 0.007678 0.024472 0.004309 0.008052 0.0034
YP9 0.000004 0.000059 0.005661 0.001498 0.002309 0.015478 0.006397 0.021212 0.003503 0.006946 0.0030
YP10 0.000001 0.000023 0.004170 0.000946 0.001787 0.012675 0.005328 0.018386 0.002838 0.005952 0.0026
YP11 0.000000 0.000009 0.003072 0.000591 0.001383 0.010380 0.004437 0.015937 0.002297 0.005081 0.0023
YP12 0.000000 0.000003 0.002264 0.000366 0.001070 0.008501 0.003696 0.013814 0.001858 0.004330 0.0020
YP13 0.000000 0.000001 0.001668 0.000225 0.000827 0.006962 0.003078 0.011973 0.001502 0.003686 0.0017
YP14 0.000000 0.000001 0.001229 0.000138 0.000640 0.005701 0.002563 0.010378 0.001215 0.003136 0.0015
YP15 0.000000 0.000000 0.000905 0.000085 0.000495 0.004669 0.002135 0.008995 0.000982 0.002668 0.0013
YP16 0.000000 0.000000 0.000667 0.000052 0.000383 0.003824 0.001778 0.007797 0.000794 0.002269 0.0011
YP17 0.000000 0.000000 0.000491 0.000032 0.000296 0.003131 0.001481 0.006758 0.000642 0.001929 0.0010
YP18 0.000000 0.000000 0.000362 0.000019 0.000229 0.002564 0.001233 0.005858 0.000519 0.001641 0.0009
YP19 0.000000 0.000000 0.000267 0.000012 0.000177 0.002100 0.001027 0.005077 0.000420 0.001395 0.0007
YP20 0.000000 0.000000 0.000196 0.000007 0.000137 0.001720 0.000855 0.004401 0.000339 0.001186 0.0006
YP21 0.000000 0.000000 0.000145 0.000004 0.000106 0.001408 0.000712 0.003815 0.000274 0.001009 0.0005
YP22 0.000000 0.000000 0.000107 0.000003 0.000082 0.001153 0.000593 0.003306 0.000222 0.000858 0.0005
YP23 0.000000 0.000000 0.000079 0.000002 0.000063 0.000945 0.000494 0.002866 0.000179 0.000729 0.0004
500A
SH
RA
E Transactions: S
ymp
osia
26 27 28
42 0.000631 0.001000 0.001165
16 0.000569 0.000921 0.001092
93 0.000532 0.000923 0.001035
98 0.000647 0.001190 0.001083
99 0.001045 0.001674 0.001346
16 0.001585 0.002164 0.001751
22 0.002050 0.002535 0.002139
81 0.002339 0.002759 0.002416
23 0.002455 0.002855 0.002567
60 0.002444 0.002856 0.002614
96 0.002350 0.002788 0.002587
34 0.002211 0.002678 0.002513
73 0.002049 0.002541 0.002412
13 0.001882 0.002391 0.002296
54 0.001719 0.002235 0.002175
97 0.001563 0.002080 0.002053
42 0.001418 0.001929 0.001933
87 0.001284 0.001784 0.001818
34 0.001161 0.001647 0.001708
83 0.001050 0.001519 0.001603
32 0.000948 0.001399 0.001505
83 0.000857 0.001287 0.001412
35 0.000773 0.001184 0.001324
88 0.000698 0.001088 0.001242
TABLE 8 Periodic Response Factors (Btu/h⋅ft2°F) for Representative Roof Types 15-28
Roof Type
PRF 15 16 17 18 19 20 21 22 23 24 25
YP0 0.002290 0.003723 0.000215 0.000423 0.000634 0.001204 0.001516 0.002973 0.001253 0.002447 0.0018
YP1 0.002856 0.004171 0.000186 0.000373 0.000644 0.001105 0.001475 0.002922 0.001212 0.002438 0.0018
YP2 0.004551 0.006232 0.000375 0.000606 0.001383 0.001452 0.002153 0.003855 0.001394 0.002885 0.0019
YP3 0.005355 0.007775 0.001275 0.001388 0.002752 0.002792 0.003473 0.005493 0.001857 0.003575 0.0023
YP4 0.005405 0.008183 0.002519 0.002348 0.003866 0.004377 0.004580 0.006763 0.002296 0.004050 0.0026
YP5 0.005240 0.008079 0.003390 0.003110 0.004483 0.005457 0.005234 0.007477 0.002568 0.004277 0.0028
YP6 0.005030 0.007815 0.003712 0.003566 0.004697 0.005940 0.005517 0.007771 0.002690 0.004340 0.0028
YP7 0.004817 0.007515 0.003635 0.003745 0.004641 0.005989 0.005545 0.007789 0.002710 0.004310 0.0027
YP8 0.004611 0.007214 0.003341 0.003717 0.004422 0.005778 0.005411 0.007634 0.002667 0.004228 0.0027
YP9 0.004412 0.006922 0.002958 0.003549 0.004112 0.005430 0.005179 0.007375 0.002590 0.004119 0.0026
YP10 0.004222 0.006641 0.002561 0.003297 0.003761 0.005022 0.004893 0.007056 0.002494 0.003997 0.0025
YP11 0.004040 0.006372 0.002187 0.003000 0.003399 0.004598 0.004580 0.006708 0.002390 0.003870 0.0025
YP12 0.003866 0.006113 0.001852 0.002688 0.003044 0.004184 0.004259 0.006348 0.002283 0.003742 0.0024
YP13 0.003700 0.005865 0.001559 0.002379 0.002709 0.003792 0.003943 0.005990 0.002177 0.003615 0.0024
YP14 0.003541 0.005627 0.001308 0.002086 0.002399 0.003428 0.003638 0.005640 0.002073 0.003490 0.0023
YP15 0.003388 0.005398 0.001095 0.001814 0.002116 0.003094 0.003348 0.005303 0.001973 0.003370 0.0022
YP16 0.003242 0.005179 0.000915 0.001567 0.001861 0.002790 0.003075 0.004980 0.001877 0.003252 0.0022
YP17 0.003103 0.004969 0.000764 0.001347 0.001634 0.002514 0.002821 0.004674 0.001785 0.003139 0.0021
YP18 0.002969 0.004767 0.000638 0.001152 0.001431 0.002264 0.002585 0.004384 0.001697 0.003030 0.0021
