Alpine Flyer,
Just a thought, but night flying is usually between Last Light and First Light, are about 20 minutes after sunset, and 20 minutes before sunrise (at least in our part of the world!).
As such, your quest for sunset/sunrise formulae would not give you your night flying time, unless your rules are different.
Airservices Australia at
www.airservices.gov.au have an online computation for LL/FL which may help.