Ammunition - Deep Thoughts

[Garufa]

I've been pondering on a couple of things and am too lazy to do any proper research, so I ask here.

1) Why are heavier bullets loaded with less powder than lighter bullets? Is it a pressure thing? Some kind of other kinetic force?

2) Why do heavier bullets, especially from a rifle, shoot higher than ligher ones at a given distance? My experience here is with surplus 7.62x54r & 8mm and noticable differences at 125-200 yards. Why would they have a higher trajectory that lighter projecticles.

Somebody break it down for me, scientific.

[Guest tnfireman]

Without doing any research myself I would say

1 Yes it's a pressure thing

2 lighter = faster = flat trajectory or you have to lob heavy bullets

Dunno if it's right but it sounds good!!!

[gregintenn]

1) Why are heavier bullets loaded with less powder than lighter bullets? Is it a pressure thing? Some kind of other kinetic force?

The heavier bullet is more difficult to shove down the barrel, therefore it allows more time for the burning powder to create pressure than a lighter bullet that leaves the barrel faster. The higher pressure results in the need for less powder.

2) Why do heavier bullets, especially from a rifle, shoot higher than ligher ones at a given distance? My experience here is with surplus 7.62x54r & 8mm and noticable differences at 125-200 yards. Why would they have a higher trajectory that lighter projecticles.

Same theory at work here. The faster bullet leaves the barrel at an earlier point, allowing less time for muzzle rise before it's out and headed toward it's destination.

[Guest mosinon]

Been some time since I finished my physics degree (useless thing btw, not a lot of work involving frictionless planes to be had) but I think if we apply some principles of physics we'll figure out the answer.

When in the cartridge the lighter bullet will, I think, take off faster than the heavier bullet. That is assuming, and I don't know about this, that the thing that is holding the bullet back isn't the brass. If the biggest thing keeping the bullet from moving is the weight of the bullet then it becomes pretty simple why the lighter bullet needs more powder.

We need an equation. Let's try the ideal gas law.

pV=nRT

I doubt that the gases from powder follow the ideal gas law perfectly but they likely follow it well enough.

So we've got

pressure*Volume=the amount*A stupid constant*Temperature

We're lucky, in this case we can kind of forget about RT and just use one symbol to represent them. We'll use Z. We'll let n be the powder

Our equation reduces to

pV=nZ

So, with the light bullet V is going to change faster than with a larger bullet because the bullet will be moving faster. At this point we should probably introduce differentials but that is a bridge to far. Let us forge ahead and use some exaggerated numbers.

Imagine we want p=100 for both bullets. As the bullets are moving and the gas is expanding the value of V will be larger for the smaller bullet than the larger bullet because the bullet has gone farther (V will be the distance the bullet has travelled*the area of the bore). Let us assume, for illustrative purposes only, that the small bullet goes twice as fast as the larger bullet.

So we get, for the smaller bullet:

p=nZ/V

or, since Z is constant

p=n/V

We are aiming for 100 so

100=n/V

But we know that V is really 2

100=n/2

So we'll need 200 globules of powder to get are bullet to 100 p.

With the heavier bullet things are different. We still want p=100 but V will only be half as much so:

100=n/1

We'll only need 100 globules of powder to get to our desired pressure.

Which explains why you need more powder for the lighter bullet.

For the second part of the question, why do the heavier bullets shoot higher?

The answer is that they don't. Motion in the x axis is independent of motion in the y axis. Or, since we live on earth, the bullet drop is independent of how far the bullet is going.

We'll forget about air resistance and such because it won't really matter for this question. Everything on earth drops at about 9.8m/s^2. This has in interesting implication. IT means that if you have a .22 phoenix perfectly level three feet off the ground, a .50 barret perfectly level three feet of the ground and an apple three feet off the ground and fire the guns at the same while dropping the apple instantaneously when the bullets leave the barrel time all three projectiles will impact the earth at the same time.

