Messages Archive

Subject:
geometry

Bill Tindall, E.Tn.
Your question hinges on whether we speak of shrinkage as an amount or a percentage. As an amount, yes C must shrink pi times something. But as a percentage pi is not a factor.

C = piD There is a linear relationship between these factors when it comes to shrinkage. If D shrinks 10% and C shrinks 10%, C still equals piD, that is to say, the circumference shrank exactly enough to accommodate the shrinkage of the diameter..... 0.9C = 0.9Dpi

If they don't shrink the same, 5 and 10%.....

0.9D =/= 0.95C C must open a crack of 0.05%D to remain stress-free.

In the pine example I measured the reduction of diameter upon shrinkage and the width of the crack and was able to compute the radial vs tangential shrinkage. ( The things one does to postpone a difficult woodworking operation)

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