D-1.i APPENDIX D-1. WATSIM-DOE TEST.XLS

TABLE OF CONTENTS

D-1.1 BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.1

D-1.2 PROGRAM DESCRIPTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.1

D-1.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.1

D-1.2.2 “Results” Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.2

D-1.2.3 “tw_vs_t1” Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.3

D-1.2.4 “EF calc” Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.8

FIGURES

Figure D-1.1 Excel Screen View of Results Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.2 Figure D-1.2 Excel Screen View (1 of 2) of tw_vs_t1

Worksheet: tw_vs_t1.out Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.4 Figure D-1.3 Excel Screen View (2 of 2) of tw_vs_t1 Worksheet:

Calculated Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1.5 Figure D-1.4 Energy Performance Values as Presented in the EF calc Worksheet . . . . . D- 1.13D-1.1 APPENDIX D-1. WATSIM-DOE TEST.XLS

This Appendix describes the spreadsheet tool “WATSIM-DOE Test.xls”, which was developed to calculate the energy efficiency characteristics of electric storage water heaters according to the specifications of the DOE test procedure 1 from a standard WATSIM output file.

D-1.1 BACKGROUND

The WATSIM electric water heating simulation program contains two simulation algorithms: one for the detailed simulation of the energy performance of water heater tanks and a second for controlling water draw profiles for use with the tank model. The output of WATSIM does not, however, include EF, RE, and UA values, which are specific to the DOE test procedure.

Since the simulation analysis must be performed according to the requirements of the DOE test procedure, the water draw profile is specified to the 64.3 gallon (243.4 liter). The specified draw profile is provided in a standard WATSIM draw file (machine.643). WATSIM provides detailed temperature profiles for the water in the water heater tank during the simulation run. The temperature profiles are specified in the WATSIM input file (baseline.dat). The draw file and input file are available in the DOE’s Office of Codes and Standards’ web-site. The temperature profile is provided in a standard WATSIM output file called tw_vs_t1.out . These temperature readings are used by the “WATSIM-DOE Test.xls” to determine EF, RE, and UA.

“WATSIM-DOE Test.xls” was developed using Microsoft Excel and is a workbook file consisting of three individual worksheets: 1) results , 2) tw_vs_t1 , and 3) EF_calc . (Note that at the bottom of the screen view are the names of all three individual Worksheets.) This is a customized analysis tool developed specifically for this analysis and, as such, it has certain limitations, descriptions of which are provided in the detailed explanation of the procedure.

D-1.2 PROGRAM DESCRIPTION

D-1.2.1 Introduction

The following requirements must be satisfied before performing the procedure:

1) “WATSIM-DOE Test.xls” works in conjunction with the standard WATSIM output file
tw_vs_t1.out. The two files need to be in the same directory.

2) The tool is customized to work with a set of parameters required by the DOE test procedure. It is necessary to supply values for the following variables used for the actual simulation:

` water heater rated input, V
st ,

` average inlet water temperature, T in,1 ,

` average ambient temperature during the total standby period, T a,stby ,

` average ambient temperature after the last draw to the end of the 24-hour test, T s,stby .D-1.2 Figure D-1.1 Excel Screen View of Results Worksheet The input cells for those variables are located in the tw_vs_t1 worksheet.

D-1.2.2 “Results” Worksheet

The purpose of the “results ” worksheet is to load WATSIM’s tw_vs_t1.out file into the spreadsheet tool. The user simply needs to “click” on the Load Data File button to activate a macro,

which loads the tw_vs_t1.out file into the spreadsheet tool. Figure D-1.1 shows an Excel screen view of the spreadsheet tool’s results worksheet.D-1.3 D-1.2.3 “tw_vs_t1” Worksheet

After the tw_vs_t1.out file is loaded into the spreadsheet tool, the user is automatically

transferred over to the tw_vs_t1 worksheet. The tw_vs_t1 worksheet is where the tw_vs_t1.out file is actually loaded. Because the tw_vs_t1 worksheet will contain a previously loaded tw_vs_t1.out file, the user will need to edit the worksheet after the current tw_vs_t1.out file is loaded. Editing consists of clearing out the data from the previous file. Figure D-1.2 shows a partial Excel screen view of the spreadsheet tool’s tw_vs_t1 worksheet. It shows the data that are provided in

WATSIM’s tw_vs_t1.out file.

