Enroute sunrise or moonrise predictions
You know the distance between departure and destination.
Calculate sunrise time for the departure and destination, using the cruise altitude. [To compensate for altitude: if using the sine formula you solve instead for hour angle, using a sun height which is the combination of -16' (semidiameter of disk), -34' (astronomical refraction), and the arcdistance to the horizon of about [-1.15'√(elevation in feet above the horizon)]. Combine that hour angle with airport longitude, then look in the almanac for when exactly the Sun had that GHA.]
The course distance divided by the time interval (between the sunrise times) is the groundspeed of the sunrise line along your direct course line.
Add your average groundspeed to that and you have the (combined) closing speed.
At the takeoff time, where was the sunrise line? You can find out because you know when it is predicted over your destination, and already found out how fast it is moving.
So you know how far away the sunrise line is at takeoff time, and about how fast you and it are converging. So you can predict how long it will take (after takeoff) for you and it to coincide. (Distance/closing speed) = time interval.
To refine the prediction, you note the time passing some known distance from the destination. That way the uncertainties of climb speed and departure routing don't influence the prediction.
Last edited by bethpage89; 10th Sep 2012 at 02:13.
Reason: Symbol and diction