Scaling a Hex Map
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- Опубліковано 2 жов 2024
- Should you make a 6 miles per hex fantasy kingdom map?, What about 5 miles/hex? 8? 10? And how does that choice impact a "continent" map and the world map?
While we do mention how this relates to a few of Worldographer's features, the core concepts apply to any hex map using any tool or on paper.
You can also read this same material here: worldographer....
I don't think we should assume a brisk walking speed. First off, aren't you carrying a bunch of camping gear. Second, even an open prairie is nowhere near the same as a paved path.
It just assumes they know where to go. Ie. There's signage, they've taken the route before, or they have a guide, they have a pack mule to carry most heavy gear, etc.
As the lunatic re-writing FATAL to be a more socially acceptable and reasonably playable game, I've personally spent days trying to figure this out. I've discovered that even with an average load for camping an adventurer could manage a speed of about 4 km/hr, so about 2 mph. And this would be without any breaks. Or a bit of a faster pace, but stopping for breaks to eat or drink water.
Good to mention the length of a mile because some other places have customary miles that are not the same size. When I went to Norway all of my relatives there spoke in miles, but not the 1,609 meter US mile. Rather, they had adapted the word mile to mean a deka-kilometer. 10,000 meters. That is the sort of unit confusion that changes a 20 minute walk into a 3 hour one.
Sounds like a throwback to when everyone used the same unit names but none of the units matched. Half the units changed depending on what was being measured!
@@Tyneras Did you hear the story about the queen wanting a bed made to fit her and her crown? Was told it in Elementary, and basically the bedmaker was imprisoned for making a bed that is not 6 feet (king said it needs to be 6 feet front to back), and the maker (being a small kid) had counted 6 of his feet. Made a model of the kings foot to make the bed right, and a happy ending all around, with the invention of the foot unit of measurement lol.
@@Suzuki_Hiakura Another version was that the inch was set as being 3 wheat seeds long, which meant that areas with poor soil had shorter inches! And the French inch was longer than the English inch, thus the myth that Napoleon was short (he'd be considered average today, and tall back then).
@@Tyneras lol. Loved that. Wonder if there is a version about miscommunication, like someone mistook a melon or pumpkin as an inch xD As big as the world is, I feel there is a good chance.
19:25 "It's more complicated when you think about the staggered nature of the hexes..." I've never seen or used the mapping program in this video, but if it has the ability to alter hex orientation between scale levels you can easily fix the staggering issue between scales. As a ADB Starfleet Battles player (which also uses hex grids), I came up with a way to create scaling hex maps that nested within each other simply by rotating the hex orientation 90 degrees between each scale.
To give you an example of what I am talking about, the large hexes on your Continent-Scale correspond to the hexes on the World-Scale above it while the smaller hexes represent the Kingdom-Scale below it. If you were to turn the Kingdom-Scale hexes 90 degrees you could probably fit 61 of them perfectly in line (5 hexes along each leg) with the border of the World-Scale hex and 9 of the the Kingdom-Scale hexes would run straight across from left-most corner to the right-most corner of the World-Scale hex. Ideally, you would reverse this and keep the Kingdom-scale hexes as they are and rotate the World-scale hexes 90 degrees so that you an easily have a straight row of hexes that can be used as the equator.
By simply alternating the hex layout 90 degrees between layers the straight row/column of one level becomes the borderline of the larger hex as you go up in scale.
At the world level, I have it at 500 miles per hex, Continent level, I set the hex size to 100 miles per hex; at the Kingdom level, I set the hex size to 20 miles per hex. I haven't used the province level very much.
Regarding travel, I set a base number of miles for each mode of transportation (walk, horse, wagon, boat - rowed or sailing) and then use % factors for different terrain. If the terrain is like western Kansas, flat as a pancake, then a person gets the full movement. If that area also has a true road (i.e., cobblestone, not dirt), they can go faster (especially with a wagon). Hills and mountains slow down travel.
Province level is kind of fun if you want to put heavy detail into specific areas (may as well draw it out by hand at that point though). Players can travel in or out of a province in a day, but it would be interesting if they only had a day to do a quest and they have to choose the best route, or they're tailing an NPC and the hours matter.
Keep in mind that while trails are not straight, diagonal movement isn't either. So in some ways you're already getting some inefficiency why time the party doesn't go in one of the six cardinal directions.
