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Title:
IMPACT BOARD WITH INDIVIDUALLY DAMPED MOVABLE PANEL INSERTS
Document Type and Number:
WIPO Patent Application WO/2012/137231
Kind Code:
A1
Abstract:
A fixed target is constituted by a board with polygonal panel inserts, especially square inserts, on telescopic guides to be hit by a body, preferably a soccer ball. Each panel is damped by helical springs, and interacts with a sensor, electrically connected to a programmable control unit which detects the position of the hit panel in the board and its distance from the target-panel. When the sensors are micro-switches, a Doppler effect radar sensor is used for measuring the speed of the ball and for evaluation of the shot force. Acceleration, speed or position transducers for the single panel may be used, as individual transducer and communicate to the control unit a signal indicative both of the position in the board and of the force of the shot. The control unit calculates as score the sum of the precision and to the force of the shot.

Inventors:
BERTOLI GIACOMO (IT)
Application Number:
PCT/IT2011/000313
Publication Date:
October 11, 2012
Filing Date:
September 13, 2011
Export Citation:
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Assignee:
BERTOLI GIACOMO (IT)
International Classes:
A63B71/06; A63B24/00; A63F7/02; F41J3/00; G01M17/007
Domestic Patent References:
WO2010128982A22010-11-11
Foreign References:
US5419549A1995-05-30
US2040228A1936-05-12
US4029315A1977-06-14
CA1289982C1991-10-01
US2247501A1941-07-01
US20100285905A12010-11-11
Other References:
None
Attorney, Agent or Firm:
LO MAGRO, Attilio (Via Aldrovandi 7, Milano, IT)
Download PDF:
Claims:
C L A I M S

1. A fixed target equipped with programmable processing and control means (38) for calculating a score to be assigned to each shot, characterized in that it includes:

- a board (1) with movable panel inserts (2, 63, 90), at least one of which marked as the one to be hit;

- means for positioning the panels in the board and for the telescopic guiding of the same (30, 430, 32; 60, 61, 64);

- resilient means (46, 75) individually connected to each panel for damping the sustained hit;

- means for detecting the impact that occurred (33, 80, 82), individually connected to each panel, directly or by means of the respective resilient means;

- means for transducing (33, 80, 100) a physical parameter indicative of the impact energy or in an equivalent manner of the shot force;

- said processing and control means (38) being timed for cyclically acquiring samples of the electrical signals generated by the detector and transducer means, on the basis of such samples calculating the force and the precision of the shot in the formation of said score (27).

2. The target of claim 1, characterized in that the face of each panel exposed to the impact is equal in shape and size to the exposed face of the other panels, and such shape is a polygon, especially a square (2) or a hexagon (14).

3. The target of claim 1, characterized in that said individual detector means for the occurred impact include a microswitch (82) for each panel (90), driven by the translation of the panel, and said transducer means include a transducer common to all the panels constituted by a tachometric radar sensor (100).

4. The target of claim 1, characterized in that said individual detection means for the occurred impact coincide with the same transducer means and include a piezometric accelerometer (80) for each panel, fixed on the back of the respective panel (63).

5. The target of claim 1, characterized in that said individual detection means for the occurred impact coincide with the same transducer means and include a linear transducer preferably of potentiometer type (33) for each panel (2), the linear transducer (33) having a slider (47) driven by the end of a pin (2c) whose other end is integral with the panel (2).

6. The target of claim 1, characterized in that several suitably spaced panels (20, 21, 22, 23, 24) are marked as the panel to be hit, and each of these is associated with a receiver for tags of RFID type (101, 102, 103, 104, 105) tuned on the signal emitted by an associated RFID tag incorporated in a body shot against the target, each incorporated tag being recognizable only to the receiver with which it is associated.

7. The target of claim 1, characterized in that said positioning and telescopic guiding means for the panels (2, 63, 90) include a cell structure (430, 61) made of modular elements (44a, 44b, 44c, 32; 85, 91).

8. The target of claim 7, characterized in that said modular elements are profiles (44) inserted at one end thereof inside notches (45), with the same shape as the profiles, present in a support plate (32) for said structure (430), the notches being arranged at the vertices of polygons with the same shape as the panels (2), first L-shaped profiles (44a) being positioned at the corners of the structure, second T-shaped profiles (44b) positioned along the sides of the structure, and third cross-shaped profiles (44c) being positioned inside the perimeter delimited by the preceding profiles.

9. The target of claim 7, characterized in that said modular elements include a rectangular plate (85) having parallel, equidistant slits (86) that are open at a longer side of the plate, orthogonally with respect to said side, and terminate at about half the width of the plate (86), the width of the slits (86) coinciding with the thickness of the plate (85), the distance between adjacent slits being nearly equal to the length of the side of a square panel (63), optionally the terminal slits having an edge (87) pre-established by both of the shorter sides, said plates (85) being orthogonally joined to each other at said slits (86) so as to form said cell structure (61).

10. The target of claim 9, characterized in that parallel plates (91) belonging to a subset of said plates (85) include identical tabs (92) on the two faces between adjacent slits (86), said tabs being orthogonal to said slits and to the face from which they are extended, at an identical distance from the edge, such distance being greater than or equal to the thickness of the panels (90).

11. The target of claim 3 or 4, characterized in that said resilient means of each panel (63, 90) include at least one helical spring (75) having one end against a stop wall (65) integral with the board (1), the spring (75) being placed astride a pin (74) having one end integral with the panel (63, 90) and being free to translate through said stop wall (65) during the compression of the spring (75), and then to return to the initial position determined by means (78, 79) for locking against said stop wall (65), such locking means reversibly integral with the other end of the pin (74).

12. A method for assigning scores to the shots against a target constituted by a board (1) with movable panel inserts (2, 63, 90), such panels damped (46, 75) and equipped with detectors and/or transducers (33, 80, 82, 100) like that described in claim 1 , characterized in that it comprises a preliminary step in which a line index and a column index k are assigned to each panel on the basis of the respective position in the board, considered to be a matrix of Ni lines and Mk columns, and the same indices , k of the panels are assigned to the respective detectors and/or transducers, and the following steps cyclically repeated:

a) writing, in a memory, the values of the samples /, k generated by all the transducers with indices , k with regard to a time window of duration comparable to the transitory time of the sampled signal, the writing of each sample being subordinate to the fact that its value exceeds an admission threshold;

b) searching for the sample i, k with highest value;

c) calculating the average distance of the panel marked as that to be hit from the panel i, k associated with the greatest value sample, and from the adjacent panels, also diagonally adjacent, associated with the above- threshold samples, obtaining a distance value representative of the shot precision;

d) summing the value of said greatest value sample , k with the values of the above-threshold samples with indices , k that are adjacent, also diagonally adjacent, obtaining a value representative of the shot force;

e) calculating a cumulative score by summing together the aforesaid representative values of the shot precision and force, possibly multiplied by respective weights.

