Patent Publication Number: US-2016236034-A1

Title: Motion analysis method, motion analysis device, and storage device

Description:
BACKGROUND 
     1. Technical Field 
     The present invention relates to a motion analysis method, a motion analysis device, a storage device, and so on. 
     2. Related Art 
     In JP-A-2008-73210, there is proposed a device having a three-axis acceleration sensor and a three-axis gyro sensor attached to a golf club for analyzing a swing using the output of these sensors. According to the document, by using this device, cameras become unnecessary, and the convenience is enhanced. 
     In the exercises such as golf, it is hoped that the skill is developed by focusing attention to a plurality of checkpoints, and improving all of these points. However, even if the plurality of checkpoints can be checked, it is difficult to evaluate the checkpoints. 
     SUMMARY 
     An advantage of some aspects of the invention is to provide a motion analysis method, a motion analysis device, and a motion analysis program each capable of evaluating the plurality of checkpoints to score a swing motion. 
     (1) An aspect of the invention relates to a motion analysis method including obtaining a plurality of analysis data related to a hit surface of a sporting device using an output of an inertial sensor, and performing scoring while performing weighting using at least two of the analysis data among, as the plurality of analysis data, a first deviation angle formed at impact between the hit surface and a virtual vertical plane to a hit target direction, a second deviation angle formed between the hit surface at the impact and a virtual vertical plane to a tangential direction at the impact touching a trajectory of the hit surface, and a deviation amount of a hit position at the impact from a virtual reference position set on the hit surface. 
     The first deviation angle formed at the impact between the hit surface and the virtual vertical plane to a hit target direction affects the hit direction of the hit ball. 
     This is because the first deviation angle is equal to the angle formed between the hit direction perpendicular to the hit surface at the impact and the hit target direction (a target line direction). The directionality becomes worse as the first deviation angle gets away from 0 degrees. The second deviation angle formed between the hit surface at the impact and the virtual vertical plane to a tangential direction at the impact touching the trajectory of the hit surface also affects the hit direction of the hit ball. This is because the hit direction departs further from a swing line as the second deviation angle gets away from 0 degrees although the hit direction of the hit ball becomes equal to the tangential direction (the swing line direction) touching the trajectory of the hit surface if the hit surface at the impact is perpendicular to the tangential direction at the impact. The deviation amount of the hit position at the impact from the virtual reference position (the centroid) set on the hit surface also affects the hit direction of the hit ball. This is because if the hit position runs off the virtual reference position, the hit surface rotates to make the directionality of the hit ball worse. Therefore, by performing scoring using the analysis data while weighting the analysis data, it is possible to evaluate the directionality of the hit ball. 
     (2) In the aspect of the invention, the plurality of analysis data may include the first deviation angle and the deviation amount, and a weighting factor for the first deviation angle maybe higher than a weighting factor for the deviation amount. 
     The first deviation angle represents the deviation angle of the hit direction from the hit target direction, and is therefore a dominant factor directly affecting the hit direction. In contrast, the deviation amount of the hit position from the centroid is a factor of changing the hit direction. Therefore, by setting the weighting factor WF for the first deviation angle to be higher than the weighting factor WH for the deviation amount (WF&gt;WH), the evaluation of the directionality can correctly be performed. 
     (3) In the aspect of the invention, the plurality of analysis data may include the second deviation angle and the deviation amount, and a weighting factor for the deviation amount may be higher than a weighting factor for the second deviation angle. 
     A dominant factor for the generation of the second deviation angle defining the orthogonality to the swing line direction is the deviation amount of the hit position from the centroid. This is because the hit surface rotates at the impact if the deviation amount is large. Further, the deviation amount of the hit position from the centroid is relatively easy to recognize compared to an angular deviation. Therefore, by setting the weighting factor WH for the deviation amount of the hit position from the centroid to be higher than the weighting factor WS for the second deviation angle (WH&gt;WS), the deviation amount of the hit position from the centroid is made to strongly reflect, and by scoring high if the deviation amount is small, and scoring low if the deviation amount is large, there is obtained the score with which the attention is easily directed to the improvement in the orthogonality with respect to the swing line. 
     (4) In the aspect of the invention, the plurality of analysis data may include the first deviation angle, the second deviation angle, and the deviation amount, a weighting factor for the first deviation angle may higher than a weighting factor for the deviation amount, and the weighting factor for the deviation amount may be higher than a weighting factor for the second deviation angle. 
     Due to the circumstances described above, by setting the relationship of WF&gt;WH&gt;WS, the evaluation of the directionality can more accurately be performed. 
     (5) Another aspect of the invention relates to a motion analysis method including obtaining, using an output of an inertial sensor, first analysis data related to a hit direction by a hit surface of a sporting device, and second analysis data related to a range of a hit ball, and performing scoring using the first analysis data and the second analysis data while weighting the first analysis data and the second analysis data. 
     According to this aspect of the invention, it is possible to provide a motion analysis method most suitable for the sports requiring directionality and the sense of distance of the hit ball such as golf. 
     (6) In the aspect of the invention, a weighting factor for the first analysis data may be higher than a weighting factor for the second analysis data. 
     Taking the influence level on the improvement in the swing and an athletic competition into consideration, importance is given to the directionality of the hit ball among the directionality and the sense of distance of the hit ball. Therefore, by setting the weighting factor for the first analysis data to be higher than the weighting factor for the second analysis data, the overall points of the directionality and the sense of distance of the hit ball can correctly be evaluated. 
     (7) In the aspect of the invention, the first analysis data may include either one of a first deviation angle formed at impact between the hit surface and a virtual vertical plane to a hit target direction, a second deviation angle formed between the hit surface at the impact and a virtual vertical plane to a tangential direction at the impact touching a trajectory of the hit surface, and a deviation amount of a hit position at the impact from a virtual reference position set on the hit surface, and the second analysis data may include either one of a speed of the hit surface at the impact, one of a swing width from a swing starting position to a swing switchback position, and a swing width from the swing switchback position to a hit position at the impact, a third deviation angle between a tilt angle of the hit surface at the impact to a vertical plane and a reference tilt angle, and a fourth deviation angle formed between a tangential direction at the impact touching a trajectory of the hit surface projected on a vertical plane, and the hit target direction projected on the vertical plane. 
     The fact that the first deviation angle, the second deviation angle, and the deviation amount from the centroid are the analysis data related to the directionality of the hit ball is as described above. Since the range of the hit ball depends on the initial speed of the hit ball, the impact speed is the analysis data related to the sense of distance. Since the range of the hit ball depends on the level of external force acting on the hit ball, the swing width is the analysis data related to the sense of distance. Since the range of the hit ball depends on rolling of the hit ball, the third deviation angle and the fourth deviation angle as the factors of the rolling of the hit ball are the analysis data related to the sense of distance. Therefore, it is possible to use at least one of these as the second analysis data related to the sense of distance. 
     (8) In the aspect of the invention, a weighting factor for one of the speed and the swing width may be higher than a weighting factor for one of the third deviation angle and the fourth deviation angle. This is because regarding the sense of distance, the impact speed and the swing width are more dominant than the third deviation angle and the fourth deviation angle affecting the rolling of the hit ball. 
     (9) In the aspect of the invention, the target range Tz based on the target value T of the analysis data R may be set to each of the analysis data R, and the score Ps of each of the analysis data R is provided as PS=P−(1−Ta)×S assuming the highest point as P, the scale factor as S, and the target zone evaluation value as Ta=(Tz−(|T−R|)/Tz. Here, regarding the analysis data except the impact speed and the swing width, the absolute target can be set, and the target range Tz can be set based on the absolute target value T. Regarding the impact speed and the swing width, the range of the standard deviation of 1σ, for example, is set as the relative target range Tz, and the central value thereof can be set as the target value T. 
     (10) Still another aspect of the invention relates to a motion analysis device including a data analysis section adapted to generate analysis data related to a hit surface of a sporting device using an output of an inertial sensor, and a score analysis section adapted to weight the analysis data from the data analysis section to perform scoring, and the data analysis section generates the analysis data including at least two of a first deviation angle formed at impact between the hit surface and a virtual vertical plane to a hit target direction, a second deviation angle formed between the hit surface at the impact and a virtual vertical plane to a tangential direction at the impact touching a trajectory of the hit surface, and a deviation amount of a hit position at the impact from a virtual reference position set on the hit surface. According to the motion analysis device related to this aspect of the invention, the motion analysis method according to the aspect of the invention can preferably be implemented. 
     (11) Still another aspect of the invention relates to a motion analysis device including a first data analysis section adapted to generate first analysis data related to a hit direction by a hit surface of a sporting device using an output of an inertial sensor, a second data analysis section adapted to generate second analysis data related to a range of a hit ball hit by the hit surface using the output of the inertial sensor, and a score analysis section adapted to perform scoring using the first analysis data and the second analysis data while weighting the first analysis data and the second analysis data. According to the motion analysis device related to this aspect of the invention, the motion analysis method according to another aspect of the invention can preferably be implemented. 
     (12) Still another aspect of the invention relates to a motion analysis program that makes a computer execute a process including generating analysis data related to a hit surface of a sporting device using an output of an inertial sensor, and performing scoring using at least two of the analysis data including a first deviation angle formed at impact between the hit surface and a virtual vertical plane to a hit target direction, a second deviation angle formed between the hit surface at the impact and a virtual vertical plane to a tangential direction at the impact touching a trajectory of the hit surface, and a deviation amount of a hit position at the impact from a virtual reference position set on the hit surface. 
     (13) Still another aspect of the invention relates to a motion analysis program that makes a computer execute a process including the steps of generating first analysis data related to a hit direction by a hit surface of a sporting device using an output of an inertial sensor, generating second analysis data related to a range of a hit ball hit by the hit surface using the output of the inertial sensor, and performing scoring using the first analysis data and the second analysis data while weighting the first analysis data and the second analysis data. 
     The program according to this aspect of the invention can be incorporated in the storage device of the motion analysis device performing the method of the invention, or can be installed in the storage device of the motion analysis device from a server or a storage medium. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
         FIG. 1  is a conceptual diagram schematically showing a configuration of a golf swing analysis device according to an embodiment of the invention. 
         FIG. 2  is a block diagram schematically showing a configuration of an arithmetic processing circuit according to the embodiment of the invention. 
         FIG. 3A  is a diagram showing a first deviation angle (an absolute face angle),  FIG. 3B  is a diagram showing a second deviation angle (a square degree), and  FIG. 3C  is a diagram showing a deviation amount from a hit point. 
         FIG. 4A  is a diagram showing a third deviation angle (a delta-loft angle) and an impact speed,  FIG. 4B  is a diagram showing a fourth deviation angle (an attack angle), and  FIG. 4C  is a diagram showing a swing width L. 
         FIG. 5  is a diagram showing an initial picture of an analysis picture. 
         FIG. 6  is a diagram showing the analysis picture displayed after “Direction” is selected in  FIG. 5 . 
         FIG. 7  is a diagram showing the analysis picture displayed after “FACE” is selected in  FIG. 6 . 
         FIG. 8  is a diagram showing the analysis picture displayed after “Histogram” is selected in  FIG. 5 or 6 . 
         FIG. 9  is a diagram showing the analysis picture displayed after “SQUARE” is selected in  FIGS. 6 through 8 . 
         FIG. 10  is a diagram showing the analysis picture displayed after “Histogram” is selected in  FIG. 9 . 
         FIG. 11  is a diagram of a display picture showing a deviation amount of a hit position from the centroid. 
         FIG. 12  is a diagram showing the analysis picture displayed after “Stroke” is selected in  FIG. 5 . 
         FIG. 13  is a diagram showing the analysis picture displayed after “SPAN-BACK” is selected in  FIG. 12 . 
         FIG. 14  is a diagram showing the analysis picture displayed after “Histogram” is selected in  FIG. 12 or 13 . 
         FIG. 15  is a diagram showing the analysis picture displayed after “SPEED” is selected in  FIGS. 12 through 14 . 
         FIG. 16  is a diagram showing the analysis picture displayed after “Histogram” is selected in  FIG. 15 . 
         FIG. 17  is a diagram showing the analysis picture displayed after “Rising” is selected in  FIG. 5 . 
         FIG. 18  is a diagram showing the analysis picture displayed after “DELTA-LOFT” is selected in  FIG. 17 . 
         FIG. 19  is a diagram showing the analysis picture displayed after “Histogram” is selected in  FIG. 17 or 18 . 
         FIG. 20  is a diagram showing the analysis picture displayed after “ATTACK” is selected in  FIGS. 17 through 19 . 
         FIG. 21  is a diagram showing the analysis picture displayed after “Histogram” is selected in  FIG. 20 . 
         FIG. 22  is a flowchart for describing a detection operation of a posture on a swing trajectory. 
         FIG. 23  is a diagram for describing first and second measurement points set so as to be separated from each other in a horizontal direction on the face surface of a club head. 
         FIG. 24  is a diagram for describing the first deviation angle (the absolute face angle) and the second deviation angle (the square degree). 
         FIG. 25  is a diagram schematically showing the probability of dropping the ball in the cup on a cup-by-cup basis. 
         FIG. 26  is a diagram showing a correlation between an angular velocity around a long axis of a shaft and a measurement value of a hit point. 
         FIG. 27  is a diagram showing a relational expression obtained from the data described in  FIG. 26 . 
         FIG. 28  is a diagram showing a display example of projecting the swing width of a backswing on a projection surface. 
         FIG. 29  is a diagram for describing the first and second measurement points set so as to be separated from each other in a vertical direction on the face surface of the club head. 
         FIG. 30  is a diagram for describing the third deviation angle (the delta-loft angle) and the fourth deviation angle (the attack angle). 
     
