Helix Arc Length

[Nigel (UK)]

...or, if you want to do it by integration, parameterise the curve as
\[x=r\cos\theta\qquad y=r\sin\theta\qquad z={l\over2\pi}\theta\]
where \(r\) is the radius and \(l\) is the distance between one turn and the next. The square root in your integral is
\[\sqrt{r^2+{l^2\over 4\pi^2}}\]
which is a constant. Integrate over \(\theta\) from \(\theta=0\) to \(2\pi\) and you get the length of one turn; then multiply by the number of turns.

Nigel (UK)