Momentum in Short vs. Long Barrels

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Not sure if this has been covered before on this forum, but I wanted to talk about barrel length vs. velocity with respect to different bullet weights. Essentially, what I was seeking was: Are shorter barrels more efficient with lighter or heavier bullets?

Obviously lighter bullets have higher velocities regardless of barrel length (up to the point where the barrel gets too long and starts creating drag), but if you are going to carry a pistol with a short barrel, or carbine, are you getting the most out of it with light bullets vs. heavy bullets?

The general equation for energy is KE=0.5m x V^2. or kinetic energy equals 1/2mass times velocity squared. It is the square of velocity which makes light faster bullets have more muzzle energy than heavy bullets assuming both are loaded to the maximum psi the cartridge can handle while mass is increased linearly.

HOWEVER!! Momentum is a key component to penetration and a key component to resisting forces acting upon the bullet (among other things). The equation for momentum is p=m x v. In this case, the relationship is linear for both velocity and mass. Therefore, a proportionate increase in one variable and decrease in the other would mean momentum stays the same.

So, if velocity increases in proportion to a decrease in mass, then momentum would not change when choosing light vs heavy bullets (at the muzzle). But we know this isn't so. Underwood's 135 gr JHP fired from a 6" barrel travels at 1600fps. Their 200 gr JHP travels at 1250 fps. The 135 gr jhp has 67.5% of the mass of the 200 gr JHP, but travels at 28% higher velocity...it would take 32.5% more velocity to equal a 1 for 1 trade off yielding the same momentum at the muzzle.

So for the same barrel/ammo type, heavier equals more momentum. But what about different barrel lengths?

I put the following chart together from a webpage where they tested 10 mm ammo of different types from 2" to 19".

The equations are natural logarithmic curves fit to each ammo type and R^2 represents how much the velocity change is explained by barrel length. The equation in the upper left is the Buffalo Bore 180 gr 10 mm, upper right is corbon 135 jhp, and the bottom is hornady 200 gr xtp.

Right off, looking at the R^2, you can see that barrel length matters more for the 180 and 135 gr bullets than the heavier 200gr xtp. Granted these are different ammo makers, but all three follow a similar velocity path.


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I have other charts like this for the AR-10/15 type rifles showing a similar relationship. Which is: Heavier bullets lose less overall energy in shorter barrels than lighter bullets do. For instance: If you shoot 55 gr FMJ's in a 24" AR, you will lose more energy AND momentum switching to a 16" AR than you would if you were using 77 grain sierra match kings. Both would lose velocity, energy and momentum. But the percentage change for the 77gr smk would be less than teh 55 gr FMJ.

You could say the reverse as well, that you will gain more energy and momentum if you add barrel length AND switch to lighter bullets.

So what is the point here?
Efficiency is important to my line of work, and it spills over into my reloading. Sometimes we chose firearms for a purpose with factors limiting performance like concealed carry pistols need to be small and easy to conceal. Or a good woods carbine that isn't burdensome to carry but still able to efficiently kill a critter. So in general, less momentum is lost with heavy bullets in short barrels while long barrels take better advantage of the velocity gains from light bullets.
 
Velocity does not increase in proportion to mass. It increases in proportion to bearing surface and friction. As a bullet is traveling through the barrel it is accelerating. After the bullet leaves the barrel, momentum become relevant.

You seem to have put a chart together that details bullets will leave a longer barrel at a higher velocity than in a shorter barrel - given a specific cartridge. This doesn't seem to be new.
 
I'm not sure what information you want to obtain here. You already know what the physics and numbers say. There is no solid proof one way or another that the momentum factor or KE factor are important, as you know. Without a solid, crystal clear set of expectations you can't get any useful information. So, considering solid non expanding bullets, will momentum be more of an influence if you slide bullet weights or velocities up and down the scale? then ask what will happen when you use an expanding bullet, then a heavy for diameter bullet, high velocity loads, low velocity loads, for example, what does this mean when testing the high velocity .357 maximum, opposed to the .38 special?

My general thoughts on the matter are that the effects of the round on the living, or otherwise reactive target. So far, nobody has ben able to give much other than speculation or some research data for these issues. Gel testing is just a benchmark and not a fact that carries over to reality.

