Hi,(adsbygoogle = window.adsbygoogle || []).push({});

Does a compression spring’s pitch or rise angle have any relation with its spring constant k?

I checked various sources and they differ on this. Some sites simply asks you to feed input into a simple formula:

k=Gdin which^{4}/3D^{3}n_{a}

k: spring constantAn example of this treatment can be found at http://www.efunda.com/DesignStandards/springs/calc_comp_designer_eqn.cfm.

G: material’s shear modulus

d: diameter of the wire

D: outer diameter of each winding

On the other hand, some other sites require knowing the pitch between each winding, or equivalently rise angle θ, and result varies with different pitch/θ even all four parameters above remain unchanged. An example is at http://www.planetspring.com/pages/compression-spring-calculator-coil-calculator.php?id=compression.

I strongly suspect the first type of treatment above is incorrect. Consider extreme case:

1. θ →0° : This means we are not winding the spring up so all windings remains on the same plane. Of course when approaching this extreme k would approach zero.

2.. θ →90°: This corresponding the case when we are pulling the string straight without any winding and it points straight upward. Trying to compressing such a “spring” on the two ends is like compressing a stick rod, and we would get extremely large resistance due

to the rigidity of the material itself. Obviously in this case k → infinity

It is then quite clear that θ cannot be overlooked, and the first kind of treatment above is obviously wrong.

I wonder why so many websites are still providing that answer? Could someone help or give a derivation of the compression spring k formula?

Bob

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Compression spring constant k?

**Physics Forums | Science Articles, Homework Help, Discussion**