RU2321825C2 - Method for launching of two-stage guided missile from air carrier - Google Patents

Abstract

FIELD: armament equipment, in particular, guided missiles of air-based anti-tank missile complexes.

SUBSTANCE: the method consists in missile launching with the aid of the booster engine from the transport-launching container located on the air carrier launcher. On termination of the booster engine operation the zero stage of the missile is separated, the ballistic flight of the zero stage and the controllable flight of the sustainer stage are accomplished, the missile control is carried out from the moment of its exit from the transport-launching container. The zero stage is used in the form of an aerodynamic stable finned body of revolution. The zero stage is separated after the missile has attained the flight speed corresponding to the Mach number within 3.0 to 4.5. Before the missile is launched the transport launching container is turned through an angle at which all possible trajectories of the separated zero stage pass below the carrier flight altitude.

EFFECT: prevented collision of the air carrier with the separated zero stage.

8 dwg, 12 tbl, 2 ex

Description

The invention relates to the field of weapons technology, in particular to the field of guided missiles of anti-tank missile systems (ATGM) air-based.

When launching guided missiles with detachable structural elements from an air carrier, measures must be taken to prevent collision of the separated rocket structural elements with the carrier.

A known method of launching an anti-tank guided missile (ATGM) Hellfire using a marching solid propellant rocket engine that runs for 3 s, accelerating the missile to a speed of 500 m / s [Collection of scientific and technical information, Special issue. - Tula: GUPKBP, 2005, p.5-26].

There is also a known method of starting an ATGM Spike using a propulsion system consisting of two engines: a starting (inseparable) engine and an accelerating-marching engine. The starting engine (SD) provides the rocket exit from the transport and launch container (TPK) at a speed of 25 m / s. Then the main engine is turned on, accelerates the rocket to a speed of 180 m / s, after which the engine thrust is reduced to a value sufficient to maintain flight speed [Scientific and Technical Information Collection, No. 3 (13) - Tula: GUPKBP, 2005, p.24- 58, p. 62-76].

With these launch methods, the rocket does not have detachable structural elements and special measures are not required to protect the carrier from the separated parts of the rocket.

Closest to the proposed is a method of launching a Mistral 1/2 guided missile (ATAM), the propulsion system of which consists of a detachable LED and a marching engine. The rocket located in the TPK installed on the launcher of the air carrier is launched using the SD, which during the time the rocket moves along the TPK informs it of the initial speed of 40 m / s and after 0.4 s after leaving the container is separated from the rocket uncontrolled at the launch section of the flight path, and falls down. After that, the main engine is turned on and accelerates the rocket to a speed of 850 m / s. [Jane's Air-Launched Weapons, 2005 March, ISSUE 45, p. 13-14].

The starting engine, separated from the Mistral 1/2 rocket (ATAM), flying at subsonic speed, is an unstoppable body of rotation of small elongation (λ <2) with a large drag coefficient and almost zero lift. Under the influence of gravity, the separated SD falls down, and its trajectory passes below the carrier, which continues to maintain the direction of flight preceding the launch of the rocket, or performs a vertical maneuver. Therefore, in this closest to the proposed method of launching a rocket from an air carrier, there is no need to provide special measures to prevent the carrier from colliding with a detached launch stage.

The objective of the invention is to create a safe way to launch from an air carrier an anti-tank two-stage guided missile with a target range of more than 20 km, which is controlled immediately after it leaves the TPK, and the starting engine is separated after it accelerates the rocket to maximum speed.

To solve this problem in the proposed method of launching a two-stage guided missile from an air carrier, including launching a rocket using a launch engine from a transport and launch container (TPK) located on the launcher, separating the rocket stages after the launch engine is finished, ballistic flight of the launch stage and controlled flight of the march stage, missile control is carried out from the moment it leaves the TPK, separation of the launch stage, made in the form of aerodynamically stable the rotation body is produced after the rocket reaches its maximum flight speed, and the TPK before launching the rocket is rotated by an angle calculated in advance for specific flight modes of the carrier according to the nature of the rocket control and the known aerodynamic characteristics of the rocket and the launch stage, in which the entire set of possible trajectories of the separated the launch stage goes below the flight altitude of the carrier.

