NISTIR 7325 

Linear-Fit-Based Rating Procedure for Mixed AirSource Unitary Air Conditioners and Heat Pumps 

Operating in the Cooling Mode 

W. Vance Payne 

Piotr A. Domanski 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

National Institute of Standards and Technology

Technology Administration

United States Department of Commerce 

NISTIR 7325 

Linear-Fit-Based Rating Procedure for Mixed AirSource Unitary Air Conditioners and Heat Pumps 

Operating in the Cooling Mode 

W. Vance Payne 

Piotr A. Domanski 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

June 2006 

U.S. DEPARTMENT OF COMMERCE 

Carlos M. Gutierrez, Secretary 

TECHNOLOGY ADMINISTRATION 

Michelle O’Neill, Acting Under Secretary of Commerce for Technology 

National Institute of Standards and Technology

William Jeffrey, Director 

ii
Use of Non-SI Units in a NIST Publication 

It is the policy of the National Institute of Standards and Technology to use the 

International System of Units (metric units) in all of its publications. However, in North 

America in the HVAC&R industry, non-SI units are so widely used instead of SI units

that it is more practical and less confusing to include measurement values in customary 

units followed by SI units. 

iii
ACKNOWLEDGMENTS 

Brian Dougherty at NIST reviewed the procedure and provided the input for the 

calculation of SEER using the EER ratio, and he also provided his work on cyclic 

degradation coefficients, which was included in the calculation of the expansion 

device/time delay correction factor. Stefan Leigh of the NIST Statistical Engineering 

Division and his associates provided gracious assistance in reviewing the uncertainty 

analysis. The authors also thank Carl Bergt of Rheem Manufacturing Company, Chad

Kirkwood of United Technologies/Carrier, Darryl Denton of American Standard/Trane,

Mark Olsen of Lennox Industries, Ray Patil of Aspen Manufacturing, and Bob Magee 

formerly of Allstyle Coil Company for their reviews and technical input. 

Thanks also to Michael Woodford of ARI for his organizational support and 

dissemination of the many drafts to the ARI Unitary Small Equipment Committee, whose 

membership also provided comments. 

The U.S. Department of Energy, Building Technologies Program, Energy Efficiency and 

Renewable Energy supported the development of this rating procedure with Michael 

Raymond serving as the project manager. 

iv
TABLE OF CONTENTS 

 PAGE 

Concept of the Linear-Fit-Based Rating Procedure.................................................1 

Section 1. Purpose .............................................................................................3 

Section 2. Scope.................................................................................................3 

Section 3. Definitions ..........................................................................................3 

Section 4. Procedure for Rating a Mixed System ...............................................4 

4.1. General.................................................................................................4 

4.2. Mixed Indoor Section Data ...................................................................5 

4.3. Outdoor Section Data ...........................................................................7 

4.4. Expansion Device and Fan Delay 

Correction Factor, Fexp .......................................................................9 

4.5. Calculations ..........................................................................................10 

4.6. Rating Values .......................................................................................13 

4.7. Restrictions...........................................................................................14 

TABLES 

Table 1. System categories for determining Fexp .............................................10 

Table 2. Fexp for various mixed and matched system combinations ................10 

Table 3. Rated cooling capacity multiples........................................................14 

Table C1. EER uncertainty for given uncertainties in capacity and power .........23 

Table C2. SEERmixed uncertainty ........................................................................24 

FIGURES 

Figure 1. Graphical illustration of the linear fit based rating procedure................ 2 

Figure C1. Uncertainty of mixed system capacity due to linear fit uncertainties.....19 

Figure C2. Uncertainty of mixed system condensing unit 

power due to linear fit uncertainties ...................................................19 

APPENDICES 

Appendix A. References – Normative ....................................................................15 

Appendix B. References – Informative...................................................................16 

Appendix C. Uncertainty of the mixed system capacity and SEER ........................18 

v
CONCEPT OF THE LINEAR-FIT-BASED RATING PROCEDURE

A given single-speed, split system outdoor unit (consisting of a condenser, compressor, 

associated tubing, and, for heat pumps, a heating mode expansion device) can be 

installed with one of several different indoor units (consisting of the indoor coil, indoor

fan, and expansion device). For each split system combination, the consumer is

provided performance information – including the Seasonal Energy Efficiency Ratio 

(SEER) and the cooling capacity at the 95 °F (35 °C) rating point, Q(95). Federal 

regulations require that the SEER rating for each model of outdoor section, when

installed with its highest sales volume indoor section, be obtained from laboratory tests 

of the complete system (CFR 2006a). This tested highest sales volume combination is 

referred to here as the matched system. For all other combinations of indoor units with

the same outdoor unit, the system ratings may be obtained by conducting the same set 

of laboratory tests or, in lieu of conducting system testing, by using a DOE approved 

methodology called an alternative rating method (ARM). Untested combinations whose 

ratings are determined using an ARM are called mixed systems. Mixed systems may 

be created using indoor units and outdoor units provided by the same manufacturer – 

referred to as the system or original equipment manufacturer (OEM) – or created by

using a third party indoor coil from an independent coil manufacturer (ICM). 

One of the more commonly used ARM’s for rating mixed systems relies upon the 

publicly available Q(95) and SEER of the tested matched system (e.g., Domanski

1989). This (and other) ARM’s require the rater to determine the cooling capacity of the 

matched system indoor coil. For an independent coil manufacturer, this requirement

can be a major hurdle because of limits on the availability of specification data on the 

matched indoor coil and, if used, the accuracy of capacity prediction algorithms or

computer simulation models. Any error in the matched indoor coil capacity propagates

to affect the error in the mixed system SEER and Q(95) ratings. Consequently, an 

alternative rating method that does not include this step – such as the linear-fit-based 

method (L-F Method) - has the inherent potential of providing more accurate ratings. 

Figure 1 shows the application of the L-F Method in graphical form for the cooling mode. 

This method uses a linear fit of the mixed indoor coil cooling capacity as a function of

the evaporator exit refrigerant saturation temperature when the coil is subjected to 

standard operating conditions. The method also uses linear fits of cooling capacity and 

power consumption of the outdoor/condensing (CD) unit as a function of evaporator exit 

refrigerant saturation temperature when operated at the standard test conditions

associated with the A Test of the DOE air conditioner and heat pump test procedure.

