Hello Internet!
Welcome to Game Theory, where the closest to failing a test I ever came was my driver’s
test.
No joke.
I was one point away.
In Ohio, we have this maneuverability test which tests ZERO real life skills.
Just give us a parallel parking challenge!
It would have saved me SO much embarrassment during my first six years out in LA until
I finally forced myself to learn!
But enough about me!
Let’s talk Mario Kart!
Loyal Theorists might remember last year when I determined that Mario Kart 8 to be Mario’s
deadliest game.
For those who haven’t seen the video and are too lazy to click on the i-card, I calculated
that the in-game collisions is as powerful as 2000 times the force of gravity.
And these collisions occur multiple times every game.
TL;DR: Racers in Mario Kart are more dead than the Ugandan Knuckles Meme.
But, oh, dear viewers, these high speed collisions are just the beginning.
It gets so...SO much worse.
So today, we rise to the occasion and calculate the lethality of Mario Kart’s most feared,
and most deadly weapon.
No Reggie, not the Blooper.
I'm talking about the Blue Shell.
The Victory Slayer.
The Great Equalizer which, upon usage, soars towards the racer is first place, circles
around them like a vulture circling its prey then dives down, stopping them dead in their
tracks as the shell explodes into a fiery inferno.
So how deadly is this weapon of mass destruction?
Lets crack out the physics textbooks and find out.
The key to determining the force of the Blue Shell lies with momentum.
Momentum is a measurement of the motion of an object and is calculated by multiplying
the mass of the object by its velocity.
A light mass, moving at slow speeds is not going to have very much momentum.
A light mass, moving at a fast speed is going to have some more momentum.
And a heavy mass, moving at fast speeds is going to have the most momentum.]
It’s like me bowling.
I’m weak...obviously...so I can throw a light 8 pound ball quickly or a heavier 16
pound ball slowly.
Both are going to yield roughly the same amount of momentum and knock down the same amount
of pins.
Were I to throw the heavy ball faster, theoretically, I would knock down more pins EXCEPT my aim
sucks, so it’d just end up in the gutter.
And if you are wondering why momentum is written with the variable “P”, I honestly don't
know.
Probably just trying to put the P into AP Physics.
Additionally, we need to take a look at one more physics concept: Impulse.
Impulse is a measurement of the total momentum transferred by an action, and it is calculated
by multiplying force times time.[ Say I’m playing Home Run Contest in Smash, and there
are two Sandbags.
I punch the first one for 2 seconds with a force of 100 Newtons.
Then I punch the second one for 1 second with a force of 200 Newtons.
Although, I punched the bags with different forces for different amounts of time, both
actions had the same amount of impulse.
Therefore, it is expected that the bags would fly the same distance.[5] And if you are wondering
why impulse is written with the variable “J”, I honestly don't know that either.
Physicists are some of the most mysterious people known to mankind.15
Now, if we can calculate the change in momentum caused by the Blue Shell, we will be able
to find its force.
Change is momentum is equal to the momentum before the shell hits you and the momentum
after the shell hits you.
The momentum of the shell after it hits you is simply zero.
You are no longer moving, so no matter what your mass is, you have a momentum of zero.
Finding the momentum before the shell slams into you is going to be a lot more difficult.
Now, in my last Mario Kart video, I determined that the fastest character/kart combination
is Dry Bowser in the B Dasher with Slick Wheels and a Super Glider.
I found that at max speed, Dry Bowser can travel 180 km/h or 50 m/s.
For fellow Americans, that translates to over 110 mph.
This is far from a light joy ride through Toad Harbor.
These races are extreme.
If you want to know how I found all that, the math is in the video hiding in that i-card
in the upper-right hand corner of the screen.
The teaser tag should be popping out right...NOW!
[Meow bit from Super Troopers] So, we know his speed, but now we need to determine his
mass.
In Mario Kart 8, the game uses a system of hidden statistics to define a given character’s
attributes.
Acceleration, on-road traction, off-road traction, and of course, weight.
And I was able to track down a chart of these hidden stats.
Dry Bowser is listed as having a mass of 9.
That’s the good news.
The bad news as that this number is unitless, so we have no clue what that actually translates
to.
However, I have one more ace up my sleeve...and that ace is Mario Jumpman Mario himself.
In Mario Kart 8 Deluxe, Mario has a weight of 6 units.
Now, in a past video by fellow Game Theorist Austin, he used Mario Sunshine’s water propulsion
to calculate Mario’s weight at just under 90 kg or 198 pounds.]
But I don’t trust Austin.
He shouts too much.
[Austin: Hey!
I am OFFENDED!]
Plus, this is my show and I don’t want to give him the sole glory of calculating Mario’s
weight, so I found another way to verify it.
If Mario is indeed 89.94 kg like Austin says, and in Mario Kart, Mario is the equivalent
of 6 units in weight, then one weight unit would be about 15 kg.
Knowing that, let’s look at the karts.
In Mario Kart, the standard kart weighs 2 units, the standard wheels weigh 2 units as
well, and the super glider weighs 1 unit.
Add these together, and the standard kart weighs 5 in-game units.
5 times 15 gets us 75 kg.
And how much does a stand ard go-kart weigh in real life?
Wouldn’t you know it...75 kilograms.
It’s almost as if Nintendo PLANNED it that way!
No...there’s no way, right?
Right, Reggie?
Reggie: What’s wrong with you?
A lot of things, Reggie.
But that’s for another day.
Seriously, though, if only you guys put as much thought into the Zelda timeline!
Reggie: Not my problem.
Where are my donuts?
Way to pass the blame there, buddy!
Anyway, that’s all the proof I need!
