View Full Version : Calculating length of tapered helix

5th Mar '10, 14:25
Is there any way to calculate theoretically the length of a tapered helix. Data given is length of the taper (both diameters)

6th Mar '10, 16:23
There is probably a way of calculating it (if anyone knows the formula it would be interesting to know it), but it can be easily be worked on Solid Works.

An important piece of data is also the no of revolutions of the spiral. Is the pitch of the spiral constant? Both these factors affect the length of the helix.

If you tell me both diameters and the no of revolutions I can calculate it for you on Solid Works on Monday!

7th Mar '10, 23:19
The length of a flat spiral is given by the equations -

" L = pi*N*(D+d)/2 where N = (D-d)/(2*t) is the number of wraps of tape of thickness t on a roll of diameter D (when full) around a core of diameter d. The formula represents the average of two estimates using the sum of circumferences of concentric circles (inside vs. outside diameters based on t). The summation formula 1+2+3+...+N = N*(N+1)/2 is needed to develop each estimate."

As noted on - http://www.newton.dep.anl.gov/askasci/m ... h99015.htm (http://www.newton.dep.anl.gov/askasci/math99/math99015.htm)

This could then be flattened out into a straight line of length L. We can use this to calculate the Lenght of the taper helix base on spiral if we use a Height of T then the length of that Helix given by H should be

H = sqrt(T^2 + L^2)

Niel Leon