First, I have searched for information for about a year and half on this subject. Some of you may know of something really good I've missed, but
the best source I have encountered for information on this topic is Al Harral. Who is Al Harral?
Al Harral is a retired guy--but one smart smart retired guy. You can find all of his fun things at https://varmintal.com/
He worked for 30 years at the Lawrence Livermore National Laboratory. For most of that time, he worked performing engineering structural analysis on complex systems using Finite Element Analysis models. He was the lab's Advanced Engineering Analysis group leader in the Weapons Division.
He has done the most extensive and best work I have found published and available on barrel harmonics. It has blown me away in terms of its complexity and its time elapsed video models or simulations of what all the different wave forms can look like in a rifle barrel. What they do to the barrel, and how it impacts your accuracy with that rifle is what I want to discuss.
The first thing we need to do is understand just how fast the bullet exits the barrel to get an appreciation for what the harmonics in the barrel can do to the bullet before and as it is leaving. Below is a graph of pressure over time for successive charge weight increases of Varget in a 30 06.
The bullet exit times are shown on the curves at about 1.3 milli seconds, or .0013 seconds as shown in the graph.
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. Actual exit times would be longer since the bullet is not under constant acceleration and the time from the firing pin first hitting the primer, ignition starts, is not included. ( Looks like about 1.3 milli seconds in the graph)
You might think, that bullet is outta there so fast, nothing in the barrel is going to affect it.....but you'd be wrong.
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.
So, this is the first part of the proof. The shock waves (pressure and sound) affect the bullet while its still in the barrel.
Now let's see what the shock waves and the harmonics are doing to the barrel itself and how that affects the bullet.
First we need to understand the method Al is using to analyze barrel movement and accuracy. He is not wading into the actual modeling of
pressure and sine wave movement up and down the barrel vs. time, nor is he taking actual pressure and sound wave frequency measurements up and down the barrel using sensors and osilligraphs to measure these things. He is modeling these things in his models from cell to cell along the barrel and by time steps in the model. I suppose he has this data in his models and could analyze it and present it, which I would like to see, but for simplicity what he is doing is focusing on the last few time steps and the position of the muzzle end as the bullet exits.
Below is a graph of the last 1/2 inch of the barrel muzzle and where on the target it is pointing at 100 yards, a projection if you will of the muzzle position at bullet exit. What has been proven with this work is that one will get smaller groups if one can design a load or use a tuner that will get the bullet to exit in terms of bullet exit time when the barrel is pointing slightly upward as is explained below in detail. Bullet exits once the position of the muzzle has peaked in pointing up and begins to point down will give the worst vertical dispersion of shots or the largest groups.
SUMMARY.... For the reader who doesn't want to wade through all the discussion here is a summary of what a tuner can do to correct for small variations in muzzle velocity from round to round. The Muzzle Projection Curve shows where the muzzle is pointing at a 100 yard target while the rifle is being fired. The most important aspect is the curve is where the muzzle is pointing at the time the bullet exits the muzzle.
Improving accuracy by compensating for small variations in muzzle velocity.
Smaller Groups Left of the Peak - UPWARD SLOPE:
Higher velocity shots exit early while pointing lower at the target but drop less in reaching the target.
Lower velocity shots exit later while pointing higher at the target but drop more in reaching the target.
Counteracting combination. Good.
Larger Groups Right of the Peak - DOWNWARD SLOPE:
Higher velocity shots exit early while pointing higher at the target and drop less in reaching the target.
Lower velocity shots exit later while pointing lower at the target and drop more in reaching the target.
Bad additive combination. Bad. This is currently being called "Negative Compensation".
The additional mass of a Muzzle Tuner slows down the muzzle movements and allows the bullet exit before the peak of the muzzle projection curve during the upward slope without resorting to high pressure loads.
If you understand this Muzzle Projection Curve and accept that getting your bullet to exit on the left side of the curve will give you smaller groups, then what are some ways to do this??
Some ways to get the muzzle exit time on the Left Side of the Peak
1. Add weight to the muzzle to slow down the muzzle movement
2. High pressure/high velocity load to make the muzzle exit time earlier
3. Faster burning powder to have the bullet gain velocity early and make the exit time earlier
4. Longer barrel to slow down the muzzle movement
I might add, to this list the following: bullet seating adjustments and crimping and neck tension adjustments, because what we are talking about is milli- seconds of milli-seconds of bullet exit time impact. So he already listed powder selection in no. 3, and in a sense charge weight variation in number 2. But, I would add bullet seating too.
The last thing I would add to his list is a barrel tuner which will in fact shift the barrel time of the bullet to a time when the muzzle is pointing slightly up. I will list how this works below.
