Hear ye, physics geniuses (I butter you up you’ll have no choice but to answer, or admit your non-geniushood)!
Momentum and kinetic energy are such tangled concepts for me. (A friend of mine has it worse; he uses momentum in place of energy in all calculation, since "energy doesn’t really mean anything. He’s not an engineer.)
You’ve got two identical guns, with two identical cartridges, with two identical propellant charges. Both bullets have the same outer dimensions, but one is made of uranium-238 and the other is made of aluminum, so they have very different masses. I assume they will have the same ___ at the muzzle, but I don’t know what ____ is.
Assume all the powder is consumed in the barrel. Disregard friction, relativistic effects, dippymonger, and powder burning rates. Are they going to have the same momentum, since momentum is conserved when all the little burning gas molecules bounce of the bullet butt? Or the same KE, since you had the same amount of CPE to begin with and it is mostly conserved? If you say “the same velocity” I will have a brain transplant.
Or could the bullets have the same energy and momentum? I don’t know why I’ve discounted this one until now; I tend to think that if you hold energy constant you can’t hold momentum constant but maybe this is a special case.
If you’re wondering why I ask this, here’s why: over at http://boards.straightdope.com/sdmb/showthread.php?threadid=27266 , Jeff_42 asserted that “more weight equals more kinetic energy”. I was gonna refute that, and then I realized I didn’t really know.
(Engineering side note: more density could mean more energy, if you used a shorter bullet and used empty space in the case for more propellant, but I don’t think that’s what Jeff is talking about, and I don’t know if DU rounds do leave more space in the case. I think Jeff is assuming equal downrange velocities, which I think is not a safe assumption. So I assumed equal propellant quantities.)
Well, if the bullets/shells have traveled the same distance downrange, they must have had approximately the same muzzle velocity to begin with. Therefore, momentum and kinetic energy scale linearly with the mass. Now, in order to have the same muzzle velocity, I imagine that the charge must be correspondingly larger for the heavier shell.
For the case of identical charges, I’m going to go out on a limb and say that the work done by the expanding gases, and thus the energy imparted to the shell, is the same for both shells. That means that the muzzle velocity is lower for the heavier shell (by the square root of the mass ratio), but the momentum is larger (by the same ratio). Also, for the same initial energy, the downrange distance is reduced for the heavier mass by the mass ratio.
I’ll try to answer this in broad terms, without reverting to pencil and paper. I will add one further simplification – that the powder detonates instantaneously, so that immediately after firing there is a hot column of gas sitting behind the bullet and no further reactions take place.
Assuming no heat loss or friction (right?) the column of high pressure gas will do the same amount of work in expanding behind a uranium bullet as it will behind an aluminum bullet. Since work and energy are equivalent then it seems to me that the bullets would exit the muzzle with the same kinetic energy. Since kinetic energy is 1/2 the mass * the velocity squared (E = 1/2mv^2) the two bullets will differ in velocity as the square root of the relative masses, v1^2 = v2^2*m2/m1.
Momentum is the product of the mass and the velocity. (M = m*v), so the relative momenta could be calculated as well. (Where’s that thread about using algebra in real life?)
Pluto’s answer assumes the force exerted by the expanding gas is the same for both bullets, and I believe this is approximately, but not exactly, correct. I would expect the aluminum bullet, since it will be accelerating faster, would experience less force. Thus it will have less kinetic energy than the uranium bullet. Unfortunately, I don’t have a good feel for whether this is a substantial effect, or a negligible one. I imagine you’d have to look at the velocity of the bullet, relative to the typical speed of the molecules in the expanding gas (both of which will vary with time).
You’re trying to make a comparison that has far too many unanswered variables. Rifle propellant is available in many varieties with different burn speed and pressure characteristics. This is even further effected by the length of the barrel and the force required to get the bullet out.
This is a bit exaggerated and ignores the huge factor of barrel friction but try this as an illustration:
When not contained, smokeless propellant just fizzles and burns. It needs to be under pressure to burn rapidly enough to transfer energy to the bullet. The aluminum bullet would not provide much resistanc due to low mass so the powder would burn inefficently. The bullet would just pop out of the barrel followed by a lot of still burning powder.
