Patent Publication Number: US-2016236061-A1

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

Description:
BACKGROUND 
     1. Technical Field 
     The present invention relates to a motion analysis method, a motion analysis apparatus, and a storage device. 
     2. Related Art 
     JP-A-2008-73210 has proposed an apparatus in which a three-axis acceleration sensor and a three-axis gyro sensor are attached to a golf club, and a swing is analyzed by using output from the sensors. If the apparatus is used, convenience is improved since a camera is not necessary. 
     Meanwhile, especially, when a golf putter is used among golf clubs, both directionality and the perception of distance are most important in order to put a ball into a cup. 
     On the other hand, even if both of the directionality and the perception of distance are accurate, it is common that a ball is not dropped in a cup due to rotation of the hit ball, or for other reasons such as duffing caused by a down-blow swing or topping caused by an upper-blow swing. 
     In cases of golf clubs other than the putter, duffing or topping causes a ball not to be shot as intended, but, while using an iron, appropriate down blow is recommended, and, while using a wood, appropriate upper blow is recommended. 
     There are cases where a ball is intentionally hit low or high. 
     However, in a motion analysis apparatus employing an inertial sensor, there is a problem in that an inclined angle of a hitting surface of an exercise appliance cannot be estimated during impact. 
     SUMMARY 
     An advantage of some aspects of the invention is to provide a motion analysis method and a motion analysis apparatus capable of estimating an angle at which a hitting surface of an exercise appliance comes into contact with a ball during impact, and a storage device. 
     (1) An aspect of the invention relates to a motion analysis method including specifying a difference between an inclined angle of a hitting surface of an exercise appliance during impact and a reference inclined angle which is acquired in advance by using an output signal from an inertial sensor. 
     According to the aspect of the invention, the difference between the inclined angle relative to a vertical plane of the hitting surface of the exercise appliance during impact and the reference inclined angle is specified. Consequently, it is possible to learn an angle at which the hitting surface of the exercise appliance comes into contact with a hit ball during impact, with high reproducibility, and thus to intentionally control the angle so as to control the hit ball or to reduce shot errors. 
     (2) In the aspect of the invention, the exercise appliance may be a golf club, and the reference inclined angle may be a standard value of a loft angle of a club head. The loft angle is an angle formed between the hitting surface (face surface) and a surface which is perpendicular to the ground surface when a sole (bottom surface) of the club head is brought into contact with the flat ground surface. If the above-described difference is small, an impact is applied in a state in which the loft angle is close to the standard value, and if the difference is large, an impact is applied in a state in which the loft angle is greatly deviated relative to the standard value. In a case of using a putter, if a swing is performed in a state in which the loft angle is the standard value, rotation of a hit ball becomes better, and thus it is possible to achieve the perception of distance as intended. On the other hand, for example, in a case where a ball is hit low with an iron, the face surface may be covered so that the loft angle is reduced, or when a ball is hit in a bunker with a sand wedge, the face surface may be intentionally opened so that the loft angle is increased. As mentioned above, the method of the invention may be used in a case of changing a loft angle as intended. 
     (3) In the aspect of the invention, the reference inclined angle may be specified by using an output signal from the inertial sensor when the exercise appliance is stopped. With this configuration, for example, in a case of a golf club, it is possible to verify whether or not a loft angle which is set during address (during stoppage) can be reproduced during impact by evaluating the difference. 
     (4) In the aspect of the invention, the inclined angle of the hitting surface and the reference inclined angle may be displayed in a coordinate system. With this configuration, it is possible to visually recognize the difference between the reference inclined angle and the inclined angle displayed in the coordinate system. 
     (5) In the aspect of the invention, an image of the exercise appliance may be displayed in the coordinate system in a superimposed manner in a front view of viewing a user handling the exercise appliance from the front side. With this configuration, it is possible to visually recognize an angle of the hitting surface from the image displayed in the coordinate system in a superimposed manner. 