The suction refrigerant saturation temperature for these fits is evaluated based on the 

pressure at the exit of the evaporator, or comparably, the inlet to the compressor. The 

CD unit cooling capacity and power consumption linear fits are depicted in Figure 1 as

q(95) and p(95) (A Test). Overlaying the indoor unit (evaporator) and CD Unit capacity 

line yields an intersection point that indicates the mixed system capacity (without indoor

fan contributions) at the A Test conditions (95 oF, 35.0 oC). By projecting the refrigerant 

saturation temperature that corresponds to the A Test capacity onto the CD Unit power

consumption plot, the power requirement for the CD Unit at the 95 oF (35 oC) rating 

1
point is determined. Although Figure 1 is convenient for explaining the L-F Method, this

method is best implemented numerically using a computer. Condensing Unit Capacity

Saturation Temperature

q(95)

Evaporator Capacity

Saturation Temperature

Po

wer

Saturation Temperature

p(95)

Compressor Condenser

Evaporator

Expansion

Device

CONDENSING UNIT

INDOOR AIR-HANDLER

Figure 1. Graphical illustration of the linear fit based rating procedure 

The rating process explained above does not account for indoor fan power. To finalize

the rating of the mixed system, heat from the indoor fan must be included, thus reducing 

the cooling capacity, q(95) , obtained from overlaying the capacity lines of the CD Unit

and mixed evaporator. The result is the actual mixed system capacity, Q(95). Also, the 

indoor fan power must be added to the CD Unit power to produce the total power for the 

system, P(95). The energy efficiency ratio at the A Test rating point, EER(95), can then 

be calculated. 

(95)

(95) EER(95) PQ=

 

To conclude with the SEER calculation of the mixed system, a value of expansion 

device correction factor for the mixed system is required. 

exp

matched

mixed

mixed matched F

EER(95)

EER(95) SEER = SEER

2
EER(95)matched is used in the SEER calculation because it may be calculated from the 

rated cooling capacity which is readily available to mixed system coil manufacturers. 

EER(82) is preferable for this calculation, but this value is not readily available. 

The expansion device correction factor must be obtained from a separate analysis. 

1. PURPOSE 

The purpose of this report is to establish the method for determining the cooling

performance ratings of air-source unitary split system air conditioners and heat pumps 

consisting of an outdoor section and an indoor section that were not tested together as

a complete system. The quantities calculated in this document are the cooling capacity

at the A Test conditions and the SEER as prescribed by the U.S. Department of Energy

in Appendix M to Subpart B of Part 430 within Title 10 of the Code of Federal 

Regulations (CFR 2006a and CFR 2006b) and by ARI Standard 210/240 (ARI 2006). 

2. SCOPE 

This procedure applies to split system residential air-source unitary air conditioners and

heat pumps. The outdoor section is characterized by a single-speed compressor with 

single-phase, electric power usage. The A Test cooling capacity of the highest sales

volume combination used in obtaining the ratings of the mixed system shall be less than 

65 000 Btu/h (19 050 W). This procedure does not apply to systems employing 

multispeed compressors or using a load following control strategy (e.g., cylinder 

unloading, hot-gas bypass). 

3. DEFINITIONS 

All definitions cited in the Code of Federal Regulations, Subpart A, Part 430.2 (CFR 

2006c) shall be considered a part of this procedure in addition to the following 

definitions. 

A Test: pertaining to data collected according to DOE specified procedures and at the 

following environmental conditions: 95 oF (35 oC) outdoor dry-bulb temperature, 80.0 oF

(26.7 oC) indoor dry-bulb temperature, and 67.0 oF (19.4 oC) indoor wet-bulb 

temperature (CFR 2006a, ARI 2006). 

Air Source Unitary Air Conditioner or Air Source Unitary Heat Pump or Unitary 

System: an outdoor unit combined with an indoor coil assembly designed to function 

together as an air conditioning (and heating) system. 

B Test: pertaining to data collected according to DOE specified procedures and at the 

following environmental conditions: 82.0 oF (27.8 oC) outdoor dry-bulb temperature, 

80.0 oF (26.7 oC) indoor dry-bulb temperature, and 67.0 oF (19.4 oC) indoor wet-bulb 

temperature(CFR 2006a, ARI 2006). 

EER: Energy Efficiency Ratio defined as the cooling capacity divided by the total power 

input. 

3
Highest Sales Volume Tested Combination: System combination of outdoor 

condensing unit or heat pump outdoor unit that is the most likely to be sold. This

is the combination that is laboratory tested per requirements in CFR Part 430. 

Indoor Section: an assembly consisting of an interior/indoor refrigerant-to-air heat

exchanger, condensate collection pan, and refrigerant expansion device, and which 

may include a blower, blower motor, and associated cabinet. 

Indoor Fan Power: power (watts) measured at the indoor unit for the included fan. If 

no fan is included, the default value for indoor fan power (and heat) is 0.365 W/scfm 

(775 W/(m3

/s)). Rated cooling capacity must always include the measured or default 

fan heat. Cooling capacity linear-fits do not include the indoor fan heat. 

Matched Coil: an indoor coil which is part of the matched system. 

Matched System: a unitary system which has been tested and rated in accordance 

with federal regulations. 

Mixed Coil: an indoor coil which is part of the mixed system. 

Mixed System: a unitary system which is not tested as a complete system in 

accordance with federal regulations but instead has its SEER and rated cooling capacity

determined using a DOE-approved alternative rating method. 

Outdoor Section: an assembly of components designed to compress and/or liquefy a 

specific refrigerant and located in the exterior/outdoor environment. It consists of at 

least a refrigerant vapor compressor, refrigerant-to-air heat exchanger, motorized fan, 

refrigerant vapor and liquid lines, and other standard components. 

Shall: where “shall” or “shall not” are used for a specified provision, that provision is 

mandatory if compliance with the procedure is claimed. 

Should, Recommended, or It Is Recommended: “should”, “recommended”, or “it is

recommended” are used to indicate provisions which are not mandatory but which are 

desirable as good practice. 

4. PROCEDURE FOR RATING A MIXED SYSTEM 

4.1. General

Below are the basic steps required when rating a mixed air conditioner using the L-F 

Method. 

 Obtain data for the matched system: SEER, Q(95), and the following information 

on the matched system indoor unit – type of expansion device, whether using a 

liquid line solenoid, whether equipped with an indoor fan delay. If the evaporator 

4
is a blower coil, the rater should obtain the power draw of the indoor fan when 

providing the rated Q(95) 

 Obtain or develop data for the outdoor section (condensing unit) 

o Outdoor section capacity linear fit at the A Test conditions as a function of the 

evaporator exit refrigerant saturation temperature 

o Outdoor section power linear fit at the A Test conditions as a function of the 

evaporator exit refrigerant saturation temperature 

 Obtain or develop data for the mixed indoor section 

o Indoor coil capacity linear fit as a function of the evaporator exit refrigerant

saturation temperature at indoor air conditions of 80.0 oF (26.7 oC) dry-bulb/ 

67.0 oF (19.4 oC) wet-bulb temperatures 

o Indoor fan power 

 Determine the expansion device and fan delay correction factor for the mixed 

system 

 Perform rating calculations 

These steps are detailed in the following sections. 