YP19 0.002841 0.004573 0.000532 0.000982 0.001252 0.002038 0.002368 0.004111 0.001613 0.002924 0.0020
YP20 0.002719 0.004388 0.000444 0.000834 0.001094 0.001835 0.002167 0.003854 0.001534 0.002822 0.0020
YP21 0.002602 0.004209 0.000370 0.000706 0.000955 0.001652 0.001983 0.003612 0.001458 0.002723 0.0019
YP22 0.002490 0.004038 0.000309 0.000596 0.000834 0.001487 0.001814 0.003385 0.001386 0.002628 0.0019
YP23 0.002383 0.003874 0.000257 0.000503 0.000727 0.001338 0.001658 0.003172 0.001318 0.002536 0.0018
AS
HR
AE
Transactions: Sym
posia501
dix B)
40 41 42
71 0.002154 0.003219 0.001812
31 0.002095 0.003149 0.001782
62 0.002054 0.003099 0.001752
09 0.002088 0.003129 0.001733
22 0.002196 0.003243 0.001743
60 0.002324 0.003384 0.001780
50 0.002437 0.003515 0.001831
73 0.002527 0.003622 0.001882
31 0.002594 0.003703 0.001927
32 0.002640 0.003760 0.001963
84 0.002668 0.003795 0.001989
95 0.002681 0.003813 0.002007
73 0.002680 0.003814 0.002018
24 0.002667 0.003803 0.002021
51 0.002645 0.003780 0.002019
61 0.002615 0.003747 0.002012
55 0.002578 0.003707 0.002001
39 0.002536 0.003659 0.001985
13 0.002489 0.003606 0.001967
80 0.002439 0.003549 0.001946
43 0.002385 0.003488 0.001922
02 0.002329 0.003423 0.001897
59 0.002272 0.003357 0.001870
15 0.002214 0.003289 0.001842
TABLE 9 Periodic Response Factors (Btu/h⋅ft2°F) for Representative Roof Types 29-42 (*See Appen
Roof Type
PRF 29 30 31 32 33 34 35 36 37* 38* 39
YP0 0.001504 0.001969 0.001794 0.004279 0.001894 0.002763 0.001255 0.001829 0.001325 0.001150 0.0046
YP1 0.001424 0.001881 0.001719 0.004106 0.001833 0.002695 0.001157 0.001725 0.001270 0.001110 0.0045
YP2 0.001526 0.001825 0.001675 0.004176 0.001825 0.002681 0.001083 0.001640 0.001218 0.001072 0.0044
YP3 0.001892 0.001936 0.001783 0.004641 0.001952 0.002804 0.001121 0.001657 0.001188 0.001043 0.0046
YP4 0.002293 0.002272 0.002067 0.005220 0.002148 0.003004 0.001322 0.001829 0.001225 0.001052 0.0049
YP5 0.002605 0.002683 0.002396 0.005718 0.002326 0.003192 0.001616 0.002088 0.001343 0.001118 0.0052
YP6 0.002819 0.003027 0.002666 0.006093 0.002460 0.003338 0.001912 0.002351 0.001506 0.001226 0.0055
YP7 0.002948 0.003258 0.002848 0.006352 0.002552 0.003440 0.002159 0.002572 0.001668 0.001342 0.0057
YP8 0.003011 0.003382 0.002948 0.006514 0.002609 0.003505 0.002340 0.002737 0.001803 0.001443 0.0059
YP9 0.003022 0.003422 0.002983 0.006594 0.002638 0.003540 0.002456 0.002849 0.001898 0.001517 0.0060
YP10 0.002992 0.003403 0.002973 0.006608 0.002644 0.003550 0.002515 0.002913 0.001955 0.001563 0.0060
YP11 0.002933 0.003344 0.002930 0.006568 0.002631 0.003540 0.002525 0.002938 0.001978 0.001585 0.0060
YP12 0.002851 0.003258 0.002865 0.006485 0.002605 0.003515 0.002498 0.002929 0.001975 0.001587 0.0060
YP13 0.002753 0.003157 0.002785 0.006368 0.002567 0.003477 0.002441 0.002894 0.001952 0.001574 0.0060
YP14 0.002644 0.003046 0.002697 0.006224 0.002520 0.003430 0.002362 0.002838 0.001914 0.001551 0.0059
YP15 0.002528 0.002930 0.002603 0.006059 0.002467 0.003376 0.002267 0.002765 0.001866 0.001520 0.0058
YP16 0.002409 0.002813 0.002507 0.005879 0.002410 0.003316 0.002161 0.002680 0.001811 0.001484 0.0057
YP17 0.002287 0.002696 0.002411 0.005689 0.002348 0.003252 0.002048 0.002584 0.001752 0.001444 0.0056
YP18 0.002166 0.002582 0.002316 0.005491 0.002285 0.003185 0.001930 0.002482 0.001690 0.001403 0.0055
YP19 0.002047 0.002470 0.002222 0.005288 0.002220 0.003116 0.001812 0.002376 0.001627 0.001360 0.0053
YP20 0.001930 0.002362 0.002131 0.005083 0.002154 0.003046 0.001694 0.002266 0.001565 0.001317 0.0052
YP21 0.001817 0.002258 0.002042 0.004879 0.002088 0.002975 0.001578 0.002156 0.001503 0.001274 0.0051
YP22 0.001708 0.002158 0.001956 0.004675 0.002023 0.002904 0.001466 0.002046 0.001442 0.001232 0.0049
YP23 0.001604 0.002061 0.001874 0.004475 0.001958 0.002833 0.001358 0.001936 0.001383 0.001191 0.0048
- tolic-e.uretheple-eatersenple-te-
CONCLUSIONS
The periodic response factor tables presented in this papersupport wall and roof conductive heat gain calculations by theperiodic response factor method. Heat gains calculated usingthe tables are equivalent to heat gains calculated using CTFsfor the same wall type. The Harris and McQuiston groupingprocedure is carried through to the periodic response factortables. As a result an “unnormalization” procedure similarthe CTF procedure is required to obtain response factors reflect correct wall and roof U-factors.