The invention is illustrated by graphic material, where figure 1 shows the appearance of the starting stage: position 1 is the engine housing, position 2 is the stabilizer block. Figure 2 shows the region of possible flight paths of the launch stage relative to the carrier for the carrier flying at a speed of 300 m / s at a height of 500 m with a rocket launch angle ϑ ₀ exceeding the permissible value величину _add . In Fig. 3, for the same flight conditions of the carrier, the region of possible flight paths of the launch stage is given for a rocket launch angle меньше ₀ less than the permissible ϑ _add . In Fig. 4, for a carrier flying at a speed of 300 m / s at an altitude of 500 m, the possible coordinates Y _o , Z _{o of the} launch stage relative to the carrier are shown, recorded at the moment the vertical stage passes through the origin of the associated coordinate system of the carrier. Figure 5 for the same flight mode of the carrier shows the flight path of the launch stage relative to the carrier at a rocket launch angle ϑ ₀ exceeding the allowable value величину _add . 6-7 show the dependence of the trajectories of the launch stage relative to the carrier on the speed V _n and the flight height Y _n of the carrier at a constant angle of launch of the rocket ϑ ₀ . On Fig presents a graph of isolines ϑ _dop as a function of speed V _n and altitude Y _n flight of the carrier.

The method is as follows. At the design stage, for the selected method of rocket control, for the operating range of the carrier flight speeds V _n and altitudes Y _n , for the given carrier flight mode (horizontal flight, dive, cabling), the values of permissible launch angles ϑ _add = ϑ _n + ϑ _pc , where ϑ _n is the pitch angle of the carrier, - _pc is the angle of rotation of the launch vehicle relative to the longitudinal axis OX _n , the associated coordinate system of the carrier, and entered into the on-board computer system (BVS) of the carrier in the form of a two-dimensional array ϑ _extra = ϑ _extra (Y _n , Y _n ). Acceptable ϑ _extra are those angles at which all possible trajectories of the separated start-up stage go below the flight altitude of the carrier at a given distance ΔL _extra .

When a target is detected, the BVS compares the value of the launch angle ϑ ₀ = ϑ _n + ϑ _pc , which is necessary for launching the missile onto the trajectory ensuring the destruction of the target, with a permissible для _extra for the current conditions of the carrier’s flight and, if the condition ϑ0≤ϑ _additional , the resolution to launch a rocket.

The trajectory of the separated launch stage relative to the carrier depends on the speed and height of the carrier’s flight, as well as on the initial disturbances that the launch stage receives after separation of the rocket stages. It is known that the main perturbing factor affecting the trajectory of the separated launch stage is the angular velocity ω of the missile axis relative to the transverse axes [Izvestia TulGU, Ser. “Problems of special mechanical engineering”, Vol. 8 - Tula: TulSU, 2005, p. 45-49]. In the case when the separation mechanism does not create additional perturbations to the separated rocket stages, the magnitude and direction of the angular velocity ω of the rocket axis are determined by the nature of the controlled movement before separation. When flying with a constant or smoothly changing command, the angular velocity ω of the missile axis relative to the transverse axes is practically zero. If a command is instantly given to the rocket, the current command is reset, or the sign of the command changes, then the axis of the rocket begins to oscillate around the center of mass with an angular velocity ω. The components of the maximum angular velocity ω along the OY, OZ axes of the associated coordinate system of the rocket are equal to: ω _{y max} = k _max · α _ball · 2π · f ₀ , ω _{z max} = k _max · β _ball · 2π · f ₀ , where k _max - casting coefficient when the team sign changes; α _ball is the balancing angle of attack, β _ball is the balancing angle of sliding, f ₀ is the natural frequency of the rocket. At the maximum angular velocity of the rocket relative to the transverse axis, the angle of attack (slip) is close to zero.

In the general case, before the separation of the rocket stages, the angular velocity of its axis can have any value in the range ± ω _max .

The flight path of the separated launch stage relative to the carrier is determined in the process of solving the system of equations of motion of the aircraft [A.A. Lebedev, L.S. Chernobrovkin. Flight dynamics of unmanned aerial vehicles. - M., Mechanical Engineering, 1973, p.467, equations 1 through 12 of the system of equations (11.1) and S.A. Gorbatenko, E.M. Makashov, Yu.F. Polushkin, L.V. Sheftel. The mechanics of flight. - M., Mechanical Engineering, 1969, p.193, equations (4.135)] together with the equations of motion of the carrier.

Performing calculations in the entire possible range of values ± ω _max , we obtain the region of possible trajectories of the starting stage relative to the carrier. If the angle of launch of the rocket exceeds the permissible value, then the case is possible when at least one of the trajectories of the launch stage passes through the carrier.

