Re: a drag equation based on "disk balloons"

[Roger Freedman <airboy@PHYSICS.UCSB.EDU>]

William Beaty <billb@ESKIMO.COM> writes:

> I used my crude "disk balloons" analogy of airplane flight to predict the
> induced drag upon an aircraft to be:
>
> Drag force = 8 * (M * g)^2 / [ pi * span^2 * V^2 * density ]
>
> M * g being aircraft weight, V is velocity of horizontal flight, and
> "density" is the density of air.
>
> How does this match conventional calculations of induced drag?  The only
> reference I have at hand is THEORY OF FLIGHT, in which I don't immediately
> find a treatment of induced drag.  If anyone here has offhand knowledge of
> this issue, can they tell me if my above equation is totally bogus?  Does
> induced drag increase as aircraft weight^2, and decrease as 1/V^2, and as
> 1/span^2?

The above equation is quite close to the mark. The standard expression for
the induced drag in level flight is

D = (weight)^2/[pi * e * (span)^2 * q],

where q is the dynamic pressure (= 1/2 * density * speed^2) measured far in
front of the wing (i. e. in undisturbed airflow) and e is an "efficiency
factor" (no greater than 1) which depends on the three-dimensional shape of
the wing. The smaller the value of e, the more induced drag is produced for
a given situation.

That's about all I know on the subject, so for further research I recommend
the following references, which I also recommended in a post on Jan. 17:

Ashley, Holt. Engineering Analysis of Flight Vehicles. Addison-Wesley,
1974. Reprinted by Dover Publications, 1992.

Hubin. W. N. The Science of Flight: Pilot-Oriented Aerodynamics. Iowa State
University Press, 1992.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++

Roger A. Freedman
Department of Physics and College of Creative Studies
University of California, Santa Barbara

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