Re: refutation of the scoop theory, revisited

[David_Anderson <dfa@FNAL.GOV>]

On Sat, 21 Aug 1999, David_Anderson wrote:

> The scoop model makes quantitatively wrong predictions about the effect of
> span and chord on induced drag, as I wrote to Prof. Eberhardt at 06:09 PM
> 1/7/99 -0500.  He wrote back at 01:08 PM 1/8/99 -0800.  He disparaged my
> analysis by pointing out a 15% correction term that I had omitted for
> simplicity.  I reiterated on 08 Jan 1999 19:06:51 -0500 that the scoop
> model was in error by something like 600%, with or without the 15%
> correction terms.


Since there is a dispute over the validity of our calculation of the
diverted air by the wing let me show the calculation so that our error can
be pointed. The key point is that we assume that the entire weight of the
plain is supported by the reaction force of diverting the air down and
that this can be calculated with Newton's second law:

F =  dp/dt    or F = dm/dt *V,

where V is the vertical velocity of the air.  For the sake of our
order-of-magnitude calculation we assumed:

mass of plane: 1045kg  (2300-lb weight)
Speed:  61 m/s   (120 knots)
Angle of attack 4.3 degrees
This yields a value of V AT THE WING of 4.6 m/s
We take half that value as the average V. (V=2.3 m/s)

We have:
dm/dt = (1045 kg * 9.8 m/s/s) / (2.3 m/s)
dm/dt = 4450 kg/s

This is a different number than in our paper.  I refined the calculation
by taking the average value of V not the maximum value.  I guess Mr.
Denker now disagrees with us by 2 X 600%. If the problem is that not all
of the lift is caused by the force of air being diverted, and that part of
it is believe to be cause by the wing surfing in its own upwash we are
back to the problem pointed out in our first communication.  Somehow the
thought of a 500,000-lb aircraft holding itself up by its bootstraps does
not ring true with me.

David Anderson
Dfa@fnal.gov