Therefore, in order to exclude the possibility of collision of the carrier with the launch stage, the launch angle of the rocket should be such that all possible flight paths of the launch stage relative to the carrier at any possible value of the angular velocity ω of the rocket axis in the range from minus ω _max to plus ω _max carrier.

By modeling the trajectory of the separated launch stage relative to the carrier at the maximum angular velocity ω and different launch angles ϑ ₀ , the allowable value of the launch angle ϑ _dop is determined at which the trajectories of the separated launch stage pass by the carrier at any possible value of the angular velocity of the rocket axis at the moment of separation of the stages .

Example 1

The carrier flies uniformly rectilinearly in the horizontal flight mode with a speed of V _n , without roll and sliding at a constant height Y _n with a pitch angle ϑ _n . The range of variation of the carrier flight speed is from 150 to 300 m / s. The range of the altitude of the carrier from 0 to 5000 m above sea level. The dependence of the pitch angle ϑ _{n of the} carrier on the speed and altitude is shown in table 1.

The launcher with TPK can be rotated in the vertical plane of the carrier relative to its longitudinal axis OX _n by an angle ϑ _pc in the range from 0 to minus 12 °. At ϑ _pc = 0 °, the axis of the TPK is parallel to the longitudinal axis of the carrier OX _n .

Table 1
Pitch angle of carrier ϑ _n , degrees V _n , m / s Y _n , m 0 3000 5000 150 5,0 8.4 10.8 200 3,1 4.3 5.5 250 2.1 2.7 3.6 300 2.0 2.6 3,5

The TPK houses a two-stage axisymmetric duck missile with a two-channel control system, which rotates during a roll over the flight due to oblique plumage.

Depending on the rotation angle of the launcher, the launch angle угол ₀ = ϑ _n + ϑ _pc can vary from 10.8 ° at при _pc = 0 ° (V _n = 150 m / s, Y _n = 5000 m, ϑ _n = 10, 8 °) to minus 10 ° at ϑ _pc = 12 ° (V _n = 300 m / s, Y _n = 0 m, ϑ _n = 2.0 °).

After the start engine starts to work (t = 0 s), under the influence of the start engine thrust, the rocket moves along the cuts of the container and by the time t _cx exits the container (t _cx = 0.2 s) it receives a longitudinal velocity V _cx of 30 m / s, and an angular roll speed ω _x equal to 5 r / s.

After the rocket leaves the container, the autonomous missile control system stabilizes its trajectory relative to the given direction of fire and, by the time of separation, the angle of the rocket pitch равен _p is equal to the launch angle ϑ ₀ .

Depending on the speed and altitude of the carrier’s flight above sea level, the speed of the rocket before separation corresponds to Mach numbers from 3.0 to 4.5. The values of the balancing angle of attack α _ball and the natural frequency of the rocket f ₀ for various Mach numbers and altitudes above sea level are shown in table 2. Here are the values of the maximum angular velocity of the axis of the rocket ω _max = k _max · α _ball · 2π · f ₀ with the coefficient throwing missiles k _max = 2.

In the general case, when the rocket stages are separated, the angular velocity of its axis in the rudder deflection channel can have any value in the range ± ω _max . When ω = ω _{max, the} angle of attack does not exceed α _ball .

table 2 M α _ball Y, m 0 1000 2000 3000 4000 5000 f ₀ ω _max f ₀ ω _max f ₀ ω _max f ₀ ω _max f ₀ ω _max f ₀ ω _max hail Hz glad / s Hz glad / s Hz glad / s Hz glad / s Hz glad / s Hz glad / s 3.0 2.0 7.8 3.4 7.4 3.2 6.9 3.0 6.5 2.9 6.1 2.7 5.7 2.5 3.5 1.9 8.4 3.5 8.0 3.3 7.5 3.1 7.1 3.0 6.6 2.8 6.2 2.6 4.0 1.9 8.8 3.7 8.4 3.5 7.9 3.3 7.4 3.1 6.9 2.9 6.5 2.7 4.5 1.8 9.5 3.8 9.0 3.6 8.5 3.4 8.0 3.2 7.5 3.0 7.0 2.8

To calculate the trajectory of the separated launch stage, we use the aeroballistic model below.

