In reading about anti-tank guns, the maxim I’ve heard is that velocity of the projectile is a more important factor than the mass of the projectile. An example is that the 88mm cannon of the king tiger was better against armor than the 122mm cannon on the JS-2 because of the greater muzzle velocity. My limited understanding of physics says that a small projectile moving fast can have the same energy as a larger slower projectile. So my question is this: If you had two identically shaped projectiles carrying the same amount of energy, would the small fast one still be better at penetrating armor than the large slow one?
Note: I realize that the 88 was probably imparting much greater energy to it’s projectile through sheer speed than the 122, but question is about theoretical projectiles.
I’ve repeatedly read the same as you. That speed is more important. I’ve never read an explanation as to why. I’ve seen this formula a few times. E=(m/2)v². Energy is half the mass times the velocity squared. Which would obviously make velocity more important, but not sure why the formula is true.
Anyway, apart from that, there are two factors I understand about why a smaller faster shell is better than a bigger slower one.
A faster shell has a flatter trajectory than a bigger slower one, making it easier to hit the target.
A smaller shell has to push less armour out of the way to penetrate. A smaller shell needs a smaller hole and therefore less energy to penetrate armour than a big one.
That’s part of why modern armour piercing rounds are actually saboted. A 120mm hvapfsds-t round is only around 25-30mm in diameter, despite being fired from a 120mm gun.
A smaller shell has a smaller cross section. A smaller shell with the same kinetic energy will penetrate more armour, as it dumps that energy into a smaller piece of armour. That’s why the KE penetrators used by modern tanks are long, thin rods with a much smaller diameter than the guns they are fired from.
I don’t understand the difference between this formula for “kinetic energy” and the formula I’ve always read as f=mv², which I thought was for momentum. Nor do I understand why the Wikipedia page for momentum uses the formula f=mv or p=ma (even given that p is apparently the equivalent of f in the formula I was familiar with).
Is kinetic energy [significantly] different from momentum? Why is the mass halved for one and not the other? Where did the square of the velocity go in the momentum formula?
Consider that kinetic energy is the capacity of a moving system to do work.
So moving from V[sub]i[/sub]=0 to V[sub]f[/sub]=V requires that work be done. Work is Force through distance.
Force is the change in a system’s momentum p=d/dt (mv). Normally people read this as F=ma since it isn’t too often that your system’s mass is changing. Rocket scientists may come and complicate this as they please.
So ultimately KE is the time integral of W which means the Vs are going to become 1/2 V[sup]2[/sup]s
Force equals Mass times the Acceleration, and Acceleration equals Velocity over Time. This is just the basic energy imparted though and has nothing to do with the material involved, it’s penetration properties, shape, explosive charge (and the shape of that), etc etc. So, perhaps the 88mm round had more kinetic energy due to much higher velocity than the 122mm Russian round (I’d have to see the numbers on both to see if this was true), or perhaps the shape and materials for the 88mm round were superior, so even though they imparted similar energy the 88 penetrated better due to some other factor (the US Army’s silver bullets, for instance, have much smaller ‘foot print’ than an 88mm round, despite being fired from a larger tube, but they develop ungodly kinetic energy due to their velocity and the density of the metal used).
Momentum is force multiplied by time. The p is specifying momentum, it is not an alternate symbol for force.
Smaller & faster will always penetrate better than larger and slower, because not only does a velocity increase have a greater effect on energy than a similar ratio of mass increase, but the smaller projectile is also focusing that energy onto a smaller area of the target substance.
However, the projectile needs to be able to withstand the impact force itself, or it will break and disperse its energy in any number of undesirable manners. The available materials and metallurgy technology of the time had a significant impact on how far velocity could be tweaked in WW2 tank rounds. After enough velocity increase, mass would have to be increased to provide greater density for the shell to impact whole, but that mass increased size and/or decreased velocity for the same propellant charge, which itself was constrained by the design of the tank in factors such as breech strength, ammo storage dimensions, and so on and so forth.
As previously mentioned, modern tank penetrators have evolved to be long, very narrow rods of a very dense material (uranium or tungsten, generally) fired at very high speed. It provides an order of magnitude greater penetration than WW2 era AP rounds.
The bolded text I think better addresses the intent my OP. The other points here are relevent and appreciated. But I was wondering if a higher velocity round does a better job of “Using” it’s energy to penetrate armor.
To further the discussion, let’s say the two projectiles are the identical size and shape, (long rod penetrator warheads) but one is depleted uranium and one is steel. The steel warhead is fired at a higher velocity than the more massive uranium round. Therefore both rounds have same size, shape and overall energy. Does your answer mean that the faster one will still perform better?
