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Denker vs Anderson and Eberhardt



Mr. Denker has been attacking our work for over a year. Other than his
web page renouncing our article in Sport Aviation
(www.aa.washington.edu/courses/aa101/lift.htm) (which was not pointed
out to us by Mr. Denker) his attacks during the last year have been behind
our backs. Reluctantly, we feel that it has come to a point that we must
make a statement.

We will not argue fine points. The bases of the disagreement can be
pretty much boiled down to a single question: Does lift require work? If
we understand Mr. Denker's web site the wing rides its own upwash and thus
does not require work. (He tries to explain this in his rebuttal to our
article with a very confusing discussion of bouncing balls between a table
an a floor.) The simplest rebuttal to his work-free lift idea is that a
wing traveling at Mach 1 or faster has no upwash.

We know where the concept comes from. We discussed it in our article. The
efficiency for producing lift with a wing is proportional to the length of
the wing. A longer wing diverts more air and thus requires a lower
velocity of that air to produce the same lift. (Less kinetic energy for
the same momentum transfer) That is why high-performance gliders have such
long wings. In aeronautics thy work with 2-D airfoils which are really
wings of infinite length. Thus, they are infinitely efficient and develop
lift without downwash or expended energy. But we are discussing finite
wings on planes.

If the wing accelerates air down to develop lift, and that air keeps
going, then lift requires work. Before the wing came by the air was
standing still and afterward it has some kinetic energy. Now we all know
that a propeller develops thrust by blowing air back, and that a
helicopter develops lift by blowing air down. And, we also know that
propellers and helicopter rotors are just rotating wings. So, why is it
so difficult to believe that a wing develops lift in the same way. The
evidence can be seen in the picture in our paper of the jet flying over
the fog. It has punched a large hole in the fog.
If Mr. Denker were right and lift did not require work, either would
propulsion, which is the same physics.

One can also look at real data. In our paper we show a plot of the
relative fuel consumption of a Boeing 777-200 as a function of load.
These data are for the plane traveling at a fixed speed. The data was fit
with a large constant (parasitic drag), a small linear term (increase in
parasitic drag of the fuselage with the increase in angle of attack), and
another large term that goes as the load squared. This last term is the
induced drag cause by the increased amount of air needed to be accelerated
down with increasing load. At a weight of 500,000 lb this plane uses
about 60% of its fuel to overcome parasitic drag and about 40% to produce
lift.

It is easy to see that we have a fundamental disagreement with Mr. Denker.
Until we resolve the question of power and lift it would only be a
distraction to get involved with any of his lesser complaints about our
article.

Sincerely,
David Anderson and Scott Eberhardt