     (6) In the aspect of the invention, the image of the exercise appliance may be displayed at a predetermined position on a display screen, and a display position of the reference inclined angle may be rotated by an angle which is the same as the difference so as to be displayed. With this configuration, an image of a relatively complex shape may be fixed on the screen, and then the coordinate system fixed as a background may be rotated by an angle which is the same as the difference so as to be displayed. Therefore, there is an advantage in that display image control is not complicated. 
     (7) In the aspect of the invention, an inclined angle of the hitting surface specified in the past may be displayed in the coordinate system so as to be differentiated from an inclined angle of the hitting surface specified this time. With this configuration, it is possible to visually recognize achievement of a practice effect when exercises are repeatedly performed. 
     (8) In the aspect of the invention, a target region including the reference inclined angle may be displayed so as to be differentiated from other regions. With this configuration, in a case where achieving the reference inclined angle during impact is a goal, since a target is a zone rather than a line, a target achievement ratio is increased, the user feels comfortable, and thus an exercise practice effect can be improved. 
     (9) In the aspect of the invention, a ratio of the number of times in which an inclined angle of the hitting surface enters the target region to the number of exercises in which the inclined angle of the hitting surface is specified may be displayed. With this configuration, a target achievement ratio can be recognized as a numerical value, and thus a notification of an exercise practice effect can be performed in a quantitative manner. 
     (10) Another aspect of the invention relates to a motion analysis method including specifying a tangential direction during impact with respect to a movement trajectory of an exercise appliance projected onto a vertical plane by using an output signal from an inertial sensor; and specifying an intersection angle between a target direction projected onto the vertical plane and the tangential direction. 
     According to the aspect of the invention, the intersection angle between the tangential direction during impact with respect to the movement trajectory of the exercise appliance projected onto the vertical plane and the target direction projected onto the vertical plane is specified. Consequently, it is possible to learn an angle (an incidence angle or the like of an upper blow or a down blow) at which the hitting surface of the exercise appliance is incident to a hit ball during impact, with high reproducibility, and thus to intentionally control the angle so as to control the hit ball or to reduce shot errors. The same aspects as in the above (3) to (9) are applicable to other aspects of the invention. Particularly, when the aspect of (5) is applied, images of the exercise appliance may be displayed at a plurality of positions along a movement trajectory prior to impact. In the above-described way, it becomes easier to visually recognize the trajectory of an upper blow or a down blow. 
     (11) Still another aspect of the invention relates to a motion analysis apparatus including an impact analysis unit that specifies an inclined angle of a hitting surface of an exercise appliance during impact by using an output signal from an inertial sensor; and a difference analysis unit that specifies a difference between the inclined angle of the hitting surface and a reference inclined angle which is acquired in advance. According to the aspect of the invention, it is possible to appropriately perform the motion analysis method of (1) according to the aspect of the invention. 
     (12) Yet another aspect of the invention relates to a motion analysis apparatus including an impact analysis unit that specifies a tangential direction during impact with respect to a movement trajectory of an exercise appliance projected onto a vertical plane by using an output signal from an inertial sensor; and an intersection angle analysis unit that specifies an intersection angle between a target direction projected onto the vertical plane and the tangential direction. According to the aspect of the invention, it is possible to appropriately perform the motion analysis method of (10) according to the aspect of the invention. 
     (13) Still yet another aspect of the invention relates to a storage device storing a motion analysis program causing a computer to execute specifying an inclined angle of a hitting surface of an exercise appliance during impact by using an output signal from an inertial sensor; and specifying a difference between the inclined angle of the hitting surface and a reference inclined angle which is acquired in advance. 
     (14) Further another aspect of the invention relates to a storage device storing a motion analysis program causing a computer to execute specifying a tangential direction during impact with respect to a movement trajectory of an exercise appliance projected onto a vertical plane by using an output signal from an inertial sensor; and specifying an intersection angle between a target direction projected onto the vertical plane and the tangential direction. 
     The program may be built into the storage device of the motion analysis apparatus performing the method of the invention, or may be installed to the storage device of the motion analysis apparatus 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 illustrating a configuration of a golf swing analysis apparatus according to an embodiment of the invention. 
