Looking to find the amount of energy stored in a clock spring

[Willber Force]

I'm looking to find formulas to calculate the energy stored in a spring you would find in a clock. I have been having a hard time finding formulas that govern these types of springs. I have found formula in similar springs, such as the spiral-torsion spring found here but I believe this type does not include multiple-turn springs you would find in a clock (I could be wrong).

I understand this is a complex system and any formulas would be approximations anyway. I'm looking to solve an optimization problem using these types of springs so I would like to get something at least in the ballpark if possible.

Thanks for any help that you could provide!

 

[Nugatory]

The easiest way might be to calculate the work done to wind the spring: torque needed to turn the winder times the total angle (360 degrees per full turn) it is turned.

The torque is going to increase with the spring tension so this calculation appears to require an integration... but I would bet that the taking the average of the torque when we start turning and when we’re done would be a good approximation, and then we have a simple multiplication.

 

[sophiecentaur]

Summary:: I'm looking to find formulas to calculate the energy stored in a spring you would find in a clock.

I'm looking to find formulas to calculate the energy stored in a spring you would find in a clock.

This is not a specific answer to the question but you could always cross-check your answer against the mgh involved with a weight driven movement. Whilst I realize that clock weights could be heavier than necessary, there is a basis of clock design that it should last for many years so the energy that you put into raising the weight every day needs to be as low as the movement will permit.
I remember an horologist friend of mine telling me that the cheaper the watch, the louder the tick because the spring needs to work against friction. "Ticka tick Timex" was a selling point because you could hear it easily. Timing was not so good though.

A very brief look at Google gave me https://www.researchgate.net/public...source/link/5a9fd5070f7e9badd99f60c1/download. That seems a pretty definitive source.