` Column A provides the DAY on which data are being recorded. Since the DOE simulated use test lasts 24 hours, a value of 1 is always recorded.

` Column B provides the TIME (in minutes) when data are being recorded. Since the DOE simulated use test lasts 24 hours, the last value in which data will be recorded is at the

1440 th minute. Obviously, all the data up the 1440 th minute cannot be shown in Figure D1.2 as hundreds of data records are contained in any single tw_vs_t1.out file.

` Column C provides the water DRAW (in gallons per minute) at the time the data are being recorded. Since the draw pattern is conducted per the requirements of the DOE simulated use test, the value recorded will either be 3 gpm or 0 gpm. It should be noted that during the water draw period, WATSIM records data into the tw_vs_t1.out file approximately every 5 seconds. Thus, during the six draw periods lasting approximately 31⁄2 minutes as prescribed by the DOE simulated use test, a wealth of data will be recorded.

` Column D provides the rate of electrical HEATER consumption (in Btu/hr) at the time in which data are being recorded. In Figure D-1.2, results are provided for a 50-gal (190- liter) electric storage water heater with two 4.5 kW electrical heater elements. Thus, in the case shown in Figure D-1.2, the rate of electrical heater consumption will always be 15,370 Btu/hr (4.5 kW) when the heater element is required to come on to maintain the temperature setpoint. It should be noted that during a non-water draw period while the heater element is on, WATSIM records data into the tw_vs_t1.out file approximately every 33 seconds. At conditions where there is no water draw and the heater element is off,

WATSIM records data into the tw_vs_t1.out file approximately every 5 minutes.

` Columns E through AB contain the HOT WATER TEMPERATURE profile data. For example, Temperature #1 corresponds to the temperature measurement taken closest to the bottom of the tank while Temperature #24 corresponds to the measurement taken closest to the top of the tank. Temperature #24 is assumed to equal the temperature of the hot water drawn from the water heater. Temperature #24 is also referred to as the DRAWTEMP. The 24 temperatures are measured at evenly spaced intervals throughout

the tank.D-1.4Figure D-1.2 Excel Screen View (1 of 2) oftw_vs_t1Worksheet:tw_vs_t1.outVariablesD-1.5Figure D-1.3 Excel Screen View (2 of 2) oftw_vs_t1Worksheet: Calculated VariablesD-1.6 Figure D-1.3 shows the remaining variables in the tw_vs_t1 worksheet. The remaining variables are NOT recorded by WATSIM into the tw_vs_t1.out file. Rather, they are variables which are automatically calculated in order to determine quantities necessary for establishing the EF, RE, and UA of the water heater being analyzed according to the DOE test procedure. Figure D-1.3 presents a partial Excel screen view of the spreadsheet tool’s tw_vs_t1 worksheet showing the

calculated variables.

` MEANTEMP is located in column AC. It represents the mean hot water tank temperature and is based on 12 of the 24 temperatures recorded in Columns E through AB. The following equation shows how MEANTEMP is calculated.

mean 

### T TT TT T T T T T T T T

= + + + + + + + + + + + 2 3 6 7 10 11 14 15 18 19 22 23



### 22 2 2 2 2

6

Since the DOE test procedure requires that six temperature readings be used to establish the mean tank temperature, those temperatures recorded in tw_vs_t1.out that best represent the six temperatures (the average of the two temperatures representing the six evenly spaced regions of the tank) are used to calculate MEANTEMP.

` DCA is located in column AD. DCA returns a value of 1 only if the row DRAW changes

from a value of 0 to 1.

` DCB is located in column AE. DCB is 1 whenever DRAW changes value (going from a value of either 0 to 1 or 1 to 0). Thus, a value of 1 will be calculated for DCB only at the beginning and end of each water draw period.

