How to draw a pattern for a "cone"?

[TheEquineFencer]

I have an idea I've been kicking around. I need to know how to lay out a pattern for a hollow cone so I can cut it out and roll it to shape. I need the small end to be 3 inch OD and the large end to be 4 inch OD with the side slope angle at 11.5*. how do i do this I' not sure if this "cone " will end up being 1/2 inch long os 2 feet long using these sizes. I'd love to be able to print them out and trace it to a section of sheet metal so I couold cut it out.

 

[Tony Wells]

This site has some information that may be useful;

http://sheetmetalworld.com/sheet-me...961-learn-how-to-layout-a-cone-in-sheet-metal

another;

http://jwilson.coe.uga.edu/emat6680/parsons/mvp6690/essay2/taper.html

Free software here for that;

http://www.i-logic.com/conecalc.htm

 

[rangerman]

This is how I would approach it.

Using the bottom circle first, you know you have a 4" dia circle.
So that means that the circumference is equal to Pi x Diameter, or 3.1416 x 4, which is 12.566" .

Therefore, the bottom of the sheet metal if laid out flat would have an arc that is 12.566" long.

Now, you have to find the hypotenuse of the the complete cone with a side sloping at 11.5°.
To do that you have to visualize the profile of the cone if viewed from the side and it should be easy to see that it would look like a triangle with base equal to the radius of the bottom of the circular base. That is 4"/2 or 2".
You now have all the necessary information to solve for all the triangle sides especially the hypotenuse.
The hypotenuse is equal to the surface length of the cone from the base to its tip if the cone were a complete cone.
Using the cosine formula in trigonometry Cos Angle = base/ hypotenuse), substituting 11.5° and a 2" base, the hypotenuse is equal to 2" /Cos 11.5°, that is 2" /.982, or = 2.037"

That hypotenuse is equal to the radius of the outside arc of the sheet metal that would be formed by the complete cone if it were spread and laid out flat.
The complete circle that would be formed with that same radius would be Pi x 2 x Radius, or 3.1416 x 2 x 2.037, or = 12.799"

We're almost done except for the chopped-off top of the cone measuring 3" in diameter.
It has a base circumference of Pi x 3" or = 9.425"

Using the same Cosine formula, with 11.5° angle for a triangle but with a base equal to the radius (1/2 of 3"),
the hypotenuse for the top triangular profile of the chopped off triangle would be 1.5"/(Cosine 11.5°), that is 1.5/.982, or = 1.527"

So, to lay out your pattern, draw two concentric circular arcs in your sheet metal, an outside arc with a radius of 2.037" and another inside arc with a radius of 1.527"

You may ask, what is the angle of the arcs?
Well since it's only 12.566" out of the whole 12.799" for a whole circle, it is logical to say that it is 12.566/12.799 of 360°, or = 353.45°

All these are just mathematical results but when you actually lay out your sheet metal for cutting you would need to make allowances because the thickness of the metal would make some differences once you start bending it.

BTW, what you are trying to form is actually a frustum of a cone.


Corrections: The figure marked in red is an incorrect value for the Cosine of 11.5° . Cosine 11.5° should be 0.980
All resulting calculations using the incorrect value should be adjusted accordingly.

 

[rangerman]

The calculations above are based on my understanding that your cone has a slope of 11.5° relative to the base of the cone.

However, if your cone is meant to have a side inclined 11.5° relative to the perpendicular, the calculation would need to be modified using the Sine formula, else you'd have to use an angle of 78.5° as the angle to be used in the Cosine formula in my previous post.

There would be a big difference between the 11.5-degree shallower cone and 11.5-degree steeper cone if references for the angles are not the same.

 

[TheEquineFencer]

The calculations above are based on my understanding that your cone has a slope of 11.5° relative to the base of the cone.

However, if your cone is meant to have a side inclined 11.5° relative to the perpendicular, the calculation would need to be modified using the Sine formula, else you'd have to use an angle of 78.5° as the angle to be used in the Cosine formula in my previous post.

There would be a big difference between the 11.5-degree shallower cone and 11.5-degree steeper cone if references for the angles are not the same.

Yes, the side incine is 11.5* . It will look like an upside down snow cone with the pointed end cut flat. One end is 3 inch, the other is 4 inch. I'm going to look at the above mention links in a few minutes and see what I come up with Thanks.