I found this article very interesting.Thought I'd share.
http://www.rifle-accuracy.com/harmonics.htm
Now I know why when you shoot a group of three its cloverd.
Cell
http://www.rifle-accuracy.com/harmonics.htm
Now I know why when you shoot a group of three its cloverd.
Cell
Rifle Stocks - Barrel Vibration and Accuracy
From the moment that trigger is pressed and the firing pin strikes the primer until the bullet leaves the muzzle, a series of many vibrational impulses begin in the rifle, all of which are transmitted to the barrel in various magnitudes. These include such minor things as; the trigger sear releasing the firing pin, the firing pin moving forward, striking the primer, and the cartridge being moved forward. The powder then begins to ignite, and the bullet starts moving forward and engages the rifling. Because of the twist of the rifling, the bullet while it is being propelled forward, begins to spin imparting a small but measurable torque, but more importantly as it traverses the barrel it also sets up a circular vibrational pattern, or arc. The heat of the burning powder along with the pressure wave generated by the expanding gasses start another vibrational pattern that is induced into the barrel. All of these movements cause the barrel to stress and vibrate with a number of different harmonic patterns which if not controlled by some means cause each projectile to leave the muzzle at a slightly different point in the vibrational arc. Some people speak about the "whip" of the barrel, which would imply to some, that the barrel simply vibrates up and down like a buggy whip. Although there are some of the vibrations that are traveling in this direction, the main vibrations are circular. If this were not true, then a 3 shot group from a rifle would always be in a vertical string. This would be because, one would leave at the bottom of the "whipping action", one would leave from the center and one from the upper travel of the "whip". As we all know this seldom occurs, and if it does, it is usually caused by the barrel being under a heavy stress, such as way to much pressure exerted against it, caused by improper bedding, usually of the barrel. Most 3 shot groups you will see will be virtually triangular in shape, this is caused because as the barrel vibrates through its "circular arc" one bullet leaves the muzzle at say 12 o?clock, another at say 4 o?clock and the third at maybe 8 o?clock. The larger the arc of the barrel, the less accurate the rifle will be, and the larger the triangle. As a rule the less mass a barrel has, (the thinner) the more it is affected by the vibrations, this is the reason that a "heavy" barrel seems to shoot more consistently than a sporter barrel, and is also easier to tune. A shorter barrel of the same diameter will also have less amplitude to its arc of movement. As you tune the barrel with the Accurizer, what you are doing is changing the vibrational length of the free floated forward end of it, causing the vibrational arc, or circular vibrations of the barrel to get smaller and smaller. As the arc gets smaller the groups get tighter. Even though the bullets may still be leaving the muzzle at 12, 4, and 8 o?clock, the diameter of the arc has been lessened, so the triangle gets smaller. Until the past couple of years, when reliable barrel vibrational control devices came upon the scene, virtually the only way to control these barrel vibrations that affected the rifles? accuracy was to custom load the ammunition until a correct combination of cases, bullets, primers, powders, seating depths and etc. could be found that would allow that particular rifle to shoot good tight consistent groups. Now however with the use of the SmartStock, it is no longer necessary for the average shooter to go to these lengths to have the accuracy previously attributed only to hand loaded ammunition. As long as you are using well made ammunition, that is consistent, whether it is factory or handloads, you can simply tune your rifles? barrel to the ammunition of your choice.
Below is a table which was kindly provided by Varmint Al. It shows the relationship of the amount of vertical movement of a fluted barrel compared to a standard barrel. It also shows how shortening the free floated length a barrel with the SmartStock's tuner, greatly reduces the amplitude of the vibrations, and therefore reduces the dispersion of the bullets in a group.
