Re: a couple of points on flight

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Fri, 15 Jan 1999, William Beaty wrote:

> 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.

Maybe we need to remind ourselves that "horizontal" here means "parallel
to the earth's surface."  The downward flowing air must eventually meet
the earth in which case it pushes on and imparts "downward" momentum to
the earth.  If you stay in the earth's frame it may look like there has
been no change in momentum, but you aren't doing your analysis in an
inertial frame.  And while 3D may offer another way around the apparent
dilemma, I don't think it is necessary in order to resolve the paradox.

John
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