Dear Nintendo, dude I got a ton of math to get through this episode.
We gotta get through rocket science, like real, actual rocket science, aerospace engineering, and, well,
that's about it, but I always take too much time doing these intros and today, it's time to rock!
Hi, it's me Austin
And I'm here for one thing Nintendo. I have come for your best. I have come for the big man himself
Mario! I've come to prove conclusively
once and for all that this man this weird, stout,
stony-eyed plumber not only makes no freakin' sense, but should be dead! ...well,
maybe, or maybe not. Maybe Mario's fine.
But in order to find out, we're gonna have to get this show started with the question
I asked myself- the thing that set me down this wily, twisting rabbit hole of chaos and
SCIENCE! How the heck does Mario fly?
Mario's had the power of flight going all the way back almost 30 years.
In Super Mario Bros 3 with the super leaf, the Tanooki suit and the P wing, but holy smokes-
Nintendo was just getting started
There's a magic feather in Super Mario World which gave you a frickin'
superhero cape, blue Yoshi that for some strange reason could fly while holding a turtle in their mouth, and my
personal favorite, the winged cap in Super Mario 64 and while there's been flying
iterations all over the place, from the return of the super leaf in the more modern titles, red stars in Super Mario Galaxy,
and the possession of flying goombas in Super Mario Odyssey, today
we're gonna be looking at the granddaddy of them all, the creme de la creme, the winged cap from Super Mario 64
because, well, I want to. Sue me.
Super Mario 64 came out forever ago,
but, you know, I wasn't a youtuber back then. In fact, nobody was.
In 1996, when Super Mario 64 came out, YouTube wouldn't be showing up for almost another decade.
It was the dark ages of the internet, but more importantly,
this is the game where we get the most data and the most interesting look into the weird,
counterintuitive, yet strangely fascinating world that almost every single Mario game takes place on.
Straightforward, airplane-ish flight mechanics are... well, simple isn't quite the right word, but achievable.
In order for something to fly, it has to create lift. And how is lift created?
Well, that's a complicated question, actually. There are two main explanations for how a wing creates lift that allow something to fly-
the Bernoulli-based explanations and the Newtonian-based explanations.
Doug McLean talks about this in-depth in his book: "Understanding Aerodynamics: Arguing From the Real Physics,"
but both explanations are somewhat incomplete but do paint part of the picture.
The "Bernoulli" explanation states that when air over the top side of a wing takes a longer path over the wing than the bottom,
it still gets to the other side at the same time as the airflow below the wing- even though it's traveling a longer distance.
This, in Theory™, creates a lower pressure system over the wing, which creates a pulling force.
The problem with this explanation alone is that, well, air is a fluid, like water,
and as a result, it doesn't always (and in fact, it frequently doesn't) actually meet up on the other side of the wing at the same time,
which is kind of a key sticking point for this specific theory.
The "Newtonian" model is a bit simpler:
the wing redirects air down, which creates an upward force.
This explanation is particularly helpful when looking at a paper airplane flying,
because it's the angle of attack from the paper that creates a functioning wing, not the shape of the wing itself.
The problem with both of these explanations is that neither of them separately, or even together[?]
describe all the things that makes a flying thing fly-
but that's okay because, honestly, we're not theoretical aerospace engineers.
It's not important for us to know the exact explanation for why flight happens-
which is good because, "current"ly, there's no actual agreement on what the full story is-
but engineers have figured out how to fly anyway, because of course they have.
We're not gonna let something as trivial as "not fully understanding the science"
get in the way of building new technology that holds people's fates in their hands like tiny birds, are we?
What we know is that, in order to have lift, you need to have something to be a wing,
and air has to flow over it. And we have a formula for that:
Air density * velocity² / 2 * the lift coefficient * the wing area
All these things together give you lift- in Newtons.