13. The method of claim 12, characterized in that by using square panels, each addend that contributes to said average distance is the Pythagoras distance calculated over corresponding indices multiplied by the real value of the side of the panel.

Description:
Impact board with individually damped movable panel inserts

Field of application of the invention

The present invention is applied to the industrial field of impact tests and manufacturing of targets in general, and more precisely to an impact board with individually damped movable panel inserts.

The board of the invention could prove useful whenever it is necessary to adapt the damping effect to the form characteristics of the impacting object; in other words, where it is necessary to selectively absorb impacts.

The board of the invention could also prove useful whenever it is necessary to evaluate the energy of impacts, separately or in combination with the evaluation of the precision of the shots, or launches, from a fixed position against a panel preselected as a target. For such purpose, the board could be equipped with sensors and transducers, and made "intelligent" by a microprocessor control. One example in such sense would be in the evaluation of the precision and force of the shots carried out with a soccer ball, whether for training professional or amateur soccer players, or for purely fun activities. More generally, the invention could be used in those areas where the technical characteristics of the board allow it, or they can be adapted to the specific use. Another application example could be in the study of multiple impacts against an obstacle, whether generated by single projectiles or by a projectile which shatters upon impact. Below, with the term "projectile" it is intended any one movable body directed against a target and preferably but not necessarily capable of rebounding. Review of the prior art

In the field of the art described above, crash test equipment is known where the projectile is a car, at whose interior a manikin sits which is equipped with numerous sensors of various types; a rigid wall is the target. After impact, the data detected by the sensors is analyzed, stored in real time by a suitable recording unit situated in the body of the manikin. The overall evaluation can lead to a "score" on the suitableness of the car protection systems. It is clear that the crash test is of destructive type, hence non-repetitive, and moreover there is a reversal of approach with respect to the invention described below, since it is the projectile and not the target to be equipped with acquisition and processing means for the impact parameters.

In the field of "intelligent" targets, electronic target embodiments are known, for example in the darts game, which mark the points of one or more players based on the precision of the shots carried out. The same is said for the shots carried out with one of the automatic rifles. In such applications, the projectile is rigid, pointed and of small size, hence it is able to have high speed and can stick into the target, damaging it. The parts subjected to impact in contact with the sensors must therefore be substituted fairly frequently. In other applications, the projectile is a metal ball used to hit a mushroom-shaped target placed at a close distance and equipped with a bumper ring, such as in the flipper game, where the score is assigned on the basis of the importance previously assigned to the type of target.

Description of the technical problem

In the examples of the prior art described above, the entire momentum of the projectile is transferred to the target, which is rigid in all of its parts or in which pointed projectiles are allowed to penetrate. Such targets do not have the capacity to selectively damp single or multiple impacts by rebounding projectiles equipped with a considerable momentum. Selective damping would not unnecessarily stress the non-hit zones, and could also facilitate the analysis of the impact parameters, especially when the projectiles are directed against predetermined zones.

Objects of the invention The present invention therefore has the object to obtain a fixed target which is capable of acting as a selective impact damper, as stated above.

Another object of the invention is to make the target "intelligent", i.e. capable of determining the force of the shot from the impact analysis and its precision in order to calculate a score to be assigned to each shot.

Another object of the invention is to be able to vary the "center" of the target as desired.

Another object of the invention is to allow simultaneous shots against respective "centers" located in very large targets, since the relative score to be assigned to the shooter can be calculated for each impact.

Summary of the invention

In order to attain such objects, the present invention has as object a fixed target equipped with programmable processing and control means for calculating a score to be assigned to each shot, wherein according to the invention it includes:

- a board with movable panel inserts, at least one of which marked as the one to be hit;

- means for positioning the panels in the board and for the telescopic guiding of the same;

- resilient means individually connected to each panel for damping the sustained hit;

- means for detecting the impact that occurred, individually connected to each panel, directly or by means of the respective resilient means;

- means for transducing a physical parameter indicative of the impact energy or in an equivalent manner of the shot force;

- said processing and control means being timed for cyclically acquiring samples of the electrical signals generated by the detector and transducer means, on the basis of such samples calculating the force and the precision of the shot in the formation of said score, as described in claim 1.

Further characteristics of the present invention, in its various embodiments that have been deemed innovative, are described in the dependent claims. According to one aspect of the invention, the face of each panel exposed to the impact has shape and size equal to the shape and size of the exposed face of the other panels, and such shape is a polygon, especially a square or a hexagon. According to one aspect of the invention, in which the board is square and contains an odd number of panels, the central panel is marked as the one to be hit.

According to one aspect of the invention, a panel situated in proximity to a corner of the board is marked as the one to hit. Such characteristic is advantageous, for example, in order to train penalty kickers to shoot at the intersection of the posts or close to the ground, depending on the angle selection.

In one embodiment, said individual detector means for the impact that occurred include a microswitch for each panel, driven by the translation of the respective panel, and the target also includes a transducer common to all the panels constituted by a radar sensor, preferably with Doppler effect. The distance of the "activated" panel from the panel to be hit provides an indication of the shot precision. By "activated" panel, it is intended that connected to the microswitch, whose open-closed state is varied with respect to the state which it had at the previous scanning. The tachometric radar sensor signals the speed of the moving mass to the control means; except for corrective factors, such speed provides an indirect indication of the shot force. The use of the tachometric radar sensor is however not optimal in the distinction of multiple projectiles.

In another embodiment, the individual detector means for the impact that occurred coincide with the same transducer means, and include a piezometric accelerometer for each panel fixed on the back of the same. Upon exceeding a discrimination threshold of the false accelerations due to the board vibrations, the accelerometer provides an indication of the impulse force acting on the mass of the hit panel, which in turn is proportional to the force of the shot by means of the ratio between the mass of the panel and the mass of the body shot against such panel. The shot precision can be evaluated as stated above. The use of accelerometers avoids using the collective radar sensor and allows the recognition of simultaneous impacts.

