How to find the taper angle of a (sliced) cone

stioc

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I have a part (it's a tire balancer cone) of an unknown taper. When I first saw the cone I figured I'd use the right triangle rule but that's not correct because the right triangle's tip isn't the tip of the cone- because the 'cone' doesn't have a point. What's the best way to find its taper angle?
cone.jpg
 
Subtract the diameter of the small end from the large end now you have a point at the top
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.
In other words: X=Inv Tan (Opposite/Adjacent)
X= Inv Tan (1.6/1)
X= 45deg

WHAT WOULD BE THE MATTER WITH USING A PROTRACTOR?
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.
 
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.

SNAG-5-17-2018 0000.jpg
 
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

Ray
 
If you want to know taper, that is normally expressed as inches per foot. The taper of a ramp in the example above would be R-r (in inches) divided by H (in feet). If you want the machine taper, you need to define if you want included angle or not. For included angle it would be D-d (in inches) divided by H (in feet). Check here and you'll see that different standards calculated taper differently (included vs non-included angle). I've encountered this confusion many times. https://en.wikipedia.org/wiki/Machine_taper

As far as the angle calculation in post #6, that is as fundamental as it gets -indisputable.
 
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 Peter. I don't get those angles so I'm trying to figure out the correct math behind 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

Ray

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:
D=3
d=2

EDIT: OOPS! you're right! I think in my second post example I didn't use the correct numbers. This is right, YAY! lol
Arctan (1.5-1)/1.6=17.35 deg

Thanks guys!
 
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3/2 = 1.5
2/2 = 1
1.5 - 1 = 0.5/1.6

arctan 0.5/1.6 =17.35 Measured from centerline of cone.




EDITED to show the calculations. I also had to edit this because I can't see a darn thing w/o my glasses using a browser on a mobile phone.
 
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Right, I was doing Arctan (H/(R-r) which gave me the angle from the other end but subtracting from 90 would set that straight. Thanks again guys. Now I can't wait to get home and see if the compound slide angle follows the part :)
 
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