Note that the Projected Exit Angle of the bullet at 100 yards in a 22" non-fluted barrel is 0.6069". Reducing the free-floated length of the forward end of the barrel to 14.6829" as is shown in the chart below, reduces the angle by 70% or nearly 3 times less vertical movement. This coincides nearly exactly with the independent barrel sag and accuracy heat testing done by me previously. You can see those results at:
http://www.rifle-accuracy.com/barrel-movement.htm
Table 1. Results for six different 416 stainless steel 6mm rifle barrels 22" long
Barrel Weight
(lb) Barrel OD
(in) Flute Root Dia
(in) Flute Depth
(in) First Mode Natural Freq
(Hz) Section Moment of
Inertia (in^4) Barrel End Sag
(in) Barrel Exit Angle Projected
to 100 Yard Target (in)
7.222 1.250 none none 73.783 0.11916 0.00278 0.6069
7.222 1.3687 1.1187 0.125 75.238 0.12390 0.00268 0.5837
7.222 1.4747 0.9747 0.250 79.278 0.13757 0.00241 0.5257
7.222 1.5674 0.8174 0.375 85.075 0.15842 0.00209 0.4565
4.820 1.2500 0.7500 0.250 67.724 0.06700 0.00330 0.7204
5.871 1.2500 1.0000 0.125 68.619 0.08378 0.00322 0.7017
4.820* 1.2500 none none 165.646 0.11916 0.00052 0.1804
5.871** 1.2500 none none 111.648 0.11916 0.00122 0.3261
* The barrel weight was reduced to 4.820 pounds by shortening the barrel to a length of 14.6829 inches.
** The barrel weight was reduced to 5.871 pounds by shortening the barrel to a length of 17.8845 inches.
The complete article by Varmint Al on fluted and non-fluted barrel harmonic vibrational movement can be found at:
http://www.varmintal.com/aflut.htm
Possible Explanation of how the Tuner Tunes a Barrel
The Tuner could be changing the frequencies so that the muzzle is just approaching the upper extreme of its swing at the time the bullet exits.
TIMING.... The approximate time that it takes a 3300 fps muzzle velocity bullet to exit the barrel, assuming a constant acceleration, is 0.0011 seconds. The velocity of sound in 416 stainless steel is 14,900 fps and a stress wave has time to propagate up and back the full length of the barrel 4 or more times after ignition and while the bullet is traveling within the barrel. The muzzle end of the barrel has ample time to "know" that something is going on at the breach end before the bullet exits.
VIBRATION PERIOD.... As an example, assume a mode 1 frequency of approximately 100 Hz that has a period of vibration of 0.010 seconds. Therefore the time it takes the barrel to make its first upward swing is a fourth of a period or about 0.0025 seconds. This is the approximate time the bullet exits. The mode 2 vibration has a period of approximately 0.0002 seconds and could be at the top of its thirteenth upward swing, at the 12.25th period swing, or about 0.0025 seconds. These two modes could add and amplify the exit angle of the muzzle near the peak of its upward swing, just as the bullet exits. The tuner could be adjusted to slightly change the two frequencies so that they reinforce each other at the time of bullet exit.
FINDING THE SWEET SPOT.... When tuning a load to a particular rifle, possibly the sweet spot is not when the bullet exits the barrel at the maximum of the vibration's upward swing but, slightly before the maximum height or exit angle of the upward swing.
UPWARD SWING.... The vertical amplitude of vibration is more heavily excited than the horizontal vibration because the center of gravity of the rifle is located below the barrel's centerline and the bullet's travel down the barrel causes a vertical turning moment about the rifles center of gravity. The vertical vibration is most important. Also, the barrel is initially slightly deflected downward due to gravity. When the round is fired, the pressure also tends to straighten the barrel like a bourdon tube in a pressure gage. As the barrel straightens, it over shoot in the upward direction and this adds to the excitation of the Mode 1 vibration. As a side note, the axial extension vibration mode is also probably heavily excited. This is the mode where the barrel extends and shortens axially. But, this axial mode should only have a negligible affect accuracy.
AVERAGE VELOCITY BULLET.... Possibly the sweet spot occurs when the bullet, with the average velocity, for a particular load, exits the barrel just before the peak of its upward swing.
FASTER BULLET.... A faster bullet will exit the barrel earlier and exit slightly before the average velocity bullet and the angle of the upward swing of the barrel will be slightly less. So the bullet's launch angle is slightly less, but the bullet is going faster and drops less.
SLOWER BULLET.... A slower bullet will exit later and the barrel's vertical swing will be higher and at a steeper angle when the slower bullet exits. The bullet is launched at a higher angle but is slower and will drop slightly more.
This combination, within limits, would print the bullet at about the same vertical location on the target for the normal variations in velocity from round to round.
Good Hunting... from Varmint Al
Rifle Accuracy