It takes 9.8 Newtons of lift to make one kilogram hover on planet earth, so you know what that means we're gonna need some numbers
The first one is the easiest Mario's flying speed we need to know this because it directly
affects how much lift is created by whatever counts as a wing on this guy using Mario's Canon height of
5:1 is a ruler I can figure out the distance between two similar bricks in cn world's pyramid using some trap
Mathematics getting a distance of four point three eight to seven meters before the pattern of pricks repeats
Then it's a simple job of counting how many of those lengths is on one side of this pyramid twelve
and how long it takes to fly that distance and boom we get a flying speed of thirteen point 13 meters four seconds or
25 miles per hour not very fast
but five speed is really important because
Forward velocity is probably the most important part of flight next things get a little bit more complicated
We got to figure out the area of Mario's wings which like
can't get it simply cannot be the wings on his hat I love to claim that things make no freakin sense the drop of a
Hat but I am not comfortable
Counting those as wings the area of wings is determined by looking at what's called the plan form of the wing surface which
For the sake of simplicity is just the top down look at the way now if we make his whole body wing which is
Somewhat problematic because the airflow over non rotating cylinders like Mario's arms generally don't produce any lift at all
But whatever let's be generous here and vulvar at it include the Hat wings we get a surface area of one
point two square meters if we take the average lift coefficient of the human as being at best
1.5 as determined by this study done in
1964 by the United States Navy where they just put a bunch of dudes in a wind tunnel and crank the wind speed up to
over 144 knots or 266 km/h or
165 miles per hour which like god bless the days before medical and scientific
Ethics boards using just his body and the wings on his hat Mario would be generating
14 Newton's of lift at standard atmospheric pressures on earth which is barely enough force to lift
something weighing one and a half kilograms or
3.3 pounds
but well
The astute among you may have noticed that we have no idea how much mario weighs for all we know maybe he's made of some
superlight mega untense material
Maybe he's actually a robot made out of tissue paper who knows in fact nobody on the entire planet knows Mario's weight
It's a complete mystery so
Guess we're dead in the water. Wait a minute....
That's it!
*Maniacal laughter*
*Inhales*
*Maniacal laughter*
I HAVE DONE IT AGAIN!
Water is the key to everything!
Nintendo has tried to hide the canon weight of Mario from us
so they can continue to get away with whatever weirdness counts as physics in their games, but they
overlooked one
key thing. I am f*****g
Unstoppable!
Before we get to the good stuff,
we got to figure out the gravity of the Mario universe. In my experience, gravity, in most platformers, is
significantly higher than it is in our world. It may seem lower because everyone jumps so high,
but I think it has more to do with how beefy their glutes are than anything else. You see falling at a rate of
9.8. Meters per second would be
agonizingly slow in a platformer game and Mario is no
exception. Each game varies slightly based on frame rate and just general game feel, but using good old pixel
measurements in Super Mario 64, I figured out that the acceleration due to gravity, in that game, is
26.12
meters per second squared or over 2 point 6 6 G's. Two and a half times as powerful as Earth's surface gravity. No wonder
his glutes are so powerful! Yikes! Now that we know that, we can do the really fun part:
rocket science. How? Super Mario
Sunshine
Believe it or not, this game is the key to figuring out how much Mario weighs and boy is it
absolutely possible, all thanks to that frickin jetpack: the Flash
Liquidiser Ultra Dousing Device, or F.LU.D.D. for short, is capable of many things, perhaps the most interesting thing being the
the ability to launch Mario up into the air. Since the water tank is easily viewable on Mario's back,
we can measure its internal volume using pixel measurements. Mario's height, again,
and the volume of a sphere. Four over three times
pi times the radius cubed. Doing so, we find out that a clocks in at a horrifyingly high
capacity of a hundred and ten liters. Now,
knowing that each tank holds enough water for twelve and a quarter jetpack launches,
we can figure out so much: that each launch uses 8.98
kilograms and/or liters of water, that a full jetpack weighs over 242 pouds, blah blah blah...
Determining the nozzle size of the flood to be little over a half a meter wide, we can get its area, which allows us to
get the velocity of the water leaving the nozzle, which turns out to be 69.48 meters per second.
This is important because
knowing the mass of the fuel used, plus the mass of the F.L.U.D.D.,
which is basically a rocket at this point, and the speed at which the exhaust exits the F.L.U.D.D., we can figure out exactly
how much Mario weighs based on how quickly he accelerates up. The last number we need is Mario's rate of
acceleration, which is a whopping
345 meters per second squared. Using this derivation of a simple Newtonian rocket formula, that yes
I know is not properly simplified,
we can plug in our known variables, hit enter, and boom eighty-nine kilograms and, just like that,
we've done something nobody in the history of the world has managed to do: figure out
Mario's weight.
Alright,
having made video game history by figuring out how much Mario weighs, and knowing that the gravity on Mario's planet is two point six six Gs
that means we need to create two
Thousand three hundred and forty nine point four five Newton's of lift in order to get him to fly with our current mass only pulling
14 Newtons that's a gap of two thousand three hundred and thirty-five Newtons. Yikes
Okay, so how do we fix this problem?