Now do you see how internal ballistics is all related to harmonics, changes in muzzle velocity, and bullet exit time??
To Recap and looking again at the muzzle projection curve above:
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.
Now, some really interesting stuff if you want to explore how barrel tuners work. Go to:
ADDING A TUNER.... Adding a tuner to the muzzle of a rifle barrel does the following:
1. The additional mass reduces the amplitude of the vibrations.
2. Decreases the natural frequencies by decreasing the lower Mode's frequencies more than the higher Modes.
3. Increases the barrel's vertical end sag due to the extra weight. This would tend to make the vertical plane the preferred plane of vibration.
4. Moves the Mode 2 node closer to the muzzle.
WHAT A TUNER DOES.... It is possible to "Tune" a rifle barrel so that where it is pointing at bullet exit time will compensate for small variations of muzzle velocity. In the "tuned" condition the slower bullets are launched at a slightly higher angle than the faster bullets. The difference in launch angle can allow the slower bullets to hit the target at the same elevation as the faster bullets. That is the simple explanation.
FLIGHT PATH.... This chart shows the slower bullet actually travels a higher path than the faster bullet for them both to hit the same 50 yard zero. It is clear that the flexible barrel's muzzle must launch the two bullets of different velocity at slightly different elevations for there to be no vertical spread at the 50 yard target. With only two place accuracy on the drop values, from 42 yards to 50 yards the round off shows the drop to be the same. With more accuracy, this would not be the case.
WHAT A TUNER DOES.... A Tuner appears to compensates for variations in muzzle velocity. It slow down the movement of the muzzle so that with safe loadings, one can be on the left side of the MPC at bullet exit time. It will also reduce the high frequency jitter at the muzzle because if its inertia.
Now, if you got this far and you enjoyed it, you really must go here and explore all the different models and cases Varmintal has to offer.
https://varmintal.com/alite.htm
I was especially interested in the ladder tests of the 24 inch barrel with and without tuner.
Note all the analysis he presents for optimum barrel length on the site too further down on this same link below the 24 inch discussion.
Have fun and enjoy and maybe you may have more an appreciation why I believe barrel harmonics are related to the empirical results we see
when we run a Satterlee, Audette ladder, or OCW Method test in load development???? Maybe I'm not crazy after all???
Maybe its Al Harral that is crazy?
the best source I have encountered for information on this topic is Al Harral. Who is Al Harral?
Al Harral is a retired guy--but one smart smart retired guy. You can find all of his fun things at https://varmintal.com/
He worked for 30 years at the Lawrence Livermore National Laboratory. For most of that time, he worked performing engineering structural analysis on complex systems using Finite Element Analysis models. He was the lab's Advanced Engineering Analysis group leader in the Weapons Division.
He has done the most extensive and best work I have found published and available on barrel harmonics. It has blown me away in terms of its complexity and its time elapsed video models or simulations of what all the different wave forms can look like in a rifle barrel. What they do to the barrel, and how it impacts your accuracy with that rifle is what I want to discuss.
The first thing we need to do is understand just how fast the bullet exits the barrel to get an appreciation for what the harmonics in the barrel can do to the bullet before and as it is leaving. Below is a graph of pressure over time for successive charge weight increases of Varget in a 30 06.
The bullet exit times are shown on the curves at about 1.3 milli seconds, or .0013 seconds as shown in the graph.
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. Actual exit times would be longer since the bullet is not under constant acceleration and the time from the firing pin first hitting the primer, ignition starts, is not included. ( Looks like about 1.3 milli seconds in the graph)
You might think, that bullet is outta there so fast, nothing in the barrel is going to affect it.....but you'd be wrong.
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.
So, this is the first part of the proof. The shock waves (pressure and sound) affect the bullet while its still in the barrel.
Now let's see what the shock waves and the harmonics are doing to the barrel itself and how that affects the bullet.
First we need to understand the method Al is using to analyze barrel movement and accuracy. He is not wading into the actual modeling of
pressure and sine wave movement up and down the barrel vs. time, nor is he taking actual pressure and sound wave frequency measurements up and down the barrel using sensors and osilligraphs to measure these things. He is modeling these things in his models from cell to cell along the barrel and by time steps in the model. I suppose he has this data in his models and could analyze it and present it, which I would like to see, but for simplicity what he is doing is focusing on the last few time steps and the position of the muzzle end as the bullet exits.
