EXTERNAL BALLISTICS FOR THE BULLET RELEASED FROM AKM Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

MILITARY SCIENCES

ЗОВН1ШНЯ БАЛ1СТИКА КУЛ1 ВИПУЩЕНО1 З АКМ

Величко Л.Д.

К.т.н., доцент, професор кафедри тженерно'1 механти (озброення та технки iнженерних вшськ)

НацюнальноЧ академИ сухопутних вшськ iменi гетьмана Петра Сагайдачного Звонко А.А.

К.т.н., доцент кафедриракетно-артилершського озброення НацюнальноЧ академИ сухопутних вшськ iменi гетьмана Петра Сагайдачного

Гузик Н.М.

К.ф.-м.н., доцент, доцент кафедри iнженерноi механк (озброення та технки iнженерних вшськ)

НащональноЧ академИ сухопутних вшськ iменi гетьмана Петра Сагайдачного Львiв, Украша

EXTERNAL BALLISTICS FOR THE BULLET RELEASED FROM AKM

Velychko L.,

Candidate of technical science, Associated Professor, Professor of the Department of Engineering Mechanics (Weapons and Equipment of Military Engineering Forces) Hetman Petro Sahaidachnyi National Army Academy

Zvonko A.,

Candidate of technical science, Associated Professor of the Department of Department of Rocket Artillery Armament Hetman Petro Sahaidachnyi National Army Academy

Huzyk N.,

Candidate of physical and mathematical science, Associated Professor, Professor of the Department of Engineering Mechanics (Weapons and Equipment of Military Engineering Forces) Hetman Petro Sahaidachnyi National Army Academy

Ukraine

АНОТАЦ1Я

У робот авторами представлена математична модель дослщження динамiки руху кул у повпр^ ви-пущено! з АКМ. Функцюнальна залежшсть сили лобового опору повгтря вщ детермшованих i недетермь нованих чиннишв описуеться окремо при руа кулi з надзвуковою та дозвуковою швидкостями. Для И ви-значення розв'язуеться обернена задача динамiки з використанням результапв експериментальних досль джень. Знаючи цю залежшсть дослщжуеться вплив температур заряду патрона i повгтря, атмосферного тиску, змши маси кулi та И початково! швидкостi на шнематичш параметри руху кулi. Здшснено порiв-няння теоретичних величин поправок стршьби, внаслвдок нестандартних умов, зi значениями поправок приведених в таблицях стрiльб.

ABSTRACT

The authors present a mathematical model for the study of the dynamics of the bullet's motion in the air released from the AKM. The functional dependence of the magnitude of the frontal air resistance force on deterministic and non-deterministic factors is determined separately for the bullet movement with supersonic and subsonic velocities. For this aim, the inverse problem of the dynamics is solved using the results of experimental studies. Knowing this dependence, the effect of the temperatures of the charge of the cartridge and air, the atmospheric pressure, the change in the mass of the bullet and its initial velocity on the kinematic parameters of the bullet's motion is investigated. The theoretical values of firing corrections due to non-standard conditions are compared with the values of the corrections given in the firing tables.

Ключовi слова: динашка руху кул^ сила лобового опору повгтря, автомат АКМ.

Keywords: dynamics of the bullet's movement, frontal air resistance force, automatic machine AKM.

The statement of the problem. The value of the kinematic parameters of the bullet movement in space depends on the deterministic (form and mass of the bullet, density and temperature of air, atmospheric pressure, derivation), non-deterministic (muzzle velocity,

magnitude and direction of wind velocity) and other factors. During the bullet's movement, its weight, frontal air resistance force, lifting force, Magnus and Coriolis forces act on it. However, its weight and the

force of frontal air resistance have a determining influence on the dynamics of the bullet's motion. Determining the functional dependence of the frontal air resistance force on the basis of only theoretical justifications is problematic. Therefore, experimental studies were conducted that determined the discrete values of the frontal air resistance force. The values of the corrections, caused by non-standard shooting conditions, were obtained on the basis of linear approximation of the results of experimental tests. Consequently, firing recommendations based on discrete values of the frontal air resistance force and linear approximations of experimental test do not always satisfy the practice of using them. Therefore, there is a need in combination of experimental results and theoretical studies to determine the functional dependence of the frontal air resistance force. This allows to increase the accuracy of the values of corrections caused by non-standard shooting conditions, and will improve the accuracy of firing.

