BEWARE Link's Hookshot in Legend of Zelda!

"Hello, Internet. Welcome to GAME THEORY. Intro, intro, intro, hookshot, let's move on."

- MatPat

BEWARE Link's Hookshot in Legend of Zelda! (subtitled FEAR the Hookshot) is the 87th episode of Game Theory on The Game Theorists.

Description
''Link's hookshot from the Legend of Zelda is one of the coolest items in all of gaming. Who WOULDN'T want to fire a grappling hook at any object and instantly get reeled back in. It's AWESOME and is definitely my favorite item from any video game ever. But is it really as awesome as we all think? Is the hookshot in Link's pack of items truly the deadliest thing in the whole Legend of Zelda franchise?''

Transcript
Today we’re finally taking on the most iconic item from the Legend of Zelda franchise. No, not the Triforce. Ok, yeah, you could say the Master Sword is pretty iconic too. Sure, that was a biggie, but it was only for one game.

(Intro)

It's the Hookshot, alright, we're talking about the hoo- Now, look, the intro card is already up. I've missed the chance to say that- Here. Hello, Internet. Welcome to GAME THEORY. Intro, intro, intro, Hookshot, let's move on.

The Hookshot: one of the many iconic items from the Zelda franchise, and my personal favorite, was first introduced in The Legend of Zelda: A Link to the Past, And a variation has appeared in nearly every game since. whether you're fond of the original Hookshot, the Longshot, the Switch Hook, or the Clawshot. At its core, the item always functions with the same basic mechanics, you, uh, you got your, your hook arrow thing that's the, eh, technical term and you shoot it! The hook lodges in place and the whole thing recoils with Link getting pulled by the chain to his new destination. It's so satisfying! Some incarnations even have a nifty little laser pointer built-in, gotta love that super consistent medieval hyrulean technology right? I'm looking at you, Skyward Sword robots. In the game, the Hookshot usually makes an appearance beginning in the underwater temple and serves double-duty as your primary weapon by stunning or killing enemies at close range. But, should the Hookshot actually be a weapon in Link's arsenal? What is the real cost of all that powerful hooking and shooting? And the biggest question: is Link's most iconic weapon, Ugh, *second* most iconic weapon, actually more dangerous to Link than the enemies he faces in the game? To answer that we'll need to use some math. So, whip out your trusty TI-83s type in the number 5318008 and laugh, because when you flip it upside down it says boobies high school humor for the win. No, but seriously, put that outdated thing away. How has technology advanced so much and yet these things are still the same? Anyway, before we get to the numbers, we need to decide which shot weapon we're going to use. Because I'm clearly compensating for something, let's go with the most powerful of Link's hookshot weapons: the Longshot from Ocarina of Time, according to the game's canon, the Longshot launches twice the distance of the Hookshot, meaning that it's going to require a greater launch force to travel further, and if we're going to test this thing out to the fullest, I say bigger is definitely better. Today we're looking at two basic forces, the first force is when he launches the Hookshot, and the second force is when the Hookshot latches in place and pulls him to his new destination, so with that being said the first thing we want to find out is the force that's being exerted on Link when the Longshot is fired. We can get to that force by using a few of our favorite Newton's, uh, not the Figgy kind, Newton's third law of motion that states "for every action there's an equal and opposite reaction." Basically this means that if we know how much force is being launched away from Link, we'll know how much force is going back towards him and being pushed through his arm. To get to that force, we'll need to take a step back in Newton's book, to his second law: force equals mass times acceleration or as I like to remember it: FMA. That's not memorable at all but just fun to say fma. Since we're looking for 'F', we'll need to fill in 'MA' with in-game information. For mass we'll need the mass of the stuff that's getting shot, which is the hook and the chain. To do that we need to take a visit to everyone's favorite: the DMV: density equals mass divided by volume. We're solving for mass, so its d times B equals M. So let's start filling in numbers. Its density depends on what it's actually made of. Try as I might, using the power of Google I wasn't able to find a credible source naming the Longshot's material. But, according to the game, we know it has to be a metal or alloy that's hard enough to pierce any wood surface. Here's our list of candidates. We know for sure that Iron exists in the Zelda universe because we see it present in the Iron Boots. but we also know that it weighs Link down like a little girly man when he's wearing them. And because he carries the Longshot around without any problem, it seems like Iron isn't going to be our mystery metal. Aluminum and other lighter metals don't really have the hardness needed to be used over and over again to attach to wood surfaces without denting or flattening over time. So, cross those things off the list. And finally, since it has to be used underwater, it can't be any metal that rusts or changes color after getting wet. The one metal that really fits the bill here is Steel. That is some Sweet Metal Man. Metal man, he's a boss from Megaman, for all you youngsters: Mega man's that guy that everyone got excited about who's in the new Smash Brothers. Yeah you wouldn't have any reason