RU2795131C1 - Method for determining the speed of a rocket during its exit from water and the range of the launch site of long-life missiles when launching from a submerged position - Google Patents

Abstract

FIELD: armaments.

SUBSTANCE: invention can be used in determining the accuracy of long-term missile systems. To implement the method for determining the speed of a rocket during its exit from water and the range of the launch site of long-life missiles when launching from a submerged position, the main characteristics of the missile weapon are determined for the underwater section of the trajectory. During rocket operation, the assigned service life of the cruise missile launcher is taken into account, which determines the proportion of the burnt powder charge, which is used to identify the change in the rocket speed during its exit from water and the range of the rocket launch site when firing from a torpedo tube according to the given mathematical expression.

EFFECT: increase in the accuracy of firing by underwater-launched missile systems for long periods of operation.

1 cl, 8 dwg

Description

The invention relates to the field of weapons, military equipment, military systems and can be used in the field of operation and restoration of weapons and military equipment, technical support.

Information from the prior art showed that the existing analogues (RU 2687694 C1 and RU 2590841 C2) make it possible to determine the ballistic characteristics at the end of the active section of the trajectory of long-term storage reactive depth bombs, as well as the main flight characteristics at the end of the launch section of the trajectory for long-term sea missiles services.

The main difference of the present invention is the determination of the range of the starting section of the trajectory and the speed of a long-life missile when launched from a submerged position, that is, the movement of the missile in water and the speed of the missile when it leaves the water.

Consider two ways to launch cruise missiles from a submerged position:

- from a torpedo tube (a complex of rocket weapons "Caliber");

- from missile silos at an angle of 45° (Granite missile weapon system).

The division of missile weapons according to the methods of underwater launch during the study is due to the fact that the passage of their underwater section differs from each other, and therefore the effect of gerontological changes on the main flight characteristics is not identical.

The main flight characteristics of cruise missiles in the underwater section of the trajectory include the speed ranges of its exit from under the water, as well as the range of the launch section during an inclined underwater launch.

At present, a number of studies have been carried out to take into account the influence of gerontological changes in the powder charges of launch units on the dynamics of rocket flight. Studies to determine the effect of the service life of cruise missiles on the change in the main flight characteristics of the underwater section of the trajectory have not been found in available sources.

Based on the review and analysis of scientific papers on determining the state of gunpowder, the change over time in the density of gunpowder was determined as the main indicator, and, consequently, the mass of the powder charge.

Thus, based on the known methods for determining the flight characteristics of missile weapons, it is necessary to improve and refine the method in such a way that it would be sensitive to the parameters of modeling gerontological changes in powder charges of launch units of underwater cruise missiles.

The missile is fired from a torpedo tube at a speed of 15-25 m/s. After the missile exits the submarine launcher, its launch unit is launched. The minimum time to turn it on is 0.6 s, and the maximum is 4 s.

The diagram of the forces and moments acting on the rocket when moving under water is shown in figure 1.

The diagram shows three coordinate systems: terrestrial O ₀ X _g Y _g , bound OXY and velocity OX _C Y _C . Figure 1 shows that the following forces act on the rocket:

G - gravity applied to the center of mass (CM) - point O;

A - buoyancy force applied to the center of magnitude (CV);

- гидродинамическая сила лобового сопротивления, приложена к ЦМ;

- hydrodynamic drag force applied to the CM;

- гидродинамическая подъемная сила, приложена к ЦМ;

- hydrodynamic lifting force applied to the CM;

P is the thrust force of the engine, applied to the CM (in hydrodynamics, it is often denoted: "T").

In addition, the hydrodynamic moment M _{Z g} acts on the rocket.

The diagram shows the angles: trajectory inclination θ, pitch (trim) ϑ and attack α.

It is believed that the centers of magnitude and mass are located on the longitudinal axis of the rocket and have a distance from each other by the value l _CV .

The equation of forces acting tangentially to the trajectory, in projections on the axis of the high-speed SC, has the form:

where Δ=G-A is the force of negative buoyancy.

The equation of forces acting along the normal to the trajectory, in projections on the axis of the high-speed SC, looks like:

The equation of the moments acting relative to the axis O _Z , in projections on the axis of the high-speed SC, has the form:

Dynamic equations (1)-(3) are supplemented by kinematic ones:

and the angle relation equation:

Taking into account the accepted assumptions about the constancy of the mass of the rocket on the starting section of the trajectory:

where P is the thrust of the rocket jet engine;

k - thrust attenuation coefficient from depth;

H is the depth of the rocket under water.

The time of passage of the underwater section of the trajectory is ~5…10 seconds.

