Got a Real-World Weapon, Armour or Tactics Question? Mk. XXIX

[Maat Mons]

You just said momentum is conserved in an elastic collision. In the firing of an arrow from a bow, the bow and arrow both start with zero momentum, since they are stationary with respect to the reference frame (the Earth). After the arrow is fired, it has positive momentum in the forward direction, because it is moving forward. The bow also has positive forward momentum, since the unbending it undergoes represents a shift in its center of mass in the same direction that the arrow travels. With the Earth itself as our reference frame, nothing moves backwards to cancel out the two masses moving forward, so momentum is not conserved.

In order to model the firing of an arrow as an elastic collision, you’d have to model the Earth as one of the colliding bodies. You can do that, sure, but bear in mind that that gives you three bodies to consider, not two. You need to model the earth, the arrow, and the bow, since each of those things experiences a different change in momentum when you fire. Also, bear in mind that, if your target is itself standing on the Earth, and thus moving with it, the movement the target experiences in the direction opposite the arrow will add to the effective force with which the arrow strikes.

Really, modeling the firing of an arrow as an elastic collision seems like an awful way to go about it. You can do it, and if you do it right, you’ll get the right answer, but doing it right requires dealing with the bow’s weight and motion. The weight of a bow and the amount by which it moves (flexes) has been consistently shown to be a huge factor in the speed of arrows. So if you’ve done math that suggests those things are unimportant, you know you’ve made a mistake. It’s a basic sanity check.

Another thing that should give you pause is to note that, if you did assume momentum of the arrow was fixed, regardless of weight, you’d get math suggesting the speed at which the bowstring drives the arrow forward goes to infinity as the weight of the arrow goes to zero. It is clear from dry-firing a bow that the string does not move with infinite speed without the weight of an arrow.

[Spiryt]

Yes, in reality heavier arrows will always have higher energy, bows are way more efficient with them. At least to a some point.


It's visible even with modern recurve and compound bows, which can be very very fast compared to most traditional bows. Still quite a few more Joules with heavier arrows.

With something like selfbow with more round crosssection, or some kind of reflexive bows, it's can be very drastic and firing light arrow can be dangerously close to dry fire.

Adam Karpowicz's 105 pound 27 inches Turkish style flight bow (so built for speed/distance) achieved about 114J with 1548 grain arrow, but only 73J with 203 grain arrow. Which is still very impressive, many wooden longbows would probably snap, or at very least kick archers' hand like a mule, without launching such a tiny arrow very fast.

[halfeye]

You just said momentum is conserved in an elastic collision. In the firing of an arrow from a bow, the bow and arrow both start with zero momentum, since they are stationary with respect to the reference frame (the Earth). After the arrow is fired, it has positive momentum in the forward direction, because it is moving forward. The bow also has positive forward momentum, since the unbending it undergoes represents a shift in its center of mass in the same direction that the arrow travels. With the Earth itself as our reference frame, nothing moves backwards to cancel out the two masses moving forward, so momentum is not conserved.

In order to model the firing of an arrow as an elastic collision, you’d have to model the Earth as one of the colliding bodies. You can do that, sure, but bear in mind that that gives you three bodies to consider, not two. You need to model the earth, the arrow, and the bow, since each of those things experiences a different change in momentum when you fire. Also, bear in mind that, if your target is itself standing on the Earth, and thus moving with it, the movement the target experiences in the direction opposite the arrow will add to the effective force with which the arrow strikes.

Really, modeling the firing of an arrow as an elastic collision seems like an awful way to go about it. You can do it, and if you do it right, you’ll get the right answer, but doing it right requires dealing with the bow’s weight and motion. The weight of a bow and the amount by which it moves (flexes) has been consistently shown to be a huge factor in the speed of arrows. So if you’ve done math that suggests those things are unimportant, you know you’ve made a mistake. It’s a basic sanity check.

Another thing that should give you pause is to note that, if you did assume momentum of the arrow was fixed, regardless of weight, you’d get math suggesting the speed at which the bowstring drives the arrow forward goes to infinity as the weight of the arrow goes to zero. It is clear from dry-firing a bow that the string does not move with infinite speed without the weight of an arrow.

Yes, in reality heavier arrows will always have higher energy, bows are way more efficient with them. At least to a some point.


It's visible even with modern recurve and compound bows, which can be very very fast compared to most traditional bows. Still quite a few more Joules with heavier arrows.

With something like selfbow with more round crosssection, or some kind of reflexive bows, it's can be very drastic and firing light arrow can be dangerously close to dry fire.

Adam Karpowicz's 105 pound 27 inches Turkish style flight bow (so built for speed/distance) achieved about 114J with 1548 grain arrow, but only 73J with 203 grain arrow. Which is still very impressive, many wooden longbows would probably snap, or at very least kick archers' hand like a mule, without launching such a tiny arrow very fast.

This is standard physics. You can probably (I don't know your physiology, maybe you can't throw?) throw a tennis ball a long way. Throwing a bowling ball your range will be less. You probably can't throw something with the mass of a person far at all, and if you can't lift something you can't throw it. Since KE is 1/2 mv^2 kinetic energy increases faster with increasing speed than speed increases with decling mass. As I said above, light things decelerate faster than heavy things, so at long range it's entirely expected that more massive arrows have more energy, it wouldn't be true point blank.

