How to determine the appropriate curvature for lines of latitude on a map gore

[waldronate]

The gores for a globe can be done in a number of different projections, but Stereographic and Sinusoidal projections are the most common, if I recall correctly. Those projections are relatively easy to calculate and are supported in most GIS packages. Sinusoidal will give you more of a flat character to individual lines of latitude when printed, but these lines will get curved slightly when applied to the globe. Wet paper stretches a bit and it also tears easily, which makes getting the spindle-shaped gores onto exactly the right place on the globe a difficult proposition.

One solution to the problem of lots of pieces of paper meeting at the poles is to arrange all of the gores for a hemisphere into a rosette pattern ( https://www.youtube.com/watch?v=tTca9f-0QVc shows how a commercial globe maker does this). This rosette technique requires larger pieces of paper. You can make a smaller polar rosette and partial equatorial gores to try to avoid some of the polar issues, but it's still a messy business.

The hardest thing about getting everything onto a globe is to get a spherical surface to put them on. The second hardest thing is to get your printouts sized correctly to go onto the globe. The simplest solution to the first one is to get a second-hand globe. They are often available with a stand for not too much money at your local thrift store. A little sanding and painting and you'll have a good surface to draw on or to apply gores to. Sizing the gores is more complex and will require some math.