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?