Analysis of recent research and publications. Fundamentals of theoretical studies of external ballistics of bullets and projectiles are presented, for example, in books [1-3]. In them and in the papers [4-7] the frontal air resistance force is described by the dependence

„ pV2 n d2 . R = ---i c,

V

v V y

projectile, c

V

V s y

is the drag coefficient.

Presentation of the main results. According to the results of experimental studies, the magnitude of the frontal air resistance force of the moving body is proportional to its speed to a certain power, and it is not necessarily the second. In addition, the magnitude of the frontal air resistance force depends essentially on whether the body's velocity is supersonic or subsonic. Therefore, the functional dependences of the values of the frontal air resistance force for the bullet's motion are determined separately for the first and second stages. It is suggested to describe them by the formula

R(t) = cx pasx (V(t))

|2+Y i

V(t) V

v y s y

. (1)

2 4

where R is the frontal air resistance force, V is the speed of the projectile, p denotes the density of

the air, Vs is the speed of sound in the air, d is the projectile's caliber, i denotes the form-factor of the

The form-factor of the projectile was determined based on the comparison of its parameters with some reference and the drag coefficient for this type of projectile was used. However, the use of this method gives some discrepancies with the practice of its application. The authors of this work pointed out that the dynamics of the movement of the bullet depends not only on the shape of the projectile, but also on the type of weapon from which the shot was fired.

In order to improve the accuracy of theoretical calculations and to avoid differences with the results of experimental studies, the authors begin to refuse the use of standard drag coefficient in favor of individual air resistance functions for specific types of projectiles, which are being developed [8].

The purpose of the article. Based only on analytical methods it is difficult to determine the functional dependence of the value of the frontal air resistance force from deterministic and non-deterministic factors. The article proposes a mathematical model of its determination using a combination of theoretical and experimental studies. Based on the established functional dependence, the magnitudes of the corrections caused by non-standard firing conditions were determined and compared with the table values.

We denote by Cx a coefficient, which takes into account the aerodynamics of the form of the bullet and the proportionality when it is wrapping by the air; pa

- the density of the air; Sx - the maximum cross-sectional; V (t ) - the velocity of the bullet at any given

time; Vs is the speed of sound in the air. The coefficients y. (i = 1,2) and (i = 1,2) have different values at supersonic (i = 1) and subsonic (i = 2) velocities.

The predominant influence on the dynamics of bullet's movement in the air has the weight of the bullet

P and the frontal air resistance force R . Based on the second law of the dynamics, we obtain the equation

ma = P + R, (2)

where m denotes the mass and a - the acceleration of the bullet.

o

Fig. 1. Scheme of bullet movement in the air

Choose the beginning of the coordinate system

Oxz at the point of departure of the bullet. We place

the axis Ox in the plane of the weapon, and the axis

Oz we direct vertically upwards.

Designing the equation (2) on the coordinate axis and taking into account (1) we obtain

mx-

■~CP aSxV

2+y

Vi

V(t)

v Vs y

cos d , (3)

z

m z = -mg - cxp asxV where g = 9,8lV 2

2+r,

V'

Vit!

v V y

sin 6

(4)

is the acceleration of the

free fall of the body, 6 denotes the angle of inclination of the vector of the velocity of the bullet to the horizon at any given time.

Taking into account the equalities

cos 6 = ^, Sin6 = ^, Vx(t) = x(t), V V

Vz (t) = z(t), V(t) = V(X(t))2 +(z(t))2, (5) the dependencies (3) and (4) will take the form

mx =

cx Pa sx x

2 , • 2 \0,5(l+/i

mz = -mg- -

V n

s

CxPa sx

■(x2 + z2 )

(6)

7

(x2 + z2 )

. (7)

V P

s

At the beginning of the bullet movement, its velocity is supersonic, so it is necessary to solve the system of differential equations (6) and (7) with i — 1. The initial conditions for this system have the view

x(0) — 0, x(0) — V cos0o, z(0) — 0 i

¿(0) — V) sin 90. (8)

We denote by V0 the initial velocity of the bullet

and by $0 - the angle of throwing.

During the experimental studies, there were obtained the numerical values: 9 0 - angle of throwing;

tfc - the duration of the bullet's flight; x(tk ) - coordinates of the zeroing point of the trajectory of the bullet; 9 - angle of incidence; V(t^ ) - final velocity of the bullet; H - maximum height of the trajectory, XH - horizontal distance to the top of the trajectory.