By the power vested in me, under the province of the Mushroom Kingdom, I officially certify
Mario’s weight to be 90 kg...89.94 kg to be exact.So with Mario’s height and weight
certified, we have now created a standardized system of weights and measures that can be
used across all of the Mario universe.
It is like the metric system, but a lot, and I mean a lot, nerdier.
It also means we can finally determine Dry Bowser’s mass.
Dry Bowser weighs 9 units, the B dasher weighs 3 units, the slick wheels weigh 3 units and
the super glider weighs 1 unit.
Add this all up and Dry Bowser in his fastest kart combination weighs 16 total units.
With each unit representing 14.99 kg, we can determine the mass of Dry Bowser and his kart
to be 239.84 kg.
Remember that momentum is equal to speed times mass.
Therefore, the 240 kg Dry Bowser traveling at a speed of 50 m/s would have a momentum
of 11,992 Newton-Seconds.
But that’s just Dry Bowser.
We’re here to calculate the devastating power of the Blue Shell, which is able to
stop that amount of momentum almost instantaneously.
And that means we need to know the Blue Shell’s impulse.
Impulse is a force applied over a period of time.
So it equals F times t.
It also equals the change in momentum, which we already know.
The change in momentum the Blue Shell causes is 11,992 Newton-seconds, aka Dry Bowser going
from top speed to a dead stop.
So if we want to know the destructive Force the Blue Shell is delivering in that moment,
all we need to do is eliminate time from our equation.
Lucky for us, Mario Kart 8 Deluxe runs at a silky smooth 60 frames per second and it
takes 33 frames for a Blue Shell to bring you to a stop, so divide that by 60 frames
per second and the time is calculated to be 0.55 seconds.
F times 0.55 = 11,992.
Divide by 0.55, and we get that the Blue Shell would need a force of 21,803 Newtons to stop
the speeding Dry Bowser.
But it gets even MORE dangerous.
You see, that 22,000 Newtons would apply if the Blue Shell hit its victims head on.
The Blue Shell takes it one step further, diving into you at an alarmingly steep 60
degree angle.
Using trigonometry, I found that Blue Shells would require DOUBLE the force, 43,607 N flying
right at the racer’s cranium in order to stop them in their tracks.
Compare that number to the Bullet Bill episode where I found that Bullet Bills have a force
of 2570 Newtons.This is 20 times the force of that.
In last year’s Mario Kart episode, I found that in a worst case scenario, some impacts
in the game reach 2000 g’s.
The Blue Shell has a force of nearly 4,000 gs!
In other words, why try competing to be in the lead when you can just kill of the player
in first with your blue shell.
‘Cause that’s what’s happening here!
It’s like sending the most family friendly hitman to someone who, sorry, was just better
that you in a stupid party racing video game!
But as any player who’s in second place knows, it’s not the impact that gets ya,
it’s the explosion around it!
Using more pixel measurements, the maximum blast radius is found to be 3.1 meters.
There’s a handy dandy formula, named “Brode’s method” that we can use to determine the
energy of this explosion.[12] I’ve mentioned it before during the “How Deadly is Bob-Omb”
episode, but since it’s a lot more math, I’m just going to speed it up:
The first variable in this equation of death is pressure.
Pressure is equal to force divide by area.
As calculated earlier, the head on force required to stop Dry Bowser at max speed is 21803 N.
Unlike with the Blue Shell, the explosion force is head on, and not at any angle.
Using pixel measurements and Mario as our newly certified ruler, I found that Dry Bowser
has a cross section 1.87 square meters while racing.
Therefore, the pressure of the blast wave would have to be 21803 N divided by 1.87 m2​
​, or 11616 pascals.
The pressure of the outside environment would be simply be one atmosphere, which can be
translated to 101325 pascals.
Additionally the volume is easy to find, as all you need to do is determine the volume
of a hemisphere with a radius of 3.1 m.
The formula of 2/3 * π * r3​ ​ calculates a volume of 62.39 cubic meters.
The final variable that is needed is the heat capacity ratio of air.
This is a constant that is equal to 1.4.
Just like that, we have found all of the variables needed to calculate the energy of the Blue
Shell explosion.
After solving the equation, I found that the Blue Shell explosion has an energy of 17,617
kJ.
For comparison that is the same energy as found in 4 kg of TnT.
Fans of my channel might remember the United Nations Explosion Consequence Analysis website
from my Bob-omb episode.
25 With an equivalent of 4 kg of TnT, anyone within 15 meters of the detonation can expect
a ruptured eardrum.
Anyone within 5.9 meters will have lung damage.
Most dangerous of all, anyone within 3.5 meters of the explosion will be killed.
Thanks to the blue shells, Mount Wario will be covered in police tape26 and huge craters
will appear will appear in Toad Harbor.
The TSA will not even let me bring hand cream on to flights, while mario and friend are
able to bring the equivalent of 4 kg of TnT into Sunshine Airport without raising any
red flags.
You better hope that you have insurance while racing.
And I am not talking about car insurance.27 Life insurance is going to be needed after
competing in these cups.
And there you have it.
Blue Shells are practically heat seeking missiles disguised as a fun turtle shell.
The shells will kill you outright upon impact, and anyone within a 3.5 radius around you
is likely dead as well.
Leave it up to Nintendo to violate the Geneva convention within a game rated “E for Everyone”.
Next time when you pick up a Blue Shell in a mystery box, take a moment to comprehend
the shear power you have in your hands.
If you’re in first place and receive the indication that a Blue Shell is approaching,
take those final seconds to make peace with your maker.
I hope those two and a half laps in first place were worth it because the true winners
of Mario Kart are the survivors, the ones who race to stay in the middle.
But that’s just a theory.
A Game Theory.
Thanks for watching.