Thanks Jason, I had looked at the loxodrome curve in my own investigations; it looked like it should be at least related, but I wasn't sure that it was what I was after. I can readily see how that describes the centreline of the "peel", but I guess what I should have asked is, how do you go from that 3D spiral to a flat development pattern? Is that where the calculus comes in?
Mike P.S. Mandy, I snicker at your pain... especially since you can dodge it; sounds like I will have to embrace it if I want an answer to this! ;) :P :) Jason Sutton wrote: > > Mike - > > The curve of the "apple-peel" (if you mean the vaguely "S"-shaped one, is > called a loxodromic curve. It's the curve you get if you hold a constant > bearing while traveling around a globe (other than due E-W or N-S).. Near > the equator, its pretty much straight, but it constantly bends toward the > poles, becoming what looks like a spiral when you get near that point. > Incidentally, a loxodromic curve is infinitely long and never actually > reaches the pole. Obviously an approximation is made when you get as near > to the polar point as you like. Since there is only one piece, the very > narrow strip must cover the entire equatorial circumference when tipped at > the bearing angle. If the width of the strip at its center is "w" and the > circumference of the globe is "c" (c = pi x diameter), then the bearing > angle is arcsine w/c. Beyond that, the solution requires calculus, not > algebra, and my old Navigator's Handbook is out in the garage in a box > somewhere...(you have to do some of the work.) > > The other globe, with the "banana-peel" shapes is a conventional gore > pattern, used on terrestrial globes from time immemoriable. The curves > along each edge are one half of a sine wave. The line between the curves, > extending from pole to pole is a line of longitude. Think of it as being 0 > degrees at the south pole, 90 deg at the equator, and 180 degrees at the > north pole. The distance from the longitude line to the sine wave edge at > any latitude "A" is K x sin A (A goes from 0 to 180 deg), and k = 1/2 > circumference at the equator divided by the number of segments you want to > have. That one's easy to calculate with a pocket calculator. > > Jayo > ----- Original Message ----- > From: "Michael G. Henders" <[email protected]> > To: <[email protected]> > Sent: Tuesday, May 12, 2009 3:20 PM > Subject: [Papermodels II 36466] "Apple peel" sphere patterns > > >> Can anyone point me at a reference that describes the >> mathematics behind a one-piece "apple peel" sphere- >> construction template, like the one provided here? >> >> <http://www.papermodels.co.il/FreeDownloads.htm> >> >> (Yes, I did leave a message on the site, but I think >> they probably have better things to do than explain >> the inner design workings of a free model...) >> >> I've had a couple of runs at trying to derive it >> myself, but so far I haven't come up with anything >> usable, and it's bugging me! :) >> >> Mike >> > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Papermodels II" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/Papermodels?hl=en -~----------~----~----~----~------~----~------~--~---
