After some research I am seriously thinking about introducing climb gradient in calculations. For example:
Climb gradient (θ) = 1,010 fpm / [(78 knots x 6,076 ft)/60 min] = ~12.78%
Climb angle = ASIN(climb gradient) = ~7° (0.122173 rad)
Height to climb = TAN(climb angle) x distance = 7,834 feet
Altitude = 1,500 + 7,834 = 9,334 feet
But still... in both cases I have to use KIAS, not the ground speed! It seems I'm stuck again...
