Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/266

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§ 171
AERODYNAMICS.
Let = direct resistance, of which—
is that due to body resistance, and
is that due to aerofoil area.
  „ = a normal plane area whose resistance is the equivalent of and
  „ = a normal plane area whose resistance is the equivalent of
  „ = velocity of flight.
  „ = coefficient of skin friction.

and are constants, as in preceding section, and are further constants.

It can be shown that—

 and

We require to know the minimum value of or, we require to solve for minimum value the expression—

Now  and so that expression becomes

or

where and are variables.

Making a temporary substitution of constants in order to abbreviate, we have—

Differentiating in respect of and gives simultaneous equations as follows:—

(1)

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