RU2670731C9 - Method for determining supersonic projectile flight trajectory - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measuring techniques, in particular to determining a gun location and parameters of the gun projectile flight trajectory. A method is proposed, in which sound sensors are oriented at an angle to the direction of the gun location. By means of a computer the information received from the sensors is processed. Herewith parameters of the projectile trajectory are determined in two stages. At the first stage the projectile firing point is determined by seismological methods. At the second stage the trajectory parameters are determined by acoustic methods. At the first stage three seismic receivers are placed along a straight line in the horizontal plane at known distances, which are used as seismic wave sensors. At the second stage three sound sensors are placed along the straight line in the horizontal plane at known distances. Fourth sound sensor is placed on the vertical line of one of the three sensors taken as the basic one. Parameters of the seismic wave at the first stage and of the sound wave at the second stage are measured using the time differences of the waves arrival to the sensors relative to the basic sensor. At the second stage maximum values of the sound wave harmonics are used found by the microcontroller and the comparator taking into account the known velocities of seismic and sound waves propagation. Basing on the known distances between the sensors and the recorded time of the waves reaching the sensor, equations are composed. Solutions of the equations make it possible to find the parameters for the first stage – the gun coordinates, and for the second stage – parameters of the projectile trajectory relative to the Earth.

EFFECT: high-accuracy determination of parameters of a projectile movement along the trajectory and the point of the projectile incidence is provided.

1 cl, 6 dwg

Description

The invention relates to measuring technique, in particular, determining the location of a firearm on the ground and determining the flight path of a projectile fired with its help.

From the existing level of technology known "Fire Detection System" Owl "" [1]. In addition, there are known methods for determining the coordinates of the position in space and time of bullets and shells, for example, patents No. 2470252, 2231738, 2392577 ... - [2, 3, 4, 5, 6].

Closest to the claimed technical solution is the patent RU 2358275, G01S 3/808. Method and system for determining the trajectory of a supersonic projectile. PCT Publication: 2006/096208 (09/14/2006) - [2].

The disadvantages of this technical solution are:

- the iterative nature of the computing process, requiring a lot of time to solve the problem;

- a large number of sound sensors, reducing the overall reliability of the system;

- low accuracy of calculations;

- lack of definition of the point of impact of the projectile.

The objective of this proposal is to accurately determine the parameters of the projectile along the trajectory, such as flight altitude, flight speed, the angle of inclination of the trajectory to the horizon, the definition of an analytical description of the trajectory of movement with reference to the earth's coordinates and the point of impact of the projectile.

The solution to this problem is achieved by the fact that it is solved in two stages. At the first stage, the projectile launch point is determined by seismology methods. At the second stage, using several acoustic measurements, the projectile’s altitude is determined, the projectile’s speed is determined, the angle of inclination of the trajectory to the horizon is determined, the launch point determined at the first stage is adjusted, an analytical description of the projectile trajectory, linked to the earth’s coordinates, is formed, and the projectile’s incidence point is determined.

Distinctive features of the prototype is that the determination of the parameters of the flight of the projectile is carried out not by the shock wave, but by the sound accompanying the supersonic flight of the projectile, the selection in the accompanying sound of the base points for determining the propagation time of the wave to the sensors, the linear arrangement of the sensors for receiving both seismic waves and and acoustic, calculation of the dynamic parameters of the flight path, estimation of the coordinates of the point of impact of the projectile, determination of the launch point from the seismic wave.

Analysis of the proposed solution and prototype allows us to conclude that it meets the conditions of patentability.

The invention is illustrated by drawings, which depict:

in FIG. 1 presents a picture of the propagation of an elastic wave over the surface of the Earth. The seismic wave propagates from point O and reaches sensors at different times.

The figure indicates: NS - the direction of fire, point O - the location point of the gun, points A, B, C - location points of the geophones, tied to the coordinates of the earth's surface, d ₀ - distance from point A to the gun, angle SAO - the angle between the direction of gun and direct speaker.

In FIG. 2 shows the geometric construction for calculating the projectile launch point in the geographic coordinate system (stage 1) and determining the coordinates of the projectile trajectory (stage 2).

FIG. 3 represents a sound wave accompanying the flight of a supersonic 152 mm projectile and determination of maximum amplitude values.

