January 04, 2011
Scott Mayer reveals how to maximize the velocity of the .17 Mach 2
The .22 Long Rifle reaches its maximum velocity in a barrel that is about 19 inches long, so Scott experimented inch by inch with barrel length and the .17 Mach2 to see where and if its length mattered.
Barrel length has an effect on muzzle velocity, but does an inch or two one way or the other make a meaningful difference? Is it possible to have a barrel so long that it reduces velocity? Is there an optimal barrel length for highest velocity? These are questions that often come up among shooters, and I recently had the chance to answer them as regards the .17 Mach2 (.17M2) rimfire cartridge.
I just completed a report on the Thompson/Center R55 semiautomatic in .17M2, which will appear in an upcoming issue of Shooting Times, and during that project I had occasion to shorten the barrel on a T/C Contender also chambered for .17M2 to the same 20-inch length as that of the T/C R55.
The purpose of the amputation was to compare muzzle velocity of the fixed-breech Contender to that of the R55 autoloader to see if there was any significant velocity loss from the self-loader. There wasn't. In fact, the R55 produced slightly higher velocity. But the project also presented an opportunity to cut the Contender barrel off in one-inch increments to see if there was an apparent optimal barrel length for velocity that I could ascribe to the little .17-caliber rimfire.
Published experiments on how barrel length affects muzzle velocity have been done with the .22 Long Rifle, and from those experiments it has been concluded that generally any barrel length greater than 18 inches is actually causing the .22 Long Rifle bullet to slow down. The precise optimal barrel length for a .22 will vary from one load to another and one gun to the next because of different powder charges in the loads and tolerances in the bore dimensions. Regardless, the reason for the bullet slow down at that short a barrel length is because the expansion ratio (the sum of the volume of the bore and powder chamber divided by the volume of the powder chamber) for the .22 Long Rifle is so high. In other words, it has a very small powder chamber relative to the bore.
As powder burns it increases in volume about 1000 times, which increases pressure if contained as within a chamber. That pressure starts the bullet down the bore against the engraving forces, bullet-on-bore friction and the pressure of the air in the bore in front of the bullet. As the bullet travels down the bore, the volume of the space behind the bullet is increasing such that after reaching a certain point, gas pressure no longer increases.
After an inch of barrel was cut off, the muzzle was crowned and 20 shots were chronographed and averaged to determine what length was optimal for highest velocity.
Eventually, the gas pressure and bullet friction reach a point of equilibrium, followed by a transition to the effects of bore friction being greater than gas pressure. If the bullet is still in the bore after that transition, it slows down. While it happens at around 18 inches in a .22 Long Rifle, it would take a barrel several feet long in a cartridge such as the .308 Winchester because it has a much lower expansion ratio. The closer you get to optimal barrel length for maximum velocity, the less significant each increase in velocity becomes, which is why we get along fine with sporter barrel lengths in centerfire rifles.
I calculated the expansion ratio for a .22 Long Rifle in an 18-inch barrel and came up with 39. For the .308 Winchester, an 18-inch barrel results in an expansion ratio of about 7. To get an expansion ratio of about 39 with the .308 Winchester takes a barrel around nine feet long. That does not mean a .308 Winchester obtains its highest velocity in a nine-foot long barrel, nor is an expansion ratio of 39 a magic number. There are other factors that influence velocity, including the difference in engraving force and coefficient of friction between the outside lubricated lead .22 bullet and the copper jacketed .308 bullet. There is also the difference in surface area between the base of a .308-inch bullet and a .224-inch bullet to consider.
To keep the muzzle the same distance from the chronograph skyscreens as the barrel was shortened, it was necessary to slide the Caldwell Tack Driver shooting bags forward to keep the muzzle in line with the indicator on the shooting bench.
So all this brings me back to the Contender project and cutting off its barrel in one-inch increments and how the velocity changed as a result of it. Because the .17M2 has such a small powder chamber (it measured .0176 in3), I assumed optimal length would also be about 18 inches, as with the .22 Long Rifle, so I started with a 23-inch factory barrel. Using an Oehler Model 35P chronograph set up with four-foot screen spacing at 15 feet from the muzzle, my procedure was to chronograph and record five shots, then clamp the barrel in a Wheeler Engineering barrel vise, cut off an inch using a hacksaw and record five new shots.
