Friday, January 1, 2010


A DF thread brought up the idea of overland travel to me again.

I've discussed movement rates, scales, etc here before, and I think that a hex-based exploration minigame would be a great addition to any version of D&D. All too often, the magic of overland exploration is lost in an orgy of mathematics, calculating movement rates, terrain modifiers, etc. That just sucks the life out of what should be a really exciting part of the game. Additionally, due to the ass-painery, all too often considerations such as encumbrance or food carried become glossed over, which means that they are not as important as maybe they should be as balancing factors. What I'd really like is a minigame similar to Barbarian Prince, perhaps, that actually is fun and exciting to play.

I think one of the first decisions that one would need to make in a "Hexploration" type game is deciding on the hex sizes and time scales. I'd imagine that for time scales, we need:

Turn (~10 minutes)
Hour/Quarterday (Somewhere between 5-10 turns?) -- I'm not sure exactly what this time scale should be... But I think you maybe need something to bridge the gap between turns and days.
Day exploration (Somewhere between 5-10 hour chunks)
Week or fortnight (7-14 days)

Now we need to think about movement rates. I like to go back to imperial units in this case, so let's say that a typical unarmored movement rate for foot travel is 1 league per hour -- ~3 miles/hour. So, a day's march is about 8 leagues, or 24 (round to 25?) miles.

This will drive the size of each hex. I want characters to move either 3 or 7+/-2 hexes each "turn," typically. Moving 3 hexes makes each move feel very special. 7+/-2 gives more fidelity for various modifiers but is still something that can be easily computed in your nugget. Given that I want complex options and modifiers to be possible, I think 7+/-2 is the right way to go. So, on our "daily" movement chart, each hex should be 4 to 6 miles across. I like 6 miles because its two leagues -- nice and easy to remember! That means a typical character on foot covers 3-4 hexes each day on easy terrain. An example could be an unburdened peasant walking a hex or so to the market on good roads, doing their business, then walking back (in a long day). I want to use 4 hexes, even though 24 miles is on the upper end of plausible, because it allows for more penalties to be applied and it keeps to our 4+/-MOD formula that I use in so many other places. The other option would be to go with 3 hexes base move and give a bonus for improved roads.

This allows for some modifiers. The most common modifier would be being mounted. Mounted troops would often move at speeds up to ~12 miles per hour in combat, but on the march movement would be significantly slower.
From wikipedia:
The speed of travel varied greatly. Large retinues could be slowed by the presence of slow-paced carts and litters, or by servants and attendants on foot, and could rarely cover more than fifteen to twenty miles a day. Small mounted companies might travel 30 miles a day. However, there were exceptions: stopping only for a change of horses midway, Richard II of England once managed the 70 miles between Daventry and Westminster in a night.

Not the most reputable source, but this squares with what I recall from earlier research and we're only interested in a ballpark estimate here. So, for game purposes, one could say that light cavalry is perhaps capable of 5-6 hexes each day under the best circumstances; that's 30-36 miles. Heavier cavalry or beasts such as mules will move slower. Let's go with 6 hexes as its easy to remember (+50% vs. foot movement) and again allows wiggle room for modifiers.

So, to sum up, for daily movement we have hexes two leagues across. Best case (good terrain, unencumbered) foot march rates are 3-4 hexes. Best case mounted march rates are 5-6 hexes. Obviously we can come up with a list of modifiers to take into account encumbrance, racial advantages/disadvantages, terrain, roads, etc -- but, our baseline numbers are reasonable enough to allow for such modifiers.


Now let's extrapolate out to a campaign map scale. We will need to decide if time is measured in weeks, fortnights, or months. I tend to think months are a bit long for this scale so I automatically lean towards weeks or fortnights. Again, we'll want to keep movement rates consistent (foot at 4 hexes, mounted at 6 hexes) so as to allow easy extrapolation between scales.

