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.
|Survey Distance||Vantage Height (ft)|
(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. 
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. ;-)
|||Whether the forest's edge "looks like" an edge from that vantage and not just trees all the way to the horizon is debatable, but you might as well give it to your players in that case since the distances and heights necessary to make it visible-yet-in-doubt at so very particular that I think it would count as screwing them over. Thus ends the minutiæ of a minutia of a minutia.|