    
    
     DESCRIPTION OF AN EXEMPLARY EMBODIMENT 
     An embodiment of the invention will hereinafter be explained with reference to the accompanying drawings. It should be noted that the present embodiment explained below does not unreasonably limit the content of the invention as set forth in the appended claims, and all of the constituents described in the present embodiment are not necessarily essential as means for solving the problem to be solved by the invention. 
     1. Configuration of Golf Swing Analysis Device 
       FIG. 1  schematically shows a configuration of a golf swing analysis device (a motion analysis device)  11  according to an embodiment of the invention. The golf swing analysis device  11  is provided with, for example, an inertial sensor  12 . The inertial sensor  12  incorporates an acceleration sensor and a gyro sensor. The acceleration sensor is capable of separately detecting the acceleration in each of three-axis directions perpendicular to each other. The gyro sensor is capable of individually detecting an angular velocity around each of the three axes (x, y, and z) perpendicular to each other. The inertial sensor  12  outputs a detection signal. The detection signal identifies the acceleration and the angular velocity for each of the axes. The acceleration sensor and the gyro sensor detect the information of the accelerations and the angular velocities with relative accuracy. The inertial sensor  12  is attached to a golf club (a sporting device)  13 . The golf club such as a golf putter  13  is provided with a shaft  13   a  and a grip  13   b.  The grip  13   b  is held by hand. The grip  13   b  is formed coaxially with the axis of the shaft  13   a.  A club head  13   c  is connected to the tip of the shaft  13   a.  It is desirable that the inertial sensor  12  is attached to the shaft  13   a  or the grip  13   b  of the golf club  13 . It is sufficient for the inertial sensor  12  to be fixed to the golf club  13  so as to be unable to move relatively to the golf club  13 . 
     Here, when attaching the inertial sensor  12 , one (the z axis) of the detection axes of the inertial sensor  12  is made to coincide with the axis of the shaft  13   a.  Another (the x axis) of the detection axes of the inertial sensor  12  is made to coincide with a direction obtained by projecting a direction (a face normal direction), which is perpendicular to a face surface (a hit surface)  13   c   1 , on a horizontal plane in the state of leveling a sole (a grounded surface) of the club head  13   c.  Since the face surface is not necessarily a vertical plane but may be tilted with respect to the vertical plane, the direction obtained by projecting the face normal direction on the horizontal plane is set as the x axis. The y axis is perpendicular to the x axis and the z axis. The x, y, and z axes define a sensor coordinate system Σxyz. 
     The golf swing analysis device  11  is provided with an arithmetic processing circuit  14 . The inertial sensor  12  is connected to the arithmetic processing circuit  14 . In the connection, a predetermined interface circuit  15  is connected to the arithmetic processing circuit  14 . The interface circuit  15  can be connected to the inertial sensor  12  with wire, or can also be connected wirelessly to the inertial sensor  12 . The arithmetic processing circuit  14  is supplied with the detection signal from the inertial sensor  12 . 
     A storage device  16  is connected to the arithmetic processing circuit  14 . The storage device  16  can store, for example, a golf swing analysis software program (a motion analysis program)  17  and related data. The arithmetic processing circuit  14  executes the golf swing analysis software program  17  to realize a golf swing analysis method. The storage device  16  can include a dynamic random access memory (DRAM), a mass-storage unit, a nonvolatile memory, and so on. For example, the DRAM temporarily holds the golf swing analysis software program  17  having been downloaded from, for example, a server in performing the golf swing analysis method. Alternatively, it is also possible for the golf swing analysis software program  17  to be stored in the mass-storage unit such as a hard disk drive (HDD) together with data. The nonvolatile memory stores a program and data relatively small in volume such as a basic input and output system (BIOS). 
     The storage device  16  stores club specification information representing the specifications of the golf club  13 , sensor mounting position information, and so on. For example, the user inputs (or selects out of a model list) the model of the golf club  13  to be used to set the specification information corresponding to the model thus input as the club specification information out of specification information (e.g., information such as the length of the shaft, the position of the center of gravity, a face angle, and a loft angle) for the respective models stored in advance in the storage device  16 . Alternatively, assuming that the sensor unit  12  is mounted at a predetermined position (e.g., 20 cm distant from the grip), the information of the predetermined position can also be stored in advance as the sensor mounting position information. In the case of, for example, the golf putter, a distance from an address position to a cup, the size of the cup, a green speed, and so on are stored as motion conditions in the storage device  16  via an input device  21 . 
     An image processing circuit  18  is connected to the arithmetic processing circuit  14 . The arithmetic processing circuit  14  transmits predetermined image data to the image processing circuit  18 . A display device  19  is connected to the image processing circuit  18 . In the connection, a predetermined interface circuit (not shown) is connected to the image processing circuit  18 . The image processing circuit  18  transmits an image signal to the display device  19  in accordance with the image data input. An image identified by the image signal is displayed on a screen of the display device  19 . It should be noted that it is possible for the arithmetic processing circuit  14  or the image processing circuit  18  to convert the coordinate space of the censor coordinate system Σxyz into an absolute reference coordinate system ΣXYZ (e.g., an X-Z plane is a horizontal plane, and an X-Y plane is a vertical plane) as the real space (a three-dimensional space). As the display device  19 , there is used a flat panel display or the like such as a liquid crystal display, and an image is displayed as a three-dimensional image or a two-dimensional image in the absolute reference coordinate system ΣXYZ. Here, the arithmetic processing circuit  14 , the storage device  16 , and the image processing circuit  18  are provided as, for example, a computer device. 
     The input device  21  is connected to the arithmetic processing circuit  14 . The input device  21  is provided with at least alphabet keys and a numerical keypad. Character information and numerical information are input to the arithmetic processing circuit  14  from the input device  21 . The input device  21  can be formed of, for example, a keyboard. A combination of the display device, the computer device, and the keyboard can be replaced with a portable terminal such as a smartphone or a tablet. 
     2. General Outline of Arithmetic Processing Circuit 
       FIG. 2  schematically shows a configuration of the arithmetic processing circuit  14  according to the embodiment. The arithmetic processing circuit  14  can be provided with a swing position coordinate detection section  50 , a speed detection section  60 , an address (resting) analysis section  70 , an impact analysis section  80 , a planar view direction analysis section  90 , a hit point analysis section  100 , a front view direction analysis section  110 , a stroke analysis section (a swing width analysis section)  120 , a score analysis section  130 , a statistic analysis section  140 , and so on. One or more of the analysis sections  90  through  120  can be omitted in accordance with the grade of the motion analysis device. 
     The swing position coordinate detection section  50  detects the coordinate of the club head  13   c  in a swing from a swing start position (an address position) to a swing end position (a finish position) through a swing switchback position (a top position) and a hit position (an impact virtual vertical plane position). 
     The speed detection section  60  detects (see  FIG. 4A ) the speed V of the club head  13   c  at, for example, the impact using an output from the inertial sensor  12 . The address analysis section  70  analyzes the posture and the position of the face surface  13   c   1  of the club head  13   c  in the address (at rest). The impact analysis section  8  analyzes the posture of the face surface  13   c   1  of the club head  13   c  at the impact, and the trajectory of the face surface  13   c   1  around the impact. 
     The planar view direction analysis section  90  analyses the direction of the club head  13   c  in the planar view. The planar view direction analysis section  90  analyses at least one of a first deviation angle (an absolute face angle) θ 1  between the face surface  13   c   1  at the impact and a virtual vertical plane  13   c   2  facing to a hit target direction (a target line direction; e.g., a direction obtained by projecting the normal direction of the face surface  13   c   1  at the address on the X-Z plane) shown in  FIG. 3A , and a second deviation angle (a square degree) θ 2  between the face surface  13   c   1  at the impact and a virtual vertical plane  13   c   3  facing to the tangential direction (the swing line direction or a hit-ball direction) at the impact touching the moving trajectory of the face surface  13   c   1  shown in  FIG. 33 . 
     As shown in  FIG. 3C , a deviation amount δ of the hit point (the hit position) of a ball  22  at the impact from a virtual reference position P 0  set to the face surface  13   c   1  is analyzed by the hit point analysis section  100  from the angular velocity around the shaft  13   a.    
     The front view direction analysis section  110  analyzes the direction of the club head  13   c  in the front view right opposite to the golfer (the user operating the sporting device). The front view direction analysis section  110  analyzes at least one of a third deviation angle θ 3  (a delta-loft angle) between a tilt angle (an actual loft angle) of the face surface  13   c   1  to the vertical plane at the impact and a reference tilt angle (e.g., a loft angle as a standard value of the putter  13 , which is drawn in  FIG. 4A  as a roughly vertical plane) shown in  FIG. 4A , and a fourth deviation angle θ 4  (an attack angle) formed between the tangential direction (the swing line direction) at the impact touching the moving trajectory of the face surface  13   c   1  projected on the vertical plane and the target direction (the hit target direction) projected on the vertical plane. 
