Determination of spin parameters of a sports ball

Description

[0001] The present invention relates to the determination of spin parameters of a sports ball while in flight, and in particular to the determination of the spin axis and/or a rotational velocity of the sports ball.

[0002] Such parameters are highly interesting both for using and developing sports balls and other sports equipment, such as golf clubs, irons, rackets, bats or the like used for launching sports balls.

[0003] For golf balls, such determinations normally have been made by adding to the golf balls strips or patterns of a radar reflecting material. This, however, can only be made for test purposes in that this type of ball is highly standardized. Technologies of this type may be seen in US-A-6,244,971, GB 2, 380 682, US 6 292 130, US 5 401 026, US 5 700 204, US 5 138 322, and US 2002/0107078.

[0004] The present invention aims at being able to perform these determinations without altering the sports balls.

[0005] A first aspect of the invention relates to a method of estimating a rotational velocity or spin frequency of a rotating sports ball in flight, the method comprising:

1. a number of points in time during the flight, receiving electromagnetic waves reflected from the rotating sports ball and providing a corresponding signal,

2. performing a frequency analysis of the signal, and identifying two or more discrete spectrum traces positioned at least substantially equidistantly in frequency and being continuous over time, and

3. estimating the velocity/frequency from a frequency distance between the discrete spectrum lines.

[0006] In the present context, any type of electromagnetic wave may be used, such as visible radiation, infrared radiation, ultrasound, radio waves, etc.

[0007] In addition, any number of points in time may be used. It may be preferred to receive the radiation as long as a meaningful detection is possible or as long as the spectrum traces may be determined in the signal. Normally, the reception and subsequent signal analysis is performed at equidistant points in time.

[0008] In order to ensure that the distance between the spectrum traces is correctly determined, preferably more than 2 equidistant spectrum traces are identified.

[0009] Naturally, the frequency analysis may result in a spectrum of the signal. This, however, is not required in that only the equidistant spectrum traces are required.

[0010] In this context, a spectrum trace is a sequence of frequencies which is at least substantially continuous in time but which may vary over time. In the present context, a trace normally is a slowly decaying function, but any shape is in principle acceptable and determinable.

[0011] Preferably, step 1. comprises receiving the reflected electromagnetic waves using a receiver, and wherein step 2. comprises identifying, subsequent to the frequency analysis, a first frequency corresponding to a velocity of the ball in a direction toward or away from the receiver and wherein identification of the spectrum traces comprises identifying spectrum traces positioned symmetrically around the first frequency.

[0012] In this manner, another frequency is determined which may aid in ensuring that the equidistant spectrum lines are correctly determined. In addition, requiring also the symmetry around this frequency further adds to ensuring a stable determination.

[0013] In a preferred embodiment, step 2. comprises, for each point in time and sequentially in time:

• performing the frequency analysis and an identification of equidistant candidate frequencies for a point in time,
• subsequently identifying those candidates which each has a frequency deviating at the most a predetermined amount from a frequency of a candidate of one or more previous points in time,
• then identifying, as the frequency traces, traces of identified candidates,

and where step 3 comprises estimating the velocity/frequency on the basis of the identified spectrum traces.

[0014] This has the advantage that the determination may be made sequentially, such as in parallel with the receipt of the reflected radiation. Also, a noise cancellation is performed in that what might resemble valid equidistant spectrum lines in one measurement may not have any counterparts in other, such as neighbouring measurement(s), whereby it may be deleted as a candidate.

[0015] In this context, the predetermined amount or uncertainty within which a candidate should be may be a fixed amount, a fixed percentage or a measure depending on e.g. an overall signal-to-noise ratio determined.

[0016] A second aspect of the invention relates to a system for estimating a rotational velocity or spin frequency of a rotating sports ball in flight, the system comprising:

1. a receiver adapted to, a number of points in time during the flight, receive electromagnetic waves reflected from the rotating sports ball and provide a corresponding signal,

2. means for performing a frequency analysis of the signal, and identifying two or more discrete spectrum traces positioned at least substantially equidistantly in frequency and being continuous over time, and

3. means for estimating the velocity/frequency from a frequency distance between the discrete spectrum traces.

