FIRE EFFECTIVITY INDICATORS OF ZU-23 ANTI- AIRCRAFT TWIN BARRELED AUTOCANNON IN DIFFERENT CONDITIONS

The results of numerical simulation of detection ranges by personnel of ZU-23 antiaircraft twin barreled autocannon in different conditions of tactical employment and values of statistical probability of aerial target detection for average prepared personnel are presented in this article. Conditional probabilities of target destruction at one and n shots are obtained. Guidance to the target along the tracks of shells and firing by a platoon armed with ZU-23 is also considered. Values of slope distances to the outedge of engagement area under various conditions of tactical employment are found. Introduction. As an indicator of the firing efficiency of ZU-23 paired anti-aircraft mount, we use a conditional probability of target destruction at n shots n R [1-3]. Range of target detection and identification depends on background situation, area and target colour, meteorological visibility range (MVR), cut-off angles of fire position and presence of optical interferences. The range of target lock-on to the collimator of the anti-aircraft sight and the values of outedge of engagement area also depend on the same factors. Analysis of publications [1-4] has shown that massive clouds with fast changes of dark and light areas underestimate the range of targets detection with the naked 126  Tendenze attuali della moderna ricerca scientifica  Band 4 . eye. The firing limit is related to the direction to the sun not less than  15  [5, 6]. Although, the sun illumination from the opposite firing direction increases the range of targets detection d D and its identification. The target colour can be concealed against the background of the sky. Thus, the target of silver-aluminium colour against the background of the cloudless blue sky reduces d R to 50% relatively to the whitegray background [5, 6]. Complex meteorological conditions as rain, fog and application of aerosol or smokescreens used by the enemy are taken into account by the MVR indicator reduction. For the target Su-7B type at MVR is only 4 km d D with the naked eye is not more than 3.5 km. The common objective for ZU-23 is Mig-17 aircraft. When MVR is not less than 10 km, the common objective for d D ~ 6.8 km, and statistical probability of detection d Р is 0.5 [5, 6]. The quality of personnel combat performance of ZU-23 is estimated from "excellent" to "satisfactory" and determines the values of systematic components of shell firing errors in the image plane of fire. The cut-off angles of fire position do not allow the personnel of AAG (anti-aircraft gun) to fire targets in a timely manner. Pulsed and continuous optical interference, power, can blind the personnel for a while, preventing firing. Signal missiles (shells, mines), routes of anti-aircraft guns, also complicate the process of aerial target detection (firing) [3-6]. The objective of this article is numerical simulation of values of ranges and probabilities of different aerial targets detection, as well as values of conditional probabilities of their destruction and, at the same time, implemented slope distances of the outedge of anti-aircraft mount engagement area. Main material. Determination of ranges and probabilities of various aerial targets detection. Firing from ZU-23 at common objective and unmanned aerial vehicles (UAVs) is being considered. The “Forpost” and “Tahion” were chosen as UAV types. The first relates to the large-size UAV, while the second one relates to the small-size UAV. To estimate the anti-aircraft mount firing efficiency, we use the approximate highest max S and the least min S target area of the image plane of fire. It was assumed for “Forpost” 2 F max m . S 7 6  , 2 F min m . S 58 0  and for “Tahion” – 2 Т max m . S 32 0  , 2 Т min m . S 04 0  . The least і min S is expected when firing at low altitudes (elevation angle  5   ) and the highest і max S –  45   . The values of UAV flight speed are averaged to 40 m/s. For common objective it is 2 о с max m . S 2 30  and . m . S 2 о с min 1 9  The target detection ranges   co s p m c со K , , , , , S D     at probability of correct detection d Р 0.5, depending on various factors we find from the approximate expression [7]:   , K S S R K , , , , , S D co s p m c co min d co s p m c co          (1) where со D – CO target detection range (~ 8.5 km [5-7]);   m . S , S 2 о с min 1 9 target image area, which is being fired and the smallest area of CO in the image plane of fire, respectively; m c ,  – factors that consider the target colour ( c  varies between 5. Juni, 2020  Stuttgart, Deutschland  127 . 0.5 and 1) and MVR ( 1 48 0 ... . m   ); p  – figure of merit of AAG personnel combat performance (”excellent” – 0.9; “good” – 0.8; “satisfactorily” – 0.7; “master” – 1.1); s  – considering factor of solar illumination of a target (in the range from 1.3 to 1.5) [57]; co K – considering factor of cut-off angles of the AAG fire position (varies within the range from 0 to 1, during simulation 1 was accepted). Average ranges of targets detection by the naked eye and its lock-on to collimator of AAG target control, at numerical simulation, were accepted for AAG average prepared personnel by 8.5 km [5, 6]. The results of calculations for the expression (1) are given in Fig. 1. The first line   S Dco1 (indicated by a continuous line) reflects a change in target detection range with probability of 0.5 when S varies within 2 m 2 10 to 2 m 10 at AAG average prepared