4.2. Mixed Indoor Section Data 

4.2.1. Correlation for indoor coil capacity 

The correlation for indoor coil capacity shall have the following form: 

 qcoil = Ccoil + Dcoil ·Tevap 4.1 

where qcoil - indoor coil cooling capacity at 80.0 oF (26.7 oC) dry-bulb/67.0 oF (19.4 oC) 

wet-bulb air temperature and at a manufacturer-specified air volume 

rate, without indoor fan heat, Btu/h (W) 

Ccoil - linear intercept, Btu/h (W) 

Dcoil - linear slope, Btu/(h oF) (W/oC) 

Tevap - refrigerant saturation temperature at the evaporator exit, oF (oC) 

Equation 4.1 shall be determined using capacities from laboratory tests, or in lieu of 

laboratory tests, from simulations using a validated simulation model, or from a 

combination of experimental and simulation results. The same refrigerant shall be used 

to rate the mixed system and the matched system. 

4.2.1.1. Determination of Equation 4.1 coefficients using laboratory test data

The constants in Equation 4.1 shall be determined by fitting the measured coil cooling 

capacities and exit refrigerant saturation temperatures using the least-squares method. 

5
The indoor coil tests shall be carried out in accordance with the procedures set forth in 

ASHRAE Standard 33 and indoor air conditions corresponding to the A and B Tests. 

The following parameters shall be controlled within the specified ranges: 

 The airflow shall match the intended coil application. The volumetric air flow 

shall not exceed 450 scfm/ton (217.4 m3

/kW) and, for coil-only indoor units, the 

maximum static air pressure drop measured across the coil may not exceed 

0.30 in H2O gage (75.0 Pa gage). 

 The refrigerant entering the expansion device shall be liquid at a temperature 

normally seen with condensing units with which the mixed indoor coil would be

paired, with a minimum of 7.5 oF (4.2 oC) subcooling. The liquid temperature 

used for a particular linear fit shall not vary more than ± 5.0 oF (± 2.8 oC) from the 

average value for all experimental data used to generate the linear fit. 

 The refrigerant superheat at the evaporator exit shall be 10.0 oF ± 5.0 oF 

(5.0 oC ± 2.8 oC). 

The tests shall be performed at different evaporator exit refrigerant saturation 

temperatures to cover the expected saturation temperature range of the mixed system, 

which typically neither extends below 40.0 oF (4.4 oC) nor exceeds 52.0 oF (11.1 oC). It 

is recommended that the range of evaporator refrigerant saturation temperatures for 

which the linear fit may be applied and the percentage uncertainty of the capacity

(±x %) be reported along with the coefficients developed for Equation 4.1. Appendix C 

presents an example uncertainty calculation that may aid in the development of

percentage uncertainties. 

4.2.1.2 Determination of Equation 4.1 coefficients using analytical predictions of coil

cooling capacity

The constants in Equation 4.1 shall be determined by fitting a line to the predicted coil 

cooling capacities for at least two different evaporator exit refrigerant saturation 

temperatures. 

Airflow and temperature parameters shall be as specified above in Section 4.2.1.1. All 

simulations shall be performed with a validated simulation tool. Refer to Section 4.7 for

simulation tool validation requirements. 

4.2.2. Indoor fan power and heat

If a fan is used with the mixed indoor section, its electrical power shall be measured with

an uncertainty of ±1 % (for a single measurement). If a fan is not included with the 

indoor coil, the default indoor fan power shall be calculated by the following equation: 

Pfan,mixed = Wf · Vind 4.2 

where: Wf = flow specific fan power multiplier of 0.365 W/scfm (775 W/(m3

/s)) 

 Vind = indoor air volume rate of standard air, scfm (m3

/s) 

6
The heat added to the air stream shall be calculated by Equation 4.3: 

Qfan,mixed = Wc· Pfan,mixed 4.3 

where: Wc = 3.412 Btu/(W·h) (1 W/W) 

4.3. Outdoor Section Data

Outdoor section cooling capacity and power shall be represented by linear functions of 

the evaporator exit refrigerant saturation temperature. The linear fit coefficients shall be 

determined from a least-squares fit at different evaporator exit refrigerant saturation 

temperatures. At least one of the data points shall be the average tested value of the 

highest sales volume tested combination (HSVTC) system. All linear fits shall be 

adjusted to pass through the average test data point for the HSVTC system.

Measurements and calculations of system performance shall be made according to ARI 

210/240 (ARI 2006). 

4.3.1. Correlation for outdoor section cooling capacity at A Test conditions

The correlation for the outdoor section cooling capacity at the A Test conditions shall 

have the following form: 

qCD(95) = CCD(95) + DCD(95) ·Tevap 4.4

where qCD - outdoor section capacity at the A (95) Test conditions, without indoor 

fan heat, Btu/h (W) 

 CCD - outdoor section capacity linear intercept at the A (95) Test 

conditions, Btu/h (W) 

 DCD - outdoor section capacity linear slope at the A (95) Test conditions, 

Btu/(h oF) (W/oC) 

Tevap - refrigerant saturation temperature at the evaporator exit, oF (oC) 

Equation 4.4 coefficients shall be determined using capacities from laboratory tests, 

from simulations using a validated simulation model, or from a combination of

experimental and simulation results. At least one of the data points shall be from the 

laboratory data utilizing the HSVTC system. 

4.3.1.1. Determination of Equation 4.4 coefficients using laboratory test data

The constants in Equation 4.4 shall be determined by fitting the measured outdoor

section cooling capacities and evaporator exit refrigerant saturation temperatures using 

the least-squares method. 

The test conditions shall be those specified for the DOE A Test (CFR 2006a, ARI 2006). 

The pressure used to calculate Tevap shall be the measured or simulated refrigerant 

7
pressure at the outlet of the evaporator. Simulations shall use the method presented in

ASHRAE 2002 to predict the refrigerant pressure drop in the suction line from the 

evaporator outlet to the compressor inlet if this is needed to determine the evaporator 

exit refrigerant saturation pressure. 

The tests shall be performed at different evaporator exit refrigerant saturation 

temperatures, which typically do not extend below 40.0 oF (4.4 oC) and do not exceed

52.0 oF (11.1 oC). 

