That title might fill you with apprehension and, in many ways, you'd be right: analyzing such a complex thing as a home's energy performance without using software is a daunting task. But it is possible. There are even several books which include worksheets and detailed descriptions of how to build a more accurate assessment than the one we'll outline here.
Start with the building's envelope. Begin with the roof and the walls. Work out their overall R-value, by adding together all the individual values for each component – insulation, drywall, shingles, tiles, wood, and whatever else. If you're talking to a professional designer or builder, there's a good chance they'll know the R-values for most standard constructions, so they can save you some time.
Convert the R-value to a U-value: U-value = 1 ÷ R-value. The U-value is used to determine how much heat is lost through the roof and walls. Once that's calculated, you'll need to include windows, doors, and foundations.
Heat is also lost through leaks in the envelope, so you'll need to know how much new air gets into the home every hour. Most passive solar homes aim for between 35% and 50% of indoor air being replaced hourly.
These two figures are added together to get a number of Btus per hour that are lost from the envelope.
Once the negatives are calculated, the positives must be weighed. The total amount of solar gain is calculated next. Window gain is based on a formula that takes a solar gain factor and the surface area of the glazing into account, with adjustments for the amount of sunlight (percentage exposure), amount of shade, and reflected light from the glass surface.
Monthly figures for solar gain can be calculated by using records of hours of sunlight per month in your region.
With those two figures in hand, the total heating requirement for the building can be calculated. This value is generated for each month of the year (or the heating period) by multiplying the total heat loss by the number of degree days in each month. Degree day figures are available from sources online or local meteorological offices.
Comparing and adjusting
So now you have the total loss and the total solar gain per month. Comparing those for each month will give you a clear view of when your solar setup will or will not provide enough heat for the home. Wherever there is a shortfall, you will need backup heating for the building.
It's worth taking the figures for the whole year and comparing them. If your solar gain covers more than 50% of your annual heating load, you're doing pretty well. But if it's not covering enough – whether that means below 50% or below your target level – you will have to go back to your design and adjust it. More insulation, more south-facing windows, a better envelope, whatever it takes. Then you will have to run the numbers again and see how they look.