Applications of modern hydrodynamics to aeronautics by Ludwig Prandtl

By Ludwig Prandtl

The document supplies, quite in brief, partly one an creation to hydrodynamics that's designed to offer those that haven't but been actively curious about this technological know-how this kind of grab of the theoretical underlying rules that they could stick to the next advancements. partly there follows a separate dialogue of the several inquiries to be thought of, during which the speculation of aerofoils claims the best component of the gap. The final half is dedicated to the appliance of the aerofoil conception to screw propellers. A desk giving crucial amounts is on the finish of the document. a brief reference record of the literature at the topic and likewise a desk of contents are added.

Translated from German through the workers of the nationwide Advisory Committee for Aeronautics.

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APPLICATIONS OF MODERN HYDRODYNAMICS TO AERONAUTICS. E. IMPROVED THEORY OF AIRPLANES HAVING MORE THAN ONE WING. 24. The knowledge obtained in the theory of a monoplane can be applied also to multiplanes and furnishes here a series of remarkable theorems. We shall limit ourselves to the theory of the first order, as designated in the theory of monoplanes, therefore we shall neglect the influences of v. Further, we shall not take into account the effect of curvature—i. " For the sake of simplicity we shall limit ourselves to multiplanes with wings which are straight and parallel to each other.

This circulation is again nothing but the circulation around the wing at the point x. If the factor ldx is omitted from both sides of equation (61), it takes, as a result of this transformation, the form dx = p ADO 'V = p V I' (63) We have thus proved in an entirely independent way, as we see, the Kutta-Joukowski theorem for a wing element, which previously we took over, without proof, from the infinitely long wing. The relations deduced in the previous paragraphs permit, in the case of a constant w, the formation of general theorems for w and TV in place of (39) and (40).

At the lifting line). If we follow the method of Lanchester, as described in section 15, the downward velocity w can also be looked upon as a diminution of the ascending flow at the leading edge of the wind due to the absence of the sidewise prolongation of the wing, i. , to the deviation from an infinitely long wing which was the basis of the treatment in section 15. Discussions very similar to this are given in Lanchester, Volume I, section 117. It may be seen from the -figure that at great distances behind the wing the descending velocity is 2w, which agrees with the relation already mentioned that the velocities due to a straight vortex filament extending to infinity in both directions are twice those due to a filament extending to infinity in one direction only, for points in the plane perpendicular to this vortex passing through its end point.

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