Would throwing Bowser rip Mario's arms off? Dear nerds, please watch the following video so I don't have to be the only one thinking about ripping Mario's arms off. Yours truly, KH. (8-bit beeping) Yahoo! The ongoing battle between Mario and Bowser is one of gaming's most legendary rivalries. As a player, you've faced Bowser in dungeons, on airships, even on the dang moon. And in one of the best games of all time, you have to fight Bowser on a stage surrounded by bombs, and Mario has to defeat Bowser by grabbing the giant turtle by his tail and flinging into his own traps. But would that rip Mario's arms off? (upbeat music) (chuckles) Oh yes. I'm of course talking about the final fights in the classic video game Super Mario 64, where our plucky plumber is tasked with grabbing Bowser by the tail, swinging him in a circle to build up speed, and then throwing the giant turtle creature into enormous landmines that the reptilian placed himself. Anyway, Bowser is a titanic turtle. How strong would Mario have to be to pull this kind of move off, and would the effort in fact pull the arms off a humanoid handyman? (8-bit beep) Whoo! If we are going to throw something like Mario throws Bowser, then it's gonna take some amount of force, and just how much force that will take will depend on exactly how massive Bowser is. There aren't any consistent canonical heights for Super Mario characters. Their sizes and their scales relative to each other are always changing game to game and are therefore up for debate. For example, if we go by the latest Super Mario Game, Super Mario Odyssey, Mario is a very short dude, just 112 centimeters, or about 3 foot 8. And we can use this relative size to scale other characters. Bowser, based on Mario here, would then be around 188 centimeters tall, or 6'2. This is interesting and a very useful figure although it doesn't really tell us how massive a turtle like a Bowser would really be. For that value, we should start looking at actual giant turtles. You can go. Oh now! If we wanna good turt comparison that actually looks like Bowser, the alligator snapping turtle wouldn't be a bad place to start. This snappy boy even kind of looks like King Koopa. However, although alligator snapping turtles get scary big, over two feet long, over 200 pounds, not even the largest snappy boys among them get to the scale of Bowser's scales. The largest living turtle on the planet, and the fourth heaviest reptile, is the leatherback sea turtle. These turtles get much closer to Bowser size. Over six feet long, over 1,500 pounds. And I know that these turtles don't exactly look as much like Bowser as the alligator snapping turtle, you know with spikes all over their bodies, but that's because the spikes are down their throat! Yeah, it's pretty metal. Although leatherback sea turtles are much closer to Bowser in size and scale, I still think they're not quite big enough, so let's take it one step further. (splashing) That was a sewage pipe. This is Archelon, an extinct turtle and the largest turtle ever documented. As you can see from this picture, the scale between Archelon and the human standing next to the specimen is a lot closer to the relative scale of Mario and Bowser. And Archelon was enormous, almost 15 feet long, almost 5,000 pounds. This creature is definitely big enough to be our Bowser basis, and it had a tail almost a meter long, which means it would be perfect if an Italian handyman had to, you know, grab onto it to defeat it. Yeah, oh! (beeping) With a more realistic Bowser mass and size, now we can start stressing Mario's blocky arms with physics. Wahoo! Oh! Those wings should be bigger. Now that we have a Bowser, we need to model Mario's throw. In all three Bowser fights, the goal is to grab the turtle by the tail, build up speed by swinging him around in a perfect circle, and then release him into a bomb. Now if Bowser is tracing out a circular path with his body during this throw, we'll have a circle with a 4.6 meter radius because that's how long Bowser is from the tip of his nose to the rotation point that is his tail. However, Bowser isn't just some two ton point mass on the end of a 4.6 meter long string. No, on our calculations, if Bowser is a real organism, then like a real organism, he's probably gonna have his mass more or less evenly distributed throughout his scaly body. So to be safe and conservative in our calculations, we're gonna assume that all the forces during this throw act through Bowser's center of mass, which we're gonna assume is at the center of Bowser's body. Which means, physics wise, this throw actually traces out a much smaller circle. Now finally onto the potentially arm ripping forces. If you've ever spun anything around on the end of a string, you intuitively know that it takes more force to spin something around more quickly than it does to spin that same mass more slowly. And so the velocity of Bowser during this spin will be critically important. At every single point on this circle, the velocity of Bowser during the spin has to equal the amount of distance Bowser is covering per some unit of time. If we choose that distance to be the full circumference of the circle and the time to be the time it takes to complete one full rotation of that circle, the circumference, then we can get the velocity. I went back frame by frame through Super Mario 64 footage and based on the frame rate of the game, I got a time. I plugged that time into our equation based on the circumference of our circle and got a velocity for Bowser during this spin of 24 meters per second, over 50 miles per hour. Now we have all the number we need to calculate a true force on Mario's arms, but I think you may suspect that swinging around 5,000 pounds at 50 miles per hour is a little tough on the old cannons. If Mario has to hold