Accuracy vs Barrel Length

[Hastings]

I was wondering about barrel length, and how much barrel is required to achieve maximum potential accuracy. It would seem that there would be a minimum barrel length given a paticular caliber/velocity/bullet weight/bullet length relationship, and any amount of barrel beyond that length would only aid accuracy by increasing the sight radius. Is anyone aware of physics formulas related to this. I am mainly interested in this as related to 44 special and 45 colt handguns, but the idea would obviously affect ideal barrel length on carbine rifles. I would think that with increased barrel length, and the comensurate increase in velocity due to higher percentage of powder burned, the formula would be exponential (perhaps this is not accurate, I'm no physicist). I am also interested in the rifling twist rate formulas. I followed another thread related to this, but I was wondering how this relates to the barrel length issue. Essentially, how much barrel length is required to accomplish maximum bullet stability given the parameters listed above?

Just curious

Hastings

 

[Majic]

Spin is imparted on a bullet to achieve stability in the first inch or two of a barrel (otherwise all snub guns would keyhole their bullets). The extra barrel length help improve sighting potential and allows increase bullet velocity.

 

[sqlbullet]

Ditto. Enough barrel to provide spin. More length gives velocity and aids the shooter in aligning the bore (sight radius), but does not inherently increase the accuracy of the gun.

 

[Pilot]

My Benelli MP95E Atlanta target pistol is my most accurate handgun. It has a sub four inch barrel, but MUCH longer site radius.

 

[feets]

BTW... more powder burning in the barrel isn't the reason for increased velocity.
The powder burns quickly and is fully consumed before the bullet moves more than an inch or so.
The remaining pressure created by the burn is allowed to push the bullet for a longer period of time in a longer barrel. In the shorter barrel the pressure is vented to the outside world before maimum velocity has been reached.

 

[MrBorland]

It would seem that there would be a minimum barrel length given a paticular caliber/velocity/bullet weight/bullet length relationship, and any amount of barrel beyond that length would only aid accuracy by increasing the sight radius. Is anyone aware of physics formulas related to this.

As others noted, a longer barrel doesn't increase the intrinsic accuracy of the gun. However, Newton's Third Law tell us that, all else being equal, a longer barrel must increase movement of the gun while the bullet's still in the barrel (derivation below). Keep in mind that we're talking about the tiny, but real recoil that happens while the bullet's traversing the barrel, not the much larger recoil most of us associate with recoil. Also, this is the "intrinsic recoil" of a free gun hanging in space. The intrinsic recoil of the gun goes way down when it's connected to the shooter (with a good grip), who, in turn, is connected to the earth. Still, all else being equal (and it won't be, since a longer barrel also adds weight), a longer barrel increases the movement of the gun while the bullet's still in the barrel. Does it affect accuracy? In the end, the effect is probably swamped by lots of other factors.



Derivation (large case refers to gun, small case to bullet):

Newton's 3rd law states that the force on the bullet moving forward equals the force on the gun moving back:

F = f = MA = ma; where A = D/t^2 (D = distance, t^2 = time squared)

MD/t^2 = md/t^2 : where D = distance the gun moves back = Recoil (R) and d = distance the bullet travels while gun is being pushed back, i.e. barrel length (L)

Therefore R = L(m/M).

Note that R is independent of time, and therefore bullet velocity. R is only dependent on bullet and gun weight and barrel length.

A 4" 40 oz revolver shooting a 158grain bullet while hanging in space, R = 0.036". If the barrel shifts from the horizontal a mere 0.5 degrees during this recoil, this translates into as much as 2.5" from the point of aim at 25yds if you've got a wimpy grip.

 

[dagger dog]

I lay terms the barrel, for maximum accuracy, needs to be long enough to touch the target where you want the bullet to impact!

 

[1911Tuner]

It's not the length of the barrel that "makes" the gun accurate. It's got more to do with the sight radius, and how the longer it gets, the more easily the shooter can detect an error.

Think about artillery. A 105 gunner working with a good forward observer can fire two for registration and drop the third one almost in your lap from 5 miles away. The ratio of barrel length to distance is off the scale.