         FIG. 2  is a block diagram schematically illustrating a configuration of a calculation processing circuit according to the embodiment of the invention. 
         FIG. 3A  is a diagram illustrating a first deviation angle (absolute face angle). 
         FIG. 3B  is a diagram illustrating a second deviation angle (square degree). 
         FIG. 3C  is a diagram illustrating a deviation amount from a hit point. 
         FIG. 4A  is a diagram illustrating a third deviation angle (delta-loft angle) and an impact speed. 
         FIG. 4B  is a diagram illustrating a fourth deviation angle (attack angle). 
         FIG. 4C  is a diagram illustrating a swing width. 
         FIG. 5  is a diagram illustrating an initial screen of an analysis screen. 
         FIG. 6  is a diagram illustrating an analysis screen when “Direction” is selected in  FIG. 5 . 
         FIG. 7  is a diagram illustrating an analysis screen when “FACE” is selected in  FIG. 6 . 
         FIG. 8  is a diagram illustrating an analysis screen when “Histogram” is selected in  FIG. 5 or 6 . 
         FIG. 9  is a diagram illustrating an analysis screen when “SQUARE” is selected in  FIGS. 6 to 8 . 
         FIG. 10  is a diagram illustrating an analysis screen when “Histogram” is selected in  FIG. 9 . 
         FIG. 11  is a diagram of a display screen illustrating a deviation amount of a hitting position from a sweet spot. 
         FIG. 12  is a diagram illustrating an analysis screen when “Stroke” is selected in  FIG. 5 . 
         FIG. 13  is a diagram illustrating an analysis screen when “SPAN-BACK” is selected in  FIG. 12 . 
         FIG. 14  is a diagram illustrating an analysis screen when “Histogram” is selected in  FIG. 12 or 13 . 
         FIG. 15  is a diagram illustrating an analysis screen when “SPEED” is selected in  FIGS. 12 to 14 . 
         FIG. 16  is a diagram illustrating an analysis screen when “Histogram” is selected in  FIG. 15 . 
         FIG. 17  is a diagram illustrating an analysis screen when “Rising” is selected in  FIG. 5 . 
         FIG. 18  is a diagram illustrating an analysis screen when “DELTA-LOFT” is selected in  FIG. 17 . 
         FIG. 19  is a diagram illustrating an analysis screen when “Histogram” is selected in  FIG. 17 or 18 . 
         FIG. 20  is a diagram illustrating an analysis screen when “ATTACK” is selected in  FIGS. 17 to 19 . 
         FIG. 21  is a diagram illustrating an analysis screen when “Histogram” is selected in  FIG. 20 . 
         FIG. 22  is a flowchart illustrating an operation of detecting an attitude on a swing trajectory. 
         FIG. 23  is a diagram for explaining first and second measurement points which are set to be separated from each other in a horizontal direction on a face surface of a club head. 
         FIG. 24  is a diagram for explaining the first deviation angle (absolute face angle) and the second deviation angle (square degree). 
         FIG. 25  is a diagram schematically illustrating a cup-in ratio in the cup unit. 
         FIG. 26  is a diagram illustrating a correlation between angular velocity and a hitting point measurement value with respect to a shaft long axis. 
         FIG. 27  is a diagram illustrating a relational expression obtained from data illustrated in  FIG. 26 . 
         FIG. 28  is a diagram illustrating a display example in which the swing width of a backswing is projected onto a projection surface. 
         FIG. 29  is a diagram for explaining first and second measurement points which are set to be separated from each other in a vertical direction on the face surface of the club head. 
         FIG. 30  is a diagram for explaining the third deviation angle (delta-loft angle) and the fourth deviation angle (attack angle). 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, an embodiment of the invention will be described with reference to the accompanying drawings. The embodiment described below is not intended to improperly limit the content of the invention, and all constituent elements described in the present embodiment are not essential as solving means of the invention. 