What we learn here is that since the heavier bullet is moving slower the trajectory has to be higher to reach the target at the same spot. And it is going slower. since the pressure of both rounds was maxed out at 100 and since F=ma we can be sure it is going slower.

Want to be sure? Well, pressure is force per area. The bullets have the same area and are subjected to the same force so the equations reduce to:

F=ma

Where m is the mass of the bullet and F is the force (or pressure) and a is acceleration.

Since the force is the same and the mass is different we'll need to find out what happens to the acceleration.

Doing some trivial algebra we find the equation for acceleration is...

a=F/m

Say the mass of the light bullet is 10 and the mass of the heavy bullet is 50. We also know the force is equal and to make it is easy we'll assume a force of 100

For the light bullet:

a=100/10

a=10

For the heavy bullet

a=100/50

a=2

So the acceleration of the light bullet is twice that of the heavy bullet. But what does that say about the velocity of the rounds?

Velocity is given by (under constant acceleration which this isn't but close enough):

v=at

a is acceleration which we already know and t is time. We'll pretend you have a really long barrel. OhShoot says you are a great marksman so you probably don't need it but this barrel is so long is takes one full second for the bullet to exit the barrel. IT is not a good option to carry concealed.

Anyway we get the velocity for the light bullet (t=1)

v=10*1

v=10

for the heavier bullet

v=2*1

v=2

So same pressure and all but the heavy bullet is going much slower as it leaves the barrel. It is going to take longer to reach the target. In our case it will take 5 times as long to reach the target.

I've been prattling too long. But with a few more equations you'd discover that the heavier has to be aimed higher to hit the same spot.

Sorry for the physics lesson, what was i thinking? Anyone who read that could have spent their time better by looking at porn. If anyone wants the derivation to continue pm me.

[Guest CJK]

That was not only clear but funny. Who knew we had physicists hanging out here? And physicists with a Feynmanesque sense of humor!

Thanks for the explanation!

[Guest mosinon]

Glad you enjoyed it CJK! And surprised...

[peejman]

A very good explanation, but the nerdy engineer will make a slight argument with the nerdy physicist (all in good fun )...

.....

For the second part of the question, why do the heavier bullets shoot higher?

The answer is that they don't. Motion in the x axis is independent of motion in the y axis. Or, since we live on earth, the bullet drop is independent of how far the bullet is going.

We'll forget about air resistance and such because it won't really matter for this question. Everything on earth drops at about 9.8m/s^2. This has in interesting implication. IT means that if you have a .22 phoenix perfectly level three feet off the ground, a .50 barret perfectly level three feet of the ground and an apple three feet off the ground and fire the guns at the same while dropping the apple instantaneously when the bullets leave the barrel time all three projectiles will impact the earth at the same time.

What we learn here is that since the heavier bullet is moving slower the trajectory has to be higher to reach the target at the same spot. And it is going slower. since the pressure of both rounds was maxed out at 100 and since F=ma we can be sure it is going slower.

The nerdy engineer says that while the above is true in the physicists' world, the engineer doesn't get to make such assumptions. Things like the ballistic coefficient play an increasing role in bullet trajectory at ranges beyond 100 yds. I assume these are both milsurp FMJ type rounds, though the design of the bullet itself may be enough different to cause a few inches difference in POI at 200 yds.

Say the mass of the light bullet is 10 and the mass of the heavy bullet is 50. We also know the force is equal and to make it is easy we'll assume a force of 100

For the light bullet:

a=100/10

a=10

For the heavy bullet

a=100/50

a=2

So the acceleration of the light bullet is five times that of the heavy bullet. But what does that say about the velocity of the rounds?

Fixed...

I'm reminded of something a math professor told us in class one day.... "Two men are 10 paces apart. When told to move, they decrease the distance between each other by 1/2. How long until they touch?"

The physicist says, "they'll never touch".

The engineer says, "after 3 steps, they'll be close enough."

And in closing....

