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Some applications of conformal transformation to airscrew theory

Published online by Cambridge University Press:  24 October 2008

F. L. Westwater
F. L. Westwater
Affiliation:
Emmanuel College
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Abstract

Recent reports contain tables of a parameter K required in calculating the performance of an airscrew by a new method.

The method of calculating K (due to Goldstein) is unsuitable for large values of the pitch especially near the tip of the airscrew.

In the case of infinite pitch we fall back, for a two-bladed airscrew, on the problem of a rotating lamina in two dimensions.

The solution for a cross lamina (corresponding to a four-bladed propeller) is given below and the tables of K for four blades are completed.

A formula for the limit of K/Kp at the airscrew tip is given for a propeller with any number of blades, where Kp is an approximate value of K due to Prandtl.

K for any number of blades is given in the form of an infinite series. The case of three blades is discussed in detail.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 32 , Issue 4 , December 1936 , pp. 676 - 684
Copyright
Copyright © Cambridge Philosophical Society 1936

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References

* Goldstein, S., “On the vortex theory of screw propellers”, Proc. Roy. Soc. A, 123 (1929), 440CrossRefGoogle Scholar; Lock, C. N. H. and Yeatman, D., “Tables for use in an improved method of airscrew strip theory calculations”, Reports and Memoranda of the Aeronautical Research Committee, No. 1674 (October 1934)Google Scholar.