 

[MachIVshooter]

It would seem that there would be a minimum barrel length given a paticular caliber/velocity/bullet weight/bullet length relationship, and any amount of barrel beyond that length would only aid accuracy by increasing the sight radius.

That's pretty much it. On that note, the faster the bullet, the lower the flight time, hence there is less time for environmental variables to act on it, which will serve to increase accuracy. This is especially true where rifle rounds and extreme range are concerned. The further out the bullet stays supersonic, the more accurate it is. So in this respect, a longer barrel can serve to increase accuracy. But then, the longer the bullet is in the barrel, the more time there is for movement of the gun to alter trajectory. Also, longer barrels are less rigid, and barrel "whip" will degrade accuracy too. Kind of a double-edged sword there........

Happy shootin'!

 

[1911Tuner]

the faster the bullet, the lower the flight time, hence there is less time for environmental variables to act on it, which will serve to increase accuracy.

While that can be factored in to determine the accuracy of the individual shot, it doesn't have anything to do with the intrinsic accuracy...the potential, or "mechanical accuracy...of the combination of gun and ammunition.

 

[Dr. Tad Hussein Winslow]

Concerning strict mechanical accuracy, here's what little I seem to know:

1. There was an ol' boy who years ago spent many a month testing various rifles under ideal conditions in a big hangar in Texas, with all different barrel lengths, and controlled variables and measured groups precisely. He settled upon the idea that the "perfect" barrel length for maximum accuracy is right around 22" - IIRC, it was 21.8".

2. The conventional wisdom on accuracy is this: "Barrel length is irrelevant to accuracy; all that matters is whether the bullet is stabilized, and if it's stabilized, it is stabilized, and after that, a barrel is only going to contribute to INaccuracy, not accuracy, due to the barrel being longer and therefore less stiff, allowing for barrel harmonics to increase. The only reason longer barrels seem more accurate is because of the longer sight radius". But I DO NOT BELIEVE THIS conventional wisdom. Why not, you ask? Because if this were true, you'd see benchrest competitors with barrels on their rifles in the 5"-10" range. You'd see guys with handguns with short 5-10' bbls, using a scope (where sight radius is irrelevant), shooting the same groups as guys with rifles. I know, I know - T/C, XP, and Striker guys (Okiecruffler) get the same groups right? But they're using 12-14"ers, not 5-10" or less, correct? There must be a sweet spot which occurs AFTER the proper spin is already imparted, but before the thickness to length ratio of the barrel makes for a "whippy" barrel.* Plus, see #1 above.

*Note: this must be true, UNLESS it is the case that it just takes that much barrel for the spin to be FULLY imparted to the bullet - maybe in the 12" range, give or take, depending on twist rate, bullet shape and length? I dunno.

 

[cornman]

I agree with sauces. Of course barrel length matters. I would think ever gun manufacturer would love to save a few bucks and sell 15" barreled rifles if there was litte difference.

 

[sqlbullet]

I would love to see a reference to the methodology used by the ole' boy in Texas. More importantly, did he hypothesize why this length was ideal? Merely arriving at a length could just as likely be an indicator to a practical accuracy nexus as an intrinsic one.

Benchrest shooters prefer the barrel length that gives them the most stable shooting position and balance, plus they consider bullet velocity which benefits from a longer barrel. These are practical accuracy considerations, not intrinsic.

Manufacturers sell rifles with barrel lengths that consumers buy. Consumers are arrogant, opinionated, self-aggrandizing jerks. (Just look at me. I buy stuff.) Ergo, the direction of the market offering is not an indicator of intrinsic or practical accuracy, but public opinion. (Further, a 15" barrel on a rifle would be illegal without a special permit.)

In the end, I will trust the scientific evidence that intrinsic barrel accuracy is not related to length. Accordingly, I select barrel length based on factors like maneuverability, required ballistics, platform stability, sight radius and desired weight.

