Friday, August 8, 2014

Counting Hexes

Are hexes just traditional for hexcrawls or do they allow for fast and accurate measurements of distances? Take a look at following image.

This is a real world map with a winding path to the observation tower. It as a small scale so we are forced to use an odd measurement for a hex. One-eighth of a mile or 660 feet per hex. When I drew this over top of the image it each hex measured from top to bottom 0.365 inches. The purple path I drew over the original map path measured 6.027 inches. Making the true length of the path, if you hiked it, 10,899 feet or 2.06 miles.

At a game table you could have a device with a wheel that you could roll along to measure the true length of anything on the map. But that not a common piece of equipment a person is likely to possess.

The virtue of a hex grid is that from each hex there are circles of hexes surrounding it out to an arbitrary distance. This makes it very useful to measure distance quickly from a center hex to an arbitrary point.

So what if you have a hex filled with winding paths inside the hexes. Well if I counted up the hexes that the path touches it comes out to 13 hexes or 1.625 miles. (the red numbers) Not very close to its true distance. However if I double counted (or even triple count) hexes (the blue numbers) with particularly convoluted paths. Then I get about 17 hexes or 2.125 much closer to the true distance of 2.064 miles.

Like any tool you need to use your best judgement in using this. In this case you need to estimate by sight whenever a convoluted path inside of a hex means you double or triple count it.


Michael Bugg said...

I think the convoluted paths needed to travel through, say, the mountains are taken into account by the reduced movement rates. It's not that your character's pace has actually slowed to 2 mph in the mountains, but that all of the twisting and backtracking and more frequently needed rests reduce you to 1/2 the usual number of hexes crossed per day.

ewookie said...

i agree with michael. outside of mountains and other rough terrains, why would a path be so convoluted at such a small scale? at 660 feet per hex, each hex is smaller than the length of an american football field (300yds = 900ft). people would easily 'short-cut' through the path. over time, this would create a new, less convoluted path. moral of the article: don't draw convoluted paths at such small scales.

Robert Fisher said...

A real-world rule-of-thumb I learned: Double the “as the crow flies” distance to get the land-travel distance. Even the most clear terrain and even when you think you’re taking a straight path, you seldom actually travel straight on land.

Rob Conley said...

I apologize for not being clear. The purple line is a preexisting path.

ewookie said...

rob, i had the impression that the purple line was a pre-existing path. from the map, it looks like some sort of tourist, 'site-seeing' path, which doesn't really seem relevant to hexcrawls or rpg's in general.

Nagora said...

A furlong isn't really that odd a unit, as these things go. I use 1 furlong hexes quite a lot, in fact.

Tim Pollard said...

Looking at the contour lines it looks like that path is actually pretty close to the ridge-lines, and a lot of paths will naturally follow ridges.

I always assumed the decreased speed for rough terrain and hills was due to the fact that it's harder to walk up and down then it is to walk on flat ground. And it's a lot harder to walk through somewhere where you have to keep stepping over things (such as rocks or fallen branches) than across a flat plain.

It's also possibly possible to estimate the distance by measuring between the two points, and then finding any point that's off the main track by a significant margin and adding it onto the total distance. Doing that I ended up with about 2.2 miles. The Hexes are probably a little faster though.