EP0232762A1 - Method for acoustically determining the trajectory of projectiles and for the determination of the shortest distance projectile/target - Google Patents

Abstract

Arrangement for acoustic storey measurement, in particular for exercise targets moving at subsonic speed, which delivers the actual minimum storey / target distance by eliminating runtime errors by means of a microphone system and an evaluation device. The arrangement is designed with a minimal number of microphones, depending on the desired significance, with none of the microphones used having to be in the center of the target. Depending on the version, the user can define a target point, a target surface or a target body. It is not necessary to set the target course and / or height and speed. This arrangement can also be used for resting exercise targets.

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 supersonic projectiles 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 vectorial sizes of bullet, 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, because of the brevity of this process, the target movement and projectile path can be a straight line and the speed frequencies are assumed to be constant. 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. That means that depending on the mechanical and functional Boundary conditions of the unit target / microphone system an optimal system can be selected.

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.

1, the target center Z _M at the time t = 0 is in the coordinate origin and moves in the direction of the Z axis. The floor is at the same time at the end of the location vector R (t = ₀ ) and it is moving in the direction G .

• Ziel bahn
  
• Geschoßbahn
  

So the following applies:

• Finish course
  
• Bullet train
  

The momentary target - floor is then

wird.This distance becomes minimal, though

becomes.

vor:The shortest distance E _min is therefore at the time

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 Ziel bahn,
  • 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 Geschoßbahnberechnungen 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 4 nach der bekannten Beziehung
  

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 floor and target path,
  • 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 floor 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 4 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 the wind noise of the target together. 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 at rest and homogeneous.

The shape of the Mach cone generated by the projectile is taken into account when determining the projectile path, 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 ₁ is first sonicated, the microphone M ₂ after the measured time difference Δt _m . The well-known microphone distance M ₁ M * ₂ is then the distance V _z . Reduce Δt _m (V _z : target speed) or extend it in the reverse order of the sound.

und für die aus der gemessenen Impulsdauer T_m zu berechnende dopplerkorrigierte Impulsdauer

For the angle of incidence β of the shock wave, the speed of sound c then applies

and for the Doppler-corrected pulse duration to be calculated from the measured pulse duration T _m

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 arise, which have linear 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 from any generatrix about the distance to a target center point Z located arbitrarily on the Z axis. This distance E _{min determined} as a rotating vector family, it can be determined from the sign of its z component whether the projectile passage was in front of or behind the center of the target (front-rear 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 R ₁ wird zur Vereinfachung in die X - Z - Ebene gelegt und lautet daher

In Fig. 4 the microphone K is in the coordinate origin, the microphone L 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 R ₁ is placed in the X - Z plane for the sake of simplicity and is therefore called

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

The distance from R ₁ and R ₂ to G is

As is well known, the Mach angle a, the Mach number of the projectile M _G and the speed V _G apply

If Δt _{l is} the measured time difference between the sonication of the microphones K and L, the projectile covers the distance Δt _L .V _G. It therefore applies

The sizes c, V _G9 M _G and are known L who have favourited Sizes | R ₁ |, | R ₂ | and Δt _L are measured. From this are the components of R ₁ and R ₂ to calculate, the floor track sought is thus fixed.

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 _l , since x _{1 is contained} in x ₂ .

ausgewählt werden.There are therefore four explicit solutions with the property of mirror symmetry to the XZ plane or to the YZ plane due to the chosen approach. 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 trajectory can even be clearly defined and a target body can be defined.

• R ₃ ist der Abstandsvektor von M und der Geschoßbahn G. Der Abstand zwischen R ₁ und R ₃ auf G ist
  
• Δ t_M ist die gemessene Zeitdifferenz zwischen der Beschallung der Mikrophone K und M, |R ₃| wird ebenfalls gemessen. Δ _M und Δ _L liegen beide auf G_i es gilt daher
  
  und
  
  Ist G zur X-Y-Ebene parallel, wird |Δ _L| = 0. Da R ₁ in der X-Z-Ebene angenommen ist, muß Δ _M parallel zur Y-Achse liegen, und es ist ein vereinfachter Ansatz ohne Berechnung von Q möglich. Im Folgenden wird nur der komplizierte Fall |Δ _L|≠ 0 betrachtet.

