I have no problem with the validity of the equations but they will mean little or nothing to many of the readers of this forum. I know because I teach a good many of them and any talk of integrals and the like will immediately make them tilt.
We can get a more inelligible picture of the situation if we imagine an aircraft with flap settings from zero to 90 degrees. The take-off run with zero flap will be quite long, but that with 90 degrees will be even longer. Now if we try 10 degrees and 80 degrees, we will find that our take-off run has decreased in both cases. Try again at 20 and 70 degrees and again the distance will have reduced. If we continue this process we will find an angle at which the take-off roll is minimum. This is the optimum angle to which I referred in my previous post.
The recommended range of flap angles for take-off in any aircraft is unlikely to include any angle greater than this optimum. So in the real world, provided you never use a flap angle beyond the recommended range, the take-off roll will decrease with increasing flap angle. But this will not be the case if we use an angle greater than recommended.
The original question concerned the use of flap angles greater than normal. If we take this to mean greater than the recommended range of angles, then take-off run and distance to screen height will both increase.
If we repeat this process and measure the climb gradient we will find that the gradient is greatest with zero flap and decreases as flap angle is increased. It is possible to create exceptions to this rule but they are probably very rare.
Last edited by Keith.Williams.; 19th Nov 2003 at 05:24.