A heavy bullet that takes alot of force to get moving would increase chamber pressure and rapidly accelerate the burn speed of the charge. Higher available pressure would provide more energy to get the bullet out of the barrel.
Perhaps I’ve got my definitions wrong but besides that aren’t people looking at this from the wrong end? Isn’t the important part what happens when the bullet reaches the target? Maybe I’m reading it wrong but the above posts seem to imply that an aluminum bullet has the same energy leaving a gun than a depleted uranium bullet. Therefore, assuming both bullets are traveling the same distance, is everyone suggesting that both bullets impart the same energy to the target upon impact (assume they are travelling through a vacuum)? Perhaps I’m fooling myself with the old trick question (What weighs more, a pound of bricks or a pound of feathers?) and am assuming a heavy projectile would do more damage than a lighter one (while clearly not accounting for the total kinetic energy of both which seems to be equal).
Something is getting lost here. Why would troops tote heavy ammunition made from lead when aluminum bullets would do as much damage and be easier to carry around? Heck…with a higher muzzle velocity the aluminum bullet should have a greater effective range as well. Also, wouldn’t a higher velocity upon impact mean a greater chance of penetrating armor which is what DU bullets were made for in the first place?
Looks like Padeye gave an answer to my post. I see why lead and not aluminum bullets are made now.
I guess I was technically correct that in the real world a DU bullet will leave the barrel with more KE than an aluminum one but I admit I thought it would be that way for all of the wrong reasons.
Cool…learned something new today (or maybe relearned it…whichever…still cool).
Jeff, Lead and soft copper are used because they are soft enough to conform to the rifling grooves of the barrel but hard enough to retain shape. That in combination with relatively high density makes it a more robust factor in all the possible variables.
Calculating correct powder charges for a given bullet/cartridge combination is touchy business as the pressures often go over 50,000psi so mistakes are most unpleasant. Small variations in any of the variables can cause disaster. Putting the right amount of the wrong kind of propellant is one of them, in fact it’s how some destructive testing is done. Substituting the quick burning propellant used in a handgun for slower burning rifle propellant will make a rifle explode like a pipe bomb. In some cases using too small a charge of a slow propellant can cause dangerously high pressures. This is because the bullet doesn’t get started with enough initial speed to overcome the static friction of the barrel. The bullet is essentially stuck while pressure builds behind it faster than it can move out of the way.
What happens at the target end is directly related to what happens at the muzzle. It’s always less (the primary thing that happens during flight is the bullet slows down. so both momentum and K.E. decrease, but K.E. decreases faster) and a lighter round of the same shape will slow much more than a heavier one (the force of drag is the same on both, but the same force has less effect on higher mass). So a heavier round will retain more of its energy/momentum during its flight.
This is an informed but uneducated opinion. IANABE (I am not a ballistics engineer). A higher velocity aluminum bullet would probably do much more damage to animal tissue (i.e. people) than a slower uranium one. Since KE=(1/2)mv^2, and hydrostatic shock increases with KE (hydrostatic shock is what makes a 12 inch gopher vaporize when shot with a .50 inch bullet. it’s caused by the fact that tissue acts more like a liquid than a solid in a high energy impact, since it’s mostly made of water), super-fast aluminum bullets might be a good anti-personnel round. But against anything more substantial you need more mass and more density (hence Lead and Uranium).
Yes and no. An aluminum bullet with higher velocity would have a greater chance of penetrating armor than, say, an aluminum bullet with lower velocity. But not compared to a DU bullet, even with much lower speed. Mass makes a big difference when it comes to impact. Aluminum would just vaporize when it hits an armored target, probably leaving a discolored area and maybe a dent, because the metal is too soft and light to do real damage (to armor. It would still kill you or me quite easily).
So the way I figure it is this: for a Soft target (humans, animals, etc) you don’t want total penetration (the bullet uses all its energy in the body instead of flying through) and you want more hydrostatic shock. So a softer, lighter, faster bullet is ideal.