Although the tables were generated specifically support the RTSM, the periodic response factor methodgenerally applicable to any conductive heat gain calculatwith steady periodic inputs. As such, it is useful for all pedesign day cooling load calculations that typically assume tprevious days were identical to the design day.
REFERENCES
ASHRAE. 1989. 1989 ASHRAE Handbook—Fundamentals. Atlanta: American Society of Heating, Refrigerat-ing and Air-Conditioning Engineers, Inc.
ASHRAE. 1993. 1993 ASHRAE Handbook—Fundamentals. Atlanta: American Society of Heating, Refrigerat-ing and Air-Conditioning Engineers, Inc.
ASHRAE. 1997. 1997 ASHRAE Handbook—Fundamentals. Atlanta: American Society of Heating, Refrigerat-ing and Air-Conditioning Engineers, Inc.
Falconer, D.R., E.F. Sowell, J.D. Spitler, and B. Todovorich.1993. Electronic tables for the ASHRAE Load Calcula-tion Manual. ASHRAE Transactions 99 (1): 193-200.
Harris, S.M., and F.C. McQuiston. 1988. A study to catego-rize walls and roofs on the basis of thermal response.ASHRAE Transactions 94 (2): 688-714.
Hittle, D.C. 1981. Calculating building heating and coolingloads using the frequency response of multilayeredslabs. Ph.D. thesis, University of Illinois at Urbana-Champaign.
Maloney, D. 1985. A verification of the use of heat conduc-tion transfer functions as used in the program BLAST.BLAST Support Office Report, University of Illinois.
McQuiston, F.C., and J.D. Spitler. 1992. Cooling and heat-ing load calculation manual, 2d ed. Atlanta: AmericanSociety of Heating, Refrigerating and Air-ConditioningEngineers, Inc.
502
tothat
to isionakhat
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-
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Mitalas, G.P., and D.G. Stephenson. 1967. Cooling load cal-culations by thermal response factor method. ASHRAETransactions 73, pp. III 2.1-2.10.
Peavy, B.A. 1978. A note on response factors and conduc-tion transfer functions. ASHRAE Transactions 84 (1):pp. 688-690.
Pedersen, C.O., D. Fisher, J.D. Spitler, and R. Liesen. 1998.Cooling and heating load calculation principles.Atlanta: American Society of Heating, Refrigeratingand Air-Conditioning Engineers, Inc.
Spitler, J.D., and D.E. Fisher. 1999. On the relationshipbetween the radiant time series and transfer functionmethods for design cooling load calculations. Interna-tional Journal of HVAC&R Research, 5 (2): 125-138.
Spitler, J.D., D.E. Fisher, and C.O. Pedersen. 1997. The radi-ant time series cooling load calculation procedure.ASHRAE Transactions 103 (2): 503-515.
Stephenson, D.G., and G.P. Mitalas. 1967. Room thermalresponse factors. ASHRAE Transactions 73, pp. III 1.1-1.7.
DISCUSSION
Byron Jones, Associate Dean of Research, KansasState University, Manhattan, Kansas: The calculationmethods used in this paper make the implicit assumption thatthe cooling system is air-based. That is, they evaluate theenergy gain of the air. Can these calculations be applied to loadcalculations when part or all of the cooling is provided by radi-ant cooling systems? How will the loads differ for a radiantcooling system as compared to an air-based system?
Jeffrey D. Spitler: In the author’s opinion, load calculations for systems involving radiant heating or cooling oughtbe performed using a load calculation procedure which expitly accounts for surface-to-surface radiant interchangTherefore, we recommend using a heat balance procedrather than the radiant time series procedure for which periodic response factors in this paper were developed. Immentation of a radiant heating and/or cooling model in a hbalance procedure has been described by Strand and Ped(1997). (Reference: Strand, R.K., and C.O. Pedersen. Immentation of a radiant heating and cooling model into an ingrated building energy analysis program. ASHRAETransactions, 103 (1): 949-958.)