     (1) Configuration of Golf Club Analysis Apparatus 
       FIG. 1  schematically illustrates a configuration of a golf swing analysis apparatus (motion analysis apparatus)  11  according to an embodiment of the invention. The golf swing analysis apparatus  11  includes, for example, an inertial sensor  12 . An acceleration sensor and a gyro sensor are incorporated into the inertial sensor  12 . The acceleration sensor can detect separate acceleration in three-axis directions which are perpendicular to each other. The gyro sensor can detect separate angular velocity around each of three axes (x, y, and z) which are perpendicular to each other. The inertial sensor outputs a detection signal. Acceleration and angular velocity are specified in each axis by the detection signal. The acceleration sensor and the gyro sensor detect information regarding acceleration and angular velocity with relatively high accuracy. The inertial sensor  12  is attached to a golf club (exercise appliance)  13 . The golf club, for example, a golf putter  13  includes a shaft  13   a  and a grip  13   b . The grip  13   b  is gripped with the hands. The grip  13   b  is formed on the same axis as an axis of the shaft  13   a . A club head  13   c  is coupled to a tip of the shaft  13   a . Preferably, the inertial sensor  12  is attached to the shaft  13   a  or the grip  13   b  of the golf club  13 . The inertial sensor  12  may be fixed to the golf club  13  so as not to be relatively moved. 
     Here, when the inertial sensor  12  is attached, one (z axis) of detection axes of the inertial sensor  12  matches the axis of the shaft  13   a . Another detection axis (x axis) of the inertial sensor  12  matches a direction in which a direction (face normal direction) perpendicular to a face surface (hitting surface)  13   c   1  is projected on a horizontal plane in a state in which a sole (grounding surface) of the club head  13   c  is made horizontal. The face surface is not limited to a vertical surface, and is inclined with respect to the vertical surface, and thus the x axis is set in the direction in which the face normal direction is projected onto a horizontal surface. The y axis is perpendicular to the x axis and the z axis. A sensor coordinate system Σxyz is defined by the x axis, the y axis, and the z axis. 
     The golf swing analysis apparatus  11  includes a calculation processing circuit  14 . The calculation processing circuit  14  is connected to the inertial sensor  12 . A predetermined interface circuit  15  is connected to the calculation processing circuit  14 . In connection, the interface circuit  15  may be connected to the inertial sensor  12  in a wired manner, and may be connected to the inertial sensor  12  in a wireless manner. A detection signal is supplied to the calculation processing circuit  14  from the inertial sensor  12 . 
     The calculation processing circuit  14  is connected to a storage device  16 . The storage device  16  can store, for example, a golf swing analysis software program (motion analysis program)  17  and related data. The calculation processing circuit  14  realizes a golf swing analysis method by executing the golf swing analysis software program  17 . The storage device  16  may include a dynamic RAM (DRAM), a large capacity storage device unit, a nonvolatile memory, and the like. For example, when a golf swing analysis method is performed, the golf swing analysis software program  17  is downloaded from, for example, a server and is temporarily held in the DRAM. Alternatively, the golf swing analysis software program  17  may be preserved in the large capacity storage device unit such as a hard disk drive (HDD) along with data. The nonvolatile memory stores a program or data with a relatively small capacity, such as a basic input/output system (BIOS). 
     The storage device  16  stores club specification information indicating a specification of the golf club  13 , sensor attachment position information, and the like. For example, a user operates an input device  21  and sequentially inputs type numbers of the golf club  13  to be used (alternatively, selects a type number from a type number list) so that specification information (for example, information regarding the length of the shaft, a central position, a face angle, and a loft angle) for each type number is stored in the storage device  16  in advance. In this case, specification information of an input type number is used as the club specification information. Alternatively, the sensor unit  12  may be attached at a predetermined position (for example, a distance of 20 cm from the grip) which is set so that information regarding the predetermined position is stored as the sensor attachment position information in advance. As exercise conditions, for example, in a case of a golf putter, a distance from an address position to a cup, a size of the cup, and speed on the turf are stored in the storage device  16  via the input device  21 . 
