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I need to find the length of thread that is winded in a bobbin. I tried to find out with the rotation of the shaft. but as the diameter of the bobbin (with thread) increases the length winded is also increasing.

Say,

on the initial stage the thread winded for 10 rotation of shaft is 13 inches

after some stage for same 10 rotation of shaft thread winded is 21 inches

and in the final stage for 10 rotation of shaft thread winded is 30 inches.

Is there any formula I can use here?

Yakeen Ul Haque
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    I suspect that you may not have sufficient information. Knowing how many rotations are needed in total might help. – Henry Feb 10 '16 at 08:32

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