In FIG. 4 shows geometric constructions for determining the distance to the sound source, the height of the trajectory and the azimuth of the trajectory point relative to the direct AC by the acoustic method (step 2).

FIG. 5 gives a geometric picture of calculating the angle of inclination of the trajectory and the parameters of the trajectory of the projectile for two design points.

In FIG. 6 is a structural diagram of a complex of equipment for determining the parameters of the projectile trajectory.

The device operates according to this method as follows.

At the first stage of measurements, the shot point is determined, that is, the location of the gun using seismology.

At the second measurement stage, the parameters of the projectile trajectory and the projectile speed are determined. Together, these two stages make it possible to determine the direction of the shot and the point of landing of the projectile (the place of destruction) and, thus, in advance, for example, by radio, to warn the personnel of the military about taking appropriate measures.

Consider the first stage - determining the location of the gun’s shot. This problem is solved using seismic waves propagating from the point of the shot.

It is known that during a shot there is a hard blow to the earth’s crust, which results in an elastic wave propagating over the Earth’s surface at a constant speed for a given area in all directions. This speed depends on the type of surface layer (e.g. sand or rock) and is on average 1,500 meters per second. As you can see, the average velocity of the elastic wave is much higher than the velocity of the projectile, so that simultaneously with the determination of the coordinates of the location of the gun, the moment of sound arrival from the passing projectile to the acoustic sensors is approximately determined. This is necessary, for example, for the timely inclusion of equipment and careful processing of acoustic information received at this time.

The 1st stage consists in determining the location of the gun according to the seismic wave from the shot. To start the measurements, it is necessary to arrange three geophones relative to the possible location of the gun. We place the geophones in a horizontal plane on one straight line at a distance of 1-5 kilometers from the possible location of the gun and preferably at an angle of 45 degrees to the direction of the location of the gun, as shown in FIG. 1. The distances between the sensors can be from units of meters to hundreds of meters.

The time of arrival of the elastic wave front to the seismic sensors is determined using seismic detectors and a central computer, as shown in FIG. 6, bypassing the microcontrollers. According to this structural diagram, the signals of each sensor are immediately transmitted by the central computer, and it records the time of arrival of the elastic wave to the corresponding sensors. Further information is processed according to the algorithm described in this paper.

Let we have the elastic wave propagation velocity equal to ν. This speed is determined mainly by the type of soil filling the area, and should be known at the time of measurement. It is necessary to determine the direction to the point O - the angle χ ₀ and the distance OA = d ₀ . Thus, to find two unknowns, two equations must be compiled. According to the figure, an elastic seismic wave arrives at some points in time both at point A, and at points B and C. The time of arrival of the wave to the sensors is fixed, and differences are formed from them: t ₁ = t _B -t _A , t ₂ = t _C - t _A. The time of arrival of the seismic wave to the sensor A will be considered as the base.

To form the calculation equations, we consider two oblique triangles OAV and OAS - Fig. 1. We use the formula (cosine theorem):

a ² = b ² + c ² -2 * b * c * cosχ,

where side a is opposite the angle χ.

For our case we have:

,

,

where the first equation is valid for the triangle OAV, the second - for OAS.

This system of two equations contains two unknown parameters: the angle χ ₀ and the distance OA = d ₀ .

In turn, the side OB = b + ν * Δt ₁ , and OS = d + ν * Δt ₂ ;

where Δt ₁ = t _B -t _A , Δt ₂ = t _C -t _A , OA = d ₀ ,

where the presented differences are based on measuring the moments of arrival of the elastic wave to the respective sensors. Given the above relations, we write:

Here, AB = a, BC = b, a and b are the previously known distances between the sensors. Index "0" for variables corresponds to the first stage of measurements.

Expand the brackets and simplify the expression, we get:

If designated

a ₁ = 2 * ν * Δt ₁ ,

a ₂ = 2 * ν * Δt ₂ ,

b ₁ = 2 * a ,

b ₂ = 2 * ( a + b),

c ₁ = a ² - (ν * Δt ₁ ) ² ,

c ₂ = ( a + b) ² + (ν + Δt ₂ ) ² ,

then we have:

This is a system of two equations with two unknowns. Denote

d ₀ = x ₁ , d * cosχ ₀ = x ₂ ;

then:

.