[0017] Naturally, the comments relating to the first aspect again are relevant.

[0018] Thus, the means 2. may be adapted to identify, subsequent to the frequency analysis, a first frequency corresponding to a velocity of the ball in a direction toward or away from the receiver and to identify, as the spectrum traces, spectrum traces positioned symmetrically around the first frequency.

[0019] A preferred manner of determining the velocity/frequency is one, wherein the means 2. are adapted to, for each point in time and sequentially in time:

• perform the frequency analysis and the identification of equidistant candidate frequencies for a point in time,
• subsequently identify those candidates which have a frequency deviating at the most a predetermined amount from a frequency of a candidate of one or more previous points in time,

then identify, as the frequency traces, traces of identified candidates,
and where the means 3 are adapted to estimate the velocity/frequency on the basis of the identified spectrum traces.

[0020] In the following, a preferred embodiment of the invention will be described with reference to the drawing, wherein:

• Figure 1 is a schematic illustration of a rotating ball and a Doppler radar,
• Figure 2 illustrates a spectrum having equidistant spectrum lines,
• Figure 3 illustrates the determination of equidistant spectrum lines,
• Figure 4 illustrates a measured 3D trajectory of a golf ball,
• Figure 5 illustrates the final spin frequency chart over time,
• Figure 6 illustrates a spin vector relating to the trajectory of figure 4,
• Figure 7 is a flow chart over the detection of spin frequency,
• Figure 8 illustrates the determination of the orientation of the spin vector, and
• Figure 9 is a flow chart of the determination of the orientation of the spin vector.
• Figure 10 is a flow chart of the determination of the orientation of the spin vector when it can be assumed that the spin axis lays in a known plane.

[0021] Using a Doppler radar to measure the spin frequency of sports balls has been known for years; see US 6,244,971 and US 2002/0107078 A1. However, all these inventions are based on modifying the reflection off some area of the ball, typically by adding conducting material either under or on the cover of the ball. The present embodiment also uses a Doppler radar, but does not require any modifications to the ball in order to extract the spin frequency. This aspect increases the commercial value of the present invention significantly.

[0022] In the past, the orientation of the spin axis of a rotating ball has been measured by using cameras placed close to the launching area. These systems only provide the orientation of the spin axis in one point in space, right after launch. The present invention uses a 3 dimensional trajectory measuring equipment to measure the spin axis orientation during flight.

[0023] The present invention makes it possible to have a continuous measurement of the spin frequency and spin axis orientation during the entire flight of the ball.

Spin frequency

[0024] Consider a Doppler radar 3 in figure 1. The Doppler radar comprises a transmitter 4 and a receiver 5. The transmitting wave 6 at frequency Ftx is reflected on the ball 1, the reflected wave 7 from the ball 1 has a different frequency Frx. The difference between the reflected frequency and the transmitted frequency, is called the Doppler shift F_dopp. F_dopp is proportional to the relative speed Vrad of the reflecting point A on the ball 1 relative to the radar 3.


, where λ is the wavelength of the transmitting frequency.

[0025] A coordinate system 2 is defined as having origin in the center of the ball and X-axis always pointing directly away from the radar, the Z-axis is in the horizontal plane.

[0026] Vrad is the change in range from the Doppler radar 3 relative to time (Vrad = dR/dt). With the coordinate system 2 in figure 1, Vrad equals the X component of the velocity of the ball 1.

[0027] The strongest reflection from the ball 1 will always be the point A which is perpendicular to the line-of-sight from the radar. When the ball 1 is spinning, the point A with the strongest reflection will in fact be different physical locations on the ball over time.

[0028] The output signal of the Doppler receiver 5 from the reflection of point A on the ball can be written as:


, where a(t) is the amplitude of the received signal.

