RU2670731C2 - 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 a measuring technique, in particular the determination of the location of a firearm on the ground and the determination of the flight path of a projectile fired with it.

From the current level of technology known "Fire Detection System" Owl "" [1]. In addition, methods are known for determining position coordinates in space and in 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 (September 14, 2006) - [2].

The disadvantages of this technical solution are:

- the iterative nature of the computational process, which requires 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;

- the lack of determination of the point of incidence of the projectile.

The objective of this proposal is to accurately determine the parameters of the movement 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 the analytical description of the trajectory of movement with reference to the earth coordinates and the point of incidence of the projectile.

The solution of the problem is achieved by the fact that it is solved in two stages. At the first stage, the starting point of the projectile is determined by seismology methods. At the second stage, several acoustic measurements are used to determine the projectile altitude, specify the velocity of the projectile, determine the angle of inclination of the trajectory to the horizon, correct the starting point determined at the first stage, form an analytical description of the projectile trajectory tied to earth coordinates, determine the point of projectile falling.

Distinctive features of the prototype is that the determination of the parameters of the projectile's flight is not based on the shock wave, but on the sound accompanying the supersonic flight of the projectile, highlighting the base points in the accompanying sound to determine the propagation time of the wave to the sensors, linear arrangement of the reception sensors of both seismic waves and and acoustic, calculation of dynamic parameters of the flight trajectory, estimation of the coordinates of the point of incidence of the projectile, determination of the launch point by seismic wave.

Analysis of the proposed solution and the prototype allows to make a conclusion about its compliance with the conditions of patentability.

The invention is illustrated by drawings, which depict:

in fig. 1 is 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 shows: NA - direction of fire, point O - point of gun location, points A, B, C - points of location of seismic receivers attached to the coordinates of the earth's surface, d ₀ - distance from point A to gun, angle of SAO - angle between direction gun and straight speakers.

FIG. Figure 2 shows the geometric constructions for calculating the launching point of the projectile in a geographic coordinate system (stage 1) and determining the coordinates of the projectile trajectory (stage 2).

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

FIG. 4 shows the 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 straight speaker using the acoustic method (step 2).

FIG. 5 gives a geometrical picture of the calculation of the angle of inclination of the trajectory and parameters of the trajectory of the projectile for two calculated points.

FIG. 6 shows a block diagram of an equipment complex for determining the parameters of a projectile path.

The device works in this way as follows.

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

At the second stage of measurements, the parameters of the projectile trajectory and the velocity of the projectile are determined. These two stages together allow us to determine the direction of the shot and the point of landing of the projectile (place of defeat) and, thus, in advance, for example, by radio contact, to warn the personnel of the military personnel about taking appropriate measures.

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

It is known that when fired, a hard blow occurs on the Earth's crust, as a result of which an elastic wave arises, propagating over the surface of the Earth with some constant speed for a given area in all directions. This speed depends on the type of surface layer (for example, sand or rock) and is on average 1,500 meters per second. As you can see, the average speed 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 arrival of the sound from the passing projectile to the acoustic sensors is approximately determined. This is necessary, for example, for the timely activation of the equipment and the careful processing of the acoustic information received at this time.

The first stage is to determine the location of the gun seismically from the shot. To begin measurements, it is necessary to place three seismic receivers relative to the possible location of the gun. Place the seismic receivers in the 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 to the location of the gun, as shown in FIG. 1. Distances between sensors can be from units of meters to hundreds of meters.

The arrival time of the elastic wave front to seismic sensors will be determined using seismic receivers and a central computer, as shown in FIG. 6, bypassing the microcontrollers. According to this block diagram, the signals of each sensor are immediately transmitted to the central computer, and the latter captures the time of arrival of the elastic wave to the corresponding sensors. Further information is processed according to the algorithm described in this work.

