How Princess Peach BEATS Gravity! | The SCIENCE of... Mario

dear nintendo do you see this thing this thing that peach does this hover in the air thing you know what i decided to do i decided to calculate whether or not this is possible in other words i made a big mistake did you know that skirts were complicated no because i do now i know all about skirts now straight a-line pleated knife pleated fly sheath box pleat eight panel four panel asymmetrical accordion draped pencil empire waist high rise low rise micro mini above the knee below the knee mid calf maxi floor length circular three quarters half and quarter circles and believe it or not seriously that is the summary that is the overview that is the beginner's course on skirts and with just these elements alone mixed and matched you can make nothing short of 1092 different completely unique types of skirts i am in way over my head i am in danger i mean i didn't even touch on fabric weights which can bump this number up to over ten thousand what have i done [Music] my spreadsheet for this episode has gone categorically off the rails but i think i have finally solved it how does peach float she doesn't end of story or is it in order to understand this question more fully we're gonna have to lay out our parameters and the limitations to the question we're asking because this drop dead floating thing she does it is actually impossible just pure and simple without a form of lift which requires a wing or a jet pack providing rocket-powered thrust this cannot be done technically it may be possible if she's moving sideways as illustrated by the real-life powered parachutes but realistically this is improbable and nothing about her shape seems to suggest that she has anything resembling an aerodynamic wing instead we're going to be treating peach as though she were a normal parachute as though she were slowing her descent by increasing her drag by the relative amount of time longer it takes her to fall to the ground from floating as opposed to when she's not floating in other words if normally it takes her a third of a second to fall to the ground but after a full float it takes her 1.3 seconds we're gonna act as though she were slowly descending the entire time as though under the effects of a parachute not as though she were stopping dead in midair this is the only way she has a chance and boy oh boy we have got a lot to get through today so let's just get started i didn't just pull these numbers out of my butt earlier these are the actual fall times i recorded for peach in super mario bros 2. these numbers may vary slightly from game to game in the series but they don't buy much and 2d games are a lot easier to measure than 3d ones so this is what i'm going to be using falling from the peak height of a full standard jump takes peach 0.333 with a line over at seconds whereas a full float extends this to 1.3 seconds an increase in fall time of almost 300 percent this is pretty significant especially if you consider the frankly relatively small fall distance using mario as a relative ruler knowing his cannon height of 1.55 meters has been pretty consistent across multiple titles we can extrapolate a few things one peach is taller than mario by quite a bit but secondly and more importantly peach jumps a very impressive 2.97 meters high easily beating out javier sotomayor's record high jump of 2.45 meters a record that has stood for over 25 years and that's not even counting peach's super high power jump move also using these numbers we can calculate the gravity in the mushroom kingdom well in this game how many mario games have i calculated gravity in is 26.12 meters per second squared in super mario 64. 33 meters per second squared in super mario galaxy 36.42 meters per second squared in super mario world man i should start like a website or something anyway get ready for a whopper because the gravity in super mario bros 2 puts them all to shame clocking in at a stupendous 55.22 meters per second squared over five times earth's gravity fun fact that means that just jumping at this height peach would be slamming into the ground at over 17 meters per second or almost 40 miles per hour or 63 kilometers per hour for you freedom-hating uh entirety of the rest of the world if peach weighs 65 kilos the average weight at her height this would mean she'd experience 352 kilos of force on her ankles as she lands which is probably enough to snap them i don't know i really don't have time for a cross-sectional analysis of bone force measurements too much to do too little time okay so having her weight her height her fall time in the gravity we have everything we need right just figure out an average fall velocity plug in some like magical parachute formula and wham bam we're all done right right right no not at all not even a little not even a tiny pit oh god what have i done to myself i'm in so much trouble [Music] you see at a glance the way parachutes work is honestly pretty simple but in order to understand what's simple and simultaneously what's complicated about them you have to understand drag and terminal velocity anything that's falling through the air experiences what's known as drag as you fall through the air pulled by gravity you have to push the air that's below you out of the way this creates a tiny force on your body pushing you back up as you fall down this force combined with the friction caused by the air as it rolls past your body is known as drag interestingly the faster you move the more force drag exerts on your body as the air is being pushed out of the way faster and is also causing more friction as it runs past you if you're falling from really high up it's possible that this force the force caused by drag can equal the force gravity is exerting on you by the way the shorthand word for the force gravity exerts on you is weight which if i had more time i would rant about how using kilogram a unit of mass to indicate weight when metric weight is actually newtons but there is no time today no time eyes on target austin anyway if the force caused by drag equals the force caused by gravity or your weight you actually cease to accelerate your acceleration hits zero this is what's known as terminal velocity and it's the speed at which any given body will just stop getting faster if it's falling in an atmosphere you're still falling mind you you're just not getting any faster every object in the world has a different exact terminal velocity because while technically you can