[0029] Consider now the situation of a spinning ball 1 with an angular velocity of ω of the ball around the Z-axis. The reflection from a fixed point B on the ball 1, with a radius of r, will have a Doppler shift relative to the radar 1 of:

[0030] The output signal of the receiver 5 from the reflection of point B on the ball can be written as:


, where d(t) is the relative amplitude of the received signal from point B relative to point A on the ball 1.

[0031] By substituting [2] and [3] in [4], one gets:

[0032] It is seen that the output signal from point B consist of the signal from point A modulated by a signal X_modB(t):

[0033] The exponential term of the modulating signal, is recognized as a frequency modulation (FM) signal, with a modulation frequency of ω/2π and a frequency deviation of 2/λ*r*ω.

[0034] From modulation theory it is well known that the spectrum of a sinusoid frequency modulation gives a spectrum with discrete frequency lines at the modulation frequency ω/2π and harmonics of this, the power of the spectrum lines of the m'th harmonic are equal to J_m(4π*r/λ), where J_m() is the Bessel function of first kind of m'th order.

[0035] The amplitude signal d(t) of the modulating signal in [6], will also have a time dependent variation. d(t) will like the exponential term in [6] also be periodic with the period T = 2π/ω. Consequently will the spectrum from d(t) also have discrete spectrum lines equally spaced ω/2π. The relative strength of the individual harmonics of d(t) will depend on the reflection characteristics for the different aspect angles.

[0036] In summary, because of reflection from a physical point B on a spinning ball from other positions than when this point is closest to the radar (at point A), the received signal will have equally spaced sidebands symmetrical around the Doppler shift F_dopp,A , caused by the velocity of the ball. The sidebands will have multiple harmonics and will be spaced exactly the spin frequency of the ball ω/2π. Only in the case of a perfect spherical ball, there will be no modulation sidebands.

[0037] On a normal sports ball there will be several areas on the ball that is not perfectly spherical. Each of these points will give discrete sidebands spaced the spin frequency. The total spectrum for all the scatters on the ball will then add up to the resulting received signal, that of course also has discrete sidebands spaced the spin frequency.

[0038] In the above the spin axis was assumed to be constant during time and parallel with the Z-axis. If the spin axis is rotated α around the Y-axis and then rotated β around the X-axis, it can easily be shown that the x-component of the velocity of point B equals:

[0039] Note that Vx,B is independent of the rotation β around the X-axis. Since Vx,B also is periodic with the period T = 2π/ω, except for the special case of spin axis along the X-axis (α = 90deg), the corresponding Doppler shift from point B with rotated spin axis will also have discrete sidebands spaced exactly the spin frequency of the ball ω/2π. This means as long as the spin axis orientation changes slowly compared to the spin frequency, the spectrum of the received signal will contain discrete frequency sidebands spaced the spin frequency of the ball ω/2π.

[0040] In figure 2 the received signal spectrum of a golf ball in flight is shown. In figure 2 It is clearly seen that the spectrum contains a strong frequency line that corresponds to the velocity of the ball, as well as symmetric sidebands around this velocity that are equally spaced with the spin frequency.

[0041] First the ball velocity is tracked 8 using standard tracking methods. Then symmetrical frequency peaks around the ball velocity is detected 9. In figure 3 the frequency offset of the symmetrical sidebands are shown relative to the ball velocity. The different harmonics of the spin sidebands are tracked over time using standard tracking methods 10. The different tracks are qualified 11, requiring the different harmonic tracks to be equally spaced in frequency. The different tracks are solved for their corresponding harmonic number 12. After this, the spin frequency can be determined from any of the qualified harmonic tracks 13, provided that the frequency is divided by the respective harmonic number.

[0042] The final spin frequency chart over time is shown in figure 5, which contains all of the harmonic tracks.

[0043] The step-by-step procedure for measuring the spin frequency is described in figure 7.

Spin axis orientation

[0044] The 3 dimensional trajectory of the ball flight is obtained by appropriate instruments. In the preferred embodiment of the present invention, the radar used for measuring the spin frequency is also used to provide a 3 dimensional trajectory of the ball flight, see figure 4.