Aeroballistic model of the launch stage movement

1. The equations of motion of the starting stage

Dynamic equations of motion of the center of mass of the SS:

Kinematic equations of motion of the center of mass of the SS:

The dynamic equations of the rotational motion of the SS around the center of mass:

Kinematic equations of rotation of the SS around the center of mass:

The values of the angles α _t , β _t and γ _{a are} determined from the following equations:

With no wind, the airspeed of the SS V is equal to the Earth's speed of the SS Y _k , and the angles of attack α, slip β are equal, respectively, to the trajectory angle of attack α _t and the trajectory angle of slip β _t . In the presence of wind and known projections of the wind speed W _x , W _y , W _z on the axis of the local geographic coordinate system, the air speed and angles of attack, SS slip are determined by the dependencies:

2. Aerodynamic forces and moments acting on the starting stage

The components of the aerodynamic forces and moments in the projections on the axis associated with the fuselage of the coordinate system OXYZ, the longitudinal axis OX of which is directed along the axis of the fuselage, are determined by the formulas:

X = -C _x · q · S _x ,

Y = C _y q q S _x ,

Z = -C _z q q S _x ,

M _x = m _x q q S _x L _x

M _y = m _y q q S _x L _x

M _z = m _z q q S _x L _x

ρ - плотность воздуха; V - скорость стартовой ступени;Where

ρ is the air density; V is the speed of the starting stage;

S _x is the characteristic area. S _x = 0.0133 m ² ;

L _x is the characteristic length. L _x = 1 m;

C _x , C _y , C _z are the coefficients of the components of the aerodynamic force (longitudinal, normal and transverse, respectively) along the axes of the connected coordinate system OXYZ;

m _x , m _y , m _z are the coefficients of the components of the aerodynamic moment along the axes of the associated coordinate system OXYZ.

The resistance coefficient C _{x is} calculated by the formula:

The values of the coefficients C _xCC and η _M as a function of the number M are given in table 3.

F _fss = π · D _fss · L _fss .

D _{f CC} - the diameter of the fuselage of the launch stage. D _{f CC} = 0.170 m;

L _{f CC} - the fuselage length of the launch stage. L _{f CC} = 1.454 m.

Δ (2s _f ) _{M = 0} = (2s _f ) _{M = 0} (N) - (2s _f ) _{M = 0} (H = 0).

The values of the coefficients (2c _f ) _{M = 0} as a function of the Reynolds number (Re) are given in table 4, the number Re is calculated by the formula:

ν is the kinematic viscosity of air. The ν values as a function of altitude H are shown in table 5.

The coefficients of normal C _y and transverse C _z forces are:

C _y = C _{y f} + C _{y st}

C _z = C _{z f} + C _{z st}

The coefficients of the normal and lateral forces of the fuselage launch stage:

The values of C _{n f CC} (M, α) and C _{n f CC} (M, β) are shown in table 6; α and β are the angles of attack and slip, degrees;

The coefficients of the normal and lateral forces of the stabilizer:

The values of C _{n st} (M, α) and C _{n st} (M, β) as a function of the Mach number and the angle of attack of the stabilizer are shown in table 8.

The values of the interference coefficients of the stabilizer K _{α article} are shown in table 10.

Roll moment ratios:

δ _st - the angle of the stabilizer arms δ _st = 0.25 °.

в функции числа Маха приведены в таблице 11.Derivatives of the angular momentum coefficients

as a function of the Mach number are given in table 11.

равна:Relative roll angular velocity

is equal to:

где ω_х - угловая скорость крена, рад/с.

where ω _x is the angular velocity of the roll, rad / s.

Yaw and pitch moment ratios:

m _y = m _{y f} + m _{y st}

m _z = m _{z f} + m _z

The coefficients of the moments of yaw and pitch of the fuselage of the launch stage:

X _t - the position of the center of gravity of the starting stage. x _t = 0.812 m.

The coordinates of the points of application of the transverse and normal forces x _{dz f} , x _{dy f} , are determined by the dependencies:

и

приведены в таблице 7.The values of the relative center of pressure of the fuselage of the launch stage

and

are given in table 7.

The coefficients of the damping moments m _{y f} (ω _y ) and m _{z f} (ω _z ) are calculated by the formulas:

Here (C _{z f} ) * = (C _{y f} ) * = C _{y f} (M, α = 1 °),

ω _y , ω _z - projection of the angular velocity vector of the starting stage on the axis OY, OZ of the associated coordinate system, 1 / rad.