just be like well when force g equals force d you're good and like well one of these is very easy to calculate specifically the force of gravity the other one is a freaking nightmare let's just compare shall we for force of gravity we get a simple mass times acceleration in this case 65 kilos times 53.2 meters per second squared which gets you 3459 newtons for princess peach and the other side looks like this now this looks intimidating but it's not actually that bad this weird looking symbol here is rho and it stands for air density this one is actually really important in calculating the force of drag because it represents how many atoms are actually in your way and represents them specifically as kilograms per cubic meter which is actually useful when you're calculating force since it's a mass pushing on you this here is velocity and it's how fast you're moving remember how i said that the faster you're moving the more drag you experience because you're moving through more air this right here is the drag coefficient and we will get to that later but it's basically the glue that holds everything together and this right here is area because the more surface area you have the more uh surface there is moving through the air and pushing molecules out of the way which in turn will increase the amount of force the air exerts on a falling object and it's this variable right here that matters the most when it comes to how parachutes work parachutes are a relatively thin relatively light sheet of fabric that you can wear that will dramatically increase your surface area they also give you a better drag coefficient but we'll get into that later and it's by and large not the most important part by creating a truly gigantic surface area compared to what is normal for a human being you can increase your drag by an order of magnitude and by comparison decrease your terminal velocity making it safe for a human being to jump out of an airplane ah i guess i have to talk about drag coefficients now okay this is actually relatively simple but it's just another complicating piece of the floating peach puzzle basically what a drag coefficient is is a numerical representation of how effective specific shapes are at creating drag a lower number means lower drag per area parachutes have one of the best shapes incidentally for drag coefficients and as a result they don't have to be like super huge because their drag coefficient is actually really really high this is also why your terminal velocity while you're falling through the air depends upon what direction you're facing if you lay flat perpendicular to the airflow your drag will be a lot higher than if you're falling feet first although this probably has more to do with increasing your surface area and the direction of the airflow and oh my god are you seeing how this gets complicated quickly okay so how does all of this apply to princess peach's ability to float well for one this formula is actually more complicated than it may first appear at a glance we have so many unknowns to figure out before we get to what the worst part of this monster is we have gravity which is important for this side of the equation and we have peach's mass mostly we'll get to that now we've got to figure out peach's drag coefficient and the surface area that's slowing her down and that's mostly it let's start with the drag coefficient probably the easiest part drag coefficients are based on shape mostly and they have been measured a lot by engineers over the years we're going to use this chart and presume that peaches dress as a hollow hemisphere because it's close enough for government work this gives us a drag coefficient of 1.42 which is pretty good not the highest possible but it is up there now the surface area we're gonna pretty much do just peach's dress because it's pretty much all that matters since her body is practically speaking not slowing her down at all and here's the part where i hope that my research into dress and skirt construction comes into play and saves me from a vicious clap back from sartorial youtube that's a thing right i'm sure it is anyway peach's dress has a floor-length a-line skirt which pixel-wise is about 78 centimeters long and we'll add another five centimeters to be safe bringing it to a cool 83. since it is a floor-length skirt this means there's most likely a full circle skirt instead of a three-quarter skirt in order to maximize mobility what does this mean well it's actually not that complicated skirts in their simplest forms are just circular fabric with a hole cut in them spread out and looked at from the top they look like this in geometry this is what's known as an analyst anyway here's where things get interesting different percentages of sectors can be cut out of this skirt before it is sewn together anywhere from 25 percent up to a whopping 75 this dictates the fullness and the structure of the skirt and how it fits around the body but for our purposes both because it's easier and it also gives peach the best chances of making it through this alive we're going to presume that she has a fully circular skirt because it maximizes her surface area we can figure out the area of this skirt and by extension get much closer to figuring out her drag by figuring out how much fabric makes up her skirt using the area of an analyst formula which is just subtracting two circular areas to account for the hole and given that she has a waist measurement of 0.39 meters this gives us an area of fabric of almost exactly 2.5 square meters now using the thinnest silk satin fabric weight to minimize the contribution of weight to peach at 24 grams per square meter this skirt is very thin weighing only about 59 grams this is not that important for now but it will become important later on trust me let's be sure to put the weight of the dress on this side of the formula to account for it and then move on to our last part which is oh all right you you see this little velocity here this is a killer this punk disrupts absolutely everything and is what changes this from a simple episode with easy math that i can just plug in and get an answer to to a freaking pain of my butt velocity in this specific context is quite the bug bear because drag changes depending upon how fast you go for example right here peach has reached the peak of her jump and is just about to start falling right now her velocity is zero which means her drag is also zero but her velocity is not going to remain zero forever because