WO2011101459A1

WO2011101459A1 - Electro-optical sensor method and system for determining the motion of a projectile

Info

Publication number: WO2011101459A1
Application number: PCT/EP2011/052475
Authority: WO
Inventors: Norman Lindsay
Original assignee: Norman Lindsay
Priority date: 2010-02-18
Filing date: 2011-02-18
Publication date: 2011-08-25
Also published as: GB2478059A; WO2011101459A9; GB201102887D0

Abstract

The motion of a golf ball or other projectile is determined as it passes through substantially-parallel fields of view (3, 4, -45, 46; 55, 56) of two line-scan sensors (1, 2; 43, 44; 53, 54) that are spaced apart from one another. The fields of view of the two sensors are each substantially-planar or wedge- shape with respective mid-way planes offset or otherwise from one another, and each sensor responds at successive intervals of time to the angular position of the projectile in its field of view. From the sample measurements of angle, velocity vectors of the projectile and its direction are calculated.

Description

ELECTRO -OPTICAL SENSOR METHOD AND SYSTEM

FOR DETERMINING THE MOTION OF A PROJECTILE

This invention relates to electro-optical sensor methods and systems for measuring the motion of projectiles.

According to the present invention there is provided in one aspect a method, and in another aspect a system, for determining the motion of a projectile in its passage through respective substantially-planar fields of view of two sensors, wherein the two fields of view are substantially-parallel to one another and the sensors are separated from one another in a direction parallel to the two fields of view, and wherein each sensor is responsive during successive intervals of time to the angle relative to the respective sensor of the position of the projectile within the field of view of that sensor.

The present invention is useful for measuring the speed and position of golf balls but may be used in other sports and other applications. For convenience, consideration below and in the specific description with reference to the accompanying

drawings, relates to circumstances in which the projectile is a golf ball.

The sensors may comprise video cameras with anamorphic optics that compress the field of view in one direction to form a substantially planar field of view. A linear position-sensitive device with standard focussing optics may be used. More especially, one or more of the sensors may be a line-scan sensor comprising a pixel line-array positioned at or near the focal plane of a single light-collecting and focussing refractive lens. More complex optical arrangements, and various other types of lenses such as reflecting, diffractive or gradient- index lenses, may be used. The field of view of a line-scan sensor comprises a fan beam enveloping the individual fields of view of every pixel in the line-scan array. The axes of the individual fields of view of the pixels may be distributed rotationally about the centre of the lens in a plane that contains the pixel array. The angular extent of the fan beam is determined by the length of the pixel line array and the focal length of the lens.

In the application of the present invention to golf, the aim is to detect and measure a golf ball flying through each field of view at different times as it passes through that field of view. The ability to resolve two closely adjacent golf balls is not required; the sensors are preferably optimised for detection rather than resolution. It is thus desirable to use large aperture but low-cost plastic lenses rather than expensive multi-element glass lenses. Fresnel lenses with grooves micro- machined or moulded onto a thin sheet of acrylic or other optically clear plastic are particularly useful . With low-cost optics, the spot size of the light reflected from a golf ball and focussed onto the pixel-line array is typically several pixels in average diameter. As a ball passes through the field of view of a sensor, it can be detected for several

milliseconds, depending on its speed and trajectory angle, the height of the pixels (that is to say the dimension of each pixel normal to the length axis of the array) , the lens focus spot size and the diameter of the light entrance pupil of the sensor. The sampling frequency of the sensor is made high enough to ensure that at least two measurement samples are completed during the time that a ball is detectable. More especially, the sampling frequency of the sensor is high enough to ensure that three or more measurement samples are completed.

