The calculations performed by the rolling +wire-strip calculator were derived by examining experimental data. +We might not have considered all of the necessary variables. Anyway, +here’s how it currently works. + +
Let’s suppose we start with square wire, with side $S$, +and we roll it to thickness $t$. Then we find that the +wire’s width is +\[ w = \sqrt{\frac{S^3}{t}} \] +Rearranging, we find that +\[ S = \sqrt[3]{w^2 t} \] +For round wire, we assume that the cross-section area is the important +bit, so a round wire with diameter $D$ ought to work as well as +square wire with side $S$ if $S^2 = \pi D^2/4$, i.e., +\[ D = \sqrt{\frac{4 S^2}{\pi}} = \frac{2 S}{\sqrt\pi} \] +Volume is conserved, so if the original and final wire lengths +are $L$ and $l$ respectively, then +\[ L S^2 = l w t \] +and hence +\[ L = \frac{l w t}{S^2} \] +Finally, determining the required initial stock length $L_0$ given +its side $S_0$ (for square stock) or diameter $D_0$ (for +round) again makes use of conservation of volume: +\[ L_0 = \frac{S^2 L}{S_0^2} = \frac{4 S^2 L}{\pi D_0^2} \] + +
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