Help needed with unfolding truncated cones

[Necroscope]

It was on Russian. But try this:
tutorials gallery

[scissorsandplanes]

Hi PlumDragon,
I only see this mail now.
I once tried to explain how to draw 2D versions of 3D cones in a text in the "one model per (non-working) day" thread.
I include the formulae here.
Hope that helps
Bruno

[adamaia]

I hope this helps. Draw 2 circles one with an a radius and the outside one with the b radius (they do not have to be full circles) use the equation and it will give you the angle in degrees of the sector you need removed...I use it for BRDM type turrets and anything of that nature. If you need further help please let me know.
[IMG]C:\users\adam\desktop\cone development.jpg[/IMG]

(for this particular shape you will need to remove 90 degrees, the edges will butt perfectly adding a tab on the inside will give you a clean joint.)

[DanBKing]

I use this which is excellent for cones. Flat Cone Template Calculator

[Plumdragon]

Thank you for these recent comments; much appreciated! I think I have enough tools in the armoury to get the job done now :-) and I hope this information will be useful to others as well.
Plumdragon

[Bonzo]

I am sorry but I do not agree that the base of an unwrapped cone is the arc of a circle. If it was the case then the overlap would surely be coincident whatever its steepness. (see picture).

My money is still on the logarithmic spiral! You know, the one on the nautilus shell. and the curve falcons follow when stooping.

[maurice]

Hi Bonzo

Indeed the statement in post # 2 of this thread is true only when describing the development of the surface of a right circular cone and when that surface does not have any thickness.

In the practical world of paper models, where in order to have a conical surface we must use paper which does have thickness, two compromises are needed.

Firstly rolling a piece of paper into a circle we need either to cut the abutting edges of the paper at precisely the right angle to fit each other or else accept there will be a slight V shaped void. It's a good idea if a seperate internal joining strip is used. (see pic)

Secondly there will be much more material than space at the apex of the cone so we must remove that excess and doing that will leave us always with a slightly truncated cone. (see pic)

With care we can finish with all but a tiny amount of the full conical surface we wanted.

(Paper thickness in the attached pic has of course been greatly exaggerated)

Because you have not made these two compromises and have allowed the the paper to overlap itself the figure in your illustration does not in fact contain the surface of a right circular cone (well not in a rigourous mathematical sense that is) and it is indeed beginning to form some sort of spiral.


BTW I greatly enjoyed viewing the ingenuity of your display at https://www.youtube.com/user/MrDalgoma

[scissorsandplanes]

Entirely agree with what you said, Maurice.
If my computer had not bugged yesterday while trying to view Bonzo's picture I would have said something similar, but probably not as clearly explained.
this is also one of the reasons I work with 80g/m² paper and try to avoid pointed cones.

Bruno

[adamaia]

I have two points to clarify, the first and more important is that the developed cone pattern IS an arc of a circle, has always been and will always be, it has been taught (in any engineering course) that way, and practiced by sheet metal workers ever since. The second part is the junction of the edges, this depends on the thickness of the material, anything around 10 thou will not be a problem, it can be butt joined with a reinforcing strip behind the joint. For model making if you are really nit picking a slight bevel could be added to the edges , still butt joined with a reinforcing strip.
The attached clearly shows the arc, besides I have been teaching this for over 40 years, can also show you how to make sloped cones. intersecting cones ..etc, all following the basic formula. Cheers, the earth is not flat after all.

[zubie]

Before I started working in Blender, I used to try all kind of different mechanisms for making cones. Since I had access to MS Excel, I tried getting it to draw the cones for me by using the formula for the surface area of a cone and the area of a circle to get the spreadsheet's chart program to draw a pie chart. The resulting cone was at a lower resolution than a handrawn one, but I could get the image into photoshop, then scale it and refinish it. Truncated cones were just subtracting the percentage of the radius excluded. I think I used to use a feature in the chart program that allowed for superimposed pies. Alas I say I think because I haven't used that code in years (I don't even have a working copy of Office right now). I admit it is a convoluted way to do it, but at the time I couldn't find anywhere the direct relationship between the cone angle and subsequent angle of the cut-out although I know a simple one must exist.