How Sonic Beat Gravity! | The Science of... Sonic the Hedgehog

dear Sega hi it's me Austin you know I've been intentionally trying to leave you alone because our channel has done a lot and I mean a lot of Sonic videos I was actually just trying to play Sonic mania to relax and relive some childhood wonderment and recreate the excitement I got playing Sonic at a friend's house since my family was a Nintendo family which altima Lee was the right choice I mean sure they had Sonic and toejam and Earl Altered Beast and Ecco the Dolphin but they also had a Sega CD in the Sega 32x while the SNES had the FX chip Mega Man X Donkey Kong Country freaking Super Mario RPG Castlevania Final Fantasy 6 and Judge Dredd what you didn't play the 1995 classic video game tie-in to the Sylvester Stallone movie Judge Dredd Wow fake gamer alerts ok I'm not here to reignite the flames the console wars that died before most of you were even born and I was just kidding about the fake gamer thing because if I wanted to actually flex my muscles on an obscure ish game you didn't play on the SNES but should've it wouldn't be judged read it it be Lufia and the fortress of doom where was I all right sanic the Hedgehog I will never not love classic platforming games and that's why they're in one of my favorite ways to relax and just kill time when I want to shut my brain off for a while but dang it mime it picky science brain has some sort of stealth mode where it just sits there passively observing while I'm trying to have fun and relax but fine maybe if I just give in and scratch this itch I can finally get back to doing what I enjoy and the Beast will be sated albeit temporarily once again we're talking about Sonic's running because literally what else is there to even talk about one that's literally 98% of the dudes entire brand and the thing is we're not talking about how surprisingly slow he is although that is part of it and we will get to it because it's definitely a classic and necessary for where we're going instead what we're gonna be talking about today is this the loop-de-loop a cornerstone of all the Sonic games even the bad ones things are awesome and they're one of the first things you experience in the franchise making an appearance little under halfway into the very first level Green Hill Zone one just far enough in to give you a few seconds to get used to the game's mechanics and dang are they super fun and amazing and make no freaking sense [Music] we've talked a lot about how loops and rings work on this show specifically how they're used to simulate gravity but we haven't talked about how they can be used for fun although interestingly the way loops like this work and the way halo rings work are not that different to tell the truth both of them work by redirecting velocity or rather changing it and the only real difference between the two is where the energy is coming from what a halo ring you appear to be stationary but you're actually moving tangentially that is this direction and the rotation of the ring is redirecting your velocity as you run into it on a microscopic level the energy that's making you feel the sensation of gravity is already in the system as the rotating ring this is exactly how a loop to loop on like Madden or roller coaster works - except instead of the energy already being in the system you put energy into it in the form of your initial speed entering it it's you that has the energy instead of being stationary and it's stationary with air quotes since technically you're not stationary but you are stationary with respect to the yeah this could get out of hand really quickly you stand on one location of the ring and the ring moves and from some frames of reference that is stationary that good enough for you well too bad we're moving on anyway instead of being air quotes stationary in the case of the loop-de-loop you are not stationary and each instant as you move forward your velocity which is tangent as well to the loop is redirected by hitting the surface of the loop this is what allows you to seemingly defy gravity in a rollercoaster by going upside down and then traveling onwards it's also what keeps you in your seat if you're traveling fast enough not only do you continue to move all way through the loop the g-forces caused by the constantly changing velocity since acceleration is change of velocity over time and that's literally what force is you will actually be pushed into your seats defying the force of gravity from the earth anyway that's how loop the loops are possible you move fast enough and redirect your energy enough you can totally make it through a loop simple enough wrong this stuff is complicated [Music] you know the difference between a rollercoaster then I don't know your feet everything absolutely everything and Sonic is totally capable of running through these loops even if he's not in ball form and that changes everything now before you go there I do know about the pepsi max loop running guy which we can't show footage of because it's been scrubbed from the internet by Pepsi for some reason and I do not want to go up against them and their team of copyright lawyers but yes running through a loop is possible and here's a picture of Damon waters a free runner partway through pulling it off the problem is that our feet aren't hot wheels and operate completely differently and transfer forces way less efficiently than wheels it's literally why we invented the wheel you may not think about this too often but walking especially