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APPENDIX A
12 13 14
26 0.025450 0.023858 0.013704
96 0.034335 0.033612 0.014552
88 0.084321 0.070812 0.024146
42 0.134410 0.097734 0.035754
25 0.154949 0.105466 0.041491
75 0.155617 0.103745 0.042803
60 0.147457 0.098389 0.041949
50 0.136228 0.091889 0.040169
53 0.124441 0.085250 0.038048
34 0.113094 0.078860 0.035850
01 0.102542 0.072855 0.033694
61 0.092876 0.067268 0.031628
90 0.084080 0.062094 0.029671
56 0.076100 0.057311 0.027827
23 0.068870 0.052894 0.026093
62 0.062324 0.048816 0.024466
43 0.056400 0.045053 0.022939
39 0.051037 0.041579 0.021508
29 0.046185 0.038373 0.020165
91 0.041794 0.035414 0.018906
07 0.037820 0.032683 0.017726
61 0.034224 0.030163 0.016620
37 0.030970 0.027837 0.015582
23 0.028025 0.025691 0.014609
TABLE A-1 Periodic Response Factors (W/m2K) for Representative Wall Types 1-14
Wall Type
PRF 1 2 3 4 5 6 7 8 9 10 11
YP0 0.043604 0.000887 0.023469 0.000067 0.001503 0.006897 0.011068 0.013634 0.000732 0.002954 0.0068
YP1 0.209101 0.031798 0.201480 0.006214 0.026544 0.060020 0.057588 0.038674 0.000954 0.008182 0.0095
YP2 0.091092 0.084006 0.237838 0.030315 0.088162 0.128601 0.074120 0.084373 0.005946 0.036614 0.0271
YP3 0.021893 0.081998 0.177612 0.048513 0.110515 0.140497 0.067359 0.098276 0.017320 0.069236 0.0460
YP4 0.005118 0.054670 0.127235 0.049432 0.100873 0.127511 0.059840 0.094913 0.026159 0.087249 0.0539
YP5 0.001195 0.030739 0.090894 0.040988 0.083504 0.109686 0.053091 0.087327 0.028946 0.092116 0.0539
YP6 0.000279 0.015817 0.064922 0.030457 0.067086 0.092817 0.047099 0.079304 0.027589 0.088870 0.0505
YP7 0.000065 0.007739 0.046370 0.021210 0.053417 0.078140 0.041783 0.071760 0.024385 0.081341 0.0460
YP8 0.000015 0.003673 0.033120 0.014175 0.042425 0.065678 0.037067 0.064868 0.020711 0.071971 0.0414
YP9 0.000004 0.001711 0.023656 0.009217 0.033670 0.055174 0.032883 0.058621 0.017214 0.062212 0.0371
YP10 0.000001 0.000787 0.016896 0.005881 0.026716 0.046343 0.029172 0.052972 0.014135 0.052877 0.0332
YP11 0.000000 0.000360 0.012068 0.003703 0.021198 0.038923 0.025879 0.047867 0.011528 0.044380 0.0296
YP12 0.000000 0.000163 0.008620 0.002309 0.016819 0.032691 0.022958 0.043253 0.009366 0.036890 0.0264
YP13 0.000000 0.000074 0.006157 0.001429 0.013345 0.027457 0.020367 0.039084 0.007592 0.030433 0.0236
YP14 0.000000 0.000033 0.004397 0.000880 0.010588 0.023060 0.018068 0.035316 0.006146 0.024956 0.0211
YP15 0.000000 0.000015 0.003141 0.000540 0.008401 0.019368 0.016029 0.031912 0.004972 0.020365 0.0188
YP16 0.000000 0.000007 0.002243 0.000330 0.006665 0.016266 0.014220 0.028836 0.004020 0.016554 0.0168
YP17 0.000000 0.000003 0.001602 0.000201 0.005289 0.013662 0.012615 0.026056 0.003250 0.013413 0.0150
YP18 0.000000 0.000001 0.001144 0.000123 0.004196 0.011474 0.011191 0.023545 0.002627 0.010839 0.0134
YP19 0.000000 0.000001 0.000817 0.000075 0.003329 0.009637 0.009928 0.021275 0.002123 0.008740 0.0119
YP20 0.000000 0.000000 0.000584 0.000045 0.002642 0.008094 0.008807 0.019225 0.001716 0.007034 0.0107
YP21 0.000000 0.000000 0.000417 0.000028 0.002096 0.006798 0.007813 0.017371 0.001387 0.005653 0.0095
YP22 0.000000 0.000000 0.000298 0.000017 0.001663 0.005709 0.006931 0.015697 0.001121 0.004537 0.0085
YP23 0.000000 0.000000 0.000213 0.000010 0.001319 0.004795 0.006149 0.014184 0.000906 0.003637 0.0076
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26 27 28
45 0.015662 0.009596 0.012209
92 0.014815 0.009207 0.011821
87 0.014581 0.008878 0.011549
73 0.016516 0.008950 0.011916
98 0.020265 0.009851 0.013207
44 0.024056 0.011374 0.014878
07 0.026953 0.012963 0.016339
71 0.028811 0.014229 0.017347
41 0.029779 0.015050 0.017908
34 0.030062 0.015458 0.018114
78 0.029842 0.015542 0.018066
88 0.029266 0.015396 0.017846
58 0.028445 0.015095 0.017516
61 0.027462 0.014696 0.017116
54 0.026379 0.014241 0.016675
80 0.025239 0.013754 0.016213
72 0.024077 0.013256 0.015741
54 0.022914 0.012756 0.015269
43 0.021768 0.012263 0.014801
54 0.020649 0.011781 0.014341
94 0.019566 0.011313 0.013891
70 0.018524 0.010859 0.013453
86 0.017525 0.010422 0.013026
44 0.016571 0.010001 0.012611
TABLE A-2 Periodic Response Factors (W/m2K) for Representative Wall Types 15-28
Wall Type
PRF 15 16 17 18 19 20 21 22 23 24 25
YP0 0.003431 0.013849 0.004175 0.008577 0.014126 0.035606 0.019325 0.003007 0.004882 0.025424 0.0089
YP1 0.003012 0.012792 0.003810 0.008028 0.013585 0.034529 0.018612 0.002575 0.004406 0.023192 0.0082
