# Extension Spring

Written by Jerry Ratzlaff on . Posted in Fastener

Extension spring is a helical spring like a compression spring with hooks on each end.  The ends of the spring are attached to other components creating a resistance force that absorb and store mechanical energy that opposes the resistance to a pulling force that wants to return back to its origional position.

### Extension Spring load when compressed to length formula

$$\large{ P = T_i + n_s \; d_s }$$

$$\large{ P = T_i + n_s \; \left( l_i - l_f \right) }$$

Where:

$$\large{ P }$$ = load when extended to length

$$\large{ d_s }$$ = deflection

$$\large{ l_f }$$ = final length (compressed)

$$\large{ l_i }$$ = initial length (free)

$$\large{ T_i }$$ = initial tension

$$\large{ n_s }$$ = spring rate

### Extension Spring Rate formula

$$\large{ n_s = \frac{ G \; d^4 }{ 8 \; n_a \; D^3 } }$$

Where:

$$\large{ n_s }$$ = spring rate

$$\large{ D }$$ = mean coil diameter

$$\large{ n_a }$$ = number of active coils

$$\large{ G }$$ = shear modulus of material

$$\large{ d }$$ = wire diameter

Tags: Equations for Spring