EP0232762B1 - Method for acoustically determining the trajectory of projectiles and for the determination of the shortest distance projectile/target - Google Patents

Description

The invention relates to an arrangement for acoustic projectile placement measurement, in particular for moving exercise targets, with a microphone system and evaluation devices which are intended to determine the minimum projectile / target distance while eliminating runtime errors.

Acoustic methods for measuring floor deposition at stationary or moving targets at subsonic speed are based on the measurement of the conical shock waves generated by ultrasound-fast guns using one or more microphones. The relationships between the distance microphone / shock wave generation point on the projectile path and the shock wave amplitude or the shock wave duration are known. In the case of non-moving targets, the shortest storey / target distance can be derived directly from this.

Furthermore, it is known that the direct measurement is incorrect in the case of moving targets, so that - depending on the vector sizes of the projectile, target and sound speed - the correct result is obtained only in rare special cases.

To avoid these errors, both the spatial and the temporal course of the floor passage must be taken into account. For such a passage process, the target movement and projectile path can be assumed as a straight line and the speeds as constant because of the brevity of this process. However, a calculation is only possible if the spatial relationship of the floor track to the target track can be established. Two options are known for this.

DE-OS 31 22 644 describes a correction method for flying training targets, which is based on a weapon location and target location-related geometry. It requires specified, precisely adhered to flight courses, flight heights and flight speeds as well as control distances and floor speeds. The microphones used must be installed in the center of the target and the entire arrangement must have an acoustic spherical characteristic.

Another possibility is described in EU-PS 0 003 095. There, a three-dimensional arrangement, consisting of a microphone system with at least four microphones and an additional system, that is to say a total of at least five microphones, provides a target-specific geometry which enables independence from flight courses and flight heights. The microphone arrangement can also be located outside the target center.

The object of the present invention is to provide an arrangement which excludes runtime errors with a minimum number of microphones and provides sufficient information for evaluation, such as signal amplitudes, signal duration and runtimes, so that only a small number of training parameters have to be defined before a shooting exercise. This object is achieved by the characterizing features of claim 1.

The measure according to the invention offers the possibility of determining the types and number of available information with the number of microphones and their geometric position to the center of the target. This means that an optimal system can be selected depending on the mechanical and functional boundary conditions of the target / microphone system unit.

Further developments and advantageous refinements of the invention can be found in the subclaims.

• Fig. 1 eine Prinzipdarstellung zur Ermittlung der Minimalentfernung Geschoß/Ziel,
• Fig. 2 eine Darstellung zur Erläuterung der Dopplerkorrektur und des rechnerischen Mikrophonortes,
• Fig. 3 ein Rotationshyperboloid,
• Fig. 4 ein Raumdiagramm mit einem Mikrophon im Koordinatenursprung und einem am Ende eines Vektors in einer Raumachse liegenden Mikrophon,
• Fig. 5 ein Raumdiagramm mit drei in einer Ebene liegenden Mikrophonen,
• Fig. 6 ein Diagramm zur Erläuterung der Koordinatentransformation und
• Fig. 7 ein Diagramm für ein dreidimensionales Mikrophonsystem mit vier Mikrophonen.

The invention is explained in more detail with reference to the drawings. Show it:

• 1 is a schematic diagram for determining the minimum distance floor / target,
• 2 shows a representation to explain the Doppler correction and the computed microphone location,
• 3 shows a rotational hyperboloid,
• 4 shows a spatial diagram with a microphone in the coordinate origin and a microphone lying at the end of a vector in a spatial axis,
• 5 shows a spatial diagram with three microphones lying in one plane,
• Fig. 6 is a diagram for explaining the coordinate transformation and
• Fig. 7 is a diagram for a three-dimensional microphone system with four microphones.

• Es gilt also:
• Zielbahn
  
• Geschoßbahn
  
• Die Momentanentfernung Ziel - Geschoß ist dann
  
  
• Diese Entfernung wird minimal, wenn
  
• wird.
• Die kürzeste Entfernung E_min liegt also zum Zeitpunkt
• tmin.
• ^tmln
  
• vor.
• Dieser Wert ist in ^*) einzusetzen und E_min zu berechnen.

In the basic illustration according to FIG. 1, the target center Z _{m is} at, time t = 0 in the coordinate origin and moves in the direction of the Z axis. The storey is at the same time at the end of the local vector R (t = 0) and it is moving in the direction of G.

