Reading In Praise of the 6 Mile Hex I started thinking about how useful it would be to be able to say how far a PC can see from any given height. How far can the halfling see while perched at the peak of a 200-foot tree? How far if the tree is surrounded by 100-foot forest canopy? How far if that tree is in the middle of an empty plain? How far if there is a 50-foot wall to the north?

All things that might be solved by guessing or just giving the most situationally-convenient answer, but for an old-school game I prefer things that eliminate my unconscious bias from the outcome, to better be a referee with all that title's implied impartiality.

I realised I needed a table. So I made one.

(Here's a more compact HTML version of the table.)

The exact numbers have been massaged to be more gameable, but not by much — 75′ instead of 76.27′, 20′ instead of 22′, ignoring the difference between how tall a human and a halfling stand, etc. I'm also using 6-mile hexes in this table; if there's demand I could work up a 5-mile hex version easily enough.

The table is easy to use:

• Survey Distance is the radius of a circle around the surveying PC. Vantage Height is the height of the object the PC is standing on (not the height of their eyes when standing on it).
• To find out how far a PC can see from a vantage of a certain height over flat terrain, find the nearest height under Vantage Height and find the answer in hexes or miles.
• If a PC wants to know how high they need to get to survey the land a certain distance away across flat terrain, find the nearest distance in miles or hexes under Survey Distance and take the answer in feet on the same line.
• If intervening terrain is taller than the Vantage Height, then it forms the visible horizon in that span of the view.

Initially I thought it would be easy to figure out the visible distance over intervening features like hills and forests (e.g., "Can I see the river valley beyond the forest from the tallest tower of my castle?"), but it turns out that's a geometrically non-trivial problem so it can't be approximated by just subtracting or adding to the values in this table. However, the answer to "Can I see the edge of this forest of 100′-tall trees from the top of this 200′ tree?" is a simple matter: just use the difference of heights, and if the Survey Distance reaches beyond the forest's edge then the edge is visible. [1]

Eventually this table will go into a set of custom landscape-oriented reference sheets to fit into my customisable DM screen, and it will be so useful the one time I ever need it. ;-)