In this article, as a boundary conditions we use the dependencies of the speed of the bullet released with AKM from the full horizontal distance it flew. That is, a set of values was used

V0 , V100, V200, V300, V400, V„00 > Vs. (9) We denotes by V the speed of the bullet

when it flew n00 meters of full horizontal distance. As the boundary conditions you can use also the flight duration of the bullet when it flew a certain horizontal distance.

We determine the values Cx , Y\ and P using the method of sequential approximations. First, we set the arbitrary values Cx and and select such value

P that provide a slight discrepancy between the theoretical values of the velocity of the bullet and the set of values (9). In the case of a significant discrepancy between the theoretical and experimental values of velocities, other values Cx and were taken and then the value of the quantity P was selected again. After the implementation of the first two steps, the tendency of changing of the values Cx , Y\ and P becomes evident. Carrying out further similar actions we define values Cx , Yi and Pi which provides insignificant

discrepancy between theoretical and experimental values of velocities of a bullet.

Making the calculations we take into account the following values: the mass of the bullet m — 0,0079 kg, the initial velocity

V0 = 715 m/s , the sx =%■ 0,00395 2 m

cross-sectional

area

the air temperature

t = 150 C , atmospheric pressure p = 99991,5 Pa, air density pa = 1,20937 kg/

m~

. We determined

the following values Cx — 0,9, yx — -0,239 and

P — -0,005 using the sequential approximation

method. They provided a slight discrepancy between the theoretical and experimental results of the kinematic parameters of the bullet's motion during its flight at supersonic speed. The presence of minor differences is possible because the experimental values are obtained with some accuracy.

Table 1.

The value of the theoretical and experimental kinematic parameters of a bullet released from AKM at supersonic

x(tk ), m 60,deg 6c ,deg tk (s) H, m x^f, m V (tk ), m/s

100 00 03' 38" 0004' 0,1502 0,028 51,23 620,18

(0o 04') (0004') (0,15) (0,03) (51) (623)

200 00 08' 03" 0010' 0,3239 0,129 104,86 535,15

(0o 08') (0009') (0,32) (0,13) (105) (537)

300 00 13' 29" 0018' 0,5257 0,340 161,05 459,26

(0o 13') (0018') (0,52) (0,34) (162) (459)

400 00 20' 14" 0030' 0,7616 0,716 219,92 391,80

(0o 20') (0031') (0,76) (0,71) (221) (391)

2

In the Table 1 in parentheses there are indicated the values of the parameters, which are experimentally determined and are given in [10].

After moments of time

tk = 0,9957

0,9964 C, the values of which de-

pends on the angles of throwing 99 , the theoretical velocity of the bullet becomes subsonic. Therefore, the functional dependence of the value of the air resistance force is determined by the formula (1), but with parameters y2 and p2. We choose their meanings as above

using the experimental results

Va - V(«+l)00, V(«+2)00, V(«+3)00,

V

(«+4)00

(10)

The initial conditions for the system of differential equations (6) and (7), at the stage of the flight at the subsonic velocity, are the values of the kinematic parameters of the bullet at a time when its velocity becomes equal to the speed of sound in the air. This provides a combination of stages of flying of the bullets at supersonic and subsonic velocities.

The magnitude of the coefficient, which takes into account the aerodynamics of the form of the bullet and

the proportionality, was left unchanged, that is c = 0,9 , and for the parameters y and p , on the stage of the flying of the bullet at subsonic velocity we gave the value: y2 = -0,327 and p2 = 2,1.

Table 2.

The value of theoretical and experimental kinematic parameters of a bullet released from AKM at its subsonic

x(tk ), m 90,deg 9c,deg tk, s H, m Xh , m V(tk ),m/s

0o 28' 43" 0048' 1,0387 1,337 281,63 335,45

(0o 29') (0048') (1,04) (1,3) (282) (334)

0o 39' 19" 1010' 1,3512 2,306 345,10 306,52

(0o 40') (1009') (1,35) (2,3) (344) (304)

0o 52' 01" 1036' 1,6908 3,700 407,38 283,64

(0o 52') (1035') (1,69) (3,7) (406) (284)

1o 06' 47" 2006' 2,0560 5,582 466,81 264,97

(1o 06') (2006') (2,05) (5,5) (468) (266)

1o 23' 38" 2041' 2,4460 8,000 523,70 249,38

(1o 22') (2039') (2,43) (7,9) (525) (250)

1o 42' 32" 3019' 2,8588 11,100 580,80 236,16

(1o 41') (3017') (2,84) (10,8) (582) (235)

Analyzing the obtained theoretical values of kinematic parameters given in the Tables 1 and 2 with the results of experimental studies we can state that the difference between them is preferably within one percent.

