Paper Shrouds/Conical nosecones

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Well-Known Member
Jan 19, 2009
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I made a thread a few years ago on T[O]RF with code for a program that would, given an input of a shroud's desired small diameter, large diameter, and length, print out the necessary central angle and two radii needed to map the shape onto a piece of paper that could then be cut out and rolled into said shroud. I've since lost all copies I had of the program, but I was a bit bored this evening and rederived the formulas for it. I know that there are online tools that can do the calculations for you, but the convenience of having the tool right on your calculator has helped me out when I'm away from the computer. So, anyway, here it is:

Works with TI-83/84, perhaps others that use the same programming language

:Input "Sm Dia? ",A
:Input "Lg Dia? ",B
:Input "Length? ",L
:Disp "Sm Rad: ",180A/C
:Disp "Lg Rad: ",180B/C
:Disp "Angle: ",C

sqrt( is the square root button
-> is created by pressing the "STO->" button
It ought to work in both Radian and Degree mode, though the output angle is always in degrees. Also, you can make conical nosecones by putting in 0 for Sm Dia.

To make the shroud itself, given the information from the program, use a straightedge to draw a straight line on the piece of paper, at least as long as "Lg Rad." Pick and mark a point at or near the end of the line as the origin. Using a protractor centered at the origin, measure the given angle off of the end of the original line, and put a dot or tick mark to indicate where this angle is with respect to the origin. Draw another straight line between the origin and the mark, again, at least as long as "Lg Rad." After this, draw the two arcs (or, if doing a conical nosecone, one arc) with the proper radii, centered at the origin, through the two straight lines, using a compass. After this is done, cut out the enclosed area and roll it into a shroud, and build something!
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