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. to the computed microphone location

• R ₃ is the distance vector from M and the bullet trajectory G. The distance between R ₁ and R ₃ on G.
  
• Δ t _M is the measured time difference between the sonication of the microphones K and M, | R ₃ | is also measured. Δ _M and Δ _L are both on G _i it therefore applies
  
  and
  
  If G is parallel to the XY plane, | Δ _L | = 0. There R ₁ is assumed in the XZ level, must Δ _{M are} parallel to the Y axis, and a simplified approach is possible without calculating Q. 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

und

ergeben sich durch entgegen- gesetzte Rotation von R₁ und R₂ um den gesuchten Winkel

Bekannt ist M, gemessen wird |R ₃| und Δt_M, xM_ψ und yM_ψ sind gesucht.This coordinate transformation is shown in FIG. 6 as a projection into the XY plane. The selected floor trajectory is by the distance vectors R ₁ and R Given ₂ , the distance vectors of the actual floor path

and

result from the opposite rotation of R ₁ and R ₂ by the angle sought

Is known M , is measured | R ₃ | and Δt _M , xM _ψ and yM _ψ are sought.

Es liefert als Lösung

Für y_Mψ existieren, bedingt durch die Spiegelsymmetrie zur X-Z-Ebene, zwei Lösungen. Die in Fig. 6 dargestellte Projektion der Lösung in die X-Y-Ebene ist also noch an der X-Achse zu spiegeln (R ₁", R ₂").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 y _Mψ . 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. 5) introduced. The rotation of M is then carried out so that A and G include the Mach angle α. | R ₃ | 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 vectors 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.

Wie in den vorstehenden Rechnungen ausgeführt, ergibt sich |Δ _N| aus einer der möglichen Laufzeitdifferenzen, zum Beispiel zu Mikrophon K, die Machkegelerzeugende e folgt dann aus der Vektorsumme

Erfüllt dieser Vektor das obenstehende Skalarprodukt nicht, ist die zweite Möglichkeit mit R ₁" und Δ _N" die damit eindeutig bestimmte Geschoßbahn.An approach using the Mach angle α without knowing the distance | R ₄ | is also possible. 7 applies

As stated in the above calculations, the result is | Δ _N | from one of the possible transit time differences, for example to microphone K, the Mach cone generating e then follows from the vector sum

If this vector does not meet the scalar product above, the second option is with R ₁ "and Δ _N "is the clearly defined bullet path.

The target center can be set arbitrarily in space 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. A sound pressure transducer arrangement for the acoustic detection of floor trajectories and storeys, in particular for moving exercise targets, with a microphone system and an evaluation device having an evaluation algorithm, characterized in that the sound pressure transducer arrangement has at least two spatially separated sound pressure transducers, the signals of which are spaced in the evaluation device on the basis of known physical relationships and data representing sound propagation time differences are implemented and fed to an evaluation computer, both for calculating a minimum storey / target distance, taking into account the spatial and temporal course of the target storey passage, and for a component of the storey passage in the direction of the connecting axis of the sound pressure transducer and that the calculated data serve to determine a plurality of projectile tracks which are rotationally symmetrical with respect to the connecting axis of the sound pressure transducers and which, in relation to d The minimum distance between target / floor and component in the direction of the named connection axis is clear, are with the target center on this axis. 2. Sound pressure transducer arrangement according to claim 1, characterized in that a further sound pressure transducer is arranged outside the connecting axis in a plane with the other sound pressure transducers, the signal of which is used to calculate an additional distance and / or a sound propagation time difference. 3. Sound pressure transducer arrangement according to claim 1 and 2, characterized in that a further sound pressure transducer is arranged so that it is off the plane and that the signal of this sound pressure transducer represents a further distance and / or a further sound propagation time difference for the unambiguous calculation of the projectile path. 4. A method for measuring the target Mach number with arrangements according to claims 1, 2 and 3, characterized in that at least two sound pressure transducers offset in the direction of target movement are sonicated jointly by a sound source moved with the target and located at a known location in front of or behind the microphones and that the transit time difference required to calculate the target Mach number is determined by means of cross-correlation of the signals from the two sound pressure transducers.

Images