Dispersion and probability

 The dispersion. However perfectly a gun may be laying, two successive rounds will never fall in the same place. This means that even with a correct aim we can never be certain of hitting the target, there is only the probability to do it. In fact if a number of rounds of ammunition of the same calibre are fired on the same conditions (position, charge, aim settings), the trajectories obtained will be different, forming a bent cone, called “cone of dispersion”. This phenomenon is called dispersion and, irrespective of human and constant error, is caused by inherent factors : muzzle velocity, angle of departure and air resistance. The distribution of bursts is roughly elliptical in relation to the line of fire. Firing a great number of rounds from gun at a given mark, we obtain the vertical pattern of the round that had hit the target. Observing their position, we find that they are not uniformly distributed over the ground, but lie more thickly towards the centre of the space. This point is called “mean point of impact”. Starting from this point the thickness of the rounds decreases gradually until only isolated rounds can be found. The greater is the dispersion the less is the probability to hit the target. Drawing at the same distance from the main point of impact two horizontal lines ef and hg containing half of the rounds, we obtain a strip, whose width is called “mean vertical dispersion”. Similarly drawing at the same distance from the main point of impact two vertical lines im and kl containing half of the rounds, we obtain another strip, whose width is called “mean longitudinal dispersion”. The rectangle abcd contains all the rounds fired; 50% of the rounds are in the strip efgh, and the remaining 50% are above and below that strip, 25% in each of the strips abef and hgdc. The same happens breadthways. The area nopq, although is only 1/16 of the total rectangle, contains 25% of the rounds. The calculus of probabilities. The artillery doctrine of late 1800 assigned great importance to the determination of the chances to hit the target. The theory of probability demonstrated that the cone of dispersion, seemingly irregular, was in fact subject to definite laws, provided that the number of the rounds fired was great enough. Every ratio between the width of a strip and the mean vertical dispersion (probability factor), corresponded to a certain number of rounds out of 100. With the aid of the table of probability factors, it was easy to find the number of rounds required to hit a target having a certain height, assuming that the point of impact was in the middle of the target. It was enough to find the probability factor and look for the corresponding number of rounds. For instance, firing with a 87mm field gun at 1500 m, how many rounds were required to hit an infantry company deployed in line? Assuming that the height of the target was 1.80 m and the mean vertical dispersion was 1.4 m, the probability factor was 1.8 : 1.4 = 1.29, that on the table corresponded to 65.5% of the rounds. The probability factor calculated theoretically with the table and the size of the target was called “change of hitting the target”, whereas the “actual change of hitting the target” was the factor esteemed in the field, when many other factors might intervene (the mean point of impact was not in the middle of the target, the level of the gun wheels was different, the dispersion was greater).

 Table of probability factors % factor % factor % factor % factor 1 2 3 4 5 0.02 0.04 0.06 0.07 0.09 26 27 28 29 30 0.49 0.51 0.53 0.55 0.57 51 52 53 54 55 1.02 1.04 1.07 1.09 1.12 76 77 78 79 80 1.74 1.78 1.82 1.86 1.90 6 7 8 9 0 0.11 0.13 0.15 0.17 0.18 31 32 33 34 35 0.59 0.61 0.63 0.65 0.67 56 57 58 59 60 1.14 1.17 1.19 1.22 1.25 81 82 83 84 85 1.94 1.98 2.03 2.08 2.13 11 12 13 14 15 0.20 0.22 0.24 0.26 0.28 31 32 33 34 35 0.70 0.72 0.74 0.76 0.78 61 62 63 64 65 1.27 1.30 1.33 1.36 1.39 86 87 88 89 90 2.18 2.24 2.30 2.37 2.44 16 17 18 19 20 0.30 0.32 0.34 0.36 0.38 36 37 38 39 40 0.80 0.82 0.84 0.86 0.89 66 67 68 69 70 1.42 1.45 1.48 1.51 1.54 91 92 93 94 95 2.52 2.60 2.69 2.78 2.91 31 32 33 34 35 0.40 0.41 0.43 0.45 0.47 41 42 43 44 45 0.91 0.93 0.95 0.98 1.00 71 72 73 74 75 1.57 1.60 1.64 1.67 1.71 96 97 98 99 3.04 3.22 3.45 3.82 Source : ROHNE : Le tir de l’artillerie de campagne… p. 343.