Wednesday, July 27, 2011

Hex Mapping Part 2: Scale

Cook’s Expert D&D says you should divide a character’s per-round movement by 5 to get the number of miles they can travel in day. At 120’ a character can move 24 miles in a day, but most groups will have someone down at the 90’ movement rate, and that would slow them to 18 miles per day. This isn’t unreasonable, as the Roman legions were thought to be incredibly fast at a speed of 20 miles per day, while Charlemagne's armies (which relied on ox-drawn carts to carry their gear and food) generally averaged just 12 miles a day. So a small band of heroes, on foot and over level ground, should be able to cover nearly 20 miles per day, especially if they’re exploring and mapping as the go.

Cook also recommends hexes that are six miles across. This works pretty well as it has our heroes crossing three or four a day. There are some other issues to keep in mind as you’re picking your scale.

One is sight distance. You don’t want the PCs to be able to see all of a single hex, especially if you’re going to be using wandering monster rolls. You may want lairs, camps, or even just the critters themselves to not be seen the first few times the PCs move through a hex (which helps explain why they’re suddenly popping up now that the dice say they should). Six-mile hexes mean each hex covers a bit more than 36 square miles. (Actually, it's a bit more than 30 square miles, but that doesn't throw us that far off. Thanks for catching my math-oops, JD!) That’s a lot of terrain for bandits or bears to hide in. Or even a castle if you need to drop one in after the fact.

Another question to consider is just what you can fit in a single hex. According to the medieval demographics calculators at the Domesday Book, a town of 5,000 people covers 83 acres, which is 0.13 square miles. Lots of room to lose small towns or villages (or orc camps) in a 6-mile hex. London in 1200 AD is assumed to have had a population of roughly 25,000. The Domesday Book page gives us a size of 412 acres, which is 0.64 square miles. At that same time, Rome was assumed to house 9,000,000 people. That may be too large for the Domesday Book page, and it returns a size of 148,258 acres or 231.65 square miles. That comes, very roughly, to 6-and-a-half of our 6-mile hexes. Paris’ population in 1200 was 110,000, which the Domesday Book page says should have covered 1,813 acres or 2.83 square miles, which fits comfortably in our 6-mile hex while still clearly dominating it.

The 6-mile hex works great for a muscle-powered world. If you want a world where people travel by jet-cycle, or live in massive cities like Tenochtitlan (possibly 212,500 people in 5.2 square miles not counting the greater metropolitan area) you might want to expand the size of you hexes. If, however, the world is full of dense jungles and tiny villages, a smaller hex (maybe 3 miles across, roughly a league) might be more appropriate.

UPDATE: More praise (and better math) for the six-mile hex at "The Hydra's Grotto."

Art by Ivan Constantinovich Aivazovsky and Alberto Pasini.


Timeshadows said...

--Thanks. :)

Dangerous Brian said...

Food for thought Troll. Many excellent points for consideration.

faoladh said...

I've been thinking about this issue for a while now, and have come to no final decision. I do know that I want to use the league measurements from Swordbearer (where 1 league = 15,000 ft, or 2.841 miles), along with the concepts of movement and resting in that game. Since visibility over land is pretty short (I think that the furthest sight distance without overlooking from a height is 5 leagues), that could serve as a useful parameter. On the other hand, a small group moving with some urgency over level ground can travel 10 or more leagues in a day, so that might also affect the potential parameters.

Still a lot to think about there.

trollsmyth said...

Thanks for the kind words and encouragement. :)

faoladh: Yeah, I think there are two schools of thought here. One is very much that of the West Marches campaign, that requires the players to go across the landscape with a fine-toothed comb and learn the territory in intimate detail. This sort of play makes optimal use of every square mile, can make the world feel extremely real, and makes the players experts in the local territory.

Unfortunately, as you say, it can run into problems if the players just flat-out push it to the horizon. Things get even worse if they have access to roads, horses, or, the gods forfend, pegasi, magic carpets or seven-league boots!

The method I'm following is more traditional. It assumes the PCs will move at a ground-eating pace and are only interested in the terrain they are crossing in a more general way. "The territory here is mostly forest," as opposed to "where the river bends around the old oak that grows up between the two halves of the shattered boulder."

The challenge in a more intimate style of game is keeping track of all those interesting features and details while still keeping ahead of the players. For the type of hex-crawl I'm working on here, the big challenge is keeping it from getting boring. "Another day of nothing but jungle? Ho-hum..." Overcoming that is going to be an ongoing issue in the rest of this series.

Dungeon Smash said...