The graph of change of magnitude of the frontal air resistance force R(V) with dimension R]=N,

from the value of the velocity V with dimension

[V] = /v , is presented in fig. 2.

Fig. 3. Graphs of the changes of the frontal air resistance force for a bullet of 7.62 mm caliber released from the

AKM depending on its velocity

When the velocity of the bullet is equal to V = 340,225^, the function of the frontal air

resistance has a jump of the first kind. On the stage of the bullet movement at supersonic velocity, the value of the frontal air resistance force is equal to

R(340,225) = 1,533 N, and at subsonic velocity - to £(340,225) = 0,918N.

Influence of the temperature of the air and cartridge charge on bullet's movement. It is assumed that the air temperature does not change at the bullet's motion and the charge temperature of the cartridge coincides with it.

As the temperature changes, the speed of sound in the air and its density is changing too. The magnitude of the speed of sound in the air is determined using the formula

pV =

mRT I

(12)

V

i

kRT

I

(ii)

where k denotes the adiabatic index and for the

J

air it equal to k = 1,4 ; R = 8314

is

universal gas const; | - 'v 1 ' ^ k

28,96-

kmol

K • mol T is absolute air temperature;

is the nominal molar mass of the

and taking into account that density of the air is determined by the formula

m

P = —, (13)

V

we obtain the equation for identification the density of the air

^ P

P * = ^ , (14)

where P denotes the absolute pressure of the air.

Taking into account (11) and (14), we find the value of the density of the air and the speed of sound at a certain temperature. These values are substituted into the system of differential equations (6) and (7).

In [10] it is stated that the increase (decrease) of the temperature of the cartridge charge by 100 C causes an increase (decrease) in the initial velocity of the bullet

by 7 m

s

Therefore, the effect of the cartridge

air.

Using the Clapeyron Mendeleev equation

charge temperature on the kinematic parameters of the bullet's movement is taken into account due to the change in the initial velocity of the bullet, which is included in the initial conditions (8).

Table 3.

The offset of the point of zeroing of the trajectory of the bullet at the change of temperature of the air and

d=200 m d=400 m d=600 m d=800 m d=1000m

00=0,002342 0o=0,005885 00=0,011438 00=0,019435 00=0,029842

ta=350C AXtheo=9,11 Axtheo=20,32 Axtheo=31,34 Axtheo=46,80 Axtheo=60,96

V=729m/s Axtabl=8,0 AXtabl=16,0 Axtabl=28,0 Axtabl=40,0 Axtabl=54,0

ta=250C Axtheo=4,57 Axtheo=10,15 Axtheo=14,80 Axtheo=23,40 Axtheo=30,46

V=722 m/s Axtabl=4,0 Axtabl=8,0 Axtabl=14,0 Axtabl=20,0 Axtabl=27,0

ta=150C Axtheo=0,00 Axtheo=0,00 Axtheo=0,00 Axtheo=0,00 Axtheo=0,00

V0=715 m/s Axtabi=0,0M Axtabl=0,0 Axtabl=0,0 Axtabl=0,0 Axtabl=0,0

ta=50C Axtheo= -4,50 Axtheo= -10,11 Axtheo= -16,52 Axtheo= -23,35 Axtheo= -30,43

V0=708 m/s Axtabl= -4,0 Axtabl= -8,0 Axtabl= -14,0 Axtabl= -20,0 Axtabl= -27,0

ta=-50C Axtheo= -9,01 Axtheo= -20,22 Axtheo= -33,05 Axtheo= -46,68 Axtheo= -60,83

V0=701 m/s Axtabl= -8,0 Axtabl= -16,0 Axtabl= -28,0 Axtabl= -40,0 Axtabl= -54,0

ta=-150C Axtheo= -13,45 Axtheo= -30,32 Axtheo= -49,57 Axtheo= -70,03 Axtheo= -91,21

V0=694 m/s Axtabl= -12,0 Axtabl= -24,0 Axtabl= -42,0 Axtabl= -60,0 Axtabl= -81,0

ta=-250C Axtheo= -17,92 Axtheo= -40,42 Axtheo= -66,05 Axtheo= -93,35 Axtheo= -121,57

V0=687 m/s Axtabl= -16,0 Axtabl= -32,0 Axtabl= -56,0 Axtabl= -80,0 Axtabl= -108,0

In the Table 3 ^ denotes the temperature of the air and cartridge charge; V is the initial velocity of the bullet; d denotes the distance of shooting; 6 0 ( [©0 ] = rad) denotes the angle of throwing of the bullet. We denote by Axth and AxtoW the values

of the offset of the zeroing point of the bullet's trajectory which are determined by the theoretical method

and specified in the firing tables [10] , a sign (-) indicates that the bullet does not fly to the distance d .

