Gores

gore n. "One of the many triangular or lune-shaped pieces that form the surface of a celestial or terrestrial globe, a balloon, the covering of an umbrella, the dome of a building, etc." – Oxford English Dictionary

calotte n. "Any segment of a sphere, especially the smaller of two unequal segments. (A French sense; but given in some English dictionaries.)" – Oxford English Dictionary

Different sources recommend different projections for globe gores, including interrupted versions of the transverse Mercator, sinusoidal, rectangular polyconic, American polyconic, and Cassini-Soldner projections. For gores of 30 degrees in width there seems to be something like a 4% difference, maximum, between any of these projections, so the debate may be a bit academic – all of them should work well enough for the purposes of amateur globe-making.

One convenient way to make map gores is to make a map in the equirectangular projection, convert it to an image, and run it through a creative piece of software called the Globus Projector, developed by Mike Wisniewski, that casts the image into the interrupted sinusoidal projection: https://www.winski.net/globus-projector/globus.html. I made the gores below by exporting a map from QGIS to a png and putting it into Wisniewski's software.

The interrupted sinusoidal projection does have its disadvantages, however. For one, the parallels are not curved, so they will make n-sided polygons (n = number of gores) rather than circles when applied to a sphere. The Globus Projector also allows you to project into Transverse Mercator, azimuthal, and a few other projections, or if you have coding skills there appears to be a way to customize your own output projection.

What if you prefer a polyconic projection or the Cassini-Soldner? In that case, you could go into QGIS or ArcGIS and re-project your map once for each gore, centering the projection on a different central meridian each time.

Cassini-Soldner

A Tissot's Indicatrix showing distortion in the Cassini-Soldner Projection.

Invented by cartographer César-François Cassini de Thury in 1745, later modified by mathematician J.G. von Soldner
The transverse aspect of the equirectangular projection (cylindrical)
Minimal distortion along the central meridian
A good projection for making globe gores

Azimuthal Equidistant

A Tissot's Indicatrix showing distortion in the Azimuthal Equidistant Projection.

First described in writing by eleventh-century Persian polymath al-Bīrūnī
A planar projection maintaining accuracy of direction and distance from the central point
Minimal distortion near the central point
A good projection for making calottes to cover the north and south poles

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