Game Theory: Chun-Li's DEADLY Helicopter Kick (Street Fighter 5)

today we're covering Chumlee one of gaming's strongest most empowered female protagonists fighting bravely to avenge her father's death and go back to being a young single girl apparently Oh video games hello Internet welcome to game theory where let's be honest with ourselves we all know that Vega was the coolest right he had the mask and the Wolverine claws like how could you not pick that guy well maybe because Street Fighter 2 had such a cool cast of characters and each one with awesome special moves you had dull Sims yoga fire Blancas electric-thunder zangief's balls to the face that's what it's called right the t-bag spin the crotch rocket 69 suplex anyway the one that's always been the most intriguing for me and that I've literally wanted to cover for years on the show is chun-li spinning bird kick in this move chun-li flips upside down does the splits in midair and then whirls or legs around so fast that she levitates off the ground and then kicks her opponent in the face she's like a helicopter made of legs it's a cool move but it's crazy right like there's no way for a human being to spin around fast enough that they could just fly away well maybe then again maybe not when you look at some of the crazy martial arts stunts that people can do nowadays self propelled flight doesn't seem all that far-fetched there's only one way to find out though so sharpen your pencils class we're about to get down to the physics of chun-li spinning bird kick and find out whether this is plausible or whether the bird kick lays an egg get it it was pretty proud of that one first we should probably start with a quick lesson on how things fly like I said I wanted to cover this topic for years but the reason it's taken so long is that while this isn't rocket science it is helicopter science and as result takes a while to wrap your head around aerodynamics gets complicated real fast can only furniture construction with nothing but images complicated but like ideas Hemnes we shall overcome flying in the simplest sense is overcoming gravity which in physics terms is a force finding a force requires multiplying the mass of an object by the acceleration of the object if you saw the Zelda hookshot episode you'll remember samaa F equals MA the force of gravity pulls down toward the earth so in order to fly you need to create a greater force in the opposite direction which is known as lift airplanes and helicopters create lift through the shape their wings which we airfoils if you look at aircraft wings from the sides they tend to be teardrop shaped with a bigger curve on the top than on the bottom when the wings pass through the sky some of the air goes underneath the wing staying relatively flat and some of the air goes over the top of the wing around the curved teardrop edge as the air goes over the top of the wing it clings to the shape of the wing by going up and over the rounded edge and then turning down toward the point of the teardrop in what's known as the quando effect this change in direction when the air on top of the wing switches from moving up to moving down is the important part according to Newton's third law of motion for every action there must be an equal and opposite reaction like when you perform the action of meeting a chipotle burrito and are greeted with the opposite reaction in a toilet stall a few hours later in the case of the air flow around the wings when the air changes direction and moves downward an opposite reaction must occur which is the air beneath the wings pushing up the wings are pushed up enough by that upward force that the whole aircraft then rises and flies truly you are the wind beneath my wings so do you get it awesome congratulations because you just learned something it took engineers millennia to figure out isn't the internet great now you might be thinking not so fast matpat that's a pretty simplified version of how things fly what about angle of attack or the Bernoulli principle if so high Massa thanks so much for watching loved your work in the Martian great effort good good job seriously though if we were trying to build a mechanical flying Chumbley robot then yeah we'd need to take some more laws into consideration but from a purely hypothetical standpoint our goal is to figure out whether a person can get around the forces that prevent human flight so it'll do for our simplified thought experiments just don't expect me to get into my hypothetical chun-li robot and fly from here to New York weirdest flight ever so now we want to apply all this lift stuff to chun-li and her spinning legs to determine how fast she has to be spinning in order to fly but not so fast there mike byson chun-li doesn't fly she hovers potato potato you might say to which I respond who says potato like what accent is that well I am seriously curious do do any of you out there actually say potato or do any of you out there know someone who says potato let's put this mystery to bed once and for all anyway hovering is not the same as flying once Chumlee gets off the ground she isn't rising she's just going forward and backward this is actually really good news because it makes her job and quite honestly our job a lot easier for a body that's hovering the force of gravity should be roughly equal to the lift and as we've covered multiple times here on the show gravity has a constant acceleration on earth of 9.81 meters per second squared meters mean I have to know the metric system for this episode yes American viewers most of the calculations will be done in metric units but don't worry we'll convert them back to our cutesy English system soon so you just sit tight anyway to figure out her lifting force all we need to do is multiply that 9.81 m/s^2 by chun-li's weights simple as that so chun-li's weight is um is uh what damn it are you kidding me every character in this game gets a weight but chun-li it's a secret I can know her blood type but not her weight it's like the world purposely trolls me okay so honestly this one is actually really hard because first the quote-unquote official heights and weights of the characters fluctuate quite a bit between installments in the series additionally after doing the pixel measurements across multiple generations of the game characters aren't always scaled appropriately relative to one another and their height constantly varies for instance chun-li's BIOS screen and Street Fighter 2 lists are at 5 foot 8 inches or 172 centimeters in all subsequent games though she's apparently shrunken ranging everywhere from 5 foot 5 inches or 165 centimeters to 5 foot 7 169 centimeters I mean I've heard of women keeping their weight a secret but their height - it's just absurd as a result the math here kept turning up inconsistent and I will not have another Wario is 10 feet tall situation so here is the best solution I came up with women's bodies are a different density than men's so I compared chun-li's bill to every other female character across the series factoring in their known heights and weights cami clocks in at 5 foot 4 and 134 pounds sixty point eight kilogram but we all know kami is much thinner than chun-li rights well kinda I was actually shocked when I went back to the game but apparently chun-li his legs have gotten a bit more exaggerated over the years when they first squared off in Street Fighter 2 they were much closer to being the same build surprised yeah so was high but without any other females to really compare again for those early games I had to keep digging into some later installments Rainbow Myka is just over five foot six inches an official Street Fighter 5 materials and comes in