In another embodiment in which the individual detection means for the impact that occurred coincide with the same transducer means, the latter include a linear transducer (or sensor) for each panel, the transducer having a slider maneuvered by one end of a pin, whose other end is integral with the damped movable panel. Upon exceeding a discrimination threshold of the spurious movements of the slider due to the board vibrations, the elongation of the slider of the linear transducer provides an indication of the impulsive force acting on the mass of the hit panel, in turn proportional to the force of the shot by means of the ratio between the mass of the panel and the mass of the body shot against such panel. The shot precision can be evaluated as stated above. The use of the linear transducers avoids using the collective radar sensor and allows the recognition of simultaneous impacts. There are various types of linear transducers/sensors useful for such purpose, such as electric, magnetic, optical sensors etc. Inductive sensors (LVDT) include a differential transformer with mutual inductance variable with the speed of the slider, and hence of the damped panel. The LVDT sensors are sensitive to small movements of the slider, even micrometric movements, and therefore they do not require the extended elastic deformations of the resilient means. Linear potentiometers are variable electric resistors capable of providing a voltage proportional to the absolute position of the slider end, comprised in a predetermined interval of positions, and for a maximum movement speed, between which the typical values of the coupling to the damped panel are contained. Linear potentiometers preferably coincide with the use of helical springs that are free to work over the entire deflection interval, which is possibly several centimeters for a more accurate quantization of the resistance measurement. The use of accelerometers and linear transducers calls for several additional considerations with respect to the use of the radar sensor, since the impact force is calculated based on the movement of the panel hit by the projectile rather than on the projectile itself. It is necessary to first state that the knowledge of the absolute force of the shot, and hence of the corresponding absolute acceleration impressed on the panel, is not strictly indispensable for the purposes of the respective component to be assigned to the overall score, since an imperfect dynamic modeling of the impact would affect shots of various strength in the same manner. That said, the measurement downstream of the transducers arises from impact dynamics considerations, in particular regarding anelastic impacts, including the impact between a deformable projectile like a soccer ball and a damped rigid panel. A thorough treatment of the impact is not at all simple, since it is necessary to consider the following factors: a) the constraint reactions which limit the conservation of the momentum of the system under examination; b) the energy dissipated in heat form by the deformation sustained by the projectile during impact; c) the energy dissipated in heat form due to the internal friction of the resilient means and the grazing friction between the edges of the panel and the guide means; d) the braking effect of the air on the projectile. One such exhaustive analysis would confirm that neither the total energy of the system nor the momentum would have been conserved in the impact. For a determination of the comparative scores, it would be opportune to establish which fraction of the vector speed v p of the projectile will be transferred to the panel, making it assume, at the instant of impact, an initial velocity v 0 in the translation direction. Such component of the velocity v p will of course depend on the position of the panel in the board with respect to the shooting position, since the constraint reactions orthogonal to the motion of the generic panel, exerted by the guide means, limit its translation component v 0 to the projection of the vector v p in the directions parallel to the constraints. By ignoring the internal and external frictions in a first approximation, it is possible to consider the impact as an elastic collision between a first body of mass mj (the ball) with velocity v 0 in the direction of the motion of the panel and a second body of mass m 2 (the panel) with initially zero velocity. In such case, it is known that the condition ni] = m 2 allows the maximum transfer of momentum from mi to m 2 : if the projectile is rigid, it would be immediately stopped and the panel would fully assume the initial velocity v 0 ; however, the fact that a soccer ball rebounds at a certain speed does not really nullify the transfer of the momentum from the ball to the panel, since the rebound energy is mainly provided by the compression of the air inside the ball.

The use of linear transducers downstream of the resilient means calls for further considerations with respect to the use of piezometric accelerometers applied directly to the panel, since in order to obtain an improved precision in the measurement, a greater translation of the panels is necessary. Below, the only resilient means described are helical springs which work under compression; nevertheless, this does not limit the possibility of using other types of resilient means, i.e. all those bodies capable of storing energy in the form of elastic deformation and of returning it to the original form. Especially by using springs with wide deflection, there is the possibility that a space is created between the completely retreated panel and the adjacent panels. It is therefore necessary to increase the "diagonals" of the polygonal panels with respect to the diameter of the deformable, spherical projectile with greater bulk, in order to avoid that in deformed configuration the projectile remains embedded between the walls of the space.

Another object of the invention is a method for calculating the scores to be assigned to the shots against the board of claim 1, whose panels are connected to the transducers of any one of the types indicated in the same number of dependent claims, said transducers being in turn connected to processing means controlled by a program stored therein in order to execute the steps of the method. It is first necessary to state that the fitting of the board by means of polygons, preferably squares and hexagons, with size comparable to that of the projectile, allows distinguishing between the following impact types: impact on the single panel; impact between adjacent panels involving two, three or four panels. The description of the method for calculating the scores will be provided in a later section of the present description.

According to one aspect of the invention, the processing and control means send the score (or scores) to a display, each score also being able to indicate two relative partial scores independently assigned to the precision and shot force. In order to avoid instability in the indications on the display, the score will be maintained for a predetermined time or until the shooter clears it by means of a button, before the next shot.

According to one aspect of the invention applied to very wide targets, with panels equipped with individual transducers, several suitably-spaced panels are marked as zones to be hit, and each of these is associated with a receiver for RFID (Radio Frequency IDentification) tags tuned on the signal emitted by an RFID tag incorporated in a projectile, each tag being recognizable only to receiver with which it is associated. The passive RFID tag is capable of being recognized in a limited area around the receiver, which ensures the correct detection of the impacts in separate areas, adjustable around the respective "centers". If a projectile equipped with a RFID tag hits the target in a zone assigned to a receiver incompatible with its tag, no score is assigned to the same even if the impact is detected. In the final score count, the missing scores will inform the shooters of the excessive imprecision of their shots (due to the fact that they missed the targets). Overlapping of shots could occur against a same "center", causing an overestimation of the impact force of the legitimate shot and consequent non-correspondence of the score. Nevertheless, these events should not on average invalidate the scores in the suitably wide boards, in the presence of accustomed shooters; therefore, it does not appear to be advantageous to study more sophisticated solutions capable of remedying the drawback, such as that of placing several RFID receivers on each target-panel. Advantages of the invention

The target obtained as indicated in the present invention lends itself to the different above-indicated uses, all united by the fact that they are able to benefit from a selective impact damping.

In particular, the use of projectiles constituted by soccer balls will allow creating centers for training activities or places where people can come together for fun activities, indoor or outdoor.

Brief description of the figures

Further objects and advantages of the present invention will be clearer from the following detailed description of an embodiment of the same and from the enclosed drawings given as a merely non-limiting example, in which: - Figure 1 is a cross section of a gym for shooting training in soccer, in which an "intelligent" impact board obtained according to the present invention is positioned;

- Figures 2, 3, 4 are respectively front views of the board of figure 1 and of two variants thereof;

- Figure 5 shows a scoreboard panel present in figure 1 in detail;

- Figure 6 is a geometric schematization of a generic shot made by the player of figure 1 against the board, which shows the elevation angle a and the horizontal angle β (azimuth) of the panel hit with respect to the shooting position;

- Figure 7 is a perspective view of a first embodiment of the board of figure l ;

- Figure 8 is an exploded perspective view of the board of figure 7;

- Figures 9, 10, 11 are perspective views of three different guide-panel elements visible in the board of figure 7;

- Figure 12 is a partial section along a vertical plane passing through the axis A-A of the board of figure 7, without impact;

- Figure 13 shows the different configuration of the movable elements of figure 12 with impact;

- Figures 14 and 15 are perspective views of the elements depicted in section in figures 12 and 13;

- Figure 16 is an exploded perspective view of a second embodiment of the board of figure 1 ;

- Figure 17 is a perspective view of the single structural element used in the embodiment of a panel-guide framework visible in the board of figure 16;

- Figures 18 and 19 show the fitting formed by two elements of figure 17;

- Figure 20 is a perspective view of a longitudinal element for fixing the springs used on the back of the board of figure 16;

- Figure 21 is a partial section along a vertical plane passing through the axis B-B of the board in exploded view of figure 16, without impact;

- Figure 22 shows the different configuration of the movable elements of figure 21 with impact;

- Figure 23 is a perspective view of two different structural elements used in the embodiment of a variant of the panel-guide framework of figure 16 characterized by a lower possibility of translation of the hit panels;

- Figures 24 and 25 differ from figures 21 and 22 mainly for the use of the structural elements of figure 23.