bipedal walking is very hard I actually had a really long section here explaining the physics of running and why it's different from wheels when it comes to creating forward movement and while it is really cool it didn't really add anything to the episode but if you're a patron of mine at patreon you get access to some of this cut content wink-wink nudge-nudge patreon.com slash a science whitey anyway our feet are great but they're way less efficient than wheels at redirecting velocity meaning that running a loop like this is going to require not only a lot more kinetic energy in order to successfully pull it off but it's gonna require very strong leg muscles in order to handle the increased g-forces especially at the beginning section this isn't a deal breaker really but it is something for you to keep in mind if you're gonna try to do this trick yourself but enough theory let's get to the numbers what you're actually here for since sonic is capable of running entirely around the loop we have a couple of things going in our favor one of them being that we can actually easily calculate how fast he needs to be going at bare minimum at the very top of the loop in order to make it around to the other side if he can make it here going fast enough in order to assure that his feet will continue to make contact and find resistance allowing him to keep moving forward he should be golden and the formula for this is very very simple velocity equals the square root of grad / the radius of the loop simple right well yes and no we have a few problems the biggest of them being that we need to do pixel measurements and we don't have a ruler thankfully Japan has discovered and have provided for us not only a cannon height but a cannon weights for Sonic and this is gonna become important later Sonic's height according to his website is exactly 1 meter and we're gonna need this for well absolutely everything one might be awesome did a video on this three years ago a video which is awesome by the way and I totally recommend you give it a watch after this one he assumed that there was a 9.8 meters per second gravity for the purposes of his math but if there's one thing I've learned from doing this job for nearly half a decade is that gravity and video games is almost never the same as the gravity on earth in fact it's often way stronger than Earth's gravity mainly because it makes platforming a way more enjoyable and fast-paced activity and since the minimum speed formula is dependent on gravity and gravity is the main force getting in the way of successfully running one of these loops it's kind of important now we measure it and after carefully timing a 513 pixel fall which is a distance of six point five eight meters according to our blue ruler and knowing that I took Sonic approximately 0.78 three seconds to make this fall we can plug in all of our unknowns into this handy formula 2d divided by x squared to get our gravity which is 21 point four three meters per second squared or over two times Earth's gravity which you know isn't all that bad for a video game I've seen way worse knowing this we also need the radius of our loop which turns out to be just over exactly 2 sonics or 2.03 meters knowing all of this you can just plug our numbers into this formula to get the blue blurs minimum speed he needs to maintain at the top of the loop in order to keep from falling down and cracking a skull open and that answer turns out to be six point six meters per second or 14 miles per hour which is surprisingly low however this is where we begin to run into problems after running extensive testing I learned two things about Sonic the Hedgehog yes he's surprisingly slow very fast for a hedgehog but that fast for a video game what's more he has a max acceleration when he's just running that is not when he's doing his little rev up ball thing of about three point four seven meters per second squared we get into why it's important later and what's more the game shows him to be capable of pulling off a successful running of the loop and his speed running into the loop is only five point zero three meters per second this is below the minimum six point six meters per second he needs to reach by the time he gets to the top of the loop is it possible that he continues accelerating up the loop so he's able to reach six point six meters per second by the time he gets there no it is not there is a reason I measured this guy's acceleration and that's because the instant he starts curving upwards he's gonna be fighting gravity even more than he is normally on flat ground and under 2.1 g's that adds up pretty quickly at first it's barely more than he normally experiences but at some point between where he enters the loop in the 90 degree point where gravity is directly opposing his tangential vector and pulling him the opposite direction of both his velocity and his acceleration the acceleration from gravity is going to completely cancel out his forward acceleration the good news is that this means he won't begin to slow down until he crosses whatever this threshold is the bad news is that with two G's and a slow max acceleration of three point four seven meters per second squared this means the closer he gets to the line the less he's going to accelerate the fastest way to figure out at what point along the loop Sonic will stop accelerating forward is to use vector sums to figure out at what angle gravity has to be to zero out three point four seven meters per second squared and to do that