to know him. Then I was able to calculate the volume of the hook using pixel measurements which I won't go into here because this video is already gonna be long and calculating mathematical volumes isn't the most thrilling YouTube content I could think of. Suffice it to say I was able to estimate the volume of the hook is .0012 Cubic Meters or 73 Cubic Inches. It's a pretty small volume but it's more than made up for when we multiply it by the density of Steel which is a whopping 8,050 Kilograms per Cubic Meter. This gives us a hook with a mass of 9.5 Kilograms or a weight around 21 Pounds for us Americans. So, okay, that seems reasonable, 20 Pounds. But remember, that's just for the hook. We also have to add the weight of the chain. We'll assume that this is also steel since it has the same in-game color and texture but how long is it? So, I went to the Water Temple, and found a room where I was able to get the Longshot to its longest possible extension. From there, I was able to estimate its length. Using the height of Adult Link, which we've calculated before in multiple ways using our Majora's Mask video to be about 5 Feet, we can figure out the height and length of the room based on the regular pattern of wall decorations around him. Blah blah blah Pixel measurements, blah blah blah lame math joke and/or pun, it ends up being that the Longshot's max extension is about 65 Feet or 20 Meters. So that's Longshot's length, but we need its mass. Steel manufacturers published the weight of their steel chains based on the Link Diameter. No, not Link's Diameter, the Link Diameter, th- the chain links though it would be cool to go into Home Depot and get some spools of green-clad Elfman. Anyway, more screenshots and pixel measurements show that the chain-link diameter is about half an inch, which would put our 65 Foot chain at a surprisingly hefty 169 Pounds of weight. That's the weight of a Baby Horse! Or me after two straight weeks of Sizzler Buffets. And here's Link just beasting this thing around with one arm. I was wrong about the whole girly-man joke, good for you elf boy. But ok, let's say that Link somehow manages to pick up all 189 Pounds or 86 Kilograms worth of Longshot which is in and of itself a longshot. What does this mean for the force of actually firing it? Well, going back to the equation, we still need acceleration, a variable we just unlocked by finding out the Longshot's length. The Longshot travels 20 Meters in one second, meaning its velocity is 20 Meters per second, shockingly difficult math, and its speed is consistent throughout. Meaning the only time it's accelerating is from that initial 0 standstill to the 20 Meters per second in that fraction of an instant right there. Just as you pull the trigger. Roughly that instant is about a tenth of a second, and since acceleration is change in velocity over time, that means a equals 20 over .1 or 200 Meters per second squared. That's a lot. It's not quite bullet level acceleration, but it is 10 times faster than the roller coaster with the fastest acceleration in the world: Dodonpa(ドドンパ) in Japan. Ok, so we're finally ready to calculate the force that the Longshot exerts on Link from firing it. F=MA, plug in some numbers, and that gives us 17,200 Newtons. So what does that mean? Well considering that Link remains completely still while launching the Longshot, it means he's absorbing all of that backward force into his arm. The force needed to break a bone varies based on the size of the bone, how the force was delivered, etc. But it's typically around 12,000 Newtons. So, based on the force applied to Link's hand by the Longshot, just the act of launching this device would, at minimum, break his fingers and his wrist. Potentially some of his arm. After an injury like that, there is no way you would be able to hold onto the Longshot's handle, let alone ride it across an open pit of hungry Tektites with one arm. No amount of Red Potion is going to fix that in a second. Hear those hearts beeping Link? oh yeah, well, get used to it because a shattered arm is going to do that to you. But wait we're not even done yet, that's just the force to launch the darn thing. It's not like Link is taking a leisurely glide over to the hook. Oh no, the Longshot immediately begins recoiling its chain as soon as the hook has landed, violently jerking Link towards the other side of the room. To calculate that force we can actually use the same equation, but now Link's mass is the thing that's doing the accelerating. We've already mentioned that Link is 5 Feet tall, and then we'll be generous and say he's a medium build. For a guy in this range, his average weight would be around 135 Pounds or 61 Kilograms. So wait, let's stop for a second to point out that the Longshot is actually heavier than Link. How is this guy possibly keeping this massive thing in his pants? Just going to let that one sit there for a second. In gameplay footage, we can see that it takes the same amount of time to launch the Longshot as it takes for Link to be pulled back to it, meaning that the distance traveled and total acceleration would be very similar to the calculations before. Plugging these into our equation we get FMA being 12,200 Newtons. Again, all this force is being handled by Link’s arm, broken hand, and area right around his shoulder as he gets dragged into the air. 12,200 Newtons is definitely enough to break a bone. I mean, even more than the ones he’s already lost, and is easily enough to rip his shoulder out of socket but that bears the question. With such an extreme force of acceleration, would it actually be enough to rip his arm cleanly off his body? Surprisingly, we can look that up.