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}}