Below is a graph of the last 1/2 inch of the barrel muzzle and where on the target it is pointing at 100 yards, a projection if you will of the muzzle position at bullet exit. What has been proven with this work is that one will get smaller groups if one can design a load or use a tuner that will get the bullet to exit in terms of bullet exit time when the barrel is pointing slightly upward as is explained below in detail. Bullet exits once the position of the muzzle has peaked in pointing up and begins to point down will give the worst vertical dispersion of shots or the largest groups.
SUMMARY.... For the reader who doesn't want to wade through all the discussion here is a summary of what a tuner can do to correct for small variations in muzzle velocity from round to round. The Muzzle Projection Curve shows where the muzzle is pointing at a 100 yard target while the rifle is being fired. The most important aspect is the curve is where the muzzle is pointing at the time the bullet exits the muzzle.
Improving accuracy by compensating for small variations in muzzle velocity.
Smaller Groups Left of the Peak - UPWARD SLOPE:
Higher velocity shots exit early while pointing lower at the target but drop less in reaching the target.
Lower velocity shots exit later while pointing higher at the target but drop more in reaching the target.
Counteracting combination. Good.
Larger Groups Right of the Peak - DOWNWARD SLOPE:
Higher velocity shots exit early while pointing higher at the target and drop less in reaching the target.
Lower velocity shots exit later while pointing lower at the target and drop more in reaching the target.
Bad additive combination. Bad. This is currently being called "Negative Compensation".
The additional mass of a Muzzle Tuner slows down the muzzle movements and allows the bullet exit before the peak of the muzzle projection curve during the upward slope without resorting to high pressure loads.
If you understand this Muzzle Projection Curve and accept that getting your bullet to exit on the left side of the curve will give you smaller groups, then what are some ways to do this??
Some ways to get the muzzle exit time on the Left Side of the Peak
1. Add weight to the muzzle to slow down the muzzle movement
2. High pressure/high velocity load to make the muzzle exit time earlier
3. Faster burning powder to have the bullet gain velocity early and make the exit time earlier
4. Longer barrel to slow down the muzzle movement
I might add, to this list the following: bullet seating adjustments and crimping and neck tension adjustments, because what we are talking about is milli- seconds of milli-seconds of bullet exit time impact. So he already listed powder selection in no. 3, and in a sense charge weight variation in number 2. But, I would add bullet seating too.
The last thing I would add to his list is a barrel tuner which will in fact shift the barrel time of the bullet to a time when the muzzle is pointing slightly up. I will list how this works below.
Now do you see how internal ballistics is all related to harmonics, changes in muzzle velocity, and bullet exit time??
To Recap and looking again at the muzzle projection curve above:
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.
Now, some really interesting stuff if you want to explore how barrel tuners work. Go to:
ADDING A TUNER.... Adding a tuner to the muzzle of a rifle barrel does the following:
1. The additional mass reduces the amplitude of the vibrations.
2. Decreases the natural frequencies by decreasing the lower Mode's frequencies more than the higher Modes.
3. Increases the barrel's vertical end sag due to the extra weight. This would tend to make the vertical plane the preferred plane of vibration.
4. Moves the Mode 2 node closer to the muzzle.
WHAT A TUNER DOES.... It is possible to "Tune" a rifle barrel so that where it is pointing at bullet exit time will compensate for small variations of muzzle velocity. In the "tuned" condition the slower bullets are launched at a slightly higher angle than the faster bullets. The difference in launch angle can allow the slower bullets to hit the target at the same elevation as the faster bullets. That is the simple explanation.
FLIGHT PATH.... This chart shows the slower bullet actually travels a higher path than the faster bullet for them both to hit the same 50 yard zero. It is clear that the flexible barrel's muzzle must launch the two bullets of different velocity at slightly different elevations for there to be no vertical spread at the 50 yard target. With only two place accuracy on the drop values, from 42 yards to 50 yards the round off shows the drop to be the same. With more accuracy, this would not be the case.
WHAT A TUNER DOES.... A Tuner appears to compensates for variations in muzzle velocity. It slow down the movement of the muzzle so that with safe loadings, one can be on the left side of the MPC at bullet exit time. It will also reduce the high frequency jitter at the muzzle because if its inertia.
Now, if you got this far and you enjoyed it, you really must go here and explore all the different models and cases Varmintal has to offer.
https://varmintal.com/alite.htm
I was especially interested in the ladder tests of the 24 inch barrel with and without tuner.
Note all the analysis he presents for optimum barrel length on the site too further down on this same link below the 24 inch discussion.
Have fun and enjoy and maybe you may have more an appreciation why I believe barrel harmonics are related to the empirical results we see
when we run a Satterlee, Audette ladder, or OCW Method test in load development???? Maybe I'm not crazy after all???
Maybe its Al Harral that is crazy?
