The Optimal Shape of a Javelin

Details The Optimal Shape of a Javelin The Optimal Shape of a Javelin

2007-11-05

arxiv.org/abs/0711.0734v1

Studies in Applied Math (115) 339-354, 2005

Physics

Mathematical Physics

15 pages, 5 figures

Scientific paper

The problem of finding the optimal tapering of a free (non-supported) javelin is described and solved. For the optimal javelin, the lowest mode of vibration has the highest possible frequency. With this tapering inner damping will lead to the cessation of the vibration at the fastest possible rate. The javelin is modeled as a beam of uniform material. The differential equations governing the vibration and the tapering of the beam are derived. These equations have a difficult singularity at the tips of the beam. A procedure using a similarity solution is used to solve this singular system, and the solution is found. The maximal frequency is found to be almost 5 times larger than the frequency of a cylindrical rod.

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