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.

F d v n w = 5 r

\(k=\dfrac {\ πEd^{4}}{64Lr^{2}}\)

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

\( v_{max}=\dfrac {\ 2rLσ} {Ed} \)

\(σ_{(F)}=\dfrac {\ 32Fr} {πd^{3}} \)