The Surprising Mechanics Of A Bow And Arrow 

This is the equivalent to the peasant railgun.

I mean that is assuming the tips don't slow down but conservation of energy exists so you can at most fire an arrow with the elastic energy stored in the bow.

An arrow does approach the speed of light. It doesnt get very close though.

I think you’re confusing the speed of the arrow with the ratio between the lateral speed of the string and the speed that the bow expands. The ratio might approach infinity, but that’s because the speed at which the bow is expanding is approaching zero. So essentially you could have 1 m/s over ~ 0 m/s and that would equal ~infinity, but the actual speed of the arrow will be 1 m/s. For clarification, I’m not saying that 1 m/s is the actual speed of an arrow. Just using that speed as an example

If we ignore the laws of physics, it breaks the laws of physics 😮🤯

When the physics teacher says you can ignore friction

NASA wasting time with rockets when all they need is a really big bow

this guy is the proof that you can state dumb facts and still sound smart gotta love a man with confidence

Your videos are like the portal 1 and 2 demonstration videos and it amazing

It will not approach speed of light. Speed will be proportional to energy stored in elastic deformation of bow. Even if we get rid of weight and drag. It is just ratio approaching infinity. Mathematicaly. It means either speed of tips approch 0, or arrow speed approch infinity. In this case it is tips approch 0. Moreover this ratio is just a result of parameters combination. It means that ratio itself do not approach infinity. It's parameters approach something, and thus ratio approach infinity.

this is why you dont dry fire a bow. Without the weight of the arrow to hold it back, all the force goes back into the bow, breaking it

The sound designer really made a pg3d level theme just for one video

The railgun of the proletariat

"Well, that explains why my fridge was unexplainably cut in half by a blazingly fast object that was falling from space."

So in a fantasy setting that already has enchantments to make everything resistanceless and weightless, arrows should be city killers?

*NASA casually building a 0.029 grams arrow and bringing it to space with a crossbow*

The speed of the arrow does not approach infinity. Just the rate of the two speeds and thats because you are dividing by a number that aproaches zero. And that doesn't really tell you much about the actual speed of the arrow because any number approaches infinity if you divide it by another ever decreasing number.

When infinity pops out of your physics equation you know you’ve either done something wrong or your model is wrong in some way.

So in vacuum sealed weightless chamber would arrows go that fast?

Shoot an arrow in space as a bucket list for bordem. Got it

Fun fact, due to their weight, speed and controlability, arrows fired from classic longbows can be much deadlier than bullets fired from assault rifles, specially when combating armored soldiers.

the arrow is accelerating because it's under a force AND the now tips are showing down because they are taxing their resting point. so of course the arrow going to move faster relative to the bow tips, it doesn't mean it's going to go to the speed of light even if it was weightless and dragless. The arrow drops accelerating as the bow tips stop moving. Only looking at that velocity ratio is silly and meaningless

And the arch it makes is different depending on the bow shape. A recurve like this is great because it has a short time where it is nearly flat, so it’s way easier to pull back than a long bow of the same draw strength

It's almost like any weightless object can easily reach the speed of light with the smallest of flicks

"If we remove the arrow and the bow the bow and arrow can achieve the speed of light." Truly inspiring! 🤯

Brother in Christ no, the velocity of the arrow depends on the elasticity of the bow and how much you stretch it. In a first approximation you can describe it with the conservation of energy: the elastic potential energy and the kinetic energy. Please stop Love✨

Dumb weight and resistence

Technically anything that moves approaches the speed of light, how close is the question. 💀

That is also why it's important to wear an armed guard when you do archery because it really REALLY hurts when your string hits your arm going that fast!

Does this mean if we shot an arrow in space it would almost go the speed of light?

The first time I used a compound bow (archery is not very popular in my home country) I was amazed with the mechanics of accelerating the arrow through pulleys. I never even stopped to realize this acceleration is a common feature in regular bows as well.

This video is both unclear and scientifically doubtful. Sorry.

Imagine if the laws of physics are just there to stop bows from becoming railguns

The slope approaches infinity, however the slope you are referencing is not a direct comparison to velocity. In fact even in a vacuum Newton’s first law still applies. It is dependent on the mass of the arrow and draw weight, not just air resistance to figure out how much energy is transferred into the arrow. Even ignoring the mass of the arrow the infinity is the ratio between the tip and the arrow speed, not actually the velocity magnitude!

very satisfying audio wtf.. your channel is underrated

Bro in space would it actually reach light speed? because you just said if there was no weight or air resistance...

So like, hypothetically, if someone made a massive bow and arrow in space…

Every time I run I "approach" the speed of light. I lied. I don't run

Don’t forget the force vectors will approach a 90 degree angle in which they are unable to convert energy further, thus becoming an effective conversion rate of approaching zero

From a math trigonometry perspective you are technically right. The best kind of right.

A rly rly rly light arrow shot in the vacuum of the space would probably (..?)

"If it weren't for the pesky details....." Yeah, it's called reality. Welcome to real life.

1:1 ratio of what? I'm not understanding...😢

This absolutely doesn't make sense: If the "upwards" direction is 0 (because you're not pulling the bowstring), and because of that the "forward" direction is infinity (infinity times longer that 0), 0 times infinity equals 0, so it doesn't move.

