AR Barrel Length - the science

mikethebike

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I have never been one to subscribe too much to the barrel length debate. I do know that through my shooting I generally keep my .308 equipped with a 20in barrel and my .223/556 barrels vary from 14.5in to 20in, depending on the application. While I understand that there is velocity loss though less gas expansion, I tend to look more at the repeatably of the shot. Is the barrel consistent enough to accurately put rounds down range as close together as possible?

Found some nice info at sadefensejournal.com published by by Dr. Philip H. Dater & Jason Wong on 8 February, 2012. :

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"The maximum velocity for the M855 projectile occurred in a 20-inch barrel. This is anticipated since the cartridge was designed specifically for this barrel length. Velocity drops rapidly as the barrel length decreases, especially below 10 inches where the velocity drops below 2,500 fps. M855 bullets traveling below 2,500 fps when impacting a target will not produce a lethal wound channel.


There have been a number of studies demonstrating the barrel external temperature gradient as a function of barrel length in addition to numerous studies of muzzle velocity as a function of length. The authors are not familiar with studies relating length to measured (rather than calculated) bore pressures, especially port pressures at the instant of bullet exit (uncorking).

Five-round average pressure in the bore at the moment of bullet uncorking is plotted against barrel length. It is apparent that the pressure rises exponentially with decreasing barrel length. This rapidly increasing pressure produces significantly higher sound levels as well as flash and strain on suppressor design. The values for 10.5 and 14.5 inches were calculated by averaging the adjacent measurements.

pressure_zpsxr8cfzzg.jpg


Data and Analysis
Measurements for barrel lengths of 24 down to 5 inches showed that the pressure in the barrel at the moment of uncorking varied from 4,800 psi for the 24-inch barrel to over 25,000 psi for the 5-inch barrel. This is represented in Graph 1 and summarized in Table 1. Plotting the logarithm of the uncorking pressure against the barrel length produces a relatively straight plot, indicating that the pressure rises exponentially with shortening of the barrel.

The pressure we measured at the port three inches from the bolt face was 55,744 psi using M855 (average of 9 rounds). There was some round-to-round variation with variations from a low of 52,500 psi to a high of 57,600 psi. Interestingly, the round-to-round variation in pressure was less pronounced at the more distal ports. We do not have the SAAMI pressure measurements for chamber pressure in the M855 5.56x45mm ammunition, but for commercial .223 Remington, the average maximum SAAMI pressure is listed at 55,000 psi.

Because these weapons are used more and more frequently with sound suppressors, it is interesting to note the uncorking pressure at the more common barrel lengths of 14.5 inches and 10.5 inches. Pressure data for the 14.5 and 10.5 inch barrels was approximated by averaging the pressure between the two adjacent measurements (14 and 15 inches, etc.) yielding pressures of 8,150 and 11,500 psi respectively. There is a passing interest in the non-serious user for suppressing the M16 with a 7-inch barrel, and the uncorking pressure at that point is 17,140 psi, approximately 50% higher than it was for the 10.5-inch barrel, which is itself approximately 50% higher than the 14.5-inch barrel.

One of the authors has measured port pressures in the entrance chamber of one of his company’s 5.56mm suppressors with both a 14.5 inch and 10.5 inch barrelled HK416, and there was a 50% increase in suppressor chamber pressure of the 10.5 inch barrelled weapon as compared to the longer 14.5 inch version. This correlates well with the difference in bore pressure at the instant of bullet uncorking.

The M855 ammunition is optimized for a 20-inch barrel with a 1:7 twist barrel. It was not surprising that the greatest velocity of 2,979 ft/sec was obtained in the 20-inch barrel, and the lower velocity on barrels greater than 20 inches is explained by decreased pressure driving the bullet no longer exceeding the slowing from friction. After all, Eugene Stoner designed the cartridge for the 20 inch barrel.

The sound pressure level was measured according to Mil-Std 1474D, which specifies A-weighting. Weighting degrades meter performance to match the frequency response of the human ear, and A-weighting is accurate and appropriate only for sound levels below 55 dB. For sound levels above 130 dB, and in particular in the 160+ dB region of the non-suppressed 5.56mm rifle, the measurements should be performed without any weighting (also called “linear” or Z-weighting, depending on the meter manufacturer’s designation). While there is a rough correlation using A-weighting between uncorking pressure and measured sound level, the sound measurements are not considered overly accurate due to compliance with the Mil-Std.

Sound levels are pressure measurements expressed as a logarithmic ratio of the actual pressure referenced to 20 micro-Pascals, the threshold of human hearing. There was a little less consistency in the sound measurements than in actual uncorking barrel pressure measurements, partially because of adding several more variables. These included the acoustic impedance of the air and wind direction/velocity. In addition, the inaccuracies in this sound intensity range by using the called-for A-weighting introduces some level of inaccuracy that would probably not be seen in unweighed measurements. When pressure is plotted against sound pressure level in decibels and sound pressure level is plotted against barrel length, there is slightly more deviation from the projected average, but the trend and general correlation is statistically meaningful. Actual sound pressure levels varied from 162.5 dB(A) in the 24-inch barrel to 165.1 dB(A) in the 5-inch barrel.

