Re: a couple of points on flight

[William Beaty <billb@ESKIMO.COM>]

On Fri, 15 Jan 1999, JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439 wrote:

> Hi all-
>         William Beatty writes:
> ***************************************************************
> Here is a central problem: in 2D, the air far upstream from the wing is
> flowing horizontally, right?  And the air far downstream is also flowing
> horizontally, correct?  These flows come about through the superposition
> of circulation and constant horizontal flight.  It seems to me that this
> guarantees a ZERO change in momentum of the air.  It looks as if the 2D
> flow diagram is symmetrical about a vertical line, and upwash exactly
> equals downwash.
> *********************************
>         Wrong.  Newton's laws work very well in both wind tunnels and 2-D
> aerodynamics.
>         The air downstream of a 2-D ideal lifting airfoil has a net
> downward component.

I agree, but that's not the problem.  To me it looks like the air upstream
from an ideal 2D airfoil has a net upward component which equals the
downstream downward component. At the position of the airfoil, the upward
velocity of the air changes to downward velocity, and this explains the
lift.  However, the airfoil caused the oncoming air to rise to meet it,
and this subtracts from the lift.  Also, the airfoil causes the descending
downstream air to deccelerate to a standstill, and this also subtracts
from lift.  If we look at the entire pattern of air surrounding the
airfoil out to a fair distance, it appears that the momentum change in the
air is first upwards in the upstream section, then downwards at the
airfoil, then upwards again in the downstream section, for a net change of
zero.

> A classic work is Glauert, "Airfoil and Airscrew
> Theory",  but I'm sure that there are many other texts available.  I
> haven't yet checked Brittannica, but that's usually a good place to
> start.

Thanks, I'll have a look at Brittannica, but I hoped that mine was a
typical student question which has been answered millions of times, and
somebody here would already know the answer offhand.

When I see those nice perfect 2D diagrams for a rotating cylinder in a
horizontal wind, the upstream air flow is a mirror image of the
downstream, which suggests to me that the net momentum change is zero,
even thought the lifting force is large.  If I am wrong, where is my error
hidden?


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