The following information shall be reported for Equation 4.4 in addition to the linear

slope and intercept coefficients: 

 The average liquid line temperature for the q(95) linear fit 

 The type of cooling mode expansion device used (non-bleed TXV, bleed-type 

TXV, electronic expansion device, capillary tube, or short tube) 

It is also recommended that the range of refrigerant evaporator temperatures for which 

the linear fit is applicable along with the linear fit percentage uncertainty (±x %) be 

reported. 

4.3.1.2. Determination of Equation 4.4 coefficients using a combination of experimental 

data and analytical predictions

This rating procedure allows using a combination of experimental data and analytical 

methods for determination of Equation 4.4 coefficients provided that the performance 

predictions will be equivalent to those obtained when steps described in sections 4.3.1.1 

are followed. 

One example of combining laboratory test and simulation results may be using an 

experiment to obtain outdoor section performance at a small range of evaporator exit

refrigerant saturation temperatures, and extrapolating these data to a wider range of 

saturation temperatures with a simulation model. All quantities reported in Section 

4.3.1.1 shall still be reported if this technique is used. 

All simulations shall be performed with a validated simulation tool. Refer to Section 4.7 

for simulation tool validation requirements. 

4.3.2. Correlation of outdoor section power at A Test conditions

Outdoor unit power at the A Test conditions shall be represented by a linear fit of the 

following form: 

pCD(95)= ECD(95) + FCD(95) ·Tevap 4.5 

where: pCD(95) - outdoor section total power without indoor fan power, W 

8
 ECD(95) - outdoor section power linear intercept at the A Test conditions, W 

 FCD(95) - outdoor section power linear slope at the A Test conditions, W/°F 

(W/°C) 

Equation 4.5 coefficients shall be determined using capacities from laboratory tests or 

from a combination of experimental and simulation results. At least one of the data

points shall be from the laboratory data utilizing the HSVTC system. 

4.3.2.1. Determination of Equation 4.5 coefficients using laboratory test data

Outdoor section power shall be measured with an uncertainty not to exceed ±1 % (for a 

single measurement). As noted previously, at least one of the data points shall be per

the tested values of the HSVTC system. Power shall be the total power of the matched 

system excluding indoor fan power. This includes the compressor, outdoor fan, 

controls, and other ancillary equipment normally associated with the outdoor unit.

Power measurements shall be taken concurrently with the laboratory measurements

used to obtain cooling capacity data. 

It is recommended that the percentage uncertainty of the condensing unit power (±x %) 

be reported along with the coefficients developed for Equation 4.5. The evaporator exit

refrigerant saturation temperature range shall be the same as that reported for the q(95) 

linear fit. 

4.3.2.2. Determination of Equation 4.5 coefficients using a combination of experimental 

data and analytical predictions

The constants in Equation 4.5 shall be determined from a linear fit of predicted outdoor 

unit power at different evaporator exit refrigerant saturation temperatures. At least one 

of the data points shall be per the tested values of the HSVTC system. All quantities

reported in Section 4.3.2.1 shall still be reported if this method is used. The resulting

equation must be adjusted to pass through the HSVTC tested value as noted at the 

beginning of Section 4.3. 

The simulation tool shall be validated against experimental data obtained during the 

tests used to validate predictions of cooling capacity described in section 4.3.1.2. The 

validation shall demonstrate that the simulation tool can predict the outdoor section 

power and EER at the A Test conditions. Refer to Section 4.7 for general simulation 

tool validation requirements. 

4.4. Expansion Device and Fan Delay Correction Factor, Fexp

The value of the expansion device/fan delay correction factor for the mixed system shall 

be selected using the procedure described below. 

9
First, determine the mixed and matched system category from Table 1 (either A, B1, B2,

or C). Then, determine the Fexp value using the system categories in Table 2

(Dougherty 2004). 

Table 1. System categories for determining Fexp

System 

Category 

System Pressure 

Equalization 

During Off Cycle 

Indoor Fan 

Turn-Off Delay System Components 

A Yes No

Cap Tube 

Orifice 

Bleed TXV 

B1 No No

Non-Bleed TXV 

Electronic Expansion Device 

Liquid Line Solenoid 

B2 Yes Yes

Cap Tube 

Orifice 

Bleed TXV 

C No Yes

Non-Bleed TXV 

Electronic Expansion Device 

Liquid Line Solenoid 

Table 2. Fexp for various mixed and matched system combinations 

Matched System 

A B1 B2 C

A 1.000 0.990 0.990 0.974

B1 1.010 1.000 1.000 0.985

B2 1.010 1.000 1.000 0.985

Mixed 

System 

C 1.026 1.016 1.016 1.000

The rating procedure shall not be used for any system if the matched system has a TXV 

and the mixed system has either a capillary tube or a short tube expansion device, 

unless the condensing unit manufacturer also certifies a system in which the TXV is

replaced by a capillary/short tube. If this is the case, the manufacturer’s condensing 

unit system with the capillary/short tube may be considered as the matched system and 

its performance data used to calculate the performance of the mixed system. 

The rater shall specify the mixed system capillary/short tube if this is the expansion 

device for the mixed system. If the mixed system capacity is similar to that of the 

matched system, specifying the same capillary/short tube as used in the matched

system may be adequate. If the mixed and matched system capacities differ markedly, 

a validated engineering analysis, accounting for the different evaporator refrigerant 

pressures, shall be used to specify the mixed system capillary/short tube. 

4.5. Calculations 

4.5.1. Rated cooling capacity at A Test conditions, Qmixed(95)

10
The indoor section cooling capacity must be corrected to the same refrigerant liquid 

temperature and evaporator exit refrigerant superheat for which the matched system 

capacity and power linear fits were generated. The corrections cannot be used for 

superheats lower than 5.0 oF (2.8 oC); therefore, if the matched condensing unit 

superheat was below 5.0 oF (2.8 oC), the correction values for a superheat of 5.0 oF 

(2.8 oC) shall be used. 

If the matched condensing unit evaporator exit refrigerant superheat is not known then 

the rater shall assume the following; if a TXV was used as the expansion device, the 

q(95) linear fit average evaporator exit superheat shall be assumed to be 10.0 °F 

(5.6 °C). If a short tube was used as the expansion device, evaporator exit superheat

shall be assumed to be 5.0 °F (2.8 °C). 

