Talk:Clackson scroll formula

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[edit] Simplify

Explain this in a little more detail,so a layman knows what it means and what each thing stands for. Trevor GH5 07:37, 9 April 2007 (UTC)

Well, in the formula

l = \pi \cdot s \cdot n^2

π is 22/7, s is the spacing between the turns of your scroll and n is the number of complete turns in your scroll (which in the formula is "squared", i.e. multiplied by itself, which is what the little 2 means). You multiply all these together, i.e.

l = 22/7 x s x n x n

would be another way of writing it.

I find this formula a very useful way of estimating pretty accurately the amount of stock I will need for a job.

As for the second formula in the article, someone else added that. It seems to be about how the scroll formula was worked out, but I am not mathematician.

Foundryman 21:58, 10 November 2007 (UTC)

[edit] Easier derivation?

For the level of approximation represented by this formula, there is a much more elementary way of getting it: if you have a scroll with n turns, spaced by s, then when you are going around the ith turn, you are approximately following a circle of radius si. The length of stock used in going around the ith turn is therefore approximately 2πsi, the circumference of such a circle. Now we sum up:

\ell \approx \sum_{i = 1}^n 2\pi si = 2\pi s \sum_{i = 1}^n i = 2\pi s \frac{n(n + 1)}{2} = \pi s n^2 \left(1 + \frac{1}{n}\right) \approx \pi s n^2.

No calculus, no mysterious polar arc length formula, and a nice geometric explanation. The best part is, I didn't even assume that the spiral obeyed a particular equation (like that of an Archimedean spiral). Ryan Reich (talk) 18:08, 22 April 2008 (UTC)