Re: misconceptions: 2D model of 3D flight

[John Denker <jsd@MONMOUTH.COM>]

By way of preamble, consider this parable:

Once upon a time somebody asserted that the moon was made of green cheese,
and set forth a proof, the first N-1 steps of which consisted of deriving
the Pythagorean theorem.  The proof ended thusly:
  N-1) And therefore a^2 + b^2 = c^2
    N) So the moon is made of green cheese, QED.

This proof was quite detailed and impeccably correct, right up to the last
step.

End of parable.

In the present case, at 02:17 AM 8/18/99 -0700, William Beaty wrote:
> On Sat, 14 Aug 1999, John Denker wrote:
> > > The wings of an airplane do not simply create a spinning pair of
> > > wake-vorticies, they also project those vorticies downwards.
/jsd/ It is not the downward motion of the
/jsd/ vortices that lifts the airplane.  It
/jsd/ is the downward motion of the *air*.
> I totally agree.

So we agree on one thing.

> > > In other words, the air within the wake-vortex pair behind an aircraft has
> > > been given a net downwards motion and this acts like a "rocket exhaust."
/jsd/ No.
>

/jsd/ Two airplanes with equal vortices can
/jsd/ produce greatly different amounts of lift.
/jsd/ For homework, explain how.
> This is interesting.  I assume that "equal vorticies" means "equal energy
> expenditure in creating those vortices?"

Yes, that's consistent with what I meant.

> There is a typical flaw in the "bernoulli-ist" argument regarding energy
> and flight.

That is the assertion which I consider implausible and unproved, analogous
to asserting the moon is made of green cheese.

> In the past I've had difficulty
> communicating my points, so this time I'm going to try using excessive
> detail so there can be no confusion.

[there now appears a long derivation using the machine-gun analogy, showing
energy is quadratic in momentum.  The derivation is correct up to the very
last step, the step that leaps to the conclusion....]

> Therefor, I argue that wings *ARE* reaction engines

... which simply does not follow from the derivation.  Adding details to
the derivation won't help.

The alleged conclusion is inconsistent with the following facts:
  *) Rocket motors and machine guns work just fine in a vacuum.  Wings
don't.  Doesn't that make you worry that your derivation isn't a reliable
predictor of how wings work?
  *) As I have pointed out to you in the past, consider two airplanes
flying separately at velocity less than Vy.  They produce a certain amount
of induced drag.  Now suppose they come together to fly in formation,
wingtip to wingtip.  The total amount of induced drag is less.  This is an
observable physical fact.  Your machine-gun and rocket-motor analogies make
totally wrong predictions about this.  Doesn't this bother you?

You need to learn to *critique* the theories you invent.  Coming up with
new theories is fun.  And it's easy.  The hard part is coming up with new
theories that stand up to scrutiny.