Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/446

Thus if the motion of turbulence is equivalent to a superposed circular motion, that is to say, if it consist of two component horizontal simple harmonic motions at right angles, and if the bird is able to abstract the total energy of both components, then V will be the maximum velocity of either component, or the uniform velocity of the equivalent circular motion; hence under the supposed conditions the maximum velocity of turbulence = 16.5 feet per second.

If the turbulence contain only one harmonic component, or if, which amounts to the same thing, the bird is only able to take advantage of the harmonic component in the line of flight, the available energy for a given maximum velocity will be only half that on the basis of circular motion; hence, in order that the necessary energy should exist in the wind, the maximum velocity must be multiplied by ${\sqrt {2}},$ or, on simple harmonic basis, the maximum velocity (plus or minus) of fluctuation becomes 23.4 feet per second.

The above estimates are on the basis of sweep. On the basis of peripteral area we have mass of air handled per foot traversed—

$={\frac {1+\epsilon }{1-\epsilon }}\ \rho \ \kappa \ A={\frac {1.75}{.25}}\times .47=3.3\ {\mbox{lbs.}}$

∴$\quad {\frac {3.3\times v^{2}}{2}}=64.4$

$v^{2}=39,\ \ {\mbox{or}},\ \ v=6.25$

∴ on the basis of circular motion the maximum velocity of turbulence = 6.25 feet per second.

Or, on the simple harmonic basis, $6.25\times {\sqrt {2}}=8.8,$ feet per second.

In the foregoing investigation the question of the means whereby the energy is trapped, or the possible percentage of the total that is available, is left untouched. The whole subject belongs essentially to the later portions of the work, Aerodonetics, where the matter will be treated more fully; the present publication is only made as an illustration of the employment of the peripteral theory expounded in the present work.

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