The Elements of Aerofoil and Airscrew Theory

In order to obtain a more detailed knowledge of the behaviour of an airscrew than is given by the simple momentum theory, it is necessary to investigate the forces experienced by the airscrew blades and to regard each element of a blade as an aerofoil element moving in its appropriate manner. It is convenient, in developing the theory, to consider an ordinary propulsive airscrew under ordinary working conditions. The conditions for other types of airscrew and for other working conditions can then be examined as modifications of the main theory.

The airscrew will be assumed to have an angular velocity Ω about its axis and to be placed in a uniform stream of velocity V parallel to the axis of rotation. The sections of the blades of the airscrew have the form of aerofoil sections and the lift force experienced by a blade element in its motion relative to the fluid must be associated with circulation of the flow round the blade. Owing to the variation of this circulation along the blade from root to tip, trailing vortices will spring from the blade and pass downstream with the fluid in approximately helical paths. These vortices are concentrated mainly at the root and tips of the blades and so the slipstream of the airscrew consists of a region of fluid in rotation with a strong concentration of vorticity on the axis and on the boundary of the slipstream.