7-G-i

APPENDIX 7-G. DETERMINATION OF FURNACE ENERGY USE IN THE LCC 

ANALYSIS 

TABLE OF CONTENTS

7-G.1 INTRODUCTION .................................................................................................7-G-2

7-G.2 DETERMINATION OF AVERAGE ANNUAL FUEL ENERGY 

CONSUMPTION (EF)...........................................................................................7-G-2

7-G.3 Determination of Average Annual Electrical Energy Consumption (EAE)............7-G-3

7-G.4 Determination of National Average Number of Burner Operating Hours 

(BOHSS) .................................................................................................................7-G-4
7-G-2

APPENDIX 7-G. DETERMINATION OF FURNACE ENERGY USE IN THE LCC 

ANALYSIS

7-G.1 0INTRODUCTION 

The energy consumption in the LCC analysis is determined using the 2007 ASHRAE 

SPC 103R “Method of Testing for Annual Fuel Efficiency of Residential Central Furnaces and 

Boilers”.1

 This approach requires the calculation of the average annual fuel energy consumption 

(EF), the average annual electrical energy consumption (EAE), and the national average number of 

burner operating hours (BOH) of furnaces.

The following calculations and summary tables describe the determination of EF, EAE, 

and BOH for gas- and oil-fired furnaces.

7-G.2 0DETERMINATION OF AVERAGE ANNUAL FUEL ENERGY 

CONSUMPTION (EF) 

The average annual fuel consumption is calculated in Appendix C section 2 of the ASHRAE 

103/2007 test procedure:1

EF = BOHSS * (QIN - QP) + 8,760 * QP , for single-stage furnaces, Eq. 1

EF = (BOHH * QIN) + (BOHR * QIN,R) + [8,760 - (BOHH + BOHR )]* QP, for two-stage furnaces 

and Eq. 2

EF = (BOHM * QIN,M) + (BOHR * QIN,R)+ [8,760 - (BOHM + BOHR )]* QP, for continuous 

modulating1 furnaces Eq. 3

where,

BOHSS = national average number of burner operating hours (see derivation in section 7-

G.2.3),

BOHH = national average number of burner operating hours at the maximum operating 

mode for two-stage furnaces (see derivation in section 7-G.2.3),

BOHR = national average number of burner operating hours at the reduced operating mode 

for two-stage or continuous modulating furnaces (see derivation in section 7-

G.2.3),

BOHM = national average number of burner operating hours at the modulating operating 

mode for continuous modulating furnaces (see derivation in section 7-G.2.3),

QIN = steady-state nameplate input rate in Btu/h for single-stage furnaces or steady-state 

nameplate maximum input rate in Btu/h for two-stage and continuous modulating 

furnaces,

 1

 In this Technical Support Documentation, “continuous modulating” term is used instead of 

“step-modulating”. Both terms are interchangeable used in the literature.
7-G-3

QIN,R = steady-state reduced fuel input rate,

QIN,M = steady-state modulating fuel input rate, and

QP = pilot flame fuel input rate in Btu/h.

QIN is based on the baseline value for each product class. We set QIN,R to be 69% of QIN

for non-condensing two-stage equipment, 67% for condensing two-stage equipment, and 40% 

for continuous modulation equipment, where this value represents the average ratio QIN/QIN,R as 

derived using manufacturer product literature and AHRI March 2010 Directory data for all listed 

two-stage furnace models.2

From the test procedure,

1 QIN,M is calculated using QOUT,M and EffySS,M (as defined in 

section 11.4.8.10 or 11.5.8.8).1 QP is zero for all product classes, except for the baseline 

manufactured-home gas furnace and gas boiler. 

