Summary
A local solution is developed for the square-root singularity at the leading edge of a rectangular flat plate of small aspect ratio. The analysis is based on the assumption that the spanwise load distribution is elliptical, and it follows that the two-dimensional lifting-surface integral equation can be reduced to a one-dimensional integral equation of the Wiener-Hopf form. A solution is then obtained, valid near the leading edge, which yields the strength of the square-root singularity. This solution is used to compute the leading-edge suction force, which differs by 15% from the known value based on the total lift and drag expressions. The local solution is applied to study the flow around the stem of a ship's bow, as a result of a yawing motion, using Lighthill's rule to correct for the finite radius of curvature at the bow.
Similar content being viewed by others
References
P. Hu, Forward speed effect on lateral stability derivatives of a ship,Davidson Laboratory Report No. 829 (1961).
M. J. Lighthill,An Introduction to Fourier Analysis and Generalized Functions, Cambridge University Press (1958).
A. Robinson and J. A. Laurmann,Wing Theory, Cambridge University Press (1956).
K. Stewartson, A note on lifting line theory,Quarterly Journal of Mechanics and Applied Mathematics, 13, 1 (1960) 49–56.
M. Van Dyke, Lifting-line theory as a singular-perturbation problem,Proceedings of the Sixth Symposium on Fluid Dynamics, Zakopane, Poland (1963) 369–382, Oxford: Pergamon Press.
M. Van Dyke,Perturbation Methods in Fluid Mechanics, New York, Academic Press (1964).
G. N. Ward,Linearized Theory of Steady High-Speed Flow, Cambridge University Press (1955).
Karl Wieghardt, Chordwise load distribution of a simple rectangular wing,Zeitschrift für angewandte Mathematik und Mechanik, 19, 5 (1939) 257–270. (English translation:N.A.C.A., T.M. No. 963).
Author information
Authors and Affiliations
Additional information
Supported by the Office of Naval Research, Contract N00014-67-A-0204-0023, NR062-411, and by the National Science Foundation, Grant GK 10846. Reproduction in whole or in part is permitted for any purpose of the United States Government.
Rights and permissions
About this article
Cite this article
Newman, J.N. Flow near the leading edge of a rectangular wing of small aspect ratio with applications to the bow of a ship. J Eng Math 7, 163–172 (1973). https://doi.org/10.1007/BF01535361
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01535361