Game Theory - Can Sonic SURVIVE His Own Speed? (Sonic the Hedgehog)

Episode Date: May 7, 2023

When you think of Sonic, the first thing that comes to mind is SPEED. This hedgehog is CRAZY FAST. But....is that speed dangerous? Could Sonic's speed ACTUALLY be hurting him? We've already talked about how "fast" he is, and now we are going to see what are the consequences. Today Loyal Theorists, we are going to find out if Sonic's speed is his worst enemy.

Welcome to Game Theory, where between all the Nintendo, Fnaf, dokey, Dokey, Fortnite, and Lute Boxes, 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. 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. I mean, it just stands to reason that it can't be good for anyone, much less a rodent that's 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 faster, 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 gonna get hit with rigid stiffness in his knees, bones grinding against one another 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 gonna 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 active 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 pettella or kneecap, and the tibia, aka the shin. Between all of those bones, you have two types of cartilage. High-aline cartilage, which covers all the areas in which the bones articulate, and fibro cartilage. that acts as padding around the balls at the end of the bones.

Articular cartilage and fibrocardilage 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 that 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 that Sonic's joint

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. You get it because that was a game that came out called Sonic forces? You know what Sir Isaac Newton would have 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 body weight when running at 5 meters per second, and 4.64 times body weight when running at 10 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 gonna be running at. We'll just need Sonic's official weight and his speeds of... Oh god! We need to calculate Sonic speed!

Now if you've watched this channel over the last five or six years, then you know! Sonic Speed has been a bit of a sensitive subject for viewers of this show, but... I'm gonna try to get a reasonable number of calculations, so hopefully even blue Hedgehog for Life and I greater than three Sonic 69 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, 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 3 foot 3 inches tall for modern Sonic, and 2 foot 6 inches 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 speed, I translated this 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 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 from across all of these different games, you get a shockingly wide range of speeds. Our lowest speed is short Sonic from Sonic 1 taking a brisk basic level just Jog, 7.13 meters per second or just under 16 miles per hour. And our fastest speed is tall Sonic and 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 want to 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-shoe Sonics to Sonics and Speed Shoes to Sonics on Speed Boosters, and even

coming off of springs. And despite running that whole gamut, Sonic mania speed still mostly clocked in in the middle With the slowest being no-shoe 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 we could expect upon impact We're looking at 115 Newtons to 402 newtons on each leg as it's striking the ground Now for context when Usain Bolt ran the 100 meter sprint back in 2009 he clocked in 12 0.27 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 we're all told that too much running is bad for us because of the pounding on our knees? Well, it's a complete lie. A total old wives tale. Multiple studies from NPR to runners world prevention all state that quote,

runners appear to have no more risk of developing osteoarthritis than non-runners. Believe me, I tried looking for for other credible sources here to refute what I thought must have assuredly been bunk science. Big runner over here is trying to pull the wool 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. Cazaa! Sorry guys, it looks like 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... Damn it, I literally feel defeated.

Ho-ho, wait a minute! That's it. Play that back, Ronnie. It's not the running that's gonna damage Sonic. It's the stopping. Look at how terrible that form is! This has gotta be the thing that's gonna do him in. After all, we know that 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 cannot be good on his hinge joint of a knee. Just when Sonic thought he was out of the Green Hills Zone, he is in for a world of scientific hurt. So is Sonic changing momentum gonna shatter his knees into a thousand pieces? I can only hope.

To figure this part out, I went back to the speed calculations again, except this this one, 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 from 16 miles per hour versus 55 miles per hour is gonna look pretty different. I calculated stopping speed using the same formula you'd use to calculate the force needed to stop a car. This is at its core an 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 equals 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 a lot 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. It's not really hard math because we have all the numbers that we need.

It's just that I did a lot 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. Oh, it's so exciting. This is me and Steph doing one half mv squared and Sonic 1 for Short Sonic. And this is me and Steph doing 1 half mv squared for short Sonic and Sonic 2. And this is me doing solo one half mv squared and Sonic 1 half mv squared for Sonic 1. for short Sonic and Sonic and Knuckles. And this is us just one half mb squaring it up.

And a few more slides. And we're done. 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 something's gonna weigh? Sonic only weighs 35 kilograms, which is just the average weight 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 like so lightweight. Once I calculated all the kinetic energies of all of our Sonics, we had a range of just over a thousand Jules of energy lost to over 10,000 joules of energy lost. That last calculation was for tall modern Sonic if he was in Sonic 2. Now that sounds like it's a huge 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've started 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 would expect the real-world behavior to be like good attention to detail guys So again I did all of 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 stopping animation in each game I found that the stopping distance is varied from just under half a meter in Sonic to using short Sonic to 6.23 meters in Sonic Mania if you choose to calculate using Tall Sonic. That is an enormous range, but again, I gotta make sure that I heart Sonic 69 is happy. So finally, after getting all the kinetic energy calculations and all the respective stopping distances, I plugged it all back into the force equals energy times distance equation, and came up with the range of stopping forces on Sonic's legs throughout the various games.

The forces ranged from 641 Newtons for short Sonic and Sonic 2, all the way up to 2,385 newts for Paul Sonic in Sonic 2. And what do these numbers mean? Did we crush Sonic's bones into a thousand pieces when he tries to stop dead in his tracks? Is the force so great that his legs would fall off or he 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 forget to square, divide by the fraction.

NO! Sonic doesn't just not shatter the bones in his body. He doesn't even sprain an ankle. Miraculously, somehow, no matter how I slice the numbers, Sonic is 100% fine. On the low end, a thousand newtons is the average bite force of an adult. It's about 225 pounds of force, which is the force that bodybuilders can achieve lifting huge weights.

Obviously, it's not gonna 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 at 2,312 newtons of force, but that's only if you're gonna take the force on one leg from a couple of very specific angles, meaning that in most cases, Sonic is gonna be completely fine. If we had any chance of breaking a bone,

we'd need to almost double the amount of force on Sonic's legs, up to about 4,000 newtons to break his tibia. And even higher if we wanted a thicker bone to break or his bones to shatter. It just turns out in the games whether the designers meant to or not, they made Sonic one, light enough, two, slow enough, and three, gave him enough stopping distance to slow him down in a safe manner. I can't believe I'm saying this, but it looks like Sonic got me. Or 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 speed a sound like his song indicates. It turns out that if you run the numbers, the stopping distance for Sonic is gonna be about 69 meters. And the force of the stop would be 29,842 Newton's. 30,000 Newton's, which is more than enough to shatter most of the bones in Sonic's body. 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 speeds, or we can just agree that Sonic is slow.

But hey, that's just a theory. A game theory! Hope you enjoyed it, Dominic.