Golf balls are usually made with optical brighteners and their dimple designs also help to ensure high visibility against a dark background. Even balls with worn outer surface maintain their brightness because the recessed surfaces of the dimples do not get worn and act as tiny reflectors. In order to enhance contrast and hence detectability, it is desirable to ensure that the background is dark compared with a golf ball and gives a fairly constant, low level of illumination. This can be achieved by arranging that the background is dark and at least partially shaded from strong sources of light such as the sun or overhead floodlights. The background can be a man-made

structure or can be naturally occurring such as the shaded canopy of hedgerow or trees.

Provided that at least two data samples (that is to say

measurements) are made in each of two co-acting line-scan sensors, a solution can be found to determine the instantaneous location of a ball in the 'mid-way plane' between the two fields of view and also the ball's velocity components parallel to this plane. In some instances the mid-way plane and the centre of both fields of view are coincident or nearly so, that is to say there is negligible separation or 'offset' between the centres of the fields of view. The present invention makes use of both types of combinations of field of view, and for convenience these are distinguished from one another by reference to 'zero offset sensors' and 'known offset sensors'. The term 'zero offset sensors' refers to circumstances in which the fields of view intentionally overlap but there is negligible separation between the centres of the fields of view of the sensors; in practice, there will always be some finite offset. By contrast, 'known offset sensors' refers to the case where the fields of view are intentionally offset by some nominally known amount, which can be found by measurement or established by design.

Whereas the invention relies on data from at least two samples from each of two co-acting line-scan sensors, it is sometimes preferable to arrange that at least three samples from each sensor are acquired. In the known offset sensors combination, a quadratic fit can be made from a minimum of three samples from each sensor to determine when a ball is central in the two fields of view and, knowing the offset of the fields of view the remaining ball velocity component (normal to the mid-way plane) can be found. Although the mid-way plane is taken as a

preferred reference plane, but a different plane may be chosen as the reference plane if required.

Whereas in imaging optics it is desirable to obtain very sharp focus, the present invention relies on at least some spreading of the focussed spot to ensure that the image of a distant golf ball flying through the field of view of the sensor overlaps several pixels and remains detectible as the focus spot moves across the line of pixels. An alternative description is that the field of view of the sensor has 'thickness' or extends to a certain degree normal to its major plane. Advantageously, the present invention does not depend on precise focus precision or adjustment .

In one preferred mode of operation, the individual pixel fields of view are expanded in the direction normal to the pixel line axis. This has the effect of spreading the field of view into a wedge-shaped volume and allows golf balls to be detected over a longer trajectory compared with what is achieved with a simple spot-focus sensor. A wedge-shaped field of view can be achieved by using anamorphic optics to elongate the focus spot.

Alternatively, the pixels themselves can be elongated so that they have higher than normal height-to-width aspect ratio.

However, this latter technique requires fabrication of a nonstandard sensor array and is not practical except for very large volumes of a fully developed design with proven market demand. The anamorphic optics solution is flexible and allows for easy adjustment of parameters. The wedge-shaped field of view is especially suitable for the zero offset sensors combination and for medium-to-small range operation. Because of practical limitations all fields of view are wedge- shaped to a certain degree so the term wedge-shaped' applied to a field of view normally refers to a field of view formed with anamorphic optics or the like as described above. In one form of the invention, only one wedge-shaped field of view is used and the second field of view is formed with circular optics (that is to say, non-anamorphic optics) .

The invention may be used to measure any uninterrupted short portion of the flight trajectory of a golf ball, including the launch trajectory, the landing trajectory and the bounce trajectory after landing. The ball is subjected to usual aerodynamic forces and gravity as it passes through the fields of view of the sensors, but if the flight trajectory is

interrupted by hitting the ground or other surface before the required measurements are completed, the calculation of ball motion will be invalid.

