Elastic stability of flat spiral springs

Summary This paper deals with the elastic stability of the flat spiral spring, that is, a structure consisting of a wire coiled into a spiral lying in a plane. A rough calculàtion valid for spiral springs having a large number of coils shows that the critical number of turns which the spring has to be wound or unwound to reach the state of instability is determined only by the ratio of the sides of the rectangular wire section. It depends neither upon the number of coils nor upon Young's modulus of the wire material.In order to verify in how far this holds for a spring with a small number of coils a second and more accurate calculation is given, though for a (fictitious) spiral spring having circular and identical coils only. Further, it is shown that the realization of a spiral spring able to undergo more than, say, three turns without becoming unstable is impossible. A survey of the results is given at the end of the paper.