.

To determine two variables - the angle χ ₀ and the distance d _0, it is necessary to solve the presented system of equations for specific values of ν, known a and b, measured Δt ₁ , Δt ₂ .

After determining the values of d ₀ and χ ₀ it is easy to determine the coordinates of the point of the shot. To do this, it is enough to postpone the angle χ ₀ from point A, i.e. to postpone the angle of SAO, and on the ray of AO, to postpone the distance d ₀ . In the geographical coordinate system, the gun’s location point can be found as follows.

According to FIG. 2, for the sensor system, the angle of inclination of the direct AC to the equator line is known — the angle γ. The azimuthal angle (the angle between the direction to the North (NA) and the direction to the gun’s location, angle NAC) will be χ + γ-90. The distance along X will be equal to: X = d ₀ * sin (χ + γ-90) + X _A , and the distance Y = d ₀ * cos (χ ₀ -γ-90) + Y _A. Using these coordinates, it is easy to find the location of the gun’s shot point.

Second phase. At this stage, the coordinates of the trajectory of a projectile flying over a given terrain are determined: the angle of inclination of the projectile flight path, the speed of the projectile, and the coordinates of the gun’s location, which duplicate the same coordinates found from the seismic wave. In this case, sound waves are subsonic waves that accompany the flight of a projectile.

According to the data found at this stage in combination with the coordinates of the gun’s location determined earlier, the point of impact of the projectile can be determined, and the coordinates of this point can be transferred to the servicemen of the fired territory for taking appropriate measures. The margin of time for taking appropriate measures can be 15-25 seconds.

The basis for determining the parameters of the trajectory of the projectile is the method of determining the distance and azimuth angle to the point of projectile motion using the acoustic method. It is known that a shell of 150 mm caliber flies with an initial supersonic speed of about 900 meters per second. Near the firing point (1 ... 10 kilometers) this speed remains supersonic. When the projectile is flying, it emits sound waves perceived by the human ear. Sound waves move after the shock wave of the projectile. These sound waves can also be a parameter for determining the trajectory of the projectile. Sound waves are easily captured by sound microphones. We will use the same points that were used for seismic measurements and place sound sensors in them, and three of them will be placed in a horizontal plane on the same line (these are previously defined points with sensors A, B, C; in this case, if the seismic wave receivers are located on some depth in the Earth, then the acoustic sensors are located above the Earth) and we place one sensor D above the sensor A in the vertical at a certain height of 2 ... 5 meters. Somewhere nearby we will place the microcontroller, connect the sensors to the microcontroller and the central computer with electric communication lines. In the process of measurements, it is important to determine the distance to the projectile, azimuthal angles in order to determine the coordinates of the trajectory and the speed of flight in a geographical coordinate system. With knowledge of the launch point, having the parameters of the projectile trajectory, it is easy to determine the direction of flight and the approximate point of impact of the projectile.

The question arises of determining the fixation point of sound from a series of sound waves emitted by a flying projectile. It is proposed to organize a search for the maximum values of sound vibrations and consider these points as the moments of the sound wave outcome, as reference points for the navigation system.

To implement this, let each microphone have its own microcontroller that processes only the signals entering its channel (Fig. 6). Let these microcontrollers work from one master clock generator. The task of each microcontroller is to receive an analog signal and translate it into a digital code with a high degree of resolution. Calculations should be carried out in real time, that is, in the rhythm of the sound wave coming from the projectile. The search for the maximum value of harmonics can be organized, for example, in this way. The harmonic supplied to the microcontroller is divided into a sequence of discrete values. Nearby discrepancies are compared in amplitude without regard to the sign. In this case, the compared amplitudes can be both positive and negative. We call the first discrete input to the microcontroller the previous one (t = i + 1), and the next one after it the next one (t = i) (Fig. 3). If, in comparison with the comparator of two adjacent discrete, the next one is larger than the previous one, there is a decrease in the harmonic value. If the subsequent discrete is equal in absolute value to the previous one or becomes larger than it, we can say that there is a passage of the maximum. In this case, the microcontroller must send a signal to the central computer about reaching a maximum on this sensor. The time for determining the maximum values should be fixed. Differences in the appearance of maximum values on the respective sensors relative to the base sensor will participate in the calculation of the trajectory parameters.

