*Click*
Dear Blizzard
Are you kidding me? Are you freaking kidding me?
What is this? What...is...this?!
Hi, it's me, Austin, Blizzard. And today I'm looking at THIS crazy idea that you came up with.
What?! I mean?! Stabbing a planet with a giant sword?! Did you think that I wouldn't notice this?!
I mean, putting aside the fact that you've stolen a vast amount of plot stuff from Final Fantasy VII,
complete with a giant space demon trying to injure a living planet. And it's blood
being jealously hunted as a natural resource.
Oi. Oi, Oi, Oi. What's that? Matt's episode on the moon in Majora's Mask?
Never heard of it!
Okay, deeeep breaths.
Coming out the gate with freaking out is gonna leave you with
quite the 10 to reach for the third act break. Okay, whoo, alright,
this thing. Let's do this. How screwed is Azeroth now that it's been stabbed by a
giant sword by a space demon? For context, for those of you who don't know because the
last time you played WoW was like 200 years ago like me before a few months
ago Azeroth is like a space egg for Titans who are the space gods of World
of Warcraft Sargeras is this guy. He's a Titan who's
been corrupted by Fel magic and is the leader of the Burning Legion who are
fairly responsible for most of the bad stuff happening in World of Warcraft.
Not all of it, but most of it. Anyway, a lot of stuff is happening and now there's a
demon moon orbiting Azeroth which has gotta be hell on the tides and boy howdy
do I wish I could get into orbital mechanics in this episode but there's no time!
Anyways, the Legion is doing Legion stuff and is trying to attack Azeroth
because of course it is. At the climax of the last expansion, "Legion", Sargeras is
launching an all-out Hail Mary attack on Azeroth and plunges his freakin' sword,
this huge thing, into the planet. That, my friends, is big sword energy if ever I
saw it. The current expansion deals with the fallout to this event which, like
apparently is not everyone digging deep into shelters to survive the coming
apocalypse? Okay then. So what would the consequences of something like this even
be? There's some speculation online, but I didn't read it because I believe in not
polluting my research, and I guarantee you they have not measured as much as I
have, because I get paid for this. Just this. It is embarrassing. I... I hate myself.
Anyway, in order to even remotely figure out what kind of damage a sword is doing
if any, we have to figure out how much force it's imparting into the planet, and
no unfortunately all you naughty Nancy's out there ready to jump on me, we
don't know how much mass the thing has because we don't know what it's made out
of. Thankfully with some clever workarounds we can still measure the
force it imparts into the planet. More on that in a bit.
Getting objective measurements in World of Warcraft is... tricky. They do have yard
specifications in some spells but, well, for one I hate yards and for two
figuring out the exact range of some of these in order to get precise
measurements is difficult, for three using this to measure the dimensions of
a giant space sword is actually more difficult than you might think.
Thankfully we have another answer. Canon heights. Now we can't use the canon
heights of important characters because part of Blizzards design philosophy is
to make the important hero's impossibly huge, but we have a sneaky workaround,
player characters have canon heights, like my Night Elf druid is exactly 7
feet tall and this is easily the most important measurement I need, because I
need to figure out a ton of stuff that vertical measurements are going to make
a hell of a lot easier than horizontal ones. First of all we need to know fall
speed because we're gonna use that to measure the length of the blade.
With a bunch of annoying pixel math that would be at this point me rehashing stuff I've
talked about a million times, I found out that the top speed is fifty three point
nine meters per second which is really interesting actually because it's
actually pretty close to the terminal velocity of humans on Earth. I'm not sure
if that was intentional or not but that's pretty cool nevertheless. Also of
note, gravity on Azeroth is way higher than Earth's clocking in at a whopping
thirty meters per second squared, that isn't that important just yet and it's
definitely not surprising since most video games have higher gravity than our
own but it does mean that Azeroth is significantly more massive than Earth
more on that later. Knowing our fall speed and acceleration rate we can
measure how long the blade of the sword is. It took me a tremendously long time
to hit the ground from the starting point, almost twenty two and a half
seconds, meaning that the blade, just the exposed part, is over a freaking
kilometer long at eleven hundred sixty-four point nine meters. Now
extending this out to the cinematic we can find out how big the sword is in
total. We have to do this because we have to know exactly how much of this thing
is embedded into Azeroth in order to know how much damage it would do.
Doing this I figured out that the blade alone is two thousand six hundred and forty
two point seven four meters long, holy crap, that's over one and a half miles
counting the hilt it's over three thousand nine hundred and fifty three
point eight one meters or two point four five miles that's freakin' nuts.