     The calculation processing circuit  14  is connected to an image processing circuit  18 . The calculation processing circuit  14  sends predetermined image data to the image processing circuit  18 . The image processing circuit  18  is connected to a display device  19 . In connection, the image processing circuit  18  is connected to a predetermined interface circuit (not illustrated). The image processing circuit  18  sends an image signal to the display device  19  on the basis of input image data. An image specified by the image signal is displayed on a screen of the display device  19 . The calculation processing circuit  14  or the image processing circuit  18  can convert a coordinate space of the sensor coordinate system Σxyz into an absolute reference coordinate system ΣXYZ (for example, an X-Z plane is a horizontal plane, and an X-Y plane is a vertical plane) which is a real space (three-dimensional space). The display device  19  employs a liquid crystal display or other flat panel displays, and displays a three-dimensional image or a two-dimensional image in the absolute reference coordinate system ΣXYZ. Here, the calculation processing circuit  14 , the storage device  16 , and the image processing circuit  18  are provided as, for example, a computer device. 
     The calculation processing circuit  14  is connected to the input device  21 . The input device  21  includes at least alphabet keys and numerical keys. Text information or numerical value information is input to the calculation processing circuit  14  from the input device  21 . The input device  21  may be constituted of, for example, a keyboard. The combination of the display device, the computer device, and the keyboard may be replaced with a portable terminal such as a smart phone or a tablet PC. 
     (2) Outline of Calculation Processing Circuit 
       FIG. 2  schematically illustrates a configuration of the calculation processing circuit  14  according to the embodiment. The calculation processing circuit  14  may include a swing position coordinate detection unit  50 , a speed detection unit  60 , an address (stoppage) analysis unit  70 , an impact analysis unit  80 , a plan-view direction analysis unit  90 , a hit point analysis unit  100 , a front-view direction analysis unit  110 , a stroke analysis unit (swing width analysis unit)  120 , a score analysis unit  130 , and a statistical analysis unit  140 , and the like. At least one of the analysis units  90  to  120  may be omitted according to a grade of the motion analysis apparatus. 
     The swing position coordinate detection unit  50  detects coordinates of the club head  13   c  during a swing from a swing start position (address position) to a swing end position (finish position) through a swing turning position (top position) and a hitting position (impact virtual vertical plane position). 
     The speed detection unit  60  detects a speed V of the club head  13   c , for example, during impact by using an output signal from the inertial sensor  12  (refer to  FIG. 4B ). The address analysis unit  70  analyzes an attitude or a position of the face surface  13   c   1  of the club head  13   c  during address (stoppage). The impact analysis unit  80  analyzes an attitude of the face surface  13   c   1  of the club head  13   c  during impact, or a trajectory of the face surface  13   c   1  on the verge of impact. 
     The plan-view direction analysis unit  90  analyzes the direction of the club head  13   c  in a plan view. The plan-view direction analysis unit  90  analyzes at least one of a first deviation angle θ 1  (absolute face angle) between the face surface  13   c   1  during impact and a virtual vertical plane  13   c   2  with respect to a hitting target direction (a target line direction which is, for example, a direction in which the normal direction of the face surface  13   c   1  during address is projected onto the X-Z plane) as illustrated in  FIG. 3A , and a second deviation angle θ 2  (square degree) between the face surface  13   c   1  during impact and a virtual vertical plane  13   c   3  with respect to a tangential direction (a swing line direction or a hit ball direction) during impact in contact with a movement trajectory of the face surface  13   c   1  as illustrated in  FIG. 3B . 
     The hit point analysis unit  100  analyzes a deviation amount δ of a hit point (hitting position) of a ball  22  during impact relative to a virtual reference position P 0  set on the face surface  13   c   1 , on the basis of angular velocity around the shaft  13   a , as illustrated in  FIG. 3C . 
