How to calculate the amount of night time during a flight?

Question

I have been asked to find a way to calculate the amount of time that a flight takes during night time.

So far, I have the departure latitude and longitude and the time of takeoff, the arrival latitude and longitude and the time of landing. I can easily calculate the sunset and sunrise time at the departure location, and at the arrival location. But I don't know how to proceed in order to find at which moment of the flight the sunrise and sunset will happen at the location where the aircraft is at that precise moment.

I'm just asking for some guidance on how to resolve this problem.

PS: The calculation does not have to be very precise, and estimation is more than enough. We are just looking for the simplest solution to obtain an acceptable result.

Answer 1

One option would be to plot the course of the flight as a set of discrete points and check if it's day or night at each point along the way to determine when the flight enters/exits the Earths shadow. Precision will be limited to the size of your time increment, but doing a once/minute check on a computer shouldn't be a problem.

For a high precision result you'd need to program in actual flight corridors; but for a rough estimate assuming the shortest direct route will probably be good enough in most cases.