Detailed description of several preferred embodiments of the invention

In the following description, equivalent elements which appear in the different figures can be indicated with the same symbols. In the illustration of a figure, it is possible to make reference to elements not expressly indicated in that figure but in preceding figures. The scale and the proportions of the various depicted elements do not necessary correspond to the actual scale/proportions.

With reference to figure 1, the cross section of a gym can be observed. Fixed on the bottom wall of such gym is a square board 1 with panel inserts 2, also square; the central panel 3 is marked with a different color in order to indicate to a shooter 4 that this corresponds with a target to be hit, in the specific case with a soccer ball 5. The board 1 is raised from the ground and can have support legs that do not preclude fixing to the wall in order to avoid oscillations. The underlying floor 6 is tilted downward for a section of suitable length, so as to facilitate the return of the ball towards the shooting position 7, set in front of the board 1 at a distance approximately comprised between 1 1 and 30 meters. On the side wall, just beyond the shooting position 7, a scoreboard panel 8 is visible, obtained with LEDs. The shooting position 7 is comprised between two parallel lines 9 and 10 which mark a shooting lane 1 1 associated with the board 1. The gym of figure 1 can contain several parallel lanes like 1 1 , separated by dividing nets. The board 1 is obtained according to the different modes that will be described below. One possible embodiment provides for the aid of a transducer of the ball speed, such as a transducer that includes a Doppler effect radar sensor 100, or Doppler effect sonar. The radar sensor 100 is placed at a distance from the shooter, preferably on the side walls turned towards the shooting position 7 in order to avoid being inadvertently hit. A terminal 110 equipped with a touch screen is placed close to the shooting position in order to allow the shooter 4 to communicate with a control unit of the board 1 and of the display 8, positioned inside the board 1 or in the terminal 1 10 itself. The latter, the display 8, and the radar 100 are connected by means of electrical cables to the board 1. Alternatively, figure 1 can be a place where people come for fun, where the board 1 is used in order to organize challenges between shooters to see who can achieve the best score.

Figure 2 reproduces the front part of the board 1, in which a frame 12 is visible which encloses five columns flanked with square panels 2, each column comprising five panels of type 2. The central panel 3 of the third column is indicated as a target. The frame 12 has a structural role in sustaining the panels 2. More generally, in order to be able to indicate a central panel as a target, the board 1 will have to have an odd number of columns, and each column will have to comprise an identical odd number of panels. The fact that the central panel is indicated in the figures as that to be hit does not limit the invention, which allows selecting any one panel as a target. The selection will have to be communicated to the control unit by means of the terminal 1 10 and such unit will update the score calculation program. The former target will have to be brought back to the condition of the other panels, while the new target will have to be visibly indicated as such, e.g. by applying a colored tape. The length of the side of the panels 2 can be selected based on the distance of the board 1 from the shooter 4; the greater the distance, the greater the side can be. If the side was sized on the diameter of a soccer ball, it will be necessary to increase it in order to account for the elastic deformation sustained at the time of impact. As an example, the regulation soccer ball has a diameter of about 22 cm and weight in the range of 410 to 450 grams. Figure 3 shows a board 13 with panel inserts 14 of hexagonal shape surrounded by a rectangular frame 16 that encloses an odd number of horizontal rows of panels 14, each row including a same odd number of panels; in alternating rows, a panel is divided into two halves placed at the two ends of the row. With one such configuration, it is still possible to highlight a central panel 15 as a target. The honeycomb inserts better approximate the imprint left by the ball on the board, and involve a maximum of three panels with respect to the four of the board 1. Figure 4 shows a variant of the board 1 constituted by a board 17 with square inserts 19 enclosed in a frame 18 of rectangular shape. The odd number of columns each comprising an odd number of panels allows highlighting a central panel 20 as target. The internal size of the frame 18 is about that of the mouth of a regulation soccer goal (732 x 234 cm); this allows indicating as additional targets the two panels 21, 22 placed in proximity to the upper corners and the two panels 23, 24 placed in proximity to the lower corners, useful for the training of penalty kickers. In order to allow the execution of nearly simultaneous, independent shots against the panels 20, 21, 22, 23, and 24, and the assigning of the same number of scores, the aforesaid panels are equipped with a receiver, respectively indicated with 101, 102, 103, 104, and 105, for RFID tags tuned on the signal emitted by an associated passive RFID tag incorporated in a body shot against the target. Each incorporated RFID tag is recognized by the single receiver with which it is associated.

Figure 5 shows in detail the LED scoreboard panel 8 managed by a microprocessor which processes two partial scores 25, 26 and a total score 27 for each shot. The scores 25 and 26 are respectively assigned to the force and to the precision of the shot. In the case of multiple shots carried out by several shooters against a single target or by several shooters against multiple targets, the display 8 will be consequently varied in order to show the overall information.

Figure 6 schematizes the geometry of a shot of the soccer ball 5 against the board 1. The impact between the ball 5 and a panel 2, different from the central target 3, is shown in figure 6 A, which shows the ovaling of the ball and the consequent increase of the transverse size, along with the retreating of the hit panel with respect to the adjacent panels. In the case of figure 6A, the side of the panel is greater than the size of the ball 5 in maximum oval shape, in order to prevent the embedding in the space that is formed between the panels adjacent to that centrally hit. In figure 6, the board 1 is shown from above (in the upper right corner of the page) and from the side (in the lower left corner of the page). With respect to the central shooting position, each panel 2 (including the hit panel) subtends two angles a and β. The angle a measures the angular elevation from the ground; the angle β measures the horizontal angular movement. The angles aj, a 2; a 3 respectively correspond to the lower, central and upper panels of a generic column; the angles -β, 0, + β respectively correspond to the panels more to the left, central and more to the right of a generic row. For each row and for each column of panels including the hit panel, a composition of vectors is shown according to the triangle rule. Although the speed of the ball 5 is the representative vector of the impact, it is correct as a first approximation to ignore the gravitational effect and to vectorially indicate the forces involved in the impact. With fj, the vector representative of the force imparted by the shot is indicated; with fR the vector representative of the constraint reaction is indicated; and with fu the vector representative of the "useful" component of the fp is indicated, such component orthogonal to the panel which determines its translation speed. In order to make the score 27 more correct, it will be necessary to take under consideration the angles a and β in order to refer the impact values to the panel indicated as the one to be hit. This requires the calculation of a corrective factor, as will be described below.

