The first time I did a sonic episode on Game Theory was 5 YEARS AGO Which makes me stop and wonder... What else was going on 5 years ago? Flashback flashback flashback flashback FLASHBACK!! *aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaah* I CAME IN LIKE A WRECKING BALL! *WHAT DOES THE FOX SAY?* *GANGNAM STYLE* *DEAD MEMES*
"Why MatPat, WHY!?" "*DOGE!*" OHOHOHOHOHOHOHO BOY Maybe we shouldn't be revisiting this era of Internet history. *Game Theory Intro* Hello Internet, welcome to GAME THEORY! Where between all the Nintendo, FNAF, Doki Doki, Fortnite, and Lootboxes, I thought we needed a dose of our favorite blue hedgehog. Now, a few months ago I got a special request for a theory about the physics of Sonic the Hedgehog's running ability from Dominic: An awesome member of the Theorist Community who I met through the Make a Wish Foundation, and who you may remember as the voice of the internet from the Mario "How Deadly is the Bomb" episode. Anything, uh, you wanna say here Dominic? Uh... Make sure to subscribe to The Game Theorists! *Whispers* And mainly for Austin 'cause he's my favorite... "HOW DARE YOU!" Last episode I did a video on the physics of Sonic, This channel had less than 50,000 SUBSCRIBERS! And now last month, we just crossed, 10 MILLION! Which means by the time we do another Sonic physics theory, It's gonna be around 20 million, hopefully, maybe... Assuming Youtube doesn't implode on itself, Gaming channels don't get demonetized to death, I don't do anything horrendous to offend everyone, and the video game industry resists the urge to make every single game a Battle Royale style game with absolutely zero plot So basically, never gonna happen. But you know what, that's probably for the best. Because just think of all the disturbing Sonic fanart, 20 million theorists could generate. *ECHOING FLASHFORWARD* "WOOSH" Anyway, when I met up with Dominic, (Which, let the record show, did not happen in my recording closet. We went out for pizza, Thank you very much. His parents were there, I am NOT as creepy as I seem.) He asked me the following: If Sonic runs so fast, what would happen to his legs? Wouldn't they wear out and get hurt? Which, honestly, is a completely legitimate question and completely deserves an answer. And even just stands to reason that it can't be good for anyone much less a rodent thats basically a mango with legs to run that much and that fast. So today we're putting this adorable little hedgehog's feet to the test to see if Sonic would survive his own primary game mechanic or whether his arthritis by the end of the first level should be sending him to REHABILITATIONOPOLIS ZONE. To figure out whether Sonic is actually going fast or whether he's dead on his feet we have to know something about the actual mechanics of running. Running is something that a lot of us are lucky enough to take for granted but it also seems like common knowledge that running puts a lot of stress on your body. I mean, we've all heard the warnings, right? "Too much running is bad for you because of all the pounding of your joints on the pavement" Especially the force delivered on your knees Knees are what are called hinge joints, made up of just three bones and a relatively thin layer of protective padding called cartilage. When running, every single step puts an immense amount of force on that one joint. To make matters worse, cartilage is one of the few types of tissue that doesn't regenerate in the body. And after so much abuse it doesn't seem unreasonable to assume that by the time Sonic's a few levels in, he's going to be hit with rigid stiffness in his knees, bones grinding against one other because he's worn out the cartilage, throbbing, agonizing pain, and an extreme loss of mobility. In other words, Sonic would be demonstrating all the hallmarks of OSTEOARTHRITIS. But, in order to know for sure, we have to dig deeper. Just how long is it going to take for Sonic's knees to give out? One game? Two games? One level? I mean, he is running super fast and taking a lot of steps in that first act of Green Hill Zone. So let's get to it FAST. As I said before, the knee is made up of three bones. Those bones are the femur, better known as the thigh bone, the patella, or kneecap, and the tibia, aka the shin. Between all those bones you have two kinds of cartilage. Hyaline cartilage, which covers all the areas in which the bones articulate, and fibrocartilage, which acts as padding around the balls at the end of the bones. Articular cartilage and fibrocartilage are found in the knees of pretty much everything that has knee joints. And yes, that includes hedgehogs. But honestly, for the purposes of this episode, I had to stop treating Sonic like a hedgehog and treat him more like a human. And that's for good reason. Hedgehogs don't actually have the physical capacity to hold themselves up the way Sonic can. Their muscles just don't support it. Their bones aren't structured for standing upright on two legs. So in order to get any kind of real-world calculations here, we need to assume Sonic's joints can function just like a normal person's would. So let's see what kind of force Sonic is producing. In other words, Sonic Forces! *BA DUM TSST* You get it? Cause... that was a game that came out? Called Sonic Forces? You know what? Sir Isaac Newton would've appreciated it, alright? In a study run by Southern Methodist University's Locomotor Performance Lab, they calculated the force of running to be 2.32 times Bodyweight when running at 5 meters per second. And 4.64 times body weight when running at ten meters per second. At the SMU lab, they use this kind of data to demonstrate that running force increases linearly with speed, making it really easy for us to calculate the force of running at higher speeds like the ones that Sonic is going to be running at. We'll just need Sonic's official weight and his speeds of--! Haha... oh God. *DUN DUN DUN!