Every time a bullet strikes flesh is a totally different occurrence. It's pretty much random within a range of possibilities. changing variables such as velocity or bullet weight won't always make a great deal of difference.

If you can forgive me, this discussion is like the sort of thing my father in law used to have with me. He had very little to do but read and think, and we spent a lot of time talking about very unusual subjects like this. We never accomplished a thing.

That said, I think that momentum may be more important in snub nosed pistols. use a bullet and cartridge that will give deeper penetration, rather than hoping that lighter faster bullets will cause extreme damage.
 
Momentum has nothing to do with barrel length. You're over thinking the whole thing too.
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Momentum is a function of velocity....which is directly correlated to barrel length holding all else equal. So...


I'm not sure what information you want to obtain here. You already know what the physics and numbers say. There is no solid proof one way or another that the momentum factor or KE factor are important, as you know. Without a solid, crystal clear set of expectations you can't get any useful information. So, considering solid non expanding bullets, will momentum be more of an influence if you slide bullet weights or velocities up and down the scale? then ask what will happen when you use an expanding bullet, then a heavy for diameter bullet, high velocity loads, low velocity loads, for example, what does this mean when testing the high velocity .357 maximum, opposed to the .38 special?

My general thoughts on the matter are that the effects of the round on the living, or otherwise reactive target. So far, nobody has ben able to give much other than speculation or some research data for these issues. Gel testing is just a benchmark and not a fact that carries over to reality.

Every time a bullet strikes flesh is a totally different occurrence. It's pretty much random within a range of possibilities. changing variables such as velocity or bullet weight won't always make a great deal of difference.

If you can forgive me, this discussion is like the sort of thing my father in law used to have with me. He had very little to do but read and think, and we spent a lot of time talking about very unusual subjects like this. We never accomplished a thing.

That said, I think that momentum may be more important in snub nosed pistols. use a bullet and cartridge that will give deeper penetration, rather than hoping that lighter faster bullets will cause extreme damage.
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Brian, I recognize that bullet construction is a very important factor when determining the effect on flesh/damage. What I am showing here, assumes we are not changing bullet construction. i.e. you could apply it to a 150, 165, 200, and 220 gr nosler partition in .308. Very similar construction though not identical even though it is the same bullet type, same diameter. But bearing surfaces and nose construction would change.

What this says is, again, holding all else equal, a heavy bullet from a shorter barrel has better potential momentum than a light bullet, compared to the same combo in a longer barrel because as a percentage, the heavy bullet's momentum is reduced less for a given length.

So what am I saying? that along with bullet construction, weight is your friend if you want penetration at low velocities.

It isn't a major revelation, just some data supporting conventional wisdom, and worthwhile to someone new to reloading new to internal/external ballistics.
 
Momentum has absolutely nothing to do with bullet performance on living animals or humans. It is a good predictor of how well bullets knock down steel plates, bowling pins and other inanimate objects. This theory has been misapplied for decades. People see heavy bullets knocking down objects more readily than lighter bullets and incorrectly assume it is relevant.

Bullet penetration in living animals is most correctly predicted by looking at a bullets sectional density. Assuming equal construction, bullets that are long/heavy in relation to diameter penetrate deeper regardless of calculated momentum.

All bullets shoot somewhat faster from longer barrels, but the difference is a lot less than most people think. But lighter bullets do seem to lose a little less speed from shorter barrels than heavy bullets. But the difference is pretty insignificant. Within the same caliber (assuming equal construction) the heavier bullet will be "LONGER" and penetrate deeper than the lighter bullet of the same caliber.

But when you compare different calibers things get interesting. A 200 gr bullet fired from a 30-06 will put penetrate a 225-250 gr bullet fired from a 35 Whelen even though the heavier bullet has more momentum. Once again assuming equal construction.

When you compare different construction things get interesting too. A 130 gr copper bullet fired from a 308 will out penetrate a 180 gr common lead bullet fired from a 300 WM.
 