Figure 7 shows an axonometric view of a first embodiment of the board 1, in which one can observe the projection of the panels 2 beyond the surface of a plate 30, windowed at the panels 2 in order to allow their translation in both directions, and whose edges correspond to the frame 12. The panels 2 are constituted by a front wall made of wood or plastic 2a rigidly connected to a base of a metal wall of box-like shape 2b open at the other base. Beyond the plate 30 in the direction of the building wall for fixing the panel 1, the following are observed in order: a protection cover 31 of a translation mechanism for the panels 2 inside the board; a perforated plate 32; the same number of rows of linear transducers 33 as there are panels 2; and a second plate 34 with longitudinal openings 53. Four spacer bushes 35 are placed at the four corners comprised between the windowed plate 30 and the perforated plate 32; four other spacer bushes 36 are placed at the four corners comprised between the perforated plate 32 and the second windowed plate 34. Four angular screws 37 cross, in order: the plate 30, the bushes 35, the plate 32, the bushes 36, and the second plate 34, against which the respective nut and lock nuts are tightened. The board 1 can be further tightened along the sides with the indicated system of screws and bushes. The board 1 includes an electronic processing unit 38 for the scores, connected to the linear transducers 33 by means of a cable 39 in order to acquire the information from the panels 2, and connected to the LED scoreboard display 8 in order to transfer the scores 25, 26, and 27.

Figure 8 is an exploded view which better shows the sequence of the elements composing the board 1 introduced in the preceding figure, where in order to simplify the design only one panel 2 is shown, although the description holds true for all the panels. Starting from the outside and moving inward, four angular screws 40 and respective nuts 41 fix the impact wall 2a to the hollow body 2b of the panel 2. The head of the screws 40 is embedded in the wall 2d. The panel 2 is placed astride the edge of an opening of square shape 42 obtained in the plate 30. A pin 2c crosses the center of the base of the box-like portion of the panel 2b but not the impact wall 2a. The portion of the panel 2 which crosses the opening 42 is housed in a seat 43 formed by four longitudinal elements 44 placed in contact with the edges of the panel 2 in order to guide its translation. The elements 44 are short metal profiles whose form depends on their placement inside the board 1 ; they are kept in their position by the perforated plate 32 which for such purposes has notches 45 with the same shape as the profiles 44, arranged at the vertices of a square with side nearly equal to the panel 2. The seat 43 is obtained by inserting one end of the profiles 44 inside the notches 45 and the other end in a perimeter recess of the opening 42. The multiplexing of the seat 43 for receiving all the panels 2 constitutes a cell structure 430 for the telescopic guiding of the same, also visible in the enlarged cross section. The seat 43 includes a helical spring 46 which works (ground) under compression. The spring 46 is longitudinally crossed by the pin 2c. The plate 32 has a hole 51 at the center of each zone delimited by the notches 45 in order to allow the passage of the pin 2c. The terminal plate 34 supports the linear transducers 33, in the current case the linear potentiometers, arranged as a matrix of lines and columns with the sliders 47 aligned with the pins 2c. Between adjacent columns of transducers, the longitudinal windows 53 are open in order to allow the exit of the connection cables 39 and the lightening of the structure. The screws 37 have smooth stem except for the terminal part, which is threaded for the tightening of a nut 37a and a lock nut 37b against the bottom plate 34.

The figures 9, 10, and 11 show the form assumed by the elements 44, respectively, on the four corners, along the sides, and inside the board 1. More precisely, in figure 9 an L-shaped 44a profile is visible, used on the four corners. In figure 10, a T-shaped profile 44b is visible, used on the four sides. And finally in figure 11, a cross-shaped profile 44c is visible, used inside the space delimited by the preceding profiles.

Figure 12 is a section along the plane A-A of figure 8 in which the exploded elements are recomposed in the translation mechanism for the panels 2 inside the board 1 , limited only to the panel 2 shown in the figure in the configuration in which it is not subjected to impact. With reference to figure 12, it is observed that the depth of the seat 43 for the translation of the panel 2 is determined by the length of the profiles 44c, and such length is approximately equal to the depth of the panel 2. The free length of the spring 46 is greater than the length of the profiles 44c, and is such to maintain the impact wall 2a and a portion of the hollow body 2b outside the windowed plate 30 for about a third of the depth of the panel 2, in such a manner ensuring a maximum travel of the panel of about a third of its depth. A travel of such length is sufficient for tracking the compression force of the spring 46 with precision. The stability of the seat 43 during the translation of the panel is ensured by the fact that the ends of the profiles 44c are respectively locked against the plates 30 and 32 in suitable seats, better visible in the enlargements E, F, G. The enlargements E and F show the two ends of a profile 44c in rectangular seats in the plates 30 and 32. The enlargement G shows a variant in which the most internal end of the profile 44c is forced in a rectangular hole of the plate 37.

The pin 2c has a stop head 2d of greater size than the diameter of the inlet hole in the base of the box-like wall 2b. The impact wall 2a has a seat for housing the head 2d. Two washers 49 and 50 are placed astride the pin 2c at the two ends of the spring 46. The stem of the pin 2c is longer than the distance between the plate 30 and the plate 32, and therefore it crosses through the respective hole 51 present at the plate 32 and comes into contact with the end of the slider 47 of the linear translator 33, maintained in maximum elongation position by a helical return spring 48. At a pre-established distance from the point, the pin 2c is orthogonally crossed by a short screw 54 locked with a nut; the task of the screw 54 is to prevent the panel 2 from being unthreaded from its seat, but nevertheless it leaves it free during the oscillatory motion to be pushed beyond the free length of the spring 46. The linear transducer 33 is fixed to the plate 34 by means of one or more bolts 52. With regard to the measurement of deflection x of the spring 46, as stated proportional to the shot force, it is necessary to position an arbitrary reference system, like that indicated in the figures having the origin on the more internal face of the plate 32; in such case, the end of the pin 2c is placed at a distance ¾ from the origin. The configuration shown in figure 13 differs from that of figure 12 for the fact that the soccer ball 5 has violently impacted against the impact wall 2a of the panel 2, making the box-like body 2b return completely inside the seat 43. The rigidity of the spring 46 is selected in a manner so that it reaches the locking length in the presence of particularly violent limit impacts (which can still be assumed);, this allows better coupling the deflection interval of the spring to the interval of shots of various strength. For example, in the case of the figure, the locking length of the spring 46 has not yet been achieved, even if the impact wall 2a is outside the plate 30 by only about half the thickness; there would still be a margin of retreat, flush with the opening, before the end of the wall 2b touches the plate 32, blocking the possible, rather improbable residual translation. In figure 13, the translation of a length % of the panel 2 towards the inside of the board 1 led to the exit of equal length of the stem 2c from the hole crossing through the plate 32, and a shortening = (x— x e J of the return spring 48 due to the return of equal length of the slider 47 of the linear potentiometer 33, which correspondingly records a voltage proportional to the variable . The return spring 48 is infinitely less rigid than the spring 46, such that its contribution to the damping of the impact is insignificant.