 

[1911Tuner]

Rule of thumb:

The shorter the barrel, the stiffer the barrel...all else equal. Stiffer means reduced vibration-induced movement equals increased *intrinsic* accuracy...or accuracy potential. Other factors must be considered. The important ones being equal lug bearing and amount of flex in the receiver...or lack thereof. This is why we lap lugs and bed actions.

 

[Dr. Tad Hussein Winslow]

Here is an article at Lilja's site about barrel rigidity and how it varies with length and diameter:

http://www.riflebarrels.com/articles/barrel_making/rigidity_benchrest_rifles.htm

And of course, barrel rigidity correlates more or less directly with accuracy. Now, forget about strict mechanical accuracy for a moment, and factor in other practical factors: Bbl length increases velocity, which increasing wind-bucking ability. Due to this velocity factor, there becomes a tradeoff of velocity to rigidity at some point beyond the 21 or 22" barrel. To get equal rigidity past a certain point, you have to add so much barrel diameter that the barrel becomes ridiculously thick and heavy (over 1.5 or 2" diameter). Combine this multiplicatively increasing barrel weight to get the proper rigidity with every extra inch of barrel length (since weight is both length TIMES diameter, and BOTH are increasing) - combine this with the diminishing returns of bbl length to velocity, as the expanding gases impart less and less marginal velocity, combined with opposing force of drag of the bullet in the bore, and you get an optimal practical real world best bbl length for a given type, usually somewhere in the 26-34" range, just depending on *how heavy* you're willing to go. Of course a lot of medium-heavy to heavy varmint/tactical contour rifles on the market have a 26" barrel. Savages 12 F Class precision target rifle has a 30" bbl, but that makes sense because it's an "ultra-heavy" contour, at a full 1.0" all the way to the end, so it should retain nearly-similar rigidity, and you get 4 extra inches of expanding gases to increase velocity. Still a heck of a heavy gun (limiting your portability). My understanding is that most benchrest competitors use right at a 20" bbl - which admittedly is odd and juxtaposed to the idea of 21.75 being ideal for pure accuracy, esp. given that benchrest DO obviously also have to consider the wind.

sqlbullet - I'm looking for that information - Art Eatman knows about it - Art, do you still have a link to the Houston Warehouse experiments? (or Houston Hangar, whatever it was). Now this guy's conclusions about barrel length and an optimal goldilocks length for best accuracy are probably limited to the type of bbl contour on the rifles he was using. With thinner or thicker, the ideal length may be shorter or longer (presumably, thicker-longer, and thinner-shorter). Whether his methodology in controlling for variables is sound or not? - maybe you can tell us after reading about it - I don't know. I'm looking for the info.....

 

[Dr. Tad Hussein Winslow]

Here we go:

http://www.angelfire.com/ma3/max357/houston.html

But no bit of information was, Virgil believes, more valuable than a little advice Jim Gilmore passed along. Jim said a barrel MUST be 21 3/4” long for optimum accuracy. That precise length, he stated, sets up a vibration pattern that duplicates well from shot to shot. Virgil faithfully followed that advice on his guns.

Anyone who strictly observes the 21 3/4" doctrine will screw off a failing barrel of that length and run a new one under it. Rechambering and rethreading, in order to achieve more pristine lands just forward of the throat, shortens the barrel. Shorten the barrel, spoil the magic length.

Through the years, the Houston Warehouse shooters were able to rate the relative accuracy of the various benchrest calibers — .22, 6mm and .30. In the perfect conditions of the warehouse, the .22’s outshot them all, followed closely by the 6mm’s. The .308 calibers were a not-too-distant third. The most accurate .30 caliber ever to find its way into the warehouse also belonged to Virgil. The rifle, built around a Shilen DGA action with McMillan barrel, shot consistently within a few thousandths of .100". The barrel length? You guessed it: 21 3/4".