In golf driving ranges, the invention may be used to provide data for identifying the position from where, and the time at which, a golf ball was launched from among a plurality of known possible launch positions and measured launch times. In this respect, it is useful to estimate the flight duration of a ball from club impact to final carry position, measure its landing position and measure the times of impact of all balls being hit at the tee-off bays on the driving range. The position from where a golf ball was launched is then found by matching its flight duration with the measured club impact time that most closely matches the estimated flight duration. The flight duration is estimated from the measured carry distance and other measurements of ball end-of-flight parameters including at least one of: the vertical component of velocity, the horizontal component of velocity, the elevation angle of descent (which is a function of the horizontal and vertical velocities) and ambient conditions including prevailing wind speed and

direction . In addition to measuring the club-impact time at each tee-off bay (or selected tee-off bays) in a driving range or other golf facility, it is useful to measure launch parameters of the ball shortly after impact. The process of identifying the position from where and the time at which a golf ball was launched is improved by correlating measured ball launch parameters with the measured carry distance and at least one measured end-of-flight parameter as described above. Preferably the measured ball launch parameters include at least one of: absolute velocity, horizontal velocity, vertical velocity, launch angle in

elevation, azimuth direction (that is to say horizontal angle) , ball spin magnitude, back-spin component, side-spin component and historic data on individual player's shot parameters found from previous shot identifications.

Methods and systems in accordance with the present invention will now be described, by way of example, with reference to the accompanying drawings, in which: Figures 1 and 2 are schematic plan and side views respectively of a sensor arrangement used in a first method and system according to the invention, at a golf-driving range;

Figure 3 and 4 are illustrative of a method of calculating ball- trajectory parameters from acquired data, used in the first method and system of the invention;

Figure 5 is a further representational diagram illustrating circumstances in which measurement uncertainties may arise during operation of the first method and system of the

invention;

Figures 6 and 7 are schematic side and front views respectively of a sensor arrangement used in a second method and system according to the invention, for measuring the launch velocities of golf balls; Figure 8 is a schematic plan view of a sensor arrangement used in a third method and system according to the invention, for short-range measurement of golf balls landing on a target; and

Figure 9 is a sectional side view through A-A of Figure 8.

Each of the sensor arrangements to be described with reference to the drawings is combined with suitable electronic processing facilities for carrying out the computations necessary to derive appropriate output or outputs representative of golf-ball motion, from the signals provided by the sensors. Details of the electronic processing facilities required in this respect are not described (or represented in the drawings) since facilities capable of the computations involved are readily available commercially.

For convenience of reference in the following description (and as illustrated where appropriate in the drawings) coordinate axes X, Y and Z are defined with the X-axis horizontal and normal to the general flight-direction of the golf ball, with the Y-axis horizontal and along the flight-direction of the ball, and with the Z-axis vertical. Referring to Figures 1 and 2, a line-scan sensor 1 at position A is spaced horizontally from a line-scan sensor 2 at position B. The boundaries of the individual fields of view of the sensors 1 and 2 are shown by dotted lines 3 and 4 respectively. As shown in Figure 2, the field of view of the sensor 1 is offset slightly above that of the sensor 2, and both fields of view are positioned just above a target area 5 of the driving range. The target area 5 is shown as a marked-out circular area (but may be an area of other shape) to represent a traditional golf green, and a flagpole 6 serves as an aiming mark for golfers hitting balls down-range along the Y-axis direction from distant tee-off bays (not shown) .

A 'background baffle' structure 7 is positioned on the far side of the target area 5 from the sensors 1 and 2. The purpose of the structure 7 is to provide a dark, low-reflectivity surface to improve the light contrast, and thus the detectability, of golf balls entering the fields of view of the sensors 1 and 2. Since the background light radiation often generates the major signal output in the sensors 1 and 2, reducing this light radiation reduces system noise and increases dynamic range and detectability.

The structure 7 has a re-entrant feature by which the surface that forms the background to the fields of view of the sensors 1 and 2 is located below one or more light shading elements 8 that at least partially block ambient light, and especially strong sunlight, from illuminating the background. This feature greatly helps to darken the background and ensures that it is less affected by variations in the ambient sunlight. A

combination of the sun high in the sky and broken clouds moving across the sky can cause strong and fairly rapid variations in ambient light. Although the background-baffle effect is achieved in the present example by the man-made structure 7, this is not necessarily the case in that a border of tall trees can provide equally-advantageous background conditions.