Coefficients of yaw moment and stabilizer pitch:

The coordinates of the points of application of forces x _{dy st} and x _{dz st} :

x _st - the distance from the tip of the rocket to the onboard chord of the stabilizer. x _st = 1.279 m

приведены в таблице 9.b _{b st} - the length of the side chord of the stabilizer. b _{b st} = 0.15 m. Values of the center of pressure of the stabilizer

are given in table 9.

The coefficients of the damping moments m _{y st} (ω _y ) and m _{z st} (ω _z ) are equal to:

Here (C _{z st} ) ^* = (C _{y st} ) ^* = C _{y st} (M, α = 1 °).

3. Initial conditions

The separation mechanism of the rocket stages does not create additional disturbances for the divided stages, therefore, the initial conditions of SS motion (V _{CC 0} , θ _{CC 0} , Ψ _{CC 0} , x _{CC 0} , for _{CC 0} , z _{CC 0} , ω _{x CC 0} , ω _{for CC 0} , ω _{z CC 0} , ϑ _{CC 0} , ψ _{CC 0} , γ _{CC 0} ) are practically equal to the values of the motion parameters that the rocket had before separation. The projections of the angle of the velocity vector of the separated SS change by

where V _p is the rocket velocity before separation, V _{y CC} = Δх _t · ω _z , V _{z CC} = Δх _t · ω _y , Δх _t is the distance between the centers of mass of the rocket and SS before separation (Δх _t = 1.284 m), ω _z , ω _у are the coefficients of the yaw moment and pitch of the rocket before separation.

4. The source data

Table 3 M 0,0 0.6 0.7 0.8 0.9 1,0 1,1 1,2 C _{x0 SD} 0.836 0.836 0.850 0.882 0.915 1,226 1,228 1,303 η _M 1,000 0.950 0.945 0.935 0.925 0.915 0,905 0.890 Continuation of table 3 M 1.3 1,5 1.7 2.0 2,5 3.0 4.0 5,0 C _{x0 SD} 1,317 1,329 1,325 1,283 1,233 1,198 1,129 1,081 η _M 0.880 0.840 0.815 0.765 0.700 0.640 0.520 0.420 Table 4
Double friction coefficient of a flat plate Re 0 1 · 10 ⁶ 2 · 10 ⁶ 3 · 10 ⁶ 4 · 10 ⁶ 5 · 10 ⁶ 7 · 10 ⁶ 1 · 10 ⁷ 2 · 10 ⁷ 3 · 10 ⁷ (2s _f ) _{M = 0} 0.00900 0.00900 0,00790 0,00730 0,00695 0,00673 0.00637 0.00596 0.00540 0,00505 Continuation of table 4 Re 4 · 10 ⁷ 5 · 10 ⁷ 7 · 10 ⁷ 1 · 10 ⁸ 2 · 10 ⁸ 3 · 10 ⁸ 4 · 10 ⁸ 5 · 10 ⁸ 1 · 10 ⁹ 1 · 10 ¹⁰ (2s _f ) _{M = 0} 0,00483 0.00469 0,00449 0.00424 0,00382 0,00361 0,00349 0,00344 0,00320 0,00320 Table 5
Kinematic viscosity of air Y, km -0.5 0 2.5 5.0 7.5 10.0 12.5 ν, m ² / s 0,0000141 0,0000146 0.0000179 0,0000221 0,0000277 0.0000352 0,0000495 Continuation of table 5 Y, km 15.0 17.0 20.0 25.0 30.0 35.0 90.0 ν, m ² / s 0.0000730 0.0001084 0.0001600 0,0003500 0,0008356 0.0011661 0.0157590