It is a legitimate approximatioin fo treat the firing of a gun or bow as an elastic collision, you have the weight of both the projectile and the launcher (with a bow, and to a lesser extent with a gun, you have to include the mass of the archer), you have the overall KE, you have (or can get, though that may not be simple) the muzzle velocity.

It wouldn't be done, and I don't suggest it would be sensible for anything other than physical research, but if we made cartridges with the same amount of propellant in them for bullets of different calibres (with the same shape of bullet for the different calibres), then the smaller calibres would be faster, and have more kinetic energy at the muzzle, while the heavier buttets would become progressively more useless as the calibre and weight of the bullets went up.

[Maat Mons]

The firing of a bow cannot be modeled in the same way as the firing of a gun. There are factors that are important to a bow’s ability to impart energy to an arrow that are not present with a gun. If your approximation does not account for that, it will give the wrong answer.

Additionally, I feel your claim that the firing of a gun can be modeled as an elastic collision needs support. By definition, an elastic collision preserves kinetic energy. When firing a gun, everything is stationary in the initial state, hence no kinetic energy. At the time the bullet exits the muzzle, it has nonzero velocity. Since the bullet also has nonzero mass, this means the system has nonzero kinetic energy. Going from zero kinetic energy to nonzero kinetic energy clearly is does not represent kinetic energy being conserved.

Bear in mind, kinetic energy is necessarily a non-negative value. It’s equal to mass times the square of velocity. Mass can’t be negative, and while velocity can be negative, squaring a negative number still results in a positive number. There’s just no way to get a negative kinetic energy, so there’s no cancelling out the kinetic energy of the bullet-in-motion.

You can use conservation of momentum if you want. That still applies. But momentum being conserved isn’t enough to call an interaction an elastic collision.

Additionally, the litmus test of the validity of any approximation is to compare the predicted results to actual experimental data. I can refer you to tests showing heavier arrows possessing greater kinetic energy even at point-blank range.

[stoutstien]

The reasons heavy arrows tend to have better energy retention is due to how
constant the rigidity the shafts/dynamic spine have when combined with heavy draw weights.

There is even a famous paradox covering it. It's very easy to "over power" light quarrels with powerful bows and sap energy, accuracy, and even structural integrity.

[Spiryt]

This is standard physics. You can probably (I don't know your physiology, maybe you can't throw?) throw a tennis ball a long way. Throwing a bowling ball your range will be less. You probably can't throw something with the mass of a person far at all, and if you can't lift something you can't throw it. Since KE is 1/2 mv^2 kinetic energy increases faster with increasing speed than speed increases with decling mass. As I said above, light things decelerate faster than heavy things, so at long range it's entirely expected that more massive arrows have more energy, it wouldn't be true point blank.

Well, no, almost nobody measures arrows velocity at long range, it's pretty challenging, to say at least. 99% measurements are from few meters at least, and mentioned Karpowicz test where made with window of chronograph about 1 yard away from the bow.... We're talking about very initial velocity.

KE energy being square of velocity obvisouly works both way, if you want to speed something up two times, you need to put in 4 times more energy. Increasing speed isn't easy.

Many very good composite bows are close to 95% efficient in ideal conditions (heavy arrows, perfect, instant release), so even if there were somehow more efficient with light arrows as with heavy ones, there wouldn't be any energy more to gain.

The fact that bows of all kind are visibly more efficient with heavier arrows really isn't disuptable.

Here are menioned Karpowicz tests:

https://www.atarn.org/islamic/akarpo..._bow_tests.htm

Here's a ballistic for some modern crossbows by deer and deer hunting.



Heavier arrows yield more KE.

It wouldn't be done, and I don't suggest it would be sensible for anything other than physical research, but if we made cartridges with the same amount of propellant in them for bullets of different calibres (with the same shape of bullet for the different calibres), then the smaller calibres would be faster, and have more kinetic energy at the muzzle, while the heavier buttets would become progressively more useless as the calibre and weight of the bullets went up.

Generally, the opposite seems to be true, if anything.

For given caliber, amount of propeller, and barrel length, and shape, heavier bullet will tend to have bit more energy.

[Gnoman]

For given caliber, amount of propeller, and barrel length, and shape, heavier bullet will tend to have bit more energy.

Note that having everything but bullet weight being identical is nigh-impossible for a large majority of firearms even if it were desirable, because anything except a single-loader has pretty major constraints on overall length (it will fit in the chamber just fine, but any kind of feeding system tends to have trouble if the bullet is much longer than expected). This means that usually to get a heavier bullet, you usually have to change the shape - a standard 115 grain FMG 9mm round comes to a smooth roundness, a 147 grain FMJ round has a massive flat tip, for example.

That said, the two rounds generally have pretty close to the same energy if the propellant and the barrel length is the same. The heavier bullet retains more velocity at range, though being slower it has just a bit worse ballistics and flight time. The heavier round having the same energy is often the reason to make it, in scenarios where a slower speed is valuable in and of itself (the most common such scenario being suppressors, where you want to drop the bullet below the speed of sound to eliminate the supersonic crack).

[LibraryOgre]

The Mod Ogre: Hey, we reached page 50! Time to start a new thread!