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Hydromechanics of swimming propulsion. Part 2. Some optimum shape problems

Wu, T. Yao-Tsu (1971) Hydromechanics of swimming propulsion. Part 2. Some optimum shape problems. Journal of Fluid Mechanics, 46 (3). pp. 521-544. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:WUTjfm71b

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Abstract

The optimum shape problems considered in this part are for those profiles of a two-dimensional flexible plate in time-harmonic motion that will minimize the energy loss under the condition of fixed thrust and possibly also under other isoperimetric constraints. First, the optimum movement of a rigid plate is completely determined; it is necessary first to reduce the original singular quadratic form representing the energy loss to a regular one of a lower order, which is then tractable by usual variational methods. A favourable range of the reduced frequency is found in which the thrust contribution coming from the leading-edge suction is as small as possible under the prescribed conditions, outside of which this contribution becomes so large as to be hard to realize in practice without stalling. This optimum solution is compared with the recent theory of Lighthill (1970); these independently arrived-at conclusions are found to be virtually in agreement. The present theory is further applied t0 predict the movement of a porpoise tail of large aspect-ratio and is found in satisfactory agreement with the experimental measurements. A qualitative discussion of the wing movement in flapping flight of birds is also given on the basis of optimum efficiency. The optimum shape of a flexible plate is analysed for the most general case of infinite degrees of freedom. It is shown that the solution can be determined to a certain extent, but the exact shape is not always uniquely determinate.


Item Type:Article
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received 21 July 1970). I am deeply indebted to Professor M. J. Lighthill for interesting and stimulating discussions, and particularly for calling my attention to the significance of leading-edge suction in this problem. My remarks in this paper would have been less complete had I not had the privilege of knowing his important contribution (1970) prior to its publication. I am also grateful to Dr T. G. Lang for discussion on his experiments, and to Professors C. R. De Prima and Duen-pao Wang for their interest in the general problem presented in §6. Assistance provided by Dr Arthur Whitney and Mr. Allen Chwang in numerical studies is greatly appreciated. This work was partially sponsored by the National Science Foundation, under Grant GK 10216, and by the Office of Naval Research, under Contract N00014-67-A0094-0012.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:345
Collection:CaltechAUTHORS
Deposited By: Theodore Yao-tsu Wu
Deposited On:05 Jun 2005
Last Modified:26 Dec 2012 08:39

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