Measuring Up the Oerth | by Gary Holian | From the Oerth Journal Vol.1 #4 August 10, 1996; the Council of Greyhawk


So, your campaign has criss-crossed the Flanaess a dozen times and you've defeated the plots of archmages, high-priests, and bandit kings alike. What's left to do, what's left to explore? The Outer Planes await, of course, as do the reaches of Greyhawk's solar system, or perhaps that alternate Prime that seems to have persistent designs on the World of Greyhawk tickles your fancy. Are they the next logical step? Ready or not, here we come? No, of course not. There is no need to leave the Oerth if you don't really find it necessary. There is a whole world left to discover right in your own backyard, of which but a fraction has scarcely been catalogued.

In his first The Good Oerth column entitled "Oerth From the Ground Up," Roger Moore addressed himself to this very endeavour. Untold adventures lie beyond the shores and expanses of Eastern Oerik and all a DM need do is let his imagination run wild. But how to begin? With a map, of course! After all, the most important issue that must be decided by an enterprising DM who wishes to create an extra-Flannish campaign is how large the Oerth is and where all of its other lands and continents lie. This article seeks to address the issue of creating this initial map so that it remains consistent with known facts about the world.

In these matters, we are not completely left in the dark. Let me begin by reiterating some basic facts about the planet, so that we can double check our assumptions and make sure we're all in agreement:

Polar circum. of Oerth: 25200.00 miles (WGCG p. 18)
Equat. circum. of Oerth: 25200.00 miles (by assumption)

It is easiest to assume that the Oerth is nearly a perfect sphere, since such an assumption reduces the complexity of future calculations and as Roger stated, it is in keeping with the numerous instances of perfection evident in the planet and its environs. Point of fact, the Earth's polar circumference and equatorial circumference only differ by order 1%. The reason our earth is an oblate spheroid is not an accident, but is strongly related to the fact that its spinning on its own axis, generating forces that tend to pull it out at the equator and squash it at the poles. Assuming Oerth rotates on its own axis as well, the greater gods must be exerting a massive amount of energy in order to prevent it from deforming from a perfect sphere...enough to make the Invoked Devastation look like a campfire by comparison. Nonetheless, the "perfect sphere" assumption is a good one.

From those numbers we know: 

Diameter of the Oerth: 8021.41 miles (25200 miles/pi)
Radius of Oerth: 4010.70 miles (1/2 diameter)
Surf. area of Oerth: 202,139,510 sq.miles (pi*diam.2)

The east-to-west distance traveled per degree of longitude along the equator is: 70 miles per degree (25200 miles/360 degrees). This number falls trigonometrically (as the sine of residual latitude to be exact) as one travels along a latitude line closer to the poles where it is unambiguously 0 miles per degree since all longitude lines converge at the pole. The north-south distance traveled per degree of latitude is similarly: 70 miles per degree (25200 miles/360 degrees) as is stated in the Glossography.

If we can agree on these basic numbers, then we find ourselves confronted with the problem laid out by Roger Moore in his article. Namely, that if we assume that the scale of Darlene's Flanaess map (30 miles/hex) applies at the equator and of course, by necessity, that the scale must therefore drop trigonometrically from the equator to the poles, we find that the entire map of the Flanaess is out of scale. All of it is smaller than we believe from 25 miles/hex in the vicinity of the City of Greyhawk to almost 15 miles/hex on the Thillonrian Peninsula. Unfortunately, as Roger pointed out, this creates significant changes to the scale of existing maps of the Flanaess, which become rather extreme as one approaches the northern verges of the continent.

As I stated, even in the vicinity of the City of Greyhawk, the scale falls to under 25 miles/hex (a drop of over 18%.) That creates significant distortion to local, more deatiled maps of the area already in existence. It also seriously impacts the maps in the Marklands and Iuz the Evil supplements. Also from a strictly personal point of view, cutting the Thillonrian Peninsula in half, making the Land of Black Ice more like a patch of discolored snow, and giving the Rovers of the Barrens a whole lot less to rove, seem like awful prospects. To some degree it is unavoidable, but it need not be so extreme, nor was it intended to be so. Let's try to preserve some of the awe and grandeur of the far north by offering a potential solution to the problem.