The field of view of each sensor 1 and 2 has a thickness (in the sense of the dimension normal to its major plane) such that at least two measurement samples of a golf ball are obtained when the golf ball passes through either field of view. However, it is preferable that three or more samples are obtained for the majority of golf shots. In the example of Figures 1 and 2, the thickness of the field of view of each sensor 1 and 2 is its vertical extent, and is dependent on various factors including the size of the light-entrance pupil of the respective line-scan sensor 1 or 2 , and the height of the pixels in the pixel-array of the sensor and the height of its focus-spot size. The thickness can vary throughout each field of view and in general will not be the same in both field at a given location.

Referring now to Figures 3 and 4, line 20 represents the trajectory of a golf ball flying through the fields of view of the two sensors 1 and 2. The path of this trajectory is of very small length compared with the full flight-trajectory of the ball, and can be considered a straight line followed through at constant speed in the direction indicated by arrow-head 21.

Optionally, drag and gravity corrections may be applied.

Orthogonal axes X, Y are represented in Figure 3 with the origin at point A and point B on the Y-axis. This simplifies the description below, but in general the sensors 1 and 2 and their respective fields of view may be otherwise positioned and oriented . The shaded areas of Figure 4 represent small sections 22 and 23 of the fields of view of the sensors 1 and 2 local to the trajectory path 20, looking into them towards the sensors 1 and 2; section 22 is associated with the sensor 1 at position A and section 23 is associated with the sensor 2 at position B. A hypothetical plane 24 (represented in broken line in Figure 4) is mid-way between the central planes of the two fields of view at height h . The dots on line 20 represent the points in time for successive measurements (that is to say the data sampling times) that occur at 5t increments. In practice, light received by sensors 1 and 2 is integrated throughout each sampling period and 'read' at the end of the integration.

The computation to fix the location and two velocity vectors of the ball requires at least two angular-position measurements relative to both measurement points A and B. In the example of Figures 1 to 4 , these angular-positions are azimuth angles or bearings that determine the angle of the ball about an axis of rotation through the measurement point, normal to the central plane of the field of view and thus normal to plane 24.

However, the distance of the ball from either of the measurement points is not known.

In Figure 4, the bearing of the ball is measured at four instants in time; to, ti, t2 and t3 where:

t₂ = to + 3.5t (2) t₃ = to + 4.5t (3)

The instantaneous positions at the ball at the four successive instants in time projected onto plane 24 are (xO, yO) , (xl,yl ) , (x2, y2) and (x3, y3 ) . Note that the Z-coordinate for each of these points is equal to h. For convenience these points are referred to collectively as 'projected points'. Because (in this example) the major planes of the fields of view of the sensors 1 and 2 are horizontal, the azimuth bearings of the projected points are equal to the measured bearings of the ball at the respective sampling times. A hypothetical line 25 in the Z = h plane is described by equation : y = Bo . x (4) where Bo is a measure of the horizontal bearing of the ball relative to point A at sampling time to. The point (xO,yO) lies on this line so the equation for xO and yO is as follows: yo = Bo . xo (5) Similarly, for the points that lie on lines 26, 27 and 28 have the following equations:

where Bi, B2 and B3 are measures of the horizontal bearing of the ball at sampling times ti, t2 and t3 respectively, and D is the distance between points A and B . (Note that B_a is equal to a pixel position rather than a true angle.) The distances between the projected points are ideally in exact proportion to the relative sampling times. The coordinates of point (xl,yl) in terms of the coordinates of points (x0,y0) and (x3,y3) are as follows : xl = xO + (x3 - x0)/(n - 1) (9) yl = yO + (y3 - y0)/(n - 1) (10) where n is the number of sampling periods that occur from the first measurement sample (at to) to the last sample (at t3> . In the case represented in Figures 3 and 4, n equals 5 but in general may be any integer number greater than 2. Similarly, the coordinate values for all points between the first and last sample can be found. There are accordingly four unknowns, namely; xO, yO, x3 and y3. These can be found by substituting for xl, yl, x2 and y2 and solving the four simultaneous

equations (5) , (6) , (7) and (8) .