If we assume 8 leagues per day, then in a week we'll cover 56 leagues (168 miles). This is ambitious. I've done a fair amount of backpacking, and while its possible to march over twenty miles a day for a week straight with a moderate load it sucks a lot. Its much more realistic to have at least one or two slow or rest days in there. So I'd be fine with reducing the weekly move rate to either an easily remembered round number like 50 leagues, or to a number easily divisible by 4 (so as to make nicely sized hexes). Luckily, 50 leagues does that as well -- it results in hexes that are 12.5 leagues or about 24 miles across.

So, make the campaign hexes 12 leagues across, and normal foot will cover 4 hexes a week, while mounted moves remain 6 hexes. This is great as many old school products use hexes 24 miles across. Tre bien! So, we'll stick with the week time scale.


One can zoom out one final time for month-sized campaign hexes. Without going into too much detail, you could have hexes about 48 leagues across. You could either round up to 50 leagues for ease of memorization (although that's again ambitious), or down to 40 or 45 for a bit more realism. Again, foot travel covers 4 hexes and mounted 6.


Sometimes you need to get more detail than daily moves but less detail than turn based moves. For this scenario, you can go to hourly or two-hourly chunks of time. We basically want a unit of time that is a reasonable number of turns in length (hopefully 7+/-2) but also splits the day into no more than 7+/-2 chunks.

Two hour chunks are 10-12 turns (depending on whether your turns are 10 minutes or 12.5 minutes in length), and split an 8 hour day into 4 chunks (or a 10 hour day into 5 chunks, or a 12 hour day into 6 chunks). That's pretty manageable -- more so than one hour chunks or three hour chunks -- so let's run with that for now.

Our daily foot movement rate is 12 leagues. That should be total movement over a 12 hour day of activity rather than an 8 hour march day -- it assumes time factored in to make and break camp, eat food, relieve one's self, etc. So, let's say that in each two hour chunk of time, 2 leagues are covered. That means hexes need to be 1.5 miles across.

If, however, we use an 8 hour march day and somehow otherwise charge characters for errands and camp time, then in each two hour chunk of time 3 leagues or ~6 miles are covered by foot. That means hexes of 2.25 miles across.

Clearly hexes of 1 league across are probably too big -- then players will cover 4 leagues in 2 hours, or 16 leagues in 8 hours, which is too fast compared to our daily established movement rate of 12 leagues/day. I think a good compromise may be either 2 miles, or 0.5 leagues (1.5 miles). With 2 mile hexes, foot covers 2.66 leagues in 2 hours or 10.66 leagues in 8 hours. With 0.5 league hexes, foot covers 2 leagues in 2 hours, or 8 leagues in 8 hours (12 leagues in 12 hours).

So, basically, we have:
- 2 mile hexes if you plan on requiring a "chunk" or two of time each day be spent on camp chores, or...
- 0.5 league hexes if you want to abstract out the down time


Finally, you can get turn based hexploration. Let's say that turns are 10-12.5 minutes. 10 minutes is the traditional AD&D turn. 12.5 minutes allows for 5 turns per hour, which may be easier to add up. Either works out similarly for distance estimate purposes.

If characters are covering 3 miles per hour on foot, then that means they are covering almost 16,000 feet or 5300 yards. So, in a 10 minute period of time they cover around 900 yards. In a 12.5 minute period of time its around 1000 yards. Again, we want to stick with 4 hexes of movement, so that means hexes need to be around 200 to 250 yards in size. Conveniently, the old imperial unit of measure for this distance fits just right: a furlong is 220 yards! So, our hexes are one furlong in size. Perfect.


Ok, let's start getting tactical just for a sense of scale here. If we can cover 4 furlongs in a turn, and a turn has 10 rounds, then in a round we're covering 0.4 furlongs or around 88 yards. That means each hex needs to be ~22 yards in size.

Going to our old imperial units, this is about 4 rods (a rod was 5.5 yards).


