• Factors Affecting Comfort in Winter
• Heat Loss Equation for a Wall Section
• R Values
• Heat Loss from a Building
• Annual Heat Loss
• Annual Heating Cost
• Delivered Energy Units
• Review Questions

Chapter 10: HEAT LOSS CALCULATIONS

In this chapter, we will examine how these factors affect the rate of heat loss from a building. We will also learn to determine the rate at which heat is lost through building components using a process called heat loss calculation. You will learn how to extrapolate your calculation of a maximum hourly rate into an annual energy usage rate. Finally, you will learn an easy way to estimate the annual cost of heating a structure.

Factors Affecting Comfort in Winter

WIND is the second greatest source of heat loss during the winter. Moving air is more efficient at removing heat from walls and roofs. Shrubs and windbreaks to keep the high winds from impacting the walls will help reduce this energy loss. Winds can also force their way through cracks in the structure, causing infiltration and drafts. In fact, up to one-third of the annual residential heating energy goes to heat this moving infiltration air many times each winter day.

HUMIDITY levels can also affect the comfort within a structure. Very low humidity levels (less than 20% relative humidity) causes scratchy throats and dry noses in most people. Very high humidity levels (over 60%) are also uncomfortable, since the body's ability to perspire is restricted.

RADIATION sources (MRT) can also affect comfort in a structure. The sun shining through a window will make a room very comfortable in winter; that same sun could make it unbearable in summer. Walls and windows also release and absorb radiation. A Trombe wall heated by the sun will keep a room feeling warm with an air temperature less than 60°F. A large expanse of cold glass windows can also make a room feel chilly with an air temperature of over 80°F.

Remember that these same four factors are also important in determining cooling requirements, but control of humidity and solar gain are much more important during that season.

When designing the heating system for a structure, the first step is to obtain data on the local micro climate of the region. This information is available from a variety of sources. The local library will probably have the climatic atlas for the United States, as well as various almanacs. The U.S. Weather Service has very good information on the various locations that it monitors. The local utility usually tracks the long term local weather variation. We will use the ASHRAE Handbook of Fundamentals as our reference here.

There are two different but related calculated values of interest to the heating system designer. To properly size the furnace, the maximum rate of energy loss (in BTU/hr) must be determined. The idea is that if the furnace is large enough to satisfy the building's needs on the coldest day of the year, then it can also keep you warm at any temperature. (Of course without a good control system, it may keep you too warm part of that time!) The second calculated value that must be determined is the annual heating bill. This is determined by calculating the annual energy requirement based from the design heat loss rate we just found, as we will soon see.

Heat Loss Equation for a Wall Section

Let's examine each one of these terms, starting at the bottom with the outside design temperature. Since the inside of the house is controlled to a fixed temperature by the thermostat, the maximum rate of heat loss will occur during the record cold temperature (neglecting the wind factor for now). Because this record temperature occurs so rarely, a 97.5% or 99% design temperature is usually used. In an average winter, the ambient air temperature will be above the design temperature the given percentage of the time. For example, the Pittsburgh, PA, 99% design temperature is 4°F. Only one percent of the hours in a typical heating season (about 30 hours total) fall at or below that temperature. Since most of these hours are during the night-time when most people are sleeping, and because these extremes are buffered by the large storage mass of the building, these cooler periods usually go unnoticed.

The inside design temperature is traditionally taken as 65°F, because in most homes there is enough heat internally generated from people, lighting, and appliances that no heat is required when the outside temperature is above that point. Today people are keeping thermostats set lower, so load predictions based on this method are usually conservative, and will result in furnace size recommendations that are slightly larger than actually needed.

The net area of each building section is determined from either the drawings (in new construction) or from field measurements (in retrofit situations). In addition to the areas of the four walls, floor, and ceiling, we must also consider heat loss from doors and windows. Finally, we will need to determine the volume of the building as an easy way to estimate the rate of infiltration into the building measured in air changes per hour.

The heat transfer coefficient is primarily determined by the construction details in each of the above sections. Mathematically, the heat transfer coefficient is the reciprocal (the "¹/_x" key on your calculator) of the total R-value. The total R-value is the sum of the thermal resistances for each component used in the construction of the wall or roof section. These individual R-values, or resistance to heat flow, for most building materials have been tabulated by ASHRAE. For example, consider a section of standard wall construction shown below:

R Values

1. Outside air film (15 mph) = 0.17 2. Wood siding (1/2 x 8") = 0.81 3. Sheathing (1/2" regular) = 1.32 4. Insulation (3-1/2" fiberglass) = 11.00 5. Gypsum board (1/2") = 0.45 6. Inside air film (still air) = 0.68

R_T = 14.43 (hr-ft²-°F / Btu)
U = 1/R_T = 0.07 (Btu / hr-ft²-°F)

Each component contributes to the total R-value. The outside air film (technically the coefficient of convective heat transfer) will always have an R-value of 0.17 hr-ft²-°F/Btu. The 1/2 by 8 inch wood siding is listed as R-0.81 hr-ft²-°F/Btu. Most of the insulating value is provided by the R-11 fiberglass batts. The 1/2 inch gypsum board and the inside air film add 0.45 and 0.68 hr-ft²-°F/Btu respectively. Adding the values together gives a total value for this wall of R-14.43 hr-ft²-°F/Btu.

