I calculated the Diameter of Azeroth

General Discussion
07/15/2018 09:51 AMPosted by Eevee
Anyway. It's pretty clear the in game world is flat, or maybe azeroth's gravity is so strong it bends light and just makes it LOOK flat.


Yeah some special and general relativity stuff going on -- it's what makes teleportation possible, not to mention the ship travel from, say, Stormwind to Northrend take only seconds. Core of Azeroth needs to be black-hole-ish -- maybe that's the void corruption that Sargeras was trying to eradicate?
07/15/2018 08:58 AMPosted by Stroude
They didn't properly show ratios when the sword drove into azeroth vs how it looks in Silithus for dramatic effect to make Sargeras look massive. Additionally, the Azeroth we see is a truncated version in game. Think of it like when you're playing an rpg and you have a world map, and your guy is bigger than the symbol for the town, which is usually a house or something.

We're not correctly proportionate to either size of the zone we're in or even the size of the places in said zone. Stormwind has hundreds of thousands of residents. When it takes us minutes to take a flightpath from Auberdine to Theramore, that may take days or weeks for an npc canonically.


You can make the argument, I suppose, that they can't show every house and dwelling in Stormwind.

I don't think you can make this argument when the game shows me every bush and tree along the way from one point to another. I am in this world, as my life-size character. This is not some representation, this is what is there.
For a second, I thought I accidentally logged into the Kerbal Space Program forums.
Assuming G, and that Azeroth's drag force is negligible* because every playable race falls at the same rate (a Tauren has way more surface area than a gnome but falls at the same rate), and using the bridge from Court of Stars to the Nighthold as a reasonable height (not short enough to be hard to measure, and not tall enough to introduce terminal velocity), I get that Azeroth has a density of 2920 g/cm^3.

Our characters hit terminal velocity pretty quickly in falls. On Earth, a skydiver might take about 15 seconds to reach it, while my toon SEEMED (emphasis since it was purely visual inspection) to reach it in maybe 3 seconds on Azeroth. I was watching the particle effects from my M BRF shoulders (which make significant trails at high quality effects) to see when they started making a straight trail, indicating I had reached a constant vertical speed.

EDIT: After numerous stopwatch timings, it looks like terminal velocity really is reached at 3.0 seconds in free fall. The particle effect trail went from a parabola to a straight line consistently at that time. So as long as a fall takes around 2 seconds, it's probably good enough for these calculations even without accounting for drag.

Looking at the equation for the drag force (which balances with gravity at terminal velocity):

F_drag = 0.5 * (mass density of fluid, in this case air) * (flow speed of object relative to fluid, in this case our characters)^2 * (drag coefficient) * (reference area)

All playable races fall at the same rate and reach terminal velocity at the same time, which means that the reference area has to be negligible compared to the other terms, and the terminal velocity is a constant. That probably means that Azeroth's atmosphere is incredibly dense, which would make sense considering the aforementioned density of the planet itself.

*I initially assumed that the drag was tiny because a tauren and a gnome fall exactly the same way, but it is more likely the case that the drag is so enormous that a tauren and a gnome fall exactly the same way.
07/15/2018 10:12 AMPosted by Sigtyr
Assuming G, and that Azeroth's drag force is negligible because every playable race falls at the same rate (a Tauren has way more surface area than a gnome), and using the bridge from Court of Stars to the Nighthold as a reasonable height (not short enough to be hard to measure, and not tall enough to introduce terminal velocity), I get that Azeroth has a density of 2920 g/cm^3.

Our characters hit terminal velocity pretty quickly in falls. On Earth, a skydiver might take about 15 seconds to reach it, while my toon SEEMED (emphasis since it was purely visual inspection) to reach it in maybe 4 seconds on Azeroth.


That number is effing terrifying.

What gravity acceleration did you calculate, by the way? I'm curious
07/15/2018 10:15 AMPosted by Eevee
What gravity acceleration did you calculate, by the way? I'm curious


About 14.6 m/s^2. Looking at my estimation of the time it takes to reach terminal velocity according to the path of my particle trails, the Nighthold bridge might be a tad too tall (~82.5 meters).

EDIT: What do you guys think about the drag? Initially I was working with the assumption that we could ignore it because a tauren and a gnome fall at the same rate, which I took to mean Azeroth's drag force was very small - but couldn't it also mean that Azeroth's drag force is so large that we can't tell the difference between how a Tauren falls and how a Gnome falls?
And the jaws of the Blizz devs collectively drop...

holy crap OP, impressive.
07/15/2018 08:43 AMPosted by Eevee
Yes, I really did it.

So in looking at the cinematic, I noticed there was one shot that could once and for all reveal the true diameter of our beloved Azeroth, it's this one right here:

https://imgur.com/435H8Ld

This is the first time we have seen the curvature of Azeroth put alongside an actual object we can view in game. Namely, Sargeras's sword.

First, I had to figure out a way to measure things in the game. Fortunately, there is an easy method to use.

First, I used my flare ability to mark the distance of 600 yards in the Barrens, 40yards at time, walking in a straight line towards a landmark on the horizon. 15 flares.

Using this fixed distance. I could now mount my flying mount and measure the time it took to fly from end to end. This came out to nearly exactly 20 seconds.

Converting the 600 yards to meters gave me 548.6m, for a flying speed of 27.5m/s

Knowing the speed of my flying mount, I then went to sargeras's sword and measured how long it took me to travel across the eye in the hilt. Which was 15.47 seconds, for a total distance of 425.4m

Knowing THIS, I can use the pixel ratios in the first image to determine some critical values in the image. The math is a little complicated, but the distance viewable is 4292.6m while the bulge in the arc is a mere 261 meters.