Step 1: Estimate the correction for the indoor section capacity equation, ε1cor 

0 0879

suph,Coil

suph,CD

0 123

liq,Coil

liq,CD

1

. .

cor T

T

T

T − −

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ε = 4.6 

where: Tliq,CD - refrigerant liquid temperature as listed for the outdoor section at the A 

Test conditions (oF) 

 Tsuph,CD - refrigerant superheat at the evaporator exit as listed for the outdoor 

section at the A Test conditions (oF) 

 Tliq,Coil - refrigerant liquid temperature used during the generation of the linear fit 

for the indoor coil (oF) 

 Tsuph,Coil - refrigerant superheat at the evaporator exit used during the 

generation of the linear fit for the indoor coil (oF) 

Step 2: Estimate the evaporator refrigerant saturation temperature at the A Test 

conditions, Tevap (95) 

CD 1cor coil

1cor coil CD

D (95) D

C C (95) (95) − ⋅

⋅ − = εε Tevap 4.7 

Step 3: Improve the estimate of the correction for indoor section capacity equation, ε2cor 

2

suph,Coil

suph,CD

1

liq,Coil

liq,CD

2

b b

cor T

T

T

T

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ε = 4.8 

where: ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − 50

95

b1 0 123 evap T ( ) .

11
 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = 50

95

b2 -0.0879 evap T ( )

 Tevap(95) - evaporator refrigerant saturation temperature calculated from 

Equation 4.7, converted to oF (if calculated in oC) 

Step 4: Calculate evaporator refrigerant saturation temperature at the A Test

conditions, Tevap(95) 

CD 2cor coil

2cor coil CD

D (95) D

C C (95) (95) − ⋅

⋅ − = ε

ε Tevap 4.9 

Step 5: Calculate mixed system capacity at the A Test conditions, Qmixed(95) 

Qmixed(95) = qCD(95) - Qfan,mixed = CCD(95) + DCD(95) ·Tevap(95) – Qfan,mixed 4.10 

4.5.2. Seasonal Energy Efficiency Ratio, SEER

Calculation of the SEER requires the energy efficiency ratio at the A Test conditions for

the mixed and matched systems, EER(95)mixed and EER(95)matched , respectively. 

4.5.2.1. EER(95)mixed calculation

The energy efficiency ratio is calculated using mixed system capacity Qmixed(95) and 

power Pmixed(95). 

P ( )

Q ( )

95

95 EER(95)

mixed

mixed

mixed = 4.11 

Pmixed(95) = pCD(95) + Pfan,mixed = ECD(95) + FCD(95) ·Tevap(95) + Pfan,mixed 4.12 

where Qmixed(95) shall be taken from Equation 4.10. 

Tevap(95) shall be obtained from Equation 4.9. 

4.5.2.2. EER(95)matched calculation

The tested value of EER(95)matched, with its associated uncertainty, shall be used if

available; otherwise, the value of EER(95)matched shall be calculated using the matched 

condensing unit capacity and power linear fits. This is done to eliminate the 

propagation of conservatively rated EER(95)matched uncertainty into the calculation of

SEERmixed. 

qCD(95)matched = QCD(95)matched + Qfan,matched 4.13 

12
D (95)

(95) C (95) (95)

CD

CD matched CD

matched

− = q Tevap 4.14

Pmatched (95) = pCD(95) + Pfan,matched 

= ECD(95) + FCD(95) ·Tevap(95)matched + Pfan,matched 4.15 

where QCD(95)matched = matched system tested (or rated is test data is not available) 

cooling capacity at A Test conditions 

 Qfan,matched = matched system indoor fan heat in Btu/h (W) (calculated or 

determined from measured fan power) 

Tevap(95)matched = calculated matched system evaporator exit refrigerant saturation 

temperature at the A Test conditions 

 Pfan,matched = matched system indoor fan power (calculated from airflow rate or 

measured) 

(95)

(95) EER(95)

matched

CD matched

matched P

Q= 4.16 

4.5.2.5. SEER calculation

SEER shall be calculated using Equation 4.17. Ideally, EER(82) for the mixed and 

matched systems should be used in this calculation, but EER(95) for the matched 

system is more readily available. SEERmatched shall be the value certified by the 

matched system manufacturer. 

exp

matched

mixed

mixed matched F

EER(95)

EER(95) SEER = SEER 4.17 

4.6. Rating Values 

The rater is responsible for all ratings obtained when using this procedure. The 

calculated ratings are strongly influenced by the input data, and particularly, by the 

goodness of the power and capacity linear fits (Payne and Domanski 2005). Therefore, 

the rater shall establish the acceptability of the input data, including all linear fits, before 

these data are used for ratings. 

4.6.1. Reported cooling capacity at the A Test Conditions (Qmixed(95))

The rated cooling capacity Qmixed(95) shall be expressed in Btu/h (W) in multiples of the

quantities listed in Table 3. 

13
Table 3. Rated cooling capacity multiples 

Cooling capacity, Btu/h (W) Multiples, Btu/h (W) 

Qmixed(95) < 20 000 (5 900) 100 (30) 

20 000 (5 900) ≤ Qmixed(95) < 38 000 (11 000) 200 (60) 

38 000 (11 000) ≤ Qmixed(95) < 65 000 (19 000) 500 (150) 

Qmixed(95) shall not exceed the value calculated using the applicable equation.

4.6.2. Reported SEER

SEER shall be expressed in multiples of 0.05 not to exceed the value calculated by

Equation 4.17. 

4.7. Restrictions 

If the rating is calculated for a heat pump system able to operate in the heating mode,

the following two conditions should be satisfied (Domanski 1989): 1) The internal 

volume of the mixed indoor coil assembly should be within 100 % to 120 % of the

internal volume of the matched coil or should not exceed the volume of the largest coil 

certified with a given condensing unit by the condensing unit manufacturer, whichever is

larger. 2) Condensing capacity of the mixed coil should be within 100 % to 120 % of 

the capacity of the matched coil, or should not exceed the capacity of the largest

certified coil, whichever is larger. 

Verification of simulation tools requires that the method predicts capacity (A Test) within 

5 % of the measured values for systems having the smallest and largest indoor units for 

which the verification tool will be applied. For example, if a manufacturer produces a 

coil family having capacities ranging from 12 000 Btu/h (3516.9 W) to 28 000 Btu/h 

(8206.0 W) and uses a simulation tool to predict the capacities, the simulation tool must

be within 5 % agreement with the test values of the smallest capacity coil and largest

capacity coil. 

A coil simulation model shall be able to account for coil design variations such as tube 

diameter, tube pitch, depth pitch, heat transfer surfaces on the refrigerant and air sides,

etc., and it should be validated for each coil family. For the purpose of this rating 

procedure, a coil family is a group of coils with the same basic design features that 

affect the heat exchanger performance (i.e. A-shape, V-shape, slanted or flat top, heat

exchanger surfaces, tube sizes, construction material, see CFR 2006c). 

The same validation approach, as explained above for capacity, shall be applied to

power prediction tools. 

