Geeking Out on Heat Loss Calculations

Still waiting for our Energy Audit analysis. Ultimately, we hope that this audit will let us decide what steps we should take to reduce our energy usage and CO₂ emissions. As we already mentioned, on average our old house uses 2746 liters of oil which provides 100 MBTU of energy for heating and hot water. According to https://www.carbonindependent.org/15.html, 2.96 kg of CO₂ is produced by burning one liter of furnace oil. Therefore, our home’s current CO₂ footprint is 8,128 kg per year.

I should mention that I am an engineer and love numbers and calculations, hence the equations and tables in the text below. I did some online research and realized I could likely do my own energy audit. Now when the Energy Auditor comes, I can better understand what he is doing and compare the results of his calculations to mine. 

The basic concept is that heat loss through the surfaces of your house must be replaced by the heat source in your home. I’m going to assume that most of the heat loss through the house is by conduction which refers to the heat lost through the walls, windows, attic, etc. I borrowed this great graphic from https://powertoswitch.co.uk/energy-efficiency/where-does-all-the-heat-go/ that illustrates it perfectly.

 To calculate the heat loss, we can use equation 1 below:

Heat Loss =A(T_in-T_out)/R

In imperial units, Heat Loss is BTU/hour, A is the exposed area in ft², T_in and T_out are the inside and outside temperatures in °F and R is the R-value rating for insulation (example R 20) which has units of (hour ft² °F BTU).

I’ve divided my old house up into different zones that have different R values, Table 1 below gives the details. The best R value is in our Attic and the worst is our windows, particularly the old single pane wood windows. The walls represent the largest area by far followed by the attic and basement.

Table 1: Details of the different zones in our old house

Item	Exterior Walls	Old single pane windows	New double pane windows	Attic	Steel Door	Basement
R value	R10	R1.2	R3.1	R20	R1.2	R5
Area	1569 ft2	135.5 ft2	121 ft2	754.75 ft2	18 ft2	754.75 ft2

 We can add up all the A/R values for each zone of the house as shown in the equation below:

Heat Loss = [(A/R)_wall + (A/R)_ow + (A/R)_nw + (A/R)_sd + (A/R)_attic + (A/R)_base](T_in-T_out)

Heat Loss = [1569/10 +135.5/1.2 + 121/3.1 + 18/1.2 + 754.75/20 + 754.75/5] (T_in-T_out)

Heat Loss = [156.9 + 112.9 + 39 + 15 +37.7 +150.9] (T_in-T_out)

If we know the temperature difference between the inside and outside, we can calculate the heat loss in BTU per hour for our old house using the following equation 2.

Heat Loss = 361.55 (T_in-T_out)  + 150.9 (T_in-T_out)                                                                      

The exterior walls, windows, doors and attic all face the outside so their T_out would all be the same. Since the basement is an enclosed space below ground, the T_out would be different. I have measured the temperature in the basement over the last month or so and it seems to stay steady at 50 °F, even when the outside temperature changes. So, I’m going to use that value for T_out for the basement heat loss calculation rather than the actual outside temperature.

We keep our thermostat set at 64 °F during the day and for 8 hours overnight we have it programmed to go down to 58 °F. Of course, the outside temperature varies from day to day and month to month. This may seem a bit obsessive/compulsive, but I managed to find the average temperature for the month of October through April for the years 2013 to 2022 for Halifax. This is approximately the time we have owned our old house. I averaged all this data to get an average temperature for the years we have owned the home for the months of October through April and those values are listed in Table 2 below.

Table 2: Historical average temperatures in Halifax from 2013 to 2022 and resulting heat loss calculation for each month of the heating season.

Heating Month	Oct	Nov	Dec	Jan	Feb	Mar	April
Average outside temperature	50.6 °F	39.1 °F	29.6 °F	23.9 °F	24.3 °F	29.1 °F	40.9 °F
Total Heat Loss in MBTU	4.49	7.26	10.06	11.59	10.38	10.19	7.45

 The heat loss for each month can be calculated by adding the time to equation 2. We have 24 hours in a day, 16 of which the inside temperature is 64°F and 8 of which it is 58°F, and 31 days in the month of October:

Heat loss (for October) = 361.55*[16(T_in-T_out)_day + 8(T_in-T_out)_night]*days + 159.5*[16(T_in-T_out)_day + 8(T_in-T_out)_night]*days                                                                                                                                     
Heat loss (for October) = 361.55*[16(64-50.6) + 8(58-50.6)]*31 + 159.5*[16(64-50) + 8(58-50)]*31

Heat loss (for October) =361.55*[214.4 + 59.2]31 + 159.5*[224 +64]*31

Heat loss (for October) = 3,066,522 + 1,424,016

Heat loss (for October) = 4,490,538 BTU

Repeating this calculation for the other heating months gives the values listed in Table 2.

As expected, the months with the lowest average temperatures, use the most energy to heat the house. Dec., Jan., Feb. and Mar. use the most energy. The total energy for the heating season calculates to be 61.34 MBTU. The furnace needs to provide that energy but is not 100% efficient. Assuming our 27-year-old oil furnace is 70% efficient means we would need to use 61.34/0.7 = 87.62 MBTU.

This value compares well to the actual average energy we have used based on our oil bills of 100 MBTU. Particularly since the 100 MBTU also includes energy we use to provide hot water. Efficiency Nova Scotia indicates that a 4-person 1700 sq. ft. home uses 32.5 MBTU to provide hot water. Since we are only two people, I will estimate our hot water usage to be 16.25 MBTU. Adding that to our above heat loss calculation results in a total energy use prediction of 103.9 MBTU. That is an amazing agreement with our actual use of 100 MBTU.

It is great that the heat loss calculations are pretty accurate and capable of predicting our actual energy used. That puts us in a position to consider different upgrades to the house, particularly in terms of insulation, and to see how much energy and cost savings they would result in. That will be the subject of an upcoming post.

Thanks for sticking with me through the numbers. Hope some of you will find it useful.