The influence of changes in atmospheric pressure on the bullet's movement. Atmospheric pressure affects the value of air density. Substituting its value into equation (14) it is determined the density of the air. Its value is taken into account when solving the system of differential equations (6) and (7) with the initial condition (8).

Table 4.

The offset of the coordinate of the zeroing point of the trajectory of the bullet's motion at the changes of atmos-___pheric pressure___

P d=200 m 00=0,002342 d=400 m 00=0,005885 d=600 m 00=0,011438 d=800 m 00=0,019435 d=1000 m 00=0,029842

760 mm Hg AXtheo= -0,46 Axtabl=0,0 Axtheo= -1,78 Axtabl= -2,0 Axtheo= -3,49 Axtabl= -4,0 Axtheo= -4,98 Axtabl= -5,0 Axtheo= -6,43 Axtabl= -7,0

750 mm Hg Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0

740 mm Hg Axtheo=0,00 Axtabl=0,0 Axtheo=1,75 Axtabl=2,0 Axtheo=3,53 Axtabl=4,0 Axtheo=5,09 Axtabl=5,0 Axtheo=6,53 Axtabl=7,0

730 mm Hg Axtheo=0,92 Axtabl=0,0 Axtheo=3,52 Axtabl=4,0 Axtheo=7,09 Axtabl=8,0 Axtheo=10,25 Axtabl=10,0 Axtheo=13,18 Axtabl=14,0

720 mm Hg Axtheo=1,39 Axtabl=0,0 Axtheo=5,30 Axtabl=6,0 Axtheo=10,74 Axtabl=12,0 Axtheo=15,51 Axtabl=15,0 Axtheo=19,98 Axtabl=21,0

710 mm Hg Axtheo=1,92 Axtabl=0,0 Axtheo=7,15 Axtabl=8,0 Axtheo=14,47 Axtabl=16,0 Axtheo=20,90 Axtabl=20,0 Axtheo=26,93 Axtabi=28,0

The influence of changes in the initial velocity of the bullet on its motion. In order to consider the changes only of the initial velocity of the bullet on its movement in the air, it is necessary to solve the system of differential equations (6) and (7) under initial conditions (8) with a specific value of the initial velocity of the bullet.

Table 5.

The offset of the coordinate of the zeroing point of the trajectory of the bullet motion at changes of the initial __ velocity___

V0 , m/s d=200 m 00=0,002342 d=400 m 00=0,005885 d=600 m 00=0,011438 d=800 m 00=0,019435 d=1000 m 00=0,029842

735 Axtheo=9,54 Axtabl=10,0 Axtheo=15,89 Axtabl=16,0 Axtheo=19,83 Axtabl=20,0 Axtheo=22,09 Axtabi=24,0 Axtheo=23,47 Axtabl=26,0

725 Axtheo=4,78 Axtabl=5,0 Axtheo=7,97 Axtabl=8,0 Axtheo=9,92 Axtabl=10,0 Axtheo=11,08 Axtabl=12,0 Axtheo=11,77 Axtabl=13,0

715 Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0 Axtheo=0,00 Axtabl=0,0

705 Axtheo=-4,70 Axtabl= -5,0 Axtheo= -7,96 Axtabl= -8,0 Axtheo=-9,99 Axtabl= -10,0 Axtheo= -11,14 Axtabl= -12,0 Axtheo= -11,88 Axtabl= -13,0

695 Axtheo=-9,40 Axtabl=-10,0 Axtheo= -15,93 Axtabl= -16,0 Axtheo= -20,02 Axtabl= -20,0 Axtheo= -22,33 Axtabi= -24,0 Axtheo= -23,85 Axtabl= -26,0

685 Axtheo= -14,07 Axtabl= -15,0 Axtheo= -23,88 Axtabi= -24,0 Axtheo= -30,08 Axtabl= -30,0 Axtheo= -33,61 Axtabl= -36,0 Axtheo= -35,90 Axtabl= -39,0

Influence of change of mass of a bullet on its movement. To account for the effect of the change in mass of the bullet on its motion in the air, it is necessary to solve the system of differential equations (6) and (7), with the specific value of the mass of the bullet, under initial conditions (8).

