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/']
1. Buy a soccer ball
2. Add velcro
3. ???
4. Profit

On a more serious note, you'd need to sort out how movement would work, and possibly subdivide each patch into 5 or 6 triangles depending on the size of the pieces you're velcroing on.

Additionally, you might want to prop the soccer ball up on stilts so that you could have units on the entire world.
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.