GB1601354A

GB1601354A - Apparatus for determining the position of an object in space

Info

Publication number: GB1601354A
Application number: GB1641177A
Authority: GB
Original assignee: MS Instruments Ltd
Current assignee: MS Instruments Ltd
Priority date: 1978-04-20
Filing date: 1978-04-20
Publication date: 1981-10-28

Description

(54) APPARATUS FOR DETERMINING THE POSITION OF AN OBJECT IN SPACE (71) We, MS INSTRUMENTS LIMITED, a British Company of Rowden Road, Beckenham, Kent BR3 4NA, do hereby declare the invention, for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement:- This invention relates to a method and apparatus for use in detecting the path of a projectile.

It is possible, by means of the invention, to compute the angles of elevation and azimuth of a projectile and to record the co-ordinates of its path by means, for example, of a computer.

In a preferred embodiment of the invention there is provided means to detect the relative times between the passage of a projectile through four planes, the relative angles of elevation and azimuth of the planes being known.

In the preferred embodiment, the planes are defined by optical sensing heads, each of which views the natural light which occurs in a fan-like region extending from it over an arc of some 30 , the region subtending a narrower angular thickness of some 0.17 at the sensing head. The projectile in passing through a plane interrupts the light normally received by the respective optical sensing head and causes an output signal to be produced from the head. The principle of operation of suitable optical sensing heads is known.

The time intervals between the interruptions of the light normally received by the heads can be related to distances and, since the angular relationships between the arcuate regions that are being monitored are known, it is possible to correlate these distances with each unique path of a projectile passing through the arcuate regions.

Other forms of sensor than those described can be employed. For example, if the projectile emits infrared radiations, sensors which detect infrared radiations in a given plane can be used.

An embodiment of the invention will now be described with reference to the accompanying drawings, in which: Figure 1 is a diagrammatic plan view of a sensor arrangement showing trigonometrical construction lines, Figure 2 is a detail of the construction line arrangement shown in Figure 1, Figure 3 is a further plan view of the construction line arrangement of Figure I, Figure 4 is a diagrammatic side elevation of the sensor arrangement showing trigonometric construction lines, Figure 5 is a plan view of a trigonometric construction based on the arrangement shown in Figure 1, Figures 6 and 7 are diagrammatic views illustrating respectively the X and Y axes of the sensor arrangement and their associated sign conventions, Figures 8 and 9 are a plan and a side elevation respectively of a different arrangement of the sensors and Figure 10 is a block schematic electric circuit diagram.

Referring to Figure 1, there is shown a plan view of six optical sensing heads, la-6a placed on the ground. For the purpose of determining the x co-ordinate of a projectile passing within the range of the sensors, the functions of the heads la-4a only will be considered. The heads la4a are arranged to view respective regions 1 to 4 which extend vertically from the respective heads over a length corresponding to an arc of 30 at the head in the particular embodiment being described. The regions 1 to 4 have a very small width and each subtends an angle of 0.17 at its respective head in the direction of its width. The regions 1 and 4 are separated by a distance d. An axis 10 at which x=0 passes effectively through the origins of the regions 1 to 4.The axis 10 is at right angles to a target reference plane 11 which is at a distance dl2 from each of the regions. The regions 2 and 3 each intersect the plane 11 at an angle 8. A velocity vector 12 of a projectile passes through the regions at an angle a to the x axis.

It will be appreciated that, since the times of travel of the projectile between the regions 1 to 4 are directly related to the distances between the regions, it is possible to measure the times taken and to consider them as distances for the purpose of the trigonometric calculations to be made.

Thus, considering T to be the transit time of a projectile between the regions 1 and 4, t, to be the transit time between the regions 3 and 4 and t2 to be the transit time between regions 2 and 4, it is possible to construct on Figure 1 two triangles about the vector 12, which are better seen in Figure 2, and from which the values A, B, D, E and tan a can be derived as follows:- BTt A = t1 - T -2 2 2 D, B coscC - A cosd , cos α (B - A) tan tan 3 tan 6 E = B COSeC + A cost - cos( (B + A) tan = D = 1 (B - A) =(T/2 - t2 + T/2 - tl) 1 E tane (B + A) (T/2 - t2 + t1 - T/2) tan e

Knowing the transit times, T, t2 and t, and the angle o it is possible to compute the azimuth angle a of the projectile.