[E4 No More]

I just had flashbacks of physics class!!!

[tyguy]

Nerd Fight!

[safeandsecure]

Garufa, I'm glad that Mosinon and Peejman explained that for you. I was gonna get all "scientific" and explain it myself, but they beat me to it.

Seriously ... holy moley and good grief!!! That was so far over my head that I think I sprained my brain just trying to read it ... ...

Glad we got smart folks on here. Honest, I am. Just reinforces my belief that I'm too old, too dumb, and too untalented to add anything of interest, so I figured I'd just ramble a while ... ... ... ...

[gregintenn]

Everything on earth drops at about 9.8m/s^2. This has in interesting implication. IT means that if you have a .22 phoenix perfectly level three feet off the ground, a .50 barret perfectly level three feet of the ground and an apple three feet off the ground and fire the guns at the same while dropping the apple instantaneously when the bullets leave the barrel time all three projectiles will impact the earth at the same time.

I agree with this.

But with a few more equations you'd discover that the heavier has to be aimed higher to hit the same spot.

I disagree with this. Without ajusting your sights, a 158 grain bullet from a 38 special WILL strike a target higher than a 110 grain bullet from the same gun; same sights, same distance, within reason. I'm talking 7-15 yards here; not 1000. If muzzle rise isn't the culprit for this, I'd like to hear a valid explanation.

I am no physicist, and I am not intending to challenge your education. I am simply stating the results of actually firing a handgun. I have not noticed this same effect with a rifle; or at least not to a degree that one would notice.

Edited December 23, 2010 by gregintenn

[Guest mosinon]

I agree with this.

I disagree with this. Without ajusting your sights, a 158 grain bullet from a 38 special WILL strike a target higher than a 110 grain bullet from the same gun; same sights, same distance, within reason. I'm talking 7-15 yards here; not 1000. If muzzle rise isn't the culprit for this, I'd like to hear a valid explanation.

I am no physicist, and I am not intending to challenge your education. I am simply stating the results of actually firing a handgun. I have not noticed this same effect with a rifle; or at least not to a degree that one would notice.

Well, when you're talking idealized physics you leave out muzzle rise, cause we've got robots that compensate for muzzle rise.

But muzzle rise might be the answer. So the muzzle filps up when you fire because the bore of the or pistol is above where your hand is. That is my suspicion, sketching it quickly it would seem that if the barrel were below your hand the muzzle would sink down and if were in line with your hand it would just be straight back. I'm going to imagine this is true.

You would also imagine it would more pronounced with a pistol since there is essentially only one pivot point.

Now the question becomes why the heavier bullet hits higher than the lighter bullet. I'd wager that heavier bullet=more recoil=more muzzle rise. But I'm going to have to bust out some ballistics tables to make sure. The rub is that F=ma and while the m of the larger bullet is greater the a is lessened. Depending on the actual values the answer might work out differently than I suspect. It is worth looking at and then running some extreme case scenarios.

Feel free to question my education all you want. I do.

[Garufa]

Garufa, I'm glad that Mosinon and Peejman explained that for you. I was gonna get all "scientific" and explain it myself, but they beat me to it.

Seriously ... holy moley and good grief!!! That was so far over my head that I think I sprained my brain just trying to read it ... ...

Excellent responses so far but maybe I should not have used the term "scientific".

I cracked open "Hatcher's Notebook" today in the throne room. Could not find an answer in the limited time I had but there sure is a lot of information in that tome.

[Guest GunTroll]

WOW! I have such a grin after reading all these post.

Lets just say I'm not a physicist nor an engineer but rather think of myself as a mechanic/artist. I don't care why what does what. I care if I can fix it or build it. The physicist has his theories and the engineer has the design and I'm where the rubber meats road.

I won't even try to answer this question but I have an idea. I won't be able to articulate it through typing so I won't try. Physicist,Engineer, when is our local ballistician gonna chime in?

