Azeroth: A Small Problem

85 Gnome Warlock
3235



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 died of dysentry. Ressurection in 6 minutes.
So...I got bored this evening. Understament of the year..

Imagine if they put the world in scale to Earth for a day..
Edited by Stagnome on 1/15/2011 8:41 PM PST
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90 Blood Elf Rogue
9560
In lore Azeroth isn't so small. I remember some 4 years ago I saw someone calculate using the data of one of the books of how long it took to get in a zep from UC to grom'gol, and it was about the same distance as from Paris to Cape Town.
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85 Human Warlock
4955
Now secondly... and this is a little off-topic, but being that you are a physics/math major (like me! =D), can you explain to me the point of limits in calculus? Like... the whole idea seems completely convoluted and pointless.


Limits are originally taught using the delta/epsilon format to get you used to the mechanic. The equations used have obvious plug-in's, so you can check your work. The point of limits is differentiation. Derivatives are defined in terms of limits (literally, f'(x) = Lim (h=>0) [f(x+h) - f(x)]/h). For example, the classic definitional example is f(x) = x^2

f'(x) = Lim (h=>0) [(x+h)^2 - x^2]/h
f'(x) = Lim (h=>0) [x^2 + 2xh + h^2 - x^2]/h
f'(x) = Lim (h=>0) [2xh + h^2]/h
f'(x) = Lim (h=>0) [2x + h]
f'(x) = 2x (because someone is going to point it out, it's technically 2xdx)

Beyond that, limits help down the line for integration and for dealing with situations of infinity. For example, a classic le'hopital's rule problem:

Lim (x=>-1) (x^2-1)/(x+1)

If you just plug it in, you get 0/0, which is an indeterminate form (ie. it can equal just about anything, depending on the equation it came from). To solve this, you differentiate the numerator and the denominator, then take the limit again:

Lim (x=>-1) 2x/1

Plug this in and you get the obvious answer -2. This wasn't possible to find from the original limit, nor does the point (-1, -2) actually exist on the graph of the function (it's undefined), but -2 is what the function limits to at that point, so even though it's undefined, you can figure out what the function is doing at that point. This has an absolutely absurd amount of applications. Just think of limits as the natural predecessor to differentiation, which (along with its inverse integration) will be the defining point of most of the next 4 years or so of your mathematical experience.
Edited by Daelyn on 1/16/2011 12:44 PM PST
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85 Goblin Mage
8050
ummm this is cool and all but how about outland?
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85 Troll Shaman
5915
You sir, are a champion
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85 Undead Rogue
7235
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. :P


population dynamics?? hehehe no one in Azeroth ever sleeps and i've only encountered about 5 people that actually own property...
and 60 percent of the population dont have stable jobs yet manage to dish out gold and assorted treasures to every passing adventurer that brings them a book or something...

imagine the rent on one of the 20 so stores that are actually IN orgrimar? the capital city of the horde?

do you know how many homeless people live in Azeroth? OVER 11 MILLION!!!! all of us!!!!!
why hasn't Garrosh done something to fix this!!!!
forget the magic sword, i want food stamps for my daily quests!!!
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87 Night Elf Druid
9875
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:

http://img836.imageshack.us/img836/6184/worldmappath.jpg

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[hypertextbook.com].

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 [hypertextbook.com]. 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


Nice thread...but believe me Blizz would NEVER be blinded by Science!!!
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85 Human Warlock
4955
forget the magic sword, i want food stamps for my daily quests!!!

I'm tempted to sig this.
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85 Human Warlock
9790
I had to login to like this post.

This is...

AWESOME!
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69 Troll Druid
840
01/11/2011 7:59 PMPosted by Daelyn
insanely fast by real-world standard (sustained ~4.2 minute mile in plate gear over rough terrain).

Warriors and such would complain that they move to slow
or
Would you like it like minecraft where if you go in water with a certain type of armor you sink like a rock
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90 Night Elf Druid
11115
Actually it takes an hour to drive from one end of Rhode Island to the other....Azeroth is slightly larger.
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Daelyn,

That is an awesome analysis. Had you considered that Azeroth may be something other than a planet? A few things to consider:


1) The Earthen Ring is worred that Deepholm will fall into Azeroth. Per our simple understanding of physics, it seems that Azeroth would fall into Deepholm, but that isn't the case according to our Shaman friends at the earthen ring. May lead to a theory that Azeroth is not an orb, or at least that we aren't on the outter surface of an orb.