YP2 0.006114 0.021567 0.004241 0.009021 0.016653 0.040215 0.019004 0.002532 0.004063 0.022015 0.0078
YP3 0.017478 0.045665 0.007182 0.013933 0.024480 0.053542 0.022081 0.004128 0.004471 0.025174 0.0086
YP4 0.031771 0.071531 0.011602 0.020266 0.031490 0.065575 0.026450 0.007563 0.006341 0.033768 0.0109
YP5 0.042301 0.089595 0.015211 0.024766 0.035392 0.072886 0.030119 0.011384 0.009229 0.044656 0.0138
YP6 0.047450 0.098700 0.017218 0.026854 0.036803 0.076180 0.032445 0.014445 0.012126 0.054641 0.0163
YP7 0.048238 0.100767 0.017849 0.027188 0.036679 0.076775 0.033569 0.016378 0.014350 0.062150 0.0180
YP8 0.046165 0.098074 0.017561 0.026495 0.035698 0.075701 0.033825 0.017254 0.015692 0.066845 0.0191
YP9 0.042480 0.092481 0.016743 0.025278 0.034270 0.073645 0.033507 0.017297 0.016227 0.069001 0.0196
YP10 0.038053 0.085324 0.015660 0.023831 0.032635 0.071042 0.032832 0.016744 0.016136 0.069113 0.0196
YP11 0.033443 0.077507 0.014474 0.022317 0.030928 0.068162 0.031946 0.015800 0.015609 0.067699 0.0193
YP12 0.028983 0.069609 0.013281 0.020820 0.029226 0.065171 0.030942 0.014625 0.014808 0.065214 0.0188
YP13 0.024854 0.061987 0.012130 0.019382 0.027568 0.062171 0.029881 0.013336 0.013853 0.062028 0.0181
YP14 0.021143 0.054845 0.011048 0.018020 0.025976 0.059222 0.028800 0.012017 0.012830 0.058427 0.0173
YP15 0.017873 0.048287 0.010045 0.016743 0.024460 0.056358 0.027722 0.010725 0.011797 0.054623 0.0164
YP16 0.015034 0.042351 0.009123 0.015550 0.023023 0.053599 0.026663 0.009495 0.010790 0.050768 0.0155
YP17 0.012596 0.037033 0.008280 0.014438 0.021665 0.050953 0.025629 0.008351 0.009831 0.046968 0.0146
YP18 0.010520 0.032307 0.007512 0.013405 0.020384 0.048425 0.024627 0.007303 0.008932 0.043294 0.0137
YP19 0.008764 0.028132 0.006813 0.012444 0.019177 0.046015 0.023658 0.006356 0.008098 0.039794 0.0128
YP20 0.007286 0.024461 0.006178 0.011552 0.018040 0.043719 0.022723 0.005508 0.007331 0.036493 0.0119
YP21 0.006047 0.021244 0.005602 0.010723 0.016970 0.041534 0.021823 0.004756 0.006629 0.033404 0.0111
YP22 0.005012 0.018433 0.005079 0.009954 0.015964 0.039457 0.020957 0.004093 0.005990 0.030532 0.0103
YP23 0.004149 0.015982 0.004605 0.009240 0.015017 0.037482 0.020125 0.003513 0.005409 0.027874 0.0096
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39 40 41
0.007049 0.007362 0.009825
0.006687 0.007054 0.009512
0.006330 0.006752 0.009202
0.006016 0.006490 0.008933
0.005885 0.006401 0.008826
0.006093 0.006626 0.008983
0.006625 0.007140 0.009380
0.007326 0.007794 0.009910
0.008043 0.008445 0.010468
0.008679 0.009005 0.010980
0.009185 0.009433 0.011404
0.009547 0.009724 0.011724
0.009771 0.009888 0.011937
0.009872 0.009941 0.012050
0.009867 0.009903 0.012075
0.009773 0.009792 0.012023
0.009607 0.009622 0.011908
0.009383 0.009408 0.011741
0.009114 0.009159 0.011532
0.008811 0.008886 0.011290
0.008482 0.008595 0.011024
0.008136 0.008293 0.010739
0.007778 0.007984 0.010442
0.007415 0.007673 0.010136
TABLE A-3 Periodic Response Factors (W/m2K) for Representative Wall Types 29-41 (*See Appen
Wall Type
PRF 29 30* 31* 32 33 34 35* 36 37* 38*
YP0 0.033682 0.008359 0.005447 0.011969 0.007872 0.028092 0.008953 0.015236 0.005075 0.005342
YP1 0.032700 0.007494 0.004959 0.011214 0.007504 0.026995 0.008625 0.014875 0.004578 0.004934
YP2 0.031988 0.006735 0.004517 0.010520 0.007160 0.026112 0.008307 0.014543 0.004101 0.004541
YP3 0.032573 0.006422 0.004244 0.010156 0.006978 0.026210 0.008057 0.014439 0.003678 0.004196
YP4 0.034867 0.007316 0.004513 0.010695 0.007269 0.027717 0.008066 0.014863 0.003464 0.004046
YP5 0.037908 0.009632 0.005547 0.012278 0.008096 0.030130 0.008487 0.015736 0.003668 0.004285
YP6 0.040746 0.012755 0.007118 0.014448 0.009191 0.032762 0.009241 0.016737 0.004333 0.004939
YP7 0.042953 0.015883 0.008798 0.016643 0.010253 0.035152 0.010108 0.017622 0.005295 0.005839
YP8 0.044449 0.018478 0.010256 0.018494 0.011110 0.037076 0.010902 0.018294 0.006341 0.006779
YP9 0.045308 0.020311 0.011330 0.019847 0.011710 0.038461 0.011525 0.018741 0.007307 0.007608
YP10 0.045646 0.021364 0.011989 0.020687 0.012060 0.039324 0.011948 0.018990 0.008096 0.008251
YP11 0.045577 0.021729 0.012271 0.021070 0.012200 0.039718 0.012184 0.019076 0.008671 0.008687
YP12 0.045202 0.021538 0.012245 0.021076 0.012172 0.039717 0.012262 0.019036 0.009032 0.008929
YP13 0.044600 0.020926 0.011985 0.020788 0.012017 0.039393 0.012217 0.018898 0.009198 0.009003
