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 DynamicsT E Simkins, Parametric Resonance in Gun Tubes. First Conference on Dynamics of Precision Gun Weapons. R-TR-77-008, US Army Armament Research and Development Command, Dover, New Jersey, January 1977.T E Simkins, Transverse Response of Gun Tubes to Curvature Induced Loads. Second US Army Symposium on Gun Dynamics, 19–22 September 1978.B A Taylor and P G Thomasson, A Consistent R and D Assessment Technique for the Modelling of Gun System Dynamics. Third US Army Symposium on Gun Dynamics, 11–14 May 1982.T. F. Erline, M. D. Kregel. Modelling Gun Dynamics with Dominant Loads. 5th. US Army Symposium on Gun Dynamics, Rensselaerville, NY. 23–25 September 1987.M. T. Soifer, R. S. Becker. DYNACODE-G/P and its Application to the 120mm Tank Gun. 5th. US Army Symposium on Gun Dynamics, Rensselaerville, NY. 23–25 September 1987. 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.
Gun designers realized that there may be an interaction between the barrel and the shot that was likely to affect accuracy and consistency. It is only since the 1970s that the ability to compute the motion has become practical. If a perfectly straight barrel was fired in zero gravity, the barrel recoiled along its central axis with no off axis forces, the shot was perfectly balanced and a perfect fit within the barrel, and all the forces were symmetrical, then the shot should exit the barrel in the direction in which the barrel was initially pointing. In practice none of these conditions can be met, and inevitably, some transverse vibration is introduced to the barrel and the shot. This results in shot jump, where the trajectory does not correspond with the initial direction of the muzzle.
Accuracy and consistency The point of aim A is the specific point the muzzle is pointing at when a gun is aimed at a flat target perpendicular to the muzzle face. When the gun is fired, the shot hits point P on the target. The distance between point A and P is sometimes referred to as an indication of the precision of the weapon. Subsequent rounds are unlikely to hit point P, and a pattern of hits will emerge after many rounds. The average of the points of impact of all the individual rounds is called the Mean Point of Impact (MPI). The dispersion around the MPI measures consistency and is often expressed as the standard deviation.
The situation is complicated because firing 10 rounds may result in an MPI that differs from the MPI obtained from another 10 rounds fired at a different time. The distribution of the MPI between occasions provides a measure of the accuracy. 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.
Figures 1 to 3 demonstrate the results for guns with good and bad accuracy and consistency.
In Figure 1, two guns have been fired, each with a set of 10 shots. The position of the shots on the target from gun A are shown as asterisks (*), and from gun B as Xs. The spread of shots from gun A is much smaller than those for gun B. Also, the MPI of A is off the target area, whereas that of B is on the target area. Figure 2 shows the MPIs of the two guns for five serials fired from each gun on different occasions. All the MPIs of gun B are on the target area, whereas those of gun A are well spread. The conclusion in this case is that gun A has good consistency, but poor accuracy. Gun B has poor consistency, but good accuracy. A more realistic possibility is shown in Figure 3. In this case, assuming that each series had the same consistency as those shown in Figure 1, gun A shows good consistency and accuracy, and gun B is poor on both counts. The fact that the MPIs of gun A are not on the target can be corrected for in the sighting. However, if this was a tank gun and the MPIs were very different for different tanks, then the users of the tanks may find this unacceptable. This is because finding a correction value for each tank by 'shooting in' can be very costly with modern ammunition.
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 sources of error are broken down as follows:
The gunner will affect the consistency, as his ability to perform from one round to the next will change. The sight and weapon harmonization will affect the occasion-to-occasion MPI. This may be because of simple maintenance, although more complex reasons have been shown to occur in certain systems. Environmental conditions will both affect consistency (e.g. variable wind conditions down range), or accuracy (e.g. change in temperature and hence air density which affects the external trajectory). In some cases, these are accountable and could possibly be corrected in the fire control system. The ammunition, both the charge and the shot, will suffer from manufacturing tolerances, which have an effect on consistency. The weapon-dependent parameters, such as the straightness of the barrel or the clearance in the bearings, will have an effect on both consistency and accuracy. As an example, when the barrel temperature rises and the bearing clearances change, the jump of the shot will change. This will affect the consistency. Similarly, the straightness of the barrel will affect the final trajectory and hence the accuracy, but it may also affect the shot pitch velocity at launch, which in turn may affect the consistency. The fire control system should represent a small part of the error budget.
