Azeroth: A Small Problem

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So...I got bored this evening. I'd been messing around with the calculations for movement speed of a character for a couple days, since characters are rather insanely fast by real-world standard (sustained ~4.2 minute mile in plate gear over rough terrain). I got to looking at the size of the zones, and that lead to me wondering just how big this world we play in is. Well, being an physics/applied math focus, I simply couldn't resist trying to figure it out.

I first started with figuring out how big the world was, on estimate. I used the macro posted on WoWpedia to calculate my speed (it uses the GetUnitSpeed function, which returns the unit (in this case, the player) speed in yards per second). I then flew a route on a slight curve from Booty Bay to the northern coast of Tirisfal Glades, following roughly the route in the screenshot below:

I used this route because supposedly Northrend, or more precisely Icecrown Citadel, is at or near the northern pole of Azeroth (based on some of the information provided in the mission chain in WC3 where Illidan tries to nuke the place). I used some of the globe images of Azeroth from around the game world to estimate that the southern pole was roughly half the distance from the southern coast of the EK as ICC was from the northern coast. Flying the route took me 9 minutes 39 seconds, which at an the 31.57 yards per second reported by the macro (~65 MPH), is slightly over 10 miles. Estimating that his is roughly half the distance along a great circle of the planet (of which my route is roughly along, if the we assume that only the oceans have been distorted by the projection), gives an estimated pole-to-pole distance of 25 miles, or a 50 mile circumference. This boils down to an 8 mile radius.

Let me repeat that for you: EIGHT MILES. To put that in perspective, Earth is approximately 4000 miles in radius [Wikipedia:Earth], the moon is slightly over 1000[Wikipedia:Moon], and Phobos, one of the asteroid-like moons of Mars, is 7 miles in radius[Wikipedia:Phobos]. To put this another way, driving around the planet at average highway speed would take around 45 minutes, if you could drive directly. You could fly around the planet at average jetliner cruising speed in roughly 5.5 minutes. If a modern jetliner took off going east from the Khaz'Modan air port, it would fly over the airport again before it reached cruising altitude[].

Now, being the physics student I am, my next thought was gravity. Azeroth possesses roughly Earth standard gravity. Falling speed can't be measured by the macro (just returns 0%), but is faster than epic flying by a good amount. I did some rough testing in Stormwind by timing how long it took me to fly up to the flight roof (310% mount with Mount Up, so 451% speed), and I fell (including the ~1 second acceleration time) in roughly 60-70% of the time it took to fly up. That gives a terminal velocity of about 110 mph, pretty close to the 120 mph it is on Earth []. Based on this, I'm estimating similar gravity. Now, an object the size of Azeroth, possessing roughly the same density as Earth, would have a surface gravity of roughly 1/250000th of Earth's (~0.0000039 m/s^2). Since we're assuming a similar gravity, that means that mass of Azeroth must be approximately 250000 times that of Earth's. Earth has a mean density of 5.515 g/cm^3 [Wikipedia:Earth], or 5515 Kg/m^3. Azeroth therefore must have an average density of roughly 1.38 * 10^9 Kg/m^3. 1E9 Kg/m^3 is roughly the density of a white dwarf star [Wikipedia:Density]. Since Azeroth obviously doesn't have a surface temperature of a few thousand Kelvin, the density must not be uniform.

My next prediction would be that Azeroth is composed of a low density by ridiculously high tensile strength shell wrapped around an extremely dense core, somewhat akin to a very very small Dyson Sphere (except that the occupants life on outside instead of the inside). Assuming that ~90% of the mass of the 'planet' is contained within the core, that gives the core a mass of roughly 8.1E17 Kg. Of this core is assumed to be a black hole (density ~4E17 Kg/m^3 [Wikipedia:Density]), the black hole would be roughly 1.5 meters across.

Lastly, we look at the atmosphere. Earth's atmosphere has a mass of ~5E18 Kg [Wikipedia:Atmosphere of Earth]. Considering this is more massive than the entirety of Azeroth, even at our predicted density, Azeroth's must be less massive. The only way I can see this being the case is if the atmosphere is cut off and held down by some sort of ceiling. Considering there IS a ceiling in-game (roughly a quarter-mile up if you're in Stormwind), I'll use that. We'll estimate that over the entirety of the planet the average ceiling is about a third of a mile above the ground. This gives a shell of volume 1.04E12 m^3. Air at sea level has a density of roughly 1.29 Kg/m^3, giving us a mass of ~1.35E12 Kg. Given that that is roughly 0.00015% of the estimated mass of Azeroth, I'm satisfied that the mass can be attributed to the 'shell' portion of the mass (which was estimated at 10% of the total mass of the planet).

I'm somewhat concerned about Roche limits and the resulting tidal forces, which would be more than 5 orders of magnitude more intense on a human-sized object on Azeroth as they are on Earth, but I'll shrug that one off. After all, it is a fantasy game... =Þ
Wow. That's a pretty freaking small planet. I don't even want to think of the population dynamics on a planet that has a circumference about as long as my weekly commute. I hope blizz knows that their world is pretty small......wait a minute.....if it's that small, I could see it being possible to create a life-sized version of Azeroth somewhere. Blizzard theme-park anyone? :P

'and here we have the barrens.' *three mile drive later* 'and now heres thousand needles!'
It's previously been discussed that the game world you can traverse in World of Warcraft has been compressed both in time and space, for player convenience. The compression ratio is variable and can differ almost infinitely at any point.
01/11/2011 9:28 PMPosted by Saarzul
It's previously been discussed that the game world you can traverse in World of Warcraft has been compressed both in time and space, for player convenience. The compression ratio is variable and can differ almost infinitely at any point.

Aye, in lore Stormwind has a population of at least 200,000 and the Barrens takes a week to navigate.

Imagine the !!*#*ing if going from Orgrimmar to Thunderbluff took a fortnight.
Aye, I know it's been compressed. Still thought it was interesting just how tiny the world turned out to be, especially with how much moaning there's been over the years as to how long it takes to get from place to place and how annoyingly large the world is. Besides, I was bored.

The idea of a scale Azerothian replica/theme park intrigues me...
It's a small world after all.
Although I lost track of what you were saying midway through the post, this is some truly awesome stuff. :)
I do have to say, without really knowing math very well, if its all correct, thats pretty damn hilarious.
Make an Azeroth condominium complex and have sides split for the horde and alliance. Watch the #$%! people will do to each other

I'm just teasing. I love this post <3
My roommate posted the exact same thing on my facebook wall as I was writing this, Cheesebread >.>

Then again, I'm not at all unhappy about being called a nerd. I am a physics major, after all. Can't get a lot nerdier than that (except, of course, the roommate that posted said message is a comp-sci major...)
Actually to be technical he's a fully-fledged computer scientist now....
A wizard did it.

That is all.
You do realize the in-game world is not to scale, right?
I think it was about the size of Rhode Island.

Azeroth, assuming the 8 mile radius, would have a surface area (including the oceans) of 804 sq miles. Rhode Island has a total area (including bodies of water) of 1214 sq miles. [Wikipedia:Rhode Island], so Azeroth is about 2/3rds the size, and that's including all that ocean space. Assuming Azeroth is roughly 1/3 land, that only gives about 275 sq miles.

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