     The stroke analysis section (the swing width analysis section)  120  identifies the swing width from a first position to a second position on the swing trajectory based on the coordinates of the two positions (the first position and the second position) provided from the swing position coordinate detection section  50 . For example, as shown in  FIG. 4A , the stroke analysis section  120  analyzes the stroke (the swing width) from the address position (the first position) to the swing switchback position (the second position). 
     The score analysis section  130  analyzes scores (performance scores) of respective swing analysis data (the deviation angles θ 1  through θ 4 , the deviation amount δ, the swing width L, and the speed V) shown in  FIGS. 3A through 3C , and  4 A through  4 C, and a score (a total performance score) obtained by performing a weighted calculation on a plurality of data selected from the swing analysis data. The statistic analysis section  140  analyzes statistic values (e.g., a total number of times, an average value, and a standard deviation) with respect to each of the plurality of swing analysis data. 
     3. Display Example in Display Device 
     3-1. Initial Picture 
       FIG. 5  is a diagram showing an example of, for example, an initial picture of the swing analysis data displayed on the display device  19 . In  FIG. 5 , in an upper part of the initial picture, there are displayed corresponding pieces of information respectively to a user name, a date, a putter type (L-mallet), a distance to the cup (10 ft), and a green speed (Slow). Further, at the center of the initial picture, there is displayed a swing trajectory, for example, the address position to the swing switchback position together with an image (a plurality of positions) representing the putter  13 . It should be noted that the swing trajectory is an image projected on the X-Y plane (a vertical plane) of the absolute reference coordinate system. The black triangular mark located on the lower left side of the swing trajectory image area is a play button. When the play button is operated, the time seek bar located on the right side of the play button moves from the left side toward the right side, and the images representing the putter  13  are additionally displayed in the swing trajectory image area at the respective positions in series in accordance with the movement of the putter  13 . The white triangles located above the moving area of the time seek bar respectively represent the address position, the top position, the impact position, and the finish position in sequence from the left. It is also possible to operate the time seek bar to point an interested position to thereby stop the image. In the center left part of the initial picture, there is displayed the performance score (e.g., 100 points) analyzed by the score analysis section  130 . In the lower column part of the initial picture, there are displayed Direction (planar view direction analysis data), Hitpoint (hit point analysis data), Stroke (stroke analysis data), and Rising (front view direction analysis data) together with the analysis data. When touching either of the four display areas in the lower column part of the initial picture, the details of the analysis data selected are displayed. 
     3-2. Picture of Individual Analysis Data 
     3-2-1. Direction 
       FIGS. 6 through 10  show picture examples displayed after “Direction” has been selected in the initial picture.  FIG. 7  shows an example of the display picture of the planar view direction analysis data of one swing.  FIGS. 6 through 10  show picture examples displayed when “Direction” has been selected in the initial picture. In  FIG. 6 , 3.4 deg is highlighted in an enlarged manner as the first deviation angle θ 1  (the deviation angle between the face surface  13   c   1  at the impact and the virtual vertical plane  13   c   2  facing to the hit target direction (the target line direction); the absolute face angle shown in  FIG. 3A ) based on the analysis data in the planar view direction analysis section  90  shown in  FIG. 2 . 
     In the central area of the picture shown in  FIG. 6  and  FIG. 7  showing the picture displayed in the case in which “FACE” in  FIG. 6  has been selected, the hit direction obtained by projecting the normal direction of the face surface  13   c   1  of the putter  13  at the impact on a projection surface (a horizontal plane), and the speed of the club head  13   c  of the putter  13  at the impact are displayed in the coordinate system in which the hit target direction is set. As the coordinate system, there is displayed, for example, a polar coordinate system. In an angle axis as one of the axes of the polar coordinate system, the direction at 0 degrees corresponds to the hit target direction. The hit direction thus identified is displayed in the polar coordinate system as a line segment extending in a direction perpendicular to the face surface  13   c   1  of the image representing the club head  13   c  of the putter  13 . It should be noted that it is also possible to always display the direction at 0 degrees as the hit direction in the angle axis as one of the axes of the polar coordinate system. 
     Further, the angle on the angle axis of the polar coordinate system is exaggerated to be larger than the actual angle, and for example, the angular range of ±5 degrees is drawn with the exaggeration to an angular range of equal to or larger than 90 degrees. This is for making it easy to visually recognize the deviation of the hit direction from the hit target direction. The other of the axes of the polar coordinate system is a speed axis. The end-point position of the line segment representing the hit direction extending from the face surface of the image representing the club head  13   c  of the putter  13  represents the speed of the club head  13   c  (the face surface  13   c   1 ) at the impact. 
     In the present embodiment, in view of the fact that the hit direction and the speed of the face surface  13   c   1  at the impact are correlated with the directionality and the sense of distance of the hit ball, the hit direction and the speed of the face surface  13   c   1  at the impact are displayed in the same coordinate system. By checking the deviation in the hit direction to the hit target direction and the speed at the impact every time the swing motion of the putter  13  is performed, accuracy of reproducing the directionality and the sense of distance of the hit ball can be acquired. Here, the hit direction at the impact can be set to the direction obtained by projecting the normal direction of the face surface  13   c   1  at the impact on the projection surface. The face surface  13   c   1  is not necessarily parallel to the vertical plane but is tilted with respect to the vertical plane in some cases, and therefore, the direction obtained by projecting the normal direction of the face surface  13   c   1  to the projection surface (a horizontal plane) can be assumed as the hit direction. Although the identification of the hit direction will be described later, it is also possible to identify the hit direction (the tangential direction at the impact with respect to the moving trajectory of the face surface) at the impact based on a movement vector of the face surface  13   c   1 . 
     It should be noted that the hit target direction can be identified as the direction obtained by projecting the normal direction of the face surface  13   c   1  at the address (at rest) before starting the swing motion on the projection surface. Although the hit target direction can be set as a known stationary direction set in advance, by identifying the hit target direction from the orientation of the face surface  13   c   1  at rest before starting the swing motion every time the swing motion is made, it is possible to make it easy to figure out the deviation between the conscious and the action. 
     Further, by setting and displaying the image representing the putter  13  in the planar view in the polar coordinate system shown in  FIGS. 6 and 7  while setting the face surface  13   c   1  in the orientation toward the hit direction, in particular by visually recognizing the deviation between the orientation of the hit surface and the hit target direction, it becomes easier to recognize the cause of the deviation of the hit direction. 
     Further, it is possible to display the target area of, for example, ±1 degree including the hit target direction (0 degrees) so as to be distinguished from other areas in the polar coordinate system shown in  FIGS. 6 and 7 . According to this configuration, since the target becomes a zone instead of a line, the target achievement rate is improved to increase the psychological easiness, and thus, an improvement in exercise effect of the sport can be achieved. It should be noted that in the case of the putter  13 , the target area can be obtained as an angular range from the target line using the distance L from the address position to the center of the cup and the radius R of the cup. For example, R=5.4 cm and L=155.4 cm are assumed, ±arcsin (R/L)=±1.9 degrees is obtained. 
     Further, in the polar coordinate system shown in  FIGS. 6 and 7 , it is possible to display the coordinate positions (the five coordinate positions in  FIGS. 6 and 7 ) determined by the hit directions and the speeds having been identified in the past so as to be distinguished from the coordinate position of the hit direction and the speed having been identified this time. According to this configuration, presence or absence of the exercise effect in the case of repeatedly performing the exercise can visually be recognized. 
     When selecting “Histogram” located in the lower left part of the picture shown in  FIG. 6  or  FIG. 7 , there occurs switching from the picture shown in  FIG. 6  or  FIG. 7  to the picture shown in  FIG. 8 . In the lower column of the picture shown in  FIG. 8 , there is displayed a histogram showing a distribution of, for example, the hit direction based on the analysis data in the statistic analysis section  140  shown in  FIG. 2 . As shown in  FIG. 8 , in this histogram, there can also be displayed the position of the hit direction having been measured this time. 
     When selecting the column of “SQUARE” located in an upper right part of each of the pictures shown in  FIGS. 6 through 8 , there occurs switching to the picture shown in  FIG. 9 . In  FIG. 9 , −0.2 degrees is highlighted in an enlarged manner in the column of “SQUARE” located in the upper right part of the picture as the second deviation angle θ 2  (the square degree; see  FIG. 3B ) of the club head  13   c  at the impact based on the analysis data in the planar view direction analysis section  90  shown in  FIG. 2 . Further, in the central area of the picture shown in  FIG. 8 , the angle axis of the polar coordinate system is converted into the angle axis of the square degree θ 2 . In the angle axis of the polar coordinate system, the position corresponding to the square degree θ 2 =0 degrees becomes the target direction. In  FIG. 9 , the normal line of the face surface of the image representing the putter  13  is displayed at the position corresponding to the square degree θ 2 =−0.2 degrees. In this case, as shown in  FIG. 9 , it is also possible to display the coordinate positions (the five coordinate positions in  FIG. 9 ) determined by the square degrees and the speeds having been identified in the past so as to be distinguished from the coordinate position of the square degree and the speed having been identified this time. 
