Thursday, December 3, 2009

In Praise of the 6 Mile Hex

It is good to be back in action. I have been away on personal business, but I should be posting a little more regularly now.

So just today I stopped by Chgowiz's page and noticed that he was talking about wilderness hexes. (and it looks like Bat in the Attic has been playing with hexes a little too here and here)(and Chgowiz got Stirgessuck thinking a bit). When I left I had actually just started to kick around the old hexagon myself on this blog. And so I have some thoughts about hexagons already to go. I hope they are helpful to Chgowiz and everybody else.

As you can tell from the title, I think that the 6 mile hex is the ideal hex for wilderness adventuring hexcrawls. I used to be a big fan of the 5 mile hex as published by Judges Guild. But someone over at the Necromancer Games (was it Rob S. Conley?) pointed out back in like 2005 that it was actually a lot easier to use 6 mile hexes. And then I learned some more things about hexagons. Check it out:

1. Navigation. Estimateing a party's route through a 6 mile hex is a lot easier than any other hex. No other hex size breaks down as cleanly as a 6 mile hex. Trust me, I did the math. The numbers above are accurate to the first decimal. Thats good enough for general overland travel. Take a look at the diagram above. Its six miles from face to face. Vertex to opposite vertex is 7 miles. From the center to any face is 3 miles (half of 6). From the center to any vertex is 3.5 miles. From a navigation standpoint pretty much any route through the hex in general is covered. Enter from the vertex and leave through a face? You can approximate it pretty easily. 5 mile hexes do not lend well to this. If you wing it go with a 6 mile hex, you'll be glad you did.

2. Horizon. Your average human in a flat area without any obstructions in view (think a becalmed sea) can see up to 3 miles. Thats the distance to the horizon best case scenario. So a party travelling straight through a 6 mile hex is not going to see out of it. Unless they climb a tree or find a high place with a view. But the idea is that a 6 mile hex with varied terrain covers the distance that the party can see. A good rule of thumb is that if they take the time to survey the surrounding land then a party should be able to be aware of the terrain of the next hex over. Some pushback might come with the idea that you can see a mountain quite a ways away. But mountains are tricky in that you really can't tell how far away they are until you are a few hexes away. Getting a good vantage point (like the top of a hill or mountain) could be the opportunity for adventure in itself and being aware of the lay of the land can be its own reward. If you want to be able to tell your players how far they can see when they climb up the hill or tree or tower a good rule of thumb is that the distance to the horizon is the square root of thirteen times the height they are viewing from (

3. Sub hexes. The 6 mile hex can break down into half mile sub hexes. That is 12 hexes accross. (Mr. Chgowiz, this next bit is for you) If you put a dungeon or a settlement or some other important element in a hex, it is good to know where in the hex it is. Thus it makes sense to map out the hex in subhexes. Having these is good for distant encounters, chases, and well looking for that dungeon that is supposed to be around here somewhere. But wait, theres more. Each of these hexes can break down into sub hexes that are 1/24 of a mile accross. At this point your hexes can start measureing thing like furlongs, chains and all the other medieval land measurements. Thats really convenient when you want to figure out how many hexes should a farm take up. Also, 1/24th of a mile is a distance you can put on a battlemat. 5280ft/24 = 220 ft. 220 ft/5 = 44 battlemat squares. A Chessex Mondomat covers that area. Furthermore, if you are always using hexes that have 12 subhexes accross you only have to use one type of graph paper to keep track of all the projections. That is, the graph paper that you use for your sub hexes is the same as the graph paper you use for your subhexes of subhexes.

What this all comes down to is: The one-page wilderness template just got a lot cooler.

Merry Christmas Chgowiz!

*Graphic is soley my own this time... free to use and distribute...


Anonymous said...

That is AWESOME.

FWIW, I double-checked the math, and you are indeed right. :)

Dr Rotwang said...

Once I get by breath back, and some dry pants, I am totally printing out a copy of this mofo post and sticking it in my GM binder.




Anonymous said...

Thanks for the diagram -- very helpful. I think I'll need to think and write more about this.

Jayson said...

Thanks for laying all this out!

Jayson said...

Marvelous. Thanks for laying this all out; it will be helpful to me very soon! (Isle of Dread, doncha know)...

Anonymous said...