The progression of the analogic voltage provided by the linear potentiometers is subjected to the processing unit 38, constituted by a circuit board on which the following are mounted: samplers, analog-digital converters, a clock generator based on a quartz oscillator, a circuit for generating the synchronism signals necessary for the various operations and a microprocessor for the processing of the scores 25, 26, 27 on the basis of the digital samples. In a suitable APPENDIX, the guide criteria for obtaining one such electronics unit are discussed, which together with the description of the method for processing the scores provides a sufficient description for the obtainment thereof

Figures 14 and 15 give a three-dimensional view of the translation mechanism shown in figures 12 and 13, with regard to a panel 2 placed in a corner of the board 1. A similar selection allows simultaneously using the three types of profiles 44a, 44b, and 44c employed in the construction of the translation seat of the panel 2.

The thorough description of the structural means of the board 1 for the panels of square shape is easily adaptable to the panels of hexagonal shape; for such purpose, it is sufficient to use the profiles 44c with three sides arranged at 120°, and profiles 44a and 44b as indicated in figure 3 at the corners and the sides of the board 1 ; of course, the shape and arrangement of the notches 45 will consequently have to be varied.

Figure 16 shows an exploded view of a second embodiment of the board 1, different from the embodiment of figure 8 mainly for the following: in the structure of the movable panels, in the structure of the telescopic guide means for the panels, in the absence of linear potentiometers in series at the helical springs which damp the impacts, in the presence of accelerometers attached directly to the panels, and optionally in the presence of microswitches driven by the movement of the panels. With reference to figure 16, proceeding from the outside towards the interior of the board 1, the following are observed in order: a first framework 60 externally similar to the frame 12; a second framework 61 structured in contiguous cells 62 organized in adjacent columns (or rows) for housing the same number of movable panels 63, preferably made of wood or plastic, potential shot targets; a third framework 64 identical to the framework 60 in mirror- image position; a series of perforated bars 65, twice the number of the cells 62 in a manner such that each column of cells 62 is opposite a respective pair of bars 65. The two frameworks 60 and 64, since they are externally similar to a frame, have a wide access window respectively for the presentation of the shooter side of the panels and for the exit of the electrical cables coming from the transducers and from the microswitches on the rear side. The frameworks 60 and 64 are shells that are windowed for receiving and locking the cell framework 61 inside the space that is created by their contraposition, as is also shown in the cross section reported in the upper left corner of the figure. Four screws 66 penetrate into the same number of holes present in the four corners of the frameworks 60 and 64; on the four screws 66 at the outlet of the framework 64, four bushes 67 are inserted of suitable length and the entire set is tightened by means of nuts 68 and lock nuts 69. The bars 65, better visible in figure 20, have parallelepiped shape with reduced thickness at the two ends, each having a pair of holes 70 for fixing to the framework 64. The body of each bar 65 beyond the two ends is flush with the internal frame of the rear framework 64, in a manner such that it abuts against the cell framework 61 for the anchoring of the respective resilient means. For such purpose, the generic bar 65 has a series of pairs of holes 71 at each cell of the framework 61 opposite such bar. The resilient means are constituted by a set of four springs 75 for each panel 63, placed astride the same number of screws 74 which cross through the panels 63 in proximity to the corners, and the holes 71 in the bars 65. The head of the screws 74 is embedded in the panels 63 while the stem crosses through a first washer 76 placed between the spring 75 and the framework 64 and a second washer 77 placed beyond the framework 64 before a stop nut 78 and relative lock nut 79. An accelerometer transducer of piezoelectric type 80 is fixed on the rear of each panel 63, as is better shown in the top enlargement in the figure. From each accelerometer 80, a cable 81 departs which crosses through the interspace between the respective adjacent bars 65 in order to head towards the control unit 38 (not shown in figure 16). A microswitch 82 for each panel 63 is optionally fixed to the center of the corresponding pair of bars 65, in whose interspace the relative electrical cables 83 pass through. The movable contact of the microswitch 82 is driven by the translation movement of the panel 63. Having four springs 75 for each panel 63 is not binding, since the cell structure 61 is capable of maintaining the telescopic alignment of the panels 63 (shaped as such) even in the presence of only one central spring.

Figures 17, 18, and 19 show the single structural element 85, preferably made of aluminum, and the mode of use of the same for composing the structure of the cell framework 61. The structural element 85 of figure 17 is a rectangular plate on which the slits 86 have been obtained; such slits 86 are parallel and equidistant, open at a longer side, orthogonally thereto, and terminate at about half the width of the plate; the two terminal slits have an edge 87 pre- established by both of the shorter sides. The width of the slits 86 coincides with the thickness of the plate 85. The distance between adjacent slits is nearly equal to the length of the side of the square panel 63. The formation of the cells 62 occurs as shown in the figures 18 and 19 in which two elements 85a and 85b are arranged orthogonally with respect to each other with the respective slits 86a and 86b opposite and aligned, after which they are made to translate towards each other until the two bottom walls of the slits come into contact and prevent further movement. The same maneuver is repeated for all of the (n+1) 2 elements 85 constituting the framework 61. It would also be possible to obtain a framework similar to the framework 61 but with a smaller number of elements 85, for example (n-1) 2 ; in such case, there would be no space for the edge 87 beyond the perimeter cells, and it would thus be necessary to modify the framework 60, which will have to provide the outermost wall of such cells, and the framework 64, which will be reduced to a flat frame.

Figure 21 is a section along the plane B-B of figure 16 in which the exploded elements are recomposed in the translation mechanism for the panels 63 inside the board 1 , limited to only the panel 63 shown in the figure in the configuration in which it is not subjected to impact. With reference to figure 21, it is observed that the depth of the seat for the translation of the panel 2 is determined by the width of the plates 85 constituting the cell framework 61, and such width is about double the depth of the panel 63, a value which does not limit the possibility to make deeper cells, even if this is unnecessary when using piezoelectric accelerometers 80. The effectiveness of the cell 62 in the telescopic guide of the panel 63 also depends on the structure of the panel, which is a parallelepiped, preferably made of wood or plastic, hollow internally for housing the accelerometer 80, as shown at the bottom of the figure. Due in fact to such structure, the lateral walls of the panel 63 are longitudinally extended as slides which maintain the panel inside its own cell 62, even when the impact wall is completely outside it. At the top of the figure, the enlargement is shown of the seat of the screw 74 in the panel 63, where it is observed that the screw 74 crosses through/screws into a threaded bush 84, such bush forced for about a third of its length into a hole present on the internal side of the wall of the panel 63. The bush 84 has an intermediate ring of greater diameter in contact with the abutment of the hole, and a terminal part which penetrates into the spring 75 at one end of the same by abutting against the intermediate ring. The bush 84 makes the screw 74 integral with the panel 63, preventing the head of the screw from projecting from the wall during the translation of the panel towards the interior. The washer 76 acts as an abutment of the spring 75 against the back-positioned bar 65. The washer 77 on the other side of the hole 71 crossed by the pin 74 cooperates with the stop nut 78 and the lock nut 79 in determining the initial compression of the spring 75, and consequently an initial length of the same such to maintain the impact surface of the panel 63 outside the opening of the cell 62. The initial compression of the spring 75 is sufficient for avoiding the impacts of the edge of the panel 63 against the bar 65. The configuration shown in figure 22 differs from that of figure 21 due to the fact that the soccer ball 5 has violently impacted against the panel 63, making it move towards the interior of the cell 62. The precompressed spring 75 reaches the locking length when the outer surface of the panel 63 is approximately flush with the edge of the seat 62. The screw 74 exits from the hole 71 for a section equal to the translation of the panel 63 corresponding to the shortening of the spring 75; nevertheless, unlike with the use of linear potentiometers, such section is not monitored for the purposes of the measurement since the piezoelectric accelerometer 80 is sensitive to an "intensive" rather than "extensive" magnitude, and contains its own inertial reference for the measurement of the acceleration. Although the optional microswitch 82 is present in figure 16, it is not used in the embodiments of figures 21 and 22 since the signal generated by the accelerometer 80, suitably filtered and compared with a threshold, is already per se indicative of the impact that occurred. The considerations on the sampling of the signals contained in the first part of the APPENDEX remain valid, also for the board 1 of figure 16.

