Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/444

App. V. wind will be reduced, and the energy thus taken from the wind may become available for the purposes of propulsion. It is further evident that if a bird can carry the procedure suggested to the extent of reducing the whole of the air handled to a uniform velocity, that is to say, to its mean velocity, it will have taken away the whole of the energy that is available; i.e., it will have removed the whole of the turbulence energy from the air within its reach. The foregoing assumes that the energy of turbulence consists wholly of motions in the direction of the main current, but the argument may, if required, be extended to include motions in the directions of the other two co-ordinate axes of space.

Without discussion of the means whereby the bird operates to play off one portion of the wind against another, we may, from the above considerations, form an outside estimate of the available energy. Thus if we prescribe some conventional form as representing the motion of turbulence, such as a simple harmonic motion in the line of flight, or a compound harmonic or circular motion of known velocity, we can calculate the turbulence energy per unit volume, and we may convert this into a thrust force per unit area of the stratum of air handled; if, then, we know the extent of this area in the case of any particular bird, and the weight of the bird, we can determine the gliding angle $$\gamma ,$$ the minimum value of which is a quantity otherwise known. Conversely we may, starting from the gliding angle and other data, determine the minimum velocity of turbulence on the convention chosen that will render soaring flight possible.

A question that presents some difficulty is the estimation of the area of the stratum of air handled. At first sight this might be supposed to be the "sweep" of the aerofoil, i.e., $$= \kappa\ A$$ (§§ 109, 160), but the energy estimated on this basis from known fluctuation data appears to be insufficient.

The conception of the peripteral area (§ 210) suggests that, as in the case of the propeller blade, the cyclic or peripteral