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Old 09-19-2009, 04:16 PM
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What is the fomula for calculating the shape of a cone?

I remember reading something about taking the height and radius of a cone and plugging them into a formula to determine the angle at which to cut it. I'm writing a book about how to create paper models manually, and I need to know this formula.
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Old 09-19-2009, 04:34 PM
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http://www.papermodelers.com/forum/d...id=72&act=down

Ryan
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Old 09-19-2009, 04:43 PM
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The formula with a good explanation for true cones
A sheet metal cone
Another approach
Learn how to layout a cone in sheet metal

online tool for truncated cones
Cones | Sheet Metal Transition (ONLY works with Microsoft Internet Explorer)
online tool for truncated and non-truncated cones
Cone and truncated cone

Or you can download Siatki 1.0.1 free from Gremir Paper Models it does a few standard shapes.

The paid version - Siatki v.3.2 does 25 different standard objects, plus, by using the Creators, can unfold objects limited by two flat surfaces (any shape and placement). Siatki software can also unfold toroids. Surfaces can be defined by the user or imported as DXF files. The software also allows you to insert panel lines on the created skins.
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Old 09-19-2009, 09:17 PM
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Jon Leslie also has a cone-o-matic spreadsheet and info at the LHV Challenger Center on his FAQ page: http://jleslie48.com/faq.html

Yogi
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Old 09-20-2009, 08:06 AM
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Here's a program to calculate cones.

ConeCalc
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Old 09-20-2009, 08:19 AM
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Fiddlersgreen has tips for designers.
See: Index of /tutorials

On pages 4 & 5 of Desigining without CAD by Professor Kel Black, the design of cones is discussed.
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Old 09-21-2009, 08:20 AM
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see attached.
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What is the fomula for calculating the shape of a cone?-interstage_calc_satv.jpg  
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File Type: zip interstage_calc_satv_pdf.zip (452.8 KB, 23 views)
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Old 09-21-2009, 12:26 PM
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Thanks for the replies! I'll have to put it into my own words, but these will definitely be a great help! :D
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Old 09-25-2009, 07:00 AM
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Might I try to help you sort out your wording ?
There is a thing called a right circular cone. Never not nothing else should it be called.
It's what most people think of in response to the word cone. So simple and obvious that I'll skip a precise definition of the animal unless you really want your ear bent.
Of the infinite variety of possible cones it is the only one of which the developed (unfolded) surface can be found by a simple numerical process.

Anyway waddever -

The developed surface of a right circular cone consits of a segment of a circular disc whose radius is equal to the slant height of the cone. (The slant height is the shortest distance down the outside of the cone.)
The angle, in degrees,included in the segment (not the angle in the bit that's discarded) and which lies at the centre of the disc, is found by dividing the radius of the base of the cone by the slant height and multiplying by 360.

That's all there is to it.

Quite obviously if the cone is truncated (chopped) by a plane normal (at right angles) to the axis of the cone then the developed shape needs to lose the chopped part and that's worked out in the same way. But it's easiest just to draw the arcs for the two slant heights at the same time.

You need to know how to do Development Drawing, either manually or in a CAD prog, or how to use an appropriatly competent computer prog if you want to develop the surface of any other sort of cone.

May you be happy with your cones.
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Old 09-25-2009, 07:32 AM
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Quote:
Originally Posted by maurice View Post
Might I try to help you sort out your wording ?
There is a thing called a right circular cone. Never not nothing else should it be called.
It's what most people think of in response to the word cone. So simple and obvious that I'll skip a precise definition of the animal unless you really want your ear bent.
Of the infinite variety of possible cones it is the only one of which the developed (unfolded) surface can be found by a simple numerical process.

Anyway waddever -

The developed surface of a right circular cone consits of a segment of a circular disc whose radius is equal to the slant height of the cone. (The slant height is the shortest distance down the outside of the cone.)
The angle, in degrees,included in the segment (not the angle in the bit that's discarded) and which lies at the centre of the disc, is found by dividing the radius of the base of the cone by the slant height and multiplying by 360.

That's all there is to it.

Quite obviously if the cone is truncated (chopped) by a plane normal (at right angles) to the axis of the cone then the developed shape needs to lose the chopped part and that's worked out in the same way. But it's easiest just to draw the arcs for the two slant heights at the same time.

You need to know how to do Development Drawing, either manually or in a CAD prog, or how to use an appropriatly competent computer prog if you want to develop the surface of any other sort of cone.

May you be happy with your cones.

best part is if you turn it upside down, it does a great job of holding ice cream

anyway this description goes a long way in describing my page of math that I supplied. The page is a specific example where the base of the cone is 396, the top is 260 ( my cone was a truncated right angle cone) and the height of the cone was 228. Using pyrathos theorem I determined that the slant height was 237.

Where you see the number 396, 260, 228, 68, on my page you should be substituting your values for your truncated right circular conic section, and solve for the arc-angle in degrees, and the length of the two radii.
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