Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/165

Rh exceed the area of the plane itself, or we have $$\kappa$$ equal to or less than unity.

By employing this in conjunction with equation (3) an outside estimate may be made of the load supported by planes of the form stated. Such estimates generally fall short of the experimental value in the relation of about one to two. By substituting a fictitious value for the “sweep” of about twice that ascertained by experiment the results of the equation can be made to agree. It is evident, therefore, that all the conditions of the problem have not so far been included in the theory.

§ 110. In the Region of a Falling Plane,—Up-current.—In the foregoing discussion the subject has been treated as if the air, coming into the immediate region of an advancing aeroplane, is in a state of rest, and as if the support is wholly derived from the downward velocity imparted to it. But it has been shown that if this were actually the case the weight supported could, as a maximum, be only about one-half of that found by experiment.

Let us take the simple case of a horizontal plane supporting a weight and allowed to fall vertically. There is at first a circulation of air round the edge of the plane from the under to the upper side, forming a kind of vortex fringe (Fig. 61), the air all round the edges of the plane being in a state of rapid upward motion. A.F.