Distance between flat sides: 8 miles
Distance between opposing points: 9.24 miles
Distance between adjacent points (along a single flat side): 4.62 miles
In a 1 hex = 24 (or 48, or 72, etc.) mile scale, just multiply by 3 (or 6, or 9, etc.).
Hex maps have several benefits, including the ability to assign each hex a single terrain type without making the map look blocky, and the possibility of accurately depicting varying distances. At small scales, hex maps very accurately portray the shape and relative positions of terrain.
The greater difficulty comes with larger-scale maps. If the scale truly remains constant throughout, then relative direction is distorted outward the farther you go from the initial reference point. This can cause some trouble when trying to line one map up with another, but hex maps still are remarkably useful for campaigning, and they make more interesting looking maps than does graph paper
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One of the great things about hex maps is that they provide distances in various directions. This can all be worked out geometrically, but here's the basics (using a 1 hex = 8 miles example, and I trust that someone can correct me if I make a math error):
Distance between flat sides: 8 miles
Distance between opposing points: 9.24 miles
Distance between adjacent points (along a single flat side): 4.62 miles
In a 1 hex = 24 (or 48, or 72, etc.) mile scale, just multiply by 3 (or 6, or 9, etc.).
Hex maps have several benefits, including the ability to assign each hex a single terrain type without making the map look blocky, and the possibility of accurately depicting varying distances. At small scales, hex maps very accurately portray the shape and relative positions of terrain.
The greater difficulty comes with larger-scale maps. If the scale truly remains constant throughout, then relative direction is distorted outward the farther you go from the initial reference point. This can cause some trouble when trying to line one map up with another, but hex maps still are remarkably useful for campaigning, and they make more interesting looking maps than does graph paper
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Thanks! This is exactly what I worked out once I knew what the 8 and 24 represented. I can see the advantage from a DMs point of view to the hex maps, but I still like the more traditional style just to look at and get an idea of what's what. Sort of like the difference between looking at the pictures in the MM vs reading the stat blocks.
The greater difficulty comes with larger-scale maps. If the scale truly remains constant throughout, then relative direction is distorted outward the farther you go from the initial reference point. This can cause some trouble when trying to line one map up with another, but hex maps still are remarkably useful for campaigning, and they make more interesting looking maps than does graph paper
Um... can you explain this in a bit more detail? I don't quite understand how such distortion should occur. If the hexes are perfect hexagons, and the 1:3 ratio is maintained between the scales (i.e. one 24 mi hex = three 8 mi hexes), why would there be distortion?
Um... can you explain this in a bit more detail? I don't quite understand how such distortion should occur. If the hexes are perfect hexagons, and the 1:3 ratio is maintained between the scales (i.e. one 24 mi hex = three 8 mi hexes), why would there be distortion?
Hi, Thorf!
I'm betting that you can come up with a lot more examples than I can of different inconsistencies among the various maps TSR produced... this is one of many factors contributing to these disagreements.
The trouble comes not in trying to convert a single map from large to small scale or vice versa: you are correct that your attention to ratio solves this. The problem exists when you try to combine information from different maps with different reference points: you don't think the Master of Hule allows the use of maps showing Sundsvall as the center of the World, do you? So what happens when the maps in VotPA conflict with those in DotE, for instance? The conversions do not distort, but they carry with them the distortions of the original maps.
To illustrate the distorting effect of maps, compare the hex map of Northern Iciria (from the HW box) with the HW world map (from the same box and the Rules Cycopedia):
The hills north of the inlet to the Bay of Tlapac (Northwest Iciria--that is, top right) are directly north of the Island of Haraga (Traldar) on the hex map.
On the world map, if you follow the 60 degree W. HW meridian south from these hills, it clearly shows that the hills are farther west than is the Island of Haraga.
On the other side of the hex map, the bits of the Hagvar Islands we see in the northeast corner (top left) appear directly north of the Desert of Boglucubul.
On the world map, following the 60 degre E. HW line northward from the Desert of Boglucubul shows that the the islands are farther east than is the desert.
If you outline the area of the hex map on the world map, it is rectangular, as both maps are centered on the Central Meridian (they both have the same reference point, so there is no relative distortion).
If, however, you were to attempt to map Aerical (the continent in the northeastern portion of the HW world map), what reference point would you use?
If you stick with the Central Meridian as the reference point, the map can be joined together with any other to form a continuous map. However, the top left corner of the map of Aerical would be utterly empty (assuming that you want the map to stop at 180 degrees HW, for continuity between the hemispheres). Aerical would appear the same size and shape that it does in the world map, but this is a distortion. The mountains along the 150 degrees W. HW meridian would not stretch north/south (as they must, if they follow the meridian), but rather would seem to angle up from southeast to the northwest (bottom left to top right).
