Medwin,
Too many variables for a general question, here are some of them -
(1) Higher Flap means lower Vs, which yields Lower V1/Vr/V2, and thus lower Takeoff Run, EXCEPT at lower weights with lower Vs, Vmcg/Vmca will govern V1/Vr/V2, and may be the same speeds for a Low or a High Flap setting. For the same speeds, lower flap would be advantageous due to improved acceleration.
(2) Screen height should be the same, assuming a performance limiting situation. Takeoff data looks at TODA, not TORA, which requires the aircraft to reach 35 feet at the end of the TODA. The airborne distance to, and gradient to achieve 35 feet will be worse with a higher flap setting, and this is added to the TORA, BUT it is unlikely that the manufacturer would have certified the aircraft for such a higher flap setting if distance to TODA was greater, and it would not be advantageous to use the higher flap setting.
(3) 1st segment gradient will be lower with higher flap. Not a problem if there are no close-in obstacles. The only advantage in the 1st segment will be a shorter 1st segment distance due to the lower speed for a fixed gear retraction time, thus the aircraft can enter the 2nd segment climb at a shorter distance from the end of TODA.
(4) 2nd segment gradient will be lower with higher flap. Again, not a problem if not obstacle limited, but if obstacles are limiting, it's time to cross compare the overall takeoff scenario to find the best flap setting.
(5) 3rd segment at higher flap can be a 'monster', particularly if a high 3rd segment acceleration altitude is required. The time taken to accelerate from the lower 'High Flap' V2 to Final Takeoff configuration (Clean) can be MUCH longer. Add the time from Brakes release to commencement of 3rd segment level flight to the LONGER 3rd segment time, and you may 'bust' the 5 or 10 minute limit at Takeoff thrust. In several airports where I've done the Airport Analysis, higher flap was necessary due to a relatively short runway, but then time to a higher than normal acceleration height plus the longer acceleration necessitated further REDUCTION in RTOW to contain the time at Takeoff thrust within the 5 or 10 minute limit. In 7 runways where I encountered this problem, solution was gained in 4 cases by reverting to the lower flap setting, with it's attendant faster climb and acceleration times.
(6) There are variables within these variables - many!
swh, a good response, but may I suggest that climb gradient depends upon Ground Speed and Rate of Climb, not IAS and Rate of Climb. Whilst we are discussing Climb Gradients, isn't it more appropriate to discuss excess THRUST, not excess Power.
Regards,
Old Smokey