I don't know what this is made out of but I'm pretty sure the structural properties-
I don't know what this is made out of but I'm pretty sure that the
structural properties of most materials would not stay together at this size and
shape, that well. Knowing this we can figure out with easy math that one
thousand four hundred and seventy seven point eight four meters of the sword is
buried into Azeroth, that's over thirteen and a half football fields deep but, I
don't know it's going pretty slowly right? I mean look, he just kind of
gently nudges it in there, it can't be that bad right? Wrong! While it looks like
the sword is moving slowly from this perspective, if you measure it out this
thing is moving at over Mach 2, almost Mach 3 at 959 meters per second, but
in order to figure out how bad this thing actually is for Azeroth we're
gonna have to use a tool that some of you might find intimidating.
Trigonometry.
trigonometry does sound intimidating at a glance but it's literally just
triangle math all math that has to do with triangles and the angles inside
them it means that in basic geometry you are probably doing some trig without
even realizing it the Pythagorean theorem is just reductive trigonometry
but in order to do this math today we're gonna have to do something a little bit
trickier 3d trigonometry you see this sword isn't flat it's not just some one
molecule thick razor blade this thing is freaking huge and remember before I said
we couldn't figure out the force imparted by this thing from the mass of
the sword because we don't know it but we do know the mass of Azeroth. And if
we can figure everything else out we can figure out how much mass it displaces
and how quickly and that will get us where we need to go and that is what
trig is gonna help us with today all the information we need is actually right
here all we need to have is the thickness of the sword at its base 166
meters the wideness here at the widest point the length which we already have
and the length of the sword that's in the ground and we have everything we
need because of two mathematical laws one of which was invented I kid you not
over 1,000 years ago in well it's not exactly certain who specifically came up
with it but it's one of four dudes in what is now known as Tajikistan Baghdad
or Afghanistan while the other law dates back to over 2400 years ago and those
are both the law of sines and the law of cosines which specifically govern angles
and how they interact with spheres and triangles
now while this sword is not a perfect geometric shape we're gonna
underestimate its size a tad so we can have some wiggle room and when you do
that this thing is what's known as a rhombic pyramid rhombic because the base
is a rhombus and it's a pyramid as opposed to a prism because it has a
point at the top called an apex we need to do three-dimensional geometry because
we need to figure out exactly how much of Azeroth is displaced by this thing
when it's stabbed into the ground and in order to figure that out we need to
figure out the volume of the section that's inside the ground like okay all
right is the whole sword right and here's the
entire thing as a triangle and we draw a line here across it to represent the
ground we have effectively two triangles now one large one and one smaller one
nested inside it on the bottom now due to the laws of geometry this angle here
and this angle here are identical so we just got to figure out what this angle
is once we know that we can bisect this thing down the middle make some right
angles abuse old Pythagoras and be on our way
thankfully since this triangle at the side view of the pyramid is an isosceles
triangle which means that these two sides are the same length and these two
angles are the same and we know what the base width is and the height is most of
our job is already done for us we just have to bust out good old sohcahtoa oh
do you not remember what that is you know what don't even feel bad I have to
look up every single time too and they even mess it up sometimes still even
then sohcahtoa is a mnemonic device it's supposed to help you remember which
functions to use to find unknowns sine is when you have the opposite side and
the hypotenuse side. Cosine is when you know the adjacent side to an angle and
the hypotenuse and tangent is for the opposite side and the adjacent side too.