Bullet penetration in living animals is most correctly predicted by looking at a bullets sectional density. Assuming equal construction, bullets that are long/heavy in relation to diameter penetrate deeper regardless of calculated momentum.
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Again, we are assuming all things equal except mass and velocity. Sectional density changes with mass. Increasing mass, increases sectional density ceteris paribus. Therefore, momentum changes are directly related to sectional density though their joint usage of mass as a component of the formula. sectional density (SD) = M/A (mass divided by area) ....Momentum ==> p=M X V.

Momentum has absolutely nothing to do with bullet performance on living animals or humans. It is a good predictor of how well bullets knock down steel plates, bowling pins and other inanimate objects. This theory has been misapplied for decades. People see heavy bullets knocking down objects more readily than lighter bullets and incorrectly assume it is relevant.
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Notice with mass in the numerator that SD increases as mass increases....and in the momentum formula as mass increases momentum increases. So saying momentum has nothing to do with performance simply isn't mathematically possible in the sense that if area is held constant, one must change with the other proportionally.


momentum, sectional density, and bullet construction are the 3 factors determining terminal bullet performance on any living target.


But again, this wasn't the debate I was seeking. I was wanting to point out the relationship between momentum, velocity, and short vs. longer barrels and heavy vs light projectiles.
 
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A real world test

I'm going to be a little less scientific and attempt to take a stab at this; although, it is against my better judgement :D . . .

I was curious myself and attempted to run a test using my 4" model 67; and my 1.875" (we'll call it 2" from here on out) model 60. (We're talking 38 Special here - didn't want to assume everybody knew S&W model #'s.)

I went to the range, chronograph in tow. Along with a whole host of 38 Special ammo. 148 DEWC's; 158 LSWC's; 178 - that's one-seventy-eight - LSWC's; 110 JHP's; 125 JHP's; 158 JHP's; Factory 135 GDHP's; Factory 95gn Silvertips; and probably some others. The jacketed were all +P loadings.

Conclusion: It was inconclusive :p. I did see a slight correlation where the heavy bullets seemed to realize a little less kinetic energy loss (as a percentage) than the light bullets. But there were quite a few exceptions to the rule.

My real conclusion is that I needed to run a test where all the ammo - and their various bullet weights - yielded the same kinetic energy through the 4" bbl; and THEN check the % loss w/ the 2" bbl over the spectrum. I have yet to build/test a whole slew of ammo just for this purpose. Nobody hold your breath - just sayin' ;).

So the data - knowing it was scientifically inconclusive - did lead me to believe that there may be less kinetic energy % loss with the heavies. That said, still leaves the question of actual terminal performance against a bad guy. I suppose, even if I did acquire "good data" the debate of actual terminal performance would still be a point of spirited discussion. I for one, sit squarely in the "you must first make a hole" camp; and thus, lean toward heavy bullets (regardless of bbl length) for self defense. That's just me.
 
So the data - knowing it was scientifically inconclusive - did lead me to believe that there may be less kinetic energy % loss with the heavies. That said, still leaves the question of actual terminal performance against a bad guy. I suppose, even if I did acquire "good data" the debate of actual terminal performance would still be a point of spirited discussion. I for one, sit squarely in the "you must first make a hole" camp; and thus, lean toward heavy bullets (regardless of bbl length) for self defense. That's just me
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Nick, first of all, good job trying it for yourself and testing. And you are asking the same question I have pondered.

The fact that the test was inconclusive just means more range time is needed!!!:D

The real difficulty in testing this stuff is that there are essentially two options, hold ALL variables constant except barrel lenght......Which means cutting down a barrel to ensure the chamber isn't changing.

Or, test a whole lot of ammo and do a multi-variant regression.

The idea being that if you cut down a couple barrels, testing velocity changes as it is shortened, you can infer that since nothing else changed, the relative velocity differences would hold in most applications.

Without cutting down barrels, you test several diffent ammo types, in many guns with different barrel lengths, and see if your hypothesis holds. I can help you with that if you collect the data.

And your tests might yield a conclusion if you implement more controls. But, if you continue to find inconclusive results, then you may decide that practically there is no advantage.
 
Not sure if this has been covered before on this forum, but I wanted to talk about barrel length vs. velocity with respect to different bullet weights. Essentially, what I was seeking was: Are shorter barrels more efficient with lighter or heavier bullets?
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Perhaps I am over simplifying, but I would tend to agree with your conclusion.