This then gives values for the X and Y components of the ball velocity as follows:

V_x = (x3 - xO) I [5t . (n - 1) ] (11) VY = (y3 - yO) I [5t . (n - 1) ] (12)

Mathematically, three bearing samples on one field of view and only one sample on another is sufficient to determine Vx and VY. However, it is preferable to have the samples evenly distributed between the fields of view. The time relationship between all measurements must be known although it is not necessary that samples are acquired at fixed periodic intervals. Other procedures for extracting the values of Vx and VY can be used.

It is to be noted that arrow 29 is parallel to trajectory 20 and its direction can be found from two pairs of bearings at equal sample increments. Provided the time duration between measuring Bo and Bi is equal to the time duration between measuring Bi and B3, the horizontal direction of the trajectory 20 can be found. However, the correct speed and the distance between the

parallels 20 and 29 require knowledge of the time duration between measuring Bi and B2 .

The above computation of simultaneous equations is necessary only for the known offset sensors combination where measurements from the two sensors occur at different times. However, the computation of Vx and VY is not dependent on knowing the value of any offset between the fields of view. In the special case where there is virtually no offset (that is to say the zero offset sensors combination) the computation of Vx and VY is much simplified. Bearing samples of the golf ball from points A and B are obtained simultaneously so that the instantaneous X and Y coordinates of the golf ball in the plane of the field of view can be found by triangulation . Knowing the coordinates (as distinct from only the bearings) at two instants in time give direct measurements of Vx and VY. When more than four bearing samples are available, data

averaging or other computation means can be used to refine the calculated values of Vx and Vr and reduce the effect of errors in the data. Other means of improving accuracy is to capture data on the bounce trajectory after landing. This is easily achieved because the fields of view are normally just above ground level. Extrapolating back from a bounce trajectory can sometimes improve the accuracy of landing-position measurement in cases where the sensors are not well orientated to

triangulate the landing trajectory.

Figure 5 represents a situation where only three sample points are available. The field of view associated with point B is above that of point A (this is the reverse of the vertical field of view positions in Figures 3 and 4) . The ball first enters the field of view associated with point B ; the hypothetical trajectories are to the right of the cross-over of the bearing lines whereas in Figures 3 and 4 the trajectory is to the left of the cross-over. As in Figures 3 and 4, two bearing samples relative to point B are available and corresponding bearing lines 30 and 31 are projected onto a horizontal reference plane (in the plane of the drawing) . Unlike Figures 3 and 4, only one bearing sample is available relative to point A , with

corresponding projected bearing line 32. In this situation, there is no unique solution for Vx and VY; two hypothetical trajectories 33 and 34 that fly in different directions and at different velocities, but could cross lines 30, 31 and 32 at appropriate points in time are shown in Figure 5. Where at least three samples from each sensor are acquired, a quadratic fit can be made to determine when a ball is central in the two fields of view and, knowing the offset of the fields of view, the remaining ball velocity component Vz can be found. The sensor measurements that lead to computation of the motion of a golf ball at the end of its carry trajectory is of especial interest in the context of driving ranges where it is desirable to identify the position from where, and the time at which, each golf ball from a plurality of balls was hit. The motivation and method of identifying golf balls in this manner is described in US-A-2010/0029415 in which identification of the tee-off bay from which a golf ball landing on a golf- range target originated, is made by calculating an estimate of flight duration of the descending ball as a function of the measured angle of descent in elevation, and, in respect of each ball launched from the bays, comparing this estimate for a match with a measured interval between the launch of the respective ball and descent of the descending ball, the originating bay of the launched ball for which there is the closest match is identified as the origin of the descending ball.