2) No heavenly bodies exist in lore (at least none that I've encountered). All alien enemies originate from other planes rather. Sargeras, who's original plan was to destroy Azeroth, did not come from outer space, but instead came from other planes. In fact, he had been travelling between planes, destroying each, until he came to Azeroth where he was defeated. The Elemental planes connect similarly: with portals (or better, Rifts).

3) Look at the destruction of Outlands, a place that has recently been "destroyed" and we are simply viewing the after effect of said destruction. If the same rules apply to each plane, shouldn't the way that Outlands split and float in the ether tell us something about the physics of the place that can be applied to Azeroth.

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85 Dwarf Hunter
5040
01/11/2011 7:59 PMPosted by Daelyn
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).



Now that you've let the cat out of the bag, Dark Helmet will swing by to steal our Atmosphere!
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85 Troll Hunter
4455
01/13/2011 6:26 AMPosted by Valanara
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.


actually us trolls are far more civilized and we simply teleport our poop to another dimension
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85 Night Elf Rogue
3915
I'm not sure if anyone mentioned this or not, but in the northern hemisphere, the sun usually sets the Southwest.

I was watching the sunset from on top of Darn the other day and noticed it was to the NW which means that Darnasus would be in the southern hemisphere.

If this is the case, why is it so cold in Northrend? Shouldn't that be towards the equator and not away?
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85 Human Warlock
4955
Actually it takes an hour to drive from one end of Rhode Island to the other....Azeroth is slightly larger.

By estimated surface area, RI is slightly larger. However, keep in mind that flying from Quel'Danas to Booty Bay would be less than half of the distance around the globe of Azeroth, not equivalent to a corner-to-corner trip across RI.

I'm not sure if anyone mentioned this or not, but in the northern hemisphere, the sun usually sets the Southwest.

I was watching the sunset from on top of Darn the other day and noticed it was to the NW which means that Darnasus would be in the southern hemisphere.

If this is the case, why is it so cold in Northrend? Shouldn't that be towards the equator and not away?


Perhaps Azeroth has a much steeper axial tilt. Hmmm. No, that would require an axial tilt on the order of about 60°, which would actually mean that Darnassus would be in the arctic circle (probably would be anyway), which would mean there wouldn't be a sunset for a portion of the year.

Given all of this, I'm forced to conclude that Azeroth is in fact not a sphere, but a flat plate of matter rotating at an angle to the sun. This would mean that Deepholm is in-fact a pustule bulging out the 'bottom'. Well, ok, it's possible that Azeroth is instead a flat-bottomed mound shape, with the 'surface' being the flat side, and Deepholm being a cavern in the massive backside. Assuming this is a mound (modeled as a parabolic) and not a full hemisphere, that makes the calculations relatively easy.

Assuming the world map is relatively accurate as far as scale of the seas goes, Azeroth is somewhere in the ballpark of 20x30 miles, for a total surface area of 600 square miles. Deepholm is roughly 1 mile deep top-to-bottom. The plate would likely have to be around 5 miles thick on average to maintain structural cohesion, giving us a total volume of around 3000 square miles, roughly 1.5 times our original estimate. This also gives a maximum thickness of ~10 miles.

This does make gravity a bit stickier. Either Deepholm would have to have a noticeably more significant gravity (90% the radius, ~124% of gravity at the Maelstrom) and Exodar would have a noticeably less significant gravity (141% radius, 50% of Maelstrom gravity), indicating a massive node of matter in at the top of the mound, or gravity works completely differently in this realm. Assuming gravity is simply a unilateral downward force, this simplifies matters.

There's still a number of questions with this model, however. Why do all the titan models show Azeroth as a sphere? Why does Azeroth appear to be one from Draenor? Hell, why can it be seen from Draenor at all? Why is Northrend so cold?

Ok, on that last one, perhaps the plate is curved, with the majority of the landmass located dead-on to the sun, while Northrend is curved away from it. That, or perhaps the presence of Ner'zhul, encased in his demonic ice torn from the bowels of the Twisting Nether, presented an abnormal chilling influence over the continent. This would also explain why the northern portions of both of the main continents don't show evidence of lower temperatures, and why the snow in Northrend tends to occur predominantly in the more central and northern portions of the continent. Then again, perhaps it's the fault of the mages, considering Dalaran is in nearly the exact center of the snowed-in area. This would also explain why proximity to the Nexus caldera seems to also correlate to lowered temperature. Perhaps density of certain types of magic is the cause and not any unexpected geographic features.
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85 Dwarf Hunter
5040
It may just be turtles all the way down...
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85 Human Warlock
4955
And the Hawking quote shows its face.
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Implying that he three continents (or possibly just large islands for that matter) make up all of Azeroth, and not just one hemisphere.
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