For a Hard target (houses, vehicles, armor, really really large animals) you want as much penetration as possible, so you want a harder, denser projectile.
This of course assumes you’re using plain old ballistic rounds, not exploding shells.
What do you mean “pluto’s answer”? I gave the same answer, but did it first. Sheesh :). Anyway, if the gas is expanding adiabatically, I think the total work done only depends on the initial and final pressure and volume. It’s been years since my last thermo course, so I might be wrong. I’ll see if I can dig out Reif’s intro stat mech book when I get home.
Padeye-
You’re probably right that the real world situation is much more complicated than this. That is why my initial response was that the more useful comparison was the distance travelled. Assuming this is the same for the two shells, we can assume that the muzzle velocities were the same, and the weapon designer already worked out exactly how to arrange this.
I’m not trying to flame you, Padeye, but how come every time I ask a theoretical question about ballistics you turn it into a practical one? In my OP I gave the conditions,
To which you replied,
How can I better answer the variables than by asking you to ignore them? I having trouble remembering where to employ “momentum = mv” and where to employ “e = 0.5mvv”. That’s all.
I’m not angry, I just can’t figure out how I could have been so unclear. Granted, the latter question was pretty much useless, but I never got the sense that anybody had any idea why I was asking.
I can’t tell if people are trying to be funny (a worthy goal even if I’m too thick to pick up on the humor), or if I’m just completely incapable of getting the idea of my question across. If I ask a question about somebody driving a Citroen, everybody tells me Citroens suck. Sorry, I know I should have said, “a car” instead; I know I should have stripped the gun language out of this question to be less distracting, but I like to color my stories. Mea Culpa
As to the Jeff_42’s point that we are looking at the wrong end of the problem, you’re right. Muzzle energy isn’t nearly as important as on-target energy.
I mainly asked the question at the muzzle because air friction is a whole new can of worms. A slower, heavier bullet will travel farther through air to get the same distance over land; that complicates things, but I don’t know how much. Different metals would have different fiction coefficients.
The main reason I was wary of your statement that more weight means more energy is, this rule of thumb is often used in contexts where it doesn’t really work. One way to increase bullet weight is to increase bullet diameter, which is going to increase frontal area and thus frictional braking. Another way is to increase bullet length, which takes up space in the case for propellant. But in the context you used it, it was actually a quite useful rule. I just started this one to help get sorted out.
Onto Joe_Cool’s point about aluminum bullets actually having some possible anti-personnel value. That’s interesting. I think more or less the same kinematic principle is at work with hyper-velocity pre-fragmented bullets. How much actual hydrostatic shock they create … I don’t know, but they are certainly light and high-energy. And they aren’t supposed to overpenetrate.
I took a spreadsheet to the momentum question. Here is the answer, which probably would have been obvious had I been really good at paperless algebra.
Assuming energy is equal at all bullet weights, the factor by which you change bullet weight is the square of the factor by which momentum will change. If you quadruple your bullet weight, your momentum will double. If you cut your bullet weight to 1% of its original value, your momentum will decrease to 10%.
(My calculations were, a muzzle energy of 100 for all loads. A bullet massing 0.5 gives you a velocity of 20 and a momentum of 10. A bullet massing 1 gives you a velocity and momentum of 14.14. A bullet massing 2 will travel at 10 for a momentum of 20, and bullet massing 200 will travel at 1 for a momentum of 200. Easier than I thought.)
DU slugs are only useful in very high velocity weapons. While the extra punch of a heavy slug will increase the kinetic energy, higher velocity is far more efficient at transferring energy to the target. (Remember where those exponents are. The square of velocity increases a lot faster than the mass.) Once you have the high velocity, the weight of the slug is a minor element of the formula for kinetic energy. The heavier slug does improve flight characteristics, and final trajectory, but it is not the weight that makes DU so effective against armor.
Penetrating power for DU slugs is not entirely a consequence of the higher density and weight of the slug. Uranium is a very hard material, and requires huge energy to deform, and retains its refractory strength at very high temperatures. Then comes the kicker, when you do deform the material at impact with a high enough kinetic energy, the Uranium compresses, and the rate of its nuclear breakdown is increased. It gets very hot. Hot in a sense unrelated to ordinary projectile weapons. Hot in the sense of nuclear processes. While it is not sustained fission, it still produces a lot of energy.
