Ah! thanks. So the resulting number will be the large diameter? the height stays unchanged? e.g. say the small end is 1" the large end is 3" so 3-1=2 - I'll use 2 as the bottom diameter.Subtract the diameter of the small end from the large end now you have a point at the top
I could just do that but I felt I should use both methods to make sure I'm on the right track. More as an academic exercise than anything else.WHAT WOULD BE THE MATTER WITH USING A PROTRACTOR?
Thanks Peter. I don't get those angles so I'm trying to figure out the correct math behind it.Not sure I understand your post-4 example, but here is a sketch with resultant dimensions. If your calculator spits out these angles, you are good to go.
Thanks Ray- I believe that's exactly how I calculated it but I'm not getting the correct angles. If you want to try it:You can't solve the problem as shown. You need to specify the small diameter too.
Let D be the big diameter and 'd' be the little diameter then R and r will be their radii respectively. Let H be the height of the cone.
R = D/2
r = d/2
Tan (angle) = (R-r)/H which means: angle = Arctan (R-r)/H
The taper is the difference in diameters divided byr the distance separating them but the half angle (measured between center line and the taper is the arctan of half the taper. The total include angle is twice that angle. Taking the arctan of the taper is close to the total angle but only when the angle is small. For small angle measured in radians, a = tan a = sin a. As the angle increases this equality falls a part. For example , for a 1º angle a = .017453 radians, tan a = .0174655, and sin a = .017452 but for a 45º angle a = .7854 radians, tan a =1, and sin a =.7071. For this reason the equality a = 2 arctan a/2 is not true.Measure the small diameter. Big diameter minus small diameter divided by taper length. The tangent of this number is your angle.
Mark, There were two errors in your previous post. The first is that to find the angle, you use the arctangent function not the tangent. The second is that you have to use the radii rather than the diameters to determine the angle as stated by Ray in posts 6 & 9. arctan(D/2-d/2)/H = arctan(.5/1.6) =17.354º while (arctan(D-d)/H/2 = 16.00º.Rj for this example the proper trig function is tangent. Opposite over ajacent. It will give you the included angle. As accurate as can be!