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

[halfeye]

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.

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.

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.




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.

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).

I admit I was assuming that light arrows were structurally capable of being fired with the bow's full power, if that's not the case then all my working was wrong, an arrow made of wet spaghetti is going nowhere.