This is awesome. I'm working on a hex crawl right now, but I'm very afraid of how much work it's going to be to map out the next hex depth down from my current map. If the smaller hexes are 6 miles, and 12 of those across is a world hex, I can set my world hex size to 72 miles.

Will need some editing to make things closer together at that point.

But what you've done here is lovely. Thanks!

Nagora said...

A quick calculation shows that a 6-mile hex is also within 0.3% of being 20,000 acres.

I think we have a winner.

Dangersaurus said...

I keep coming back just for this post. You've made your stamp on my campaign map.

Confirmation: recorate, what Shaggy did, like, to his pad, man.

netherwerks said...

Late to the party, but this is a great idea and we're going to adopt it for our maps from now on. This is a sensible, and effective standard. If the D30 gets a whole Order promoting it, then the Six Mile Hex ought to have some sort of icon or whatever as well, don't you think?

Anonymous said...

I don’t get the math.

7² - 6² ≠ 3.5²

Steamtunnel said...

@2097 you need to re-read. You are correct, 7^2-6^2 does not = 3.5^2

And 6.98^2 - 6^2 does not = 3.49^2

That is because these numbers are longer decimals that have been rounded up to the nearest 100th of a mile (or 52.8 ft). What you need to do is start with a 6 mile line and then determine what the lengths of an equalateral triange with a height of 3 is. This will get you the more precise numbers you so eagerly desire.

Brett Slocum said...


These. Good.

Piper said...

I find this information very useful. Thank you for posting.

Antariuk said...

Great article that has been part of my bookmarks for quite some time now. I am posting this comment however with a question : would you mind if I use your article in a adventure supplement (released under Creative Commons) I am working on? With recognition of your authorship of course.

Fr. Steve said...

I would break the 6 mile hex down into six 1 mile hexes. After that, I would break that down into 8 furlong hexes.

On the encounter level, I would use the fathom, which is the length from one finger tip to the other if you hold your hands out (measured as 6 foot).

The basic unit of measure for land in the medieval period was the Furlong. It is 1/8th of a mile. 660 feet. 220 yards.

110 fathom hexes would make up one furlong. You could use any typical battlemat with that system.

Michael Prescott said...

Very cool, steamtunnel. I'm especially interested in the horizon calcluations. I think your recommendations might be a bit short, given the horizon calculations on the wikipedia page.

A 1,000-foot prominence (a large hill, half the size of the smallest mountain, by one definition) is visible from 38 miles away, which is roughly 6.5 6-miles hexes.

A 9,000-foot prominence (which is roughly the distance that Everest towers above its base camp), is visible from 19 hexes away!

Now, all I'm doing to get these numbers is to assume that you can see anything that can see you.

Oh, actually, I see I'm doing that wrong. According to WP, the way to tell the distance to tall objects is to add together the observer's to-the-horizon distance with that of a hypothetical, second observer, atop the thing you're trying to see.

So if you're on a 1,000-foot prominence trying to see a 9,000 foot prominence, you can see that from 6.5+19=25.5 hexes away. (Woah.)

Zombie Neighbours said...

Can you suggest a graph paper that lets you do the 12 mile super hex well?

STAR*Connect Aviation said...

I'm sold on 6 mile hexes.

I looked up distance and I get this

if we figure earth with an atmosphere then d= 1.32(sqrt(h))

d=statue miles
h= feet.

close enough anyways.

Unknown said...

I keep coming back to this post and rereading it because it is so tracking cool and makes such sense. Thanks for it.

RMcD94 said...

How do you break the hex down into more hexes? Surely they won't fit without overlapping with another hex?

Unknown said...

If anyone wanted to know ('cause I did!) the area of the 6 mile hex. is: 31.82643359m2.

A hex is 6 Equilateral Triangles, the base and sides are 3.5, so I figured out the height:

3.5xCos30 = 3.031088913

Then to find the area of each Triangle:

1/2x3.5x3.031088913 = 5.304405598

Multiplied that by 6 for the full area of the hexagon:

5.304405598x6 = 31.82643359m2 per 6 mile hex.

OR if you replace the 3.5 with the actual 3.49 as it should be, the answer becomes: 31.64482806m2

And someone please correct this if it's wrong <3

brandon karlis said...

