Help needed with unfolding truncated cones

[Plumdragon]

Hello friends I used to know this, 35 years ago, but I seem unable to get my memory jogged or find the info I need, so I'm hoping someone can help. The diagram shows a truncated cone, could be a missile nose cone, part of a tip tank, or smoke stack on a wood burner old time loco, or anything similar.
The section is taken from a scale drawing, so the length (or height) is a known dimension, as are the radii and/or circumference of the end sections. I have no idea how to draw out on paper, using geometry, maths, formulae or any combination thereof, the piece 'in the flat' because I'm unable to fathom the connection between the shape of the arced lines on the flat piece and the sectional drawing, or how to calculate the angle of the edges where the piece would join. I have always made bits like this by trial and error.
I stress that I need to be able to physically draw this out on paper; if I can do that, I can do it in Photoshop. I have no programs at all for this kind of thing (other than my PC's calculator) and I can't add any programs as my 15 year old machine is a little stingy on the RAM....
Hoping someone can help
Plumdragon

[maurice]

I'm sure you'll remember and have no problem.
The developed surface of a right circular cone consists of a segment of a circular disc whose radius is equal to the slant height of the cone, the slant height being 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.
Then for a truncated cone just draw an arc with radius equal to the slant height of the bit that ain't there.

Or you can cheat
Cones

[maurice]

Or you could cheat if the link worked
Cone and truncated cone

[mbauer]

Here is a link I did years ago on hand drawing cones.

Questions just ask away.
How to Hand Draw Cones

Hope it helps.

Mike

[Plumdragon]

Thank you to both of you; useful links too! I shall make notes of this and go try it out for myself, after the head cold has subsided Many thanks
Plumdragon

[maurice]

Definitely a good idea to stay away from cones when you have a head cold.

[Necroscope]

First pic looks like you are working in Rhino. In Rhino you can unfold any single-curvature surface in two clicks with Unfold command.

[Plumdragon]

Hello Necroscope :-) If that's my 'first pic' you are referring to, then perhaps I should take that as a compliment. That's my 'best guess at what it looks like' hand drawn in Photoshop 7 - No Rhino's here! You must be referring to Maurice's drawing XD
Plumdragon

[Necroscope]

Plumdragon,
I'm reffering to this one:


It looks like Rhino drawings indeed. Appreciating your "hand drawn in Photoshop 7" skill.

Btw - Rhinoceros will help you with design a lot. It's just awesome software. It takes 3 days with "Rhino teach-yourself" book for me to learn all basic stuff required to design my own paper model. )

Best of luck.

[Renaud]

Which is this so-called book making you learn Rhino basis in less than 3 days? I need it!