weighing 154 pounds or about 70 kilograms then there's the real wild card Laura Matsuda powers over everyone at 5 foot 9 inches but then weighs in the exact same range as everyone else at 159 pounds or 72 kilograms after looking at this data I then went and compared her body type to real-life female athletes Chumley's bill doesn't fit that of say an Olympic weightlifter so it makes more sense to compare her to mixed martial artists the most famous of these is definitely rowdy Ronda Rousey Ronda stands at 5 foot 7 inches tall right around chun-li's height and weighs 135 pounds which converts to about 61 kilograms so based on the statistics of all the other female fighters as well as real-world research as well as the fact that Chun Lee's body isn't too far off size-wise from any of these other fighters I'm assuming her weight is around 155 pounds or 70.3 kilos and honestly don't worry if we're a couple pounds off it's not gonna throw off the math all that much now that we have that number we can plug it into our formula 9.81 times 70.3 and we get that the force of gravity acting on chun-li is 680 9.6 Newtons and honestly 700 Newtons isn't all that much to give you a point of reference punches from boxers have been measured to be upwards of 5,000 Newton so while the amount of force isn't that huge the way we're creating it makes things a little extra complicated we need a lifting force that'll reach 700 Newton's created by spinning legs lifting force is a complicated equation it's equal to the lift coefficient times the city the air times velocity of the blade squared over two times the area the wings hover we're trying to determine the velocity of the blades V or in this case the velocity of her legs and we already know the force we need it to equal six eighty nine point six Newtons so that leaves us with unknown area density and lift coefficient the density of air represented in the equation by Greek letter Rho doesn't usually vary that much until you get to pretty high altitudes since chun-li isn't fighting on top of Mount Everest or anything we can use standard sea level air density of one point two to five kilograms per cubic meter someone call Staples cuz that was a one-and-done next let's figure out the area part of the equation the area the wings cover for a helicopter refers to the area of the circle the blades go around as they turn since chun-li's spinning legs resemble helicopter blades all we have to do is determine how big of a circle she's making with the ends of her feet and boom we got our next variable so to do that we need to find the radius of the circle first which is approximately the length of one of Chumley's legs from her hip down to her foot though no one before has calculated this exactly we use pixel measurements on this picture of chun-li and her Street Fighter 2 profile page to figure it out so using pixel measurements the top of chun-li's pelvis is about fifty nine point one percent of the way upper body which would translate to a leg length of about forty point two inches or 1.0 two meters plug that 1.0 two into the formula for an area of a circle high r-squared and you get an area of three point two seven meters with that we have three variables down and one more to go the lift coefficient now lift coefficient is a constant that depends on how aerodynamic wings are and is literally different for every single object only calculated after running multiple tests in a wind tunnel and let me say fan fiction is put chun-li into some weird positions weird and disturbing positions but not anywhere like that so I had to talk to an aeronautics engineer to make sure that we were doing the right thing here's the conclusion that we all reach typically the lift coefficient for helicopter rotors is between 0.5 and point 8 now this may come as a surprise but legs are not as aerodynamic as the blades of a helicopter shocking revelations so if the low end range for helicopter blades is 0.5 it would be reasonable to estimate the lift coefficient for Chun these legs at point two and if what have you watching out there happens to be some lift coefficient connoisseur and you're like oh no it looks more like 1.55 hey don't blame me blame the aeronautics engineer all right if we plug all those values in we'll finally get the speed chun-li's legs need to go to keep her in the air six eighty nine point six Newtons equals point two times one point two to five times b squared over two times three point two seven solving solving solving that speed would need to be 41 point five meters per second at the end of her feet for us american viewers that means she's spinning around at nearly 93 miles per hour she would be making about three hundred and eighty seven revolutions per minute more than six full spins every second oh yeah she's also upside-down and doing the splits that is insane but just how insane let me explain what this really means well to put it bluntly both were legs would get dislocated every time she performed the move door I suppose the first time she performed the move she ain't getting time to pop those suckers back into place during the fight let me explain as her legs start to spin they would be experiencing a tremendous amount of force centripetal force the force created as they accelerate around the circle you know when you swing a stone around your head on a string and then cut the string the stone goes flying off in a straight line well in this case the stone is Chumley's legs and the string that got cut is the connection between her legs and her hip that's a pretty picture to calculate the strain that would put on her this area let's um hmm let's call that the rotor head that's the official helicopter term it's the mass of the leg times the velocity at travel squared over the length of the leg aka the radius of the circle so all we need here is the weight of one of her legs according to the book human body dynamics classical mechanics and human movement sixteen percent of the body's weight is in one leg on chun-li we can estimate it's probably a bit closer to twenty percent and that's on low estimate plugging in those numbers you get a centripetal force of almost get this twenty four thousand Newtons let me translate that for you the force of a professional baseball batter hitting a fastball thrown at 90 miles per hour or forty point two meters per second is around eighteen thousand four hundred Newtons an equivalent of four thousand pounds of force on the ball Charlie's helicopter legs are delivering 6,000 Newton's more than that has recovered in a Zelda hookshot video that's enough to dislocate a limb but it's not enough to rip and clean off she'd get one chance to pull off her spinning bird kick before just walking around all jelly legs except here's the thing one chance is all she would need like I just said 24,000 Newton's of force is more than a baseball batter hitting a ninety mile per hour fastball think about that force being directed straight into your face she'd 1 hit ko any opponent who came her way according to the Journal of neurosurgery 2,300 Newtons is all you need to crush a human skull and she's delivering ten times that amount with her foot and if the skull wasn't crushed it might just be kicked clean off like a gory soccer ball cadaver data shows that it takes 1,500 Newton's to break the c2 vertebra so the neck would snap instantly muscles and skin would rip and the head would go fly she'd tear through the ranks of bison in no time as long as their legs were able to withstand the pain of popping in and out repeatedly forget one punch man Adam has got a new hero and her name is chun-li one kick woman but hey that's just a theory a game theory thanks for watching