• So the following applies:
• Finish line
  
• Bullet train
  
• The momentary target - floor is then
  
  
• This distance becomes minimal, though
  
• becomes.
• The shortest distance E _min is therefore at the time
• tmin.
• ^t mln
  
• in front.
• This value must be inserted in ^* ) and E _min calculated.

• A) Der kürzeste Abstand Geschoß/Ziel wird in vier Schritten ermittelt:
  • 1. Erfassen und Übertragen der erforderlichen akustischen Daten,
  • 2. Berechnung der räumlichen Lage der Geschoßbahn oder der Geschoßbahnschar, deren Elemente in Bezug auf die Zielbahn alle den gleichen Informationsgehalt haben,
  • 3. Berechnung der Zeitparameter auf Geschoß- und Zielbahn,
  • 4. Berechnung des kürzesten Abstandes Geschoß/Ziel.
  
  Die Zeitparameter sind elementar aus Geschoß-, Ziel- und Schallgeschwindigkeit sowie dem Abstand zum ersten beschallten Mikrophon ableitbar. Die Geschoßbahnberechnugen werden im weiteren Verlauf ausführlich dargestellt.
• B) Die Mikrophonsignale werden mittels eines geeigneten Telemetrieverfahrens einem Auswertungscomputer, der die erforderlichen Berechnungen durchführt, zugeführt.
• C) Sollen Temperatur- und Höheneinflüsse berücksichtigt werden, erfolgt die Bestimmung der aktuellen Schallgeschwindigkeit aus der Temperatur 5 nach der bekannten Beziehung
  
  
  Die Messung erfolgt in der Nähe der Mikrophone, die Information wird ebenfalls mittels Telemetrie dem Auswertungscomputer zugeführt.
• D) Mindestens zwei Mikrophone sind hintereinander in Zielbewegungsrichtung angeordnet, alle Mikrophonorte in Bezug auf den gewünschten Zielmittelpunkt sind bekannt.
• E) Die Abstände Mikrophon/Geschoßbahn werden über die bekannten Zusammenhänge zwischen Abstand und Stoßwellenamplitude bzw. -dauer bestimmt.

Before the systems are described in detail, there are a few explanations and agreements that apply to all systems:

• A) The shortest distance between floor and target is determined in four steps:
  • 1. acquisition and transmission of the required acoustic data,
  • 2. Calculation of the spatial position of the floor track or the floor track family, the elements of which all have the same information content in relation to the destination track,
  • 3. calculation of the time parameters on the projectile and target track,
  • 4. Calculation of the shortest floor / target distance.
  
  The time parameters can be derived from the floor, target and sound speed as well as the distance to the first sonic microphone. The projectile path calculations are shown in detail in the further course.
• B) The microphone signals are fed to an evaluation computer, which carries out the necessary calculations, by means of a suitable telemetry method.
• C) If temperature and altitude influences are to be taken into account, the current speed of sound is determined from temperature 5 according to the known relationship
  
  
  The measurement is carried out in the vicinity of the microphones, and the information is also fed to the evaluation computer by means of telemetry.
• D) At least two microphones are arranged one behind the other in the direction of target movement, all microphone locations with respect to the desired target center are known.
• E) The distances between the microphone and the bullet path are determined via the known relationships between distance and shock wave amplitude or duration.

When evaluating both pieces of information, the floor caliber used can be recognized within certain limits.

• F) With fast moving targets a Doppler correction of the measured pulse duration is necessary. The angle of incidence of the sound wave front required for this in relation to the direction of target movement is determined from a difference in sound propagation time between the microphones mentioned under D).
• G) Differences in sound propagation time between microphones are preferably carried out by forming and evaluating the cross-correlation function of the two microphone signals involved. This method provides great accuracy and further information even with high noise levels. The microphones mentioned under D) are exposed to wind noise from the target. The cross-correlation function therefore receives a maximum, from the position of which the Mach number of the target can be determined at a known speed of sound.
• H) The calculations are based on the principles of geometric acoustics. The air as a medium of propagation is assumed to be dormant and homogeneous.

The shape of the Mach cone generated by the projectile is taken into account when determining the projectile hand, there is no approximation by a flat wavefront. However, the shape is idealized. Errors that are known to occur at small intervals are corrected by the evaluation computer. Isotropic properties of the microphones are still assumed. The evaluation computer also corrects actual deviations from this.