The U-factor is determined by taking the reciprocal of the R-value. For this example U = 1 / R = 1 / 14.43 = 0.07 Btu/hr-ft²-°F. The U-factors for various standard construction details are given later in this chapter. Notice that the R-value for windows is about equal to the number of panes (a double pane window is R-2), and that wood doors are about R-1 per inch (a two inch thick door is R-2). (Note: These are just approximate values to avoid getting you confused with all the detail.)

Heat Loss from a Building

Notice that three values are already given in the table as constants. For a concrete slab-on-grade floor, the thermal resistance to heat loss into the ground is close to an R-value of 10 hr-ft²-°F/Btu (U = 1 / 10 = 0.1 Btu/hr-ft²-°F), and the ground temperature is fairly constant at about 45°F in the winter (65 - 45 = 20°F). The U-factor listed on the last line for infiltration converts the hourly rate of air change (cubic feet per hour) into the proper units to determine the energy required to heat the cold outside air leaking into the building. A very tight house will lose about 0.5 air changes per hour; an average house is about 1.0 air change per hour and a leaky, older home can lose well over 2.0 air changes per hour throughout the winter.

After determining the total heat loss rate, heating system designers can usually move on to the next design project. But we are going to take our calculation one step further to determine the annual heating loss and its related cost.

Annual Heat Loss

By comparing degree-days for various locations, the average coldness of the climate can be estimated. For example, Pittsburgh, Columbus, Ohio, and Denver, Colorado, have comparable annual degree days (about 6000 DD/year). It can be expected that the same structure in all three locations would have about the same heating bill. Move the building to Great Falls, MT (7800 DD/year) and it would have a higher heating bill; but in Albuquerque, NM, (4400 DD/year) it would have a relatively lower heating cost.

From the above calculations, we know the rate of energy loss per hour at the design temperature difference. To determine the annual heat loss, divide the energy loss rate by the design temperature difference (next to last column in the table above), and then multiply it by 24 hours per day and the number of annual degree days that you looked up in the table for that location. For example, a house with a design heating load of 30,000 Btu/hr in Pittsburgh (design temperature of 4°F) will use:
 

Notice that the value is rounded to the nearest million Btu. Since the numbers we are using in our calculations are very squishy (the infiltration rate can change by over 200%), the answer we get is really nothing more than an educated guess. To say that a house will use 70,819,672.13 Btu per year indicates that we know exactly how many clocks are in the house since each clock generates around 400 Btu/yr alone.

Annual Heating Cost

For the purposes of this course, all energy will cost exactly $10 per million Btu. At today's energy prices, this average value is high for gas heat (by about a factor of 2), about right for fuel oil, and low for electric resistance heat (by about a factor of 2). Even these prices vary substantially across the nation. Natural gas in New York sells for almost three times the price in Colorado and Louisiana. Electricity on Long Island costs almost ten times more than the price that Bonneville Power Administration gets for their hydroelectric power in Montana. And electric prices in California in the past few years have been totally crazy!

So for our example building above using 71 million Btu/yr, we would calculate the heating cost to be 71·$10 = $710 per year. But in reality the heating cost might range from under $350 for gas heat to over $1400 for electric resistance heat.

Delivered Energy Units

Remember that the actual efficiency and energy content values may vary drastically, especially for wood and coal. An old fuel oil furnace may only be 40% efficient, while a new high-efficiency gas furnace can be over 95% efficient. So, use these numbers as guidelines only when no better values are available.

As an energy system designer, you must learn the purchasing units associated with each energy source. You should memorize reasonable values for the energy content and for the furnace efficiency. Rounding things off can make it a little bit easier. For example, natural gas contains about 1000 Btu per cubic foot. So, one hundred cubic feet (CCF) contains about 100,000 Btu. A gallon of fuel oil delivers almost 100,000 Btu per gallon. Knowing the unit efficiency allows you to calculate the original content. Notice that the efficiency of the electric resistance heat is 1.0, since all of the energy is delivered to the space. The efficiency of the heat pump is listed as 2.0, since typically one kwhr of energy is extracted from the outside air (or other heat source) for each kwhr of electric that the compressor uses.

Review Questions

1. Name four weather factors that affect residential heat loss.
2. Name the three areas that each lose about a third of the thermal loss.
3. State the value must be determined to size a furnace.
4. Name two values are required to determine the annual heating bill.
5. For each term in the equiation Q=U·A·(Ti-Ta), know the units and how the term is determined.
6. Given an RT value of "25," calculate the U value.
7. Know the U-value for the both inside and outside air film resistance.
8. Estimate the U-value for: a (1,2,3) pane window; a (2-)inch thick wood door; a slab-on-grade floor; infiltration.
9. State the (Ti-Ta) for a slab-on-grade floor.
10. Estimate the infiltration rate for a (tight/average/leaky) home.
11. State how the size of the furnacebvaries with the outdoor design temperature.
12. State how the annual heating bill varies with annual degree days for a location.
13. Calculate the number of degree days in a month with an average temperature of "35°F"
14. Estimate the annual heating bill for a house, given the MMBTU/year.
15. For common fuel source, State the purchase units and combustion efficiency.