Heating Calculations
The size of the heating system is directly related to the amount of heat lost from the house or building. All structures lose heat to the outdoors or to adjacent unheated or partially heated spaces when the temperatures of the outdoor air or adjacent spaces are colder than those inside the structure. The heat within the building is normally lost by transmission through the building materials and by infiltration around doors and windows.
The loss of heat from a structure must be replaced at the same rate that it is lost. Consequently, determining the correct size of the heating system, and the rated capacity of the heating plant required by the system is very important. It should be obvious that an oversized heating plant will cost more to install than a smaller one and will provide more heat than the structure requires. On the other hand, an undersized heating plant lacks the ca pacity to provide sufficient heat, particularly during cold spells. The heating system and the selection of the heating plant must be carefully planned in order to adequately and efficiently replace the lost heat.
This chapter will describe several methods for calculating heat loss, ranging from rule-of-thumb methods to the rather more precise method of using overall coefficients of heat transmission (U-values) computed for the various construction materials and combinations of construction materials through which heat is commonly transmitted.
USING COEFFICIENTS OF HEAT TRANSMISSION
The more precise methods of calculating heat loss from a structure require a thorough knowledge of the thermal properties of the many materials and combinations of materials used in its construction. The term “thermal property” is used here to mean the overall coefficient of heat transmission (i.e. the rate of heat flow through a material). Each type of construction material (or combinations of materials) will have its own coefficient of heat transmission. Before continuing any further, it would be advisable to review the sections of Chapter 3 (INSULATION PRINCI PLES ) that specifically pertain to the problem of heat loss (e.g. see PRINCIPLES OF HEAT TRANSMISSION; THERMAL CONDUCTANCE; THERMAL RESISTANCE; etc.).
The ASHRAE and other authorities suggest the following basic steps (in the sequence given) for calculating heat loss:
1. Decide upon the desired inside air temperature for the structure.
2. Obtain the winter outside design temperature for the location of the structure from published lists or a local weather bureau.
3.Determine the design temperature difference (the differ ence between the temperatures found in Steps 1 and 2).
4.Identify on the heat loss worksheet each room or space in the structure.
5.List every structural section in each identified room or space that has an outer surface exposed to the outdoors or to an unheated or partially heated space.
6.Determine the coefficient of heat transmission (U-value) for each structural section (e.g. walls, glass, ceiling, etc.).
7.Calculate the infiltration heat loss for each identified room or space.
8.Calculate the total area for each exposed surface (i.e. the total outside wall area, the total floor area, etc.).
9.Calculate the area for each door and window in the walls, and add these figures together to obtain the total area for these openings.
10.Subtract the total area for doors and windows from the gross outside wall area (obtained in Step 8) to determine the total net outside wall area. Enter the amount on the heat loss worksheet.
11. Multiply the total net wall area determined in Step 10 by the U-value (Step 2) by the design temperature dif ference (Step 3) to obtain the total heat loss for walls (expressed in Btuh).
11. Make the same calculations for the other surface areas (floors, ceilings, etc.) determined in Step 8.
12. Add the heat loss figures calculated for each surface category and the infiltration heat loss to obtain the total heat loss for the identified room or space.
13. Repeat the procedure outlined in Steps 1-11 for each identified room or space in the structure.
14. Add the various totals to obtain the total heat loss from the structure (expressed in Btuh).
These fifteen basic steps for calculating heat loss are pro vided as a useful means of reference for the more detailed descrip tion of the procedure contained in the paragraphs that follow.
OUTSIDE DESIGN TEMPERATURE
In heating calculations, the outside design temperature is the coldest outside temperature expected for a normal heating season. It is not the coldest temperature on record, but rather the lowest one recorded for a particular locale over a three to five year period.
Lists of outside design temperatures are published for selected localities throughout the United States (Table 1). If a locality is not included on the list of winter outside design temperatures, check with a local weather bureau. Using an outside design tem perature from the nearest locality on the list can be misleading, because even closely located cities can differ widely in weather conditions as a result of different altitudes, the effects of large bodies of water, and other variables.
INSIDE DESIGN TEMPERATURE
The desired inside design temperature will depend upon the intended use of the space. In a large structure, such as a hotel or a hospital, there will be more than one inside design temperature, because there is more than one type of space usage. For example, hospital kitchens will generally have an inside design temperature of about 66°F. The wards, on the other hand, will range from 72°F to 74°F.
Residences will generally have a single inside design tempera ture for the entire structure, with 70°F or 71°F being the most commonly used temperatures.
DESIGN TEMPERATURE DIFFERENCE
The design temperature difference is the variation in degrees Fahrenheit between the outside and the inside design tempera tures. It is used in the heat transmission loss formula (see below), and is a crucial factor in heating calculations.
Be careful that you obtain the degree difference between the
two temperatures, and do not simply subtract the smaller figure from the larger one. For example, if the outside and inside design temperatur s are -20°F and 70°F respectively , the design tem perature difference will be 90 degrees (20 degrees below zero plus 70 degrees above zero).