Hey -
Just thought I'd chip in to say that 24 miles a day is VERY fast. Assuming you go 8 hours a day, that's 3 mph. That's about average speed for a hiker with minimal gear travelling on a level, paved road. Most hikers probably travel more like 2 mph, and that's assuming pretty reasonable terrain. I would imagine that in Ye Olden Tymes, wearing chainmail, hacking through unexplored bush, with god-only-knows what kind of footwear, and mapping as you go, 2 miles per hour is pretty generous. There's a reason people didn't travel much in the middle ages - it took a long dang time to get anywhere

trollsmyth said...

Dungeon Smash: Yeah, everyone thought the Roman legions were blazingly fast at 20 miles per day. As you'll see in the next installment (probably go up on Friday if all goes well) I'm assuming an average of 12 miles per day, with varied terrain and somebody in the party dealing with encumbrance issues. That's actually noticeably slower than your 2 miles per day, assuming eight hours of walking.

faoladh said...

The justification for the travel rates given in Swordbearer reads as follows:

"[T]he travel rates given here are based on wilderness walking and hiking experience in unpopulated areas of the US by small groups, and information on travel times for such provided by various walking, hiking, and mountaineering groups. This is probably a fairer test of typical travel rates than military values, since very few groups of casual adventurers and travellers function with military discipline or fitness, but yet few are plagued by military bureaucracy!"

The way that game deals with the slower travel times of larger groups is by extending the amount of time required for the mandatory rest breaks and requiring more breaks. The baseline is half-hour breaks, requiring one at the beginning and two at the end of the day, plus one during the day. Larger groups require twice as long for each break, and there are five conditions (exhaustion, poor travelers, extreme temperatures, precipitation, poor ground conditions) that double the time to cross a league (for each) and add an extra break during the day (also for each).

Natalie said...

Unfortunately, as you say, it can run into problems if the players just flat-out push it to the horizon. Things get even worse if they have access to roads, horses, or, the gods forfend, pegasi, magic carpets or seven-league boots!

My understanding is that the WM model has a couple of features that prevent this from happening.

One, it's low level. So they don't have the really crazy stuff.

Two, it's set out on the edge of civilization, so there aren't any roads, either.

Three, the area is really, really dangerous, and only gets more so as you get further from civilization, so pushing out as far as you can immediately will almost certainly get you killed.

Four, you and the other players are in quasi-competition for most treasure brought back from the wilderness, and most secrets uncovered. Just randomly travelling doesn't tend to get you very far with that, because the player pool in a well-run WM game knows about at least a handful of possible adventure sites at any given time.

trollsmyth said...

Oddysey: And, as I think you pointed out or I read somewhere, the campaign is designed to transform into something new when the PCs reach high enough level that these don't work as effective hobbles anymore. It's a well-designed system.

JDJarvis said...

"Six-mile hexes mean each hex covers a bit more than 36 square miles."

That depends on how yuo measure a hexes size. If it's from flat face to flat face a hexes area is W * (W * .86)

A 6 mile hex would have an area of 30.96 square miles. Not really a significant difference for traveling and heroic adventure but if you ever get down to bean counting and farm/estate size
19,641.6 acres is much smaller then 23,040 acres.

JDJarvis said...

The area for cities should be the actual physical area of common's, roads, houses, churches and administration and defenses.
There should likely be 2.5 acres of farmland and pasture per citizen within a days walk of the town/city. It's easy to find a village or town becasue of the fields surrounding it.

A town of 5,000 could easily fill over half a six mile hex with the town proper and fields.

trollsmyth said...

JDJarvis: Ack! Ok, check my math here: if it's 6 miles from flat side to flat side, I get side length of 3.46 miles and an area of 31.1 square miles. That look right to you?

JDJarvis said...
This comment has been removed by the author.
trollsmyth said...

JDJarvis: Not at all! You're keeping me honest; that's important. Thanks for following up on this. Ditto for the land use. That'll be pretty important later.

JDJarvis said...

whoops my math was off last reply.

my earlier quickie formula certainly comes up short.

I just drew a hex 6 inches across and measures the hex segment to get it right and it's 3.4605 which is 3.46 in a sensible world.
with the (3/2)*SQRT(3)*s^2 formula the answer is 31.1

double whoops, you commented on my earlier comment as I deleted it ...sorry

faoladh said...

S. John Ross, in "Medieval Demographics Made Easy", gives hex area as "To determine the area of a hex, multiply its width by 0.9306049, and square the result." Is this inaccurate?

trollsmyth said...

faoladh: I think JD and I have been chopping the hex into triangles and doing it that way. Ross' formula comes up with a number that's pretty darn close to what JD and I came to, so I'm guessing it'll work just fine.

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