I have bounced back and forth using a 5 mile or 6 mile hex. Would love to see a map option to deal with the issues of hex scale near the poles.
I had a generated world map that I used a tool to render into Sinusoidal Projection. After a bunch of work in GIMP, I created an interrupting sinusoidal map, and applied hex grids to each segment. At the edges, you jump directly to the next segment, though I did my best to place the segment boundaries on the sea.
Suffice it to say, the geometry of a spherical world is too difficult to deal with otherwise and I doubt anyone will be able to make a singular program to handle all those steps.
Villages would typically be roughly 5 miles from other villages/towns and at least within 6 miles of a water source. So either hex size is appropriate. Walking speed is 100% irrelevant since realistic travel speeds have far more to do with terrain than how quick legs move
this only works if you are thinking of d&d like it's actually european medieval.... it's very much based on the old west and midwestern scale of towns. with the trappings of medieval fantasy
@@Grimmlocked Not really. Most DnD settings are based on pre-settled continents, not old westerns.
Though that does beget a campaign idea of modeling a setting around Jamestown or other colonial settlements where the players are in a remote environment with no access to reliable support/supplies and surrounded on all sides by potential threats.
that's how i framed my lost mine of Phandelver back in the day. @@Droid6689
There's a rule of thumb in land navigation that if you measured your walking speed in flat easily traversable terrain, while you're fresh; then every factor that's complicating your travel slows you by about10%. Heavily loaded? Tired? Uphill? Dark? You're walking through trees? Uneven ground? (Wind too, probably.) All roughly 10%. (Though truly difficult terrain like swamps, heavily brush-covered forest floor or piles of boulders would have a larger impact.)
To get that fidelity in modeling the daily marching distance, it would make sense if a "normal amount" of walking took you through roughly 10 tiles. (Or a low multiple of 10 tiles.) A quick google seems to suggest that up to 20 miles (32km) is about typical for a day of (backpacked) marching that doesn't wear the troops out. This would lead to at most a *cell size of 2 miles (3km).*
Also, those 3 miles distance to the horizon in perfectly flat terrain; that's not relevant very often. How often are you in perfectly _Kansas-flat_ terrain, with no obstructions all the way to the horizon? If you want to quote a fact about how far humans can see, then that should start with us defining *in which way* viewing distance would define a cell. The above implies that a cell is how far you can see _the terrain._
How far you can see the terrain would in a hexcrawl simply define how many hexes around you get revealed as you go. Setting that rule to "3 miles" would then make most sense.
I think a better type of vision distance might be the distance at which you can _reliably_ spot one person or a handful of people. That seems like a good definition for what being "in the same hex" would imply. (Although I don't have any argument if you think that being in the same hex and not seeing each other should be possible.) And it would apply to all relatively open terrain, even hills and with other occasional obstructions.
If at a certain distance you can spot someone only by luck and not reliably, then that should be reflected in that distance putting the two parties in separate hexes. And a perception check would be required to notice someone in an adjacent hex.
A bit of googling suggests that seeing a person _as a dot_ is possible from 2km (low contrast) to 3km=2miles (fair contrast) and another source claims up to 8km=5miles (which I think would then be full black-to-white contrast). But that's only _seeing_ them, which probably assumes you know where to look. _Noticing_ someone would more often than not happen at much shorter distances.
From that point of view (and the "fraction of 2 miles" requirement), we could make *hexes on the order of half a mile across.* Noticing someone from a quarter mile (400m) shouldn't be too difficult to assume it's a given (unless you're distracted or it's dark). And it would take a check to notice someone between the distances of "on a neighboring hex" and "2 miles"(=4 hexes), terrain permitting. (Which means you'd walk 40 hexes in a day, 6 hexes around you revealed, and noticing someone is possible 4 hexes away.)
On the other hand, it might make for a better scale if a *hex was 1 mile* (1.6km) across, with 20 hexes per day traversed (30 in an exhausting forced march, and 40 being the absolute daily limit), 3 hexes of terrain around you revealed, noticing a person or animal up to 2 hexes away being possible with a check.
Or hexes - as implied at the top - could be *2 miles* (3km) across, with 10 hexes per day traversed, noticing someone being possible only in a neighboring hex, and 2 hexes of terrain around you revealed.