` DCC is located in column AF. DCC sums up the values in column AE (variable DCB) if and only if DCB equals a value of 1 and DRAW changes value. Thus, a value of 1 or greater will be calculated for DCC only at the beginning and end of each water draw period. For example, during the first draw period, DCC will equal a value of 1 at the beginning of the draw and a value of 2 at the end of the draw. During the second draw period, DCC will equal a value of 3 at the beginning of the draw and a value of 4 at the end of the draw. DCC gets increased by a value of 1 for each subsequent draw.

` DCD is located in column AG. DCD changes to an incrementally larger value for the length of each of the six draw periods. For example, DCD is a value of 1 during the length of the first draw period, a value of 2 during the length of the second draw period, a value of 3 during the length of third draw period, and so on for each subsequent draw period.D-1.7 ` HCA is located in column AH. HCA is comparable to variable DCA except that its value is based on the status of HEATER rather than DRAW. HCA changes to a value of 1 only when HEATER changes from a value of 0 to 1.

` HCB is located in column AI. HCB is comparable to variable DCB except that its value

is based on the status of HEATER rather than DRAW. HCB switches to a value of 1 whenever HEATER changes value (going from a value of either 0 to 1 or 1 to 0). Thus, a value of 1 will be calculated for HCB only at the beginning and end of each time period

in which the heater element is on.

` HCC is located in column AJ. HCC is comparable to variable DCC except that its value

is based on the status of HEATER rather than DRAW.

` HCD is located in column AK. HCC is comparable to variable DCC except that its value is based on the status of HEATER rather than DRAW. HCD changes to an incrementally larger value for the length of each time period that the heater element is on. It should be noted that, unlike the water draw periods, there may be more than six time periods in

which the heater element comes on. The heater element comes on to maintain temperature setpoint; thus, it cycles during standby operation after all six water draws have been completed. For example, a typical baseline 50-gal (190-liter) electric water heater will have its heater element cycle 9 to 10 times in the course of the 24-hour DOE

simulated use test.

` HCF is located in column AL. HCF switches to a value of 1 and remains a value of 1 after the heater element has cycled for sixth time.

` TIMEDIFF is located in column AM. TIMEDIFF tracks the time difference between each

set of recorded data.

` TDIFF_TEMP is located in column AN and is used to calculate “time-weighted average” mean tank temperatures. Because the time difference between data records varies depending on the status of the water DRAW and the HEATER elements, the mean tank temperature for a time period spanning multiple water draws cannot be determined directly from the values calculated for MEANTEMP. TDIFF_TEMP allows for the determination of accurate mean tank temperatures. TDIFF_TEMP is calculated by multiplying TIMEDIFF by MEANTEMP. Thus, for any desired time period, the mean tank temperature is determined by summing the values for TDIFF_TEMP and dividing by the elapsed time for the time period.D-1.8 D-1.2.4 “EF calc” Worksheet

This worksheet shows the results of the procedure. After all of the data have been loaded and intermediate values generated in the tw_vs_t1 worksheet, the user must manually switch to the EF

calc worksheet to see the results of the energy performance calculations. All the energy performance

calculations in the EF calc worksheet, including those for EF, RE, and UA, are done automatically. Figure D-1.4 shows the energy performance values as they are presented in the EF calc worksheet.

All the variables in the EF calc worksheet are required by the DOE test procedure equations in order to determine RE, UA, and EF. The EF calc worksheet uses the same nomenclature as in the DOE test procedure in order to maintain consistency and to enable the user to easily identify and define

all the variables.

All shaded areas in the EF calc worksheet represent variables that are determined directly

from the data in the tw_vs_t1 worksheet. All other variables are determined from DOE test procedure equations or are equal to default values provided in the test procedure. A list of variables

in the EF calc worksheet determined from the data in tw_vs_t1 worksheet is provided below.

