1. ## Calculating Radius at End of Taper

I have a piece of steel I was going to mill like this:

I think I’d like to mill it like this, with a radius at the end of the tapers:

...which raises the question of how I calculate the radius.

I found the following in Holbrook Horton’s “Mathematics at Work”, 4th ed., p. 13-2.:

Horton solves for the diameter bc, given radius de and the angle of taper A as known.

My question: I’m wondering if its possible to solve for the radius de given bc and the angle of taper A as known, or some other known values, such as the length from the beginning of the taper to b and c???? I want to be able to drop that radius value into a CNC G03 command.

The formula Horton gives to solve for bc is:

The derivation goes like this:

Thanks for any help with this. I'm just starting to learn trig, and get a little lost around cotangents, but I can plug known dimensions into formulas.

2. This may be of some help.
de = (bc/2) / tan((90-(A/2))/2)

eg
de = (20/2) / tan((90-(80/2))/2)
de = 10 / tan((90-40)/2)
de = 10 / tan(50/2)
de = 10 / tan (25)
de = 21.4451

3. Thanks a million for that. Exactly what I was looking for. Really appreciate it.

I found your diagram super helpful. What did you create it with??? I'm a little limited in what I can work out with the software I have, and would love to get something inexpensive that would let me do exactly what you've done: draw angles and radii to scale.

I can't afford anything fancy, just want to draw angles and radii to scale, literally. Can you think of anything???

Thanks

• Thanks. Downloading it now. Look forward to giving it a test drive when I get home from work.