     When selecting “Histogram” located in the lower left part of the picture shown in  FIG. 9 , there occurs switching from the picture shown in  FIG. 9  to the picture shown in  FIG. 10 . In the lower column of the picture shown in  FIG. 10 , there is displayed a histogram showing a distribution of the speed of the square degree based on the analysis data in the statistic analysis section  140  shown in  FIG. 2 . As shown in  FIG. 10 , in this histogram, there can also be displayed the position of the square degree having been measured this time. 
     3-2-2. Hitpoint 
       FIG. 11  shows a part of the picture displayed when “Hitpoint” has been selected in the initial picture. In the picture shown in  FIG. 11 , there is shown the face surface  13   c   1  of the club head  13   c,  wherein the dashed-dotted line SS as the vertical line in the drawing indicates the centroid of the golf club  13 . 
     The circular marks shown in  FIG. 11  show the hit positions in the case in which the swing has been done ten times. The diameter in the horizontal direction of each of the circular marks represents the width of the position where the ball has been hit, and in the example shown in  FIG. 11 , the width is “5 mm.” In other words, the number of the circular marks located on the same vertical line represents the frequency of the hit position of the ball. For example, it is understood that in the example shown in  FIG. 11 , the frequency of the hit position “−5±2.5 (mm)” is “two times.” 
     The circular mark indicated by hatching represents the latest hit position of the ball. In the example shown in.  FIG. 11 , since the latest hit position of the ball is “+1 mm,” the circular mark indicated by hatching is displayed in the class of “0±2.5 (mm).” It should be noted that regarding the hit point, it is also possible to display a histogram similar to the histogram shown in  FIG. 8  or  FIG. 10  by selecting “Histogram.” 
     3-2-3. Stroke 
       FIGS. 12 through 16  show picture examples displayed after the “Stroke” is selected in the initial picture.  FIG. 12  shows an example of a display picture of stroke analysis data of one swing in the case in which “Stroke” has been selected in the initial picture. Further,  FIG. 13  shows a picture displayed in the case in which “SPAN-BACK” has been selected in the picture shown in  FIG. 12 . In  FIGS. 12 and 13 , 34 cm is highlighted in an enlarged manner as a stroke (SPAN-BACK) of the backswing of the putter  13  based on the analysis data in the stroke (swing width) analysis section  120  shown in  FIG. 2 . When selecting “Histogram” located in the lower left part of the picture shown in  FIG. 12  or  FIG. 13 , there occurs switching from the picture shown in  FIG. 12  or  FIG. 13  to the picture shown in  FIG. 14 . In the lower column of the picture shown in  FIG. 14 , there is displayed a histogram showing a distribution of the stroke of the backswing based on the analysis data in the statistic analysis section  140  shown in  FIG. 2 . As shown in  FIG. 14 , in this histogram, there can also be displayed the position of the stroke having been measured this time. 
     When selecting the column of “SPEED” located in an upper right part of each of the pictures shown in  FIGS. 12 through 14 , there occurs switching to the picture shown in  FIG. 15 . In  FIG. 15 , 4.6 m/s is highlighted in an enlarged manner in the column of “SPEED” located in the upper right part of the picture as the speed of the club head  13   c  at the impact based on the analysis data in the speed detection section  60  shown in  FIG. 2 . Further, a speed display meter is displayed on the right side of the enter of the picture shown in  FIG. 15 . When selecting “Histogram” located in the lower left part of the picture shown in  FIG. 15 , there occurs switching from the picture shown in  FIG. 15  to the picture shown in  FIG. 16 . In the lower column of the picture shown in  FIG. 16 , there is displayed a histogram showing a distribution of the speed of the club head  13   c  at the impact based on the analysis data in the statistic analysis section  140  shown in  FIG. 2 . As shown in  FIG. 16 , in this histogram, there can also be displayed the position of the speed having been measured this time. 
     3-2-4. Rising 
       FIGS. 17 through 21  show picture examples displayed after the “Rising” is selected in the initial picture.  FIG. 17  shows an example of a display picture of front view direction analysis data of one swing in the case in which “Rising” has been selected in the initial picture.  FIG. 18  is a picture displayed when “DELTA-LOFT” of the picture shown in  FIG. 17  has been selected. In  FIGS. 17 and 18 , −0.8 deg is highlighted in an enlarged manner as the third deviation angle θ 3  (the delta-loft angle; DELTA-LOFT) shown in  FIG. 4A  based on the analysis data in the front view direction analysis section  110  shown in  FIG. 2 . 
     In the central area of each of the pictures shown in  FIGS. 17 and 18 , the tilt angle thus identified is displayed in an angular coordinate system showing the deviation angle from a reference tilt angle. In the angular coordinate system, 0 degrees represent the reference tilt angle. There is displayed an image showing the club head  13   c  of the putter  13  in the front view in a direction right opposite to the golfer (the user using the sporting device). In the angular coordinate system, the tilt angle thus identified is displayed as an extended line of the face surface in the image. 
     In  FIGS. 17 and 18 , the tilt angle thus identified is displayed so as to coincide with the centerline of the angular coordinate system, and the position representing the reference angle is displayed so as to be rotated in the opposite direction to the sign of the crossing angle described above as much as the crossing angle. It should be noted that it is also possible to make the centerline of the angular coordinate system coincide with the reference tilt angle (0 degrees), and display the line representing the tilt angle thus identified so as to be rotated in the direction coinciding with the sign of the tilt angle as much as the tilt angle. As described above, by displaying the reference tilt angle and the tilt angle in the same coordinate system, the difference between the reference tilt angle and the tilt angle can visually be recognized. 
     Further, the angle in the angular coordinate system is exaggerated to be larger than the actual angle, and the angular range of 1 degree is drawn with the exaggeration to a range several times through more than ten times as large as the angular range. This is for making it easy to visually recognize the deviation of the tilt angle from the reference tilt angle. 
     Further, it is possible to display the target area of, for example, ±1 degree including the reference tilt angle (0 degrees) so as to be distinguished from other areas in the angular coordinate system shown in  FIGS. 17 and 18 . According to this configuration, since the target becomes a zone instead of a line, the target achievement rate is improved to increase the psychological easiness, and thus, an improvement in exercise effect of the sport can be achieved. 
     Further, in the angular coordinate system shown in  FIGS. 17 and 18 , it is possible to display the tilt angles (the five tilt angles in  FIGS. 17 and 18 ) having been identified in the past so as to be distinguished from the tilt angle having been identified this time. According to this configuration, presence or absence of the exercise effect in the case of repeatedly performing the exercise can visually be recognized. 
     When selecting “Histogram” located in the lower left part of the picture shown in  FIG. 17  or  FIG. 18 , there occurs switching from the picture shown in  FIG. 17  or  FIG. 18  to the picture shown in  FIG. 19 . In the lower column of the picture shown in  FIG. 19 , there is displayed a histogram showing a distribution of the tilt angle based on the analysis data in the statistic analysis section  140  shown in  FIG. 2 . As shown in  FIG. 19 , in this histogram, there can also be displayed the position of the tilt angle having been measured this time. 
     When selecting the column of “ATTACK” located in an upper right part of each of the pictures shown in  FIGS. 17 through 19 , there occurs switching to the picture shown in  FIG. 20 . In  FIG. 20 , −7.6 degree is highlighted in an enlarged manner in the column of “ATTACK” located in the upper right part of the picture as the fourth deviation angle θ 4  (the attack angle) of the club head  13   c  at the impact shown in  FIG. 4B  based on the analysis data in the front view direction analysis section  110  shown in  FIG. 2 . Further, in the central area of the picture shown in  FIG. 20 , the angle of the angular coordinate system is converted into the angle axis of the attack angle. In the angular coordinate system, the position of attack angle=0 degrees is set at a horizontal position on the picture, and 0 degrees become the reference tilt angle. In  FIG. 20 , the normal line of the face surface of the image showing the putter  13  in the front view in the direction right opposite to the golfer (the user using the sporting device) is displayed at the position of attack angle=−7.6 degrees. The normal line indicates the tilt angle thus identified. In this case, as shown in  FIG. 20 , it is also possible to display the attack angles (the five attack angles in  FIG. 20 ) having been identified in the past so as to be distinguished from the attack angle identified this time. 
     When selecting “Histogram” located in the lower left part of the picture shown in  FIG. 20 , there occurs switching from the picture shown in  FIG. 20  to the picture shown in  FIG. 21 . In the lower column of the picture shown in  FIG. 21 , there is displayed a histogram showing a distribution of the attack angle based on the analysis data in the statistic analysis section  140  shown in  FIG. 2 . As shown in  FIG. 21 , in this histogram, there can also be displayed the position of the attack angle having been measured this time. 
     4. Operation of Swing Position Coordinate Detection Section 
     An operation in the swing position coordinate detection section  50  shown in  FIG. 2  will be described.  FIG. 22  is a flowchart showing an example of a procedure of a process calculating the posture (the initial posture through the posture at the time N) of the sensor unit  12  in the swing position coordinate detection section  50 . 
     As shown in  FIG. 22 , the swing position coordinate detection section  50  sets (S 1 ) time t=0 to identify the direction of the gravitational acceleration from three-axis acceleration data at rest, and then calculates (S 2 ) a quaternion p(0) representing the initial posture (the posture at the time t=0) of the sensor unit  10 . 
     The three-dimensional coordinate position is expressed by Formula (1) below as a quaternion q representing a rotation of a position vector. 
         q= ( w, x, y, z )   (1)
 
