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
(Game Theory theme starts)
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-
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 will 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No, but seriously, put that outdated thing away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 farther
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 is 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=Full Metal Alchemist
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 everyone's favorite:
the DMV
density equals mass divided by volume
we're solving for mass, so it's 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 under water
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 Metalman
Metal Man, he's a boss from Mega Man
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 point zero zero one two cubic meters
or seventy three 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 eight thousand fifty kilograms per cubic meter
this gives us a hook with a mass of nine point five kilograms
or a weight around 21 pounds for us American
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 ingame 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 extention
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 five 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
not Link's diameter
the link diameter
th- the chain links
though it would be cool to go into home depot and get some schools 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
hundred and sixty-nine 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 of 189 pounds
or eighty six kilograms worth of Longshot which is in and of itself a long shot
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 point one
or two hundred 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 equals ma, plug in some numbers
and that gets 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 a hundred and thirty five pounds
or sixty one 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
twelve thousand and two hundred 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 amount of acceleration
would actually be enough to rip his arm cleanly off his body?
surprisingly, we can look that up
figures and statistics actually exist on how much force you literally need to rip someone limb from limb
because the Internet is a dark dark place sometimes
take for instance the people have been reported to lose limbs
after getting them stuck in a clothes dryer
seriously dude, just let the quarter and live trap go. It's not worth it bro.
Not worth it.
from what I can tell it takes about thirty thousand Newtons
to rip the arm off, but this also utilizes the torque of the dryer
in most cases the force needed to physically rip off an arm is greater
than the force applied to Link by the Hookshot
so ok, he's made it to the other side with a shattered hand, some other broken bones
and his arm hanging out of socket but hey, it's still attached to his body
he can go limp on to collect another small key
victory across the board right?
wrong
even though the force exerted on Link isn't enough to take his arm off
there's another phenomenon we need to account for in this situation
Link is being pulled to his destination in an incredibly short amount of time
like we said, his acceleration is about 200 meters per second per second
and accelerating that fast is technically ok
if you're a solid piece of metal like the Longshot
but if you're a person?
the human body isn't a solid mass
which means that even if you pull one part of us
technically, all the other parts might not be able to keep up
in particular, your inner organs are going to be a lot slower to get moving
than the solid parts like bone and cartilage
and that means, while the rest of you is taking off to fight Ganondorf
those soft internal organs are still going to be sloshing around there for a second
accelerating Link like this is the equivalent of accelerating him to 45 miles per hour in a fraction of a second
a rate that would put his organs under a staggering force of 20 Gs
20 times the force of gravity here on earth
that is a massive number
but to truly understand the damage that could cause
we need to take into account a few things
first, Link is feeling this for less than a second
his body position also makes a tremendous amount of difference
g-forces are a lot easier to tolerate when they're felt perpendicular to the spine
like when you're sitting down in a car but you're moving forward
they're hardest tolerate when they're parallel to the spine
like when a person is facing down and moving forward
in other words, the position Link would be in as he's being reeled to the Hookshot
this position is particularly dangerous because the tiny blood vessels in your head
and the retinas of your eyes are more easily damaged in this direction
it's estimated that, when trained,
humans can endure this level of g-forces for about 10 seconds before they die
in actual experiments done with humans in the range of 20 G's by NASA and other international space agencies
one second of exposure permanently damaged the subjects' spines
but even worse, because of that whole blood vessel thing in the eyes,
made them permanently or semi permanently blind
which means that in one use of the Longshot
Link breaks all the bones in his hand upon pulling the trigger
then undergoes complete dislocation of his shoulder
and probably a couple other random broken bones
as he's torn from his standing position
before he's finally given a 20g slap to the face due to acceleration
pulling apart his vertebra and damaging his retinas for life
and you thought the water temple was bad before
but hey, that's just a theory
a Game Theory!
thanks for watching
so here's a fun fact
I live just outside of Los Angeles and traffic here is bad
I mean really bad
every day that I drive into town it literally takes me
an hour and 15 minutes at least to get into the city
and that's only one way
and believe me you can only listen to a wrecking ball so many times before it makes you nauseous
and that number of times 1
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well I know you've seen a bunch of other youtubers promote audible
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so take it from me, it really is a great service
it's like reading but better
currently I'm listening to Bill Nye's book
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because it's by Bill Nye the Science Guy
Why wouldn't I listen to it? What's not to love?
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give it a trial run, and let me know if you find a good book
I'm always looking for more fodder for the commute
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it really does help us keep this little business running
so that way I can keep finding new and awful miserable ways to torture our favorite video game characters