personnel ( 8 0. p   ). The second line (dots   c 2 со D  ) and the third line (dashes   m 3 со D  ) give values of detection range of large-dimensional UAV “Forpost” type F min S at influence of target color and MVR, respectively. The significant dependence і со D on target parameters m c , , S   can be noticed. The fourth line (dots and dashes   р 4 со D  ) is calculated with account of AAG personnel combat performance. The fifth line (··○··○··○··),   s со D  5 ) is received when the target is highlighted by the sun. Taking into account the flight speed of different targets, the AAG personnel cannot always fire at the outedge of engagement area. At the same time, firing remains on a pursuit course. According to the studies, if there is only an alert (no target designation), the probability of CO passing at low altitudes is approximately 0.4, and at altitudes of 2.5...3 km is 0.8, that is the statistical probability of CO detection is within the range of only from 0.6 to 0.2, respectively [5]. On the basis of polygon tests [5, 6] the values of statistical probabilities of different targets detection by ZU-23 personnel, depending on the range to them, are found by approximation [7]:

. eye. The firing limit is related to the direction to the sun not less than  15  [5,6]. Although, the sun illumination from the opposite firing direction increases the range of targets detection d D and its identification. The target colour can be concealed against the background of the sky. Thus, the target of silver-aluminium colour against the background of the cloudless blue sky reduces d R to 50% relatively to the whitegray background [5,6]. Complex meteorological conditions as rain, fog and application of aerosol or smokescreens used by the enemy are taken into account by the MVR indicator reduction. For the target Su-7B type at MVR is only 4 km d D with the naked eye is not more than 3.5 km. The common objective for ZU-23 is Mig-17 aircraft. When MVR is not less than 10 km, the common objective for d D ~ 6.8 km, and statistical probability of detection d Р is 0.5 [5,6].
The quality of personnel combat performance of ZU-23 is estimated from "excellent" to "satisfactory" and determines the values of systematic components of shell firing errors in the image plane of fire. The cut-off angles of fire position do not allow the personnel of AAG (anti-aircraft gun) to fire targets in a timely manner. Pulsed and continuous optical interference, power, can blind the personnel for a while, preventing firing. Signal missiles (shells, mines), routes of anti-aircraft guns, also complicate the process of aerial target detection (firing) [3][4][5][6].
The objective of this article is numerical simulation of values of ranges and probabilities of different aerial targets detection, as well as values of conditional probabilities of their destruction and, at the same time, implemented slope distances of the outedge of anti-aircraft mount engagement area.
Main material. Determination of ranges and probabilities of various aerial targets detection. Firing from ZU-23 at common objective and unmanned aerial vehicles (UAVs) is being considered. The "Forpost" and "Tahion" were chosen as UAV types. The first relates to the large-size UAV, while the second one relates to the small-size UAV.
To estimate the anti-aircraft mount firing efficiency, we use the approximate highest max S and the least min S target area of the image plane of fire. It was assumed for "Forpost" performance ("excellent" -0.9; "good" -0.8; "satisfactorily" -0.7; "master" -1.1); s  considering factor of solar illumination of a target (in the range from 1.3 to 1.5) [5][6][7]; co Kconsidering factor of cut-off angles of the AAG fire position (varies within the range from 0 to 1, during simulation 1 was accepted).
Average ranges of targets detection by the naked eye and its lock-on to collimator of AAG target control, at numerical simulation, were accepted for AAG average prepared personnel by 8.5 km [5,6].
The results of calculations for the expression (1) are given in Fig. 1. According to the studies, if there is only an alert (no target designation), the probability of CO passing at low altitudes is approximately 0.4, and at altitudes of 2.5…3 km is 0.8, that is the statistical probability of CO detection is within the range of only from 0.6 to 0.2, respectively [5].
On the basis of polygon tests [5,6] the values of statistical probabilities of different targets detection by ZU-23 personnel, depending on the range to them, are found by approximation [7]: where  D target range, which varies from 100 m to 10 4 m.
The results of calculation by expression (2)   Analysis of the magnitude of firing errors associated with the initial projectile velocity, air density, projectile weight and wind shown that projectile velocity and air density had the greatest miss impact. On the basis of the conducted numerical simulation, the systematic components Probability of target engagement    G at target hitting  projectiles is equal During firing the battlefield fighter (BFF)  is within the range from 2 to 6 and for medium bomber is not less than 15 shells [8,10] 1   ). The same, but when direct projectiles along the tracks gave the third line (dashes) and the fourth line (dots and dashes). We note an increase in firing efficiency during the guidance of the AAG along the projectile tracks.
We find conditional probabilities of targets destruction by a platoon armed with four 23-mm AAGs і nв R from the expression [3,8]: