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.
The problem with the Mario = 6 and DryBowser = 9 thing is that it's not only unitless but it looks more like a rating and ratings don't need to be proportional.
And there are also ways to dodge the Blue shell, how do you explain that? :p
MatPat says it takes 33 frames for a blue shell to stop a kart, but I don't buy it. First of all, he assumes it's a continuous deceleration, which it isn't. If you look at it, it seems to be an almost immediate stop, plus enough of a DOWNWARD blast to bounce a kart off the ground for ~30 frames of movement. The impulse numbers are WAY higher than he's saying.
Yay, he covered impulse! Attaboy, Matthew.