Gun dynamics
Gun dynamics describes the physical causes of barrel and shot vibration, and the effect they may have on accuracy and consistency.
It is employed to predict firearm performance, such as recoil, using theoretical methods and mathematical modelling techniques.
In the 1970s, the United States Army Symposium on Gun Dynamics[1][2][3][4][5] defined it as the study of internal ballistics that are unrelated to propellants and combustion.
In particular, it is concerned with the interactive dynamics between the projectile, barrel, and mounting, and the effect that they have on the accuracy and consistency of the gun.
In practice none of these conditions can be met, and inevitably, some transverse vibration is introduced to the barrel and the shot.
This may be complicated even more when a complete weapon system is considered, and the MPI is found to vary for (as an example) different barrels of the same type.
[citation needed] Figures 1 to 3 demonstrate the results for guns with good and bad accuracy and consistency.
[citation needed] When considering the chance of hitting a target with the first round fired, both accuracy and consistency must be taken into account.
Figure 4 categorizes the sources of error for a tank gun which may affect its ability to hit the target.
The gravitational and aerodynamic effects including drag can be calculated and the initial pointing angle of the muzzle adjusted accordingly.
It is caused by the fact that the trajectory of the shot as it leaves the gun may not be the same as the initial pointing direction of the muzzle.
In this case, it is the difference between the initial pointing direction of the muzzle and the final trajectory of the center of gravity of the shot as it leaves the barrel.
[citation needed] Most guns have the center of gravity of the total recoiling mass offset from the center-line of the bore.
[citation needed] As an example, in most tank guns the center of gravity of the breech is normally below the barrel axis.
Figure 6 shows the typical response of a tank gun barrel for an off-axis breech.
Therefore, the transverse motion caused by the off-axis muzzle reference sight occurs before the wave from the breech gets there.
The fire control system would therefore have to modify the azimuth as well as the elevation for different charges and shot types.
Friction in bearings at start of recoil may be significant, and repeat fire weapons can be affected by shot ejection or a muzzle brake.
In practice the shot can move relative to the barrel and can bounce and pitch or yaw within the bore.
As an example, consider a shot which has its center of mass slightly displaced from the geometrically central axis.
In this case if the shot is spun by the rifling about its geometric axis, a centrifugal force will be generated which will affect the barrel.
These vary considerably depending on barrel straightness, shot band stiffness, pressure, time curve, and other factors.
For example, the prediction of shot band forces, or the bending stresses in long rod penetrators, gives added confidence to the strength of design process.
Other components, such as the mounting or the buffers, will be able to interact with the barrel, and any mathematical model should take this into account.
As with any dynamic model it is easiest to treat each component separately, and derive equations of motion which are general enough to allow changes in the system to be made easily.
The following list shows many of the parameters which are normally included in a typical simulation: The barrel can normally be considered a flexible tube, which for dynamic analysis is a multi-degree of freedom system.
In this case, the program runtime for a single round from a 120 mm tank gun can exceed many hours.
In the case of a simple single plane simulation (2 dimensional) the same axes can be used directly in the shot analysis.
The stiffness need not necessarily be linear, as long as it is assumed that the torque is some function of the relative displacements between the shot and the barrel.
In a two dimensional simulation, purely in the OXY plane, the definition of shot pitch would be fairly obvious.