[0045] Assuming that the ball is spherical rotational symmetric to a high degree, their will be three and only three forces acting on the ball. Referring to figure 8, the accelerations will be:

• gravity acceleration, G
• air resistance / drag acceleration, D
• and lift acceleration, L

[0046] The total acceleration acting on a flying ball is consequently:

[0047] Examples of balls that satisfy the rotational symmetry criteria are: golf balls, tennis balls, base balls, cricket balls, soccer balls etc.

[0048] The drag is always 180 deg relative to the airspeed vector Vair. The lift acceleration L is caused by the spinning of the ball and is always in the direction given by ωxVair (x means vector cross product), i.e. 90 deg relative to the spin vector ω and 90 deg relative to the airspeed vector Vair. The spin vector ω describes the orientation of the spin axis, identified with the spin unity vector ωe, and the magnitude of the spin vector ω is the spin frequency ω found through the algorithm described in figure 7.

[0049] The airspeed vector is related to the trajectory velocity vector V by:

[0050] The procedure for calculating the orientation of the spin vector ω is described in figure 9.

[0051] From the measured 3 dimensional trajectory, the trajectory velocity V and acceleration A are calculated by differentiation 14.

[0052] The airspeed velocity is calculated 15 using equation [9], using a priori knowledge about the wind speed vector W.

[0053] The gravity acceleration G is calculated 16 from a priori knowledge about latitude and attitude.

[0054] Since drag and lift acceleration are perpendicular to each other, the magnitude and orientation of the drag acceleration D can be calculated 17 using equation [10].


, where • means vector dot product.

[0055] Hereafter the magnitude and orientation of the lift acceleration L can be easily found 18 from [11].

[0056] As mentioned earlier, by definition the lift vector L is perpendicular to the spin vector ω meaning that:

[0057] The spin unity vector ωe is normally assumed to be constant over time for rotational symmetrical objects due to the gyroscopic effect. If the spin unity vector ωe can be assumed to be constant over a time interval [t1;tn], then equation [12] constructs a set of linear equations [13].


, where L(t) = [Lx(t), Ly(t) , Lz(t)] and ωe = [ωex, ωey, ωez]

[0058] The linear equations In [13] can be solved for [ωex, ωey, ωez] by many standard mathematical methods. Hereby the 3 dimensional orientation of the spin axis in the time interval [t1,tn] can be determined. The only assumption is that the spin axis is quasi constant compared to the variation of the direction of the lift vector L.

[0059] By combining the spin frequency ω found from the algorithm described in figure 7 with the spin unity vector ωe found from equation [13], the spin vector ω can be found 20 by using equation [14].

Partwise known orientation of spin axis

[0060] In many cases it is known a priori that the spin axis lies in a known plane at a certain point in time. Let this plane be characterized by a normal unity vector n. This means:

[0061] An example of such a case is the spin axis orientation right after launch of ball. When a ball is put into movement by means of a collision, like a golf ball struck by a golf club or a soccer ball hit by a foot, the spin vector ω will right after launch to a very high degree be perpendicular to the initial ball velocity vector V. The normal unity vector n in [15] will in this case be given by equation [16].

[0062] The procedure for calculating the orientation of the spin vector ω in the point in time t0 where the spin vector lays in a known plane characterized by the normal unity vector n is described in figure 10.

[0063] First following the exact same steps 14-18 as described in Figure 9 to obtain the lift acceleration at the time t0.

[0064] Now determine 21 a rotation matrix R that converts the coordinates for the normal unity vector n in the base coordinate system to the x-axis unity vector [1,0,0], see equation [17]. The rotation matrix R can be found by standard algebraic methods from n.

[0065] The coordinates for the lift acceleration L from equation [11] is now rotated 22 through R represented by the Lm vector, see equation [18].

[0066] Similar coordinate transformation for the spin unity vector ωe, see equation [19].