7-G.3 0Determination of Average Annual Electrical Energy Consumption (EAE) 

Using the ASHRAE SPC 103/2007 test procedure,1 the average annual auxiliary 

electrical energy consumption is calculated in Appendix C section 3:

EAE = BOHSS (yP * PE + yIG *PEIG + y * BE), for single-stage furnaces, Eq. 4

and

EAE = BOHR (yP,R*PER + yIG,R *PEIG,R + yR*BER) + BOHH or M (yP*PEH + yIG *PEIG,H + 

y*BEH)

2

, for two-stage and continuous modulating furnaces, Eq. 5

where

BOHss = as defined in section 7-G.2.3,

BOHH = as defined in section 7-G.2.3,

BOHM = as defined in section 7-G.2.3,

BOHR = as defined in section 7-G.2.3,

yP = ratio of induced or forced draft blower on-time to average burner on-time,

yP,R = ratio of induced or forced draft blower on-time to average burner on-time, 

measured at the reduced fuel input rate,

PE = burner (or draft inducer) electrical power input at full-load steady-state operation 

in kW,

PER = burner (or draft inducer) electrical power input at full-load steady-state operation 

in kW, measured at the reduced fuel input rate,

PEH = burner (or draft inducer) electrical power input at full-load steady-state operation 

in kW, measured at the maximum fuel input rate,

 2

 The ASHRAE test procedure does not deal with ignitor energy consumption. The ratio of 

ignitor on-time to burner on-time and the ignitor power consumption variables come from the 

DOE test procedure.3
7-G-4

yIG = ratio of burner interrupted-ignition device on-time to average burner on-time,

yIG,R = ratio of burner interrupted-ignition device on-time to average burner on-time, 

measured at the reduced fuel input rate,

PEIG = electrical input rate to the interrupted ignition device on the burner,

PEIG,R = electrical input rate to the interrupted ignition device on the burner, measured at 

the reduced fuel input rate,

PEIG,H = electrical input rate to the interrupted ignition device on the burner, measured at 

the maximum fuel input rate,

y = ratio of blower or pump on-time to burner on-time,

yR = ratio of blower or pump on-time to burner on-time, measured at the reduced fuel 

input rate,

BE = circulating-air fan or water pump electrical energy input rate in kW,

BER = circulating-air fan or water pump electrical energy input rate in kW, measured at 

the reduced fuel input rate, and

BEH = circulating-air fan or water pump electrical energy input rate in kW, measured at 

the maximum fuel input rate.

The values yP and yP,R are calculated using tP (post-purge time). For this calculation, 

DOE took tP to be 5 seconds for furnaces, which is less than or 30 seconds and is therefore set 

equal to 0 seconds, according to Appendix C section 1 of the ASHRAE SPC 103/2007 DOE 

calculated the values y and yP,R using t+ (blower or pump on-delay) and t- (blower or pump offdelay). For furnaces, t+ = 2 min and t- = 0.5 min, which are values obtained for the generic 

furnace models. For gas furnaces, PE is equal to 75 W for non-condensing furnaces and 90 W 

for condensing furnaces. For oil furnaces, PE is set to 220 W. 6 For design options which 

include modulating controls, we set PER and PEH to have the same values as PE, since it is 

assumed that there is no inducer modulation. For gas furnaces, PEIG, PEIG,R, and PEIG,H are set 

equal to 400 W.7

 For oil furnaces, PEIG is equal to 45 watts for oil equipment without 

interrupted ignition and 25 watts with oil equipment with interrupted ignition.8 For design 

options which include modulating controls, we set PEIG,R and PEIG,H to have the same values as 

PEIG, since it is assumed that there is no ignition modulation. For furnaces, BE and BER values 

are calculated using equations in Appendix 7-G for the different design options.

7-G.4 0Determination of National Average Number of Burner Operating Hours (BOHSS) 

From the ASHRAE SPC103/2007 test procedure,1 the national average number of burner 

operating hours for furnaces and boilers is calculated in Appendix C section 1:

BOHSS = 2080 * 0.77 * A * (QOUT / (1 + α)) - 2080 * B, for single-stage furnaces,