it's pretty simple all you have to do is take square reduces sum of the squares of 3.47 meters per second squared in 21.4 meters per second squared in order to get your B vector don't worry about what that is it's not important but the answer is 20 1.15 meters per second squared and when you take the gravity vector 21.4 divide it by 20 1.15 the B vector take the arc tangent or inverse tangent of the answer to get 44 degrees subtract that from 180 degrees to figure out the angle gravity needs to be at from your acceleration vector and bada-bing bada-boom you get 135 degrees which means when sonic is only 2.4 meters into the loop or about 18% of the way through not even a quarter of the way up all of his forward acceleration is canceled out by gravity meaning he only reaches a top speed of 5.8 m/s before it starts falling again meaning he would not be able to make it to the top of the loop safely oh math but see absolute slowest sonic can make the loop in game I can forgive that what if he's running at top speed would he be able to make it then well his top not balled up speed is ten point three meters per second which is already promising because it's faster than the minimum six point six meters per second that we need and it was here that I was tempted to use calculus and jerks which are an actual unit I promise you that in order to figure out if this would work but there's a better way thankfully that does not involve calculus and it boils down to one simple principle energy balance you see Sonic at this here hat rat here above the ground at the top of the loop has energy and we can calculate what it is technically we don't need to know his mass although it's helpful we just need to know that the energy that's up here at this peak is less than or equal to the energy Sonic has as he enters the loop as he enters the loop his energy is entirely kinetic energy as he rises up however and begins to slow down that kinetic energy starts to change into potential energy which is the amount of energy Sonic is essentially storing as the energy he would release if he fell to the ground at the very peak of this loop his kinetic energy is at its lowest and his potential energy is at its highest before it begins to switch back again as he runs down the other side of the loop and it turns back into kinetic energy so our friends in Japan said that sonic weighs 35 kilograms meaning at the peak here using the kinetic energy formula of one-half mass times velocity squared Sonic is going the minimum speed of six point six meters per second he's got seven hundred and sixty-two joules of kinetic energy which we can add to his potential energy which is mass times gravity times height which gets us 3049 joules of potential energy see that's much much higher than its kinetic energy adding these two together we get a total energy requirement of 3811 joules energy that sonic needs to put into this system in order to pull off this loop properly which we can get by rearranging the kinetic energy formula to put velocity on this side and plug in our numbers which nuggets matter right nuggets plug our numbers in which gets us fourteen point seven five meters per second as a bare minimum speed Sonic needs to be going in order to pull off this loop way more that he's doing even when he's running at top speed which is more like 10 meters per second that's over 33 miles per hour the speed limit of most small towns and neighborhoods in America I'm starting to doubt this guy can make this loop at all you little liar not to mention that he'd be experiencing at least seven GS of peak force pulling all his blood directly out of his head increasing the chance that he'd pass out and end up smacking his head against the side of the loop but here is where the game finally saves us because I still haven't tested his revved up ball form which not only goes much faster than him on foot it also seems to behave like an actual ball meaning that it would be way more efficient at changing velocity than feet would in a fully revved up ball form Sonic passes 280 pixels in 13 frames which is three point five nine meters per point two one six seven seconds which becomes a speed of sixteen point five seven meters per second which is bigger than 14 point seven five meters per second which means we did it son-of-a-gun we did it the absolute man let pulled it off finally something is an unambiguous win for a video game in one of my shows well just sidestep answering the question of how sonic somehow avoids getting a chronic case of vertigo and vomiting all over Stardust Speedway from all that violence spinning that's a brief aside this website claims that he can travel with the speed of sound which is utterly ridiculous and don't even get me started on how stupid that gets stupid blue blur better luck next time sonic sincerely Austin here's a shout out to all the patrons who make me making goofy videos 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Channel: The Game Theorists

Views: 1,399,201

Keywords: sonic, sonic the hedgehog, sonic hedgehog, sonic movie, mario sonic, sonic full movie, sonic 2020, summer sonic 2020, ok ko sonic, old sonic vs new sonic, sonic loops, sonic physics, sonic olympics, sonic mania, sonic music, sonic exe, the science of, the science, science of sonic, sonic games, sonic game, the game theorists, game theory, matpat, game theory sonic, mario & sonic at the olympic games, mario sonic olympic games

Id: OeZg1geQS9I

Length: 17min 12sec (1032 seconds)

Published: Thu Jun 18 2020