Hi there,
I'm new to hexcrawling & sandboxing in general, and your blog (this post) is constantly linked to whenever people talk about learning about hexcrawling. I'm working on a campaign that should span the party around 3 months of in-game time, and I'm wanting to present it as a hexcrawl. My idea is to create the size/scale of the campaign region based around that. That gives me roughly 90 in-game days to work with.

If I want the party to reasonably be able to explore 1 full hex in a day (assuming no adverse conditions, so they're all healthy, not trudging through swamps, etc), it looks to me like the 6 mile hex should be good for that (since a 6 mile hex is just slightly less than 24 square miles) - in fact, if they were in a plains area and could see all around, I would assume the could do it in much less time than a day. Is this reasonable for me to assume?


Red_Five_Standing_by said...

This is so amazing! Thank you!

GamesBook said...

@Bradon - A 6 mile hex is actually 31 square miles, not 24. To get that area, you'd need a five-and-quarter mile hex.

Unknown said...

Daniel, that's slightly incorrect. You assumed a 3.5 (or 3.49) mile side for your triangles to find the height, but that's only an approximate length based on the already known triangle height of 3 (hex width /2).

Going with the height of 3, the sides are actually 6tan(30), or 3.464...

I calculate the area to be 31.1769... sq.mi.

Side note: vertex to vertex is 6/cos(30)= 6.9282...

Andrew Sawyer said...

I did the math, and this may not be perfect, heavy approximations and such, but the US is about 121,777 6-mile-hexes squared.

unknown2 said...

1. As someone else commented just above, I also noticed using that the side/center-to-vertex lengths and vertex-to-vertex lengths aren't quite the values the blog posts claimed, but actually 3.46 and 6.92 miles. This isn't a particularly bad mistake, but a 5 mile hex has sides/side-to-vertex of 2.9 (so about 3) and vertex-to-vertex length of 5.8 (so about 6) miles when rounded to 1 decimal too, so it's not really that different.

2. One could also argue that with the horizon of a flat plane being about 3 miles away for an observer at a height of 6 feet, a 5-mile hex is the better choice for a part being able to see from the edge (last half-mile or so) from the previous hex to the middle of the one they're about to enter. Or from the middle of the one they're in to the first half-mile or so of each neighbouring hex. In a 6-mile hex, in the middle they can *only* see their current hex. I would think that which option is better depends in part on if you want to use single-biome hexes or not, whether rivers and roads neatly follow hex borders (even subhex ones!), etc. And of course the average/maximum height of vegetation (if you're on a grassy plain where the grass is 3 feet high all over, a 6-foot observer is only observing from a height of 3 feet, and their horizon is 2.1 miles away), hills and other topography changes etc. likely matter much more how far something can be seen. In Fantasy RPGs, levitation (if you can control the altitude)/flight spells become very useful for mapping if you take observer height into account.

3. Point 3 is basically meaningless, at least for just wanting half-mile subhexes. You could have a 5-mile hex which is 10 subhexes across instead of 6 and 12 and it would achieve the same thing. The rest of the math regarding 1/24 mile sub-subhexes (an arbitrary choice in itself) would work out the same.

There's nothing wrong with 6 mile hexes, but it's not *that* superior to a 5-mile one either. Or most other sizes used in various games. I say use whatever works or is supported by the general travel, encounter, and other systems you're using. For example, Harnmaster uses 5-league hexes, and a league was/is customarily defined as about as much as a person walks in an hour, about 2.5 miles or 4 km (so a hex is 12.5 miles or 20 km). The travel system outlines travel in 4-hour intervals, and in that time 5 leagues is possible on roads or trails through flat areas, but not through cropland, forests, hilly terrain, etc. It doesn't use subhexes that I'm aware of, instead just mapping everything naturalistically, and showing a scale in addition to the 5-league hexes.

And lastly, especially down at the level of 1/24 miles, things start getting really opaque for those of us more used to km. 1 mile is still "something more than 1.5 km" (1609 meters and change) and half a mile is "less than 1 km" (0.8 and change), but 1/24 needs a calculator. Another reason why I like Harnmaster's travel/distance, since it offers conversion ratios to both metric and US/Imperial, and doesn't strongly favour either (smaller-scale stuff mostly uses feet iirc). 5 miles is 8.05 km and 6 miles 9.66 km, but those 5:8 or 6:10(ish? 9.5? 5 miles may be slightly better here!) ratios are rarely mentioned in most mainstream or even indie RPG stuff due to the US standards dominating.