     The front-view direction analysis unit  110  analyzes the direction of the club head  13   c  in a front view of viewing a golfer (a user handling an exercise appliance) from the front side. The front-view direction analysis unit  110  analyzes at least one of a third deviation angle θ 3  (delta-loft angle) between an inclined angle (actual loft angle) with respect to the vertical surface of the face surface  13   c   1  during impact and a reference inclined angle (which is, for example, a loft angle as a standard value of the putter  13  and is illustrated as a substantially vertical surface in  FIG. 4A ) as illustrated in  FIG. 4A , and a fourth deviation angle θ 4  (attack angle) between a tangential direction (swing line direction) during impact in contact with the movement trajectory of the face surface  13   c   1  projected onto the vertical surface and a target direction (hitting target direction) projected onto the vertical surface. 
     The stroke analysis unit (swing width analysis unit)  120  specifies a swing width from a first position to a second position on a swing trajectory on the basis of coordinates of the two positions (the first position and the second position) from the swing position coordinate detection unit  50 . For example, as illustrated in  FIG. 4C , a stroke (swing width) from an address position (first position) to a swing turning position (second position) is analyzed. 
     As illustrated in  FIGS. 3A to 4C , the score analysis unit  130  analyzes a score (performance score) for each of a plurality of swing analysis data items (the deviation angles θ 1  to θ 4 , the deviation amount δ, the swing width L, and the speed V), or a score (comprehensive performance score) which is computed by weighting data selected from the plurality of swing analysis data items. The statistical analysis unit  140  analyzes statistical values based on the accumulated data (a total number of times, an average value, a standard deviation, and the like) for each of the plurality of swing analysis data items. 
     (3) Display Example in Display Device 
     (3-1) Initial Screen 
       FIG. 5  is a diagram illustrating an example of, for example, an initial screen of swing analysis data displayed on the display device  19 . In  FIG. 5 , an upper part of the initial screen displays respective information pieces such as a user name, the date and time, the type of putter (L-mullet), a distance (10 ft) to a cup, and a speed (Slow) on the turf. The center of the inertial screen displays, for example, images (a plurality of positions) indicating the putter  13  along a swing trajectory from an address position to a swing turning position. The swing trajectory corresponds to an image projected onto the X-Y plane (vertical plane) of the absolute reference coordinate system. A black triangular mark on the left side under the swing trajectory image region indicates a reproduction button. If the reproduction button is operated, a time seek bar on the left side of the reproduction button moves from the left to the right, and images indicating the putter  13  are sequentially additionally displayed in the swing trajectory image region at a plurality of positions according to movement of the putter  13 . White triangular marks over the movement region of the time seek bar indicate positions of an address, a top, an impact, and finish in this order from the left side. The time seek bar may be operated and be held and stopped at a position of interest. A performance score (for example, 100 points) analyzed by the score analysis unit  130  is displayed on the left side of the center of the initial screen. A lower part of the initial screen displays Direction (plan-view direction analysis data), Hitpoint (hit point analysis data), Stroke (stroke analysis data), and Rising (front-view direction analysis data) along with analysis data. If any one of four display regions of the lower part of the initial screen is touched, details of selected analysis data are displayed. 
     (3-2) Screen of Individual Analysis Data 
     (3-2-1) Direction 
       FIGS. 6 to 10  illustrate screen examples which are subsequently displayed when “Direction” is selected on the initial screen.  FIG. 7  illustrates an example of a display screen of plan-view direction analysis data in one swing.  FIG. 6  is a screen displayed when “Direction” is selected on the initial screen. In  FIG. 6 , on the basis of analysis data from the plan-view direction analysis unit  90  illustrated in  FIG. 2 , 3.4 degrees is enlarged and displayed in an emphasized manner as the first deviation angle θ 1  (as illustrated in  FIG. 3A , a deviation angle (absolute face angle) between the face surface  13   c   1  during impact and the virtual vertical plane  13   c   2  with respect to the hitting target direction (target line direction)). 