onto a giant turtle while swinging it in a circle, Mario's arms are gonna have to provide enough of a tension force to keep Bowser moving in that circle. That tension force, in this idealized case, will be mass times acceleration, like all forces are, except when you have a circular motion, the equation looks a bit different. We have mass here, and then the acceleration will be the square of the velocity divided by the radius of the circle that Bowser is tracing out. And guess what? We already have all those numbers. Do the math and you find that the required tension force in both of Mario's arms to keep Bowser moving in a circle is over half a million newtons, 125,000 pounds. By our estimates, it would be harder for Mario to hold onto Bowser's tail during this spin move than it would be to tie a rope to a F-22 Raptor and keep it from taking off. Harder than this! Well, you know, if you weren't incinerated by the engines and all that fire! (Bowser laughing) With a force value now in hand, we can estimate what would happen to Mario's hands, fleshy blocks? Wa-ha! A brute force way of approximating what would happen to Mario's arms under a Bowser force is to consider Mario's arms like a solid piece of material, like a steel rod. Any force acting on Mario's arms, Bowser or otherwise, is gonna act across the cross sectional area of each of Mario's arms. Then we have a force over a unit area which gives us a pressure. And with pressure, we can compare the strength of Mario's arms to the ultimate tensile strengths of known materials. Using the cross sectional area of my arms, just to be very conservative, I'm a lot bigger than that dude. Oh no! I get a value for pressure on each of Mario's arms of 60 megapascals, 60 million pascals of pressure. As a point of comparison, this is just about the ultimate tensile strength of copper so you gotta imagine it would do something pretty bad to a humanoid's arms. If we separate the human arm into its components, we can get a little bit more specific. The ultimate tensile strength of human muscle is just .1 megapascals. The ultimate tensile strength of human skin is 10 of our tendies 70, and human bone has an ultimate tensile strength of 110 megapascals. As you can see here, our value of 60 megapascals on each of Mario's arms is well within the range to do some serious damage to his arms, at least to his muscles and to his skin. However, it would be impossible to say exactly what would happen to Mario's arms without knowing exactly the composition of his arms. So since we are taking a more brute force approach, let's go back in time to our more brutal history to look at just one more thing. Hey, get back here! Give me that! You are way too cute and whimsical for what we're about the talk about. About 800 years ago, England decided that the punishment fitting the crime of treason was quartering, among other ghastly things, or having someone's body separated into four distinct pieces, often forcibly by horses attached to ropes, which were attached to the victim. Okay, well that's terrible, but how much force can a horse pull with? That would give us an idea if we have enough force to remove Mario's limbs possibly. Well thanks to horse pulling competitions where pairs and teams of horses compete to pull the heaviest masses possible, we know that the strongest horses on the planet can pull with many thousands of pounds of force. Not a few hundred, not tens of thousands, but a few thousand. Then, because we know in history people have had their limbs removed by horses forcibly, again terrible, that a few thousands of pounds of force would remove Mario's limbs. During the throw, Mario's limbs, each of them, would experience 20 times more force, 60 thousand pounds of force, than the current world record for the strongest horse pull. Now we cannot do this experiment, and I don't think we want to see what happens, but I think we can safely say that if Mario was spinning around Bowser like this and all our numbers are correct and he was standing magically still, then it would be terrible. Tearing, dislocation, probable-- Oh no! Dismemberment. Nothing that you wanna see in a kids' game. Let's-a go. So would the famous Super Mario 64 Bowser toss actually rip Mario's arms off? Well if all of our estimations, and calculations, and comparisons are correct, yes, that's very likely that that would happen. Without some kind of super durability or super strength, if he was firmly planted during this feat, this plumber would lose his pipes because science. See what I did there with the pipes thing? Because he's a plumber and 'cause he uses pipes and that's. (upbeat music) Like we said in the previous episode about how important assumptions are for conclusions, there's another way to go at this, too. I mean, under this kind of force, the same amount of pulling force is on Bowser's tail that is on Mario's arms. So would the turtle's tail rip off before Mario's arms would rip off? That gets into fictional biology I don't know, but it would probably be gross either way. Also this is only happening because when you spin as Mario, you are stuck magically in one spot like he is a pole planted in the ground. In real life, if you try to spin something around that fast that's that heavy, you would start to move and wobble, and it would lessen or greaten the forces of you. So it's Super Mario's fault that we did this to him. Thank you so much for watching Kristen and a big thanks to Askalon on Youtube who actually gave me the idea to do this episode. See, it really happens! If you wanna give me a suggestion for a future episode, you can follow us here at these handles. Also, the third episode of The Science of Mortal Combat is now live! Oh-ho we built an ice ax out of nothing but ice. You wanna see what happens because it's-a brutal. (calm music)
