Thanks for the feedback from yesterday’s posts. Today I’m going to concentrate on applying the different placements of Davania and the resulting latitudes to the 3D model.
Unfortunately, it turns out that this is not as easy as I would have liked. Why? Because of the polar openings.
The size of the Hollow World is reasonably fixed. Official sources give a circumference of 11,908 miles, and the full extent of official maps fits quite neatly into this space. The only question for me is how much land to fold into the polar openings; recently I have been thinking that the majority of land shown on the Hollow World poster map should not fold into the openings. Official maps seem to support this.
The problem is, if there is a large difference in size between the inner and outer worlds, the polar openings get smaller and smaller, and eventually disappear. This can be fixed by lowering the latitude of the beginning of the polar lip, but that of course means folding even more land into the openings.
The problem lies in the amount of space the hex mapped areas take up on the Outer World.
Let’s take a look at the placements I proposed yesterday, and see how they do.
Count the hexes between the two horizontal graticule lines here:
I count roughly 12.75 hexes from line to line; this represents 10º of latitude. At 72 miles per hex, we can do a simple calculation to find out how much land 1º of latitude on the Outer World takes up: 12.75 x 72 / 10. 12.75 x 72 = 918. 918 / 10 = 91.8, so that’s 91.8 miles per 1 degree of latitude.
In comparison, earth has roughly 69 miles per degree. So this Mystara is going to be significantly larger than earth. How large? Simply multiply by 360 to get the circumference of the spheroid: 33,048 miles, compared to earth’s 24,860 miles.
Some of you may at this point think, “Wait a minute, isn’t earth an ellipsoid, not a sphere?” Yes, it is, and the circumference I just quoted is the polar circumference (since we’re measuring latitudes). The equatorial circumference is about 24,902 miles. So yes, there’s a difference of around 42 miles — a pretty minor difference, and one that’s not hugely relevant to this discussion. I will likely define Mystara as an ellipsoid later in this project, when I create a coordinate system, complete with its own reference ellipsoid. But note that this minor equatorial increase in circumference is not really enough to help us solve the problems at hand, so let’s ignore it for now.
Getting back to Placement 1, what would this look like on our model, with the polar lip starting at 66º in both the Hollow and Outer worlds?
Oh dear. So there would be no polar openings at all.
In order to fix this, we need to do one or all of the following:
- Decrease the size of the Outer World.
- Increase the size of the Hollow World.
- Move back the lips of the polar openings in one or both worlds.
Happily, we have already done this with Placement 2: by rescaling the latitudes, I shrunk the dimensions of the Outer World. But is it enough? Let’s count the hexes and see.
I count roughly 12.25 hexes. 12.25 x 72 = 882. 882 / 10 x 360 = 31, 752 miles circumference. Radius 5,053 miles, diameter 10,107 miles.
It still seems rather big, but let’s mock it up anyway, just to be sure:
Still no good.
Talk about hitting a brick wall!
I don’t like option 3 (bringing back the polar lips to lower latitudes), which leaves us with just the first two options: further shrink the Outer World, and enlarge the Hollow World. Maybe we can try and make things meet halfway.
We can probably squeeze the Outer World a bit more. These circumference numbers in the thirty thousands were unexpected, because previous fan estimates have been in the twenty thousands, with a Mystara just a little bit bigger than Earth. The true size of the world doesn’t really matter, as long as everything fits, so we can play with this further.
It actually also deals with an issue I had, which is that at 30ºN, the Sea of Dread coast with Karameikos and Thyatis seems awfully tropical. However, shifting latitudes will also result in northern Alphatia and northern Norwold being at a much higher latitude. Perhaps this fits, too, though.
But let’s start with the easier part of this next attempt.
The Hollow World
Back in 2012, there was a great discussion at The Piazza about World Dimensions. We didn’t come to any firm conclusions, due to all of the issues I’ve been working through on this project. But there was a lot of discussion of the Hollow World, which we can draw from here.
Here’s the composite I came up with to measure the extents of the Hollow World’s landmasses:
A couple of interesting things to note: the latitudes near the equator are larger north-south than the extremes near the poles; and the map shows 90ºN and S, despite the lack of an actual pole.
Regardless of the marked latitudes, it seems clear from the hex map that all of this terrain is supposed to be on a constant north-south scale. In other words, the closer together lines from 60º outwards can be safely ignored. I’m not at all worried about having to reassign latitudes, either, as it may be a necessary evil in order to get the world working right.
A little hex counting will reveal 62.5 hexes (at 40 miles per hex) from the equator to “90ºN” and 62 from the equator to “60ºS”. The north shows more water, so let’s ignore that and call it 124 hexes. 124 x 40 = 4,960 miles. Or we could think of it as 125 hexes for a nice even 5,000 miles.
At this point in the 2012 map I went on to extrapolate the circumference, assuming these figures stretched from imaginary pole to pole; the “extra” lands could then be folded into the actual polar openings. (Given the above figures, this would be 9,920 or 10,000 miles.)
But that’s not what I’m thinking this time. First, the compressed latitudes are a big clue that these lands are not supposed to extend to the imaginary poles, and therefore are not supposed to fall into the polar openings — at least not very much. Further, my reproduction of the Hollow World map, which “fixed” these squashed latitudes, turning them into regular latitudes, was probably a mistake. I now believe that these regions should be left unstretched.
The biggest point is that I think these lands should largely fit into the unwarped space between the polar lips, i.e. between 66ºN and 66ºS — or at least a smaller area.
We can calculate an ideal area by extrapolating the circumference in the same way we did with the Outer World: by counting hexes and finding out the number of miles per degree. If we do this for the equatorial area, I think we will reach a larger figure than we did before.
I count roughly 8 hexes, so: 8 x 40 = 320. 320 / 10 * 360 = 11,520 miles. (This is also what Hugin came up with in the 2012 thread.)
Unfortunately, this is not helping: the official measurement was 11,908 miles, and our estimate has actually ended up smaller. If that’s the case, we’d be better to go with the official number, because making the Hollow World smaller at this point is simply not an option.
So we’re left with shrinking the Outer World. I’m beginning to feel increasingly desperate… Are we going to be able to make this work at all? Keeping Davania in the same Champions of Mystara-based location, I’ve squashed the latitudes as much as I dare to.
Lands past the red line start to fold into the polar openings, but until around 70º it’s not really obvious that this is starting to happen. Nevertheless, Frosthaven will be squarely within the opening.
Ambur, Ar and Frisland now fall between 60 and 63ºN or so, and Alpha is at about 60ºN too. Farend looks to be almost at 65ºN. Take a close look at the map to see all the other latitudes.
So how does this measure up? Time for some more hex counting:
I count about 10.75 hexes. 10.75 x 72 = 774. 774 / 10 x 360 = 27,864 miles circumference. Better, but is it going to work?
We do at least have polar openings this time, but I don’t know if I’d call this working.
And yet I can’t see shrinking the Outer World any more than this — we’re already going into dangerous territory by shrinking it this much.
What other options could there be?
Should we move the equator north to the PWA2 location? I somehow doubt that would allow us to shrink the world much more, if at all, because southern Davania can’t all be shunted into the polar openings.
But what else is there to do?
Should we enlarge the Hollow World? We may be able to squeeze another thousand miles or two in there, in order to open up the polar openings a bit. That may be the best bet — and I can stretch the northern and southern areas to compensate a little, or rather leave them as they are on my reprojected Hollow World map.
Any thoughts on all of this?