` M 1 , mass of water (lb

m ) withdrawn during the first draw: Determined by multiplying the DRAW rate (3 gpm) during the first draw by the elapsed time of the first draw. Once the total draw is determined in gallons, it is converted to lb

m using conversion factors. The

calculation is based on the use of variable DCC in the tw_vs_t1 worksheet. The TIME when DCC equals 1 (the beginning of the first draw) is subtracted from the TIME when DCC equals 2 (the end of the first draw) in order to calculate the elapsed time.

` T del,1 , average delivery temperature ( b F) for the first draw: Determined by calculating the average draw temperature during the first draw. The calculation is based on the use of

variable DCD in the tw_vs_t1 worksheet. First, all the DRAWTEMPs (hot water temperature #24) for the period when DCD equals 1 (the length of the first draw) are summed. Then, the summed DRAWTEMP value is divided by the number of times in which DCD equals 1 to arrive at the average delivery temperature during the first draw.

` T max,1 , maximum mean tank temperature ( b F) recorded after cutout following the first draw: The key to to determining T max,1 is selecting the maximum temperature after the HEATER element first cycles off. This determination is based on the use of variable

HCC in the tw_vs_t1 worksheet. Since the maximum temperature occurs immediately after the HEATER element cycles off, the value for the maximum MEANTEMP is when HCC equals 2 (the end of the first HEATER cycle).

` T

o , maximum mean tank temperature ( b F) recorded prior to the first draw: This is simply

the first value for MEANTEMP recorded in the tw_vs_1 worksheet.

` Q

r , total energy (Btu) used by the water heater between cutout following the first draw, including auxiliary energy such as pilot lights, pumps, fans, etc.: Determined by multiplying the HEATER’s rate of consumption (15,370 Btu) during its first cycle by theD-1.9 elapsed time of the HEATER’s first cycle. Key to determining Q

r is the calculation of the elapsed time of the first HEATER cycle. The calculation is based on the use of

variable HCC in the tw_vs_t1 worksheet. The TIME when HCC equals 1 (the beginning of the first cycle, i.e., when the HEATER element first turns on) is subtracted from the TIME when HCC equals 2 (the end of the first cycle, i.e., when the HEATER element first turns off) in order to calculate the elapsed time.

` Q stby , total energy (Btu) consumed by the water heater between the time at which the maximum mean tank temperature is observed after the sixth draw and the end of the 24- hour test period: Determined by calculating the total HEATER energy consumption during the standby period of the water heater. The standby period, with respect to calculating Q stby starts immediately after the sixth cycle of the HEATER element. This is because the maximum mean tank temperature occurs immediately after the HEATER element cycles off for the sixth time. Key to determining Q stby is the calculation of the elapsed time of each HEATER cycle after the HEATER element’s sixth cycle. The calculation is based

on the use of variable HCC in the tw_vs_t1 worksheet. At the TIME when the HEATER cycles off for the sixth time, HCC equals 12. Thus, the elapsed time of the seventh HEATER cycle is determined by subtracting the TIME when HCC equals 13 (the beginning of the seventh cycle) from the TIME when HCC equals 14 (the end of the seventh cycle). The elapsed times of all subsequent cycles are determined in the same manner with the beginning and ending HCC values for each cycle incremented by 1. Once all the elapsed times are determined, they are summed and then multiplied by the HEATER’s rate of consumption to come up the total HEATER energy consumption during the standby period.

` T 24 , mean tank temperature ( b F) at the end of the 24-hour test period: This is simply the value for MEANTEMP corresponding to the last record in the tw_vs_1 worksheet (i.e., when TIME equals 1440).

` T

su , maximum mean tank temperature ( b F) observed after the sixth draw: Key to determining T

su is selecting the maximum temperature after the HEATER element cycles

off for the sixth time. This determination is based on the use of variable HCC in the
tw_vs_t1 worksheet. Since the maximum temperature occurs immediately after the HEATER element cycles off, the value for the maximum MEANTEMP is when HCC equals 12 (the end of the sixth HEATER cycle).