YP14 0.043834 0.020014 0.011555 0.020280 0.011768 0.038814 0.012077 0.018688 0.009196 0.008941
YP15 0.042952 0.018903 0.011009 0.019613 0.011452 0.038040 0.011867 0.018423 0.009056 0.008771
YP16 0.041991 0.017673 0.010393 0.018839 0.011090 0.037120 0.011607 0.018120 0.008805 0.008519
YP17 0.040978 0.016387 0.009737 0.017996 0.010700 0.036097 0.011312 0.017790 0.008467 0.008205
YP18 0.039936 0.015089 0.009067 0.017115 0.010293 0.035003 0.010994 0.017441 0.008063 0.007845
YP19 0.038878 0.013815 0.008400 0.016219 0.009878 0.033865 0.010660 0.017080 0.007610 0.007453
YP20 0.037817 0.012586 0.007750 0.015325 0.009462 0.032703 0.010319 0.016712 0.007124 0.007040
YP21 0.036762 0.011418 0.007125 0.014445 0.009050 0.031534 0.009974 0.016341 0.006617 0.006616
YP22 0.035718 0.010322 0.006531 0.013588 0.008647 0.030370 0.009630 0.015970 0.006101 0.006187
YP23 0.034690 0.009301 0.005971 0.012762 0.008253 0.029221 0.009289 0.015601 0.005585 0.005761
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12 13 14
56 0.020401 0.009027 0.005829
80 0.038276 0.015993 0.008048
97 0.108191 0.039082 0.016688
98 0.169331 0.053185 0.022392
73 0.195852 0.055210 0.023469
41 0.198684 0.052373 0.022663
32 0.189092 0.048271 0.021324
85 0.173948 0.044098 0.019903
22 0.156977 0.040179 0.018530
79 0.140081 0.036582 0.017238
97 0.124167 0.033299 0.016033
22 0.109614 0.030310 0.014910
60 0.096525 0.027588 0.013866
97 0.084870 0.025111 0.012895
14 0.074551 0.022856 0.011991
93 0.065449 0.020803 0.011152
13 0.057437 0.018935 0.010370
58 0.050394 0.017235 0.009644
11 0.044209 0.015687 0.008969
59 0.038780 0.014278 0.008340
91 0.034016 0.012996 0.007756
95 0.029836 0.011829 0.007213
62 0.026169 0.010767 0.006708
84 0.022952 0.009800 0.006238
TABLE A-4 Periodic Response Factors (W/m2K) for Representative Roof Types 1-14
Roof Type
PRF 1 2 3 4 5 6 7 8 9 10 11
YP0 0.027654 0.003156 0.035160 0.000022 0.000594 0.020865 0.005693 0.019691 0.000826 0.003524 0.0022
YP1 0.207035 0.070157 0.252727 0.003734 0.015074 0.198207 0.054949 0.128446 0.002057 0.004413 0.0026
YP2 0.150283 0.114644 0.268687 0.024245 0.043597 0.311286 0.099112 0.255807 0.014833 0.018433 0.0083
YP3 0.050619 0.070966 0.200944 0.044043 0.049870 0.284994 0.099862 0.267821 0.033958 0.043089 0.0174
YP4 0.014549 0.032932 0.148093 0.046896 0.043836 0.237722 0.088098 0.242607 0.042351 0.058310 0.0230
YP5 0.004017 0.013831 0.109105 0.039265 0.035550 0.195273 0.074774 0.212598 0.041039 0.061629 0.0245
YP6 0.001097 0.005571 0.080381 0.029047 0.028009 0.159997 0.062673 0.184784 0.035797 0.058285 0.0236
YP7 0.000298 0.002201 0.059219 0.020026 0.021825 0.131038 0.052310 0.160278 0.029872 0.052296 0.0216
YP8 0.000081 0.000861 0.043628 0.013228 0.016932 0.107313 0.043598 0.138949 0.024469 0.045717 0.0194
YP9 0.000022 0.000336 0.032142 0.008504 0.013113 0.087883 0.036319 0.120443 0.019889 0.039440 0.0171
YP10 0.000006 0.000130 0.023680 0.005372 0.010148 0.071971 0.030251 0.104397 0.016116 0.033793 0.0150
YP11 0.000002 0.000051 0.017446 0.003354 0.007851 0.058939 0.025195 0.090489 0.013042 0.028851 0.0132
YP12 0.000000 0.000020 0.012853 0.002078 0.006074 0.048268 0.020983 0.078433 0.010549 0.024585 0.0115
YP13 0.000000 0.000008 0.009469 0.001280 0.004698 0.039528 0.017476 0.067984 0.008530 0.020929 0.0100
YP14 0.000000 0.000003 0.006976 0.000786 0.003634 0.032371 0.014554 0.058926 0.006898 0.017807 0.0088
YP15 0.000000 0.000001 0.005139 0.000481 0.002811 0.026510 0.012122 0.051075 0.005577 0.015147 0.0076
YP16 0.000000 0.000000 0.003786 0.000294 0.002175 0.021710 0.010095 0.044271 0.004510 0.012882 0.0067
YP17 0.000000 0.000000 0.002790 0.000180 0.001682 0.017779 0.008408 0.038373 0.003646 0.010955 0.0058
YP18 0.000000 0.000000 0.002055 0.000110 0.001301 0.014560 0.007002 0.033260 0.002948 0.009316 0.0051
YP19 0.000000 0.000000 0.001514 0.000067 0.001007 0.011924 0.005832 0.028829 0.002384 0.007922 0.0044
YP20 0.000000 0.000000 0.001115 0.000041 0.000779 0.009765 0.004857 0.024988 0.001928 0.006736 0.0038
YP21 0.000000 0.000000 0.000822 0.000025 0.000602 0.007997 0.004045 0.021659 0.001559 0.005728 0.0033
YP22 0.000000 0.000000 0.000605 0.000015 0.000466 0.006549 0.003369 0.018773 0.001260 0.004871 0.0029
YP23 0.000000 0.000000 0.000446 0.000009 0.000360 0.005363 0.002806 0.016272 0.001019 0.004142 0.0025
AS
HR
AE
Transactions: Sym
posia507
26 27 28
60 0.003580 0.005678 0.006612
09 0.003233 0.005231 0.006201
14 0.003018 0.005242 0.005877
16 0.003672 0.006757 0.006148