It is known that:

where μ is the fraction of the burnt powder charge;

Q ₀ - caloric content of gunpowder;

u _e - effective speed of the outflow of gases.

Integrating expression (8) from the beginning of the rocket movement to an arbitrary point in time, we obtain:

where τ is the burning time of the powder charge;

Q ₀ - caloric content of gunpowder;

WITH _X0 - drag coefficient.

Therefore, the speed of the rocket during its exit from the water:

In the process of long-term operation (storage), due to gerontological changes in the powder charge, the average density of the powder changes due to the processes of mass transfer and autocatalysis. In the model problem, these changes are taken into account in the form of a change in the proportion of the burnt powder charge of the starting unit (μ), the value of which for a conditioned powder charge is equal to 1.

1.This means that in the model task of taking into account the effect of gerontological changes in the powder charges of launch units on the characteristics of underwater-launched cruise missiles, it is assumed that when a rocket with a conditioned powder charge of the launch unit is fired, the entire charge burns out, which is reflected by the expression (μ=1). Then for gunpowders of long service life, the effect of their depletion is considered as incomplete combustion of the powder charge of the propulsion system, that is, μ

1.

Considering that nitroglycerine powders contain low-resistant chemicals that contribute to their chemical decomposition (nitrogen contained in gunpowder (no more than 14.14%), reacting with atmospheric hydrogen forms nitric and nitrous acids, therefore the reaction is autocatalytic), and also, as the analysis of the chemical composition of powders and studies on the reduction in the mass of the powder charge during their long-term storage, in the range of 30-40 years, showed that the reduction in the mass of the charge is 3-7%, and sometimes more, it is advisable to consider the range of change in the proportion of burnt powder charge reactive solid fuel engine μ=0.85…1.

Due to the fact that the designs of both underwater and surface-launched missiles are the same, the values of the proportion of the burnt powder charge of the cruise missile launcher are as follows:

- for conditioned powder charges of the launching units of the CR, the service life of which is guaranteed, the proportion of the burnt powder charge μ=1;

- for powder charges of starting units, the service life of which is in the range of 25-30 years, the proportion of the burnt powder charge μ=0.95;

- for depleted, in the process of long-term operation (30-35 years), powder charges of starting units, the proportion of burnt powder charge μ=0.9;

- critical depletion of powder charges of starting units (35 years or more) will be expressed as the value of the proportion of burnt powder charge μ=0.85.

Based on the values of the fraction of the burnt powder charge μ, for certain assigned service lives of sea missiles, we determine the dependence of its speed at the time of exit from the water, depending on the service life (Fig. 2).

The resulting dependence (Fig. 2) serves as the basis for identifying the pattern of change in the speed of the rocket at the time of its release from the water as a function of the degree of depletion of the powder charge, which is expressed through the fraction of the burnt powder charge μ (Fig. 3).

аппроксимировались полиномиальной функцией, после чего было получено обобщенное выражение в виде:curve functions

were approximated by a polynomial function, after which a generalized expression was obtained in the form:

The obtained values of rocket velocities at the time of exit from the water (11), which take into account the assigned service life of sea missiles, make it possible to determine their maximum service life, after which the intended use can lead to an emergency scenario.

An analysis of the calculations performed showed that the maximum decrease in the speed of a rocket at the time of exit from the water, depending on the assigned service life, occurs for cruise missiles with a service life exceeding 35 years and is 56% of the trajectory required to reach the marching section.

The resulting expression (11) makes it possible to determine the speed of a cruise missile at the moment of exit from the water when firing from a torpedo tube, depending on the proportion of the burnt powder charge of the starting unit (μ).

Naval missiles launched from inclined launchers (45°) of submarines, as a rule, experience the maximum force in the underwater section of the trajectory. It is these loads that determine the requirements for the strength and reliability of rocket launch units.

The analysis of the available methods of inclined underwater launch of missiles gives grounds, from the point of view of hydrodynamics, to restrict ourselves to consideration from a flooded mine when implementing the continuous flow around the missile (“wet” launch method).

When determining the effect of gerontological changes in the powder charges of rocket launch units on the possibility of their accident-free use for their intended purpose, it is necessary to solve hydrodynamic problems that involve studying physical phenomena at launch and determining hydrodynamic loads in the mine section of movement, as well as determining the hydrodynamic characteristics of the rocket in the underwater section and the intersection section water surface.