An extremely viable option, then, is to "peg" the scale of the Flanaess not at the equator (itself an arbitrary decision), but at a point at which it makes most sense to do so. I don't believe the scale of 30 miles/hex at the equator was intended by the designers, particularly since none of those lands even appear on Darlene's map (to which the scale was applied in the first place.) Instead, I suggest that one fix the 30 miles/hex scale at a point further north in the Flanaess. My personal suggestion (from which forthcoming calculations will derive) is that of the 35 N parallel. Fortuitously, this is almost exactly along the same line as the Free City of Greyhawk and it falls almost exactly in the center of the Flanaess, allowing the largest possible area to be within a few percent of true scale (particularly those areas which have already been extensively developed and mapped.) Then, we allow the distortions to propagate north and south of this line to determine the scale of all the other latitude zones. By setting the 30 miles/hex line at 35 N, a great deal of Darlene's map ends up being relatively undistorted, and the distortions propagate away from this line to the north and the south in both directions, being more or less balanced across the sub-continent. This contrasts with the initial methodology, in which all the resulting distortions propagated from the equator northwards, leaving the whole northern hemisphere in "negative distortion", meaning that all distances are smaller than was assumed. Why not choose 40 N or 45 N and increase the degree to which the Northern Flanaess that is in scale? That is also a possibility, but it does not come without a price. There is some give with this take. The further north one brings the 30 miles/hex line, the greater the equatorial scale becomes. You sacrifice more and more territory in which to add oceans, continents, etc. 35 N strikes a good balance, as well as being bolstered by historical reasons, since after all, the Savant-Sage, a resident of Greyhawk and the Campaign Guide's author, probably copied the map from the Free City's Cartographers Guild who no doubt drew it to local scale.

Now, one might ask, why correct at all? Why not assume that the scale is constant everywhere in the Flanaess (30 miles/hex) and simply let the lines of longitude adjust to describe the extent of Oerik? Under that view, the maps (Darlene's and p 18's) are simply a kind of distortion-corrected representation of Oerik. Now, if one's campaign was centered in the Flanaess and never expected to explore beyond those bounds, then fine, this is a viable option. However, the premise of this piece is that of a person who wishes to develop an Oerth campaign, including lands yet to be created and explored. In that light, the reason we can't assume constant scale is actually aesthetic and practical. If that were the case, then the top of the Oerik map would represent well over 200 degrees in longitude! Ack! That would mean that almost two-thirds of the northern hemisphere (at 60 N) would already be represented on the map...with not much room for anything else, eh? Not to mention the fact that we know the Solnor is at least three thousand miles wide, adding further to the space consumed by the know world. Oerik becomes more distorted (on a global scale) than we could possibly imagine. Further, the number of longitude lines represented by the Oerik map would be a function of latitude. In fact, they would no longer be lines at all, but curves. Not only would the creation of such a map be an odious task, but it tends to defeat the purpose of this treatise, namely to create the room needed to generate the other three continents, islands, and vast oceans of the Oerth.

So, taking 30 miles/hex as the true east-west scale at 35 N allows us to calculate the east-west scale as a function of latitude for the globe. More importantly, it gives us the equatorial scale, which will help us to calculate the width of the Oerik map on p.18 of the Glossography in degrees of longitude. Since 30 miles/hex was "pegged" at 35 N, then the equatorial scale is simply:

(30 miles/hex) / (sin(90-35)) = 36.62 miles/hex\

All the latitudinal scales can be easily calculated from this equatorial reference number of 36.62 miles/hex, as Roger did for an equatorial scale of 30 miles/hex, and as I summarized for every five degrees in the table below. Notice that the vast majority of the Flanaess (between 25 N-45 N) remains within 10% of the observed scale of 30 miles/hex, now centered around the latitude of the City of Greyhawk. That keeps most of the local, smaller-scale maps pretty decent and close to true. It also has the added benefit of increasing the size of those largely unknown, but already mapped lands to the south of Oerik and Hepmonaland making them even more ripe for development.