IMO, it's because for any given caliber a heavier bullet will have less powder which will burn more quickly versus a lighter bullet with more powder which may not be half burned by the time the light bullet leaves the barrel where the heavier bullet moving slowing is taking better advantage of available pressure.

Plus, I just like heavy for caliber bullets better.

:-)
 
first of all, good job trying it for yourself and testing.
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Thank you. But you're being a bit kind. It didn't seem like it at the time as it was a long day at the range. And the 38 snubbie got to beating me up a bit by the end of the day. But all said and looking at it retrospect, it was a rather half-hearted attempt.

I have lead slugs for 38 at 105, 125, 148, 158, & 178 grains. What I need to do is start with my already set load of 3.3 grains W231 under the 178 LSWC's. I already have that chrono data and KE. Then, still using W231, do load work ups with all the other bullet weights to match (or very nearly) the KE. At that point, we'll have the same propellant and the same KE. Not meaning to get into the weeds too deep (too late :p), but since the bullets will seat at different depths and be of different weights, the same W231 will have different burn rates in each loading. So it's still not exactly apples to apples. But MAY be close enough to show a trend line with KE % drop.

The real challenge is to do all the work ups to create matching KE ammo of different weights. I've rather gotten tired of chronographing. I like just shooting better these days. As it is, when the weather warms a bit, I'll need to put a couple chronograph irons in the fire. Need to find more usable loadings with Unique - but that's a whole 'nuther subject.
 
there are times when math makes my head hurt!!

There are times when math is "bumblebee" math.
(this is referring to the old story about an engineer who's math (using all the variables, power/weight ratio, wing area,etc) "proved" a bumblebee cannot fly. The bee, not knowing this, flies just fine. ;)

I'm not questioning your math, or that it shows a difference, but is the difference MEANINGFUL???

A longer arm can throw a rock faster than a shorter one. Given.
A lighter rock can be thrown faster than a heavier one. Given.

We know this, so what are you trying to tell us??

Velocity and weight/mass are measured values. Energy and momentum are calculated values, and are what they are because of the formulas used to calculate them. Very useful for some things, not so much, for others.

You mention wondering about what/which is more "efficient", but your measure of efficiency seems to be the percentage of change in calculated numbers. Most of us are more concerned with amount of difference in the effect of a bullet in what it hits, than in calculated performance numbers at the muzzle.

Put another way, you can calculate the difference in "efficiency" between a sports car hitting you at 100mph and a Greyhound bus hitting you at 70mph. Does it matter to the person hit? Does it change the result? Are you "deader" because you got hit by a bus?

My signature line is my opinion, based on a lifetime of observed results. You can probably prove it with math. You can probably disprove it, with math. Matters not, its still happens.
 
we can maybe say that getting a bullet with higher than average sectional density, in identical construction, will be likely to penetrate better.

Maybe it should be pointed out that as velocities go up, KE goes up exponentially, rather than just simply. Momentum does not go up exponentially. Momentum is a better measure of what depth of penetration can reasonably expected. Putting any complications in the way, like expansion, just blows everything out of the water.
 
Put another way, you can calculate the difference in "efficiency" between a sports car hitting you at 100mph and a Greyhound bus hitting you at 70mph. Does it matter to the person hit? Does it change the result? Are you "deader" because you got hit by a bus?
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And yet it does matter at the margins. You see, in many, most, or some no descript figure greater than half the time, things go the way they are supposed to go and the critter or enemy dies. Does 1 more inch golf penetration matter? Does a few moa less drop matter?

Usually no if the measure of success is s dead critter, and eliminated threat or a hole in the paper. But then there are those situations where a shot quartering towards you on a bull moose requires more . Or your attacker is wearing thick clothing, smashing his way through a door, while hopped up on PCP. And shooting through the door is the best choice.

When I was training for non-compliant and opposes hoardings for MIO at Blackwater I saw several videos of guys getting shot multiple times and still coming (9mm). One fella was shot center mass 9 times with pauses in between before he finally stopped attacking. No bullet exited.

There are two types of questions in economics. Positive and Normative....And they are very different. Positive questions are objective fact, basically what is. Normative questions are subjective "what should be"

My post is a positive statement, how much it matters teeters on normative

:)
 
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