If they have the same energy and same shape, and they’re hitting surfaces of hardness & density difference in proportion to the projectiles’ own differences, then they will perform the same.
Velocity isn’t important by itself, it’s just what turns a plain old lump of mass into kinetic energy. Maybe velocity gets special as you approach the speed of light, but decent people shouldn’t think too much about that.
It’s fun…and not that hard!..to derive these basic equations at home or in a classroom, using inclined planes, metal balls to roll down them, springs to bounce the balls around, etc. Very simple stuff. The “1/2” in 1/2 m v-squared is actually measurable. If it were “1” instead of “1/2,” the ball would roll only a fraction of the way up the next ramp than what you can actually observe.
Total cost: under $50, and a couple of weeks of evening observations. You don’t even need a stopwatch; you can measure time by heartbeats, the way Galileo did.
:smack: More of a brain seizure, actually. The sentence SHOULD read, "So increasing the SPEED has a significantly greater effect on the energy imparted to the target at the end.
Anecdotally: the 7.62x25mm round is known for two things: 1) being one of the few pistol rounds that can penetrate things like a military helmet, and 2) being absurdly fast with a rather lower mass.
Generally, penetrating armor needs speed and a harder bullet, “stopping power” needs a heavier bullet, and often a method to increase expansion like hollow points.
Just to note: barrel length had a lot to do with muzzle velocity, and why an 88 could out penetrate a 122. Even calling them an 88 and a 122 isn’t so useful. For example, you said the 88mm of a King Tiger. The King Tiger used an 88mm L/71, while the 88 on a Tiger I and the towed anti-aircraft/anti-tank 88 was an 88mm L/56. The L/## is barrel length in calibers; 88mm times 56 is a barrel length of 4928mm while 88mm times 71 is 6248mm. The result was the 88 of a King Tiger had much better armor penetration than that of the 88 on the Tiger I. The 75mm gun on the Panther would out-penetrate the 88mm L/56 of the Tiger I as a result of muzzle velocity from barrel length; the Panther used a 75mm L/70. A similar example is the Sherman, which was armed with a 75mm, a 76mm and the British 17 pounder (which was 76.2mm). Although virtually identical in diameter, in armor penetration the 17 pounder was by far the best, followed by the 76mm and then the 75mm, largely as a result of barrel length.
All of this pretty much goes out the window in present day tank guns, and even to some extent WW2 guns; all modern anti-tank kinetic energy rounds and a few from WW2 use discarding sabots.
As long as we’re going there: The 122 had a major advantage in most combat actions. It’s 25Kg round carried a monster load of explosive. Since most shells fired in action are HE rahter than AT, this meant that the 122 was more useful more often than any type of 88.
One caveat about increased velocity however: beyond a certain point you get into the physics of “hypervelocity” impacts, defined as impacts at speeds greater than the velocity of sound through the material the target is made of. Since the energy of the impact just doesn’t have time to propagate away through the target, the result is usually the projectile and a limited outer layer of the target being vaporized. However for steel the speed of sound is over five kilometers per second, so it’s unlikely to be an issue anytime soon.
there are a number of ways to defeat tank armor and actual penetration is the most complelling. i can’t google it but in the 80s the soviets were experimenting with a slow full-caliber round made of some dense metal, sort of like a fast cannonball. it was the americans who realized (through computer simulation) that such a round could possibly crack western MBTs’ ceramic or composite armor. you might think a cracked armor isn’t as bad as one that’s cleanly penetrated but it’s just as bad. now this method highlights one advantage of a heavy projectile with modest velocity: the ability to transfer much of its energy to the target upon impact (assuming similar material.)
you can’t compare the german high velocity 88mm to the soviet 122mm adequately. both guns already provided an overmatch to most world war 2 tank armor. why you said the 88 was better requires some cites. for one, the 88 shoots faster and flatter and that is a definite plus for a tank gun, but not straightaway a better armor puncher.
I recall reading an article once about armour and defence.
the latest and greatest armour piercing rounds were actually a long narrow rod of depleted uranium (for density, high m for size) jacketed in steel (for strength). The steel would not penetrate the armour, but it flattened on the surface on impact and kept the uranium rod inside intact, so its full energy was expended against very small surface area, cross ection of the uranium - creating the steel armour vaporization result mentioned above.
One defence was “active armour” where shingles of explosives were hung about the tank. the round hits the explosive, which then goes off in a localized explosion which counters the penetraton attempt of the shell. You can see this in recent actions involving tanks and possible AT weapons, where the tanks seem to have metal squares draped over the outside.