We place the sound sensors at the same points as the geophones, that is, at points A, B, C, but above the Earth. Recall that the location of sound sensors must satisfy the following conditions: they must be located along one straight line and in a horizontal plane. In addition, we place the fourth sound sensor above point A (base point) at a certain height (2-3 meters) on the vertical of this point.

To form the calculation equations, we consider two oblique triangles O ₁ AB and O ₁ AC (Fig. 4). Point O ₁ is the point of the projectile flight path, the parameters of which must be determined. We use the formula (cosine theorem):

a ² = b ² + c ² * b * c * cosχ ₁ ,

where side a is opposite the angle χ ₁ , angle CAO ₁ .

The calculations are similar to the calculations of the first stage (for seismic waves).

For our case we have:

,

,

where the first equation is valid for the triangle OAV, the second - for OAS.

This system of two equations contains two unknown parameters: the angle χ ₁ and the distance OA = d ₁ .

In turn, the side OB = d ₁ + ϑ * δt ₁ and OS = d ₁ + ϑ * δt ₂ ;

where δt ₁ = t _B -t _A , δt ₂ = t _C -t _A , ϑ is the speed of sound,

where the presented differences are based on measuring the moments of arrival of the elastic wave to the respective sensors. Given the above ratios, we write:

Here, AB = a , BC = b, a and b are the previously known distances between the sensors.

Expand the brackets and simplify the expression, we get:

If designated

a ₁ = 2 * ϑ * Δt ₁ ,

a ₂ = 2 * ϑ * Δt ₂ ,

b ₁ = 2 * a ,

b ₂ = 2 * ( a + b),

c ₁ = a ² - (ν * Δt ₁ ) ² ,

c ₂ = ( a + b) ² - (ν + Δt ₂ ) ² ,

then we have:

,

,

This is a system of two equations with two unknowns. Denote

d ₁ = x ₁ , d ₁ * cosχ ₁ = x ₂ ;

then:

To determine two variables - the angle χ ₁ and the distance d ₁ (equal to the segment AO ₁ ), it is necessary to solve the presented system of equations for specific values of известных, known a and b, measured δt ₁ , δt ₂ .

After determining the values of d ₁ and χ _1, you can determine the coordinates of the point of the trajectory in the geographical coordinate system.

An acoustic sensor at point D will determine the angle of elevation of point O of the trajectory above the horizon — angle h.

Consider the triangle O ₁ AD (Fig. 4).

It can be seen from the figure that the sound signal will come first to the sensor D, and then to the sensor A. If the distance to point O ₁ is known, this distance has been determined, it is d ₁ , and the angle O ₁ AO = β can also be determined.

From the triangle O ₁ AD it is seen that

DO ₁ = d ₁ -δt ₃ * ϑ

To find the angle β, we use the cosine theorem for the triangle AO ₁ D:

O ₁ D ² = d ² + l ² -2 * d * l * cosβ, whence

Next, we find the elevation angle of the trajectory h relative to the horizon: h = 90-β.

From the triangle O ₁ AM ₁ then you can find the height of the trajectory O ₁ M ₁ and the distance AM ₁ :

O ₁ M ₁ = O ₁ A * sinh, AM ₁ = O ₁ A * cosh.

Find the binding of the found flight parameters of the projectile with geographical coordinates. To do this, determine the geographical coordinates of point M.

Consider the triangle ASO ₁ . According to the cosine theorem, we have:

.

.

Find the length of the side

.

.

From the right triangle O ₁ CM ₁ we have

.

.

Three sides are known in the oblique triangle AM ₁ C. Using the cosine theorem, we can find the angle at the vertex A:

MC ² = AC ² + AM ² -2 * AM * AC * cosA, whence:

angle A = -arccos (MS ² -AC ² -AM ² ) / 2 * AC * AM

Having found the angle at the vertex A, we can find the azimuthal angle of point M relative to the known coordinates of point A: X _A , Y _A :

∠A _East = ∠CAN-∠A,

where истA _East - the azimuth of point M ₁ relative to point A.

CAN angle - the angle of the interdirect speaker and the direction to the North.