* We need to calculate Sonic's speed! Now, if you've watched this channel over the last five or six years, then you know Sonic's speed has been a bit of a sensitive subject for viewers of this show, BUT! I'm going to try to get a reasonable number of calculations so even BluHedgehog4Lyfe and I<3Sonic69 in the comments will be satisfied this time. We have some canon information that we can absolutely start with, specifically according to Sega of Japan's Sonic profile that Sonic weighs in at 35 kilograms, (77lb) which honestly is pretty heavy for a hedgehog but only about half the weight of your typical human. I also know, based on your very vehement comments from that Sonic is Slow episode, that Sonic actually has two officially canon heights, which are 3ft 3in tall for modern Sonic, and 2ft 6in for classic Sonic, which we know from the original Japanese Sonic CD game manual. We also see the height difference at play in any game where classic Sonic and modern Sonic appear together, one great example is in Sonic generations, but to absolutely, 100% make sure that everyone is happy here, I ran all of today's calculations with BOTH MEASUREMENTS. Now, to calculate Sonic's speed I translated his canon height into pixel measurements so I could then get a pixel-to-centimeter ratio for each of three separate Sonic games: Sonic 1, Sonic 2, and Sonic Mania. And yes, technically all three of these should be classic Sonic heights, but again, I wanted to be thorough here. This is IMPORTANT because i wanted to to not only establish just a single Sonic speed, but his speed in the specific context of the game that he's in at any given point in time. So using all of this overwrought logic and the different heights and the different pixel measurements across all of these different games, you get a shockingly wide range of speeds. Our lowest speed is short Sonic from Sonic One taking a brisk basic level jog: 7.13 meters per second or just under 16 miles per hour. And our fastest speed is tall Sonic in Sonic 2 at a whopping 24.8 meters per second or 55.4 miles per hour top speed... where I guess, he decided he really did wanna go... ...somewhat fast? Or at least around the speed limit of a highway. For Sonic Mania, I even went so far as to calculate individual speeds for his different boosts, and special items. So I calculated everything from no-shoes Sonics, to Sonics in speed-shoes, to Sonics on speed boosters, and even comin' off of springs. And despite running that whole gamut, Sonic Mania's speed still mostly clocked in in the middle, with the slowest bring no-shoes Sonic at 17 miles per hour and the fastest being spring-loaded Sonic at 44 miles per hour. plugging in the top and bottom of our speed ranges here to calculate the type of forces that could expect upon impact, we're lookin at 115 Newtons to 402 Newtons on each leg as it's striking the ground. Now, for context when Usain Bolt ran the hundred meter sprint back in 2009, He clocked in at 12.27 meters per second, and weighing in at 88 kilograms, EVEN HE is putting more force on his legs at 440 Newtons than Sonic is. But there's an even BIGGER ISSUE here Remember how I said that too much running is bad for us because the pounding on our knees? Well, it's a complete LIE! A total old wive's tale! Multiple studies from NPR to Runner's World Prevention all state that, quote: "Runners appear to have no more risk of developing osteoarthritis than nonrunners." Believe me, I tried looking for other credible sources here to refute what I thought must've assuredly been bunk science. Big Runner over here is trying to pull the wall over all of our eyes, but no. Quote again: "In a cross-sectional study of almost 75.000 runners, there was no evidence that running increases the risk for osteoarthritis, including marathon participation." I. Was. SHOOKETH. And, believe me, this totally bums me out, because I'll take any excuse to not exercise. But it turns out that running is, unfortunately, good for us. The cartilage doesn't wear away, it actually gets stronger when you use it. *mumbling* huzzah. Sorry, guys, it looks that I have to invest in a treadmill. So there you have it. The idea that running causes injuries is a total myth and has been debunked by repeated scientific studies. Sonic's running would not be bad for his health AT ALL. This theory just, dammit, I literally feel defeated HOHO! WAIT A MINUTE! That's it. play that back, ronnie. *laughing* It's not the running that's going to damage sonic, it's the stopping. Look at how terrible that form is! This has got to be the thing that's gunna do him in. After all. We know that's he's traveling really fast. and he's just digging his heels into the ground. We can clearly see in the games how