The following website is a good reference for calculating the amount of energy that will fall on a solar collector, depending on your location, the collector inclination, time of the year...
I estimated my solar fraction using this calculator.
First of all, solar irradiance vs tilt:
Here is an estimation of the area of the collector that will get shaded, for each month:
Next, solar fraction for space heat, assuming a 300sqft collector (second row=consumption, 3rd row=solar fraction, 4rth row=savings):
Finally, i will add the estimated savings from a $8000 heat pump. The savings calculation assumed 73°F winter temperature settings (we are at 68°F), resulting in a $2000 heating bill (our total electric bill is less than $2000, with about 40% for heat, and 15% for hot water). Due to these false assumptions, the savings are inflated, so I applied a correction factor equal to the actual vs estimated heating bill:
Estimated savings from heat pump = $880 / year (assuming $2000 yearly heating bill).
Savings after correction = $352 (assuming 40% of $2000 total electric bill).
The solar system will cost less than $8000 (cost estimated between $4000 and $5000), yet provide twice the savings of the heat pump.
The solar fraction is estimated at 80% of heating bill, and 45% of total electric bill.