In order to resolve any ambiguity or uncertainty between which bay is identified, additional measurements of the launch parameters can be made using the method and system of Figures 6 and 7.

Referring to Figures 6 and 7, a golf ball 40 is initially at rest on a tee-off mat 41 and after being struck by a golf club (not shown) flies along a trajectory shown by broken line 42. Two sensors 43, 44 are positioned in front of the tee-off mat 42 with respective fields of view shown by dotted lines 45 and 46. The two fields of view are directed downwardly towards a region forward of the tee-off mat 41 and are substantially parallel to one another and offset by a known distance D . As the fields of view fan out from the sensors 43 and 44, they are preferably collimated such that they have thickness d . The thickness d is determined by the entrance apertures of the sensors 43 and 44 and by beam divergence due to finite spot size. With focal length f the focus spot size is s, the beam diverges by amount s for every f increment in distance. The number of samples that can be measured as a ball flies through each field of view of the sensors 43 and 44 is dependent on the thickness of the field of view, the speed of the ball normal to the field of view and the data sampling rate. In the application represented in Figures 6 and 7, a maximum ball speed of 80 m/s normal to the fields of view can be expected, and a sampling rate of 4 kHz ensures that at least two data samples are acquired. At maximum speed the ball travels 20mm between successive samples and consequently a thickness of 40mm is required to ensure that at least two samples are acquired.

However, since most of the light reflected from the ball comes from a central area of about 10mm diameter, it is preferable for the thickness of the field of view to be increased by 10mm to 50mm.

The majority of golf shots result in the speed of the ball being considerably less than 80 m/s, so frequently three or more samples are acquired. For example, at a moderately fast ball- speed of 53 m/s at least three samples are acquired within a central 40mm field of view, or up to four samples provided they are symmetrically located about the central plane of the field of view.

In the system represented in Figures 6 and 7, where the offset between the sensors 43 and 44 is known, the component of velocity normal to the plane of the fields of view can be found if at least three bearing samples of the ball are made in each field of view. In practice, the amplitude response of a detected golf ball as it flies through a field of view is a bell-curve, with a well defined peak at the centre of each field of view. A quadratic fit of three samples gives the coordinate of the ball at the centre of the field of view, and, knowing the vertical distance between the centres, the value of the velocity normal to the field of view can be found. The light reflected, from the ball 40 preferably comes from a dedicated source (not shown) that can be modulated to be synchronous with electronic shuttering of the sensors 43 and 44. This arrangement can ensure that the light reflected from the ball 40 is substantially constant with little contribution from variable ambient light sources. Provided that the light conditions are stable, data from golf shots that result in three or more data samples in either field of view can be used to map and record the characteristics of the peak responses. These data can then be used to determine the normal component of velocity of high speed balls when only two data samples are available in one or both fields of view.

An alternative, but less accurate means, of estimating the normal component of velocity, uses knowledge of the thickness of just one field of view. This is useful where it is desirable to find the approximate normal velocity where there is zero offset between the fields of view of the sensors, or where only one field of view is available (for example due to an obstruction shadowing part of the second field of view) . The thickness of the field of view varies but in a predictable manner. For paraxial rays (close to the optical centre axis) aberrations will be smallest but coma and other aberrations will tend to enlarge the focus spot for off-axis images. As well as

enlarging the focus spot, these aberrations distort the shape of the spot (such as comet shaped coma aberrations) . However, since the light-collecting optics and pixel array are symmetrical about a central axis, the time-dependant amplitude response of a ball flying through the field of view is also symmetrical.

Calibration means can be provided to record 'thickness' data such as the rising and falling 50% levels of the bell-curve peak response at different parts of the field of view.