[0067] Since it known from equation [15] that ωexm equals 0, then equation [13] simplifies to equation [20].

[0068] By using that the length of ωem equals 1, the spin unity vector ωe can be found 23 from either equation [21] or [22].

[0069] By combining the spin frequency ω found from the algorithm described in figure 7 with the spin unity vector ωe found from equation [21]-[22], the spin vector ω can be found 20 by using equation [14].

Claims

1. A method of estimating a rotational velocity or spin frequency of a rotating sports ball in flight, the method comprising:

1. a number of points in time during the flight, receiving electromagnetic waves reflected from the rotating sports ball and providing a corresponding signal,

2. performing a frequency analysis of the signal, and identifying two or more discrete spectrum traces positioned at least substantially equidistantly in frequency and being continuous over time, and

3. estimating the rotational velocity/spin frequency from a frequency distance between the discrete spectrum traces.

2. A method according to claim 1, wherein step 1. comprises receiving the reflected electromagnetic waves using a receiver, and wherein step 2. comprises identifying, subsequent to the frequency analysis, a first frequency corresponding to a velocity of the ball in a direction toward or away from the receiver and wherein identification of the spectrum traces comprises identifying spectrum traces positioned symmetrically around the first frequency.

3. A method according to claim 1 or 2, wherein step 2. comprises, for each point in time and sequentially in time:

- performing the frequency analysis and an identification of equidistant candidate frequencies for a point in time,

- subsequently identifying those candidates which each has a frequency deviating at the most a predetermined amount from a frequency of a candidate of one or more previous points in time,

- then identifying, as the frequency traces, traces of identified candidates,

and where step 3 comprises estimating the velocity/frequency on the basis of the identified spectrum traces.

4. A system for estimating a rotational velocity or spin frequency of a rotating sports ball in flight, the system comprising:

1. a receiver adapted to, a number of points in time during the flight, receive electromagnetic waves reflected from the rotating sports ball and provide a corresponding signal,

2. means for performing a frequency analysis of the signal, and identifying two or more discrete spectrum traces positioned at least substantially equidistantly in frequency and being continuous over time, and

3. means for estimating the velocity/frequency from a frequency distance between the discrete spectrum traces.

5. A system according to claim 4, wherein the means 2. are adapted to identify, subsequent to the frequency analysis, a first frequency corresponding to a velocity of the ball in a direction toward or away from the receiver and to identify, as the spectrum traces, spectrum traces positioned symmetrically around the first frequency.

6. A system according to claim 4 or 5, wherein the means 2. are adapted to, for each point in time and sequentially in time:

- perform the frequency analysis and the identification of equidistant candidate frequencies for a point in time,

- subsequently identify those candidates which have a frequency deviating at the most a predetermined amount from a frequency of a candidate of one or more previous points In time,

- then identify, as the frequency traces, traces of identified candidates,

and where the means 3 are adapted to estimate the velocity/frequency on the basis of the identified spectrum traces.

7. A method of estimating a spin, comprising a spin axis and a spin frequency, of a sports ball while in flight, the method comprising estimating the spin frequency according to claim 1 and the steps of:

1. determining at least part of a 3D-trajectory of the flying sports ball,

2. estimating, from the trajectory, an acceleration of the sports ball at a predetermined position along the trajectory,

3. estimating an acceleration of the sports ball caused by gravity at the predetermined position,

4. estimating an acceleration of the sports ball caused by air resistance/drag at the predetermined position, and

5. estimating the spin axis, at the predetermined position, on the basis of the estimated accelerations.

8. A system for estimating a spin, comprising a spin axis and a spin frequency, of a sports ball while in flight, the system comprising the system according to claim 4, the system further comprising:

1. means for determining at least part of a 3D-trajectory of the flying sports ball,

2. means for estimating, from the trajectory, an acceleration of the sports ball at a predetermined position along the trajectory,

3. means for estimating an acceleration of the sports ball caused by gravity at the predetermined position,

4. means for estimating an acceleration of the sports ball caused by air resistance/drag at the predetermined position, and

5. means for estimating the spin axis, at the predetermined position, on the basis of the estimated accelerations.