Then, I can apply those values to the following diagram:

https://imgur.com/GgPXQKt

We now have a right triangle with only a single missing value of x. Creating an equation to solve of:

x^2 - (x-261)^2 = 2146.3^2

Solving for X means the radius of Azeroth is 8955.4m

For a diameter of 17910.8m or 17.9km and a circumference of 56268.5m or 56km

For those curious, Earth's diameter is 12,700,000m or 12,700km wide, almost 710 times larger.

But I'm not done!

I went ahead and measured the width of Kalimdor and the eastern kingdoms using my flight method. Each one is roughly 6700m or 6.7 kilometers across.

This means that at the equator, Kalimdor and Easter Kingdoms represent 23% of Azeroth's circumference even if they had no ocean between them.

Conclusion:
Azeroth is tiny, and Easter Kingdoms and Kalimdor are far enough apart relative to the curvature of azeroth that the sun should rise and set at different times based on which continent you are.


Well done Sir, well done.
You could probably use the Evermoon Terrace as a decent cliff. It falls into water and is shorter than the bridge - my shoulder particles were still making a parabolic path when I hit the water, so it's certainly not tall enough to introduce terminal velocity.
07/15/2018 10:32 AMPosted by Woodspath
And the jaws of the Blizz devs collectively drop...

holy crap OP, impressive.


I was genuinely expecting my numbers to completely fall apart when I double checked them by measuring the continents. The fact that they represent a reasonable proportion of the planet (And not, as I worried, too large or insingificantly small) means that Blizzard has probably thought this through.
07/15/2018 10:38 AMPosted by Sigtyr
You could probably use the Evermoon Terrace as a decent cliff. It falls into water and is shorter than the bridge - my shoulder particles were still making a parabolic path when I hit the water, so it's certainly not tall enough to introduce terminal velocity.


Actually, Now that you mention it, it would be WAY more accurate to have somebody else do the jump and record it from a distance. I could get a pretty good measurement that way.
The devs have hinted we have only seen the northern hemisphere tho
I'm going to sleep! If the question of Azeroth's density isn't conclusively solved by tomorrow I'll tackle that too.
Nice math, Eevee.

Unfortunately there's a fatal flaw in it.

The game world is scaled down for playability purposes.

We've seen plenty of stances of lore characters taking days to travel through zones in books or comics, yet the in-game zones take minutes to cross.

They are smaller in the game than they should be according to lore.

The same applies to the sword. If the sword was not scaled down it would likely cover the entirety of Silithus since Silithus itself is scaled down.

So basically the in-game representation of Azeroth would have a 17 km diameter but the real in-universe Azeroth would be much bigger :D
didn't someone already calculate it long ago? was like a college math or science teacher i think
07/15/2018 09:19 AMPosted by Eevee
07/15/2018 09:17 AMPosted by Hexellu
"a diameter of 17910.8m"

With a diameter of only 18 km (11 miles), Azeroth must be made of extremely dense material to have enough gravity for hydrostatic equilibrium. The giant asteroid Ceres (at roughly 600 miles in diameter) is generally considered the minimal size for a celestial body (ie, one made of ordinary rock and metal) with sufficient gravity to pull itself into a spherical shape.

The alternative, of course, is that Azeroth is full of compactified dimensions, each with an odd number of coherent, oscillating eigenvectors (yet no two with the same number occupying an identical locality in the manifold).

Damn Escherspace.


Given the center of azeroth is literally a celestial being, you can probably claim whatever density you want and get away with it.

Does make me wonder if we'll all float away after she wakes up and leaves though.


Yeah, you can pretty much explain the rest with 'cuz magic'.
07/15/2018 10:29 AMPosted by Sigtyr
07/15/2018 10:15 AMPosted by Eevee
What gravity acceleration did you calculate, by the way? I'm curious


About 14.6 m/s^2. Looking at my estimation of the time it takes to reach terminal velocity according to the path of my particle trails, the Nighthold bridge might be a tad too tall (~82.5 meters).

EDIT: What do you guys think about the drag? Initially I was working with the assumption that we could ignore it because a tauren and a gnome fall at the same rate, which I took to mean Azeroth's drag force was very small - but couldn't it also mean that Azeroth's drag force is so large that we can't tell the difference between how a Tauren falls and how a Gnome falls?


I'd guess that, for some reason, CdS (the product of drag coefficient and reference area) is the same for all of us -- humans, gnomes tauren, and the rest. If I were doing the computation, I'd take values that I'd already computed elsewhere for CdS and density, and use those to compute the acceleration of gravity.

The interesting thing here is that using your "g" and my "CdS", g/CdS -- dynamic pressure at terminal velocity -- is almost exactly 10 pounds per square foot. A curious coincidence, that.

And from that, and increasing the density in accordance with the gravitational acceleration, I get a terminal velocity of almost precisely 25 yards per second. How does that compare with measurement?
Interesting experiment but I do wonder if each zone is really the same size in relationship to one another. Meaning a "yard" in one zone may not be the same "yard" in another zone.

The other issue here is if they made Azeroth Earth-sized our travel times would be quite long and while time sinks are a great way to gate content, I don't think Blizzard would want to go to that extreme. I'm sure the goblins would be more than happy to open travel agencies to help us plan our travel, however. :)
Clearly you didn't because I read on the forums that it is flat and thus i can not have a diameter!
After discussing this with an expert (Kyrie Irving) we've concluded that Azeroth is. as many felt, flat.

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