he's stopping almost on a dime. And turning around so quickly. That can not be good on his hinge joint of a knee! JUST when sonic thought he was out of the green hill zone he is in for a world of scientific hurt. we have talked about this problem in the past with everything from link's hookshot to assassin's creed's leap of faith, but video game characters still can't seem to learn their lessons about momentum. specifically that when you change it really fast, you tend to loose an arm. or rip yourself in half. or just plain kill yourself. so, is sonic changing momentum gonna shatter his knees into a thousand pieces? I can only hope. because then I can put it in the title and it'll be really exciting and no one will claim clickbait! to figure this part out, I went back to the speed calculations again, except this time i didn't just need to know his speed, I also needed to know how fast he stops. so once again I used that whole range of speeds calculated over multiple sonic heights and multiple sonic games using multiple sonic speed multipliers since the impact of stopping at 16 miles per hour versus 55 miles per hour is gonna look pretty different. I calculated stopping speed using the same formula you would use to calculate the force needed to stop a car. This is at its core in energy transfer problem. So we basically need to calculate how much kinetic energy sonic is losing from stopping using the classic equation kinetic energy equals one half times mass times velocity squared. Then, figure out how much force that translates to using the energy force equation; energy = force times distance, and this all makes sense if you think back to physics, right? As sonic slows down He's losing kinetic or movement energy. But, remember that energy can't be destroyed so it has to go SOMEWHERE. In this case, to stop quickly, Sonic is gonna have to be losing alot of energy FAST. Which means that his legs are gonna have to take a big impact to get that kinetic energy to drop to zero (0) It's not really HARD math, because we have all the numbers that we need its just that I did alot of permutations across all three games, two sonic heights and then all those speed boosts. So THIS is a little slideshow I put together of me running ALL those calculations *fangirling over math* ahhh so exciting!* This is me and Steph doing one half mV squared in Sonic 1 for short Sonic, and this is me and Steph doing one half mV squared for short Sonic in Sonic 2 and this is me doing SOLOYOLO one half mV squared for short Sonic and Sonic and Knuckles and this is us just one half mV squaring it up anddd a few more SSLIDESSS ANNND were done *clap* In calculating how much kinetic energy sonic is LOSING, I notice two things right away. ONE big factor in kinetic energy is mass. How much somethings gonna weigh. Sonic only weighs 35kg Which is just the average weigh of an 11 year old girl in the US. So no matter how fast Sonic is going, he's always gonna have less kinetic energy because he's just so light-weigh. Once I calculated all the kinetic energy's of all of out sonics, We had a range of just over 1000 joules of energy loss to over 10,000 joules of energy loss. That last calculation was for tall modern sonic if he was in sonic 2. NOW, that sounds Like it's a HUGEE spread. And honestly, it is but the actual force of the stop has to do with another big variable here, and that is stopping distance. One detail in the sonic franchise that I never noticed, and am only now appreciating that I have started to do the research on it, is that sonic has a slightly different stopping distance across each game And as he goes faster, His stopping distance tends to increase. Which is what you'd expect the real world behavior to be like. Good attention to detail, guys. SO AGAIN I did all the same calculations using pixel measurements From tall and short sonic across all three games, Across all different scenarios. Based on pixel measurements and sonic's stopping animation in each game, I found that The stopping distances vary from just under half a meter in Sonic 2 using short sonic to six point two three meters in sonic MANIA If you choose to calculate using tall sonic. THAT IS AN ENORMOUS range BUT again, gotta make sure that I<3Sonic69 is happy. If you see him in the comments, make sure you say hi. I'm sure he could use a friend today. SO finally, after getting all the kinetic energy calculations and all the respective stopping distances I PLUGGED IT BACK into the force = energy x distance equation and came up with the range of stopping forces of SONIC'S LEGS throughout the various games. The force's ranged from 641 newtons for short sonic in sonic two, ALL THE WAY UP TO 2395 newtons for tall sonic oof in sonic two. AND WHAT DO ALL THESE NUMBERS MEAN MATPAT?? did we CRUSH sonic's bones into a thousand pieces when he tries to stop ded (dead) in his tracks? IS THE FORCE SO GREAT, that his legs would fall off or EXPLODES upon impact before Green Hill zone is finished??? My little theorist heart went pitter-pat as I looked up the scale of what these numbers translate to AND I FOUND... THAT THEY DON'T DO ANYTHING. wait... what? that can't be.. right! Carry the two, don't forgot the square divided by the fraction.. NOnoOoOoOoO! Sonic doesn't just NOT shatter the bones in his body, he doesn't even break an ankle!