BOHH = XH * (2080) * (0.77) * AH * (QOUT / (1 + α)) - 2080 * BH, for two-stage furnaces 

at the maximum operating mode, Eq. 7

BOHR = XR * (2080) * (0.77) * AR * (QOUT / (1 + α)) - 2080 * BR, for two-stage and 

continuous modulating furnaces operating at the reduced 

operating mode, Eq. 8
7-G-5

and

BOHM = XH * (2080) * (0.77) * AM * (QOUT / (1 + α)) - 2080 * BM, for continuous 

modulating furnaces operating at the modulating operating mode, Eq. 9

where

2080 = national average heating load hours,

0.77 = adjustment factor to adjust the calculated design heating requirements and heating 

load hours to the actual heating load experienced by the heating system,

A = 100,000/ [341300(yP * PE + yIG,R *PEIG,R + y * BE) + (QIN - QP) * EffyHS]

3

AH = 100,000/ [341300(yP * PEH + yIG,R *PEIG,R + y * BEH) + (QIN - QP) * EffyU,H]

a

, 

, 

AR = 100,000/ [341300(yP,R * PER + yIG,R *PEIG,R + yR * BER) + (QIN,R - QP) * EffyU,R]

a

, 

AM = 100,000/ [341300(yP * PEH + yIG,R *PEIG,R + y * BEH) + (QIN,M - QP) * EffyU,M]

a

, 

B = 2 * (QP) * (EffyHS) * (A) / 100,000,

BH = 2 * (QP) * (EffyU,H) * (AH) / 100,000,

BR = 2 * (QP) * (EffyU,R) * (AR) / 100,000,

BM = 2 * (QP) * (EffyU,M) * (AM) / 100,000,

QOUT = maximum fuel input rate heating capacity,

α = oversize factor,

XH = fraction of heating load at maximum fuel input rate operating mode,

XR = fraction of heating load at reduced fuel input rate operating mode (1-XH),

QIN = as defined in section 7-G.2.1 of this appendix,

QIN,R = as defined in section 7-G.2.1 of this appendix,

QIN,M = as defined in section 7-G.2.1 of this appendix, 

QP = as defined in section 7-G.2.1 of this appendix, 

yP = as defined in section 7-G.2.2 of this appendix,

yP,R = as defined in section 7-G.2.2 of this appendix,

PE = as defined in section 7-G.2.2 of this appendix,

PER = as defined in section 7-G.2.2 of this appendix,

PEH = as defined in section 7-G.2.2 of this appendix,

yIG = as defined in section 7-G.2.2 of this appendix,

yIG,R = as defined in section 7-G.2.2 of this appendix,

PEIG = as defined in section 7-G.2.2 of this appendix,

PEIG,R = as defined in section 7-G.2.2 of this appendix,

PEIG,H = as defined in section 7-G.2.2 of this appendix,

y = as defined in section 7-G.2.2 of this appendix,

yR = as defined in section 7-G.2.2 of this appendix,

BE = as defined in section 7-G.2.2 of this appendix,

 3

 The ASHRAE test procedure does not deal with ignitor energy consumption. The ratio of 

ignitor on-time to burner on-time and the ignitor power consumption variables come from the 

DOE test procedure.3
7-G-6

BER = as defined in section 7-G.2.2 of this appendix,

BEH = as defined in section 7-G.2.2 of this appendix,

EffyHS = ratio of the average length of the heating season in hours to the average heating load 

hours,

EffyU,H = average part load efficiency at the maximum fuel input rate,

EffyU,R = average part load efficiency at the reduced fuel input rate, and

EffyU,M = average part load efficiency at the modulating fuel input rate.

Equations 6 through 9 are modified to account for the fact that we know the house 

heating load (HHL) for each RECS household (see Chapter 7). First we set HHL equal to the 

factors in equations 6 through 9 used to approximate HHL:

HHL = 2080 * 0.77 * (QOUT / (1 + α)) Eq. 10

Therefore α is set equal to: 

α = QOUT * (2080) * (0.77) / (HHL) - 1 Eq. 11

instead of being equal to the constant value 0.7 as defined in the ASHRAE SPC103/2007 test 

procedure.1

The modified equations used in the LCC spreadsheet are as follows (Note that the 

maximum value for BOH is set to 8760):