` t stby,1 , elapsed time (hours) between the time at which the maximum mean tank temperature is observed after the sixth draw and the end of the 24-hour test period: Very similar to determining T

su . Key to determining t stby,1 is selecting the maximum temperature after the HEATER element cycles off for the sixth time. This determination is based on

the use of variable HCC in the tw_vs_t1 worksheet. Since the maximum temperature occurs immediately after the HEATER element cycles off, the value for the maximum MEANTEMP is when HCC equals 12 (the end of the sixth HEATER cycle). The TIMED-1.10 corresponding to when HCC equals 12 is subtracted from 1440 (the TIME at the end of the test period) to arrive at the elapsed time.

` T t,stby , average storage tank temperature ( b F) between the time at which the maximum mean tank temperature is observed after the sixth draw and the end of the 24-hour test period: Key to determining T t,stby is selecting the maximum temperature after the HEATER element cycles off for the sixth time. This determination is based on the use

of variable HCF in the tw_vs_t1 worksheet. Since the maximum temperature occurs immediately after the HEATER element cycles off, the value for the maximum MEANTEMP is when HCF equals 1 (the end of the sixth HEATER cycle). HCF remains a value of 1 for the remainder of the 24-hour test period. For time period when HCF equals 1, the sum of the TDIFF_TEMP values and the sum of the TIMEDIFF values are calculated. The average storage tank temperature is determined by dividing the sum of the above TDIFF_TEMP values by the sum of the above TIMEDIFF values.

` M 2 , mass of water (lb

m ) withdrawn during the second draw: Determined by multiplying the DRAW rate (3 gpm) during the second draw by the elapsed time of the second draw. Once the total draw is determined in gallons, it is converted to lb

m using conversion

factors. The calculation is based on the use of variable DCC in the tw_vs_t1 worksheet. The TIME when DCC equals 3 (the beginning of the second draw) is subtracted from the TIME when DCC equals 4 (the end of the second draw) in order to calculate the elapsed

time.

` T del,2 , average delivery temperature ( b F) for the second draw: Determined by calculating the average draw temperature during the second draw. The calculation is based on the use

of variable DCD in the tw_vs_t1 worksheet. First, all the DRAWTEMPs (hot water temperature #24) for the period when DCD equals 2 (the length of the second draw) are summed. Then, the summed DRAWTEMP value is divided by the number of times in which DCD equals 2 to arrive at the average delivery temperature during the second draw.

` M 3 , mass of water (lb

m ) withdrawn during the third draw: Determined by multiplying the DRAW rate (3 gpm) during the third draw by the elapsed time of the third draw. Once the total draw is determined in gallons, it is converted to lb

m using conversion factors.

The calculation is based on the use of variable DCC in the tw_vs_t1 worksheet. The TIME when DCC equals 5 (the beginning of the third draw) is subtracted from the TIME when DCC equals 6 (the end of the third draw) in order to calculate the elapsed time.

` T del,3 , average delivery temperature ( b F) for the third draw: Determined by calculating the average draw temperature during the third draw. The calculation is based on the use of

variable DCD in the tw_vs_t1 worksheet. First, all the DRAWTEMPs (hot water temperature #24) for the period when DCD equals 3 (the length of the third draw) are summed. Then, the summed DRAWTEMP value is divided by the number of times in which DCD equals 3 to arrive at the average delivery temperature during the third draw.D-1.11 ` M 4 , mass of water (lb

m ) withdrawn during the fourth draw: Determined by multiplying the DRAW rate (3 gpm) during the fourth draw by the elapsed time of the fourth draw. Once the total draw is determined in gallons, it is converted to lb

m using conversion factors.

The calculation is based on the use of variable DCC in the tw_vs_t1 worksheet. The TIME when DCC equals 7 (the beginning of the fourth draw) is subtracted from the TIME when DCC equals 8 (the end of the fourth draw) in order to calculate the elapsed time.

` T del,4 , average delivery temperature ( b F) for the fourth draw: Determined by calculating the average draw temperature during the fourth draw. The calculation is based on the use

of variable DCD in the tw_vs_t1 worksheet. First, all the DRAWTEMPs (hot water temperature #24) for the period when DCD equals 4 (the length of the fourth draw) are summed. Then, the summed DRAWTEMP value is divided by the number of times in which DCD equals 4 to arrive at the average delivery temperature during the fourth draw.