     In Formula (1), assuming that the symbol θ represents the rotational angle of the intended rotation, and the symbol (r x , r y , r z ) represents a unit vector of the rotational axis, the values w, x, y, and z are expressed by Formula (2) below. 
     
       
         
           
             
               
                 
                   
                     w 
                     = 
                     
                       cos 
                        
                       
                         θ 
                         2 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     x 
                     = 
                     
                       
                         
                           r 
                           x 
                         
                         · 
                         sin 
                       
                        
                       
                         θ 
                         2 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     y 
                     = 
                     
                       
                         
                           r 
                           y 
                         
                         · 
                         sin 
                       
                        
                       
                         θ 
                         2 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     z 
                     = 
                     
                       
                         
                           r 
                           z 
                         
                         · 
                         sin 
                       
                        
                       
                         θ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Since the sensor unit  10  is at rest at the time t=0 at the start of the swing (at the address), θ=0 is set, and therefore, the quaternion q(0) representing the rotation at the time t=0 is expressed as Formula (3) below from Formula (1) with Formula (2) in which θ=0 is substituted. 
         q (0)=(1,0,0,0)   (3)
 
     Then, the swing position coordinate detection section  50  updates (S 3 ) the time t to t+1. Here, since the time t=0 has been set, the time is updated to t=1. 
     Then, the swing position coordinate detection section  50  calculates (S 4 ) the quaternion Δq(t) representing the rotation per unit time at the time t from the three-axis angular velocity data at the time t. 
     For example, assuming the three-axis angular velocity data at the time t as ω(t)=[ω x (t), ω y (t), ω z (t)], the magnitude |ω(t)| of the angular velocity per sample measured at the time t is calculated by Formula (4) below. 
       |ω( t )=√{square root over (ω x ( t ) 2 +ω y ( t ) 2 +ω z ( t ) 2 )}  (4)
 
     Since the magnitude |ω(t)| of the angular velocity is defined as the rotational angle per unit time, the quaternion Δq(t+1) representing the rotation per unit time at the time t is calculated as Formula (5) below. 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       q 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                   
                   = 
                   
                     ( 
                     
                       
                         cos 
                          
                         
                           
                              
                             
                               ω 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                       
                       , 
                       
                         
                           
                             
                               ω 
                               x 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           
                              
                             
                               ω 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                         
                          
                         sin 
                          
                         
                           
                              
                             
                               ω 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                       
                       , 
                       
                         
                           
                             
                               ω 
                               y 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           
                              
                             
                               ω 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                         
                          
                         sin 
                          
                         
                           
                              
                             
                               ω 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                       
                       , 
                       
                         
                           
                             
                               ω 
                               z 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           
                              
                             
                               ω 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                         
                          
                         sin 
                          
                         
                           
                              
                             
                               ω 
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Here, since t=1 is set, the swing position coordinate detection section  50  calculates Δq(1) from the three-axis angular velocity data ω(1)=[ω x (1), ω y (1), ω z (1)] at the time t=1 using Formula (5). 
     Then, the swing position coordinate detection section  50  calculates (S 4 ) the quaternion q(t) representing the rotation from the time  0  to the time t. The quaternion q(t) is calculated using Formula (6) below. 
         q ( t )= q ( t− 1)·Δ q ( t )   (6)
 
     Here, since t=1 has been set, the swing position coordinate detection section  50  calculates q(1) from q(0) in Formula (3) and Δq(1) having been calculated in the process S 4  using Formula (6). 
     Then, the swing position coordinate detection section  50  repeats the processing of the processes S 3  through S 5  until t=N is achieved, and when t=N is achieved (YES in S 6 ), the swing position coordinate detection section  50  calculates (S 7 ) the quaternion p(N) representing the posture at the time N from the quaternion p(0) calculated in the process (S 2 ) and representing the initial posture and the quaternion q(N) calculated in the most recent process S 5  and representing the rotation from the time t=0 to the time t=N, and then terminates the processing. 
     It is possible for the swing position coordinate detection section  50  to obtain the coordinate (X, Y, Z) in the absolute reference coordinate system of the club head  13   c  of the putter  13  from the time t=0 to the time t=N based on the posture information obtained in such a manner as described above, the distance information from the sensor unit  12  to the club head  13   c  (first and second measurement points  13   d,    13   e  described later), and so on. Further, it is possible for the speed detection section  60  shown in  FIG. 2  to detect the speed based on the output from the inertial sensor  12  with respect to the coordinate position obtained in the swing position coordinate detection section  50 . 
     5. Analysis Section 
     5-1. Analysis and Display of First Deviation Angle θ 1 , Second Deviation Angle θ 2 , and Speed V 
     Then, a configuration and an operation of each of the address analysis section  70 , the impact analysis section  80 , the planar view direction analysis section  90 , the statistic analysis section  140 , and the image processing circuit  18  involved in the generation of the analysis pictures shown in  FIGS. 6 through 10  will be described with reference to  FIGS. 23 through 25 . Firstly, the first measurement point  13   d  and the second measurement point  13   e  on the face surface  13   c   1  of the club head  13   c  will be described with reference to  FIG. 23 . As shown in  FIG. 23 , in order to identify the posture and the position of the face surface  13   c   1 , the first measurement point  13   d  and the second measurement point  13   e  are set on the face surface  13   c   1 . The first measurement point  13   d  and the second measurement point  13   e  are disposed at positions distant from each other. Here, the first measurement point  13   d  is located on the heel side of the face surface  13   c   1 , and the second measurement point  13   e  is located on the toe side of the face surface  13   c   1 . The first measurement point  13   d  and the second measurement point  13   e  are preferably disposed on a face line h, which is parallel to the ground, and passes through the centroid of the face surface  13   c   1 . Therefore, it is possible for a line segment  13   f  connecting the first measurement point  13   d  and the second measurement point  13   e  to each other to identify the orientation of the face surface  13   c   1  when being projected on the ground. 
     As shown in  FIG. 2 , the arithmetic processing circuit  14  shown in  FIG. 1  includes the address (resting) analysis section  70  and the impact analysis section  80 . The address analysis section  70  is provided with a posture identification section  71  and a position identification section  72 . The posture identification section  71  identifies the posture of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ at rest (i.e., at the address). When identifying the posture, as shown in, for example,  FIG. 24 , the posture identification section  71  connects the coordinate (=r h (0)) of the first measurement point  13   d  and the coordinate (=r t (0)) of the second measurement point  13   e  at rest to each other with a first line segment L 1 . The posture of the face surface  13   c   1  is identified by the first line segment L 1 . On this occasion, the first line segment L 1  is projected on a horizontal plane (the X-Z plane; a plane expanding in parallel to the ground) perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ. It should be noted that regarding the coordinate (=r h (0)) of the first measurement point  13   d  and the coordinate (=r t (0)) of the second measurement point  13   e  at rest, the positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the address (t=0) can be identified by the swing position coordinate detection section  50 . 
     The position identification section  72  identifies a second line segment L 2  perpendicular to the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ at rest. The second line segment L 2  intersects perpendicularly with the face surface  13   c   1  at the first measurement point  13   d  (=r h (0)). When identifying the second line segment L 2 , the position identification section  72  identifies the first line segment L 1 . The position identification section  72  sets the second line segment L 2  at the first measurement point  13   d  in a direction perpendicular to the first line segment L 1 . The second line segment L 2  represents a so-called target line, which is the hit target direction. On this occasion, the second line segment L 2  is projected on a horizontal plane perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ similarly to the first line segment L 1 . 