The effects of external ballistics are ignored in this context, and only effects that occur while the shot is in the barrel are considered. Hence, the interest will be in the weapon dependent part of the error budget, together with the part of the ammunition segment which affects the dynamics of the shot in the bore. Even so, some of the launch parameters may still contribute to what occurs after the shot has left the barrel. In particular, the yaw angle and angular velocity affect stabilization and aerodynamics following launch.Textbook of Ballistics and Gunnery, London, Her Majesty’s Stationery Office
Barrel and shot jump The shot will not necessarily hit the point of aim. In practice, a gunner will aim a gun with reference to the trajectory of the shot. The gravitational and aerodynamic effects including drag can be calculated and the initial pointing angle of the muzzle adjusted accordingly. A further adjustment then must be made for the difference between the calculated point of impact and the actual anticipated point of impact. This difference will normally be a known value obtained from initial development of the gun, and is usually given the term 'gun jump'. 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. There may also be further external ballistic effects which may in themselves be a function of the launch parameters of the shot. The components of gun jump are shown in Figure 5.
When a gun is fired, the angle of the muzzle changes, and there is a transverse velocity component of the muzzle. If the shot followed the center-line of the bore exactly, then the difference in initial trajectory of the shot compared to the initial pointing angle of the muzzle would be equal to the change of muzzle angle plus its transverse velocity component divided by the shot velocity relative to the muzzle at exit. This may be referred to as barrel jump. In the case of a perfectly fitting non-spinning solid ball, this would compose all of the gun jump.
In practice, the shot is bouncing relative to the barrel. Adding this to barrel jump results in shot jump. 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.
After the shot leaves the muzzle, there will be aerodynamic effects which modify the trajectory. Adding these to shot jump results in total gun jump.E M Schmidt, "Analysis of Sources of Firing Error." 9th International Symposium on Ballistics, UK, 29 April to 1 May 1986.
Mechanisms producing shot jump Introduction When a gun is fired it recoils and various forces are introduced which cause the barrel and shot to move in a direction perpendicular to the axis of the barrel.S. E. Powell, P. G. H. Penny. The Theoretical Modelling of the Dynamics of Initially Non-straight Barrels using Finite Difference Techniques. 6th. US Army Symposium on Gun Dynamics, Rensselaerville, NY. 23–25 September 1987.D. N. Bulman. Simulation of Gun Dynamics to Improve Accuracy and Consistency. 15th International Symposium on Ballistics, Jerusalem, Israel. 21–24 May 1995T E Simkins, Resonance of Flexural Waves in Gun Tubes. 5th US Army Symposium on Gun Dynamics, 23–25 September 1987. The shot may also have angular displacements about axes perpendicular to its longitudinal axis. Shot pitch is defined as angular displacement about a horizontal axis perpendicular to the barrel axis. Shot yaw is defined as angular displacements about a vertical axis perpendicular to the barrel axis.
There is an interaction between the shot and the barrel such that each affects the motion of the other. Factors cause the barrel to vibrate independently of and due to the shot.
Off-axis masses
Most guns have the center of gravity of the total recoiling mass offset from the center-line of the bore. This is normally caused by specific components which are asymmetric.
As an example, in most tank guns the center of gravity of the breech is normally below the barrel axis. Therefore, when the barrel recoils the inertial force from the breech produces a moment on the rear end of the barrel. This causes a wave to travel down the barrel which quickly overtakes the shot and results in a deflection of the muzzle before shot exit. Figure 6 shows the typical response of a tank gun barrel for an off-axis breech. Each line represents the shape that the barrel takes up at 0.5 millisecond intervals. These curves were produced by a simulation of an actual system.
Another off axis component found on some tank guns is a muzzle reference sight (MRS). As the muzzle recoils, the moment produced by the inertial force on the muzzle reference sight causes the muzzle to move downwards. In this case, the barrel does not recoil as a solid mass. In practice the barrel lengthens, and a longitudinal wave travels up the barrel. The muzzle does not therefore move backwards at the same time as the breech and the time delay can be significant on the effect of the muzzle reference sight. However, the longitudinal wave travels faster than the bending wave along the barrel. Therefore, the transverse motion caused by the off-axis muzzle reference sight occurs before the wave from the breech gets there. Figure 7 shows a plot of muzzle motion caused by an off-axis breech, and a second curve with an added muzzle reference sight.
Any off-axis masses can affect the barrel motion. In the case of asymmetrical barrels, the fact that the center of mass of the barrel sections may not coincide with the principal bending axes is also significant.
Barrel curvature