the angle there's also some other crappy pneumonic devices like some of her
children are having trouble over algebra and Tom's old aunt sat on her chair and
hollered and I proposed a new one can Austen help shouting over his tinnitus
oppressed audience
honestly there's like so much to do here so I'm like gonna have to go through
this really fast so strap your butts into the chairs it's time to go fast we
know how long the sword is in total we know the base length and if we bisect
this here and divide the base by two we can use the Pythagorean theorem C equals
the square root of a squared plus B squared to get the hypotenuse the long
side of the sword here since we know all these sides we want to know this angle
here we got a lot of options but we're gonna use the inverse tangent function
since we know the sides we don't know the angles which gets us an angle of
eighty five point six five degrees which means the angle here where the sword
meets the ground is also eighty five point six five degrees now we're cooking
with gas now we gotta figure out a few things to get all of our answers all
of the dimensions of the sword cross-sections on the front all of the
dimensions of the sword cross-section from the side and the dimensions of the
rhombic base now let me know this angle here eighty five point six five we also
know this angle here because this is a right triangle and all angles in a
triangle have to add up to 180. So 180 minus 90 minus eighty five point six
five gives us four point three four five degrees here now we can use another
function to find this site here which one do we use can't Austin help shouting
over is tonight a suppressed audience tonight a suppressed audience because we
know the angle and the adjacent side 1477 tangent four point three four five
degrees it gets us one hundred and twelve point two nine meters or a full
base of this cross-section of two hundred twenty four point five meters
divide that by two back to one hundred and twelve point two nine Pythagorean
some stuff and we get a length of this edge here of 1082 meters BAM
cross-section one done cross section two is exact same math let's cross section
one but with different umbers which gives us a base of 93 divided by two
pythagoras by BAM! These sides are 1478 meters one more cross-section to go
looking down on the sword you can see that we've already figured out these
diagonals this is the base of cross-section one and this is the base
across section two which we can multiply together divided by two to get the area
ten thousand four hundred and seventy-three square meters and we can
use the Pythagorean theorem again to get the sides 121 meters Wow done with the
dimensions of the sword! Woohoo! All of this means we have an internal volume of the sword
just in the ground of over five point 1 million cubic meters that's like the
size of the entire freaking Hoover dam but what does this mean what does it mean
because well it's meaningful to say that five point 1 million square meters of
Azeroth is displaced by the sword we don't know of what and this is where the
acceleration due to gravity I mentioned earlier becomes
really important because knowing the surface gravity all we have to know is
the size of Azeroth to make it figure out its mass which allows us to get its
density perspectives are difficult but using the most revealing angle in the
cinematic we can expand Azeroth to a full circle and use the sword length
which we know of three thousand nine hundred and fifty three meters and we
can figure out that Azeroth has a radius of four thousand two hundred and forty
three meters. Point of interest this means that Sargeras stabs his sword over a
third of the way toward Azeroth core if that were scaled up to our planet it'd
be a sword stabbing over twenty-two hundred kilometers over 1,000 miles
anyway using some gravitational formulas and isolating our unknown variables we
can figure out that Azeroth has a mass of eight point one six quintillion
kilograms which sounds like a lot but it's actually only point zero zero zero
one three six seven eight three two eight eight seven percent of the mass of
the earth that's less massive than three Juno the largest asteroid in the
asteroid belt but Azeroth is very dense it has over 25 million kilograms of mass
per cubic meter over four thousand times the density of Earth so this means that
when this sword is inserted over three seconds it's displacing 1.3 1 trillion
kilograms of mass pushing it to the side in the same volumetric space as a sword
itself over a hundred and eighteen point two three meters one whole football
field in three seconds at a top speed of 39 meters per second or 88 miles per
hour with an acceleration of 13 meters per second a force when you accommodate
a modest force of friction of over 2.5 quadrillion newtons over one thousand
four hundred and seventy-seven meters releasing 3.8 quintillion joules of
energy the power released by over 14 of the world's most powerful nuclear bomb
ever detonated the Tsar Bomba or the kinetic energy released by over
21 sixtillion fart's all at once which is
1.1 million times the total number of farts that have ever been farted by all
the humans in all of human history Azeroth would be totally screwed I'm
talking about fallout and winters caused by what is effectively a giant doomsday
device detonated on an absolutely tiny planet and on a planet this small this
would easily be deep enough to trigger cataclysmically huge earthquakes that
would trigger massive collapses of cities not to mention the massive
shockwave caused by a sword this large displacing over 64 million kilograms of
what is a pretty thick atmosphere which would create the loudest well I was
going to say sound but at some point rushing molecules of air smooshed
together to form a giant wall of four stops being a sound and just starts
being terrifying in any case everyone everyone not completely buried
underground or in raids would have their eardrums burst this single thing would
be the worst thing that's ever happened to Azeroth and yet everyone's just like
no big deal let's walk around minding God blood sure buddy as far as I'm
concerned all of world of warcraft now is some collective hallucination from a
handful of dying sentient races as they bleed out under rubble of what once used
to be a beautiful planet but is now a crumbling pile of garbage. Sincerely,
Austin Hey do you want to join my discord and
talk with other people who like my show and like to talk about science and like
the other random garbage like we have a thousand people so it's like a lot yeah
go to discord dock GG / the science and you will be able to join right away and
get the talk with a bunch of other fans and there should be a link in the
description I think should be good somewhere in there you can dig for it
it's in there also subscribe to the game theorists
Do it.
Do it right now.