Suppose we have an elastic wave propagation velocity equal to ν. This speed is mainly determined by the type of soil that fills the area, and must be known by 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, you need to make two equations. According to the figure, the elastic seismic wave arrives at some points in time at both point A and points B and C. The time of arrival of the wave to the sensors is fixed and differences are formed from it: t ₁ = t _B -t _A , t ₂ = t _C - t _A. The arrival time of the seismic wave to the sensor A will be considered as the base.

To form the calculated equations, we consider two oblique triangles ОАВ and ОАС - FIG. 1. Use the formula (cosine theorem):

a ² = b ² + c ² -2 * b * c * cosχ,

where side a is located opposite the angle χ.

For our case we have:

,

,

where the first equation holds for the triangle OAB, the second one is for OAC.

This system of two equations contains two unknown parameters: angle χ ₀ and 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 compiled on the basis of measuring the moments of arrival of the elastic wave to the corresponding sensors. Given the above ratios, we write:

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

Open the brackets and simplify the expression, we get:

If to designate

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 ,

we have:

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

d ₀ = x ₁ , d * cos χ 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 by 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 set the angle χ ₀ from point A, i.e to postpone the angle of the SAO, and on the ray AO to postpone the distance d ₀ . In the geographic coordinate system, the location of the gun can be found as follows.

According to FIG. 2, for the sensor system, the angle of inclination of the straight speaker to the equator line is known - angle γ. The azimuth angle (the angle between the direction to the North (NA) and the direction to the point of location of the gun, the angle NAC) will be equal to 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. From these coordinates, it is easy to find the location of the point of the gun shot.

Second phase. At this stage, the coordinates of the projectile passing over a given terrain are determined: the angle of inclination of the projectile’s trajectory, the speed of the projectile passing, the coordinates of the location of the gun, which duplicate the same coordinates found along 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 previously determined coordinates of the location of the gun, the point of fall of the projectile can be determined, and the coordinates of this point can be transferred to the serviceman of the shelling territory for taking appropriate measures. The time limit for taking appropriate measures can be 15-25 seconds.

The basis for determining the parameters of the trajectory of the projectile is a method for determining the distance and angle of the azimuth to the point of movement of the projectile using the acoustic method. It is known that a 150-mm projectile flies at an initial supersonic speed of about 900 meters per second. Near the point of the shot (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 be a parameter for determining the projectile flight path. Sound waves are easily recorded by sound microphones. We will use the same points that were used in seismic measurements and place sound sensors in them, with three of them placed in a horizontal plane on the same line (these are previously defined points with sensors A, B, C; however, if the seismic receivers are located on some depth in the Earth, the acoustic sensors are located above the Earth) and one sensor D is placed above the sensor A in the vertical at a certain height of 2 ... 5 meters. We will locate a microcontroller somewhere close by, connect the sensors to the microcontroller and the central computer with electric communication lines. In the measurement process, it is important to determine the distance to the projectile, the azimuth angles in order to determine the coordinates of the trajectory and the speed of flight in a geographic 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 incidence of the projectile.

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

To implement this, let each microphone have its own microcontroller, processing only the signals arriving in its channel (Fig. 6). Let these microcontrollers operate on a single master clock generator. The task of each microcontroller is to accept an analog signal and translate it into a digital code with a high degree of discreteness. Calculations should be carried out in real time, that is, in the rhythm of the sound wave coming from the projectile. 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 discretes are compared in amplitude without a sign. In this case, the compared amplitudes can be both positive and negative. The first discrete input to the microcontroller is called the previous one (t = i + 1), and the next one after it is the next one (t = i) (Fig. 3). If by comparison the comparator of two adjacent discrete ones is higher than the previous one, a decrease in the harmonic value takes place. If the subsequent discrete is equal in magnitude to the previous one or becomes larger than it, it can be stated that the passage of the maximum takes place. In this case, the microcontroller should send a signal to the central computer to reach the maximum on this sensor. The time to determine the maximum values should be recorded. Differences in the appearance of maximum values on the respective sensors relative to the base sensor will be involved in calculating the trajectory parameters.