` M 5 , mass of water (lb

m ) withdrawn during the fifth draw: Determined by multiplying the DRAW rate (3 gpm) during the fifth draw by the elapsed time of the fifth draw. Once the total draw is determined in gallons, it is converted to lb

m using conversion factors. The

calculation is based on the use of variable DCC in the tw_vs_t1 worksheet. The TIME when DCC equals 9 (the beginning of the fifth draw) is subtracted from the TIME when DCC equals 10 (the end of the fifth draw) in order to calculate the elapsed time.

` T del,5 , average delivery temperature ( b F) for the fifth draw: Determined by calculating the average draw temperature during the fifth draw. The calculation is based on the use of

variable DCD in the tw_vs_t1 worksheet. First, all the DRAWTEMPs (hot water temperature #24) for the period when DCD equals 5 (the length of the fifth draw) are summed. Then, the summed DRAWTEMP value is divided by the number of times in which DCD equals 5 to arrive at the average delivery temperature during the fifth draw.

` M 6 , mass of water (lb

m ) withdrawn during the sixth draw: Determined by multiplying the DRAW rate (3 gpm) during the sixth draw by the elapsed time of the sixth draw. Once the total draw is determined in gallons, it is converted to lb

m using conversion

factors. The calculation is based on the use of variable DCC in the tw_vs_t1 worksheet. The TIME when DCC equals 11 (the beginning of the sixth draw) is subtracted from the TIME when DCC equals 12 (the end of the sixth draw) in order to calculate the elapsed

time.

` T del,6 , average delivery temperature ( b F) for the sixth draw: Determined by calculating the average draw temperature during the sixth draw. The calculation is based on the use of

variable DCD in the tw_vs_t1 worksheet. First, all the DRAWTEMPs (hot water temperature #24) for the period when DCD equals 6 (the length of the sixth draw) are summed. Then, the summed DRAWTEMP value is divided by the number of times in which DCD equals 6 to arrive at the average delivery temperature during the sixth draw.D-1.12 ` Q, total energy (Btu) used by the water heater during the 24-hour simulated use test including auxiliary energy such as pumps, fans, etc.: Determined in a very similar manner to Q stby . Key to determining Q is the calculation of the elapsed time of each HEATER cycle in the 24-hour test period. The calculation is based on the use of variable HCC in

the tw_vs_t1 worksheet. The variable HCC increments by a value of 1 each time the HEATER turns on and off. Thus, for the first HEATER cycle, HCC equals 1 when the

HEATER turns on and increases to a value of 2 when the HEATER turns off. For each subsequent HEATER cycle, the value of HCC increases by 1. Thus, the elapsed TIME of any given cycle is determined by subtracting the TIME corresponding to the “beginning” HCC value for that cycle from the TIME corresponding to the “ending” HCC value for the same cycle. The “beginning” HCC value for any cycle will have an odd numerical value while the “ending” HCC value will have an even numerical value. Thus, if the HEATER cycles ten times in a 24-hour period, the “beginning” HCC value will equal 19 and the “ending” HCC value will equal 20. Once the elapsed times of all HEATER cycles are determined, they are summed and then multiplied by the HEATER’s rate of consumption to come up the total HEATER energy consumption during the 24- hour test period.

` T stby , mean tank temperature ( b F) during the total standby portion of the 24-hour test: Determined by calculating the average mean tank temperature whenever a DRAW is not occurring. This determination is based on the use of variable DCD in the tw_vs_t1 worksheet. Whenever DCD equals 0 (i.e., when a DRAW is not occurring), the sum of the TDIFF_TEMP values and the sum of the TIMEDIFF values are calculated. The average mean tank temperature is determined by dividing the sum of the above TDIFF_TEMP values by the sum of the above TIMEDIFF values.