With each inch, velocity declined until I got to 20 inches, then velocity appeared to climb again. By the time I had the barrel cut to 17 inches, velocity appeared to be going back down. Physically, that little increase in the velocity can't occur, and indeed when I checked the data using Tioga Engineering's Baltec1 program, it showed that the blip in velocity was not statistically significant and might not have actually occurred.
Blip or not, I decided to repeat the test using a special 27-inch barrel T/C made for the occasion and to fire 20 shots per inch of barrel to try and lower the standard deviation. I also made it a point to control my variables a lot better by crowning the muzzle between cuts using a brass round-head screw and valve-grinding compound in a cordless drill.
This time I also cleaned the bore thoroughly between groups of shots using a Hoppe's BoreSnake, fired one fouling shot before recording velocities for each group of shots, and used an indicator on the shooting bench top to make sure that regardless of barrel length, the muzzle was always at the same distance from the "start" chronograph screen. This time, muzzle velocity appeared to increase steadily as the barrel was shortened until a barrel length of 23 inches was reached. There was no "blip" in velocity like I had with the previous barr
el, and velocity appeared stable between 16.5 and 23 inches of barrel length. A line graph of those results is shown nearby.
Because of the .17M2's small powder chamber, I assumed it, like the .22 Long Rifle, had a high expansion ratio and expected similarly to find a barrel length near 18 inches where velocity would be highest. To check expansion ratio, I measured the volume of the little .17's powder chamber by pulling a bullet, dumping the powder, filing a small groove along the length of the bullet, and then weighing the two in grams on a PACT electronic scale. Next, I filled the case with water, reseated the bullet allowing the water to be displaced through the groove I had filed, and weighed the assembled cartridge. The difference between the empty and full case is the weight of the water in grams, which, through the magic of the metric system, was also the volume of the powder area in cubic centimeters, which I converted to cubic inches.
The average velocity for 20 rounds with each inch of barrel was plotted and the data was "smoothed." Scott's results agreed with what Hornady
found when developing the .17M2 in that sporter-length barrels produce essentially the same velocity, though 19 to 20 inches seems to produce the highest velocity.
Bore volume was obtained by multiplying the effective length of the barrel (distance from the boltface to the muzzle, plus the seating depth of the bullet, minus the case length) by IIr2. That value was taken at 98.5 percent to account for volume displaced by rifling. Measured as such, the .17M2 fired in an 18-inch barrel has an expansion ratio of about 25.
With the special 27-inch barrel T/C made, expansion ratio is around 38, so I reasoned 27 inches would be about optimum for highest velocity with the .17M2 and expected velocity to decline with each inch of barrel less. Because my experiment indicated otherwise, I contacted Dave Emary of Hornady to see if he had done any similar experiments when initially developing the .17M2.
"We did the same thing very early on with a minimum spec test barrel. We found that with barrel lengths over 21 to 22 inches, we started to lose velocity. Barrel lengths from 16 to 21 inches produced virtually the same velocity," Emary said.
You can clearly see on the line graph that velocity for the .17M2 is reduced using a barrel more than 23 inches long. From previous discussions with ballistics experts William C. Davis Jr. and Charles R. Fagg of Tioga Engineering, I knew there could be more information in the raw data than was readily apparent. I consulted with them, and Davis was kind enough to use various data smoothing techniques to find a smooth curve that best fit the raw data. Smooth curves filter out normal fluctuations in data allowing you to see through to the changes occurring in the sample. From the nine different curves Davis tried, a parabola was chosen as the best fit. The smoothed data is shown as the red trend line.
With the data smoothed, it showed that maximum velocity for the .17M2 is obtained with a 19- to 20-inch barrel and, as Hornady found in the development of the cartridge, that velocity is essentially the same for all sporter barrel lengths. What this means to a .17M2 shooter, then, is that you can opt for a rifle with a shorter barrel and not sacrifice anything in the way of velocity, and if maximum velocity is what you're after, you should realize it with a barrel 19 to 20 inches long.