I was sooo positive that he would meet the same sort of end all all the other video game characters that I have running into walls, leaping off of buildings, in the like, but MIRACULOUSLY, SOMEHOW no matter HOW I slice the numbers, sonic is 100 percent FINE. On the low end 1,000 newtons is the average bite force of an adult. About 225 pounds of a force. Which is the force that body-builders can achieve lifting huge weights. Obviously, It's not going to be breaking any bones. At our maximum force calculation of 2,385 newtons, There is a chance that sonic could tear his ACL Which will technically tear a 2,312 newtons of force. But, that's ONLY if you're gonna take the force on one leg from a couple of vary specific angles. Meaning that in most cases Sonic is going to be completely fine. If we had any CHANCE at breaking a bone, We'd need to almost DOUBLE the ammount of force on sonic's legs. Up to about 4,000 newtons to break his tibia. And even HIGHER if we wanted a thiccer (thicker) bone to break. OR his bones to SHATTER. It just turns out in the game whether the designers meant to or not They made sonic, 1; Light enough, 2; slow enough and 3; gave him enough stopping distance To slow him down in a safe manor. I can't believe I'm saying this, but, It looks like sonic got me. OOOR did he? I measured his speed in a variety of 2D games using a variety of speed boosters. BUT WHAT IF sonic IS truly able to roll around at the speed of sound like the song indicates It turns out that if ya run the numbers, the stopping distance from sonic is gonna be about 69 meters. And the force of the stop would be 29,842 newtons 30 THOUSAND NEWTONS. Which is MORE THAN Enough the SHATTER most of the bones in sonic's body. HUZZAH! AND yes, that's the sound of me celebrating a fictional hedgehog BREAKING EVERY single bone in his body... Because here's the long story short, if sonic truly Lived up to his own height, he'd be completely debilitated every time he tried to stop So it's here, loyal theorists, that I leave you with a choice. Either, sonic destroys his body every time he fires up his top speed, or we can just agree that sonic is slow.BUT HEY THAT'S JUST A THEORY, A GAME THEORY. Hope you enjoyed it, Dominic! If you want to see my first ever controversial "sonic is slow" theory, then SPEED your way over to the box on the LEFT. Look at how much more sophisticated the process has gotten since the last 6 years I'm actually impressed. We've come a long way. LONG GONE ARE THE DAYZ (days) where I strung a bunch of sonic png's together and then based sonic's time to run that distance by the time It took a speedrunner to get through the level. OR race YOUR way over the the subscribe button! Where, if we finally hit 20 million subscribers, we'll be able to do ANOTHER PHYSICS of sonic the hedgehog video. You made it this deep into THIS video where only 10 million subscribers away!
MatPat and Steph need to explain the context behind this photo on GTLive one day.
https://em.wattpad.com/f762d6ddb0647b6a2cc25775a8d450417dd8f0c3/687474703a2f2f36382e6d656469612e74756d626c722e636f6d2f36373831633530633630313763623263623831396661656439643333643837312f74756d626c725f6f696c69306274733269317338736d626c6f315f3534302e706e67?s=fit&h=662&w=1349&q=80
Matthew said that he had only done one sonic episode (Sonic is Slow episode) but he forgot the Chaos emeralds episode.
Oh damn. 5 years ago was an internet culture treasure trove. And maybe not in the best way, but we loved all of those things at the time. And thinking back on them makes me smile.
During the video ( at 13:35) mat said the the force equals the energy * distance which is not true , it's equal to energy / distance so I grabbed a calculator to figure out the actual number ... Turns out that mat used the correct formula but was too lazy to edit the wrong one sooooooo if you are having a physics test soon remember that it's E=FD not F=ED
It's been a while since I've used hs physics but for those equations at 11:02. Can anyone confirm/deny that you can also use the impulse equation? (force) x (change in time) = (mass) x (change in velocity). To me it's a very intuitive way to calculate force from a stopping distance because we experience it all the time whenever we brake in our cars.
Nice Theroy video. I just wanted to say that the speed measurements are only true if the Game shows us the world in Real-Time. Maybe the world is slowed down while we play.