Equally illuminating in this study was the correlation between velocity and barrel length (see Graph 1). To generate a lethal wound channel, the M855 projectile must have a velocity of at least 2,500 ft/sec on impact with the target. Below that critical velocity, the M855 bullet simply drills a 1/4 inch hole in the target, which too frequently is not lethal unless it passes through a vital structure. Some of this limitation is being addressed with newer projectiles not available to the authors at the time of the study. In the longer barrels, the maximum velocity of 2,979 ft/sec was in the 20-inch barrel with a velocity of approximately 2,700 ft/sec in the 14.5-inch barrel. The critical velocity of 2,500 ft/sec was in a barrel between 9 and 10 inches in length, which further shows the folly of considering a 7-inch barrel for this cartridge.
(...)
With shorter barrels, tuning of the gas port for weapon cycling becomes far more critical. Adding a suppressor, which does slightly increase bore pressure, will result in more erratic and forceful cycling of the weapon leading to earlier weapon failure. It is necessary to remember that the 5.56×45 NATO cartridge was designed specifically for a 20-inch barrel on a gas operated weapon with 7 inches of dwell time after the gas port. The 14.5-inch M4 barrel retains the 7 inch dwell length after the gas port.

Lastly, decreased velocity with barrels much shorter than 14.5 inches have a number of unwanted effects. Lowered linear velocity produces lower rotational velocity, which will result in diminished gyroscopic stability of the bullet. It will also result in significantly decreased projectile kinetic energy, decreased ability to generate a significant would channel, and will reach a point of diminishing returns where lethality of the projectile definitely comes into question.

Thus, it is the opinion of the authors that barrel lengths less than 14.5” in this calibre introduce effectiveness issues that may be detrimental to the user."


Here is some more graphs from rifleshooter.com

maximum point blank range
The maximum point blank range, allows a shooter to sight in his weapon at a given distance to hit a target of a given size when holding center mass. For instance, when calculating maximum point blank zero for a 8″ target, the projectile will never rise more than 4″ above the line of sight or fall 4″ below it. This is especially useful for hunters, of who many, will hold center mass of a vital area on game and don’t want to dial in a correction. Our calculations assume a 1.75″ sight over bore height.
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m193 ballistics with barrel length
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223 55gr ballistics with barrel length
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xm855 ballistics with barrel length
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bh ballistics with barrel length
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Wound channel at 3038 FPS velocity on ball ammo
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Wound channel at 2322 FPS velocity on ball ammo
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I read some where that 2700 ft/sec velocity is required for fragmentation of M855.
According to that data,
Distance to 2700 fps
20” Barrel
16” Barrel
14.5” Barrel
11.5” Barrel
M193
190-200m
140-150m
95-100m
40-45m
M855
140-150m
90-95m
45-50m
12-15m
 
I think where the problem lies with both articles is that force is measured by mass x velocity squared

since force is what is required to fragment, weight of the projectile should be considered even though velocity is a square factor

just saying 2700 or 2500 doesnt account for mass

ill try to find something with pounds square inch
 
Effective range has two meanings: effectiveness based on eternal and terminal ballistics, and effectiveness based on human ability to make hits.

The point is, unless you can observe and identify a target, and shoot at it, it is a moot point to have something that can go beyond that range.

For example, unless you carry a spotting scope or other observation equipment, good luck on finding a static target that doesn't wear orange at 500m using naked eyes.
 
Effective range has two meanings: effectiveness based on eternal and terminal ballistics, and effectiveness based on human ability to make hits.

The point is, unless you can observe and identify a target, and shoot at it, it is a moot point to have something that can go beyond that range.

For example, unless you carry a spotting scope or other observation equipment, good luck on finding a static target that doesn't wear orange at 500m using naked eyes.


Good point!
 
It is my opinion that the authors are dumbasses with no field experience.

You think Phil Dater is a dumbass? The guy is one of the most knowledgeable and thorough designers I have ever met. He knows 1000x more than anyone in this board ever will.

The issue with this article is that it is only relevant to military users constrained by the requirement to use M855 ball ammo. U.S. Civilians are under no such constraints and thus this is not relevant to us.

The issue is that M855 is designed to yaw, bend and break into pieces within a specific velocity range. This performance is required to increase the lethality of the bullet. Below the velocity range the M855 bullet does not perform as designed and thus suffers reduced terminal performance.

A 22 rimfire can be lethal at 200 yds if the bullet hits in the correct place. Don't confuse this as meaning the bullet is always lethal. Simplistic comments such as yours demonstrate a level of ignorance of the subject.
 
Well since we are just poor civvies, and are not forced to use M193 or M855, barrel length isn't such a big deal.....we can load 75-80gr for a 10" barrel which are pretty effective wound makers, or 50-55gr Ballistic tips/Vmax for a 7" barrel that are effective down to 1600 fps and make big holes in things.
m193 and m855 are probably the last bullets I would want to use given the choice.
 
Twist rate and bullet weight play a big part in all of this.This is particularly important for shorter barrels needing heavier grain. A 10 inch 1-7 barrel shooting a 55 grain bullet is far from optimal. Longer barrels compensate with velocity.

223and556twistgraphed.png
 
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So, should I even bother with my 7" PDW build? Or will it just be a cool looking, but ultimately useless gun?

I still think it will leave a fatal wound channel in the paper target :p

You will probably find that the novelty of the 7 inch wears off quickly, using anything other than a linear comp just makes them obnoxious to shoot and you will start getting headaches from the concussion blast.

The 6.5 inch upper I built (barrel compliments of Suputin) was fun but I got bored and sold the barrel. It was accurate though and with 77gr black hills match I could shoot around 2 moa at the 100 yard targets.
 
I like the profile of 10.5/11.5 inch, but the standard M4 in the U.S is 14.5 inch. {& some of the C 8's too} From seeing the charts, makes sense.
 
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