she's experiencing a force from gravity let's fast forward a whopping frame a singular 1 60th of a second forward in time assuming that the mushroom kingdom has an atmosphere similar to earth's meaning it has an air density of 1.225 kilograms per cubic meter and the gravity we measured before of 53.22 meters per second squared peach will be moving down after this short period of time at .69 nice meters per second which means now that she's moving she will finally be producing drag each frame she advances we will have to calculate a whole new drag which impacts the acceleration which will impact her velocity for the next frame it's not impossible mind you it's just a lot of work a lot of work that i did for you the people so how does peach's dress fare once it starts moving under mushroom kingdom's default conditions well at frame 1 moving at 0.69 nice meters per second with all the other numbers we've derived this means she will be producing a tremendously impressive 1 newton of drag compared to the over 3 400 newtons caused by the force of gravity and it gets worse from there working at maximum efficiency at peach's top speed she never gets close to terminal velocity here right before she hits the ground moving at 15.88 meters per second she will be producing 548 newtons of drag force pitiful a normal princess a-line floor-length skirt would be entirely incapable of slowing anyone's fall down from 330 milliseconds to 1.3 seconds it would slow you down a little bit though parachuteless peach hits the ground at 17.7 meters per second after 330 milliseconds of falling with a parachute skirt she hits the ground two meters per second slower and almost 20 milliseconds later so it is doing something okay so what if we just make the skirt bigger so it actually behaves like an actual parachute i mean all we have to do is make it really big and we should be fine right well yes and no you see if we make the surface area bigger approximately 900 square meters which is pretty big it's almost 20 peaches wide we can actually make it so when the chute opens peach does indeed float to the ground in about 1.3 seconds like we want unfortunately this is where fabric weight actually starts to come into play that 24 grams per square meter really adds up when you start adding zeros to your fabric area this means our skirt which weighed almost nothing before now weighs over 21 kilograms one-third the massive peach and it really makes a dent in the left side of the formula bringing us from 3569 newtons of weight up to over 4600. this added mass means we'll need more fabric which will add more weight which means we'll need more fabric which means we'll add more weight which means we'll need more fabric and we'll add more weight okay while it is an infinite series problem thankfully it is a convergent one not a divergent one meaning we can actually calculate how much fabric we'll need even taking into account the added weight that that fabric will produce and that answer is four thousand and eight hundred square meters for comparison a standard football field is 7 140 square meters fully fluffed up this thing would be 45 princess peaches wide and weigh an astonishingly high 115 kilograms or over 250 pounds lord at these dimensions peach would reach terminal velocity just 67 milliseconds after starting her downward descent and would slowly float to the ground at 1.59 meters per second until gently lighting up on the ground 1.3 seconds after beginning to fall of course you're probably saying to yourself this is ridiculous oh my god and you know what i agree with you thankfully there is actually a solution to this problem that doesn't involve lugging around 250 pounds of fabric hanging around your waist and it's actually a solution that i mentioned over two years ago in my mario flight episode and it is this air density if we up the atmospheric air density we can actually make peach's skirt and its original dimensions work perfectly all we gotta do is like pump way more air into the atmosphere the higher gravity certainly helps because air density is aided by gravity air molecules being pulled down and pushed together by gravity after all is pretty much what makes air pressure to begin with that said venus actually has a higher air density than earth by over 90 times in spite of having less gravity than earth and this is because there's just way more gas in the air and if we crank the air density up to 967 kilograms per cubic meter peach's default skirt would be able to reach terminal velocity from a shortfall all on its own without the extra fabric of course for comparison purposes this means that the air in the mushroom kingdom would be almost as dense as earth's oceans just running through this atmosphere would be like trying to run through water and breathing it would be like well it would feel a lot like breathing water but at least mario would be able to fly and peach would be able to float using nothing but her skirt who cares if you drown to death a little bit while trying to breathe i mean that's just the cost of doing my business sincerely austin whoa that was a long one sorry tonya i guess that's why we have patrons like adam barber jared beecher emma sims francis gagnon royal gaming16 edidam dp nicholas splinger marissa resnick ziggy and mazurf who make this stupid show possible thanks a lot you guys and we'll see the rest of you later after i take like 40 naps holy cow [Music] you

Channel: The Game Theorists

Views: 1,288,378

Rating: 4.8924546 out of 5

Keywords: mario, super mario, super mario bros, princess peach, peach, peach float, princess peach float, yoshi, kirby, luigi, paper mario, mario kart, mario maker, super mario maker, mario maker 2, super mario maker 2, super mario moves, mario theory, the science of mario, mario science, the science, the science of, game theorists, game theory, matpat

Id: VpsMPgNjQOk

Length: 18min 54sec (1134 seconds)

Published: Thu Oct 01 2020

Reddit Comments

[u/tundrat]

Early in the video when he said there's no lifting force, what about farts?

[u/Nintendoomed89]

What's the name of the song playing in the outro, I am really digging it.

[u/Walter_Alias]

4:40 That makes no sense, Peach would have to decelerate over a distance of nearly 3 meters, implying Peach in roughly 10m tall.

11:43 R should be 83cm. I have no idea what 2.55m is supposed to mean.

13:08 That's not the gravitational acceleration he calculated earlier.

13:11 That should be 0.88m/s. Never sacrifice correctness for a joke, Austin.