Re: refutation of the scoop theory, revisited

[brian whatcott <inet@INTELLISYS.NET>]

At 13:46 8/21/99 -0500, David Anderson wrote:
> ... we assume that the entire weight of the
> plane 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
....
> David Anderson
> Dfa@fnal.gov

Continuing with this 'teaching' model, let us say that air at STP weighs
1.293 kg/m^3 and so the requisite mass rate implies a volume
affect of 3442 m^2 per second, hence at a forward speed of 61 m/s the
modelled cross section of
downturned air could be 56 m^2.

If we imagine the modelled plane had a span of 7 meters tip to tip
then a possible value for the vertical extent of the downthrust air
'window' (limited to the span) would be 8 meters.

Now it happens that it is found experimentally that certain values of
lift and drag of ordinary airplanes start changing when they approach
within a wingspan of the ground, so this represents a (very) weak
observation that is not in dissonance with Anderson's cheap and
cheerful model.

I expect it is this sort of calculation that gives rise to strong
disagreement.
brian whatcott <inet@intellisys.net>
Altus OK