Then the coordinates of the point M ₁ can be found:

Y ₁ = AM ₁ * cos A _source + Y _A , X ₁ = AM ₁ * cos A _source + X _A ,

where X _A and Y _A are the geographical coordinates of point A.

After the second acoustic measurement (similar to the first), we will have the coordinates of the second point of the trajectory - X ₂ , Y ₂ . At two points on the earth's surface, you can draw a straight line - the projection of the trajectory of the projectile on the Earth's surface in the form of a straight line equation:

Y = k * X + Y ₁ ,

where k = (Y ₂ -Y ₁ ) / (X ₂ -X ₁ ).

Putting the projectile’s flight range on this straight line, we get the projectile’s point of impact: X _K , Y _K. The coordinates of the endpoint of the projectile flight and the equation of the direct trajectory can be communicated to interested persons, military and civilian, so that they take appropriate measures.

According to FIG. 5 after the second measurement, you can clarify the values of the projectile speed and the angle of inclination of the trajectory. We have:

O ₂ K = O ₂ M ₂ -O ₁ M ₁ , then tgα = O ₂ K / O ₁ K, α = arctgO ₂ K / O ₁ K

Refinement of the projectile speed ϑ _sn can be carried out if the time between two consecutive measurements Δt ₁₂ is known:

Given the decrease in the projectile trajectory over time, the above expressions allow you to independently determine the projectile launch point, that is, to clarify the coordinates of the guns found previously using geophones.

The projectile motion parameters found in the work make it possible to clarify the point of incidence by modeling or to determine this point directly, according to the shooting tables.

The information transmitted by radio can be the calculated point of incidence and the equation of the line corresponding to the projectile flight path.

The considered system for determining the parameters of the trajectory of a supersonic projectile can be mounted on a car and quickly put forward for measurements. Information transfer can be organized on a certain frequency of the radio channel and can be automated.

Literature

1. Dzhereleiko R. Fire Detection System "Owl". Military equipment, 2011.

2. RF patent No. 2358275, G01S 3/808. Method and system for determining the trajectory of a supersonic projectile. Barter James I. - US, Milligan Stephen D. - US, Brynn Marshall Set - US, Mullen Richard J. - US. PCT Publication: WO 2006/096208 (09/14/2006).

3. RF patent No. 2516205, F41J. The method of determining the coordinates of the point of incidence of ammunition. Koziratsky Yu.L., Kuleshov P.E., Chernukho I.I. Publication date Thursday, October 10, 2013.

4. Patent No. 2470252, F41J. A method for determining the position coordinates in space and in time of bullets and shells. Bliznyuk A.M., Kochnev Yu.V., Khoroshko A.N. Publication date Thursday, December 20, 2012.

5. Patent No. 2231738, F41J. A method for determining the external ballistic characteristics of the flight of bullets and shells. Date of publication: Tuesday, February 10, 2010.

6. Patent No. 2392577, F41J. Device for determining external ballistic parameters based on acoustic sensors. Afanasyeva N.Yu. et al. Date of publication: Wednesday, January 27, 2010.

7. Krasilnikov V.A. Sound and ultrasonic waves in air, water and solids. - M .: State publishing house of physical and mathematical literature, 1960.

Claims (1)

A method for determining the flight path of a supersonic projectile, including sound sensors oriented at an angle to the direction of the gun’s location, and a computer that processes the information received from the sensors, characterized in that the projectile path parameters are determined in two stages, the first of which determines the projectile launch point by seismological methods, and at the second - the determination of the trajectory parameters is carried out by acoustic methods, while at the first stage I use as seismic wave sensors there are three geophones located along one straight line in the horizontal plane at known distances, and on the second there are four sound sensors, three of which are located along the straight line in the horizontal plane also at known distances, and the fourth is located on the vertical of one of the three sensors taken as the base , as the measured parameters in both cases, the differences in the time of arrival of waves to the sensors relative to the base sensor are used, while the second stage uses dedicated micro roller and comparator maximum harmonics of the sound wave, then, taking into account the knowledge of the propagation velocity of seismic and sound waves, knowledge of the distances between the sensors and the time it takes for the sensor waves to form equations, the solution of which allows you to find the parameters for the first stage - the coordinates of the gun, and for the second stage - parameters projectile trajectories relative to the Earth.

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