chiark / gitweb /
rolling.html, rolling-eqn.html: Describe the calculation.
authorMark Wooding <mdw@distorted.org.uk>
Mon, 28 Jan 2013 01:11:08 +0000 (01:11 +0000)
committerMark Wooding <mdw@distorted.org.uk>
Sat, 2 Feb 2013 10:17:27 +0000 (10:17 +0000)
Use MathJax for equations.

rolling-eqn.html [new file with mode: 0644]
rolling.html

diff --git a/rolling-eqn.html b/rolling-eqn.html
new file mode 100644 (file)
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@@ -0,0 +1,50 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
+          "http://www.w3c.org/TR/html4/strict.dtd">
+<html>
+<head>
+  <title>Rolling wire-strip calculator: equations</title>
+  <script type="text/x-mathjax-config">
+    MathJax.Hub.Config({
+      tex2jax: { inlineMath: [['$', '$'], ['\\(', '\\)']] }
+    });
+  </script>
+  <script type="text/javascript"
+         src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_HTML">
+  </script>
+  <link rel=stylesheet type="text/css" href="rolling.css">
+<head>
+<body>
+
+<h1>Rolling wire-strip calculator: equations</h1>
+
+<p>The calculations performed by the <a href="rolling.html">rolling
+wire-strip calculator</a> were derived by examining experimental data.
+We might not have considered all of the necessary variables.  Anyway,
+here&rsquo;s how it currently works.
+
+<p>Let&rsquo;s suppose we start with square wire, with side&nbsp;$S$,
+and we roll it to thickness&nbsp;$t$.  Then we find that the
+wire&rsquo;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&nbsp;$D$ 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&nbsp;$L$ and&nbsp;$l$ respectively, then
+\[ L S^2 = l w t \]
+and hence
+\[ L = \frac{l w t}{S^2} \]
+Finally, determining the required initial stock length&nbsp;$L_0$ given
+its side&nbsp;$S_0$ (for square stock) or diameter&nbsp;$D_0$ (for
+round) again makes use of conservation of volume:
+\[ L_0 = \frac{S^2 L}{S_0^2} = \frac{4 S^2 L}{\pi D_0^2} \]
+
+<p>[This page uses <a href="http://www.mathjax.org/">MathJax</a> for
+rendering equations.  It probably doesn't work if you don't enable
+JavaScript.]
+
+</body>
+</html>
index 07ba2c8..3ac3555 100644 (file)
@@ -171,6 +171,9 @@ roll down to the required thickness of strip.
 
 <p>For best results, roll the strip in as few passes as you can handle.
 
+<p>You can see the <a href="rolling-eqn.html">detailed equations</a>
+used for this calculation if you're interested.
+
 <h3>Use</h3>
 
 <p>Boxes with light red or white backgrounds are entry boxes for you to