[gregintenn]

Now the question becomes why the heavier bullet hits higher than the lighter bullet. I'd wager that heavier bullet=more recoil=more muzzle rise.

I'll buy that. And take away the effects of muzzle rise and recoil, and I'll agree with your earlier post. So I guess now the question is whether this is caused by a slower bullet taking longer to leave the barrel allowing for more muzzle rise, or it is caused by the increase in recoil, causing more muzzle rise. I'm betting on a combination, but I simply lack the education to determine which is the case. I'd be interested to know, however.

[gregintenn]

I love this type of discussion! I should have went to college in pursuit of an engineering degree.

[Guest GunTroll]

Well, when you're talking idealized physics you leave out muzzle rise, cause we've got robots that compensate for muzzle rise.

But muzzle rise might be the answer. So the muzzle filps up when you fire because the bore of the or pistol is above where your hand is. That is my suspicion, sketching it quickly it would seem that if the barrel were below your hand the muzzle would sink down and if were in line with your hand it would just be straight back. I'm going to imagine this is true.

You would also imagine it would more pronounced with a pistol since there is essentially only one pivot point.

Now the question becomes why the heavier bullet hits higher than the lighter bullet. I'd wager that heavier bullet=more recoil=more muzzle rise. But I'm going to have to bust out some ballistics tables to make sure. The rub is that F=ma and while the m of the larger bullet is greater the a is lessened. Depending on the actual values the answer might work out differently than I suspect. It is worth looking at and then running some extreme case scenarios.

Feel free to question my education all you want. I do.

What we need is one of these to answer the muzzle rise question.

Benchrest shooting - Wikipedia, the free encyclopedia

Ooops I meant to drop this link.

http://en.wikipedia.org/wiki/File:Railgun1.jpg

Edited December 23, 2010 by GunTroll

[peejman]

While muzzle rise may contribute to the difference in POI, don't forget about barrel harmonics, particularly with rifles. Super-slow video of a rifle barrel will clearly show that it vibrates while the bullet travels down the barrel. Where it is in it's oscillation cycle when the bullet exits the muzzle is important.

I believe this video is of an air rifle. I'd assume the much higher pressures/forces would result in even more flex with a high powered rifle. YouTube - 29426129's Channel

edit... here's one of a .50 BMG ->

The idealized physics model assumes an infinitely stiff barrel mounted to a base of infinite mass, hence nothing moves. The photo above looks like a reasonable attempt at that idealization. That plus a chronometer would be excellent for a hand loader to test out various bullet types and provide some hard data to answer our many questions. And it sounds like GunTroll volunteered to build one for us.

Edited December 23, 2010 by peejman

[gregintenn]

And it sounds like GunTroll volunteered to build one for us.

That's what I heard!

[E4 No More]

What we need is one of these to answer the muzzle rise question.

Benchrest shooting - Wikipedia, the free encyclopedia

Ooops I meant to drop this link.

File:Railgun1.jpg - Wikipedia, the free encyclopedia

You'd still have problems with harmonics in the barrel...just say'n.

[Guest GunTroll]

I don't know how to embed videos but I'd strongly lean that this is your explanation. With the difference in weight & velocity of your bullet, in the same firearm (same twist rate) a direct effect in POI could and probably does come from this..... Like I said I'm horrible at articulating my thoughts through typing

Someone please embed this

EDIT:

Also its probably just your sights. If you don't adjust them for the different loads you'll get different POI because.... the arc is obviously different for the different loads. A lighter bullet has less arc and a heavier one has a more profound. The heavier projectile probably hasn't reached the apex of its path when it reaches the target/paper. Bullets don't rise above the bore line after being fired but yet it is easily misunderstood that bullets go up after leaving the muzzle. Less mass projectiles have a truer path. Heavier projectiles do not. There are so many sites out there that explain all of this. My Google-Fu is weak.