 

[pitty920]

I'm sorry but u can throw all that physics jumbo jumbo out the door.
longer barrel = more accuracy
A lot of people who buy 6" plus barrels on revolvers shoot out past 100 yards. a snub nose won't do that as well. longer barrel is more spin, speed, screw the sight radius lets say there is a scope. More spin and speed is less effected by wind a gravity. do u see snipers using 14" barrels hell no, and they don't use sights they use scopes.
now all u snub guys ar talking 50 yards MAX. And yeah maybe there they ar close, but when u take it off the rest the slightest movement of that 2" barrel is going to equal missed shots.
snubs are good conceal and carry guns that's it. Why buy a revolver if your not going to fully utilize its power and accuracy, I am not saying get some 10" barrel, 6-7.5" is ideal.

once again go tella sniper that barrel length means nothing but speed and get laughed off the forum!

 

[Remllez]

All other things being equal.....Young Eyes will yield better results.....

 

[earplug]

I'm sorry but u can throw all that physics jumbo jumbo out the door.

Nonsense
In my limited experience with testing my own weapons. Barrel length on pistols has little effect on accuracy.
Military rifles shooters need power transferred to the down range target. Higher velicity fights the wind better, That's why the longer barrels. Accuracy at 100 yards is less with a longer then a shorter barrel as was proved due to harmonics.
For pure accracy little power is needed to punch paper.
I went from a 8 3/8 revolver to a 4 inch for shooting bullseye and accuracy is as good or better with the same 38 spl LWC. I used a red dot scope on each gun.
I did the same testing with a 4 and 5 inch 625 in 45 acp and noticed no change.
Various target 22 lr pistols have less then 5 inch barrel and they win medals.
Another shooter tested the velocity of various light target loads in a 38 spl and found that going from six to 8 3/8 gained no velocity.
You can only push the bullet as fast as the expanding gases. Additional barrel length past that point will slow the bullet down.

 

[rcmodel]

longer barrel is more spin,

Wrong!

A 1 7/8" snub-nose revolver barrel imparts all the spin that can be imparted.
If it didn't, that would indicate the bullet is slipping in the first inch or so of rifling.
And that would indicate severe barrel leading or jacket fouling, depending on the type of bullet used.

Recovered bullets would show no rifling marks, because they would be wiped slick by slippage.
And neither one of those things happens.

Accuracy of a longer handgun or iron sight rifle barrel is due to the longer sight radius, nothing more.
Accuracy of a longer scoped rifle barrel is due to higher velocity, and less drop and wind drift.

And there is a lot to say that a short stiff rifle barrel is more accurate then a long whippy one.

At least, that's what the most accurate rifles in the world, those used by the bench-rest shooters, seems to indicate.

rc

 

[skidder]

The longer/heavier barrel also reduces the human error of "shaky hands".

 

[jmr40]

once again go tella sniper that barrel length means nothing but speed and get laughed off the forum!

A 3.5 year old thread ressurected by someone who knows just enough to get into trouble. Ask these snipers what they think of shorter barrels.

http://www.tacticaloperations.com/SWATbarrel/

 

[The Lone Haranguer]

A longer barrel may (but not necessarily) impart greater mechanical accuracy to the gun itself. It improves the accuracy of the shooter by being more forgiving of tiny errors in sight alignment, due to the greater distance between the front and rear sights (aka "sight radius).

 

[Pyro]

What about gain twist rifling? Can't do that on a short barrel.

 

[GregGry]

Actual absolute accuracy doesnt have much of a pratical application for most shooters. Your average person will shoot a long slide handgun better then a compact. To them the long slide is more accurate. Yet put them in a vise and the difference is likely small. It's their abilities that are holding them back, not the accuracy of the barrel.

With rifles it's much the same thing. Your average shooter will shoot a longer barrel rifle more accurately at longer ranges then with a short barrel. Why? Simple, the increased velocity of the longer barrel reduces the flight time and bullet drop, making it easier to hit the target. At longer distances barrel length is critical, you need as much velocity as possible. Extra flight time and extra bullet drop are more variables that hurt consistency shot to shot.

So yes in my opinion there is a correct barrel length needed to hit a target. That length is determined by the distance your shooting from. Unless lobbing lead like a motar to hit a target is consistent.