If you re-center the Aerical map, probably along the 150 degrees W. HW line, you will still have some distortion around the edges, but it will represent Aerical more accurately. It will not, however, match up correctly with the Iciria map, as they are distorted differently.
This is more readily demonstrated with the increased curvature of the HW, but, man, it's confusing having west be east, but only some of the time ;)
As for how this impacts the outer world: the most significant distortions lie at the edges of maps and in higher latitudes. This helps explain why some of the most frustrating inconsistencies in mapping Mystara come in Esterhold, Norwold, and the Northern Wildlands. On the other hand, it's easy enough to just dismiss this as the vagaries of the unknown wilderness.
It's also worth noting that hex maps are not at all unique in this distortion--it's something cartographers always struggle with, and which has been discussed before both here and on the MML, as I recall.
At the scales normally used for DMing, all this is purely academic, and probably not worth worrying too much about. TSR built plenty of vagaries into this world without getting to concerned about the hexes
I'm betting that you can come up with a lot more examples than I can of different inconsistencies among the various maps TSR produced... this is one of many factors contributing to these disagreements.
The trouble comes not in trying to convert a single map from large to small scale or vice versa: you are correct that your attention to ratio solves this. The problem exists when you try to combine information from different maps with different reference points: you don't think the Master of Hule allows the use of maps showing Sundsvall as the center of the World, do you? So what happens when the maps in VotPA conflict with those in DotE, for instance? The conversions do not distort, but they carry with them the distortions of the original maps.
Yes I see what you're getting at. The problem you're talking about is the same problem as real life cartographers have, of trying to map a 3D spherical surface onto a 2D flat map.
The hexes themselves don't cause the problem, since they're just an overlay anyway, but they don't help either, since they can't help but ignore the gradual distortion that should be present.
The simple answer of course is that Mystara's cartographers have mostly ignored this problem altogether. It's a complete headache, and to be frank I don't think most of us have the knowledge (or tools) to be able to work out how the distortion affects parts of the map.
Speaking from a personal point of view, I really don't have the motivation to deal with Mystara as a real globe, either. Working with all the various sources is hard enough as it is, without complicating things to such a degree that it would be impossible for me to continue. I'm not convinced that TSR worried about this, either.
To illustrate the distorting effect of maps, compare the hex map of Northern Iciria (from the HW box) with the HW world map (from the same box and the Rules Cycopedia):
I see exactly what you're getting at. Re-centring the map would indeed seem to depict the edge areas more accurately.
But again, most Mystaran cartographers have so far instead chosen to simply ignore this distortion and map things exactly as the Hollow World appears on the main reference map - including TSR.
As for how this impacts the outer world: the most significant distortions lie at the edges of maps and in higher latitudes. This helps explain why some of the most frustrating inconsistencies in mapping Mystara come in Esterhold, Norwold, and the Northern Wildlands. On the other hand, it's easy enough to just dismiss this as the vagaries of the unknown wilderness.
This doesn't explain the worst Norwold inconsistencies, because you don't need to go any further than the hex maps in their different scales to find massive differences there.
I'm not sure how the rest of the world is affected. I'm not sure I want to think about it too much.
It's also worth noting that hex maps are not at all unique in this distortion--it's something cartographers always struggle with, and which has been discussed before both here and on the MML, as I recall.
At the scales normally used for DMing, all this is purely academic, and probably not worth worrying too much about. TSR built plenty of vagaries into this world without getting to concerned about the hexes
I would be interested to hear if anyone has any ideas for practical strategies for dealing with distortion in the maps, actually. Programs that could help us, ways to change the perspective, etc., any hints would be very useful. However, that said, I really don't think that I'm going to be able to do anything better than simply ignore the distortion and keep mapping.
I'm not sure how the rest of the world is affected. I'm not sure I want to think about it too much.
I would be interested to hear if anyone has any ideas for practical strategies for dealing with distortion in the maps, actually. Programs that could help us, ways to change the perspective, etc., any hints would be very useful. However, that said, I really don't think that I'm going to be able to do anything better than simply ignore the distortion and keep mapping.
For what it's worth, I think you've come up with the perfect solution: don't worry about the distortion. You're doing a fantastic job with these maps as it is--keep up the great work. If anyone ever gets around to making more detailed maps of the other hollow world continents, the Peninsula of Vulcania or the Tangor Chain/Tangor Peninsula, these issues might bear consideration, but as it is, I think they are simply too complicated to deal with. The only case in which this would absolutely need to be addressed, I think, is if you (or someone) were to try to make a corollary of the Iciria maps from the HW box covering Aerical, Suridal, and Jomphur. Such maps would cover about the same area as the two Iciria maps (each map, at the equator, goes about a third of the way around the world), but it would pretty much need to be reconfigured in order to provide an accurate image. I'd say don't worry about it :P