Compute Length of Helix Given Radius & Pitch

[zd1899]

Given the radius and pitch , how can we compute the length of a helix??

 

[HallsofIvy]

If the helix has radius R and pitch a, meaning that the helix rises a distance a with each loop, parametric equations for the helix are $x= Rcos(t)$, $y= Rsin(t)$, z= at.

The length of a curve, with x, y, and z functions of t, from t= a to b, is given by
$$\int_a^b\sqrt{\left(\frac{dx}{dt}\right)^2+ \left(\frac{dy}{dt}\right)^2+ \left(\frac{dz}{dt}\right)^2}dt$$
Can you get it from there?