Azeroth: A Small Problem

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eh bashiok won't show up, the cm's have more pressing matters to attend to


Would be really interesting to have the exact values on those figures...
I run a 4 minute mile. It's not THAT big of a stretch.
01/12/2011 3:46 PMPosted by Tuky
I run a 4 minute mile. It's not THAT big of a stretch.

To use a possibly over-used stereotype not many 'gamers' can do that. I know i sure as hell can't. Also when you run a four minute mile im guessing youre not carrying 5 bags full of random crap as well as wearing slightly uncomfortable armor and various metallic weapons :P
You have to realize that the size of the game is not equal to the size of the actual world.

How many times do I have to re-iterate, I know the game world is a massively compressed version of the actual 'Azeroth' of lore. The point of this thread wasn't to point out that the game world was inconsistent with lore, it was to show just how small this the planet would be if the game world was accurate. It was just a fun little exercise in math, which is something I enjoy.
Did you happen to look at the sizes of any mountains? (hyjal, for example? Given a measly 8 mile radius, the size of hyjal and the proportion of the mass that must be contained in it would probably send Azeroth off axis really fast. Also, doesn't deepholm mean that a pretty considerable portion of azeroth is hollow? Being in deepholm should be squashing anyone who goes there immediately.
01/11/2011 7:59 PMPosted by Daelyn
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

You have way too much free time on your hands.
While fascinating, it's like asking where all the toilets are or where do people actually go to bed at night.

I think it'd be equally fascinating to calculate how much bodily refuse is piling up in cities due to the lack of said toilets.

01/12/2011 11:31 PMPosted by Ziarin
While fascinating, it's like asking where all the toilets are or where do people actually go to bed at night.

I think it'd be equally fascinating to calculate how much bodily refuse is piling up in cities due to the lack of said toilets.

What do you think fills the canals of Stormwind? What do you think all those canal crabs eat? Same thing as real world crabs...poop.

Ironforge obviously burns theirs in the lava.

Night Elves don't poop.

Worgen go on the lawn. Sometimes on the carpet, and you gotta make sure you rub their nose in it before they forget what they did and just think you are mean.

Dirty Hordies enjoy wallowing in it, so its not a concern for them.
Very nice job.

This may mean why Azeroth was so special for the Titans. I mean look at the Maelstrom, or look how deep we can enter in MC or alike.

But yeah, good job there :)

What we can also assume is all those BIG distances of ocean. Have you tried to travel from Eastern Kingdom to Northreand? The scales show in the map are not 100% precise.
omg imagine wow like minecraft, that would be massive and epic :D
ok project for the year, make an exact replica of azeroth on minecraft!! :D
this is amazing, thank you, i had never even thought of this.
First of all I have to say that if what you're saying is correct, you sure are smart for figuring all this out in your spare time.
But really, this is like two kids arguing over whether Superman or Goku would win in a fight, when we all know it would end in a draw after 5 minutes and then they would team up to defeat some half-assed villain so as to add some semblance of plot to this abomination of a direct-to-video special.
I hope that made sense. <_<
01/11/2011 9:56 PMPosted by Sayroth

I can see guilds making massive /follow caravans, rotating leaders over several days in order to get to a remote raid instance.

They could call it the Mulgore Trail! I just hope we bring enough Axels and Oxen to last the whole journey...

You won't need any Oxen, you could simply capture tauren along the trail.
You know let's look at it this way, the continents at most of the diameter we look at (Plus we should factor in outland) ... so blizzard had designed roughly 16 miles of interactive 3d enviroments... quite an impressive feat
Love this post!

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