Ansprüche

1. Verfahren zum Abschätzen einer Drehgeschwindigkeit oder einer Eigendrehfrequenz eines sich drehenden Sportballs im Flug, wobei das Verfahren

1. eine Anzahl von Zeitpunkten während des Flugs, an denen von dem sich drehenden Sportball reflektierte elektromagnetische Wellen empfangen werden und ein zugeordnetes Signal bereitstellen,

2. Durchführen einer Frequenzanalyse des Signals und Identifizieren von zwei oder mehr diskreten signifikanten Spektralbereichen, die wenigstens im Wesentlichen bezüglich der Frequenz äquidistant und über die Zeit beständig sind, und

3. Abschätzen der Drehgeschwindigkeit/Eigendrehfrequenz von einem Frequenzabstand zwischen den diskreten signifikanten Spektralbereichen aufweist.

2. Verfahren nach Anspruch 1, bei dem der Schritt 1. das Empfangen der reflektierten elektromagnetischen Wellen mit einem Empfänger umfasst und bei dem der Schritt 2. nach der Frequenzanalyse ein Identifizieren einer ersten Frequenz umfasst, die einer Geschwindigkeit des Balls in einer Richtung auf den Empfänger zu oder von diesem weg entspricht, und bei dem ein Identifizieren der signifikanten Spektralbereiche ein Identifizieren von signifikanten Spektralbereichen aufweist, die symmetrisch um die erste Frequenz angeordnet sind.

3. Verfahren nach Anspruch 1 oder 2, bei dem der Schritt 2. für jeden Zeitpunkt und über die Zeit aufeinanderfolgend

- Durchführen der Frequenzanalyse und ein Identifizieren von äquidistanten Anwärterfrequenzen für einen Zeitpunkt,

- danach Identifizieren derjenigen Anwärter, die jeweils eine Frequenz aufweisen, die höchstens um einen vorbestimmten Betrag von einer Frequenz eines Anwärters an einem oder mehreren Zeitpunkten abweichen,

- danach Identifizieren als die signifikanten Spektralbereiche Bereiche von identifizierten Anwärtern aufweist,

und wobei der Schritt 3 das Abschätzen der Geschwindigkeit/Frequenz auf der Basis der identifizierten signifikanten Spektralbereiche umfasst.

4. System zum Abschätzen einer Drehgeschwindigkeit oder einer Eigendrehfrequenz eines sich drehenden Sportballs im Flug, wobei das System

1. einen Empfänger, der dazu eingerichtet ist, bei einer Anzahl von Zeitpunkten während des Flugs elektromagnetische Wellen zu empfangen, die von dem sich drehenden Sportball reflektiert worden sind und ein zugeordnetes Signal bereitstellen,

2. Mittel zum Durchführen einer Frequenzanalyse des Signals und Identifizieren von zwei oder mehr diskreten signifikanten Spektralbereichen, die wenigstens im Wesentlichen bezüglich der Frequenz äquidistant liegen und über die Zeit beständig sind, und

3. Mittel zum Abschätzen der Geschwindigkeit/Frequenz von einem Frequenzabstand zwischen den diskreten signifikanten Spektralbereichen aufweist.

5. System nach Anspruch 4, bei dem die Mittel 2. dazu eingerichtet sind, nach einer Frequenzanalyse eine erste Frequenz zu identifizieren, die einer Geschwindigkeit des Balls in einer Richtung auf den Empfänger zu oder von diesem weg entspricht, und als die signifikanten Spektralbereiche signifikante Spektralbereiche zu identifizieren, die symmetrisch um die erste Frequenz angeordnet sind.