What penetrates the armor is an expanding ball of plasma. That has other destructive results on the other side of the armor as well. The material of the armor is less a factor than the thickness when it is opposed by the impact of DU weapons. Anything under three or four feet of fairly refractory material is ineffective against the twenty-millimeter cannon version of the DU slug. I don’t think hand held rifles produce the requisite velocity, but an anti tank round from a fifty caliber machine gun would probably be strong enough to penetrate any mobile armor. (I could be wrong about that, but the DU commando rifle is probably a special effects prop.)
Momentum (simplified): Measure of damage that will be inflicted.
Energy (simplified): Measure of the most possible damage that can be inflicted.
If a 5 lb baseball is thrown at your head with a starting speed 60 mph, is it going to hurt more or less than a 1 lb pebble with all other variables the same?
Obviously not. Thus, the heavier one has a greater momentum.
Also, if we change the starting speed the answer will always be that the baseball is gonna hurt more.
So, to directly answer the question: The u238 has a greater momentum and more potencial and kinetic energy. Yea, it’s all been said, I just tried to simplify it.
BorisB, I understand your frustration when people cannot concentrate on the substance of the issue and go off in all sorts of directions at once. I see it happen in many threads and I guess we are all somewhat guilty of that. We do not want so much to answer the question that was intended as much as put in whatever we want to say and if that doesn’t answer the question then too bad. I also notice a lot of stuff posted that does not take into account earlier posts. If it gets out of hand it can be very frustrating but many people’s brains work like that.
Just a few days ago I was having a very frustrating argument with a woman who, when I ordered coffee, jumped all over me because “coffee is so bad for you”. I asked her if she could provide any support for that claim and for a while she just beat around the bush with things like “everybody knows it” and “so-and-so, after the bypass surgery, the doctor told him not to drink coffee”.
In the middle of this I said, “It’s like tampons…” I was going to say there is a “common” but unproven belief they are unhealthy, but she cut me right there and said “I don’t use tampons!” I thought “What the f**k does that have to do with anything?” I looked at her and said: Oh… Ok… I guess that settles it… coffee must be bad for me.
The problem with those people is they are not concentrating on trying to understand what you are trying to say and responding to that. They just hear something that reminds them of something else and they have to tell you what just crossed their mind while they ignore what you were just talking about. I find it very difficult to carry on a conversation like this because my patience is in short supply. During that conversation I was imagining what it must be like to be married to someone like that…
OOps… sorry for the hijack… you can get back to the OP
which, by the way, What I would do is this: make a spreadsheet comparing two bullets of equal energy and different momentum and then make one comparing equal momentum and different energy. Make some graphs and analyze… it will probably be interesting. That’s the way I tend to analyze such problems
For real!! Fascinating. I always thought the depleted uranium ammunition was effective because of density and hardness but your’re saying it has a quasi-nuclear (or however described) process going on at impact that generates enough heat to burn through armor! Neato.
So if I squeeze/compress a ball of depleted unranium hard enough (analogous to high speed ammo impact) it will get super hot but won’t fission? Interesting.
This sounds fishy to me. Do you have a source for this? How much does the Uranium compress? If enough of a reaction occurs to create a plasma, wouldn’t the DU rounds be hot all the time? Wouldn’t having a few of them near each other be dangerous?
There is NO fission happening. Remember, almost all of the fissionable stuff has been removed from DU. Even bullets made from the ‘good’ stuff bombs are made out of probably wouldn’t start a fission reaction as A-bombs require a neutron source to kick the process into gear (it can happen without a neutron source but is far less likely). You also need a critical mass to get a fission process into high-gear and I don’t think a bullet would have near enough mass (I think a few kilos is the minimum amount for critical mass…not sure though).
I imagine that the density and/or molecular nature of DU makes it such that it gets VERY hot before simply vaporizing allowing it to do more damage (than lead for instance) before simply dissipating into nothing (or nearly nothing).
