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FLIES FASTER

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by Michael Selig, © Copyright 1989 and 1998

Ever
wonder why a sailplane with low drag "flies faster" than a sailpane
with high drag? Probably not, since it makes perfect sense. But does
it? From the
well-known equation for the lift
we can write

This equation shows that the speed depends on the wing loading
(W/S), density, and lift coefficient. The speed does not depend on the
drag – a result that does not seem to make the perfect sense we
expected. The equation is correct, but the approach is incorrect.

The flaw is related to what is meant by "flies faster." When we
directly compare two sailplanes in flight side-by-side, we fly them at
approximately the same glide slope (or L/D). In other words, we do not
match the lift coefficient C_{L} but instead the L/D, which
equals the ratio C_{L}/C_{D}. For the two aircraft,
this requirement gives

where the subscript (1) refers to the sailplane with the lower drag
and (2) the one with the higher drag. Equation (3) gives:

Since

we get the result that

Thus, if we assume that the two sailplanes have the same wing
loading, then through equation (1) we find that the speed V of the
sailplane with the lower drag (flying at C_{L1}) is higher
than that of the sailplane with the higher drag (C_{L2})
– a result that agrees with the "right answer" – our expectation.

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