Let's split the one minute round up now. We can split it into ten easy to measure segments of six seconds length. Or we can go to six segments of ten seconds each (mirroring the six turns to an hour).

If we go with the traditional 6-second segment, then we get a movement rate of about 9 yards/segment. This requires hexes of 2.2 yards in size -- which is just a bit larger than a Roman Pace (of 5 feet).

If we go with six segments of ten seconds each, then we get a movement rate of about 15 yards per segment. That requires hexes of about 3.75 yards, which is a bit over two paces.


This is what we've got, put into tabular format. Base movement rates are 4 hexes for foot and 6 for horse. I've also included the area that you can depict on an 8.5 x 11" sheet of paper, assuming 1" margins and 1" hexes. That's six hexes across and nine hexes tall.
  • 1 month: 48 leagues (consider rounding to 40, 45, or 50) -- ~850 x 1300 miles (empire or small continent)
  • 1 week: 12 leagues -- ~215 x 325 miles (kingdom)
  • 1 day: 2 leagues -- 36 x 54 miles (duchy?)
  • 2 hour "chunks:" 2 miles (if you require 2 chunks/day for downtime)...or 0.5 leagues (if downtime is abstracted -- 12 x 18 miles or 9 x 13.5 miles (barony?)
  • 1 turn (~10 mins): 1 furlong (220 yards) -- 6/8 mile x 9/8 mile (manor)
  • 1 round (~1 min): 4 rods (22 yards) -- ~130 x 200 yards (5 acres)
  • 1 segment (~10 seconds): 2 paces (10' or ~3 yards) -- 20 x 30 yards (1/2 rood; about 1/8 acre)
  • 1 segment (~6 seconds): 1 pace (5' or ~1.5 yards) -- 10 x 15 yards (perch, or 1/160th of an acre)
This table makes it easy to see that if exploring a small manor or village, a turn based scale is most appropriate. If exploring a barony, you can use two hour chunks. If traveling across a duchy, then a scale of days is most appropriate. And so on.

Note that if combat occurs in rounds, this leads to large battle spaces. If characters can cover 4 x 20 yard hexes/squares at a walking pace without hustling in a one-minute round, then your battlefield needs to be at LEAST 80 yards across! That's a far cry from the 20' x 20' dungeon room! Its interesting that 3.5, with its six-second combat rounds and 5' square grid, really gets the most "realistic" for tactical movement.

In AD&D, ranges outside were measured at 1" per 10 yards. If you allowed 12" of movement (or 120 yards) in a one minute round, its also pretty accurate. My system lets someone cover about 2/3 that at a walking pace, so 120 yards at a hustle is reasonable.

However, its hard to have dungeon rooms that are 240 yards across, so AD&D had to include an arbitrary 1/3 reduction in speed to make combat on the smaller dungeon scale work well while retaining one minute combat rounds -- that reduced the distance covered in one minute to 120 feet, which is really slow when you think about it in context. While you might be able to justify that sort of movement rate on "difficult terrain" (like, say, inside a slippery, dark, dank, trapped, cramped dungeon), its hard to justify it on a wide open plaza, an open field, or other open terrain.


It'd be very useful to have a relatively consistent ratio between units. This allows for some common formulas that allow conversion between different time scales at relative ease. Here's one system that tries to preserve a 1/10 (or close to it) ratio:
  • 1 month:1 week = 1/4
  • 1 week:1 day = 1/7
  • 1 day:10 x 2 hour chunks (the other 2 chunks assumed to be used for sleeping or otherwise wasted -- or you can pad the chunks to make them 2.4 hours long instead of 2 hours long) = 1/10
  • 1 2 x hour chunk:10 turns of 12 minutes each = 1/10
  • 1 turn:10 rounds of one minute each = 1/10
  • 1 round:10 segments of six seconds each = 1/10
Not bad! This works nicely up until the higher levels of the campaign. So you could come up with a rule of thumb that covers conversions between almost all time/distance scales.

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