     As shown in  FIG. 2 , the impact analysis section  80  is provided with a posture identification section  81 , a trajectory identification section  82 , and a speed identification section  63 . The posture identification section  81  identifies the posture of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ at the impact. When identifying the posture, as shown in, for example,  FIG. 24 , the posture identification section  81  connects the coordinate (=r h (imp)) of the first measurement point  13   d  and the coordinate (=r t (imp)) of the second measurement point  13   e  at the impact to each other with a third line segment L 3 . The posture of the face surface  13   c   1  at the impact is identified by the third line segment L 3 . On this occasion, the third line segment L 3  is projected on a horizontal plane perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ. It should be noted that regarding the coordinate (=r h (imp)) of the first measurement point  13   d  and the coordinate (=r t (imp)) of the second measurement point  13   e  at the impact, the positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the impact (t=timp) can be identified by the swing position coordinate detection section  50 . At the point of the impact, high acceleration, for example, is observed in a specific direction as an output of the inertial sensor L 2 . The point (t=timp) of the impact can be identified based on such a threshold value of the acceleration. 
     The trajectory identification section  82  identifies the trajectory of the first measurement point  13   d  in the absolute reference coordinate system ΣXYZ at the impact. When identifying the trajectory, the trajectory identification section  82  identifies a first coordinate point P 1  on the absolute reference coordinate system ΣXYZ indicating the position r h (imp) of the first measurement point  13   d  at the impact, and a second coordinate point P 2  on the absolute reference coordinate system ΣXYZ indicating the position r h (imp−1) of the first measurement point  13   d  at a sampling point coming before the impact as shown in  FIG. 24 . Here, the sampling point immediately before the impact is assigned to the second coordinate point P 2 . The first coordinate point P 1  and the second coordinate point P 2  are connected to each other with a fourth line segment L 4 . The direction and the length of the fourth line segment L 4  represent the direction and the magnitude of the movement vector. On this occasion, similarly to the above, the fourth line segment L 4  is projected on a horizontal plane perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ. The direction L 4 ′ (the tangential direction of the trajectory at the impact), along which the fourth line segment L 4  projected on the horizontal plane extends, is defined as a correct hit-ball direction at the impact. 
     The speed identification section  63  identifies the speed of the face surface  13   c   1  at the impact, which is displayed in the polar coordinate system together with the absolute face angle θ 1  or the square degree θ 2 . The speed of the face surface  13   c   1  at the impact can be obtained from information of the acceleration at the impact position and so on. 
     As shown in  FIG. 2 , the planar view direction analysis section  90  includes a first deviation angle analysis section  91  and a second deviation angle analysis section  92 . The first deviation angle analysis section  91  is connected to the position identification section  72  of the address analysis section  70  and the trajectory identification section  82  of the impact analysis section  80 . On this occasion, the first deviation angle analysis section  91  identifies the extended line L 4 ′ of the fourth line segment L 4 , which has been identified by, for example, the trajectory identification section  82 , as the hit-ball direction. The first deviation angle analysis section  91  calculates the crossing angle (the first deviation angle; the absolute face angle) θ 1  between the second line segment L 2  (parallel to the hit target direction or the target line) orthogonally crossing the face surface  13   c   1  at the first measurement point  13   d  of the face surface  13   c   1  at the address, and the extended line L 4 ′ (the correct hit-ball direction) of the fourth line segment L 4  orthogonally crossing the face surface  13   c   1  at the first measurement point  13   d  of the face surface  13   c   1  at the impact. The first deviation angle analysis section  91  can be connected to the position identification section  72  of the address analysis section  70  and the posture identification section  81  of the impact analysis section  80 . In this case, it results that the first deviation angle analysis section  91  identifies the hit-ball direction L 5  to a direction perpendicular to the third line segment L 3 , which has been identified by the posture identification section  81 , as a presumption. The first deviation angle analysis section  91  calculates the crossing angle (the first deviation angle; the absolute face angle) θ 1  between the second line segment L 2  (parallel to the hit target direction or the target line) orthogonally crossing the face surface  13   c   1  at the first measurement point  13   d  of the face surface  13   c   1  at the address, and the hit-ball direction L 5  orthogonally crossing the face surface  13   c   1  at the impact. 
     The second deviation angle analysis section  92  is connected to the posture identification section  81  and the trajectory identification section  82  of the impact analysis section  80 . The second deviation angle analysis section  92  identifies the hit-ball direction L 5  to a direction perpendicular to the third line segment L 3 , which has been identified by the posture identification section  81 , as a presumption. In other words, the correct hit-ball direction L 4 ′ is set on the extended line (in the tangential direction of the trajectory at the impact) of the movement vector (the fourth line segment L 4 ) as described above on the one hand, the face surface  13   c   1  in the actual posture does not necessarily cross orthogonally the correct hit-ball direction L 4 ′ in some cases. This is because the face surface  13   c   1  closes or opens at the impact, and is therefore not perpendicular to the correct hit-ball direction L 4 ′. The second deviation angle analysis section  92  identifies the crossing angle θ 2  between the correct hit-ball direction L 4 ′ and the virtual hit-ball direction L 5  as the square degree. The square degree θ 2  represents the deviation angle between the virtual vertical plane with respect to the correct hit-ball direction L 4 ′ and the face surface  13   c   1  measured at the impact. 
     The statistic analysis section  140  is capable of calculating a statistical value representing the variation in the absolute face angle θ 1 , the square degree θ 2 , or the speed V at the impact. The statistic analysis section  140  includes a histogram generation section  141 . The histogram generation section  141  classifies the absolute face angle θ 1 , the square degree θ 2 , or the speed V thus measured into a plurality of zones, and then counts the number of the samples included in each of the zones as the data for the histogram shown in  FIG. 8  or  FIG. 10 . Further, the statistic analysis section  140  includes a variation analysis section  142 . The variation analysis section  142  calculates an average value, a standard deviation, and so on with respect to all of the numbers of the samples of the absolute face angle θ 1 , the square degree θ 2 , or the speed V. In such a manner as described above, by displaying the statistical value representing the variation in the absolute face angle θ 1 , the square degree θ 2 , or the speed V, it is possible to evaluate the reproducibility of the directionality and the sense of distance of the hit ball. 
     The image processing circuit  18  is capable of generating the display information shown in  FIGS. 6 through 10  displayed on the display device  19  based on the information from the planar view direction analysis section  90  and the statistic analysis section  140 . Besides the above, the image processing circuit  18  is capable of displaying the degree of the deviation of the hit direction from the target area with a multiple number of the unit representing the area corresponding to the target area based on the information from the planar view direction analysis section  90 . For example, citing the example of the golf putter  13 , the unit representing the area corresponding to the target area is the size of the cup, and by displaying the deviation as, for example, two cups, it becomes easy to recognize the deviation from the target. 
     The image processing circuit  18  is capable of displaying the proportion (e.g., 46%) of the number of times of the trial, in which the hit direction has fallen within the target area, to the number of times of the exercise in which the hit direction has been identified based on the information from the statistic analysis section  140 . By adopting such a configuration, it is possible to make the target achievement rate be recognized as a numerical value, and thus make a notification of the exercise effect of the sport in a quantitative manner. 
     5-2. Analysis and Display of Deviation Amount From Centroid 
     The hit point analysis section  100  shown in  FIG. 2  includes an at-impact angular velocity acquisition section  101  and a deviation amount analysis section  102 . The at-impact angular velocity acquisition section  101  obtains the angular velocity around the long axis (the z axis of the sensor coordinate system) of the club shaft  13   a  at the impact from the output of the inertial sensor  12 . The deviation amount analysis section  102  analyzes the deviation amount δ from the hit point shown in  FIG. 3C  from the angular velocity thus obtained. 
     Here, the relationship between the angular velocity GyroZ around the long axis (the z axis of the sensor coordinate system) of the club shaft  13   a,  and the deviation amount δ of the hit position from the centroid in the horizontal direction of the face surface  13   c   1  is shown in  FIG. 26 . According to  FIG. 26 , it is understood that the deviation amount of the hit position from the centroid has been “8 (mm)” in the case in which the GyroZ shown is “−114.6 (rad/s).”  FIG. 27  is a diagram obtained by making a graph of the relationship shown in  FIG. 26 . In the graph shown in  FIG. 27 , the horizontal axis represents the angular velocity, and the vertical axis represents the deviation amount of the hit position. In  FIG. 27 , the correlation can be expressed by a linear expression. The coefficient and the intercept of the linear expression can be obtained by a regression analysis, and in the case of the example shown in  FIG. 27 , the linear expression is shown as Formula (7) below. 
         y=− 0.0604 x+ 2.4944   (7)
 
