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ARTICLE IN PRESS
Progress in Aerospace Sciences 42 (2006) 85–128 www.elsevier.com/locate/paerosci The aerodynamics of propellers
Quentin R. WaldÃ
102 Cape George Road, Port Townsend, WA 98368, USA
Abstract
The theory and the design of propellers of minimum induced loss is treated. The pioneer analysis of this problem was presented more than half a century ago by Theodorsen, but obscurities in his treatment and inaccuracies and limited coverage in his tables of the Goldstein circulation function for helicoidal vortex sheets have not been remedied until the present work which clarifies and extends his work. The inverse problem, the prediction of the performance of a given propeller of arbitrary form, is also treated. The theory of propellers of minimum energy loss is dependent on considerations of a regular helicoidal trailing vortex sheet; consequently, a more detailed discussion of the dynamics of vortex sheets and the consequences of their instability and roll up is presented than is usually found in treatments of propeller aerodynamics.
Complete and accurate tables of the circulation function are presented. Interference effects between a fuselage or a nacelle and the propeller are considered. The regimes of propeller, vortex ring, and windmill operation are characterized. r 2006 Elsevier Ltd. All rights reserved.
Contents
1.
2.
3.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
1.1. Present status of propeller aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
1.2. Historical development of propeller theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Basic principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.1.
Progress in Aerospace Sciences 42 (2006) 85–128 www.elsevier.com/locate/paerosci The aerodynamics of propellers
Quentin R. WaldÃ
102 Cape George Road, Port Townsend, WA 98368, USA
Abstract
The theory and the design of propellers of minimum induced loss is treated. The pioneer analysis of this problem was presented more than half a century ago by Theodorsen, but obscurities in his treatment and inaccuracies and limited coverage in his tables of the Goldstein circulation function for helicoidal vortex sheets have not been remedied until the present work which clarifies and extends his work. The inverse problem, the prediction of the performance of a given propeller of arbitrary form, is also treated. The theory of propellers of minimum energy loss is dependent on considerations of a regular helicoidal trailing vortex sheet; consequently, a more detailed discussion of the dynamics of vortex sheets and the consequences of their instability and roll up is presented than is usually found in treatments of propeller aerodynamics.
Complete and accurate tables of the circulation function are presented. Interference effects between a fuselage or a nacelle and the propeller are considered. The regimes of propeller, vortex ring, and windmill operation are characterized. r 2006 Elsevier Ltd. All rights reserved.
Contents
1.
2.
3.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
1.1. Present status of propeller aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
1.2. Historical development of propeller theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Basic principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.1.
References: [3] Drzewiecki S. Bulletin de L’Association Technique Maritime, Paris. A Second Paper in 1901, 1892. AIAA Paper 2001-3386, Joint Propulsion Conference, Salt Lake City, 2001. [5] Betz A. with Appendix by L. Prandtl, 1919, Schraubenpropeller mit Geringstem Energieverlust, Gottinger Nachrich¨ ten, Gottingen, p David Taylor Model Basin, Report 1534, Applied Mathematics Laboratory, Washington, DC, 1964. [10] Larrabee EE. Practical design of minimum induced loss propellers, SAE Technical Paper 790585, 1979. 2299, Supt. of Documents, US Gov’t Printing Office, 1967. State University, Nord 16597-5, 1956. Meeting, New York, 1964. Meeting, Society of Naval Architects and Marine Engineers, New York, November 17–20, 1982.