Table 6
Coefficients C _{n f SS} (M, α) of the normal strength of the fuselage SS
If β = α, then C _{n f CC} (M, β) = C _{n f CC} (M, α)
C _{n f CC} ((M, (α <0)) = - C _{n f CC} (M, (α> 0)) M α, degree 0 2 four 6 8 10 12 fourteen 16 eighteen twenty 89 0
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.7
2.0
2.5
3.0
4.0
5.0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0.130
0.131
0.131
0.131
0.132
0.137
0.144
0.147
0.150
0.157
0.164
0.171
0.176
0.176
0.169 0.279
0.281
0.282
0.283
0.285
0.295
0.307
0.315
0.319
0.336
0.349
0.364
0.375
0.379
0.374 0.447
0.451
0.452
0.454
0.457
0.472
0.492
0.503
0.511
0.538
0.559
0.588
0.613
0.665
0.704 0.633
0.640
0.642
0.646
0.651
0.672
0.699
0.715
0.726
0.769
0.804
0.868
0.961
1.084
1.093 0.837
0.848
0.853
0.860
0.868
0.895
0.929
0.952
0.971
1.038
1.114
1.297
1.452
1.538
1.511 1.057
1.078
1.086
1.095
1.107
1.143
1.192
1.225
1.251
1.390
1.575
1.854
1.981
2.021
1.962 1.292
1.327
1.339
1.353
1.376
1.427
1.488
1.532
1.582
1.897
2.186
2.442
2.537
2.530
2.447 1.542
1.596
1.613
1.642
1.678
1.742
1.822
1.917
2.014
2.556
2.856
3.057
3.121
3.071
2.985 1.805
1.884
1.918
1.962
2.010
2.106
2.252
2.418
2.595
3.286
3.532
3.693
3.720
3.646
3.538 2.080
2.195
2.252
2.311
2.391
2.561
2.811
3.069
3.343
4.031
4.238
4.346
4.350
4.270
4.111 18.584
23.307
24.365
24.717
24.542
24.369
10.248
23.845
23.758
22.934
22.443
22.446
22.448
22.447
22.442

фюзеляжа СС в долях длины фюзеляжа
Отсчитывается от носка корпуса
Если β=α, то

Table 7
Center of pressure position

SS fuselage in fractions of the fuselage length
Counted from the toe of the case
If β = α, then

M α, degree 0 2 four 6 8 10 12 fourteen 16 eighteen twenty 89 0
0.6
0.7
0.8
0.9
1,0
1,1
1,2
1.3
1.7
2.0
2,5
3.0
4.0
5,0 0.117
0.118
0.119
0.119
0.121
0.124
0.129
0.131
0.134
0.144
0.153
0.169
0.186
0.216
0.234 0.134
0.135
0.136
0.136
0.138
0.140
0.144
0.146
0.148
0.157
0.166
0.181
0.197
0.226
0.245 0.165
0.166
0.166
0.167
0.168
0.169
0.172
0.173
0.175
0.183
0.191
0.205
0.221
0.251
0.276 0.191
0.193
0.193
0.194
0.195
0.196
0.197
0.198
0,200
0.208
0.215
0.231
0.249
0.297
0.334 0.215
0.217
0.217
0.218
0.220
0.220
0.222
0.222
0.224
0.233
0.242
0.264
0.297
0.345
0.366 0.235
0.238
0.240
0.241
0.243
0.243
0.244
0.245
0.248
0.259
0.275
0.313
0.343
0.371
0.386 0.254
0.258
0.260
0.262
0.264
0.265
0.267
0.268
0.272
0.292
0.319
0.354
0.370
0.389
0.400 0.271
0.277
0.279
0.281
0.284
0.286
0.288
0.290
0.296
0.333
0.359
0.379
0.389
0.402
0.412 0.286
0.294
0.296
0,300
0,305
0,307
0,309
0.316
0.326
0.369
0.386
0.396
0.402
0.413
0.423 0,300
0.310
0.314
0.319
0.323
0.327
0.334
0.345
0,358
0.394
0.403
0.409
0.413
0.422
0.431 0.313
0.325
0.330
0.335
0.342
0.350
0.362
0.374
0.387
0.412
0.417
0.420
0.422
0.431
0.439 0.551
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553
0.553

Table 8
Coefficients C _{n st} (M, α) of the normal strength of the isolated stabilizer
Related to the area of two stabilizer consoles
If β = α, then C _{n st} (M, β) = C _{n st} (M, α)
С _{n ст} (М, (α <0)) = - С _{n ст} М, (α> 0)) α, degree M 0 0.6 0.7 0.8 0.9 1,0 1,1 1.3 1,5 1.7 2.0 2,5 3.0 4.0 5,0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 twenty 0,996 1,084 1,124 1,174 1,248 1,416 1,298 1,122 0.986 0.864 0.742 0.572 0.494 0.360 0.284

центра давления стабилизатора в долях бортовой хорды.
Отсчитывается от начала передней кромки стабилизатора.
Если β=α, то

Table 9
Position

the center of pressure of the stabilizer in shares of the side chord.
It is counted from the beginning of the leading edge of the stabilizer.
If β = α, then