The initial placement of the ball 40 on the tee-off mat 41 can be used to improve the accuracy and/or calibrate the measuring system of Figures 6 and 7. Three points on the initial launch trajectory can be measured by placing the ball 40 at a known position on the tee-off mat 41 and recording the exact time of impact. Different known, initial ball positions can be used to fully characterise the system throughout its operating range. Optionally, means can be provided to measure automatically the initial position of the ball 40 on the mat 41 and to include such measurement as data in the computation of launch

parameters . Referring now to Figures 8 and 9, a raised sloping target 50 is provided for short chip-shot practice by several players concurrently on a golf driving range. Several tee-off mats 51 are provided, each having a ball-impact sensor 52 that

electronically measures the exact time of club-on-ball impact.

Sensors 53 and 54 are configured with zero offset between their respective, overlapping fields of view 55 and 56 (shown in dotted line) that are formed using anamorphic optics. The focus spot inside each sensor 53 and 54 is elongated vertically so that the fields of view diverge vertically with angle B as shown in Figure 9. In plan (Figure 8) the fields of view both have a ^v fan angle' a ; the fan angle comprises the combined fields of view of a large number of pixels. The azimuth bearing of a ball relative to sensors 53, 54 can be measured with high resolution by determining the pixel position (including the fractional pixel position) of the image of the ball on the pixel array. Thus, the X and Y coordinates of a ball as it passes through the combined fiels of view can be accurately found by triangulation . There is no means of accurately determining a ball's elevation within the vertical divergence β . The vertical component of the velocity of a ball can be determined only by the duration of the transit of the ball through the fields of view and knowing the approximate variation in thickness of the fields of view. The vertical divergence of the fields of view provides the advantage that the ball remains within the fields of view longer (in comparison with the situation where the fields of view are of fixed thickness) and thus several azimuth bearing samples can be acquired before the ball lands on the ground 57 or the target 50.

It follows that the azimuth speed and direction of a ball can be sampled several times before dropping onto the landing surface. This provides a very reliable means of identifying from which tee-off mat (from the several mats 51) any ball was hit.

A first means of identification is the ball's azimuth velocity, which can be found from two or more azimuth coordinate samples and the time duration between the samples. For short chip- shots, the aerodynamic forces on the ball are very small, with the most significant force being drag. This can reduce the ball speed by about 10% (for a twenty metre shot) but in a

predictable manner. A crude measure of vertical speed as disclosed above, can refine the prediction if required. Knowing the final horizontal speed before landing, the average

horizontal speed during flight can be found by adding a small correction (of the order of 5%) . The duration of flight can be found by dividing flight-length by the average velocity of flight, and the azimuth position of the ball at the end of flight is accurately known and its initial position is known to be one of several possible tee-off points. Shot identification is then determined by matching exactly when a ball was hit at each of the tee-off mats 51, with the possible flight-durations computed. Because chip shots are of very short duration

(typically less than two seconds) , the error in computing flight duration is mainly dependent on knowing the exact initial position of each ball on the tee-off mats 51.

A second means of identification is the azimuth direction on landing. Since sidespin has negligible effect on low velocity golf balls (as in chip shots) , the initial direction and final direction before landing are invariably almost identical. Measuring the X and Y components of velocity gives the approach direction and thus a fairly accurate bearing on the position of the tee-off mat 51 relative to the landing position. This, combined with the flight duration calculation and matching, gives a very reliable indication of where each successive shot was made .

An additional advantage of the vertical divergent beam as shown in Figure 9 is that it extends onto the target surface itself and can be used to follow the bounce and roll trajectory of balls landing on the target 50, including balls that roll into the target hole marked by the flag 58. The target slope combined with a low rolling friction surface ensures that balls roll off the target surface and are collected in a trench 59 at the bottom of the slope. This ensures that balls do not collect on the target surface where they would impede fresh shots and create an unwanted bright background in the fields of view of the sensors 53 and 54. The arrangement of Figure 8 and 9 can also be used to measure balls as they bounce onto a distant target. In this application, a system similar to that of Figures 1 and 2 measures the carry approach and the system of

Figures 8 and 9 measures the subsequent bounce and roll of balls that land on or slightly in front of the target.

