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Re: a drag equation based on "disk balloons"

On Tue, 2 Feb 1999, Roger Freedman wrote:

billb@eskimo.com wrote:

Drag force = 8 * (M * g)^2 / [ pi * span^2 * V^2 * density ]


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],

Interesting. If my equation had done something nonphysical (such as
predicting a direct dependance of drag upon weight, rather than weight^2 )
that would have been the end of it.

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.

In my calculations I assumed that the lifting force is evenly distributed
along the span. If it was not, then this simply multiplies the entire
equation by some fudge factor (or divides it by e, as appears in your
equation.) Cool!

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.

Thanks for those, I'll try to lay hold of them through interlibrary loan.
I did see your earlier reference list (I've added it to the top of the
phys-L messages on my K-6 wing misconceptions page)


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