From: Mark Wooding Date: Mon, 28 Jan 2013 01:11:08 +0000 (+0000) Subject: rolling.html, rolling-eqn.html: Describe the calculation. X-Git-Url: https://git.distorted.org.uk/~mdw/dep-ui/commitdiff_plain/ef43c7018f16f7b92c93e85098a52fd6817b5bca rolling.html, rolling-eqn.html: Describe the calculation. Use MathJax for equations. --- diff --git a/rolling-eqn.html b/rolling-eqn.html new file mode 100644 index 0000000..9c03c3d --- /dev/null +++ b/rolling-eqn.html @@ -0,0 +1,50 @@ + + + + Rolling wire-strip calculator: equations + + + + + + +

Rolling wire-strip calculator: equations

+ +

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: +\[ L_0 = \frac{S^2 L}{S_0^2} = \frac{4 S^2 L}{\pi D_0^2} \] + +

[This page uses MathJax for +rendering equations. It probably doesn't work if you don't enable +JavaScript.] + + + diff --git a/rolling.html b/rolling.html index 07ba2c8..3ac3555 100644 --- a/rolling.html +++ b/rolling.html @@ -171,6 +171,9 @@ roll down to the required thickness of strip.

For best results, roll the strip in as few passes as you can handle. +

You can see the detailed equations +used for this calculation if you're interested. +

Use

Boxes with light red or white backgrounds are entry boxes for you to