THE EAST-WEST SCALE IN THE FLANAESS AS A FUNCTION OF LATITUDE

LAT Appar. E-W Scale Actual E-W Scale Features/Locations
90 N 30 0.00 North Pole
85 N 30  3.19
80 N 30 6.36
75 N 30 9.48
70 N 30  12.53
65 N 30 15.48
60 N 30 18.31 Northern verges of Oerik map.
55 N 30  21.01 Blackmoor, Land of Black Ice, N. Thillonrian
50 N 30 23.54 Wolf/Tiger Nomads, Rovers, Suel Barbarians
45 N 30 25.90 Ekbir, Dorakaa, Wintershiven, Pale, Ratik
40 N 30  28.06 Chendl, Shield Lands, Urnst, N. Province
35 N 30 30.00 Veluna, Greyhawk, Rel Mord, Sea Barons
30 N 30 31.71 Niole Dra, Highport, S. Province, Rel Astra
25 N 30  33.19 Yeomanry, Sunndi, Spindrift Isles, Lendore
20 N  30 34.41 Hellfurnaces, Tilvanot Penin., Lordship Isles
15 N 30 35.38 Sea of Dust, Amedio Jungle, N. Hepmonaland
10 N 30  36.07 Densac Gulf, Hepmonaland
5 N 30 36.48
0 30 36.62 Equator
5 S 30 36.48

So, now that we know the equatorial scale of the Flanaess as a result of our correction (36.62 miles/hex), how wide is the Oerik map on page 18 of the Glossography? Unfortunately, it is not possible to use the known N-S distance from 0 to 60 N (4200 miles), in order to accurately estimate the E-W distance across the map of Oerik. Curved surfaces prove to be more problematic, and one is bound to get a significant underestimate of the distance. So, we need to use another source for the east-west distance in order to estimate the east-west distance of the Oerik map. The most obvious, and fortuitously easy source to use is the ready-made colorful Flanaess map by Darlene that we all have sprawled across our walls which is simply an inset of the map on p18. (By the way, this methodology has the added benefit of making whatever estimates we come up with inherently consistent with Darlene's map which in the end is what we want.) So, I physically measured the Flanaess map (keeping in mind the inset on page 18) along the 35 N parallel, and came up with the following figures:

1) Width (inches): 41.60 inches (remember to ignore the overlap)
2) Hexes/inch: 3.12 hex/inch (also determined by measurement)

Therefore,

3) Width (in hexes): 1 * 2 = 129.79 hexes

So, the inset map of the Flanaess is 41.60 inches or 129.8 hexes wide. At a scale of 30 miles/hex along the 35 N parallel, that's a distance of 3893.76 miles (almost 4 thousand miles from the Sea Barons to the lands west of Ull!) That's important to know, but we want the width of the whole Oerik map, not just the inset. So, next I photocopied the map on page 18 and blew it up to 8.5 by 11 inches wide in order to make it easier to measure accurately.

Measuring carefully (east to west), I discovered that the larger map that includes the rest of Oerik was 1.68 times as wide as the inset map of the Flanaess (you can argue proportionality of distances between spans of identical curvature). That result, lets us make the following estimates for the whole map of Oerik:

Width (in hexes): 1.68 * 129.79 hexes = 218.05 hexes
At 35 N, the map of Oerik is therefore its scale times its length:
30.00 miles/hex * 218.05 hexes = 6541.50 miles, wide.