Channel: The Game Theorists

Views: 3,351,968

Keywords: Street Fighter, Street Fighter 5, Street Fighter V, Chun-Li, Ryu, Capcom, Fighting Games, Street Fighter 2, helicopter kick, chun li, street fighter 3, street fighter 4, game theory, Game Theory (Field Of Study), matpat, matthew patrick, MatthewPatrick13, history, video game, game

Id: 1DRHU1-SnvM

Length: 14min 54sec (894 seconds)

Published: Thu Mar 10 2016

Reddit Comments

[u/Toastrz]

Best episode in a while. It's finally the type of episode we've all been asking for!

[u/Coocoro]

This episode is a major step in the right direction! Good job getting back to the roots of what made me fall in love with game theory.

[u/JediRalts]

Because why did I actually think we'd get the dating sim episode? But in all honesty, loved this video. Felt like vintage Game Theory.

[u/kidelaleron]

So... no initial jump and inertia? Martial artists can do spinning kicks in the air without the need of helicopter movements. The initial jump force is enough to lift you, and the inertia will have you stay in the air for a bit. The spinning legs are just helping.

[u/Samthefab]

You don't need to actually lift, the initial jump does that. She just needs to be near to the force to maintain her height. If she did 600 newtons, she'd still stay relatively stable, and since velocity is squared she's now moving at a far slower rate.

Also, about kicking a head of. The vertabrae are not the issue with snapping a neck. It's actually the sinew and muscle which would be the problem. She'd probably break any bone in the way, but not actually crush the skull or kick it clean off.

[u/OtterInAustin]

IMO, best GT episode in months. It's about time we got back to actual analysis and left out most of the hypotheses.

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[u/culture_shock]

Wouldn't it have made more sense to count the amount of times she rotated in the time it takes to do the helicopter kick?

[u/[deleted]]

The lift coefficient of someone's legs is most likely going to be 0.