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# Spiral wound spring with round cross section

Determine mechanical properties of a spiral wound spring with wire diameter d, radius r, Young's modulus E and L as spring length. Calculate also deflection v and tension σ as a function of force F.

$$k=\dfrac {\ πEd^{4}}{64Lr^{2}}$$

$$v_{(F)}=\dfrac {\ 64FLr^{2}} {πEd^{4}}$$

$$v_{max}=\dfrac {\ 2rLσ} {Ed}$$

$$σ_{(F)}=\dfrac {\ 32Fr} {πd^{3}}$$