6. System nach Anspruch 4 oder 5, bei dem die Mittel 2. dazu eingerichtet sind, um für jeden Zeitpunkt und über die Zeit aufeinanderfolgend

- die Frequenzanalyse und die Identifikation von äquidistanten Anwärterfrequenzen für einen Zeitpunkt,

- aufeinanderfolgend diejenigen Anwärter zu identifizieren, die eine Frequenz aufweisen, die höchstens um einen vorbestimmten Betrag von einer Frequenz eines Anwärters an einem oder mehreren früheren Zeitpunkten abweichen, und

- danach Identifizieren als die signifikanten Spektralbereiche Bereiche von identifizierten Anwärtern durchzuführen,

und wobei die Mittel 3 dazu eingerichtet sind, die Geschwindigkeit/Frequenz auf der Grundlage der identifizierten signifikanten Spektralbereiche abzuschätzen.

7. Verfahren zum Abschätzen eines eine Eigendrehimpulsachse und eine Eigendrehimpulsfrequenz aufweisenden Eigendrehimpulses eines im Flug befindlichen Sportballs, wobei das Verfahren das Abschätzen der Eigendrehimpulsfrequenz gemäß Anspruch 1 und die Schritte aufweist:

1. Bestimmen wenigstens eines Teils einer 3D-Trajektorie des fliegenden Sportballs,

2. ausgehend von der Trajektorie Abschätzen einer Beschleunigung des Sportballs an einer vorbestimmten Position entlang der Trajektorie,

3. Abschätzen einer durch die Schwerkraft an der vorbestimmten Position verursachten Beschleunigung des Sportballs,

4. Abschätzen einer durch den Luftwiderstand/Strömungswiderstand an der vorbestimmten Position verursachten Beschleunigung des Sportballs und

5. an der vorbestimmten Position Abschätzen der Eigendrehimpulsachse auf der Grundlage der abgeschätzten Beschleunigungen.

8. System zum Abschätzen eines eine Eigendrehimpulsachse und eine Eigendrehimpulsfrequenz aufweisenden Eigendrehimpulses eines sich im Flug befindlichen Sportballs, wobei das System nach Anspruch 4 aufweist und wobei das System weiterhin aufweist:

1. Mittel zum Bestimmen wenigstens eines Teiles einer 3D-Trajektorie des fliegenden Sportballs,

2. Mittel zum Abschätzen von der Trajektorie einer Beschleunigung des Sportballs an einer vorbestimmten Position entlang der Trajektorie,

3. Mittel zum Abschätzen einer durch die Schwerkraft an der vorbestimmten Position verursachten Beschleunigung des Sportballs,

4. Mittel zum Abschätzen einer durch den Luftwiderstand/Strömungswiderstand an der vorbestimmten Position verursachten Beschleunigung und

5. Mittel zum Abschätzen der Eigendrehimpulsachse an der vorbestimmten Position auf der Grundlage der abgeschätzten Beschleunigungen.

Revendications

1. Procédé d'estimation de la vitesse de rotation ou de la fréquence de spin d'une balle de sport en rotation en vol, le procédé comprenant :

1. pour un certain nombre de points temporels au cours du vol, la réception d'ondes électromagnétiques réfléchies par la balle de sport en rotation, et la fourniture d'un signal correspondant,

2. la réalisation d'une analyse de fréquence du signal, et l'identification de deux ou plus de deux tracés de spectre discrets, situés au moins à distance sensiblement égale en fréquence et continus dans le temps, et

3. l'estimation de la vitesse de rotation / fréquence de spin à partir d'une distance en fréquence entre les tracés de spectre discrets.

2. Procédé selon la revendication 1, dans lequel l'étape 1 comprend la réception des ondes électromagnétiques réfléchies au moyen d'un récepteur, et dans lequel l'étape 2 comprend l'identification, à la suite de l'analyse de fréquence, d'une première fréquence correspondant à la vitesse de la balle en direction du récepteur ou en provenance de celui-ci, et dans lequel l'identification des tracés de spectre comprend l'identification de tracés de spectre situés symétriquement de part et d'autre de la première fréquence.

