The Science of Tuning: The Important Correlation between Muzzle Angle and Bullet Exit Time
Updated: Dec 2, 2022
In the competition world, having a tuned rifle is a prerequisite for making it into the winners circle. In the hunting world, a tuned rifle could be the difference between a quick kill or hours spent tracking.
Most shooters already know that a rifle “in tune” will shoot smaller groups than a rifle that is “out of tune.” But, what does it scientifically mean for a rifle to be in tune?
I am not educated enough to answer that question. However, I know someone who is. Dr. Keith Sharp is a retired engineering professor from the University of Louisville. Keith also happens to be an experienced Benchrest shooter. I asked Dr. Sharp if he would explain what it means to be in tune. When needed, I translated his reply.
Dr. Sharp 1: When a round is fired, the gas pressure from a combustion reaction propels the bullet down the barrel. The gas pressure also creates an equal and opposite force on the rifle, which causes it to move in all directions - vertical, horizontal, longitudinal and torsional. This motion which includes not only position, but also velocity, in all these directions, can change where the bullet hits the target relative to where you aimed.
Stanley: The forces that propel the bullet down the barrel also move the rifle in all directions. This motion of the rifle will influence where the bullet impacts.
Dr. Sharp 2: Because the bullet exits the barrel in a millisecond or so after the powder burn begins, oscillations and harmonic motion are irrelevant. The bullet is gone before such motion becomes recognizable.
Stanley: When discussing tuning, we do not need to worry about the barrel “whipping.”
Dr. Sharp 3: It is the initial, transient response while the bullet is still in the barrel that is important for tuning.
Stanley: The bullet is in the barrel for a very short amount of time. Yet how the rifle moves, while the bullet is traveling down the barrel, is important for the tune.
Dr. Sharp 4: The longitudinal and vertical motion of the barrel are typically the greatest. Longitudinal motion is the straight-back recoil that you can feel in your shoulder. It has little effect on bullet impact at the target, since it is “straight back.” It does reduce absolute bullet velocity, but so long as it is consistent, the effect is small.
Stanley: Motion of the barrel in the x dimension (back/forth) and y dimension (up/down) are the greatest. In terms of tuning, we do not need to concern ourselves with the x dimension because it is straight back and does very little to influence the bullet.
Experience Tip: Do not confuse this with follow-through. Follow-through is a very important piece of the accuracy puzzle, however this writing is concerned with tuning. As long as follow through is kept consistent, we can negate it's effect on tuning. For more information on this important topic, see Blog titled Follow-Through
Dr. Sharp 5: The vertical motion, in particular, the angle of the muzzle when the bullet exits, is the primary factor that we can try to control by tuning. A rifle that is in “tune” compensates for rounds with different muzzle velocities by increasing its muzzle angle as slower bullets exit the muzzle later.
Stanley: When we tune our rifle; we are trying to control the timing of the bullet leaving the muzzle in relation to the rise and fall of the muzzle angle. This correlation is critical to accuracy/precision. For example: A muzzle angle change of just 0.01 degrees can translate into 0.63” of vertical at 100 yards.
Dr. Sharp 6: The objective of tuning is to adjust the dynamic response of the whole rifle (not just the barrel – everything on the rifle and everything about its setup can influence the muzzle angle) so that bullets exit during a part of the muzzle angle history that has this optimal rate of increase, or something close to it.
Stanley: Most people understand that cartridge components (bullet, powder, primer, neck tension, and seating depth) affect tune. Many people also comprehend the importance of matching up the barrel’s twist rate with the proper bullet to have a chance of being in tune. Fewer people realize that tune is also affected by anything touching the rifle (action, scope, front/rear rests, shoulder/cheek pressure, etc). All of those variables can have an effect on the relationship between muzzle angle and exit timing of the bullet.
Experience Tip: Consistency is paramount when tuning a rifle. The ideal situation is when only one variable is changed at a time. This not only includes the cartridge components but also the set up and follow-through.
Experience Tip: For all the hunters out there, this is the major reason why the barrel should be free floated and should never be placed on the rest (tree limb for example). The stock’s forend should be placed on the rest, not the barrel.
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Dr. Sharp 7: Bullets may exit near the peak of the rise, at which point the muzzle angle changes very little for small changes in bullet exit time. This is bad. Here, slow bullets hit the target lower than fast bullets because they have more drop.
Stanley: When the muzzle is near the peak of the rise, the muzzle angle does not change very much compared to bullet exit times. This is not good for tuning because slower and faster bullets will leave the muzzle at roughly the same angle. Due to the slower bullets having more drop, they will impact lower on the target.
Dr. Sharp 8: Even worse is when bullets exit during the decrease in angle. Here, the slower bullets hit lower not only because they have more drop, but also because the muzzle is pointed lower.
Stanley: If a slower bullet exits after the peak of the rise (when the muzzle angle is on the way back down) it will hit lower on the target for two reasons: The slower bullet drops more and the muzzle is already pointed more downward compared to a faster bullet’s earlier exit time.
Dr. Sharp 9: It is only during the rise in angle that positive compensation occurs. Here, slower bullets exit later when the muzzle is pointed higher. If the rate of change of muzzle angle is perfect, then slow and fast bullets strike the target at exactly the same vertical position and the whole system can be said to be in perfect tune.
Stanley: A rifle that is “in tune” has the bullets leave as the muzzle angle is increasing. Here, faster bullets leave earlier, when there is less of an upward muzzle angle compared to the target. Slower bullets will leave later when there is slightly more of a muzzle angle. This will provide a greater muzzle angle to compensate for slower bullets increase in drop. Therefore, a slower bullet will impact in the same spot as the faster bullet. Or...to put it another way...Tuned rifles will shoot smaller groups.
I would like to thank Dr. Keith Sharp for taking the time to share this information. Through his efforts, this blog may help dispel some myths about tuning.
My junior high science teacher once said, “The more you know about something, the more you can do with it.” The more we learn about tuning a rifle, the higher we can place on the results list and the cleaner our shots will be on the game we pursue. Until next time, enjoy the experience.
Dr. Sharp also included the following information. If you are science-minded, then you will appreciate the knowledge Keith is willing to share.
It is straight-forward to calculate the necessary change in angle. Just try different angles in a ballistics program. Let’s say your muzzle velocity averages 3000 feet per second. Input a slower velocity, say 2990 feet per second, into the program and adjust the muzzle angle until the bullet strikes the target at the same height as the 3000 feet per second bullet. The necessary increase in angle must occur in the extra time that the slower bullet takes to exit the muzzle. The difference in angle divided by the difference in time defines the optimal rate of change of angle, in units of, for instance, degrees per second.
The muzzle angle of a typical benchrest rifle drops a little before a stronger rise and fall (see VarmintAl’s website for a plot of muzzle projection to the target (muzzle angle) for his simulations of Esten’s tuner). The tuner, the pressure curve of the powder, the compliance of the stock and the front rest position are all shown by VarmintAl to affect the muzzle angle curve.
The vertical velocity of the muzzle is also imparted to the bullet as it exits, but again, the change in this velocity has a small effect on downrange trajectory if it is consistent.
If the angular rate of change is positive but not perfect, vertical spread is still smaller than the uncompensated case. This can be called a partially tuned condition, which is better than no tune at all.