It is the purpose of this paper to develop, with mathematical means, a general equation between the free shape of a piston ring in its unrestrained state and the consequent radial-pressure pattern against the cylinder wall after its installation. It is up to the designer, first to decide upon the proper pressure distribution for his particular need, and then to use such an equation as a first guide to evaluate the proper free shape of the ring so that it will give him the required radial-pressure pattern after its installation in the cylinder.

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