Based on the analysis of the ongoing research, it can be assumed that the features of hydrodynamic processes during launch from a flooded mine are associated with the formation of jet flows of liquid, gas cavities in the mine volume and the surrounding liquid, changes in the position of their boundaries over time, depressurization of the mine volume when the rocket leaves it, followed by flooding with water. Hydrodynamic processes in the launcher shaft begin from the moment the engine membrane breaks. Under the influence of excess pressure and engine thrust, the rocket exits the shaft with simultaneous displacement of the water column from the annular gap into the surrounding liquid. As a result, a cocurrent jet of liquid is formed. The cocurrent velocity at the beginning of the rocket exit is higher than hers. Then the velocities equalize, but at the end of the rocket exit from the mine, the cocurrent velocity again becomes greater than the rocket velocity. This leads to the formation of a gas bubble at the mine cut. Later, as the volume of the bubble grows and a cylindrical gas cavity forms behind the bottom of the rocket, the gas pressure drops and changes in time according to a law close to the law of damped oscillations.

When a rocket moves in water, cavitation may occur on the nose of the rocket, where the greatest dynamic vacuum is achieved, since the minimum values of the pressure coefficient for the used nose fairing profiles of rockets reach minus 0.4. The saturated vapor pressure at a temperature of 20 ° C is only 0.002 MPa, and at a speed of 20-40 m / s, cavitation can occur at a depth of about 20 m. The missile is controlled under water using aerodynamic and jet rudders. Then cavitation will develop with a decrease in hydrostatic pressure as the rocket approaches the free surface.

The calculation of the hydrodynamic characteristics of rockets in a continuous flow regime is reduced to the determination of the added masses and coefficients of hydrodynamic forces and moments.

The movement of the rocket under water (launch angle 45°) is described by the diagram (Fig. 4).

Figure 4 shows:

O _a X _a Y _a Z _a - coordinate system associated with the rocket;

About _a - the center of mass of the rocket;

- полусвязанная система координат;

- semi-coupled coordinate system;

- местная географическая система координат, жестко связанная с неподвижным репером;

- local geographic coordinate system, rigidly associated with a fixed reference point;

- возмущающие силы и силы гидродинамического сопротивления по осям О_аХ_а и O_aY_a соответственно;

- disturbing forces and forces of hydrodynamic resistance along the axes O _a X _a and O _a Y _a respectively;

- силы, создаваемые движителями по осям О_аХ_а и O_aY_a соответственно;

- forces created by propellers along the axes O _a X _a and O _a Y _a respectively;

F _A - strength of Archimedes;

- возмущающий момент, момент, создаваемый движителями, и гидродинамический момент вокруг оси O_aZ_a соответственно;

- the disturbing moment, the moment created by the propellers, and the hydrodynamic moment around the axis O _a Z _a respectively;

H - depth of immersion of the rocket;

h is the metacentric height of the rocket;

ϑ - trim angle.

We express the hydrodynamic forces in the following form:

- гидродинамические коэффициенты, вычисленные для данной ракеты и плотности воды;Where

- hydrodynamic coefficients calculated for a given rocket and water density;

V _x , V _y - linear velocities of the rocket along the axes O _a X _a and O _a Y _a respectively;

ω _z - angular velocity of the rocket around the axis O _a Z _a .

The coefficients C _x1 , C _y1 can be found by the following formulas:

where C _x , C _y , are dimensionless hydrodynamic coefficients for the axes O _a X _a and O _a Y _a respectively;

S _x , S _y , - characteristic areas corresponding to C _x , C _y ;

ρ is the density of water.

Based on the scheme of missile movement under water during an inclined launch (Fig. 4) and taking into account expression (12), we will compose a system of equations describing the movement of a rocket in a vertical plane:

where m, j _z , g - mass of the rocket, the moment of inertia about the axis O _a Z _a and the free fall acceleration, respectively;

λ ₁₁ , λ ₁₂ , λ ₆₆ - attached masses along the axes O _a X _a and O _a Y _a and the attached moment of inertia around the axis O _a Z _a respectively;

и O_aη соответственно; ζ, η - linear velocities of the rocket along the axes

and O _a η, respectively;

- производные по времени величин V_x, V_y, ω_z, ϑ соответственно.

- time derivatives of the values V _x , V _y , ω _z , ϑ respectively.

Taking into account the assumptions made about the constancy of the mass of the rocket on the starting section of the trajectory, the speed of the rocket on the underwater section of the trajectory will take the form:

Based on studies that confirm the influence of the proportion of the burnt powder charge μ on the change in the density of the powder and the thrust of the starting unit, and hence the speed of the rocket during its exit from the water, when performing an inclined launch, expression (15) will take the form:

We will consider the change in the speed of a rocket at the moment it leaves the water (during an inclined launch) using the example of the Granit missile weapon complex.

The following were chosen as initial data:

- the interval of the proportion of the burnt powder charge is 0.85≤μ≤1, which depends on the designated service life of the missiles;

- burning time of the starting unit t _CA ≈13.5 sec;

- the time of passage of the rocket underwater section t≈5 sec;

- depth of a possible underwater launch (H) from 50 m to periscope.