     The contribution ratio is “R 2 =0.8954.” 
     Formula (7) is calculated in advance, and is stored in the storage device  16 . Thus, it is possible for the deviation amount analysis section  102  to calculate the deviation amount δ of the hit position from the centroid based on the information from the inertial sensor  12  and the storage device  16 . 
     It is possible for the statistic analysis section  140  to calculate the statistical value representing the variation in the deviation amount δ. The histogram generation section  141  classifies the deviation amount δ thus measured into a plurality of zones, and then counts the number of samples of the deviation amount δ included in each of the zones in a similar manner to the manner shown in  FIG. 8  or  FIG. 10 . The variation analysis section  142  calculates an average value, a standard deviation, and so on with respect to all of the numbers of the samples of the deviation amount δ. In such a manner as described above, it is possible to display the statistical value representing the variation in the deviation amount δ. 
     The image processing circuit  18  is capable of generating the display information shown in  FIG. 11  to be displayed on the display device  19  based on the information from the hit point analysis section  100  and the statistic analysis section  140 . 
     The image processing circuit  18  is capable of displaying the proportion of the number of times of the trial, in which the deviation amount δ has fallen within the target area (e.g., ±5 mm from the centroid), to the number of times of the exercise in which the deviation amount δ has been identified based on the information from the statistic analysis section  140 . By adopting such a configuration, it is possible to make the target achievement rate be recognized as a numerical value, and thus make a notification of the exercise effect of the sport in a quantitative manner. 
     5-3. Analysis and Display of Swing Width 
     Then, the analysis and display of the stroke (the swing width) L shown in  FIGS. 12 through 16  will be described. As shown in  FIG. 2 , the stroke (swing width) analysis section  120  can be provided with a position determination section  121  and a stroke (swing width) determination section  122 . The position determination section  121  determines a first position as a start point of the swing width, and a second position as an end point of the swing width based on the output from the inertial sensor  12  and so on. In the present embodiment, since the first position is the address position, it is possible to designate the position corresponding to t=0. The second position is the swing switchback position, and as this position, there can be designated a position where the sign of the acceleration in the X-axis direction (the backswing direction) in, for example, the absolute reference coordinate system is switched. The position determination section  121  is also capable of determining the hit position (the impact position). At the point of the impact, high acceleration, for example, is observed in a specific direction as an output of the inertial sensor  12 . The point of the impact can be identified based on such a threshold value of the acceleration. It is possible for the speed detection section  60  to obtain the speed of the club head  13   c  at each of the positions from the information of the positions from the first position to the second position, and the acceleration at the impact position, and so on. 
     It is possible for the stroke (swing width) determination section  122  to calculate the length of a way extending along the swing trajectory from the first position (the address position) to the second position (the swing switchback position) as the swing width L. Since a number of coordinate positions having been sampled have been obtained from the first position to the second position, by accumulating (integrating) the distance in the three-dimensional space between the coordinate positions adjacent to each other having been sampled at a minute pitch, the length of the way can almost exactly be calculated. 
     Instead thereof, it is possible for the stroke (swing width) determination section  122  to obtain the distance between the coordinates in the horizontal axis X of the first position and the second position projected on the projection surface (e.g., the vertical X-Y plane of the absolute reference coordinate system) to thereby obtain the swing width L from the first position to the second position. This is because it is sufficient for the golfer to obtain the length of a taking back action toward the backswing direction (i.e., the distance between the coordinates thus projected) as the swing width L of the backswing rather than the more accurate swing width along the way. In  FIG. 28 , the distance between the coordinates in the horizontal axis X of the first position and the second position is shown on the horizontal axis. In  FIG. 28 , the distance between the coordinates in the vertical axis Y of the first position and the second position projected on the vertical X-Y plane of the absolute reference coordinate system is shown on the vertical axis. It should be noted that the distance between the coordinates in the vertical axis Y can also be omitted. 
     It is possible for the statistic analysis section  140  to calculate the statistical value representing the variation in the swing width L. The histogram generation section  141  classifies the swing width or the speed thus measured into a plurality of zones, and then counts the number of the samples included in each of the zones as the data for the histogram shown in  FIG. 14  or  FIG. 16 . Further, the variation analysis section  142  of the statistic analysis section  140  calculates an average value, a standard deviation, and so on with respect to all of the numbers of the samples of the swing width L or the speed V. By displaying the statistical value representing the variation in the swing width L or the speed V in such a manner as described above, it is possible to evaluate the reproducibility of the swing width L and the speed V of the sporting device in accordance with the range of the hit ball. 
     The image processing circuit  18  is capable of generating the display information shown in  FIGS. 17 through 21  displayed on the display device  19  based on the information from the front view direction analysis section  110  and the statistic analysis section  140 . Besides the above, it is possible for the image processing circuit  18  to display the proportion (e.g., 48%) of the number of times of the trial, in which the third deviation angle θ 3  or the fourth deviation angle θ 4  has fallen within the target area (e.g., θ 3 =θ 4 =±1°), to the number of times of the exercise, in which the third deviation angle θ 3  or the fourth deviation angle θ 4  has been identified, based on the information from the statistic analysis section  140 . By adopting such a configuration, it is possible to make the target achievement rate be recognized as a numerical value, and thus make a notification of the exercise effect of the sport in a quantitative manner. 
     The image processing circuit  18  is capable of generating the display information shown in  FIGS. 12 through 16  displayed on the display device  19  based on the information from the stroke (swing width) analysis section  120  and the statistic analysis section  140 . In particular, the display pitch of the images showing the putter  13  displayed at the plurality of positions in  FIG. 13  can be shortened in the period in which the swing speed obtained by the speed detection section  60  is high, or elongated in the period in which the swing speed is low. It should be noted that the image showing the putter  13  can be displayed one at a time every predetermined time interval (every plurality of sampling data). Thus, both of the swing width and the swing speed of the putter  13  can visually be recognized. 
     It is possible for the image processing circuit  18  to sequentially display the images showing the putter  13 , which are displayed at a plurality of positions in  FIG. 13 , in accordance with the swing motion of the putter  13  in sync with the swing motion. Thus, it is possible to dynamically and visually recognize the swing width of the putter  13 . 
     It should be noted that the first position as the start point of the swing width L and the second position are not limited to those set respectively to the address position and the swing switchback position described above. As the combination of (the first position)/(the second position), it is also possible to adopt combinations of (the swing switchback position)/(the impact position) defining the swing width L of the downswing, (the impact position)/(a swing end position) defining the swing width of the follow-through, and (the swing start position)/(swing end position) defining the swing width L of the whole swing. These swing widths L are also correlated with the swing width of the backswing, and each can make a contribution to experiencing the sense of distance with good reproducibility using, for example, the golf putter, or in a half swing with an iron club. 
     5-4. Analysis and Display of Third Deviation Angle θ 3  and Fourth Deviation Angle θ 4   
     Then, a configuration and an operation of the front view direction analysis section  110 , the statistic analysis section  140 , and the image processing circuit  18  involved in the generation of the analysis pictures of the third deviation angle θ 3  (the delta-loft angle) or the fourth deviation angle θ 4  (the attack angle) shown in  FIGS. 17 through 21  will be described with reference to  FIGS. 29 and 30 . Firstly, the first measurement point  13   d  and the second measurement point  13   e  on the face surface  13   c   1  of the club head  13   c  will be described with reference to  FIG. 29 . As shown in  FIG. 29 , in order to identify the posture and the position of the face surface  13   c   1 , the first measurement point  13   d  and the second measurement point  13   e  are set on the face surface  13   c   1 . The first measurement point  13   d  and the second measurement point  13   e  are disposed at positions distant from each other. Here, the first measurement point  13   d  is located in an upper part of the face surface  13   c   1 , and the second measurement point  13   e  is located in a lower part of the face surface  13   c   1 . The first measurement point  13   d  and the second measurement point  13   e  are preferably disposed on a face vertical line v, which is vertical to the ground, and passes through the centroid of the face surface  13   c   1 . Therefore, it is possible for the line segment  13   f  connecting the first measurement point  13   d  and the second measurement point  13   e  to each other to identify the tilt angle of the face surface  13   c   1  with respect to the vertical plane when being projected on the ground. 
     As shown in  FIG. 2 , the arithmetic processing circuit  14  includes the address (resting) analysis section  70  and the impact analysis section  80 . The posture identification section  71  of the address analysis section  70  identifies the posture of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ at rest (i.e., at the address). When identifying the posture, as shown in, for example,  FIG. 30 , the posture identification section  71  connects the coordinate (=r h (0)) of the first measurement point  13   d  and the coordinate (=r t (0)) of the second measurement point  13   e  at rest to each other with the first line segment L 1 . The posture of the face surface  13   c   1  is identified by the first line segment L 1 . On this occasion, the first line segment L 1  is projected on a vertical plane (the X-Y plane; a plane perpendicular to the ground) perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ. It should be noted that regarding the coordinate (=r h (0)) of the first measurement point  13   d  and the coordinate (=r t (0)) of the second measurement point  13   e  at rest, the positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the address (t=0) can be identified by the swing position coordinate detection section  50 . 
     The position identification section  72  identifies the second line segment L 2  perpendicular to the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ at rest. The second line segment L 2  intersects perpendicularly with the face surface  13   c   1  at the first measurement point  13   d  (=r h (0)). When identifying the second line segment L 2 , the position identification section  72  identifies the first line segment L 1 . The position identification section  72  sets the second line segment L 2  at the first measurement point  13   d  in a direction perpendicular to the first line segment L 1 . The second line segment L 2  represents a so-called target line, which is the hit target direction. On this occasion, the second line segment L 2  is projected on a vertical plane perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ similarly to the first line segment L 1 . 
     The posture identification section  81  of the impact analysis section  80  identifies the posture of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ at the impact. When identifying the posture, as shown in, for example,  FIG. 30 , the posture identification section  81  connects the coordinate (=r h (imp)) of the first measurement point  13   d  and the coordinate (=r t (imp)) of the second measurement point  13   e  at the impact to each other with the third line segment L 3 . The posture of the face surface  13   c   1  at the impact is identified by the third line segment L 3 . On this occasion, the third line segment L 3  is projected on a vertical plane perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ. It should be noted that regarding the coordinate (=r h (imp)) of the first measurement point  13   d  and the coordinate (=r t (imp)) of the second measurement point  13   e  at the impact, the positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the impact (t=timp) can be identified by the swing position coordinate detection section  50 . At the point of the impact, high acceleration, for example, is observed in a specific direction as an output of the inertial sensor  12 . The point (t=timp) of the impact can be identified based on such a threshold value of the acceleration. 
     The trajectory identification section  82  identifies the trajectory of the first measurement point  13   d  in the absolute reference coordinate system ΣXYZ at the impact. When identifying the trajectory, the trajectory identification section  82  identifies a first coordinate point P 1  on the absolute reference coordinate system ΣXYZ indicating the position r h (imp) of the first measurement point  13   d  at the impact, and a second coordinate point P 2  on the absolute reference coordinate system ΣXYZ indicating the position r h (imp−1) of the first measurement point  13   d  at a sampling point coming before the impact as shown in  FIG. 30 . Here, the sampling point immediately before the impact is assigned to the second coordinate point P 2 . The first coordinate point P 1  and the second coordinate point P 2  are connected to each other with the fourth line segment L 4 . The direction and the length of the fourth line segment L 4  represent the direction and the magnitude of the movement vector. On this occasion, similarly to the above, the fourth line segment L 4  is projected on a vertical plane perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ. The direction L 4 ′ (the tangential direction of the trajectory at the impact projected on a vertical plane), along which the fourth line segment L 4  projected on the vertical plane extends, is defined as a hit-ball direction at the impact. 
     As shown in  FIG. 2 , the front view direction analysis section  110  includes a third deviation angle analysis section  111  and a fourth deviation angle analysis section  112 . The third deviation angle analysis section  111  is connected to the position identification section  72  of the address analysis section  70  and the posture identification section  81  of the impact analysis section  80 . On this occasion, the third deviation angle analysis section  111  identifies the crossing angle between the first line segment L 1  (the line segment representing the reference tilt angle) identified by the position identification section  72  and the third line segment L 3  (the line segment representing the tilt angle) identified by the posture identification section  81  as the third deviation angle (the delta-loft angle) θ 3 . 
     The fourth deviation angle analysis section  112  is connected to the posture identification section  71  of the address analysis section  70  and the trajectory identification section  82  of the impact analysis section  80 . The fourth deviation angle analysis section  112  identifies the extended line L 4 ′ of the fourth line segment L 4 , which has been identified by, for example, the trajectory identification section  82 , as the hit-ball direction. The fourth deviation angle analysis section  112  calculates the crossing angle between the second line segment L 5  (parallel to the hit target direction or the target line) orthogonally crossing the face surface  13   c   1  at the first measurement point  13   d  of the face surface  13   c   1  at the address, and the extended line L 4 ′ (the correct hit-ball direction) of the fourth line segment L 4  orthogonally crossing the face surface  13   c   1  at the first measurement point  13   d  of the face surface  13   c   1  at the impact, namely the fourth deviation angle (the attack angle) θ 4 . 
     The statistic analysis section  140  is capable of calculating the statistical value representing the variation in the third deviation angle θ 3  or the fourth deviation angle θ 4 . As the data for the histogram shown in  FIG. 19  or  FIG. 21 , the third deviation angle θ 3  or the fourth deviation angle θ 4  thus measured are classified into a plurality of zones, and the number of the samples included in each of the zones is counted. Besides the above, it is also possible for the statistic analysis section  140  to calculate the average value, the standard deviation, and so on with respect to all of the numbers of the samples of the third deviation angle θ 3  or the fourth deviation angle θ 4 . In such a manner as described above, by displaying the statistical value representing the variation in the third deviation angle θ 3  or the fourth deviation angle θ 4 , it is possible to evaluate the reproducibility of the directionality and the sense of distance of the hit ball. 
     The image processing circuit  18  is capable of generating the display information shown in  FIGS. 17  through  21  displayed on the display device  19  based on the information from the front view direction analysis section  110  and the statistic analysis section  140 . Besides the above, it is possible for the image processing circuit  18  to display the proportion (e.g., 48%) of the number of times of the trial, in which the third deviation angle θ 3  or the fourth deviation angle θ 4  has fallen within the target area (e.g., θ 3 =θ 4 =±1°), to the number of times of the exercise, in which the third deviation angle θ 3  or the fourth deviation angle θ 4  has been identified, based on the information from the statistic analysis section  140 . By adopting such a configuration, it is possible to make the target achievement rate be recognized as a numerical value, and thus make a notification of the exercise effect of the sport in a quantitative manner. 
     6. Scoring 
     Then, the score analysis section  130  for scoring the swing based on the plurality of analysis data described above will be described. In the general classification, scoring is divided into scoring of the analysis items (the first through fourth deviation angles θ 1  through θ 4 , the swing width L, the deviation amount δ from the centroid, and the speed V at the impact) and scoring of the overall points obtained from a plurality of analysis items weighted. 
     6-1. Scoring of Each of Analysis Items 
     The performance score (PS) is expressed by the following formula. 
       PS= P− (1 −Ta )× S    (8)
 
