Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/316

§ 201 with the subject of the present work, the screw propeller and wing propulsion; the former alone being deemed suitable for treatment in the present volume, the latter being reserved for the section on “Avian Flight” which will form part of Vol. II.

§ 202. The Screw Propeller.—We will presume a general knowledge of the screw propeller, and proceed at once to the attack.

The theory of the screw propeller will be discussed on the basis of the peripteral theory of the foregoing chapters; this constitutes a new method which sheds considerable light on a hitherto somewhat obscure subject.

We shall in the following demonstration take the helical surface of uniform pitch as strictly the analogue of a plane in the foregoing theory, and we shall presume that the various propositions already proved in the case of the aerofoil apply mutatis mutandis to the helical equivalent. Thus the blade of a propeller becomes an aerofoil of a form suitable to glide in a helical path, the reaction on the blade (whose resolution is the torque and thrust) is the analogue of the weight, the helical surface at right angles to the blade reaction is the analogue of the horizontal plane, and concentric cylindrical surfaces represent vertical planes in the axis of flight.

We will begin by an examination of an element of a propeller blade represented by its section on one of the aforesaid cylindrical surfaces, of which we will suppose the development is given in Fig. 124. Now, on this development a helical surface will appear as an inclined straight line; let $$O\ a$$ represent the