In designing things tapered, I find myself needing to do some calculations. I thought I'd toss out the formulas I use.
There are four factors...
A = Angle of taper L = Length of taper DL = Larger diameter DS = Smaller diameter
I started with this formula:
L * 2 * Tan(A) = DL - DS
Given any three of the four factors, the fourth is easily calculated using one of the permutations...
L = (DL - DS) / (2 * Tan(A))
A = Arctan ((DL - DS) / (2 * L))
DL = 2 * L * Tan(A) + DS
DS = DL - (2 * L * Tan(A))
For example, a Morse Taper #2 has a large diameter of .700" and small diameter of .572" over a distance of 2.500". Therefore, the angle would be calculated as Arctan(.128/5) or 1.46645 degrees. Now if I could just figure out how to scale my compound to nail that angle.
-Bruno