14
APPENDIX A. REFERENCES - NORMATIVE 

ANSI/ASHRAE 2005. ANSI/ASHRAE Standard 37. Methods of testing for rating unitary

air conditioning and heat pump equipment. American Society of Heating,

Refrigerating and Air-Conditioning Engineers. 1791 Tullie Circle NE, Atlanta, GA, 

30329 USA. 

ASHRAE 1991. ASHRAE terminology of heating, ventilation, air conditioning, and 

refrigeration, 2nd Edition, American Society of Heating, Refrigerating and AirConditioning Engineers. 1791 Tullie Circle NE, Atlanta, GA, 30329 USA. 

ASHRAE 2002. ASHRAE Handbook: Refrigeration, Chapter 2, American Society of 

Heating, Refrigerating and Air-Conditioning Engineers. 1791 Tullie Circle NE, 

Atlanta, GA, 30329 USA, page 2.3. 

ARI 2006. Standard 210/240, Standard for unitary air-conditioning and air-source heat 

pump equipment, Air-Conditioning and Refrigeration Institute, 4100 North Fairfax 

Drive, Suite 200, Arlington, VA 22203. 

CFR, 2006a. Code of Federal Regulations, Title 10 (Department of Energy), Chapter 2,

Part 430.23, Subpart B, Appendix M, “Uniform test method for measuring the 

energy consumption of central air conditioners,” U.S. Government Printing Office,

Washington, DC. 

CFR, 2006b. Code of Federal Regulations, Title 10, Chapter 2, Part 430.24, Subsection 

m1, “Units to be tested,” U.S. Government Printing Office, Washington, DC. 

CFR, 2006c. Code of Federal Regulations, Part 430.2, Definitions, U.S. Government 

Printing Office, Washington, DC. 

Domanski, P.A., 1989. Rating procedure for mixed air-source unitary air conditioners 

and heat pumps operating in the cooling mode – revision 1, NISTIR 89-4071, U. 

S. Dept of Commerce, Natn’l Institute of Standards and Technology, 

Gaithersburg, Maryland USA 20899. 

15
APPENDIX B. REFERENCES - INFORMATIVE 

ASHRAE 2000. ASHRAE Standard 33-2000. MOT Forced circulation air cooling and 

air heating coils, American Society of Heating, Refrigerating and Air-Conditioning 

Engineers. 1791 Tullie Circle NE, Atlanta, GA, 30329 USA. 

ARI 2001. Standard 410, Standard for forced-circulation air-cooling and air-heating 

coils, Air-Conditioning and Refrigeration Institute, 4100 North Fairfax Drive, Suite 

200, Arlington, VA 22203. 

Code of Federal Regulations 2006. Web Link. http://www.access.gpo.gov/nara/cfr/cfrtable-search.html#page1 

Code of Federal Regulations, Part 430 2006. Web Link. 

http://www.access.gpo.gov/nara/cfr/waisidx_05/10cfr430_05.html 

Coleman, H.W. and Steele, W.G., 1989. Experimentation and uncertainty analysis for

engineers, John Wiley and Sons, New York, NY USA. 

Domanski, P.A., 1999. “Finned-Tube Evaporator Model With a Visual Interface”, 20th Int. 

Congress of Refrigeration, Sydney, Australia, September 19-24, 1999, 

International Institute of Refrigeration, Paris. 

Dougherty, B., 2004. Personal communications, National Institute of Standards and 

Technology, Gaithersburg, Maryland, USA, 20899-8632. 

Graybill, F. A. and Iyer, H. K., 1994. Regression Analysis: Concepts and Applications, 

Duxbury Press, Wadsworth Publishing Company, Belmont, California USA

94002, pp. 194-209. 

Lemmon, E. W., McLinden, M. O., and Huber, M. L., 2002. NIST Standard Reference 

Database 23: NIST Reference Fluid Thermodynamic and Transport Properties – 

REFPROP, Version 7, U. S. Dept of Commerce, Natn’l Institute of Standards and 

Technology, Gaithersburg, Maryland USA 20899. 

Moffat, R. 1988. Describing the uncertainties in experimental results. Experimental 

Thermal and Fluid Science. Vol. 1. pp. 3-17. 

Neter J., Wasserman W., and Kutner M.H., 1990. Applied linear statistical models, 

regression, analysis of variance and experimental design, 3rd edition, Irwin 

publishing, Burr Ridge, Illinois, USA, pp.10. 

Ott, L., 1984. An introduction to statistical methods and data analysis, 2nd edition,

Duxbury Press, Boston, Massachusetts USA, pp. 280-324. 

16
Payne, W. V. and Domanski, P. A., 2005. A curve-based mixed system rating method 

for unitary air conditioners. NISTIR 7225. U.S. Dept. of Commerce. National 

Institute of Standards and Technology. Gaithersburg, Maryland USA 20899.

Ryan, Thomas P. 1997. Modern regression methods. John Wiley and Sons, Inc. 605 

Third Avenue, New York, NY 10158-0012. 

Taylor, B. N., and Kuyatt, C. E., 1994. “Guidelines for evaluating and expressing the 

uncertainty of NIST measurement results”, NIST Technical Note 1297, 1994 

edition, U.S. Department of Commerce. 

Timm, M. L. 1991. “An improved method for calculating refrigerant line pressure drops,” 

ASHRAE Transactions, Vol. 97, No. 1, pp. 194-203. 

17
APPENDIX C. UNCERTAINTY OF THE MIXED SYSTEM CAPACITY AND SEER 

The methods illustrated here for calculating uncertainty in mixed system capacity and 

power will produce combined uncertainties larger than the standard propagation of error 

technique due to the mathematical addition of uncertainties instead of a root-meansquare calculation of uncertainties. All uncertainty calculations assume no statistical 

correlation between the capacity, power, EER, and SEER. The analysis presented in 

this section and calculation examples require use of the same confidence level for all 

linear fits. 

C1. A Simplified Calculation of Uncertainty for Q(95)mixed

The technique for calculating the uncertainty in Q(95) and P(95) explained here 

assumes that the linear fits have a total uncertainty expressed as a percentage. For

example, the q(95) for the condenser and evaporator plus p(95) for the condenser

equation would be expressed as: 

qCD (95) = CCD (95) + DCD (95) Tevap ± x% C1 

qcoil = Ccoil + Dcoil Tevap ± y% C2 

pCD (95) = ECD (95) + FCD (95) Tevap ± z% C3 

Graphically, the linear fit method intersection of the condensing unit and coil capacity

linear fits may be seen below in Figure C1. 