26 0.005932 0.009507 0.007642
87 0.009000 0.012289 0.009943
22 0.011638 0.014392 0.012146
88 0.013278 0.015665 0.013720
59 0.013942 0.016213 0.014575
02 0.013876 0.016214 0.014840
42 0.013345 0.015833 0.014687
87 0.012551 0.015205 0.014268
39 0.011637 0.014428 0.013694
99 0.010689 0.013574 0.013038
67 0.009758 0.012690 0.012348
44 0.008874 0.011810 0.011656
28 0.008049 0.010952 0.010977
19 0.007289 0.010132 0.010322
18 0.006593 0.009354 0.009697
25 0.005959 0.008624 0.009104
38 0.005384 0.007943 0.008543
59 0.004863 0.007309 0.008015
86 0.004392 0.006722 0.007518
20 0.003966 0.006179 0.007051
TABLE A-5 Periodic Response Factors (W/m2K) for Representative Roof Types 15-28
Roof Type
PRF 15 16 17 18 19 20 21 22 23 24 25
YP0 0.013002 0.021141 0.001218 0.002401 0.003600 0.006837 0.008610 0.016880 0.007113 0.013896 0.0104
YP1 0.016218 0.023683 0.001053 0.002118 0.003656 0.006275 0.008375 0.016593 0.006881 0.013843 0.0103
YP2 0.025842 0.035386 0.002130 0.003441 0.007854 0.008243 0.012223 0.021887 0.007914 0.016380 0.0113
YP3 0.030405 0.044148 0.007240 0.007883 0.015626 0.015853 0.019719 0.031186 0.010544 0.020299 0.0136
YP4 0.030691 0.046465 0.014305 0.013333 0.021953 0.024855 0.026005 0.038400 0.013035 0.022994 0.0153
YP5 0.029753 0.045871 0.019247 0.017657 0.025455 0.030987 0.029720 0.042455 0.014582 0.024282 0.0159
YP6 0.028561 0.044373 0.021078 0.020246 0.026668 0.033729 0.031325 0.044127 0.015275 0.024645 0.0160
YP7 0.027352 0.042669 0.020640 0.021265 0.026352 0.034008 0.031486 0.044229 0.015387 0.024474 0.0157
YP8 0.026179 0.040962 0.018969 0.021106 0.025107 0.032808 0.030725 0.043346 0.015146 0.024009 0.0154
YP9 0.025053 0.039305 0.016797 0.020154 0.023350 0.030831 0.029408 0.041872 0.014706 0.023390 0.0151
YP10 0.023974 0.037710 0.014544 0.018720 0.021355 0.028512 0.027781 0.040063 0.014161 0.022697 0.0147
YP11 0.022942 0.036179 0.012420 0.017036 0.019298 0.026108 0.026005 0.038086 0.013569 0.021973 0.0143
YP12 0.021954 0.034710 0.010514 0.015264 0.017286 0.023757 0.024185 0.036046 0.012962 0.021245 0.0140
YP13 0.021009 0.033301 0.008852 0.013510 0.015383 0.021532 0.022388 0.034011 0.012358 0.020524 0.0136
YP14 0.020104 0.031948 0.007427 0.011843 0.013622 0.019466 0.020654 0.032024 0.011770 0.019819 0.0133
YP15 0.019238 0.030651 0.006217 0.010299 0.012017 0.017569 0.019008 0.030108 0.011201 0.019133 0.0130
YP16 0.018410 0.029406 0.005197 0.008899 0.010569 0.015841 0.017460 0.028277 0.010655 0.018468 0.0127
YP17 0.017617 0.028212 0.004340 0.007647 0.009276 0.014273 0.016018 0.026538 0.010133 0.017824 0.0124
YP18 0.016858 0.027066 0.003622 0.006541 0.008126 0.012855 0.014680 0.024893 0.009635 0.017202 0.0121
YP19 0.016132 0.025967 0.003022 0.005574 0.007109 0.011574 0.013444 0.023342 0.009161 0.016601 0.0118
YP20 0.015438 0.024913 0.002521 0.004734 0.006212 0.010419 0.012305 0.021882 0.008709 0.016021 0.0115
YP21 0.014773 0.023901 0.002102 0.004009 0.005424 0.009378 0.011258 0.020510 0.008280 0.015460 0.0112
YP22 0.014137 0.022930 0.001753 0.003386 0.004733 0.008441 0.010297 0.019221 0.007871 0.014920 0.0109
YP23 0.013528 0.021999 0.001461 0.002854 0.004128 0.007597 0.009416 0.018012 0.007482 0.014398 0.0107
508A
SH
RA
E Transactions: S
ymp
osia
dix B)
40 41 42
23 0.012232 0.018278 0.010291
26 0.011896 0.017882 0.010120
35 0.011663 0.017594 0.009951
68 0.011857 0.017764 0.009842
47 0.012471 0.018411 0.009895
68 0.013193 0.019215 0.010107
15 0.013837 0.019958 0.010396
81 0.014349 0.020565 0.010687
77 0.014729 0.021024 0.010941
48 0.014991 0.021347 0.011144
44 0.015150 0.021549 0.011295
10 0.015220 0.021648 0.011397
85 0.015215 0.021659 0.011456
03 0.015144 0.021593 0.011477
92 0.015020 0.021462 0.011465
77 0.014849 0.021278 0.011425
79 0.014641 0.021047 0.011359
16 0.014400 0.020778 0.011272
01 0.014134 0.020477 0.011168
48 0.013847 0.020150 0.011048
67 0.013543 0.019802 0.010915
67 0.013227 0.019437 0.010771
56 0.012901 0.019060 0.010618
39 0.012568 0.018672 0.010457
TABLE A-6 Periodic Response Factors (W/m2K) for Representative Roof Types 29-42 (*See Appen
Roof Type
PRF 29 30 31 32 33 34 35 36 37* 38* 39
YP0 0.008540 0.011181 0.010188 0.024294 0.010753 0.015686 0.007126 0.010387 0.007526 0.006529 0.0265
YP1 0.008087 0.010682 0.009758 0.023314 0.010409 0.015305 0.006572 0.009795 0.007211 0.006304 0.0257
YP2 0.008667 0.010363 0.009513 0.023710 0.010363 0.015221 0.006152 0.009313 0.006915 0.006088 0.0253
YP3 0.010741 0.010994 0.010124 0.026353 0.011083 0.015921 0.006363 0.009408 0.006744 0.005925 0.0261
