JPH04372889A - Apparatus for measuring coordinates of supersonic flight body - Google Patents

Abstract

PURPOSE:To realize the title apparatus reduced in economical load and convenient to handle. CONSTITUTION:When orthogonal coordinates wherein the flight direction of a supersonic flight body to be measured is set to a Z-axis direction are set to X, Y, Z, a first shock wave detection sensor S0 is arranged to the origin O thereof and a second sensor SD is arranged on the negative coordinates (-d) of a Z-axis while a third sensor SR is arranged on the positive coordinates (a) of an X-axis and a fourth sensor SL is arranged on the negative coordinates (-b) of the X-axis. The detection outputs of the first-fourth sensors are respectively passed through first fourth waveform shaping devices E0-E1 to be inputted to a time interval measuring device F to measure the time intervals tauD, tauR, tauL of the output pulses of the first and second waveform shaping devices, the first and third waveform shaping devices and the first and fourth waveform shaping devices and the respective measured values are inputted to an operation device G. The operation device G calculates the x, y coordinates of the flight body piercing an XY plane using those measured values, preset coordinates (-d), (a), (-b) of the sensors and sonic velocity (c).

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for measuring the coordinates of a point passing through an XY plane perpendicular to the trajectory of a bullet, such as a bullet or a cannonball, flying at supersonic speed.

0002

[Prior Art] The first method conventionally used for this type of measurement is to set a target perpendicular to the trajectory of the bullet and measure the position of the hole made by letting the bullet hit the target, which is the most classic method. method, and is still the mainstream method. The second method uses shock waves, and as shown in Figure 6, the XY
In this method, an X-axis rod 3 and a Y-axis rod 4 are arranged at positions corresponding to the X-axis and Y-axis of the plane, respectively. In this method, vibration sensors 5 are attached to both ends of these rods whose lengths and vibration propagation speeds are known, and the positions xa and ya where the shock waves 6 generated by the bullet hit these rods at right angles are detected by the vibration sensors 5. This method is calculated from the time difference between the detected vibrations.

0003

[Problem to be Solved by the Invention] Generally, bullets are assumed to fly parallel to the ground, and of the x and y coordinates to be found, the X axis is set parallel to the ground and the Y axis is set perpendicular to the ground. , the detection part of a conventional device of this type needs to have a height greater than the y-coordinate measurement range. In the case of artillery shells, a coordinate measuring range generally extending over several meters is required, either by placing a target at a height of several meters (in the case of the first method) or by installing a Y-axis rod 3 (in the case of the second method). ), which was burdensome in terms of cost and inconvenient to handle. The present invention aims to solve the conventional difficulties and realize a measuring device that is easy to handle and has a low economic burden.

0004

[Means for Solving the Problems] When X, Y, and Z are orthogonal coordinates in which the flight direction of the supersonic flying object to be measured is the direction of the Z axis, in this invention, the system is installed at the origin O of the coordinates. a first shock wave detection sensor (hereinafter referred to as sensor) SO;
a second sensor SD installed on the negative coordinate (-d) of the Z axis; a third sensor SR installed on the positive coordinate (a) of the X axis; A fourth sensor SL installed on the coordinates (-b) of is used.

The detection outputs of the first to fourth sensors are input to first to fourth waveform shapers, respectively, and the output pulses of the first to fourth waveform shapers are inputted to a time interval measuring device. and the first and second, the first and third, and the first and fourth
Measure the time intervals τD, τR, and τL of the output pulses of the waveform shaper. Further, the coordinates -d, a, -b of the second to fourth sensors and the speed of sound c are set in advance in the calculation device, and the measured values τD, τR, τ of the time interval measuring device are set in advance.
By inputting L, the coordinates of a point P where the flying object passes through the XY plane of the orthogonal coordinates are calculated.

[0006]

[Embodiment] It is assumed that a flying object to be measured is moving in the atmosphere at a constant speed and supersonic speed in the vicinity of the measurement position. At this time, a conical shock wave whose shape is determined by the velocity v [m/s] of the flying object and the speed of sound in the atmosphere c [m/s] is generated. As shown in FIG. 3A, the trajectory 11 of the flying object is a straight line, the position of the flying object at an arbitrary time is P1, and the flying object is at a time delayed by an arbitrary time t [s] from the time when the projectile is at P1. Let the position of P2 be P2. If P3 is the point of contact when a tangent to a sphere of radius c·t [m] centered at P1 passes through P2, the shape of the shock wave generated by the projectile is as follows, with the trajectory 11 of the projectile as the central axis of rotation, Straight line P2 P3
It is a cone whose generating line is . ∠P1 P2 P3 as α
If [rad] is set, the following equation holds true.