     Here, the symbol P represents the perfect score (100 points). The symbol Ta represents a target zone evaluation, and is expressed as follows. 
         Ta =( Tz −(| T−R| ))/ Tz    (9)
 
     Here, the symbol Tz represents a target zone, the symbol T represents a target value, and the symbol R represents the analysis data. If (1−Ta) is in a range of 0 through 1, there is indicated the fact that the analysis item falls within the target zone. It means that the closer (1−Ta) approaches 0, the closer the analysis item is to the target value. If (1−Ta) is equal to or larger than 1, it means that the analysis item is out of the target zone. Further, the symbol S represents a scale number, and is used to match the scale between the score and the numerical value of the data. S=P/A is true, and the symbol A represents an analyzable range. 
     6-1-1. Performance Score PsF of First Deviation Angle θ 1   
     In the case of applying the impact square to the target line, the first deviation angle θ 1 =0 is achieved, and in this case, the performance score PsF=100 points is provided. The score of the first deviation angle θ 1  is calculated by substituting, for example, P=100, T=0, Tz=1°, A=30, and R=θ 1  into Formulas (8) and (9). On this occasion, the target zone Tz is a variable, which can be set in the range of ±arcsin (R/L) using the radius R of the cup, and the distance L from the address position to the center of the cup as described above. 
     6-1-2. Performance Score PsS of Second Deviation Angle θ 2   
     In the case of applying the impact square to a club path, the second deviation angle θ 2 =0 is achieved, and in this case, the performance score PsS=100 points is provided. The score of the second deviation angle θ 2  is calculated by substituting, for example, P=100, T=0, Tz=1°, A=30, and R=θ 2  into Formulas (8) and (9). 
     6-1-3. Performance Score PsH of Deviation Amount δ From Centroid 
     In the case of hitting the ball at the centroid, the deviation amount δ=0 is achieved, and in this case, the performance score PsH=100 points is provided. The scoring of the deviation amount δ is calculated by substituting, for example, P=100, T=0, Tz=5°, A=100, and R=δ into Formulas (8) and (9). 
     6-1-4. Performance Score PsB of Swing Width L 
     The target of the swing width L is to fall within the standard deviation of 1σ. The scoring of the swing width L is calculated by substituting, for example, P=100, T=0, Tz=1σ°, A=100, and R=L into Formulas (8) and (9). 
     6-1-5. Performance Score PsI of Impact Speed V 
     The target of the impact speed V is also to fall within the standard deviation of 1σ. The scoring of the impact speed V is calculated by substituting, for example, P=100, T=0, Tz=1σ, A=10, and R=V into Formulas (8) and (9). 
     6-1-6. Performance Score PsL of Third Deviation Angle θ 3   
     In the case of applying the impact with the same loft angle as the standard loft angle or the measured loft angle at the address, the third deviation angle θ 3 =0 is achieved, and the PsL=100 points is provided. The scoring of the third deviation angle θ 3  is calculated by substituting, for example, P=100, T=0, Tz=1°, A=15, and R=θ 3  into Formulas (8) and (9). 
     6-1-7. Performance Score PsA of Fourth Deviation Angle θ 4   
     In the case of applying the impact in parallel to the target line, the fourth deviation angle θ 4 =0 is achieved, and the performance score PsA=100 points is provided. The scoring of the fourth deviation angle θ 4  is calculated by substituting, for example, P=100, T=0, Tz=1°, A=15, and R=θ 4  into Formulas (8) and (9). 
     The performance score PS of each of such analysis items as described above is displayed in the PS column of the analysis picture of the corresponding analysis item described above as a numerical value. 
     6-2. Scoring of Overall Points 
     The analysis items described above are generally classified into the analysis items related to the directionality (the first deviation angle θ 1 , the second deviation angle θ 2 , and the deviation amount δ from the centroid), and the analysis items related to the sense of distance (the impact speed V, the swing width L, the third deviation angle θ 3 , and the fourth deviation angle θ 4 ). Therefore, as the overall points obtained from the analysis items weighted, the three types, namely (1) the overall points related to the directionality, (2) the overall points related to the sense of distance, and (3) the overall points related to both of the directionality and the sense of distance, are useful. 
     6-2-1. Scoring of Overall Points of Analysis Items Related to Directionality of Hit Ball 
     The weighting factors for the case of using the three analysis items (the first deviation angle θ 1 , the second deviation angle θ 2 , and the deviation amount δ from the centroid) related to the directionality are defined as follows. The weighting factor of the performance score PsS related to the first deviation angle (the absolute face angle) θ 1  is represented by WS, the weighting factor of the performance score PsF related to the second deviation angle θ 2  is represented by WF, and the weighting factor of the performance score PsH related to the deviation amount δ from the centroid is represented by WH. 
     Taking the influence level related to the directionality of the hit ball into consideration, the weighting factor WS with respect to the first deviation angle θ 1  is higher than the weighting factor WH with respect to the deviation amount δ (WS&gt;WH). Further, the weighting factor WH with respect to the deviation amount δ is higher than the weighting factor WF with respect to the second deviation angle θ 2  (WH&gt;WF). Therefore, the relationship between the three weighting factors is as follows. 
       WS&gt;WH&gt;WF   (10)
 
     In the case of using the three types of data θ 1 , θ 2 , and δ, the overall points of the analysis items related to the directionality of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsF×WF+PsS×WS+PsH×WH )/( WF+WS+WH )   (11)
 
     In the case of using the two types of data θ 1  and δ, the overall points of the analysis items related to the directionality of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsF×WF+PsH×WH )/( WF+WH )   (12)
 
     In the case of using the two types of data θ 2  and δ, the overall points of the analysis items related to the directionality of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsS×WS+PsH×WH )/( WS+WH )   (13)
 
     In the case of using the two types of data θ 1  and θ 2 , the overall points of the analysis items related to the directionality of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsF×WF+PsS×WS )/( WF+WS )   (14)
 
     6-2-2. Scoring of Overall Points of Analysis Items Related to Sense of Distance of Hit Ball 
     The weighting factors for the case of using the four analysis items (the impact speed V, the swing width L, the third deviation angle θ 3 , and the fourth deviation angle θ 4 ) related to the sense of distance are defined as follows. The weighting factor of the performance score PsI related to the impact speed V is represented by WI, the weighting factor related to the performance score PsB of the swing width L is represented by WB, the weighting factor of the performance score PsL related to the third deviation angle (the delta-loft angle) θ 3  is represented by WL, and the weighting factor of the performance score PsA related to the fourth deviation angle (the attack angle) θ 4  is represented by WA. 
     Taking the influence level related to the sense of distance of the hit ball into consideration, the weighting factor WI with respect to the impact speed V is higher than the weighting factor WB with respect to the swing width L (WI&gt;WB). The weighting factor WB with respect to the swing width L is higher than the weighting factor WL with respect to the third deviation angle θ 3  and the weighting factor WA with respect to the fourth deviation angle θ 4  (WI&gt;WB&gt;WL, WI&gt;WB&gt;WA). Since the third deviation angle θ 3  and the fourth deviation angle θ 4  are correlated with each other, the weighting factor WL with respect to the third deviation angle θ 3  and the weighting factor WA with respect to the fourth deviation angle θ 4  can be set, for example, equal to each other (WL=WA). Therefore, the relationship between the four weighting factors is as follows. 
         WI&gt;WB&gt;WL=WA    (15)
 
     In the case of using the four types of data V, L, θ 3  and θ 4 , the overall points of the analysis items related to the sense of distance of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsI×WI+PsB×WB+PsL×WL+PsA×WA )/( WI+WB+WL+WA )   (16)
 
     In the case of using the three types of data V, L, and θ 3 , the overall points of the analysis items related to the sense of distance of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsI×WI+PsB×WB+PsL×WL )/( WI+WB+WL )   (17)
 
     In the case of using the three types of data V, L, and θ 4 , the overall points of the analysis items related to the sense of distance of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsI×WI+PsB×WB+PsA×WA )/( WI+WB+WA )   (18)
 
     In the case of using the two types of data V and L, the overall points of the analysis items related to the sense of distance of the hit ball becomes as follows. 
       SUM ((each PS)×(corresponding weighting factor))/SUM (each weighting factor)=( PsI×WI+PsB×WB )/( WI+WB )   (19)
 
     6-2-3. Scoring of Overall Points of Analysis Items Related to Directionality and Sense of Distance of Hit Ball 
     Taking the influence level on the improvement in the swing and an athletic competition into consideration, importance is given to the directionality of the hit ball among the directionality and the sense of distance of the hit ball. Further, among the analysis items related to the directionality of the hit ball, it is possible to give importance to the analysis items (e.g., V and L) high in influence level rather than the analysis items (e.g., θ 2 ) low in influence level. Therefore, as the relationship between the weighting factors with respect to the seven analysis items (θ 1 , θ 2 , δ, V, L, θ 3 , and θ 4 ) related to the directionality and the sense of distance of the hit ball, the following is determined based on Formulas (10) and (15). 
         WS&gt;WH&gt;WI&gt;WB&gt;WF&gt;WL=WA    (20)
 
     The total performance score Ps ((directionality)+(sense of distance)) of the performance score Ps (directionality) related to the directionality represented by either of Formulas (11) through (14) and the performance score Ps (sense of distance) related to the sense of distance represented by either of Formulas (16) through (18) is as follows. 
       Performance score  Ps  ((directionality)+(sense of distance))= a× (performance score  Ps  (directionality))+ b× (performance score  Ps  (sense of distance))   (21)
 
     Here, the weighting factors a, b can be set so as to fulfill a=b=1, or besides the above, can be set so as to fulfill a&gt;b to give importance to the directionality. 
     It is also possible to display the score of the performance score Ps ((directionality)+(sense of distance)), a×(performance score Ps (directionality)), or b×(performance score Ps (sense of distance)), and at the same time, display the analysis data of the plurality of analysis items used for the performance score thus displayed with, for example, a cobweb chart. 
     Although the present embodiment is hereinabove explained in detail, it should easily be understood by those skilled in the art that it is possible to make a variety of modifications not substantially departing from the novel matters and the advantages of the invention. Therefore, such modified examples are all included in the scope of the invention. For example, a term described at least once with a different term having a broader sense or the same meaning in the specification or the accompanying drawings can be replaced with the different term in any part of the specification or the accompanying drawings. Further, the configurations and the operations of the inertial sensor  12 , the golf club  13 , the arithmetic processing circuit  14 , and so on are not limited to those described in the present embodiment, but can variously be modified. For example, the invention can be applied to sporting devices of baseball, tennis, and so on besides golf. 
     The entire disclosure of Japanese Patent Application No.2015-025691, filed Feb. 12, 2015 is expressly incorporated by reference herein.