Solar Energy Hot Water and Calculation

Calculating Heat Loss of Windows

Example 1

A house in State College, PA has 380 ft 2 of windows (R = 1.1), 2750 ft 2 of walls and 1920 ft 2 of roof (R = 30). The composite R-Value of the walls is 19. Calculate the heating requirement for the house for the heating season. What is the percentage of heat that is lost through the windows?

Solution:

Heat loss in a heating season is given by

Heat Loss=Area×HDD×24R−value  

 

Heat Loss through windows =

380 ft 2 ×6000   0 F   days×24 h  /day1.1ft 2    o F   h  Btus  =49,745,455 Btus 

Heat loss through walls =

2750 ft 2 ×6000   0 F   days×24 h  /day19ft 2    o F   h  Btus  =20,842,105 Btus 

Heat loss through roof =

1920 ft 2 ×6000   0 F   days×24 h  /day30ft 2    o F   h  Btus  =9,216,000 Btus 

 

Total heat loss = 79,803,560 BTUS

Percentage of heat loss through the windows =

Heat Loss=49.74 MMBtus79.8 MMBtus ×100=62.3% 

Example 2

Windows in the house described in Example 1 are upgraded at a cost of $1,550. The upgraded windows have an R-value of 4.0.

· What is the percent savings in the energy and the heating bill if the energy cost is 11.15/MMBTUs.

· What is the pay back period for this modification?

Solution:

a) New heat loss for the same window size with the new R-value is

380 ft 2 ×6000   0 F   days×24  h  /day4.0ft 2    0 F    h  Btus  =13,680,000 Btus 

Annual energy savings = 49.745 MMBTUs -13.680 MMBTUs = 36.06 MMBTUs

The percent savings is

36.06MMBTU79.84MMBTU ×100=45.1% 

Cost effectiveness of using improved windows
Performance	Base Model	Recommended Level	Best Available
Window Description	Double-paned, clear glass, aluminum frame	Double-paned, low-e coating, wood or vinyl frame	Triple-paned, tinted, two spectrally selective low-e coatings, krypton-filled, wood or vinyl frame
SHGCa	0.61	0.55	0.20
U-factor b	0.87	0.40	0.15
Annual Heating Energy Use	547 therms	429 therms	426 therms
Annual Cooling Energy Use	1,134 kWh	1,103 kWh	588 kWh
Annual Energy Cost	$290	$240	$210
Lifetime Energy Cost c	$4,700	$3,900	$3,400
Lifetime Energy Cost Savings	-	$800	$1,300

The old heating bill would be

79.803MMBtu*$11.15MMBtu =$889.80 

The new heating bill would be

43.743MMBtu*$11.15MMBtu =$487.73 

The monetary savings =\ $402.06 per year.

The Pay Back Period =

Additional InvestmentSavings per year =$1550.00$402.06 =3.85 years 

The table shows the cost effectiveness of replacing old windows with new and improved windows. The costs are calculated using a computer program called RESFEN developed by US Department of Energy.

  a SHGC, or Solar Heat Gain Coefficient, is a measure of the solar radiation admitted through a window. SHGC ranges between 0 and 1; the lower the number, the lower the transmission of solar heat. SHGC has replaced shading coefficient (SC) as the standard indicator of a window's shading ability. SHGC is approximately equal to the SC multiplied by 0.87. b U-factor is a measure of the rate of heat flow through a window. The U-factor is the inverse of the R-value, or resistance, the common measure of insulation. c Lifetime energy cost savings is the sum of the discounted value of annual energy cost savings, based on average usage and an assumed window life of 25 years. Future energy price trends and a discount rate of 3.4 percent are based on Federal guidelines (effective from April 2000 to March 2001).Assumed electricity price: $0.06/kWh, the Federal average electricity price in the U.S.Assumed gas price: $0.40/therm, the Federal average gas price in the U.S.

Cost-Effectiveness Assumptions: The model shown above is the result of a simulation using a residential windows modeling program called RESFEN. Calculations are based on a prototype house: 1,540 sq. ft., two stories, a standard efficiency gas furnace and central air conditioner, and window area covering 15 percent of the exterior wall surface area.