The dependence of the rocket speed at the moment of leaving the water during an inclined launch on the degree of depletion of the powder charge of the starting unit is described in the MathCAD computing environment (Fig. 5).

The resulting dependence (Fig. 5) allows us to determine the pattern of change in the speed of the rocket at the moment it leaves the water, during an inclined launch, as a function of the degree of depletion of the powder charge, which is expressed in terms of the fraction of the burnt powder charge μ (Fig. 6).

аппроксимировались полиномиальной функцией, после чего было получено обобщенное выражение в виде:curve functions

were approximated by a polynomial function, after which a generalized expression was obtained in the form:

The obtained values of the rocket velocities at the moment of leaving the water during an inclined launch (17), which take into account the degree of depletion of the powder charges as a result of the long assigned service life, make it possible to determine their maximum assigned service life, after which the intended use can lead to an emergency scenario.

The analysis of the performed calculations showed that the maximum decrease in the speed of the rocket at the moment of exit from the water during an inclined launch, depending on the assigned service life, occurs for missiles with exorbitant service life (35 years or more) - 55% of the required one to the point of reaching the marching section of the trajectory .

To determine the range of the launch section of the trajectory for an inclined underwater launch of cruise missiles, we use an expression that determines the same range when firing a missile from a surface ship. However, the initial data for this expression will be the speed of the rocket at the time of exit from the water, obtained using expression (17). Underwater launch depth H=50 meters:

As a result of calculations, the dependence of the change in the starting section of the trajectory on the fraction of the burnt powder charge was obtained during an inclined underwater launch of a cruise missile (Fig. 7).

The resulting dependence (Fig. 7) allows us to determine the pattern of change in the range of the starting section of the trajectory, including the underwater section, during an inclined underwater missile launch, as a function of the degree of depletion of the powder charge, which is expressed in terms of the fraction of the burnt powder charge μ and depends on their assigned service lives (Fig. . 8).

аппроксимировались полиномиальной функцией, после чего было получено обобщенное выражение в виде:curve functions

were approximated by a polynomial function, after which a generalized expression was obtained in the form:

The obtained values of the distances of the starting section of the trajectory (including the underwater section) during the implementation of an inclined launch (19), which take into account the degree of depletion of the CA powder charge, make it possible to determine the boundary service life of the rocket and the possibility of their intended use.

The analysis of the performed calculations showed that the maximum change in the starting section of the rocket trajectory during an inclined underwater launch, depending on the depletion of the SA powder charge, as a result of the long assigned service life, occurs for missiles with exorbitant service life (35 years or more) - 27% of the required to the exit point on the marching section of the trajectory. This is due to a change in the density of the powder, which leads to a critical decrease in the speed of the rocket in the underwater section of the trajectory.

The technical result is achieved by the fact that during the service life (storage) of an underwater-launched cruise missile, the degree of depletion of the powder charge of the starting unit is taken into account, which determines the proportion of the burnt powder charge, which determines the change in the main flight characteristics in the underwater section of the trajectory when firing from a torpedo tube according to the following expression:

and for inclined start - according to the following expressions:

- изменение скорости КР в момент выхода из под воды;Where

- change in the speed of the CR at the time of exit from under the water;

- изменение скорости КР в момент выхода из под воды при наклонном пуске;

- change in the speed of the CR at the time of exit from under the water with an inclined start;

- изменение дальности стартового участка траектории КР в при наклонном подводном пуске;

- change in the range of the starting section of the trajectory of the CR in the case of an inclined underwater launch;

μ is the range of change in the proportion of the burnt powder charge during storage of the rocket for up to 40 years or more (0.85≤μ≤1).

The technical and economic effect of this invention involves an increase in the accuracy of firing by long-term submarine-launched missile systems.

Claims (9)

A method for determining the speed of a rocket during its exit from the water and the range of the launch section of long-life missiles when launching from a submerged position, which consists in determining the main characteristics of a rocket weapon in an underwater section of the trajectory, characterized in that the designated service life of the launch unit is taken into account during the operation of the rocket cruise missiles, which determines the proportion of the burnt powder charge, which determines the change in the speed of the rocket during its exit from the water and the range of the launch site of the missiles when firing from a torpedo tube according to the following expression:

Where

- the speed of a long-term missile during its exit from the water when firing from a torpedo tube; μ is the fraction of the burnt powder charge, and for inclined start - according to the following expressions:

Where

- the speed of a long-term rocket during its exit from the water during an inclined launch;

- range of the launch site of long-life missiles in the implementation of an inclined underwater launch; μ is the fraction of the burnt powder charge.

Images