Dispersion (ballistics)

The spread is the deviation of a series of hits from an averaged target point. The scatter is a quantity of external ballistics .

The trajectories of fired projectiles never follow exactly the same course, so that it is practically impossible to hit exactly the same point with two or more shots. This hit deviation is the spread. In addition to the errors when aiming at the target (shooter error), there is a technical scatter caused by internal and external ballistic disorders such as manufacturing-related tolerances of weapons and ammunition, temperature fluctuations, soiling and wear. The dispersion of a weapon is an important quality characteristic.

There are exceptions for shotgun shots , for submachine guns , which are used to fire sheaves , and for certain artillery operations , where it is desirable to distribute the hits over a certain area. In the case of modern guns with a low basic dispersion, the fire control computer can produce artificial dispersion by continuously changing the directional data. The aim is to cover the entire area with hits for area targets.

causes

As soon as it is fired , until the projectile leaves the barrel, numerous internal ballistic parameters influence the dispersion that can be achieved with a weapon. These are, for example, barrel vibrations and technical features of the weapon and ammunition. The ignition and the burning of the propellant charge never take place in exactly the same way and the projectile is always pressed into the rifle with slight positional deviations and driven through the barrel.

The shape and mass of the projectile differ slightly from each other in each cartridge and the mass and position of the propellant charge is subject to slight fluctuations. In the case of a series of shots, the heating of the weapon has an effect on the hit location, which can also lead to a temporary slight thermal deflection of the barrel.

All of this means that with each shot the bullet leaves the barrel with a slightly different muzzle velocity, position, direction and rotation.

After firing, external ballistics parameters act on the projectile and influence its flight path. In the case of bullet trajectories with high speed , these influences remain small; with increasing firing range or decreasing speed, these forces become decisive. When firing at great distances, wind has the greatest influence on dispersion.

Scattering circle

Center of scattering circles, on the left an acute-angled triangle, on the right an obtuse-angled triangle

The scattering circle is the circle around the outermost hits in a series of shots. If the connecting lines of the three outer hits form an acute or right-angled triangle, the perimeter of this triangle is the scattered circle and the perpendiculars along the sides of the triangle meet in the center of the scattered circle . If the connecting lines form an obtuse triangle, the straight line between the two outer hits forms the diameter of the scattered circle. The center of the straight line is the center of the scattering circle.

Medium meeting point

Finding the mean point of impact by averaging the coordinates of the hits

graphical determination of the middle point of impact (red in each case) for shot patterns with two to five hits

The middle meeting point can be understood as the common center of gravity of all floors that form the scattering circle. In a simplified way, the storeys are viewed as points with mass.

The mean meeting point can be determined from the coordinates of the hits. The hits are mapped to any dimensioned coordinate system. The x-values of the hits are summed up, as are the y-values. The totals are divided by the number of shots . The result is the coordinates of the central meeting point. ${\ displaystyle n}$

The middle meeting point can also be determined by drawing. For example, if there are three hits, a straight line is drawn between the first and the second hit. The straight line is divided into two equal parts and a straight line is drawn from the division to the third hit. This straight line is divided into three equal parts. The point of the first division is the middle meeting point. If there are more hits, each additional connection line is divided into one more part. The first dividing point of the last connecting line is the middle meeting point.

Mean square deviation

The diameter of the scattering circle is determined by the outermost hits. This has the disadvantage that, regardless of the rest of the shot, a single hit far away from the other hits increases the scattering circle, so that no conclusive statements about the actual statistical hit performance are possible based on the scattering circle alone.

In order to be able to make such statements, the mean square standard deviation must be determined. To do this, the distances between the hits and the middle point of the meeting are required. From the squares of the distances and the number of hits , the mean square standard deviation is calculated with. ${\ displaystyle l_ {m}}$ ${\ displaystyle l_ {1}, l_ {2}, ...}$ ${\ displaystyle n}$
${\ displaystyle l_ {m} = {\ sqrt {\ frac {\ sum l ^ {2}} {n-1}}}}$

If, for example, with four hits, the distances to the central point of impact are 35.3 mm, 9.6 mm, 17.6 mm and 20.7 mm ( ), then : ${\ displaystyle l_ {1}, l_ {2}, l_ {3}, l_ {4}}$ ${\ displaystyle l_ {m}}$
${\ displaystyle l_ {m} = {\ sqrt {\ frac {l_ {1} ^ {2} + l_ {2} ^ {2} + l_ {3} ^ {2} + l_ {4} ^ {2} } {n-1}}}}$

${\ displaystyle l_ {m} = {\ sqrt {\ frac {35 {,} 3 ^ {2} +9 {,} 6 ^ {2} +17 {,} 6 ^ {2} +20 {,} 7 ^ {2}} {4-1}}}}$

${\ displaystyle l_ {m} = {\ sqrt {\ frac {2076 {,} 5} {3}}}}$

${\ displaystyle l_ {m} = 26 {,} 31}$

The mean square deviation in this case would be 26.31 mm.

literature

Willi Barthold, Jagdwaffenkunde, VEB Verlag Technik Berlin 6th edition 1984
Scharnhorst, GJD, on the effect of the fire rifle, Nauck 1813 , empirical study of field guns, mortars and infantry rifles