The whole topic of barrel whip, harmonics and etc are way too complicated for me. Basically I don't care. If it shoots...it shoots is how I feel about it. It seems one could go mad trying to master ballistics because of all the variables that NO one can control. It is fun for me to at my level, but I just don't get into the nit and griddy of it.

While Google-n' I found a better explanation from some random guy...

I also have this in my fixed sight 9mm. 115 grain bullets while they group nicely all this low, while 124's at the same ranges are right on. Actually a significant number of fixed sight 9mm's are regulated for 124 gr bullets.

The simplest explanation that I can think of is when the sights are set for a certain bullet weight at a certain distance that is where the line of sight intersects the drop of the bullet. A heavier bullet drops quicker, which makes them hitting higher seem quite backwards.

Just remember that handguns are typically short range firearms, and at short ranges the bullet is still on the "upswing" of the arc. Which is really a misnomer as bullets do not rise, but meaning it is above the intersection point of the sights to target.

A heavier bullet drops quicker so the sights are set to hit a little higher than for a lighter bullet. At short distances the flatter trajectory of a lighter bullet will actually hit below the point of aim, due to the lighter bullet moving a little faster and therefore having less arc. The sights are set figuring more arc to the path, so at shorter distances the impact is below the sights. While at longer ranges the flatter trajectory will rise above the the trajectory of a heavier bullet, such as what we are accustomed to with rifles.

Edited December 24, 2010 by GunTroll
had another point to add

[E4 No More]

While muzzle rise may contribute to the difference in POI, don't forget about barrel harmonics, particularly with rifles. Super-slow video of a rifle barrel will clearly show that it vibrates while the bullet travels down the barrel. Where it is in it's oscillation cycle when the bullet exits the muzzle is important.

I believe this video is of an air rifle. I'd assume the much higher pressures/forces would result in even more flex with a high powered rifle. YouTube - 29426129's Channel

edit... here's one of a .50 BMG ->

The idealized physics model assumes an infinitely stiff barrel mounted to a base of infinite mass, hence nothing moves. The photo above looks like a reasonable attempt at that idealization. That plus a chronometer would be excellent for a hand loader to test out various bullet types and provide some hard data to answer our many questions. And it sounds like GunTroll volunteered to build one for us.

Doh! I should have read further before posting about harmonics.

[gregintenn]

That's very interesting. Thanks for posting.

[Guest Archminister01]

Well, when you're talking idealized physics you leave out muzzle rise, cause we've got robots that compensate for muzzle rise.

But muzzle rise might be the answer. So the muzzle filps up when you fire because the bore of the or pistol is above where your hand is. That is my suspicion, sketching it quickly it would seem that if the barrel were below your hand the muzzle would sink down and if were in line with your hand it would just be straight back. I'm going to imagine this is true.

You would also imagine it would more pronounced with a pistol since there is essentially only one pivot point.

Now the question becomes why the heavier bullet hits higher than the lighter bullet. I'd wager that heavier bullet=more recoil=more muzzle rise. But I'm going to have to bust out some ballistics tables to make sure. The rub is that F=ma and while the m of the larger bullet is greater the a is lessened. Depending on the actual values the answer might work out differently than I suspect. It is worth looking at and then running some extreme case scenarios.

Feel free to question my education all you want. I do.

The muzzle doesn't rise until after the bullet has left the barrel...so it hits where it is pointed. Any following bullets fired may be subject to muzzle rise and in fact are. If you have ever fired a weapon on full auto, your point is clear. Single shot slow fire will usually hit where it is aimed without muzzle rise even becoming an issue.

One thing, and I may have missed it in all of that intellectual fray, is case volume. A larger bullet displaces more area inside the case and thus less powder is used to generate the same pressure.

As for bullet rise..I am going with barrel harmonics.

Edited December 23, 2010 by Archminister01

[gregintenn]

The muzzle doesn't rise until after the bullet has left the barrel

I'm not doubting you, but can this be proven?

As for bullet rise..I am going with barrel harmonics.

I can't dispute that theory.