well
there's a few variables we can mess with we can assume that Mario is way more efficiently built for flying than a human which like
No
But fine. Keeping all the numbers the same in order to pull this off. He need to have a lift coefficient of eighteen point eight
Which is freakin
Impossible.No
Seriously the most efficient flying machines in the world have lift coefficients of like 2.5
No, no way no way is this it and Mario is not the most
Aerodynamically efficient thing in the entire universe just look at that big goofy face. So no that can't possibly be it there is
Something we can change however something that honestly isn't even that much of a stretch that air density
earth has an average air density at sea level of
1.2 kilograms per cubic meter that means for every cubic meter of space there's 1.2 kilograms of mass
interestingly
Gravity and the air density are closely related because higher gravity means that more gas is pulled downward, which means it condenses more
But even if we multiply normal earth density by Mario's gravity. We still come up short with the lift coefficient dropping only to
7.08 which is still way too high, but while gravity is an important factor in air density
It's not the only one the most important factor is
Ultimately how much gas is actually in the atmosphere. Take
Venus for example. Venus has a surface gravity of about .9 G's
It's almost got the gravity of Earth, but it's not quite there
But the atmospheric pressure of Venus is over 90 times that of Earth's because of the voracious
volcanic activity, high heat that keeps basically everything evaporated in the
Specific combination of gases that are native to that planet. In fact, if it weren't for the fact that you definitely
Melt to death in seconds if you were to set foot on Venus unprotected if you could generate enough thrust
You'd be able to fly on Venus
Just using your arms and body as a wing surface and in Mario's planet if we raise the air density to 15
kilograms per cubic meter only 12 and a half times the density of Earth's
That means that with the hat and the right body placement and speed Mario is
Totally capable of creating enough lift to fly this means several things
In the franchise make a ton of sense why he can only fly top speed in the early games
And why he eventually falls down to the ground he's not maintaining enough thrust to keep flying
But the tanuki suit and the cape give him just enough
extra surface area that he can achieve liftoff and glide
Just from his running speed this also means that the wing cap doesn't really work by creating lift at all what it does the most
Important thing that it does is create
Constant thrust instead of thinking of it as a wing cap we should be thinking of it as a propeller hat
Constantly providing Mario with forward momentum, which allows him to achieve
Infinite flight and you know what else this means don't you the planet of Super Mario the one we spend so much time on
Cannot be Earth. Mario cannot be a human being
Everyone everyone on the planet is a vaguely humanoid looking alien
Which honestly I take is a thing of comfort it certainly makes Mario's height less
Contentious although what that gives New Donk City all about
Duh, so that's how Mario flies
There's just a lot more
Atmosphere on Mario's home planet is it because of all those volcanoes and Bowser likes to hang out in who knows
But hey at least Mario isn't dead. At least, not today. (MWAHAHAHAHAHAHAHA)
Sincerely ,Austin
P.S.
All right, all right. I made a mistake last time
Well a couple of tiny ones
But one really big one those of you who watched my getting over it video will have noticed that I like an idiot
Got my newtons wrong one kilogram on earth takes 9.8
Newtons to live F equals MA force the Newton's is mass kilograms times acceleration
9.8. Meters per second squared Earth's gravity equals
9.8. Newtons you might think this means I got all my
Forces math wrong in the video and fair, you can think that but I didn't and here's why I use
Kilogram forces for all my math and only converted to Newtons at the very end of the research for the purposes of the video
Since Newtons are considered more acceptable units of force than kilogram forces
Why did I do that because I used the kitchen scale for all my math a scale
while appearing to measure in kilograms and pounds actually measures
Kilogram force or pound force the force exerted by whatever mass is placed on top of it under Earth's gravity
And that's why I use it for all my math
It's not the most scientifically appropriate unit but people in engineering
Fields use it all the time because they're constantly using weights in their machines. I screwed up because it was 2:00 a.m.
When I was doing my research, I'm a parent. I'm chronically tired and well sometimes silly mistakes happen my bad(Chuckles)
The math and the conclusions are all still correct. Just you know irritating to anybody who took a high school physics course
Choking up my own spit. I'll try to do better next time where I guess that would be this time
Thank you everyone for watching my video on how Mario fly is pretty awesome. I didn't expect all the math to check out
That's pretty cool quick shout-out to shatter e45 who was an aerospace
Engineering major on my discord channel for helping me clear up a few misconceptions
I had about lift
And if you liked this video be sure to subscribe to the game theorist give it a like to balance out all the people who
Find my voice irritating. Tell me how awesome you think I am in the comments, and you know watch some other videos?
I'm sure you can watch the one about the Mario's a
Sociopath is a good one hood when the Olympics is a good one by Matt. There's also mine
If you want to know Mario's dead if you want some good Mario's dead stuff you watch my one on uhh Mario Galaxy
That's it. I'm gonna go now boom sucka. See you later
Captioning by Chicken Nuggets. Check out the Super Mario Galaxy Video on the left. It's a good one!