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/']
Mike Krahulik of Penny Arcade modeled spherical, planar combat in *[D&D in the Elemental Chaos part 1](http://www.penny-arcade.com/2010/06/28/dd-in-the-elemental-chaos-part-1)* and *[D&D in the Elemental Chaos part 2](http://www.penny-arcade.com/2010/06/30/dd-in-the-elemental-chaos-part-2)*.

A concern exists that LOE and AOE in Krahulik's models, as well as, prolonged combat and movement were not possible in the models documented. 

However, both context of Krahulik's efforts and his entries, he notes that the oddites of modeling the grid on the sphere as well as the success of the models in play. 

Krahulik talks about "...I was drawing these squares on a curved surface they got sort of wonky in some places, but that is why **I made separate [areas] of grid zones on each planet.**" The photo of these grids clearly shows Krahulik "solving for wonky" with compromises to aesthetic problems by ignoring the curvature of the sphere and scale at the polar coordinates.

![enter image description here](https://i.stack.imgur.com/Qs5qf.jpg)  

Image © Copyright 1998-2013 Penny Arcade, Inc.

The disconnected grid addresses the "wonkiness" as well as LOS...and likely solved for AOE too (constrained within the "separate areas of grid zones"). Nearby grid zones could be handled as a "hand wave" or even built-in as player-GM expectation.

Both articles are great resources for creatively solving a problem and delivering an exciting table experience.

**Hexagons**

Read [*Geodesic Discrete Global Grid Systems*](http://webpages.sou.edu/~sahrk/dgg/pubs/gdggs03.pdf) by Kevin Sahr, Denis White, and A. Jon Kimerling. I skimmed it, but it offers some great ideas to **achieve full coverage with hexagons.** The research is quite detailed and expounds at length regarding the popularity and resolution available with hexagons.
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.