α,
hail M 0 0.6 0.7 0.8 0.9 1,0 1,1 1.3 1,5 1.7 2.0 2,5 3.0 4.0 5,0 0 0.298 0.291 0.285 0.276 0.264 0,304 0.460 0.534 0.556 0.562 0.559 0.554 0.551 0.547 0.543 twenty 0.298 0.291 0.285 0.276 0.264 0,304 0.460 0.534 0.556 0.562 0.559 0.554 0.551 0.547 0.543 Table 10 Coefficients of interest of the stabilizer M about 0.6 0.7 0.8 0.9 1,0 1,1 1.3 1,5 1.7 2.0 2,5 3.0 4.0 5,0 K _{α article} 1.81 1.81 1.81 1.81 1.81 1.81 1.77 1,69 1,62 1.55 1.45 1.32 1.24 1.17 1.15 K _{α article} 1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.32 1.30 1.26 1.20 1.16 1.13 1.13 Table 11
Roll moment ratios M 0 0.6 0.7 0.8 0.9 1.0 1.1 1.2

, l / city 0,0307 0,0307 0,0314 0,0323 0,0335 0,0365 0,0368 0,0358

, l / glad -0.527 -0.527 -0.540 -0.555 -0.576 -0.627 -0.633 -0.614 Continuation of table 11 M 1.3 1,5 1.7 2.0 2,5 3.0 4.0 5,0

, 1 / city 0,0348 0,0323 0.0299 0,0266 0.0215 0.0187 0.0140 0.0148

1 / rad -0.598 -0.560 -0.514 -0.457 -0.370 -0.321 -0.279 -0.279

Solving the above system of equations of motion of the launch stage, we determine its coordinates x, y and z in the start coordinate system, the position of which relative to the ground is fixed at the moment the start engine starts to work, and the beginning is located in the center of mass of the rocket in the TPK.

With a uniform straight flight of the carrier, its coordinates at time t in the starting coordinate system in the general case are determined by the dependencies:

x _n = V _n · (tt _cx ) · cosθ · cosΨ _n ;

y _n = V _n · (tt _cx ) · sinθ _n ;

z _n = -V _n · (tt _cx ) · cosθ _n · sinΨ _n .

In this example, the carrier is in the horizontal flight mode and after the launch of the rocket does not change the direction of flight. In this case, θ _n = Ψ _n = 0 and in the starting coordinate system at time t

x _n = V _n · (tt _cx );

_n = z _n = 0.

The coordinates of the rocket relative to the carrier at time t are equal to:

x _O = xx _n ;

y _o = yy _n ;

z _o = zz _n .

We introduce the concept of “security criterion” - the minimum permissible distance between the carrier and the separated start stage

We set the value of the "security criterion" equal to 100 m.

ϑ _add grad

Table 12 V _n , m / s Y _n , m 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 150 21,4 21.7 22.0 22.4 22.6 22.7 22.9 23.1 23,2 23.5 23.9 200 9.2 9.2 8.8 8.7 8.4 8.1 7.8 7.8 7.8 8.0 8.3 210 7.4 7.2 6.9 6.6 6.2 5.8 5.5 5,4 5,4 5,6 6.0 220 5.7 5.3 5,0 4.7 4.2 3.8 3,5 3.3 3.3 3,5 3.9 230 4.2 3,7 3.3 2.9 2,4 1.9 1,6 1.4 1.4 1.7 2.0 240 2.7 2,3 1.8 1.3 0.7 0.2 -0.1 -0.3 -0.3 0,0 0.2 250 1.4 0.9 0.3 -0.2 -0.9 -1.4 -1.7 -1.8 -1.7 -1.5 -1.3 260 0.2 -0.4 -1.0 -1.6 -2.3 -2.7 -3.1 -3.2 -3.0 -2.8 -2.6 270 -0.9 -1.6 -2.1 -2.9 -3.5 -3.9 -4.3 -4.3 -4.2 -4.0 -3.7 280 -1.9 -2.6 -3.3 -4.0 -4.6 -5.1 -5.4 -5.3 -5.3 -5.0 -4.7 290 -3.0 -3.6 -4.4 -5.1 -5.6 -6.2 -6.3 -6.3 -6.2 -5.9 -5.5 300 -3.9 -4.6 -5.4 -6.0 -6.6 -7.0 -7.1 -7.1 -7.0 -6.7 -6.3

Calculating the flight paths of the separated launch stage relative to the carrier for various values of the launch angle ϑ ₀ , we determine the minimum value - the permissible launch angle ϑ _additional - at which the entire set of possible paths passes below the carrier at a distance of L _o ≥L _min .

The calculation results are shown in table 12.

