jason.jardine72
New member
The pressure pulse from the gasses in the chamber cause a traveling wave of stress that bounces back and forth along the barrel between receiver and muzzle, slightly changing the bore diameter in the process. Minimum dispersion of the shots will result when the rate of change of the bore diameter is at a minimum, and this dispersion will present the least sensitivity to load variations (charge, seating depth).
It is the position of this wave and its effect on the muzzle at the point of bullet exit that is the cause of the majority of the dispersion around the mean POI.
Stress Waves
Treat the barrel as a “conductor” of sound or applied stress, and imagine for a moment that it is infinitely long. If you bang on your section of the barrel with a hammer, it will generate an acoustic or stress wave in the steel, which will travel in both directions away from the hammer impact point at the speed of sound in the barrel. The stress wave is a wave of force on the steel, some of which is in the radial (in and out from the bore across the direction of travel) direction, called a transverse stress component, and some of which is in the direction of travel, called a longitudinal stress component. An acoustic wave in air is primarily longitudinal, where the air compresses and expands along the direction of travel. In a solid, such as steel, both components can exist at the same time. In our infinite barrel, the wave travels on and on until the mechanical losses in the steel dissipate the stress energy as heat.
Reflections
However, we do not shoot infinitely long barrels, so what happens to the stress wave in a real rifle barrel? Just like in the TV tower guy wire, if a stress wave reaches a mechanical discontinuity in the object it is traveling in, such as the muzzle end of the barrel, or the solidly bedded receiver end of the barrel, it will reflect back in the opposite direction. In steel, the speed of sound is very close to 0.227 inches per microsecond, or about 18916 FPS. A wave will travel from the receiver to the muzzle in the barrel in about 0.12 mS. It can make around 4 or 5 round trips before the bullet leaves. Note that it does not matter how heavy the barrel is, or the profile, as the wave travels at almost exactly the same speed in all cases.
Stress Causes Strain or Distortion of the Muzzle – Explaining Observation #2
What does this stress wave do? Remember that stress is the amount of force or pressure applied to a material, which usually results in the material moving, bending, or displacing. This is called strain. So, the pressure stress from the gasses in the chamber causes a resulting strain in the barrel. Because the stress is applied very rapidly, the some of the stress launches down the barrel as a wave, causing a proportional strain to the barrel as it passes. This strain is initially a slight enlargement of the bore, followed by a slight constriction, eventually dropping off to no change in the bore diameter at all.
As this pulse travels to and fro, it passes by itself, and in the process constructively and destructively adds to itself, all in some predictable way. The shape of the pulse is driven by the pressure/time profile from the propellant burn, and the mechanical properties of the barrel. The theory nicely provides an explanation why very small changes in load parameters could result in large changes in dispersion. If the muzzle diameter is changing very rapidly at a particular time after shot initiation, and if the bullet exits at this time, then very small changes in the load will result in small changes in the exit time, but large changes in the exit direction since the muzzle diameter is always different. Think of this as a dynamic variation of the muzzle crown shape. It is well known that the crown is perhaps the most critical part of the barrel as regards accuracy. So, this theory or model can explain the sensitivity to the load, and explain observation #2 above.
Model and Simulation
Nice theory, but where is the proof? To prove a theory, you have to first make a model that can (hopefully) predict the behavior of the real system, and then use that model to predict the outcome of some controlled experiments. If the experimental data fits the model data, then you can at least say that the test did not disprove the theory
It is the position of this wave and its effect on the muzzle at the point of bullet exit that is the cause of the majority of the dispersion around the mean POI.
Stress Waves
Treat the barrel as a “conductor” of sound or applied stress, and imagine for a moment that it is infinitely long. If you bang on your section of the barrel with a hammer, it will generate an acoustic or stress wave in the steel, which will travel in both directions away from the hammer impact point at the speed of sound in the barrel. The stress wave is a wave of force on the steel, some of which is in the radial (in and out from the bore across the direction of travel) direction, called a transverse stress component, and some of which is in the direction of travel, called a longitudinal stress component. An acoustic wave in air is primarily longitudinal, where the air compresses and expands along the direction of travel. In a solid, such as steel, both components can exist at the same time. In our infinite barrel, the wave travels on and on until the mechanical losses in the steel dissipate the stress energy as heat.
Reflections
However, we do not shoot infinitely long barrels, so what happens to the stress wave in a real rifle barrel? Just like in the TV tower guy wire, if a stress wave reaches a mechanical discontinuity in the object it is traveling in, such as the muzzle end of the barrel, or the solidly bedded receiver end of the barrel, it will reflect back in the opposite direction. In steel, the speed of sound is very close to 0.227 inches per microsecond, or about 18916 FPS. A wave will travel from the receiver to the muzzle in the barrel in about 0.12 mS. It can make around 4 or 5 round trips before the bullet leaves. Note that it does not matter how heavy the barrel is, or the profile, as the wave travels at almost exactly the same speed in all cases.
Stress Causes Strain or Distortion of the Muzzle – Explaining Observation #2
What does this stress wave do? Remember that stress is the amount of force or pressure applied to a material, which usually results in the material moving, bending, or displacing. This is called strain. So, the pressure stress from the gasses in the chamber causes a resulting strain in the barrel. Because the stress is applied very rapidly, the some of the stress launches down the barrel as a wave, causing a proportional strain to the barrel as it passes. This strain is initially a slight enlargement of the bore, followed by a slight constriction, eventually dropping off to no change in the bore diameter at all.
As this pulse travels to and fro, it passes by itself, and in the process constructively and destructively adds to itself, all in some predictable way. The shape of the pulse is driven by the pressure/time profile from the propellant burn, and the mechanical properties of the barrel. The theory nicely provides an explanation why very small changes in load parameters could result in large changes in dispersion. If the muzzle diameter is changing very rapidly at a particular time after shot initiation, and if the bullet exits at this time, then very small changes in the load will result in small changes in the exit time, but large changes in the exit direction since the muzzle diameter is always different. Think of this as a dynamic variation of the muzzle crown shape. It is well known that the crown is perhaps the most critical part of the barrel as regards accuracy. So, this theory or model can explain the sensitivity to the load, and explain observation #2 above.
Model and Simulation
Nice theory, but where is the proof? To prove a theory, you have to first make a model that can (hopefully) predict the behavior of the real system, and then use that model to predict the outcome of some controlled experiments. If the experimental data fits the model data, then you can at least say that the test did not disprove the theory