In an upcoming campaign I'm planning, I would like a combat encounter to take place on a small sphere, with gravity pointing in towards the center. I'd like a sphere about 50' in diameter - something large enough to allow plenty of movement on its surface, but small enough so that players can typically run around it in a few turns.

My problem is setting up the map. My first thought is to purchase a to-scale foam craft sphere, and provide miniatures with small pins so that they stick into the "board." The problem with this, tho, is that I would either need to draw on a geodesic grid by hand or go grid-less, which my group has not done before.

My second thought is to simply use a flat map with "wrapping" edges, so that it acts somewhat sphere-like. The problems with this are that it distorts the distances greatly, and, more importantly, doesn't show the affect that the curvature of the sphere has on line-of-sight. I could get around this by imposing a circular limit to line-of-sight, but I feel it loses much of the effect.

Has anyone attempted to run grid-based combat on a non-flat surface like this? What tools and rules made the combat go smoothly without ignoring important aspects of the unique terrain?
['https://rpg.stackexchange.com/questions/29234', 'https://rpg.stackexchange.com', 'https://rpg.stackexchange.com/users/2161/']
The line-of-sight benefits are not actually very much, if any. If you've every played wargames with model-based LOS, you're familiar with the excruciating process of eyeballing, using bits of string, and finally arguing over whether being able to draw LOS to a teeny bit of the tip of a sword sticking up above terrain counts as having LOS or not.

Using real LOS, you lose much of the time saved by using a grid. Either go gridless on a sphere and measure everything in real inches, or use a flat, imprecise abstraction with extra LOS limits and movement rules to roughly emulate a spherical surface. Besides which, there's no good tiling of squares onto a sphere that doesn't introduce aberrations in how they connect to each other. To get regularity you have to use a different tile shape, at which point you'd have to make up new rules for adjacency and AOE coverage.
If you are free to alter the dimensions of your planet, you can use any [one of these nice projections](http://en.wikipedia.org/wiki/List_of_map_projections) of a sphere's surface. 

Note that the projections have 24 squares across and top to bottom (15 degrees lat/long each) ie. a 24x24 grid. At 5' per grid square you end up with a circumference of 120' and a 19' radius.

Note that most projections lose a lot of latitude squares near the poles.

Now the trick becomes distance to visual horizon. But again the internet provides a [handy calculator](http://www.neoprogrammics.com/spheres/distance_to_horizon.php).

Using this tool, assuming 6' person gives a surface to horizon of 13'. Making an assumption that double that is hidden. So absolute LOS = 26' = 5 or 6 squares. For fun give anyone in squares 5 and 6 a cover save.