el’s

ofs-ande-of

Thete-all orrs:

ndpre-

ef-e

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.

SE-99-1-1

491

ore

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

–•=

ASHRAE Transactions: Symposia

the

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

–

ASHRAE Transactions: Symposia

as

n-eri-

ter-

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).

493

494 ASHRAE Transactions: Symposia

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

496A

SH

RA

E Transactions: S

ymp

osia

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

-

-

-

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.)

ASHRAE Transactions: Symposia

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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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dix B)

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.