The board 1 in the embodiment of figures 8 and 16, i.e. including a transducer for each panel, is treated in the same manner by the microprocessor control program present in the processing unit 38.

The microprocessor executes an initial step of the score-assigning method in which it assigns a line index / ' and a column index k to each panel based on the respective position in the board 1 , considered to be a matrix of Ni lines and Mk columns; to the detectors and/or transducers, the same indexes i, k are assigned of the relative panels. After which, the following steps of the method, from the second step onward, are cyclically repeated:

a) Written into a memory in the second step are the values of the samples , k generated by all the index transducers , k with regard to a time window of duration comparable to the transitory time of the sampled signal, the writing of each sample being subordinate to the fact that its value exceeds an admission threshold.

b) The third step consists of seeking the sample i, k with the highest value. c) In the fourth step, the distance is calculated of the panel marked as that to be hit from the panel /, k associated with the greatest value sample, and from the adjacent panels, also diagonally adjacent, associated with the above-threshold samples. The adjacent panels are those with indices: i+l,k; i-J,k; i,k+l; i,k-l; i+l,k+l; i+l,k-l; i-l,k+l; i-l,k-l. The aforesaid distance is the Pythagoras distance calculated over corresponding indices multiplied by the real value of the side of the square panel. For example, the distance between two horizontally flanked square panels with 40 cm side if given by: M& k + D* + ( )* x 40 = 40 em , T h e distance between two square panels with 40 cm side with an upper right corner in common is given by:

d) V(i - l, fc + l) a +- (i, k) 2 X 40 cm = 40 J2 = 56,56 cm

e) In the fifth step, the values of the distances calculated in the preceding step are summed together and the total divided by the number of the addends, obtaining a value representative of the shot precision.

f) In the sixth step, the sample k with greatest value is summed with the above-threshold samples of adjacent indices i, k, also diagonally adjacent, obtaining a representative value of the shot force.

g) In the seventh step, a score is calculated by summing together the aforesaid representative values of the precision and the shot force, possibly multiplied by respective weights.

Since the shooter sees the panels from different angles, one same shot will have a dynamic component useful for computing the force of the shot of different weight according to the hit panel. By selecting a generic panel as a target, it is instead desirable that the shots which hit the center of the panel are assigned the highest score. With regard to the component of the score due to the shot force fj, it will be necessary to introduce correctives. Therefore, before the summation in step 6), each sample of the signal can be multiplied by a corrective factor depending on the position of the panel with indices /, k originating from the sample. The corrective factors to be associated with the panels , k are calculated as follows (it is useful to refer to figure 6):

- calculating the cosine of the angle a subtended from the line joining the shooting position with the center of the panel i, k and the orthogonal projection of such joining line in the vertical plane that contains it;

- calculating the cosine of the angle β subtended from the line joining the shooting position with the center of the panel /, k and the orthogonal projection of such joining line in the horizontal line that contains it. The two cosines both decrease the module of the shot force fj with respect to a panel "ideally" hit by a vector f T orthogonal thereto. The overall decrease AF is given by COs a ÷ cos ϊ. The correct factor FC that multiplies the value of the generic sample /, k is therefore: FC = Λ— AF . It can be verified that also for the closest shots, from 11 meters, against a square board with two meters per side, the corrective factors assume such low values that they can be ignored, due to the properties of the cosine function which decrease much more slowly at the origin.

The teaching imparted for the assignment of the score to the single impact can be repeated with several simultaneous impacts, simply by repeating the preceding steps for each panel indicated as target and for each impact identified by a sample of higher value with respect to the samples i, k, whose mutual distance evaluated in the corresponding indices is sufficient for deeming the impact zones to be separate.

The remaining figures 23, 24, and 25 illustrate a minimal variant of the board 1 of figure 16, particularly suitable for the use of the Doppler effect radar sensor 100 (figure 1) for measuring the speed of the soccer ball 5. Such tachometric sensor is advantageous because it provides a signal directly proportional to the speed of the tracked body, in the current case the soccer ball 5, but does not exclude the use of a radar sensor capable of measuring only the distance between the source and the movable body, the average speed being easily obtainable from measurements of incremental distances compared with the differences in the measurement times. Thus, the size of the translation required by the single hit panels is actually quite small, just that required for activating the microswitch 82, which is now no longer optional but necessary for signaling the impact that occurred. The placement of the microswitches 82 to form a matrix makes such devices like the position transducers of the panels. The minimum required movement of the latter suggests a modification of the panels themselves, and likewise a modification of the plates 85 which constitute the structure of the cell framework 61. Figure 23 shows both modifications in the right part of the page. With reference to figure 23, it is noted that a first plate used is still the plate 85, while a second plate used is a profile 91 which differs from the plate 85 due to the presence, on the two faces of the profile 91, of identical tabs 92 between adjacent slits 86. The tabs 92 are orthogonal to the slits 86 and to the face of the profile 91 from which they extend, at an identical distance from the edge. Such distance is greater than or equal to the thickness of the panels 90, now constituted by the single impact wall with the four angular holes for the passage of the screws 74, which cross through the spring 75. The profile 91 therefore provides the abutments for the row of panels 90 housed in the strips 93 comprised between the longitudinal edge and the tabs 92. Figures 24 and 25 are longitudinal sections which differ from the sections of figures 21 and 22 due to the differences in the abovementioned constituent elements. With reference to figure 24, showing the configuration of the board 1 without impact, it can be observed that the spring 75, precompressed by the partial screwing of the nuts 78 and 79, has an initial length such to maintain the panel 90 exiting outward from its own positioning cell in the board 1 by more than half the thickness. Between the internal edge of the panel 90 and the two abutment tabs 92, a rubber gasket 94 is visible which cooperates with the spring 75 in damping the hit. In the figure it is clear that there is a scarcity of free space available for the translation of the panel 90. The end of the pivoting contact arm of the microswitch 82 touches the wall of the panel 90, forming an angle with width such that the electrical contact is open. The configuration shown in figure 25 differs from that of figure 24 since the soccer ball 5 has violently impacted against the panel 90, making it in turn impact against the abutment tabs 92 by means of the rubber buffer 94. At the time of impact, the panel 90 is nearly flush with the inlet space of its positioning cell, and the difference of position is sufficient for driving the closing of the electrical contact of the microswitch 82.

