I am not an experienced hex mapper, but your question is interesting to me and I like math. I am always looking up distances and such to strengthen my grasp of the scale I am working with. I am an American though so I generally think in feet and miles. The way I think that works best for me is to use roots of the circumference of the Earth, though of course I guess you could also say that if you have no intention of using a scale as large as a globe you have no need to use this kind of method. Here it is anyway:
C of Earth = 25,000 miles = 131,480,184 feet
(131,480,184 feet)^(1/3) = 509 feet per smallest hex with 3 levels of hexes and a diameter of 3 hexes per every larger hex layer and a hex count of 3 at the highest level (at least in the direction of the circumference or the x axis which is really the same as the equator).
(131,480,184 feet)^(1/4) = 107 feet per smallest hex with 4 levels of hexes and a diameter of 4 hexes per every larger hex layer and a hex count of 4 at the highest level.
(131,480,184 feet)^(1/5) = 42 feet per smallest hex with 5 levels of hexes and a diameter of 5 hexes per every larger hex layer and a hex count of 5 at the highest level.
(131,480,184 feet)^(1/6) = 23 feet per smallest hex with 6 levels of hexes and a diameter of 6 hexes per every larger hex layer and a hex count of 6 at the highest level.
I'm sure it has to depend on the scale you want to work with. If you have no upper size limit like some planetary circumference or continental width or unsurpassable mountain barrier which you will never travel beyond I suppose it makes sense just to use the simplest and most basic measurement for the smallest hex and decide if you like the look of hexes with 3's, 4's, or 5's for hex diameter. Could be also that I just presented information that isn't new or helpful at all and just got a kick at the expense of your reading time or whatever.
My math was wrong. Sorry. I should have been doing:
D / (H^H) = F
where D = the maximum distance from one edge of the map to the other, or in the case I presented the circumference of the Earth in feet
H = the number of hexes within a larger hex as well as the number of hex layers
F = the width in feet of a single hex on the bottom layer
So the results are listed below in the form:
3: 4,869,636 feet
Alternatively if you wanted to work from a bottom size up, say F = 100 feet hex diameter (making one hex about the average size of a single family house lot in the United States) you could do:
F * (H^H) = D
to find the maximum size of your map
3: 2,700 feet (half a mile - distance an out of shape guy like me can run in 5 minutes)
4: 25,600 (5 miles)
5: 312,500 (60 miles)
6: 4,665,600 (884 miles - distance between New York City and St Louis)
7: 82,354,300 (15,600 miles - average distance an American drives in a year)
8: 1,677,721,600 (317,750 miles - almost 13 trips around Earth or about 1.3 times the distance from Earth to the moon)
I've had another thought. Take for example a hex layout where:
H = 5
D = 312,500 feet
F = 100 feet
Perhaps you don't need or want your very top layer at all. After all having just five hexes across your map (about 25 total if you have a squarish mapping area) might not be very helpful. If you want to remove this layer then to give an idea of how many hexes the top layer would contain, it would be H^2. So if you removed the very top layer of this particular map, the map would have a top layer width of 25 hexes, though all other values would be the same.
Last edited by Sam Conifer; 03-02-2011 at 02:51 PM.
Ideally I'd like 5' smallest hex and then scale up from there. I'd like to pass through a few key scales for city mapping, ranged melee such as 100' and 1, 2 or 3 mile(s), to easily track overland movement. I just can't seem to get 5' to scale into something without having some visually unrelated hex scale (where 8/17 of a hex is in this upper scale map and 9/17 of the hex is in another upper scale hex - if that makes sense).
Oh, I so wanted to come in here and just say that "Dragon Scales" are the best. Or go to my bathroom and get the brand of my scale and explain how it's only because it was on sale. Hehe...ok, smart-alek I know.
Pretty much all the maps I've made are 1" = 5", hex or squares. That's just because it works for most miniatures in tabletop games.
I think the scale depends on what the usage will be. If you want a space ship to land on a hex and fill it up then figure out how large the ship is and go from there. If it's just a visual representation of say a planet what's the use of the hexes anyway? If you are going to put a marker down where your adventure party is that might matter, but again, it really depends on what you are trying to display. If the part is in the same hex for a week or so game-time then that's really probably not the map you will be using as you would probably have a more detailed map to work from.
You seem to have hexes within hexes so I think you just need to determine what your smallest hex is and go from there. I'm thinking there hasn't been a lot of response because most probably change the scale to fit the map.
“When it’s over and you look in the mirror, did you do the best that you were capable of? If so, the score does not matter. But if you find that you did your best you were capable of, you will find it to your liking.” -John Wooden
* My Finished Maps
* My Challenge Maps
* My deviantArt