Aerodynamic Forces on a Propeller in Non-Stationary Motion

The non-stationary lift and moment of an oscillating propeller blade element are determined. The solutions are obtained in the form of double definite integrals which are evaluated for one numerical example in Appendix A. The three-dimensional nature of the problem is accounted for by determination of the induced velocity field due to an approximate vorticity distribution in the propeller wake. The corresponding blade element circulation is calculated by means of the classical Munk integral theorem. The two dimensional results for non-stationary lift and moment, expressed in terms of the circulation, are then used to obtain the results of this paper. Derivations of the lift and moment equations are included. The resultant forces on the blade element are resolved into thrust and torque. Also, a qualitative discussion of the effects of compressibility is made based upon the Prandtl-Glauert transformation. Finally, the results are compared with two dimensional theory and a discussion of the application to problems of flutter and forced oscillations of propellers is made. The discussion is illustrated by means of the numerical example.