The capacity range indicated in Figure C1 will be the maximum variation in capacity due 

to the uncertainty in linear fits for the condensing unit and evaporator. This uncertainty 

will be greater than the uncertainty calculated by a standard propagation of error using 

summation of variances; therefore, the capacity uncertainty will be a conservative 

estimate. Likewise, the maximum evaporator exit refrigerant saturation temperature 

range indicated in Figure C1 will be greater than that determined from a propagation of

error method. This large evaporator saturation temperature range propagates to the 

calculation of power uncertainty as seen in Figure C2. 

The maximum ranges of capacity and power occur along the diagonals of the 

quadrilateral created by the intersection of the condensing unit and evaporator coil 

capacity linear fit uncertainty lines. The region within the quadrilateral formed by the 

intersection of the uncertainty ranges represents all possible evaporator saturated 

refrigerant temperatures for the given level of uncertainties. The worst case 

uncertainties for capacity and power (across the diagonals of the quadrilateral) will be

considered and used to develop the uncertainty in EER. 

18
20000

22000

24000

26000

28000

30000

32000

34000

44 46 48 50 52 54 56

Evaporator Exit Saturation Temperature (F)

Cooling Capacity (Btu/h)

Condensing Unit

Evaporator

Maximum Capacity Uncertainty

Maximum Range of

Evaporator Temperature

T evap(p-) T evap(q+) T evap(q-) T evap(p+)

Parallelogram of Possible T evap's

Figure C1. Uncertainty of mixed system capacity due to linear fit uncertainties

1700

1800

1900

2000

2100

2200

2300

2400

2500

44 46 48 50 52 54 56

Evaporator Exit Saturation Temperature (F)

Power (Watts)

Maximum Capacity Uncertainty at this ▲T

Maximum Power Uncertainty at this ▲T

T evap(p-) T evap(q+) T evap(q-) T evap(p+)

Maximum Power Uncertainty

Figure C2. Uncertainty of mixed system condensing unit power due to linear fit 

uncertainties 

19
The refrigerant saturation temperature range at the evaporator exit for the maximum

capacity uncertainty and maximum power uncertainty occurs at the corners of the 

quadrilateral in Figure C1 and may be calculated by the following equations: 

 Let CCD(+) = CCD (1 + x%) and DCD(+) = DCD (1+ x%) 

 Ccoil(+) = Ccoil (1 + y%) and Dcoil(+) = Dcoil (1 + y%) 

 CCD(-) = CCD (1 – x%) and DCD(-) = DCD (1 – x%) 

 Ccoil(-) = Ccoil (1 – y%) and Dcoil(-) = Dcoil (1 – y%) 

 ECD(+) = ECD(1 + z%) and FCD(+) = FCD(1 + z%) 

 ECD(-) = ECD(1 – z%) and FCD(-) = FCD(1 – z%) 

CD coil

coil CD

evap D D

C C

−

− T = C4 

( )

+ − (+)

+ − +

+ =

CD coil

coil CD

D ( ) D

C C ( ) T (q ) evap C5 

( )

− − (−)

− − − − =

CD coil

coil CD

D ( ) D

C C ( ) T (q ) evap C6 

( )

− − (+)

+ − − + =

CD coil

coil CD

D ( ) D

C C ( ) T ( p ) evap C7 

( )

+ − (−)

− − + − =

CD coil

coil CD

D ( ) D

C C ( ) T ( p ) evap C8 

Tevap(q+) is the refrigerant evaporator temperature that occurs at the intersection of the 

coil and condensing unit’s upper uncertainty % line. Tevap(q-) occurs at the intersection 

of the coil and condensing unit’s lower uncertainty % line. These two intersections

occur at the largest possible cooling capacity range, but these temperatures do not 

represent the largest possible range in refrigerant evaporator exit saturation 

temperature. The largest possible range in refrigerant evaporator exit saturation 

temperature occurs between Tevap(p-) and Tevap(p+). 

The maximum percentage uncertainties in capacity and power may be calculated as

follows using the linear fits from the condensing unit or the coil (reference the 

quadrilateral in Figure C1): 

q = qcoil = qCD = ( ) + + (+)T + C D evaluated at the upper intersection C9 

q = qcoil = qCD = ( ) − + (−)T − C D evaluated at the lowest intersection C10 

q ( ) Tevap ( ) q + − q (Tevap (q −)) = ∆q + − C11 

( ) %

q T

q %

evap

100 ∆ Uq = × C12 

p = pCD = ( ) + + ( ) + T + E F evaluated at the right-hand intersection C13 

20
p = pCD = ( ) − + ( ) − T − E F evaluated at the left-hand intersection C14 

p ( ) Tevap (p +) − p (Tevap (p −)) = ∆p + − C15 

( ) %

p T

p %

evap

100 ∆ Up = × C16 

where %U = percent uncertainty in capacity or power. 

Now the uncertainty in the rated capacity may be found following the same logic as

illustrated above, i.e. the linear addition of uncertainties. If the measured indoor unit fan

power or indoor volumetric air flowrate has an uncertainty of ±u % then the uncertainty

on the rated cooling capacity is given by the equations below. 

Qfan = WC Pfan or Qfan = WCWf Vind C17 

= (1+ u%) + Qfan Qfan and = (1− u%)) − Qfan Qfan C18 

( ) Q = q Tevap −Qfan C20 

+ + − Q = q −Qfan and C21 − − + Q = q −Qfan

( ) %

Q

Q Q %UQ × 100 − =

+ −

 C22 

where: Wf = flow specific fan power multiplier of 0.365 W/scfm (775 W/(m3

/s)) 

 Vind = indoor air flow rate of standard air, scfm (m3

/s) 

 Wc = 3.412 Btu/(W·h) (1 W/W) 

The uncertainty in the mixed system total power is also given below. 

( ) P = p Tevap + Pfan C23 

= (1+ u%) = (1+ u%) + Pfan Pfan WfVind C24 

= (1− u%) = (1− u%) − Pfan Pfan WfVind C25 

+ + + P = p + Pfan and C26 − − − P = p + Pfan

( ) %

P

P P %UP × 100 − =

+ −

 C27 

C2. Uncertainty Propagation for SEERmixed

The previous section illustrated a simplified linear addition of uncertainties technique for 

determining the uncertainty in the linear fits. The linear fits for q(95) and p(95) along 

with fan power are used to calculate the value of EER(95)mixed. The value of 

EER(95)mixed is then combined with the matched system quantities to determine the 

21
rated SEERmixed. This section will explore the propagation of error into EERmixed and 

SEERmixed brought about by uncertainty in the quantities used to calculate them. 