To establish the x co-ordinate of the velocity vector at its point of intersection with plane 11, let us consider the distance of the intersection with the plane 11 from the x=0 axis to be xt.

Referring now to Figure 3, it can be shown that, if the vector 12 of the projectile were parallel with the x=0 axis 10 along the line 14, the x co-ordinate of the point of intersection of the vector 12 with the plane 11 would be: (T 2t1)d x= (2) 2T tan 0 It is thus possible to rotate the line 14 mathematically through the angle a so that the line 14 coincides with the vector 12 in order to determine the x co-ordinate x, for a velocity vector at an angle a to the x axis 10 as follows::- Upon rotation of the line 14 through the angle a, T becomes T cos a, A is increased by A (cosa+tan8 sina) to become A1, and t1 becomes A (cosα+tan# sina)+T/2 cosa, where A=(t1-T/2) on substituting T cos a for T, and T/2 cos a+A(cos a+tan 0 sin a) for t1 in equation (2) above, we obtain:- (T-Zt1)(1+tan 0 tan a)d x,= (3) 2 T tan U Referring now to Figure 4, the determination of the co-ordinates and the angle of the vector 12 about they axis will now be described with reference to a side view of the sensors taken in the direction of the arrow IV in Figure 1. It will be appreciated that the sensors 5a and 6a are immediately behind the sensors 4a and la and are not visible in this Figure. Furthermore, the regions 2 and 3 are not indicated since they are not involved in the present considerations.

It will be noted that the arcuate planar regions 5 and 6 extending from the sensors 5a and 6a are inclined with respect to the regions 4 and 1 respectively, by angles .

A y=O axis 15, which passes through the cross-over point of the regions 5 and 6, is parallel to and at a distance h from the plane in which the sensors lie. The distance between the regions 1 and 4 is d and the vector 12 is at an angle A with respect to the y axis 15.

Thus, considering T to be the transit time of the projectile between the regions 1 and 4, t3 to be the transit time of the projectile between the regions 6 and 4 and t4 to be the transit time between the regions 5 and 4, we can note the similarity with the trigonometric construction shown in Figure 1 and substitute the above terms T, t3 and t4 in equation (1) to obtain the value for tan 25.

Similarly, the y co-ordinate value for the vector 12 in the target reference plane I I can be shown by comparison with equation (3) to be (t-2t3)(ltan # tan P)d (5) 2 T tan y The velocity v of the projectile is given by: d # = --------- T cos α cos p It will be seen that the height h of the y--O axis above ground=d/2 tan (90-qli) or h=d/2 tan r.

Referring now to the arrangement shown in Figure 5, an explanation will be given of the way in which the coordinates of the vector 12 can be determined at a new target plane which is spaced from, but parallel to, the reference plane 11. In Figure 5 a target plane 16 is at a distance D from the reference plane 11. The vector 12 crosses the plane 16 at a distance X from the x=0 axis 10, is at an angle a with respect to the x=0 axis and crosses the reference plane 11 at a distance xl from the x=0 axis.We thus have X=x,+D tan t giving:

Similarly, in the case of the separation of the target plane by D from the y reference axis, the co-ordinate Y of the point at which the vector crosses the new target plane is:

Sign conventions indicating the positions of the co-ordinates and the angular directions of the vector 12 are shown with respect to the x=0 axis in Figure 6 and with respect to the y=O axis in Figure 7. The signs of the co-ordinates and of the angular values derived from the above calculations are used in accordance with the conventions illustrated in Figures 6 and 7 to resolve any ambiguities there may be about the position of a co-ordinate or the direction of a vector.

With the configuration of sensors described above, it is not possible to calculate the angles a and P for the particular case when a projectile passes centrally through the array, because the values of t, and t2 are then equal to zero.