` t stby,2 , the number of hours during the 24-hour simulated test when water was not being withdrawn from the water heater: Determined by calculating the elapsed times between DRAWS and the elapsed time between the end of the last (sixth) DRAW and the 24-hour time period. This determination is based on the use of variable DCC in the tw_vs_t1 worksheet. The TIME when DCC equals 3 (the beginning of the second draw) is subtracted from the TIME when DCC equals 2 (the end of the first draw) in order to calculate the elapsed time between the first and second draw periods. For each subsequent time period between draws, the elapsed time is calculated in the same manner. The TIME when DCC equals 12 (the end of the sixth draw) is substracted from the TIME at the end of the 24-hour test period in order to calculate the elapsed time between the end of the 24 test period and the last draw. After all the elapsed times when water is not being drawn are determined, they are summed to arrive at the value for t stby,2 .D-1.13RECOVERY EFFICIENCY (nr) CALCULATIONSM1Tdel,1Tin,1(Tdel,1+Tin,1)/2Cp1Tmax,1To(Tmax,1+To)/2 Cp2VstpQrnrlbmFFF Btu/lbm-FFFF Btu/lbm-F gal lbm/gal Btu88.00 135.0058.0096.50 0.99 131.42 131.42 131.42 1.00 45.00 8.23 6936.990.9669UA CALCULATIONSQstbyT24Tsu(T24+Tsu)/2tstby,1Cpp MQhrTt,stbyTs,stbyUABtu F F F hoursBtu/lbm-Flbm/gallbmBtu/hr FFBtu/hr-F4598.19 132.28 131.41 131.84 18.54 1.00 8.23 370.13 230.12 130.8267.503.63PRELIMINARY CALCULATIONSM1Tdel,1Cp1M2Tdel,2Cp2M3Tdel,3Cp3lbmFBtu/lbm-FlbmFBtu/lbm-F lbmF Btu/lbm-F88.00 135.00 1.00 88.00 134.60 0.99 87.50 134.60 0.99PRELIMINARY CALCULATIONSM4Tdel,4Cp4M5Tdel,5Cp5M6Tdel,6Cp6lbmFBtu/lbm-FlbmFBtu/lbm-F lbmF Btu/lbm-F87.50 134.60 0.99 88.00 134.60 0.99 88.24 134.60 0.99ENERGY USED TO HEAT WATER (QHW) -- CALCULATIONSM1Cp1(Tdel,1-Tin)/nrM2Cp2(Tdel,2-Tin)/nrM3Cp3(Tdel,3-Tin)/nrM4Cp4(Tdel,4-Tin)/nrM5Cp5(Tdel,5-Tin)/nrM6Cp6(Tdel,6-Tin)/nrQHWTinF7007.066901.386863.156862.726901.386921.1541456.8558.00ENERGY USED TO HEAT WATER IF DELIVERED TEMPERATURE EQUALS 135'F (QHW,77) -- CALCULATIONSM1Cp1(135-58)/nrM2Cp2(135-58)/nrM3Cp3(135-58)/nrM4Cp4(135-58)/nrM5Cp5(135-58)/nrM6Cp6(135-58)/nrQHW,777007.506937.426898.566898.566937.426956.8541636.31130.75MODIFIED DAILY WATER HEATING ENERGY CONSUMPTION (Qdm) CALCULATIONSQ QdTstbyTa,stbytstby,2QdaQHWDQdmBtuBtuFFBtuBtu Btu46640.2746311.71130.1167.5023.6446731.63 179.4746911.10127.22ENERGY FACTOR (Ef) CALCULATIONSM1Cp1(135-58)/QdmM2Cp2(135-58)/QdmM3Cp3(135-58)/QdmM4Cp4(135-58)/QdmM5Cp5(135-58)/QdmM6Cp6(135-58)/QdmEf0.14440.14300.14220.14220.14300.14340.858Figure D-1.4 Energy Performance Values as Presented in theEF calcWorksheetD-1.14 REFERENCE

1. Title 10, Code of Federal Regulations, Part 430- Energy Conservation Program for Consumer Products, Appendix E to Subpart B- Uniform Test Procedure for Measuring the Energy Consumption of Water Heaters, January 1

, 1998.