YP4 0.013017 0.012901 0.011735 0.029640 0.012197 0.017059 0.007508 0.010383 0.006954 0.005973 0.0279
YP5 0.014794 0.015232 0.013603 0.032465 0.013207 0.018126 0.009177 0.011858 0.007624 0.006347 0.0298
YP6 0.016006 0.017188 0.015139 0.034594 0.013969 0.018954 0.010856 0.013350 0.008549 0.006960 0.0315
YP7 0.016741 0.018499 0.016171 0.036068 0.014493 0.019535 0.012258 0.014603 0.009473 0.007621 0.0327
YP8 0.017096 0.019202 0.016737 0.036985 0.014816 0.019904 0.013287 0.015542 0.010235 0.008192 0.0336
YP9 0.017156 0.019432 0.016940 0.037442 0.014978 0.020099 0.013946 0.016176 0.010777 0.008612 0.0342
YP10 0.016990 0.019324 0.016880 0.037521 0.015011 0.020155 0.014278 0.016541 0.011100 0.008874 0.0345
YP11 0.016652 0.018987 0.016634 0.037294 0.014940 0.020100 0.014340 0.016680 0.011233 0.008998 0.0346
YP12 0.016188 0.018502 0.016265 0.036823 0.014789 0.019956 0.014185 0.016633 0.011216 0.009010 0.0344
YP13 0.015633 0.017924 0.015813 0.036157 0.014574 0.019743 0.013862 0.016435 0.011084 0.008939 0.0342
YP14 0.015015 0.017293 0.015311 0.035339 0.014310 0.019476 0.013414 0.016116 0.010869 0.008806 0.0337
YP15 0.014357 0.016636 0.014780 0.034405 0.014010 0.019168 0.012873 0.015702 0.010595 0.008630 0.0332
YP16 0.013676 0.015970 0.014236 0.033384 0.013682 0.018828 0.012270 0.015216 0.010283 0.008425 0.0326
YP17 0.012986 0.015308 0.013690 0.032300 0.013334 0.018464 0.011626 0.014675 0.009946 0.008201 0.0320
YP18 0.012298 0.014658 0.013148 0.031175 0.012974 0.018084 0.010960 0.014095 0.009595 0.007965 0.0313
YP19 0.011620 0.014025 0.012616 0.030025 0.012605 0.017693 0.010287 0.013489 0.009239 0.007723 0.0305
YP20 0.010958 0.013411 0.012098 0.028863 0.012231 0.017294 0.009618 0.012868 0.008884 0.007479 0.0297
YP21 0.010316 0.012820 0.011595 0.027701 0.011857 0.016891 0.008961 0.012241 0.008532 0.007236 0.0289
YP22 0.009698 0.012251 0.011109 0.026547 0.011485 0.016488 0.008324 0.011615 0.008187 0.006996 0.0281
YP23 0.009105 0.011704 0.010640 0.025410 0.011116 0.016086 0.007711 0.010995 0.007852 0.006760 0.0273
ASHRAE Transactions: Symposia 509
APPENDIX B
After the review process and very near to press time, itwas determined that the conduction transfer function coeffi-cients originally published by Harris and McQuiston (1988)were inaccurate for a few of the very high mass walls androofs. Furthermore, these CTF coefficients have beenpublished in the 1989, 1993, and 1997 editions of theASHRAE Handbook—Fundamentals. Presumably, this is dueto precision problems in the CTF calculation program,although this has not been investigated in detail by theauthors. The errors may be quantified by checking whether ornot the CTF coefficients satisfy a fundamental relationshipbetween the U-factor and the CTF coefficients:
(B-1)
The surfaces for which the discrepancy between theactual U-factor and the U-factor determined from the CTF
coefficients exceeds 1% are Roof 37 (3%), Roof 38 (8%),Wall 30 (2%), Wall 31 (6%), Wall 35 (16%), Wall 37 (30%),Wall 38 (30%). In every case, the U-factor based on the CTFcoefficients is lower than the actual U-factor. Hence, theerrors in the CTF coefficients will result in under-predictingthe cooling loads.
Therefore, new CTF coefficients were determined usingSeem’s method (Seem et al. 1989). For each of the massivesurfaces, either 12 or 13 temperature history terms (b coeffi-cients) and 12 or 13 flux history terms (d coefficients)resulted. Periodic response factors were determined fromthese CTF coefficients using the procedure described in thepaper. Surfaces for which new CTF coefficients were used todetermine the periodic response factors are marked with anasterisk in Tables 6, 9, A-3, and A-6.
REFERENCES
Seem, J.E., S.A. Klein, W.A. Beckman, J.W. Mitchell. 1989.Transfer functions for efficient calculation of multidi-mensional transient heat transfer. Journal of Heat Trans-fer, 11: 5-12, February.
∑∑
=
=
+=
1
0
1n
n
nn
d
b
U
This paper has been downloaded from the Building and Environmental Thermal Systems Research Group at Oklahoma State University (www.hvac.okstate.edu) The correct citation for the paper is: Spitler, J.D., D.E. Fisher. 1999. Development of Periodic Response Factors for Use with the Radiant Time Series Method. ASHRAE Transactions. 105(2): 491-509. Reprinted by permission from ASHRAE Transactions (Vol. #105 Part 2, pp. 491-509). © 1999 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.