Table 6.

The offset of the coordinate of the zeroing point of the trajectory of the bullet at changes of its mass

m,kg d=200 m 00=0,002342 d=400 m 00=0,005885 d=600 m 00=0,011438 d=800 m 00=0,019435 d=1000 m 00=0,029842

m+0,03m Axtheo=1,04 Axtheo=3,85 Axtheo=7,75 Axtheo=11,22 Axtheo=14,42

m+0,02m Axtheo=0,68 Axtheo=2,59 Axtheo=5,18 Axtheo=7,50 Axtheo=9,65

m+0,01m Axtheo=0,37 Axtheo=1,28 Axtheo=2,60 Axtheo=3,78 Axtheo=4,82

m Axtheo=0,00 Axtheo=0,00 Axtheo=0,00 Axtheo=0,00 Axtheo=0,00

m-0,01m Axtheo= -0,33 Axtheo= -1,34 Axtheo= -2,68 Axtheo= -3,80 Axtheo= -4,88

m-0,02m Axtheo= -0,71 Axtheo= -2,69 Axtheo= -5,32 Axtheo= -7,59 Axtheo= -9,78

m-0,03m Axtheo= -1,09 Axtheo= -4,05 Axtheo= -8,00 Axtheo=-11,41 Axtheo= -14,70

The proposed mathematical model allows to deter- An example: it is assumed that there are shooting

mine the kinematic parameters of the bullet's motion in at the 600 meters under the following values: 1,02m the air at physically justified values of temperatures of

the air and cartridge charge, the initial velocity and - mass of the bullet, ta = 240 C - air temperature, mass of the bullet, atmospheric pressure.

V0 = 728 - initial velocity of the bullet,

p = 744 mmHg - atmospheric pressure. Using the dependencies (11) and (14), the values of sound speed and air density are determined. Then we substitute their values into the system of differential equations (6) and

(7). This system is solved under the initial conditions

(8). We obtain the following values: tk = 1,3828s -

the duration of the bullet's motion, x(tk ) = 692,28m

- the coordinate of the zeroing point of the trajectory,

X(tk ) = 314,01^ and z(tk ) = -6,37 m/$ - the

projection of the velocity of the bullet on the corresponding axis of coordinates at the time of zeroing the

trajectory of the bullet, V(tk ) = 314,08^ - the final velocity of the bullet, H = 2,41m - the maximum height of the trajectory of the bullet, = 361,41m - horizontal distance to the top of the trajectory.

Conclusions. Knowing the functional dependence (1) there is determined the values of the corrections caused by the influence of changes in air temperature, atmospheric pressure, the temperature of the cartridge charge, the initial velocity of the bullet and its mass. The differences between the results of the theoretical studies and the magnitudes of the corrections given in the tables [10] are because the latter were determined by decomposing the corresponding dependences into numerical series taking into account only the first terms of the decomposition. The corrections in determining the form factor of the bullet and the drug coefficient are also taken into account. Application of the proposed mathematical model for determination of the corrections caused by the non standard firing conditions allows to increase the accuracy of shooting. Note that all calculations were performed using Mathcad Math Software.

REFERENCES

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RECONNAISSANCE-STRIKE AND RECONNAISSANCE-FIRE COMPLEXES AS A WAY TO IMPROVE THE EFFECTIVENESS OF THE ARMED FORCES

Dautov A.

National defense University named after the First President of the Republic of Kazakhstan-Elbasy,

Nursultan Ulakov E.

National defense University named after the First President of the Republic of Kazakhstan-Elbasy,

Nursultan

ABSTRACT

All States of the world strive for high combat capability of their armed forces (AF). Each country chooses its own path of development of the army. Determining the overall development trend of the armed forces will allow you to work out the most optimal way for your army.

For example, the US considers the network-centric principle for the development of the armed forces as the most promising way. This principle involves the deployment of a global information network that optimizes the processes of working with information, delivery and distribution among consumers. Information superiority over the enemy allows you to achieve victory in a short time with minimal costs.

The development of the armed forces in the Russian Federation is seen in the direction of integrating a multilevel intelligence system, a control system and a shock-fire system. The actions of the Russian aerospace Forces