Values ϑ _add = ϑ _add (V _n , Y _n ) are entered into the on-board computer system of the carrier, which gives permission to launch the rocket if the required launch angle does not exceed the permissible.

Example 2

For the carrier and rockets from example 1, we consider a special case.

The carrier flies uniformly rectilinearly in the horizontal flight mode without roll and slip. V _n = 300 m / s, Y _n = 500 m, ϑ _n = 2.1 °.

There are two targets in front of the carrier.

To hit the first target, the missile needs to be launched at an angle ϑ ₀ = ϑ _n + ϑ _pc = 0 °, to hit the second target - at an angle ϑ ₀ = ϑ _n + ϑ _pc = -6.5 °.

Based on safety conditions, the angle of launch of the rocket at V _n = 300 m / s, Y _n = 500 m should not exceed ϑ _extra = -4.6 ° (table 12). Therefore, the rocket must be launched on the second target.

Let's see what can happen if the rocket is launched on the first target at a launch angle ϑ ₀ = 0 °.

At the moment of separation of the stages, the rocket's motion parameters are as follows: V = 1305 m / s (M = 3.82), θ = -0.9 °, Ψ = 0, x = 1323 m, y = -11 m, z = 0, ω _x = 10.5 rpm, ω _y = 0, ω _z = 2.34 rad / s, ϑ = 0, ψ = 0, γ = -2.5 °).

The separated launch stage has the same initial motion parameters as the rocket before separation, with the exception of the projections of the angle of the velocity vector, which will change by

sign(l_o)=sign(y_o) приведена на фиг.5. При x_о=0 расстояние l_о между носителем и стартовой ступенью равно нулю: происходит столкновение носителя со стартовой ступенью.Solving the above system of equations of motion, we obtain the flight path of the launch stage relative to the carrier, which in coordinates x _o ,

sign (l _o ) = sign (y _o ) is shown in Fig. 5. At x _о = 0, the distance l _о between the carrier and the starting stage is zero: the carrier collides with the starting stage.

In passing, we note that at the time of separation of the stages, the rocket can have any angular velocity values ω _у , ω _z ranging from minus 3.54 rad / s to plus 3.54 rad / s (table 2), and the angle of heel of the rocket γ is any value in the range from 0 to 360 °. The coordinates of the launching step relative to the carrier at the moment the launching stage passes the vertical plane passing through the origin of the associated coordinate system of the carrier, at ω _у = ω _z = 3.54 rad / s for values of γ from 0 to 360 ° are shown in Fig. 4. Here is a graph for the variant ω _у = 0, ω _z = 2.34 rad / s and γ from 0 to 360 °.

It can be seen from the figure that when the rocket is launched at an angle ϑ ₀ , the magnitude of which exceeds ϑ _extra , there will be at least one flight path of the launch stage passing through the carrier.

When launching a rocket at the second target at an angle ϑ ₀ = ϑ _n + ϑ _pu = -6.5 °, the value of which is less than ϑ _extra = -4.6 °, all possible flight paths of the launch stage will pass below the carrier (Figs. 3, 4 )

The design of the missile that implements this method is similar to that which is part of the Hermes multipurpose missile system presented at the IDEX-2005 exhibition [Arms Markets, ARMS-TASS, 2005, No. 1-2, p.6-9]. In this design, the rocket is controlled immediately after the rocket leaves the TPK, and the starting engine is separated after it accelerates the rocket to maximum speed. For such missiles, the starting stage, which separates after the start of the starting engine, is an aerodynamically stable feathered body of revolution of large elongation. A similar construction of the launch stage is described in the invention RU 2202761. The mechanism of separation of stages, the design of which is similar to that described in the invention RU 2233424, does not create additional disturbances to the separated stages of the rocket.

The presented method for launching a two-stage guided missile from an air carrier makes it possible to exclude a collision of the separated launch stage with the carrier at any possible control commands at the time of separation of the rocket stages.

Claims (1)

A method of launching a two-stage guided missile from an air carrier, including launching a rocket using a launch engine from a transport and launch container (TPK) located on the air carrier launcher, separating the rocket launch stage after the launch engine has finished, ballistic launch stage flight and controlled flight flight stages, characterized in that they control the rocket from the moment it leaves the TPK, use the launch stage in the form of aerodynamically stable operas body of revolution, and the launch stage is separated after the missile reaches a flight speed corresponding to Mach numbers 3.0-4.5, while the TPK before launching the rocket is rotated at an angle at which all possible trajectories of the separated launch stage are below the flight altitude of the carrier.

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