This is highly misleading. Ignoring the pesky details, the maximum speed of the arrow is predetermined by the potential energy. While the velocity ratio approaches infinity, the velocity of the tips of the bow approach zero. So the speed of the arrow, under idealized circumstances, still approaches a finite limit - like sin(x)/x approaching the origin.

There are infinite sums wich all add positive integers together. An infinite amount of positive integers. However the end result of such a sum is still a finite number. Look up the harmonic series. 1+1/2+1/4+1/8+...=2. The same principle can be applied here. Even though the ration approaches infinity the change in distance approaches zero. The outcome will be a finite velocity.

I feel like cave johnson would be saying this in a demonstration video

That's... a very bad interpretation of the math. If se say that the strings of the bow form radii of two circles and track the movement of the arrow's fletching relative to those circles, you'll see what they're trying to animate is that the strings are basically just the radii of the circles turning around the centre (being the tips of the bow, OR you can do the reverse and visualize the centre as the arrow's fletching). If you imagine it like that, then you can model the velocity of the bow tips as cos(t) and the velocity of the arrow tip as sin(t). What they're doing is saying that if you divide the velocity of the arrow tip by the velocity of the bow tips, you get sin(t)/cos(t) which is just tan(t), and so as you approach the end of the arc, i.e. pi/2, tan(t) approaches infinity. However, that's a misrepresentation, as the arrow is still only moving at a rate of sin(t), it's just that the ratio of movements approaches infinity, not because sin(t) is become infinite, but because cos(t), the bow tips, are approaching 0.

So if i could negate basic laws of physics and all that, i could have lightspeed arrows?

Mewing motivation

What would the max speed be for a compound bow and arrow in the vacuum of space?

Imagine guns has never invented how advanced bow would be

so if you shoot it in space it will go almost the speed of light?

The ends of the bow are moving less so they are pulling the string and arrow less.

when are you gonna get back into modelling? your work on the nerd emoji was truly inspiring

Well no one is stronger than GOD. And according to indian relegion gods actually use bows One example of such a bow is shivdhanus I am not saying that hindu religion is higher than others

basically, bow make arrow go _YIPEEEEE_

Then if weight and resistance is the problem then just go to space

And compound bow spread the energy even more extremely

Oh so you're saying just go in a vacuum chamber shoot an arrow and now you got yourself a very very fast and deadly weapon only that it has to be in a large vacuum Too bad nobody's that crazy to try it😂

So, if we make the arrow a lot lighter, and shoot it in space. it might go very very fast

I run faster with the sun behind me because the millions of photons hitting my back are pushing me so hard that I can reach the speed of light

Should’ve had bows in Star Wars 😂

I aint tryin to be rude or nothin, but he kinda sound like that one fish guy from homestuck ngl

The acceleration increases, but the time for it to accelerate decreases, so they would cancel each other out. and so they probably wont go to the speed out light.

So what if we fired a bow in zero gravity would it even work and if it did could it reach the speed of light

The last number before infinity in this vid is 99999999

Do in space it moves faster if it wasn't in the solar system?

Or conservation of energy. In a perfect system without any losses, 100% of the potential energy in the bow would get converted to kinetic energy in speed of the arrow. If a bow could store 10kJ of energy, it wouldn’t be able to shoot a 20g arrow faster than 100m/s even without losses. It is cool that the bow approaches an infinite relationship as you approach the end of travel. I’m guessing that this 0/0 indeterminate situation is why the energy is finite even though you’re dividing by zero.

That's an interesting insight.... Insight, right? Or?

:"if you shoot an arrow in space it will go as fast as light" that what you saing?

If i shot a bow in space would it move at the speed of light if not how could we shoot a bow at the speed of light

So if I shoot a arrow in space it would go at the speed of light?

Does this apply to compound bows?

Now someone gotta try shooting an arrow in space 🤔

Have you heard of the archer paradox? If it weren’t for the ability of arrows to wobble they would get launched to the sides

Failed to mention: displacement and applied force at that point are near-zero, which cancels out the near-infinity. Many leverage systems are like this. And any mass with any applied force would approach infinite speed if we ignore mass.

In theory couldnt ypu test this by firing a bow in space? No weight no air resistance and drag. The only thing slowing the arrow down would be friction from rubbing against the bow, no?

What if we shoot it while in space?

Out of context moment

What if we do that in space

This is why I always consult with an engineer and not a physicist or mathematician. Because they're going to forget some important practical detail in hypothetical land and suddenly my arrows will not be traveling at the speed of light as promised

Could hurt Gojo.

Gun is better

Near light travel is so simple, we just need a really big ballista.

Shoot arrow in space

Interesting

Just do it in space

Song name?

Bows in space?

Pesky details 😂

Wheres THE LOOP

Those pesky details stopping me from creating a black hole, smh

😅 don't listen to this channel. It graduated from hoaxford university. That's not how bow works, at all. Cast efficiency is highest at initial acceleration, and decreases as it approaches brace height position.

I don't get it

Ama bu hızda gitmesi icin kütlesiz olması lazım yani paradoks

Can you tell me how you create such videos.. Please reply sir..

I don't really get this graph

Thanos: I have the Infinity Gauntlet 🌈 Hawkeye: Hold my bow 🏹

I love the way you said “du pesky details 🙄.” Like, oh brother physics stopping us from reaching C speed AGAIN. 😂