[0007] sin α=P1 P3 /P1 P2 =c
t/vt=c/v (1)
cos θ={1-(sin α)2}1/2=
(1-c2 /v2)1/2 (1') In the example shown in Figure 1, four sensors are used to detect this shock wave, and the passing position of the flying object is measured on the coordinates determined by the sensor arrangement. do. Assuming that the trajectory of the flying object is a straight line, the direction of the speed of the flying object is the Z-axis direction. The shock wave sensor is a small device that detects the arrival of a shock wave and outputs a pulse, like an ultrasonic microphone or a pressure sensor, and its size can be ignored.

As shown in FIG. 3B, first, the first sensor S
0 and set this position as the origin O. The second sensor SD is installed at a negative position on the Z axis, and this position is called D. The third sensor SR is installed at a positive position on the X-axis, and this position is called R. The fourth sensor SL is installed at a negative position on the X-axis, and this position is called L. It is assumed that the flying object has a trajectory 11 orthogonal to the XY plane in a half space where the y coordinate is positive, and the intersection of the XY plane and the trajectory 11 is P. Here, a=OR[m], b=OL[m],
d = OD [m], r = PO [m], rR = PR [m]
, rL = PL [m], θ = ∠POR [rad]. The coordinates (x, y) of the desired point P are expressed by the following equation.

[0009] x=r・cos θ[m], y=r・sin θ[
m] (2)
Data a, b, d and the sound velocity c, which will be required later, are set in advance in the arithmetic unit F in FIG. Trajectory 1 of the flying object to be measured
1 can be set parallel to the ground, so in that case, the four sensors only need to be installed at the same height above the ground.

The pulse outputs of the sensors SO, SD, SR, and SL are transmitted through the first to fourth waveform shapers EO to 4, respectively.
It is input to the time interval measuring device E via EL, SD,
The pulse intervals between SO, between SO and SR, and between SO and SL are measured. The interval τD [s] between the detection pulses of the sensors SD and SO is the time from when the pulse of the sensor SD is generated until the pulse of the sensor SO is generated, and always has a positive value. Further, the interval τR [s] between the detection pulses of the sensors SO and SR is the time from the generation of the pulse of the sensor SO to the generation of the pulse of the sensor SR, and has positive, negative, or zero values. Sensor SO, SL
The detection pulse interval τL [s] is the time from the generation of the pulse of the sensor SO to the generation of the pulse of the sensor SL, and has positive, negative, or zero values. These measured values τD, τR, τL are supplied to the arithmetic unit G.

Since the projectile moves at a constant speed parallel to the Z-axis connecting D and O, the position of the projectile when the shock wave reaches D is PD and the shock wave reaches O as shown in FIG. 3C. If the position of the flying object at that time is PO, then the distance PD
PO [m] is equal to the distance DO [m]. Therefore, the velocity v [m/s] of the flying object is given by the following equation. v=P
O PD /τD = OD/τD = d/τD [m/
s] (3) Hereinafter, it will be explained with reference to FIG. The time from the moment the flying object reaches point P (the intersection of the XY plane and trajectory 11) to the point PO
[s] is, as is clear from the explanation using FIG.
It is equal to the time it takes for a sound wave to reach a conical surface with an apex angle of 2α with O as its apex. From the geometric properties of O, P, PO and the two conical surfaces, the shortest distance between the two conical surfaces is PO・cos α, which is equal to the length of the perpendicular drawn from the point P to the straight line OPO
= r·cos α [m] (Fig. 4A). Therefore, the time to for the sound wave to propagate through this shortest distance is given by the following equation.

[0012] to = (r・cos α)/c[s]

(4) The position of the flying object when the shock wave reaches R is PR (Figure 4B), the position of the flying object when the shock wave reaches L is PL (Figure 4C), and the flying object moves from point P to point Letting the time to reach PR be tR [s] and the time to reach point PL from point P to tL [s], then t
Similarly to the calculation of O, tR and tL are given by the following equations.

tR = (rR ・cos α)/c[s]

(5) tL = (rL ・cos α)/
c [s]
(6) The pulse interval τR [s] between the sensors SO and SR and the pulse interval τL [s] between the sensors SO and SL are obtained from equations (4) to (6) and given by the following equation. τR = tR −to = cosα・(rR
-r)/c[s] (7)
τL = tL −to = cosα・(rL
-r)/c[s] (8) rR
can be expressed by r, θ, a. As shown in FIG. 5, by drawing a perpendicular line from point P to the X axis and using the three-square theorem, the following equation can be obtained.

(r・sin θ)2+(a−r・cos θ
)2=rR2 ∴rR=(r2 −2・r・
a・cos θ+a2 )1/2 [m]
(9) Similarly, rL can be represented by r, θ, and b. (r・sin θ)2 + (b+r・cos
θ)2=rL2 ∴rL=(r2 +2・r
・b・cos θ+b2) 1/2 [m]
(10) Therefore, τR, τL are r, θ,
It can be represented by a, b, c, and α.

