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Flow near the leading edge of a rectangular wing of small aspect ratio with applications to the bow of a ship

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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.

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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.

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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

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  • DOI: https://doi.org/10.1007/BF01535361

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