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

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

a ² = b ² + c ² * b * c * cos χ ₁ ,

where side a is located opposite the angle χ ₁ , angle SAO ₁ .

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

For our case we have:

,

,

where the first equation holds for the triangle OAB, the second one is for OAC.

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 OC = 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 compiled on the basis of measuring the moments of arrival of the elastic wave to the corresponding sensors. Given the above ratios, we write:

Here, AB = a , B = b, a and b are known distances between sensors.

Open the brackets and simplify the expression, we get:

If to designate

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 ,

we have:

,

,

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

d ₁ = x ₁ , d ₁ * cos χ 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 ϑ, 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 geographic coordinate system.

Acoustic sensor at point D will determine the elevation angle of the point O of the trajectory above the horizon - the angle h.

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

It can be seen from the figure that the sound signal comes first to sensor D, and then to sensor A. If you know the distance to point O ₁ , this distance was determined, it is d ₁ , you can determine the angle O ₁ AO = β.

From the triangle O ₁ AD you can see 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, from where

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 a binding of the found parameters of the flight of the projectile with geographic coordinates. For this it is necessary to determine the geographical coordinates of point M.

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

.

.

Find the side length

.

.

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, from where:

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

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

∠A _ist = ∠CAN-∠A,

where ∠A _east is the azimuth of point M ₁ relative to point A.

The CAN angle is the angle between the direct 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 conducting the second acoustic measurement (similar to the first), we will have the coordinates of the second point of the trajectory - X ₂ , Y ₂ . You can draw a straight line at two points on the earth’s surface - a projection of the projectile’s trajectory on the surface of the Earth as a straight line equation:

Y = k * x + y ₁ ,

where k = (Y ₂ -Y ₁ ) / (X ₂ -X ₁ ).

Putting off on this straight range of the projectile, we get the point of falling of the projectile: X _K , Y _K. The coordinates of the final point of the projectile’s 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, it is possible to clarify the values of the velocity of the projectile and the angle 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 velocity of the projectile ϑ _cf can be carried out if the time is known between two successive measurements of Δt ₁₂ :

Taking into account the reduction of the trajectory of the projectile with time, the above expressions allow you to independently determine the launch point of the projectile, that is, to clarify the coordinates of the gun, found earlier with the help of seismic receivers.

The parameters of the projectile motion found in the work make it possible to specify the point of incidence by simulating or determine this point directly using the firing tables.

As information transmitted by radio, there can be a calculated drop point and the equation of a straight 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 vehicle and be promptly advanced for measurements. Information transfer can be organized on a certain frequency of the radio channel and can be automated.

Literature

1. Dzhereleiko R., “Owl” fire detection system. Military equipment, 2011.

2. RF patent №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 Seth - US, Mullen Richard J. - US. PCT Publication: WO 2006/096208 (September 14, 2006).

3. RF patent №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. The method of determining the coordinates of the position 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. The method of 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. Afanasyev N.Yu. and others. Publication date: Wednesday, January 27, 2010.

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

Claims (1)

The method for determining the flight path of a supersonic projectile, including sound sensors, oriented at an angle to the direction of the gun, and a computer processing information obtained from sensors, characterized in that the parameters of the projectile trajectory are determined in two stages, the first of which determines the launch point of the projectile seismological methods, and on the second - the definition of the trajectory parameters is conducted by acoustic methods, while at the first stage I use as sensors for seismic wave sensors There are three seismic receivers located along one straight line in the horizontal plane at known distances, and the second has four sound sensors, three of which are located along a 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 baseline. , as measured parameters both in one and in the other cases, the differences in the time of arrival of the waves to the sensors relative to the base sensor are used; in the second stage, the selected microconds are used a roller and a comparator, the maximum harmonic values of the sound wave, further, taking into account the knowledge of the propagation speeds of seismic and sound waves, knowledge of the distances between the sensors and the time at which the sensors reach the waves, equations are compiled, the solution of which allows finding the parameters for the first stage — the coordinates of the gun, and for the second stage — the parameters trajectory of the projectile relative to the Earth.