[0015] τR = cos α {(r2 −2・r・a・
cos θ+a2)1/2 -r}/c[s]


(11) τL = co
sα{(r2 +2・r・b・cos θ+b2)1/
2 -r}/c[s]

(
12) Next, solve equations (11) and (12) for r and cos θ.

A=τR ・c/cosα; B=τL ・c
/ cosα (
13), equations (11) and (12) become respectively
A=(r2 −2・r・a・cos θ+a2)1
/2 −r (11'
) B=(r2 +2・r・b・cos θ+b
2) 1/2 -r (
12'). From (11') (A+r)2=r2 -2・r・a・cos
θ+a2 A2 +2・A・r=−2・r
・a・cos θ+a2
From (11″) (12′) B2 +2・B・r=2・r・b・cos
θ+b2 (12
″) (11″) and (12″) are added here and there.
A2 +B2 +2r(A+B)=a2 +b2
∴r=(a2 +b2 −A2 −B2)/
2(A+B) (14)(
12″) for cosθ, we get c
os θ=(B2 +2・B・r−b2)/2rb
(15) If we substitute equation (14) for r in equation (15), we get cos θ
= {A(B2-b2)+B(a2-A2)}/b(a
2+b2-A2-B2)


(16) Using r in equation (14) and cos θ in equation (15), the coordinates x, y of point P are x = r cos
θ
(
17) y=rsin θ=r(1-cos2
θ) 1/2
(18) is required.

The procedure for measuring the coordinates (x, y) of the intersection point P between the flying object and the XY plane in the embodiment of FIG. 1 described above is summarized as shown in FIG. In step S1, the values of the sensor intervals a, b, and d and the sound speed c are preset in the arithmetic unit G. In step S2, shock waves are detected by the first to fourth sensors. In step S3,
The time intervals τD, τR, τL are measured by the time interval measuring device F.
are measured, and the measured values are supplied to the arithmetic unit G.

The arithmetic unit G calculates the velocity v of the flying object in step S4, and calculates the velocity v of the flying object in step S5.
sα (however, α is 1/2 of the apex angle of the cone created by the shock wave generated by the flying object), and in step S6, A=τR ・c/cosα; B=τL ・c/cos
Calculate α. Arithmetic unit G calculates r and cos θ (however, r and θ are polar coordinates of point P) in step S7, and calculates the x, y coordinates of point P in step S8.

These calculated values are displayed on the display H or outputted to the outside from the output terminal 20, if necessary.

[0020]

[Effects of the Invention] The coordinate measuring device according to the present invention can detect coordinate positions by arranging four small shock wave detection sensors on a plane parallel to the trajectory of a flying object, such as the ground. Compared to the conventional method of setting up a large coordinate detection target on the ground or erecting a pole with a vibration sensor, it can be constructed more economically and is extremely convenient to handle.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of the invention.

FIG. 2 is a waveform diagram of the main part of FIG. 1.

[Fig. 3] A is a cross-sectional view for explaining shock waves generated by a supersonic flying object, and B is a cross-sectional view of the first to fourth sensors SO in Fig. 1.
-C is a diagram for explaining the arrangement position of the flying object PO and PD at the time when the shock wave is detected by the first sensor SO and the second sensor SD, respectively.

[Figure 4] A shows the first, third and fourth sensors (SO , SR and S
L ) detects each shock wave tO ,
A diagram for explaining tR and tL.

[Figure 5] Passing position P of the flying object on the XY plane and the first
, a diagram showing the positions of the third and fourth sensors (SO, SR, and SL).

FIG. 6 is an operation flowchart of the embodiment of FIG. 1;

FIG. 7 is a diagram showing how a vibration sensor is installed in a conventional supersonic flying object coordinate measuring device.

Claims (1)

[Claims] Claim 1: When X, Y, and Z are orthogonal coordinates in which the flight direction of the supersonic projectile to be measured is the Z-axis direction, a first shock wave detection sensor (hereinafter referred to as sensor) SO and the negative coordinate of the Z axis (-d)
A second sensor SD is installed on the top, a third sensor SR is installed on the positive coordinate (a) of the X-axis, and a third sensor SR is installed on the negative coordinate (-b) of the X-axis. Fourth sensor S
L and the first to fourth sensors input the detection outputs of the first to fourth sensors, shape the waveforms, and output pulses.
by inputting each output pulse of the waveform shaper and the first to fourth waveform shapers, and output pulses of the first and second, first and third, and first and fourth waveform shapers. time interval τD
, τR and τL, and the coordinates -d, a, -b and sound speed c of the second to fourth sensors are set in advance, and the measured values τD,
A supersonic projectile coordinate measuring device, comprising: an arithmetic device that inputs τR and τL and calculates the coordinates of a point P where the projectile passes through the XY plane of the orthogonal coordinates.