C2.1. EER(95)mixed Uncertainty Propagation

Equation C28 lists the variables involved in calculating EER(95)mixed. The linear fit 

standard error and the chosen confidence interval (80 %, 90 %, 95 %, etc.) will 

determine the percentage error for the linear fit as illustrated by Equation C6. One way 

to illustrate the effects of various percentage errors in capacity and power is to develop

a table of error percentages for capacity and power and show how this uncertainty 

propagates to the uncertainty in EER. 

fan,mixed

fan,mixed

mixed 95

95 3 412

EER(95)

p( ) P

q( ) . P

+

− = C28 

The uncertainty in EER from Equation C28 may be calculated from Equation C29 (Ott 

1984). 

2

Pfan

fan

2

(95)

2

q(95)

2

EER U EER U

(95)

EER U

(95)

EER U ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

∂

∂ = q p P p C29 

where ( ) 1 95 fan,mixed (95)

EER − = +

∂

∂

p( ) P

q 

 ( )2

fan,mixed

fan,mixed

95

( 95 3 412 )

(95)

EER

p( ) P

q( ) . P

p +

− − = ∂

∂

 ( )

( )

( )2

fan,mixed

fan,mixed

2

fan,mixed

fan,mixed

fan 95

3 412 95

95

EER -( 95 3 412 )

p( ) P

. p( ) P

p( ) P

q( ) . P

P +

+ − +− = ∂

∂

 UEER = uncertainty in the EER 

 Uq(95) = uncertainty in q(95) 

 Up(95) = uncertainty in p(95) 

 UPfan = uncertainty in the indoor fan power 

and 3.412 is the conversion from (W) to (Btu/h). 

The uncertainty in the EER is a function of the three quantities q(95), p(95), and 

Pfan,mixed and their respective uncertainties. As an illustration, we will examine a

hypothetical system which has an EER of 13.5 and a cooling capacity (Q(95)) of 

34 458 Btu/h (10.09 kW). 

Therefore q(95) = 36 000 Btu/h 

 p(95) = 2100 W 

 Pfan = 452 W. 

Table C1 shows the calculated EER percentage uncertainty for various percentage 

uncertainties in the capacity, power, and fan power. 

22
Table C1. EER uncertainty for given uncertainties in capacity and power 

Uq(95) UPfan 0 % 0 % 1 % 5 % 10 % 20 % 

0 % 0.0 1.04 5.22 10.45 20.90 

1 % 0.82 1.33 5.29 10.48 20.91

5 % 4.11 4.25 6.65 11.23 21.30

10 % 8.23 8.29 9.75 13.30 22.46

Up(95)

20 % 16.46 16.49 17.27 19.49 26.60 

Uq(95) UPfan 1 % 0 % 1 % 5 % 10 % 20 % 

0 % 0.22 1.07 5.23 10.45 20.90

1 % 0.85 1.35 5.29 10.48 20.91

5 % 4.12 4.25 6.65 11.23 21.30

10 % 8.23 8.30 9.75 13.30 22.46

Up(95)

20 % 16.46 16.49 17.27 19.50 26.60 

Uq(95) UPfan 5 % 0 % 1 % 5 % 10 % 20 % 

0 % 1.11 1.52 5.34 10.51 20.92

1 % 1.38 1.73 5.40 10.54 20.94

5 % 4.26 4.39 6.74 11.28 21.33

10 % 8.30 8.37 9.81 13.35 22.48

Up(95)

20 % 16.50 16.53 17.30 19.53 26.62 

Table C1 shows that the condensing unit power uncertainty and the capacity uncertainty

propagate equally into the uncertainty in EER. Fan power uncertainty carries little 

weight for the values selected above. 

C2.2. SEERmixed Uncertainty Propagation

Equation C30 is used to calculate the SEER of the mixed system. It utilizes the 

matched system rated SEER and EER at A Test conditions. These values are 

published by most manufacturers. EER(95)mixed is calculated using the linear fit 

procedure with Fexp determined according to Section 4.4. The following will illustrate the 

propagation of error into the mixed system SEER by considering various uncertainty 

percentages in the independent quantities of Equation C30. 

exp

matched

mixed

mixed matched F

EER(95)

EER(95) SEER = SEER C30 

The mixed system SEER is a function of four independent quantities: 

1. SEERmatched

2. EER(95)matched 

3. EER(95)mixed

4. Fexp

23
The uncertainty in SEERmixed may be calculated as follows: 

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ =

2

EER(95)matched

matched

mixed

2

SEERmatched

matched

2 mixed

SEERmixed U

EER(95)

SEER U

SEER

SEER U .................. 

2

Fexp

exp

mixed

2

EER(95)mixed

mixed

mixed U

F

SEER U

EER(95)

SEER

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ C31 

where exp

matched

mixed

matched

mixed F

EER(95)

EER(95)

SEER

SEER = ∂

∂

 exp

matched

2

mixed

matched

matched

mixed F

EER(95)

EER(95) SEER

EER(95)

SEER = − ∂∂

 exp

matched

matched

mixed

mixed F

EER(95)

SEER

EER(95)

SEER = ∂

∂

 

matched

mixed

matched

exp

mixed

EER(95)

EER(95) SEER

F

SEER = ∂∂ 

 

 USEERmatched = uncertainty in the matched system rated SEER 

 UEER(95)matched = uncertainty in the A Test EER of the matched system 

 UEER(95)mixed = uncertainty in the calculated mixed system EER(95) 

 UFexp = uncertainty in the expansion device/fan delay correction factor 

As an illustration, we will examine a hypothetical system which has the following 

characteristics: 

 SEERmatched = 13 

 EER(95)matched = 14 

 EER(95)mixed = 15 

 Fexp= 1.026 from Table 1 and Table 2 going from an A-type matched 

 to C-type mixed system 

 SEERmixed = 14.291. 

Table C2 shows the percentage uncertainty in SEERmixed for the given uncertainties in 

the four independent quantities. 

Table C2. SEERmixed uncertainty 

Squared UncertaintyTerms from Equation C31 

Given 

%U SEERmatched EERmixed EERmatched Fexp

%U

SEERmixed

1% 0.02042 0.02042 0.02042 0.02042 2.0

5% 0.51056 0.51056 0.51056 0.51056 10.0

10% 2.04225 2.04225 2.04225 2.04225 20.0

20% 8.16898 8.16898 8.16898 8.16898 40.0

50% 51.05613 51.05613 51.05613 51.05613 100.0

24
Table C2 shows the contribution of each uncertainty term to the sum of squares for the 

total uncertainty. The row indicates the percentage uncertainty in the four independent

variables. The column indicates the squared terms as shown on the right-hand-side of 

Equation C31. SEERmatched, EERmixed, EERmatched and Fexp uncertainties propagate 

equally because these quantities are of the same order of magnitude in Equation C31 

and are multiplicative in Equation C30. 

25