## Flat layout of frustums and cones

First, please note that, apparently, the correct spelling is frustum, not frustrum. Hmmm…. You learn something new everyday!

Second, you might ask why am I talking about this? Isn’t this subject more appropriate to a blog on sheet metal work? Well, think about it. What if you’re designing a chair with a back that is laid out as a portion of a frustum? What if you want to make a brass lamp shade? How about a coopered pail? How about a dunce cap for your friends? I mean, the potential for this method is unlimited. Right? Okay. Maybe unlimited is a bit of a stretch. But understanding this layout may help visualize measurement of these shapes (or portions of them) in a number of scenarios. Remember diameter x 3.1417 = circumference.

If you should ever find yourself in the highly unlikely situation of having to layout a truncated cone, here’s an excellent tutorial site: http://leonjane.hubpages.com/hub/How-to-develop-a-Truncated-Cone#

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February 25, 2015 at 10:42 pm

Excellent. I would have no idea how to do that and actually have wanted to make some funnels for various purposes. thanks!

February 26, 2015 at 2:39 pm

The link shows a nice classical exercise of descriptive geometry. Although it also could have shown how to construct the real shape of the top.

Your example is useful for those wanting to build a cyclone.

A slightly more difficult exercise is the intersection of the inlet tube with the cylindrical part on top of the cone. Altough the method is is similar to the one showed in the link.

For those who like graphical construction of compound joinery, visit

http://thecarpentryway.blogspot.be/

look for “treteau” and “Mazerolle”.

Sylvain

February 27, 2015 at 4:15 pm

It seems you just eyballed the 0.1415…D you added after reporting 3X the diameter D.

If B is the radius of the big circle on your drawing, then the angle Alpha of the yellow sector must be such that

Pi X D = B X Alpha ; all angles being expressed in radians.

Knowing that 2 X Pi radians = 360°

the angle in degree is = Alpha X 360 / 2Pi

After simplification we obtain : angle in degree = (D/B) x 180

On your drawing, you easely measure B without having to calculate it.

(The diameter B of the big circle is the square root of (D/2)²+H² where H is the height of the full cone.)

Sylvain

February 27, 2015 at 5:24 pm

Hi Sylvain,

You’re absolutely right, I just eyeballed it. Thanks for the additional information.

Dennis