Obviously, this is the *smallest scale* which governs interactions between groups. (Which makes it seem sensible to call it the *'A'* scale.) A map of this scale could only really cover the area for a single day of travel. That fact and the scale might be useful for when you're trying to locate or meet a person or creature. Let's for the sake of argument assume you want with the 1-mile hexes. (reminder: 20/30/40 traveled per day, 2 hexes spotting, 3 hexes terrain reveal).
For the next scale up (call that *'B'* scale), it would make then sense to have hexes that are a multiple of 5 larger; so that you can track travel distances in 0.4 (or 0.2 on an exhausting march) of those 'B' scale hexes. (That's your 5-mile=8km hexes; 4/6/8 'B' hexes traveled per day, terrain of 1 'B' scale hex revealed around you.) That last point makes this scale useful for exploring of an area that you have no map (or no detailed map) for.
The *'C'* scale could then be 4 'B' hexes, as that gives a nice round 20 mile=32km hex size. You'd travel about 1/1½/2 'C' hexes on a good day and keep track of distances in multiples of 0.10 hexes (or 0.05 on an exhausting march). The former fact seems to make this a good map for travel along known routes. This could be a map of a Kingdom (of the size of a larger European nation or a larger US state).
The *'D'* scale could then again be 5 'C' hexes for another nice round 100 mile=160km size. This could be an "Empire" map, where that Empire is of the size of an Australian state (700x700 miles, mathematically), Canadian province/territory (540x540 miles, mathematically) or if it encompasses a few US states (250x250 miles, mathematically) or modern European nations (240x240 miles, mathematically, though in reality varying wildly in size). And each of the 160km cells would be about the size of a medieval (central) European princedom. At this point the maps kind of loose their purpose for travel.
And then the *'E'* scale - if you went with each being 5 'D' hexes - would be a continent scale map with it's 500mi=800km hexes. 12.5 hexes from pole to equator for an earth-sized planet.
And finally the *'F'* scale - assuming each being 4 'E' hexes - I don't think would make sense for this to be a hex map. But if it was, then it would be a planet scale map with (for earth) 3 hexes from pole to equator, 6 hexes pole to pole and 12(.5) hexes equatorial circumference. But if you made this a hex map, then the planetary curvature would probably require inclusion of pentagons; or in other words, earth would pretty exactly be a soccer ball (60 faces).
In the other direction, you'd be dividing by /4/4/4/4/4 (5 divisions by 4) or by /6/6/6/5 (4-ish divisions by 6) to arrive at the DnD-typical 5-foot hex. If you started labeling those scales from 'Z' backwards, it would put a hex battle map at the 'V' or 'W' scale.
Pictured: 10,000 square kilometers of swamp. :P
Scale that's approx the size of earth though would be 500 miles per hex on 50x50 (reasonably sized hex map). That's 625 million square km, where earth ~500
Memory is still an issue. 200 million faces is quite unwieldy if you want a mile scale map if a planet. Not impossible but unwieldy.
The horizon distance thing is basically irrelevant for most real terrain that isn't ocean. I can see Mount Hood from my street despite it being easily 50 miles away. Moreover, I can also see a lot of the terrain between here and there because it gain elevation faster than the horizon drop off. At the same time, if I go into the nearby trails, I can see just 100 meters at most because it's all blocked by trees, and I'm many directions that drops to about 10 meters.
So an earth sized map would have about 100 hexes at the equator roughly? trying to figure all this math out for my own world tbh
Yeah, if you want to go with 250 mile hexes that could work. Again, because of the curvature of a planet it will get skewed as you get further from the equator--or maybe in this case it'll be a bit too small at the equator (every two hexes might be 575 or so miles because of the hex staggering if you have columns lining up) but then at the 10-20 degrees latitude it will be right, then the scale gets further and further off as you approach the poles.
Allow me to offer up an idea that may or may not be interesting or helpful: if this is a fantasy world, it doesn't HAVE to be a globe. Make a (for lack of a better term) Flat Earth that is floating on the back of four elephants standing on the back of a giant turtle or whatever you like. Then you don't have to account for curvature. The odds of any players even ever getting out to that scale are remote to begin with, but also imagine if they DO reach the literal edge of the world and just see a gargantuan waterfall draining off into a star-studded abyss.
Which program is this?
Worldographer: worldographer.com/
Great video! Thanks.
Glad you liked it!