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ClanKiller.com :: View topic - Geometical Problem
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Geometical Problem
https://forums.clankiller.com/viewtopic.php?f=8&t=2640		 Page 1 of 1
Author:  derf [ Mon Oct 29, 2007 12:28 pm ]
Post subject:  Geometical Problem
Alas a problem that my brain is incapable of even putting into context... The G-meister might be able to get his head around it, even Satis might try but i fear he will eventually turn to his beer bottle sitting on his desk and think...."nah, fuck it". :D

I need to be able to make cones from a flat piece of flexible plastic. The tips of these cones will be snipped off to let a paintball easily through. The purpose of these cones is that theyll be glued inside a cylinder which will act as a silencer for a paintball marker.

Does anyone know how to go about drawing the right dimensions on the flat plastic so i can start cutting them out?

The approx diameter of my silencer cylinder is 47mm. Obviously, the diameter of a paintball is about 17mm so I need a 25mm hole on the top of the cone for any ballistic mishaps.

Author:  RB [ Mon Oct 29, 2007 1:56 pm ]
Post subject: 
I found you a nice image:

http://de.wikipedia.org/wiki/Bild:Kegelstumpf.PNG

So, you need to make a ring sector. As for dimensions, let see. I will provide the calculations too, so that you can correct it, if I'm doing something wrong. To construct it, you'll firstly need s and S. (see the attached images) Let first determine y:

y/12,5 = (y+30)/23,5 => y = 34,(09)

Now:

s = sqrt( (23,5 - 12,5)² + 30² ) = sqrt(1021) ≈ 31,95
S = sqrt((23,5)² + (30+34,(09))²) ≈ 68,26

Now, the length of the bigger arc is 2rπ = 2(23,5)π, while the whole perimeter is 2Sπ = 2(68,26)π.

The angle α is thereby α = 2rπ / (2Sπ) · 360° = r/S · 360° ≈ 123,93°

That's enough to construct the thing. :) Thou, try it with paper first.

Now tips:
1. You may like to try with a bigger angle (say 130°) and then overlap two ends in order to attach them with superglue.
2. If you need it to have bottom, just make a circle of radius bigger than 23,5. Say 23,7.
3. And again: try it with paper first. (you can scale it by 1/10 or 1/5 in order to use just an A4 piece)
Author:  derf [ Mon Oct 29, 2007 2:18 pm ]
Post subject: 
Tried it with paper to scale and checked dimensions & angles. Result = perfection.

Thanks G. Would never have found this out.
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