I) In order to simplify the geometric representations, the microphone arrangement is assumed to be static. The microphone and target center are, however, not the actual, but "arithmetical" locations that are determined from the order of the sound, from measured time differences and the target speed. The shape of the Mach cone is taken into account. Only the locations calculated in this way are included in the floor path calculation.

2 shows an example to explain points F and I. The microphone M, is sonicated first, microphone M ₂ after the measured time difference △ t _m . The known microphone distance M, M ₂ ^* is then by the distance V _Z. To decrease Ot _m (V _z : target speed) or to extend it in the reverse order of the sonication.

und für die aus der gemessenen Impulsdauer T_. zu berechnende dopplerkorrigierte Impulsdauer

The angle of incidence β of the shock wave then applies with the speed of sound c

and for the measured duration of the pulse _T. Doppler corrected pulse duration to be calculated

The previous knowledge of the current speed of sound is not necessary for this correction.

In the simplest system, the target center and two microphones are on the target movement axis Z. Because of its rotational symmetry, such a one-dimensional arrangement is not able to clearly define a projectile path, but essential information is available.

With an imaginary rotation of the projectile path around the Z axis, the rotationally symmetrical surfaces of the second order are created, which have straight-line generators, that is, in the general case, a single-shell rotational hyperboloid with two generators. Only this is considered below, the simple special cases of circular cones and cylinders with one share each are included.

Such a rotational hyperboloid is shown in FIG. 3. G and G ^* are any generatrix of the two groups. It can be seen that the rotational symmetry can be used to derive the same information about the distance from a target center Z _m arbitrarily located on the Z axis from any generator. If this paragraph _t and _determined as a rotating vector family, its z-component can be determined from the sign if the bullet passage in front of or behind the aiming point was made (front-back detection).

Any projectile path G that is conveniently located in the coordinate system can be selected for the calculations, since the distance to be determined is the same for all paths.

Der Abstandsvektor ₁ wird zur Vereinfachung in die X-Z-Ebene gelegt und lautet daher

In Fig. 4 the microphone K in the coordinate origin, the microphone at the end of the vector L on the Z axis. The computed location of the microphone L is therefore in vector notation

The distance vector ₁ is placed in the XZ plane for simplification and is therefore called

Der Abstand von R, und ₂ auf G ist

Mit dem Machwinkel a, der Machzahl des Geschosss M_G und der Geschwindigkeit V_G gilt bekanntlich

It stands like vector R ₂ perpendicular to the floor trajectory G. For ₂ no component can be assumed to be zero.

The distance from R, and ₂ to G is

The Mach angle a, the Mach number of the projectile M _G and the speed V _G are known to apply

If △ t _{L is} the measured time difference between the sound of the microphones K and L, the floor covers the distance △ t _L V _G. It therefore applies

The sizes c, V _G , M _G and, the sizes | are known ₁ |, | R ₂ ] and △ t _L are measured. The components of ₁ and _{2 are} to be calculated from this, the floor track sought is thus fixed.

Die Lösung dieses Gleichungssystems liefert die 5 unbekannten Komponenten

4, the following system of equations can be applied:

The solution to this system of equations provides the 5 unknown components

The solution shows that the z-component of the distances required for the front-rear detection is clearly determined.

The signs of x ₁ and y ₂ are freely selectable, the sign of x ₂ must be the same as that of x ₁ , since x is contained in _X2 .

There are therefore four explicit solutions based on the chosen approach with the property of mirror symmetry to the X-Z plane or to the Y-Z plane. However, none of the solutions need to be the actual floor trajectory. Any path can be used to calculate the shortest distance

to be chosen.

Using a third microphone outside the Z axis creates a two-dimensional microphone system. It is thus possible to select two tracks from the projectile track sets described above which are mirror-symmetrical to the microphone plane, each of the two track sets providing a solution. The desired target center no longer has to lie on the Z axis, but can be moved to the microphone plane. It is also possible to define target areas in this level, for example in the form of vehicle silhouettes in the evaluation computer. If the target is shot from only one of the half-spaces defined by the microphone level, the projectile rail can even be clearly defined and a target body can be defined.