The score calculation method differs from that previously described only in the sixth execution step, in which the representative value of the shot force is proportional to the speed measurement of the ball 5 provided by means of tachometric radar sensor 100. On the basis of the description provided for a preferred embodiment, it is obvious that any changes can be introduced by the man skilled in the art, without departing from the scope of the invention as results from the following claims.

APPENDIX

Since the shots carried out against the board 1 are entirely random, the microprocessor which processes the score cannot know the instant of impact nor the panel that will be hit ahead of time; for this reason, the microprocessor must employ means which cyclically interrogate the transducers coupled to all the panels. Therefore, the processing and control means must include the sampling (sample&hold) devices for the voltage generated by each transducer, followed by respective analog-digital converters and by a timed multiplexer in a manner so as to sequentially transfer the digital samples coming from all the samplers to a work memory of the microprocessor, repeating the cycle over the entire duration of the activity period of the board 1. Such task requires a suitable processing speed by the processor, which will have to complete the operations aimed for the determining the score in the time which passes between one sample and the next, or alternatively in the time which passes between the acquisition of one batch of M samples from each single transducer and the next batch. In the presence of N panels, the control frequency of the multiplexer will have to be Nfc, where fc is the sampling frequency. It is necessary to specify that most of the signals generated by the transducers are under-threshold; hence the signals only engage the processor so they can be recognized as over- or under-threshold. The sampling frequency fc is therefore the magnitude that conditions the processing speed. The Nyquist criterion establishes that in order to be able to reconstruct a signal from the sequence of its own samples, and thus capture the sample with maximum value representative of the force acting during the impact, the frequency fc will have to be at least double the maximum frequency fb contained in the frequency spectrum of the sampled signal. The frequency spectrum is a curve which shows the progression of the power of a signal as a function of the frequency considered to be an independent variable. The spectra generally have a maximum around a center band frequency and then monotonically decrease to the sides of the same, so that it is correct to ignore the contribution beyond a certain frequency which marks the band limit, like the frequency fb.

In the specific case of figures 12 and 13, the frequency spectrum is that of the signal generated by each linear potentiometer 33, which "follows" the mechanical characteristics of the helical spring 46 used for damping the relative panel 2. It is therefore necessary to determine, analytically or by means of direct measurement, the bandwidth of the analog signal at the output of the generic linear potentiometer 33. The system constituted by the panel 2, by the spring 46, and by the sliding guide 44c of the panel 2a, 2b can be mechanically modeled as a damped harmonic resonator, of which it is possible to obtain the response to the impact in analytical form by knowing the following parameters: the position x 0 of the movable end of the spring at rest; the speed ¾ transferred to the panel at the instant of the impact, the free pulsation ω « of the resonator in the absence of friction, the viscous damping factor f due to all the frictions which brake the motion of the panel. The following relations hold & is the rigidity of the spring, m is the oscillating mass corresponding in a first approximation to the mass of the panel,

corresponding to the sliding friction factor between the panel and the guide, while is the critical damping which will be described below. Operatively, the impact imparts an initial velocity ¾ to the panel, which compresses the spring by making it undergo a shortening &x = (x - x e ) proportional to the shot force. The elastic energy accumulated in the spring at the end of the compression imparts a velocity to the panel in the opposite direction, which makes it return towards the starting position in accordance with one of the three possible modes determined by the damping factor. For systems characterized by ζ = I , i.e. whose damping factor is equal to the critical factor, the panel returns to the initial position in an aperiodic manner. For systems characterized by ξ < 1 , i.e. whose damping factor is less than the W

27 critical factor, the panel in its return travel goes beyond the initial position, being projected beyond the surface of the board by a length section less than the initial ; this causing a lengthening of the spring with respect to the free length o , after which the panel oscillates around the initial position as the amplitude &x decreases, until it stops flush with the board. For systems characterized by ζ > 1 , i.e. whose damping factor is greater than the critical factor, the panel compresses the spring for a shorter section than that of the critical damping, before returning to the initial position in an aperiodic manner. Finally, the damped harmonic oscillator is the following

x(t) = X 0 e -f a« f ■ sin ((ω„^1 - ξ) - t + ) ^ where: ω ρ = ω « γ 1 ~ £ is the characteristic pulsation of the system, while %o and are two arbitrary constants that can be determined by setting two initial conditions if the state of the harmonic oscillator is known, e.g.: x(0) = x 0 and i(0) = ¾ experimentally determined in a specific impact. The (1 ) provides the transitory response of the mechanical system to the initial impulse imparted by the impact with the projectile, from which one can calculate the corresponding Fourier integral:

Χ(ω) = I x(£)t? dt

m (2)

which provides the frequency spectrum of the signal and thus the bandwidth fb at which the sampling frequency f c 2 fb can be traced, upon filtering the components of the spectrum (ω) with negligible amplitude around the center band frequency f . . As an alternative to the analytical obtainment of fb, it is also possible to apply a spectrum analyzer to the output of the generic transducer. From the theory of the Fourier transform, it is known that the lower the time employed by the signal x(t) in reaching the maximum elongation 5 the greater its bandwidth fb will be. The lower duration of the rise time depends in turn on the smaller value of the damping factor ξ . Critical damping would be the ideal condition, since it allows obtaining the greatest elongation of the spring, and hence of the measurement interval, without oscillations of the panel. Damping values around the critical value nevertheless do not invalidate the quality of the signal, since critical damping is difficult to calibrate. Given the same damping, the lower rise time will depend on the initial velocity of the panel, so that the maximum bandwidth will have to be evaluated when the panel is hit by the projectile launched at the maximum speed provided. Since the panel-spring harmonic oscillator is of mechanical type, the value set at the minimum sampling frequency fc fully falls within the limits of consumer electronic components; there will also be a margin for an oversampling, useful for lessening the importance of the filtering characteristics. It is reasonable to assume that the interval between subsequent shots exceeds the processing times of the relative scores by the current processors - by several orders of magnitude. Therefore, the scores can be traced in real time, even in the case of simultaneous shots. Operatively, the processor can access a work memory via writing and reading, such memory's capacity such to be able to contain the samples generated by all the transducers in a time window whose duration is compatible with the typical duration of the transitory time of the signal x ( t) . Such duration for a signal which exponentially declines is on the order of three time constants ~ "ω « . By operating in such a manner, one will be certain that each stored burst will contain the sample with maximum value necessary for the calculation of the scores.