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5 <title>Rolling wire-strip calculator: equations
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18 <h1>Rolling wire-strip calculator: equations
</h1>
20 <p>The calculations performed by the
<a href=
"rolling.html">rolling
21 wire-strip calculator
</a> were derived by examining experimental data.
22 We might not have considered all of the necessary variables. Anyway,
23 here
’s how it currently works.
25 <p>Let
’s suppose we start with square wire, with side
$S$,
26 and we roll it to thickness
$t$. Then we find that the
28 \[ w = \sqrt{
\frac{S^
3}{t}} \]
29 Rearranging, we find that
30 \[ S = \sqrt[
3]{w^
2 t} \]
31 For round wire, we assume that the cross-section area is the important
32 bit, so a round wire with diameter
$D$ ought to work as well as
33 square wire with side $S$ if $S^
2 = \pi D^
2/
4$, i.e.,
34 \[ D = \sqrt{
\frac{
4 S^
2}{\pi}} =
\frac{
2 S}{\sqrt\pi} \]
35 Volume is conserved, so if the original and final wire lengths
36 are
$L$ and
$l$ respectively, then
39 \[ L =
\frac{l w t}{S^
2} \]
40 Finally, determining the required initial stock length
$L_0$ given
41 its side
$S_0$ (for square stock) or diameter
$D_0$ (for
42 round) again makes use of conservation of volume:
43 \[ L_0 =
\frac{S^
2 L}{S_0^
2} =
\frac{
4 S^
2 L}{\pi D_0^
2} \]
45 <p>[This page uses
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</a> for
46 rendering equations. It probably doesn't work if you don't enable
~mdw / dep-ui / blob