However, it is more important for us to know how wide it is at the equator (in order to get a correct value for the longitudinal extent of Oerik), so we need to scale up to 36.62 miles/hex:

At 0 (the equator), the map of Oerik is therefore:
36.62 miles/hex * 218.05 hexes = 7984.99 miles, wide

That is a considerable distance at the equator, equivalent to:

7984.99 miles / (70 miles/degree) = 114.07 degrees of longitude

So, the entire map of Oerik covers about 115 degrees of longitude (115 of 360 degrees!) and over 60 degrees in latitude. However, not all of it is 7985 miles wide like it is at the equator. As we noted above, the map is 6541.5 miles wide at 35 N. The following table shows how the width of the Oerik map varies as a function of latitude over the map on p.18:

LAT      Actual Width
----------------------
60 N     3992.50 miles
55 N     4580.00 miles
50 N     5132.65 miles
45 N     5646.24 miles
40 N     6116.86 miles
35 N     6541.50 miles
30 N     6915.20 miles
25 N     7236.86 miles
20 N     7503.44 miles
15 N     7712.91 miles
10 N     7863.68 miles
5 N       7954.60 miles
0 N       7984.99 miles

So, since the Oerik map covers a little over 60 degrees in latitude and nearly 115 in longitude, we can go ahead and determine how much area it covers.

Measuring Surface Areas on a Perfect Sphere: The formula which estimates these areas (for quasi-rectangular areas) is actually quite simple:

Area= 2*pi*[sin(lattop)-sin(latbot)]*[LW/360]*radius-squared
lattop is the highest latitude line bounding the area. latbot is the lowest latitude line bounding the area. LW is the longitudinal width, ranging between 0 and 360. The radius of Oerth is the relevant quantity for the last term.

(Note: these values for latitude are in "North" degrees, so don't forget that latitudes to the south of the equator are negative, ie. they run from 0 to -90.)
As a first example (and a quick check), let's use the formula to calculate the surface area of Oerth once again:

The lattop is 90 degrees, of course. Similarly, the latbot is -90 degrees. The longitudinal width is a full 360 degrees. The radius of the Oerth squared is: 16,085,714.49 sq. miles.
Area = 2*pi*[sin(90)-sin(-90)]*[360/360]*16,085,714.49 sq. miles
Answer = 202,139,050 sq. miles. To within rounding error, that is exactly the same result as we had before.

Now, for a more challenging example, the area of the Oerik map on page 18:

The lattop is about 62.0 degrees. (est.) The latbot is about -2.0 degrees. (est.) The longitdinal width is about 115 degrees (as we calc'd before) The radius of the Oerth squared is 16,085,714.49 sq. miles.
Area = 2*pi*[sin(62)-sin(-2)]*[115/360]*16,085,714.49 sq. miles
Answer = 29,633,701.31 sq. miles.

That means our infamous map of Oerik is showing us about 14.66% (29,633,701/202,139,049) of the globe! That's about one seventh of the planet, with six-sevenths to go that are totally unmapped and unexplored! (Alright, with the possible exception of Aquaria).

(FYI, the area from 62 N to 90 N above the Oerik map (across the same width in longitude) is: 3,779,165 sq. miles. Though half as "tall" in degrees, it is only a tenth the size. There is very little else of any significant size that can lie north of Oerik, save perhaps islands and a polar cap, so we must look south, east, and west for our three other mysterious continents.)

So, now that we know more about the Oerth you know, let's tell you a little about the Oerth you don't:
About 85% of the Oerth is unrepresented on the Oerik map of p18. It comprises the entire Southern Hemisphere of the planet, as well as 245 degrees of longitude (over-two thirds) of the area in the Northern Hemisphere under 60 N, and the entire northern polar cap above 60 N. Oerik probably extends some more distance west than is revealed on the map and the Solnor Ocean adds 3000 miles between the Flanaess and its nearest eastern neighbor, so that extends the known borders somewhat farther. As I said before, it would be impossible to fit a sizable continent to the north of Oerik, so we must look east, west, and south for our other three contenders. It seems likely that Hepmonaland is one such place, even if it's northern verges only reveal little about its true vastness. Aquaria (or whatever is may called by the natives) lies beyond the Solnor, which is surely one of the four great oceans. Where else then, can the fourth continent lie but far to the West, guarded by lands as mysterious in Oerik than could ever be found there.

There you have it. Draw a map 360 degrees wide and 180 tall, then place the Oerik map between the equator and 60 N, allowing it 115 degrees in width. The rest of the Oerth is for you to create as you wish, giving you a complete and consistent planet ripe for development.


built by unclefester | sternzwischen | updated 14-05-29 23:15:23