DETERMINING COEFFICIENTS OF HEAT TRANSMISSION
The overall coefficient of heat transmission or U-value, as it is commonly designated, is a specific value used for determining the amount of heat lost from various types of construction. It represents the time rate of heat flow and is expressed in Btu’s per hour per square foot of surface per degree Fahrenheit tempera ture difference between air on the inside and air on the outside of a structural section. Furthermore, the U-value is the reciprocal of the total thermal resistance values (R-values) of each element of the structural section, and may be expressed as:
U = 1/Rt
Professional organizations such as the American Society of Heating, Refrigeration and Air-Conditioning Engineers (ASHRAE) have already determined the U-values for a wide variety of floor, ceiling, wall, window, and door construction. Tables of these U-values are made available through ASHRAE publications (e.g check the ASHRAE 1972 Handbook of Fundamentals ) found in many libraries. Many manufacturers of heating equipment also provide tables of U-values in their literature. When calculating heat loss, you have the option of selecting U-values from the tables provided by manufacturers and certain professional asso ciations, or computing them yourself. The latter method, if done correctly, is the more precise one.
CALCULATING NET AREA
Having determined the design temperature difference and computed (or selected) an overall heat transmission coefficient for each construction material or combinations of materials, you are now ready to calculate the net area of each surface exposed to the outside or adjacent to an unheated or partially heated space.
The best procedure for calculating surface area is to work from a building plan. If one is not available, you will have to make your own measurements. Measurements for calculating net area are taken from inside surfaces (i.e. inside room measure ments ). You will not be concerned with structural surfaces (e.g. walls, ceilings , floors) between rooms and spaces heated at the same temperature , because no heat transmission occurs where temperatures are constant.
Calculating the total area for each surface should be done as follows :
1. Multiply room length by room width to determine floor and ceiling area.
2. Multiply room length (or width) by room height to deter mine the outside wall area for each room.
3. Multiply door width by door height to determine the sur face area for each door.
4. Multiply window width by window height to determine the surface area for each window.
Whether you use room length or room width in calculating the outside wall area will depend upon which wall surface is exposed to the outside. In some cases (e.g. corner rooms) , both are used and require at least two separate calculations (i.e. room length X room height and room width X room height).
Add the calculated surface area of each outside wall (see Step 2 above) to obtain the gross wall area for the structure. Subtract the sum of all door and window surface areas from the gross wall area. The result will be the net wall area for the struc ture. Multiply the net wall area by the heat loss in Btu’s per hour per square foot to calculate the heat loss through the walls.
HEAT TRANSMISSION LOSS FORMULA
The heat loss (expressed in Btuh) of a given space is deter mined by multiplying the coefficient of heat transmission by the area in square feet by the design temperature difference (i.e. the difference between the indoor and the outdoor design tempera tures). Because a heating system must supply an amount of heat equal to the amount of heat lost in order to maintain a constant indoor design temperature, heat loss is approximately equal to heat required. This may be expressed by the following formula:
Ht = AU ( ti – to)
Where:
Ht = Heat loss transmitted through a structural section (e.g. roof, floor, ceiling, etc.) expressed in Btu’s per hour.
It represents both the heat lost and the heat required ,
A Area of structural components in square feet,
u Overall coefficient of heat transmission,
To = Outdoor design temperature,
Tt = Indoor design temperature.
c;OMPUTING TOTAL HEAT LOSS
The commonly accepted procedure for calculating the total heat loss from a structure is to calculate the heat loss for each room or space separately and then add the totals.
The heat loss calculation worksheet you use should contain a
column in which each room or space can be identified separately. Under the identification are listed those structural sections through which heat transmission losses occur. When applicable, these will include all or most of the following:
1. Walls,
2. Glass,
2. Ceiling,
3. Floor,
4. Door(s).
In addition to the five types of structural sections listed above, each identified room or space should also include a line for heat loss by air infiltration. Figure 1 illustrates how your worksheet should appear at this point.
Now that you have identified the room or space, have listed the structural sections through which heat loss occurs, and have calculated the rate of air infiltration, you must now determine the net surface area and the U-value for each structural section. The design temperature difference must also be determined and entered for each structural section. Except where surfaces are exposed to partially heated spaces (e.g. a garage, attic, or basement), each structural section will have the same design temperature differ ence. An example of how your worksheet should look at this point is illustrated in Fig. 2.
Each identified room or space should also include the calcu
lated air infiltration heat loss (see INFILTRATION HEAT
LOSS below). The amount of heat loss due to air infiltration will depend upon the size, type, and number of windows and doors, and other variables.
The bedroom given, as an example in Fig. 1, has two ex posed walls ( 8 ft. X 15 ft. and 8 ft. X 20 ft.) . The number of air changes suggested for a room with two exposed walls is 1’h changes per hour.
The volume of air infiltration for the bedroom can be calcu lated as follows:
Knowing that the volume of air infiltration is 1800 cfh, the heat loss in Btuh’s can be calculated as follows:
Heat loss 0.018 X Q(ti – t0 )
= 0.018 X 1800 X 90
2916 Btuh
The total heat loss for bedroom No. 1 (as it would be desig nated on the worksheet) is 12,378 Btuh. If there is a door in one of the outside walls, its heat loss would also have to be calculated and entered on the worksheet. Furthermore , the door area (in sq. ft.) would have to be subtracted from the surface area for the walls, because the latter is always a net figure.
After calculating the heat loss for each room or space in the structure, the results are added to obtain the total heat loss (in Btuh) for the structure.