To overcome this problem it is possible to arrange the sensors in a different way, for example, that shown in Figures 8 and 9 in plan view and side view respectively, with a new x=0 axis 20 and a newsy=0 axis 21, each being displaced by a distance W from the original x=0 axis 10 and=0 axis 15.To determine the values of x' and ' with this configuration, it is necessary to subtract the offset distance W from the values of x and y determined according to the equations (3) and (5) above, as follows: (T-2t,)(l+tan 0 tan a)d -W 2T tan 0 (T-Zt,)(l+tan $ tan p)d Y'= -W 2T tan x,b Referring now to Figure 10, there is shown an arrangement in which the three pairs of optical sensors la to 6a are positioned with a distance of 5 meters between the pairs of sensors 6a, la, and 5a, 4a. A target plane 25 is arranged at a distance of 2 metres from the sensors 5a, 4a and 4.5 metres from the reference plane (not shown) in the manner described with reference to Figure 5. The outputs from the sensors la to 6a are fed by cables 26 to a junction box 27 and thence via a cable 28 over a distance of some 1,500 metres to a computer 29. The computer 29 is programmed to perform the calculations set out above and to feed the results to a printer 30.

It will be appreciated that, although the invention has been described, by way of example, with reference to a particular embodiment, variations and modifications can be made within the scope of the invention. For example, it is possible when the projectile is a bullet or a shell, to measure the muzzle velocity of the projectile by means of detectors adjacent to the muzzle of the rifle or gun and at a known distance from the optical sensing heads, to feed this information to the computer 29, to correct for any retardation on the projectile in crossing the space above the optical sensors and to correct for any effect resulting from the fact that the arcuate regions viewed by the optical sensors have slightly different widths at different heights.

WHAT WE CLAIM IS: 1. A method for use in detecting the path of a projectile which includes arranging a first pair of electromagnetic radiation detectors to detect the passage of a projectile through a first pair of planar regions parallel to a target reference plane and a second pair of electromagnetic radiation detectors to detect the passage of the projectile through a second pair of planar regions each arranged at a predetermined angle of azimuth 0 with respect to the target reference plane, determining the projectile transit times T between the first pair of planar regions, t1 between a first one of the second pair of planar regions and one of the first pair of planar regions and t2 between the second one of the second pair of planar regions and the said one of the first pair of planar regions and computing the angle of azimuth a of the projectile from the said times T, t1, and t2 and the value of the said predetermined azimuth angle 0.

2. A method as claimed in claim 1 including the further step of computing the x co-ordinate of the point of intersection of the projectile with the target reference plane from the said time values T, t1, and the predetermined angle of azimuth 0, the separation distance d of the first pair of planar regions and the angle of azimuth a.

3. A method as claimed in either claim 1 or claim 2, including a third pair of electromagnetic radiation detectors arranged to detect the passage of the projectile through a third pair of planar regions, each of the third pair of regions being arranged at a predetermined angle of inclination (,b with respect to one of the first pair of planar regions, determining the projectile transit times t3 between one of the

**WARNING** end of DESC field may overlap start of CLMS **.

Claims

**WARNING** start of CLMS field may overlap end of DESC **. angular values derived from the above calculations are used in accordance with the conventions illustrated in Figures 6 and 7 to resolve any ambiguities there may be about the position of a co-ordinate or the direction of a vector. With the configuration of sensors described above, it is not possible to calculate the angles a and P for the particular case when a projectile passes centrally through the array, because the values of t, and t2 are then equal to zero. To overcome this problem it is possible to arrange the sensors in a different way, for example, that shown in Figures 8 and 9 in plan view and side view respectively, with a new x=0 axis 20 and a newsy=0 axis 21, each being displaced by a distance W from the original x=0 axis 10 and=0 axis 15.To determine the values of x' and ' with this configuration, it is necessary to subtract the offset distance W from the values of x and y determined according to the equations (3) and (5) above, as follows: (T-2t,)(l+tan 0 tan a)d -W 2T tan 0 (T-Zt,)(l+tan $ tan p)d Y'= -W 2T tan x,b Referring now to Figure 10, there is shown an arrangement in which the three pairs of optical sensors la to 6a are positioned with a distance of 5 meters between the pairs of sensors 6a, la, and 5a, 4a. A target plane 25 is arranged at a distance of 2 metres from the sensors 5a, 4a and 4.5 metres from the reference plane (not shown) in the manner described with reference to Figure 5. The outputs from the sensors la to 6a are fed by cables 26 to a junction box 27 and thence via a cable 28 over a distance of some 1,500 metres to a computer 29. The computer 29 is programmed to perform the calculations set out above and to feed the results to a printer 30. It will be appreciated that, although the invention has been described, by way of example, with reference to a particular embodiment, variations and modifications can be made within the scope of the invention. For example, it is possible when the projectile is a bullet or a shell, to measure the muzzle velocity of the projectile by means of detectors adjacent to the muzzle of the rifle or gun and at a known distance from the optical sensing heads, to feed this information to the computer 29, to correct for any retardation on the projectile in crossing the space above the optical sensors and to correct for any effect resulting from the fact that the arcuate regions viewed by the optical sensors have slightly different widths at different heights. WHAT WE CLAIM IS:

1. A method for use in detecting the path of a projectile which includes arranging a first pair of electromagnetic radiation detectors to detect the passage of a projectile through a first pair of planar regions parallel to a target reference plane and a second pair of electromagnetic radiation detectors to detect the passage of the projectile through a second pair of planar regions each arranged at a predetermined angle of azimuth 0 with respect to the target reference plane, determining the projectile transit times T between the first pair of planar regions, t1 between a first one of the second pair of planar regions and one of the first pair of planar regions and t2 between the second one of the second pair of planar regions and the said one of the first pair of planar regions and computing the angle of azimuth a of the projectile from the said times T, t1, and t2 and the value of the said predetermined azimuth angle 0.

first pair of regions and one of the third pair of regions, and t4 between the other of the third pair of regions and said one of the first pair of regions and computing the angle of elevation fi of the projectile from the said times T, t3 and t4 and the value of the predetermined angle of inclination .

4. A method as claimed in claim 3 including the further step of computing the y co-ordinate of the point of intersection of the projectile with the target reference plane from the said time values T and t3, the distance d between the first pair of planar regions and the said angles of elevation fi and inclination .

5. Apparatus for use in detecting the path of a projectile which includes a first pair of electromagnetic radiation detectors arranged to detect the passage of a projectile through a first pair of planar regions parallel to a target reference plane, a second pair of electromagnetic radiation detectors arranged to detect the passage of the projectile through a second pair of planar regions each arranged at a predetermined angle of azimuth 0 with respect to the target reference plane, means coupled to the detectors for determining the projectile transit times T between the first pair of planar regions, t1 between a first one of the second pair of planar regions and one of the first pair of planar regions and t2 between the second one of the second pair of planar regions and the said one of the first pair of planar regions and means for computing the angle of azimuth a of the projectile from the said times T, t1, and t2 and the value of the said predetermined azimuth angle 0.

6. Apparatus as claimed in claim 5 including means for computing the x coordinate of the pont of intersection of the projectile with the target reference plane from the said time values T, t1 and the predetermined angle of azimuth 0, the separation distance d of the first pair of planar regions and the angle of azimuth .

7. Apparatus as claimed in either claim 5 or claim 6, including a third pair of electromagnetic radiation detectors arranged to detect the passage of the projectile through a third pair of planar regions, each of the third pair of regions being arranged at a predetermined angle of inclination # with respect to one of the first pair of planar regions, means for determining the projectile transit times t3 between one of the first pair of regions and one of the third pair of regions, and t4 between the other of the third pair of regions and said one of the first pair of regions and means for computing the angle of elevation fi of the projectile from the said times T, t3 and t4 and the value of the predetermined angle of inclination .

8. Apparatus as claimed in claim 7 including means for computing the y coordinate of the point of intersection of the projectile with the target reference plane from the said time values T and t3, the distance d between the first pair of planar regions and the said angles of elevation fi and inclination .

9. A method for use in detecting the path of a projectile substantially as described herein with reference to the accompanying drawings.

10. Apparatus for use in detecting the path of a projectile substantially as described herein with reference to Fig. 10 of the accompanying drawings when operated by a method substantially as described with reference to Figs. 1 to 7, or Figs. 8 and 9 of the accompanying drawings.