R₃ ist der Abstandsvektor von M und der Geschoßbahn G. Der Abstand zwischen R, und ₃ auf G ist

△t_M ist die gemessene Zeitdifferenz zwischen der Beschallung der Mikrophone K und M, |₃| wird ebenfalls gemessen. _M und _L liegen beide auf G; es gilt daher

und

5 shows a flat microphone system. It corresponds to that from FIG. 4 with the additional third microphone M. In order to simplify the calculation, it lies in the XZ plane with the vector M for the computed microphone location

R ₃ is the distance vector from M and the bullet trajectory G. The distance between R, and ₃ at G is

△ t _M is the measured time difference between the sound of the microphones K and M, | ₃ | is also measured. _M and _L are both on G; therefore it applies

and

If G is parallel to the XY plane, | _L | = 0. Since ₁ is assumed in the XZ plane, must Δ _{M are} parallel to the Y axis, and a simplified approach is possible without calculating 0. In the following only the complicated case | Δ _L | 0 considered.

The search for the pair of projectile paths is carried out by selecting any projectile path from the family and a mathematical rotation of M around the Z axis until the conditions of a system of equations are met.

The coordinates of the microphone to be rotated through the angle Ψ are then

This coordinate transformation is shown in FIG. 6 as a projection into the XY plane. The selected floor track is through the distance verifiers R ₁ , and R Given ₂ , the distance verifiers of the actual floor track R ₁ 'and R ₂ 'result from opposite rotation R ₁ and R ₂ around the searched angle Ψ = arctan

Is known M , is measured | R ₃ | and △ t _M , xM _Ψ and y _MΨ are wanted.

5 and 6, the following system of equations can be applied:

It provides a solution

Due to the mirror symmetry to the XZ plane, there are two solutions for yM _Ψ . The projection of the solution into the XY plane shown in FIG. 6 is therefore still to be reflected on the X axis ( R ₁ '' R ₂ '').

The floor track pair can also be determined using a different approach. The Mach cone is used for this A (See Fig. Introduced. The rotation of M is then performed so that A and G enclose the Mach angle a | R31 | then there is no need to measure.

If the two-dimensional microphone system is expanded by a fourth microphone outside the microphone plane XZ, a projectile path can be clearly determined. In Fig. 7 this fourth microphone N is, for example, in the YZ plane at the computed microphone location N shown. There are several possible solutions, for example, as already explained, with the aid of the measured distance and the scalar product with the two possible path verifiers or by means of arithmetical rotation of N around the Z axis. The latter approach then results in a double solution which is symmetrical to the YZ plane, of which only one is identical to a solution which was obtained with the aid of the microphone M.

An approach using the Mach angle a without knowing the distance | R4 | is also possible. 7 applies

As stated in the above calculations, we have | △ _N | from one of the possible transit time differences, for example to microphone K, the Mach cone generating B then follows from the vector sum

If this vector does not meet the scalar product above, the second option with R, "and G _N " is the uniquely determined projectile path.

The target center can be fixed anywhere in the room with the solutions resulting from the above approaches, and therefore a target body can be defined in the evaluation computer under all bombardment situations.

Claims (4)

1. An arrangement for converting sonic pressure in order to detect acoustically the paths and deviations of projectiles for moving practice targets, having a microphone system and an evaluation device having an evaluation algorithm, characterised in that the microphone system has at least two microphones separated in the direction of movement of the target, their signals being converted in the evaluation device on the basis of known physical relationships into data representing spacings and differences in sound propagation time and being fed to an evaluation computer, both for calculating a minimum spacing between projectile and target, while taking into account the path of the target-projectile in space and time, and a component of the projectile travel in the direction of the connection axis between the microphones and that the calculated data serve to determine a plurality of projectile paths running rotationally symmetrical to the connection axis between the microphones, said paths being synonymous, in relation to the minimum spacing between target and projectile and to the component in the direction of the said connection axis, with the centre point of the target on this axis.

2. An arrangement for converting sonic pressure according in claim 1, characterised in that a further microphone is arranged outside the connection axis in a plane with the other microphones, its signal serving to calculate an additional spacing and/or difference in sound propagation time.

3. An arrangement for converting sonic pressure according to claim 1 and 2, characterised in that a further microphone is so arranged that it lies outside the plane and that the signal of this microphone represents a further spacing and/or a further difference in sound propagation time in order to calculate the projectile path accurately.

4. A method of measuring the target Mach number with arrangements according to claims 1, 2 and 3, characterised in that at least two microphones offset in the direction of movement of the targets are jointly provided with sound from a sound source located at a known place before or after the microphones and moved along with the target and that the difference in propagation time required in order to calculate the target Mach number is ascertained with the aid of cross correlation of the signals of the two microphones.

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