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[Phys-L] Re: thrust > drag



1) We can agree that the total aerodynamic force of
the wing is tilted "somewhat" toward the rear of the
aircraft.

So far so good.

2) In a previous message, it was suggested that this
was due to the geometry of the situation, i.e. the
tilt was controlled by the angle of attack.

This is a misconception.

==============

Let's try to sort this out.

For simplicity, let's focus on the linear regime, in
which that lift is proportional to the angle of attack,
and induced drag is proportional to the square of the
angle of attack.

In addition to induced drag, there will also be some
parasite drag. This does not have a strong or systematic
dependence on angle of attack. This is already a sufficient
reason for concluding that the total tilt of the aerodynamic
force vector does *not* simply follow the geometry of the
angle of attack, because the vector is tilted even when
there is no angle of attack.

Furthermore, and even more profoundly, even if we disregard
parasite drag and consider only induced drag, geometry is
still not the answer. The force-tilt is not controlled by
the angle of attack.

It turns out that induced drag depends very strongly on the
length of the wing. If you make the wing longer (perhaps
by flying in formation, wingtip-to-wingtip, with other
aircraft) you can make the induced drag (per unit lift)
as small as you like. To repeat: without changing the
angle of attack, and without changing the amount of lift
per unit span, you can reduce the amount of induced drag
per unit span ... simply by adding more span. Same
geometry, different tilt.

============

In general:

a) Wings are amazing things.

b) Beware of all simple "geometry-based" explanations of
how wings work.

c) You can pretty much assume that any alleged explanation
that doesn't talk about _circulation_ is probably hopelessly
wrong.

For a detailed explanation of how wings work, with lots of pictures:
http://www.av8n.com/how/htm/airfoils.html
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