BOHSS = A * HHL - 2080 * B, for single-stage furnaces, Eq. 12

BOHH = XH * AH * HHL - 2080 * BH, for two-stage furnaces at the maximum operating 

mode, Eq. 13

BOHR = XR * AR * HHL - 2080 * BR, for two-stage and continuous modulating furnaces 

operating at the reduced operating mode, Eq. 14

and

BOHM = XH * AM * HHL - 2080 * BM, for continuous modulating furnaces operating at 

the modulating operating mode, Eq. 15

To calculate factors A, AH, AR, AM, B, BH, BR, and BM, DOE calculated yP, yP,R, PE, PER, 

PEH, yIG, yIG,R, PEIG, PEIG,R, PEIG,H, y, yR, BE, BER, BEH, , PE, yIG, PEIG, y, BE, QIN, and QP yP ,

as described in section 7-G.2.2 of this appendix. For factor B, if QP = 0, then B = 0, which is true 

for all cases except for the baseline manufactured-home gas furnace and the baseline gas boiler. 

We calculated EffyHS, heating seasonal efficiency, as defined in sections 11.2.11, 11.3.11.3, 

11.4.11.3, and 11.5.11.3.1 For QP = 0, EffyHS is equal to the annual fuel utilization efficiency 

(AFUE). For QP > 0, EffyHS is calculated using EffySS (as defined in section 11.2.8.11

). EffySS is 

calculated using QOUT (as defined below), K (factor that adjusts the jacket losses, where K = 1.7 
7-G-7

for non-weatherized furnaces and Lj (jacket loss, where Lj = 1 is the default value as described in 

section 11.2.8.11

)

QOUT for all product classes is calculated using the following equations based on AHRI 

Directory data for Non-Weatherized Gas Furnaces2:

QOUT = QIN (0.7247 * AFUE + 0.22346), for non-condensing equipment, and Eq. 16

QOUT = QIN (0.8127 * AFUE + 0.17557), for condensing equipment. Eq. 17

DOE calculated XH by using TC (balance-point temperature as defined in section 11.4.8.4 

1

), α (the oversize factor, as calculated in Equation 11), QOUT, and QOUT,R (reduced fuel input rate 

heating capacity). QOUT,R is set equal to 69% QOUT for non-condensing equipment and 67% QOUT

for condensing equipment, as derived using manufacturer product literature and AHRI Directory 

data for all listed two-stage furnace models.2 XR is set equal to 1-XH. EffyU,H = EffyU,R and 

therefore using the equation in section 11.5.11.31 is equal to EffySS. EffyU,M is calculated using 

the equation in section 11.4.9.2.3.1
7-G-8

REFERENCES

1. American Society of Heating Refrigerating and Air-Conditioning Engineers Inc., Method 

of Testing for Annual Fuel Utilization Efficiency of Residential Central Furnaces and 

Boilers, 2007. Atlanta, GA. Report No. ASHRAE Standard 103-2007.

2. AHRI. AHRI Directory March 2010, 2010.

3. U.S. Department of Energy, Title 10, Code of Federal Regulations, Chapter II Part 430 

Appendix N, Subpart B-Uniform Test Method for Measuring the Energy Consumption of 

Furnaces and Boilers, January 1, 2007. 

4. Honeywell Inc., Hot Surface Modules: S89C, D, G, H, J and S890C, D, G, H, J, 1989. 

Form Number: 68-0079-1. 

5. Carlin Combustion Technology Inc., Oil Burner Ignition Systems: Interrupted Duty vs. 

Intermittent Duty, 2002. (Last accessed October 29, 2002.) 

<http://www.carlincombustion.com/TechLib/tech_speaking1.html> 

6. Brookhaven National Laboratory, Comparison of Burner Operating Options, 1994. 

Brookhaven National Laboratory. 

7. Gable, G., Report to Lawrence Berkeley National Laboratory on Gas Furnace Ignition 

Systems, 2003. 

8. Oswald, K., Report to Lawrence Berkeley National Laboratory on Pumps and Burners, 

2002. 

9. Taco Inc., 110-120 Red Baron Circulators, 2003.