3. Procédé selon la revendication 1 ou 2, dans lequel l'étape 2 comprend, pour chaque point temporel et en séquence temporelle :

- la réalisation de l'analyse de fréquence et l'identification des fréquences candidates équidistantes pour un point temporel,

- l'identification ultérieure des candidates dont chacune possède une fréquence déviant au plus d'une amplitude prédéfinie, à partir de la fréquence d'une candidate d'un ou plusieurs points temporels antérieurs,

- puis l'identification, en tant que tracés de fréquence, des tracés des candidates identifiées,

et dans lequel l'étape 3 comprend l'estimation de la vitesse/fréquence sur la base des tracés de spectre identifiés.

4. Système permettant d'estimer la vitesse de rotation ou la fréquence de spin d'une balle de sport en rotation en vol, le système comprenant :

1. un récepteur conçu pour recevoir, pour un certain nombre de points temporels au cours du vol, les ondes électromagnétiques réfléchies par la balle de sport en rotation et fournir un signal correspondant,

2. des moyens permettant de réaliser une analyse de fréquence du signal, et d'identifier deux ou plus de deux tracés de spectre discrets situés au moins à distance sensiblement égale en fréquence et continus dans le temps, et

3. des moyens permettant d'estimer la vitesse/fréquence à partir d'une distance en fréquence entre les tracés de spectre discrets.

5. Système selon la revendication 4, dans lequel les moyens 2 sont conçus pour identifier, à la suite de l'analyse de fréquence, une première fréquence correspondant à la vitesse de la balle en direction du récepteur ou en provenance de celui-ci, et pour identifier, en tant que tracés de spectre, des tracés de spectre situées symétriquement de part et d'autre de la première fréquence.

6. Système selon la revendication 4 ou 5, dans lequel les moyens 2 sont conçus pour, pour chaque point temporel et en séquence temporelle :

- réaliser l'analyse de fréquence et l'identification des fréquences candidates équidistantes pour un point temporel,

- identifier ultérieurement les candidates dont chacune possède une fréquence déviant au plus d'une amplitude prédéfinie, à partir de la fréquence d'une candidate d'un ou plusieurs points temporels antérieurs,

- puis identifier, en tant que tracés de fréquence, les tracés des candidates identifiées,

et dans lequel les moyens 3 sont conçus pour estimer la vitesse/fréquence sur la base des tracés de spectre identifiés.

7. Procédé d'estimation d'un spin, comprenant un axe de spin et une fréquence de spin, d'une balle de sport en vol, le procédé comprenant l'estimation de la fréquence de spin selon la revendication 1 et les étapes de :

1. détermination au moins partielle d'une trajectoire en 3D de la balle de sport en vol,

2. estimation, à partir de la trajectoire, de l'accélération de la balle de sport au niveau d'une position prédéfinie sur la trajectoire,

3. estimation de l'accélération de la balle de sport engendrée par la gravité au niveau de la position prédéfinie,

4. estimation de l'accélération de la balle de sport engendrée par la résistance de l'air/la traînée aérodynamique au niveau de la position prédéfinie, et

5. estimation de l'axe de spin, au niveau de la position prédéfinie, sur la base des accélérations estimées.

8. Système d'estimation d'un spin, comprenant un axe de spin et une fréquence de spin, d'une balle de sport en vol, le système comprenant le système selon la revendication 4 et comprenant en outre :

1. des moyens de détermination au moins partielle d'une trajectoire en 3D de la balle de sport en vol,

2. des moyens d'estimation, à partir de la trajectoire, de l'accélération de la balle de sport au niveau d'une position prédéfinie sur la trajectoire,

3. des moyens d'estimation de l'accélération de la balle de sport engendrée par la gravité au niveau de la position prédéfinie,

4. des moyens d'estimation de l'accélération de la balle de sport engendrée par la résistance de l'air/la traînée aérodynamique au niveau de la position prédéfinie, et

5. des moyens d'estimation de l'axe de spin, au niveau de la position prédéfinie, sur la base des accélérations estimées.

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