Alternatively, other means such as radar tracking can be used to measure the carry approach. Since golf balls lose a large portion of their kinetic energy when impacting turf or simulated turf, the ball trajectories after landing are similar in length and speed to chip shots, so the measurement system and ball identification methods described above are appropriate.

Claims

Claims :

1. A method for determining the motion of a projectile in its passage through respective substantially-planar fields of view of two sensors, wherein the two fields of view are substantially- parallel to one another and the sensors are separated from one another in a direction parallel to the two fields of view, and wherein each sensor is responsive during successive intervals of time to the angle relative to the respective sensor of the position of the projectile within the field of view of that sensor .

2. A method according to Claim 1 wherein the substantially- parallel fields of view are spaced apart in a direction normal to them .

3. A method according to Claim 1 or Claim 2 wherein the substantially-parallel fields of view overlap one another.

4. A method according to any one of Claims 1 to 3 wherein each sensor is responsive during at least three successive intervals of time to the angle relative to the respective sensor of the position of the projectile within the field of view of that sensor .

5. A method according to any one of Claims 1 to 4 wherein the sensors are line-scan sensors and the angle of the position of the projectile is determined in dependence upon the location in the line scan of the response to the projectile.

6. A method according to Claim 5 wherein each line-scan sensor comprises a linear array of sensing elements each of which has an individual field of view that is more divergent in the direction normal to the linear array than in the direction parallel to the linear array.

7. A method according to any one of Claims 1 to 6 including determining components of velocity of the projectile from the relative timings with which the two sensors respond to the uninterrupted passage of the projectile through both fields of view.

8. A method according to any one of Claims 1 to 6 wherein the projectile is a golf ball.

9. A method according to Claim 8 including determining the flight duration of the ball from measurements of the flight distance from launch and at least one of: the angle of descent of the ball at the end of its flight, the speed of descent of the ball at the end of its flight, the vertical component of velocity of the ball at the end of its flight, the horizontal component of velocity of the ball at the end of its flight.

10. A system for determining the motion of a projectile in its passage through respective substantially-planar fields of view of two sensors of the system, wherein the two fields of view are substantially-parallel to one another and the sensors are separated from one another in a direction parallel to the two fields of view, and wherein each sensor is responsive during successive intervals of time to the angle relative to the respective sensor of the position of the projectile within the field of view of that sensor.

11. A system according to Claim 10 wherein the substantially- parallel fields of view are spaced apart in a direction normal to them .

12. A system according to Claim 10 or Claim 11 wherein the substantially-parallel fields of view overlap one another.

13. A system according to any one of Claims 10 to 12 wherein each sensor is responsive during at least three successive intervals of time to the angle relative to the respective sensor of the position of the projectile within the field of view of that sensor.

14. A system according to any one of Claims 10 to 13 wherein the sensors are line-scan sensors and the angle of the position of the projectile is determined in dependence upon the location in the line scan of the response to the projectile.

15. A system according to Claim 14 wherein each line-scan sensor comprises a linear array of sensing elements each of which has an individual field of view that is more divergent in the direction normal to the linear array than in the direction parallel to the linear array.

16. A system according to any one of Claims 10 to 15 including computing means for determining components of velocity of the projectile from the relative timings with which the two sensors respond to the uninterrupted passage of the projectile through both fields of view.

17. A system according to any one of Claims 10 to 16 for use in a golf driving range for determining the motions of golf balls.

18. A system according to Claim 17 wherein the system is operative to determine the flight duration of each ball from measurements of the flight distance from its launch and at least one of: the angle of descent of the ball at the end of its flight, the speed of descent of the ball at the end of its flight, the vertical component of velocity of the ball at the end of its flight, the horizontal component of velocity of the ball at the end of its flight.