     In the screen center of  FIG. 6  and  FIG. 7  illustrating a screen displayed when “FACE” in  FIG. 6  is selected, a hitting direction in which the normal direction to the face surface  13   c   1  of the putter  13  during impact is projected onto the projection plane (horizontal plane), and a speed of the club head  13   c  of the putter  13  during impact are displayed in a coordinate system in which the hitting target direction is set. As the coordinate system, for example, a polar coordinate system is displayed. The direction of 0 degrees is the hitting target direction in an angle axis which is one axis of the polar coordinate system. A specified hitting direction is displayed as a line segment extending in a direction which is perpendicular to the face surface  13   c   1  of the image indicating the club head  13   c  of the putter  13  in the polar coordinate system. The direction of 0 degrees may be displayed as a hitting direction at all times in the angle axis which is one axis of the polar coordinate system. 
     An angle in the angle axis of the polar coordinate system is exaggerated to be larger than an actual angle, and, for example, an angle range of ±5 degrees is illustrated to be exaggerated to an angle range of 90 degrees or more. This is so that deviation of a hitting direction relative to a hitting target direction can be easily viewed. Another axis of the polar coordinate system is a speed axis. An end position of the line segment indicating the hitting direction extending from the face surface of the image indicating the club head  13   c  of the putter  13  indicates a speed of the club head  13   c  (the face surface  13   c   1 ) during impact. 
     In the present embodiment, in light of a hitting direction and a speed of the face surface  13   c   1  during impact being associated with the directionality and the perception of distance of a hit ball, the hitting direction and the speed of the face surface  13   c   1  during impact are displayed in the same coordinate system. The user checks deviation of a hitting direction relative to the hitting target direction and a speed during impact for each swing motion of the putter  13 , and can thus gain accuracy of reproducing the directionality and the perception of distance of a hit ball. Here, the hitting direction during impact may be set to a direction in which the normal direction to the face surface  13   c   1  during impact is projected onto the projection plane. Since the face surface  13   c   1  is not limited to a plane which is parallel to the vertical surface and may be inclined with respect to the vertical surface, the direction in which the normal direction of the face surface  13   c   1  is projected onto the projection plane (horizontal plane) may be assumed to be a hitting direction. Specifying a hitting direction will be described later, and a hitting direction (a tangential direction during impact with respect to a movement trajectory of the face surface) during impact may be specified on the basis of a movement vector of the face surface  13   c   1 . 
     The hitting target direction may be specified as a direction in which a normal direction to the face surface  13   c   1  during address (during stoppage) before starting a swing motion is projected onto the projection plane. The hitting target direction may be a preset known fixed direction, but may be specified on the basis of the direction of the face surface  13   c   1  during stoppage for each swing motion before starting the swing motion so as to easily recognize deviation between intended swing and actual swing. 
     In the image indicating the putter  13  in a plan view, the face surface  13   c   1  is set to be directed in a hitting direction and is displayed in the polar coordinate system illustrated in  FIGS. 6 and 7 , and, thus, particularly, deviation between the direction of the hitting surface and the hitting target direction is visually recognized, thereby allowing the cause of the deviation of the hitting direction to be easily recognized. 
     In the polar coordinate system illustrated in  FIGS. 6 and 7 , a target region of, for example, ±1 degree including the hitting target direction (0 degrees) may be displayed so as to be differentiated from other regions. In the above-described way, since a target is a zone rather than a line, a target achievement ratio is increased, the user feels comfortable, and thus an exercise practice effect can be improved. In a case of the putter  13 , the target region may be obtained as an angle range from a target line on the basis of a distance L from the address position to the cup center, and a radius R of the cup. For example, if R=5.4 cm, and L=155.4 cm, the target region is ±arcsin (R/L)=±1.9 degrees. 
     In the polar coordinate system illustrated in  FIGS. 6 and 7 , coordinate positions (five coordinate positions in  FIGS. 6 and 7 ) defined by a hitting direction and a speed specified in the past may be displayed so as to be differentiated from coordinate positions defined by a hitting direction and a speed specified this time. In the above-described manner, in a case where exercise is repeatedly performed, the achievement of a practice effect can be visually recognized. 
     If “Histogram” on the lower left in  FIG. 6  or  FIG. 7  is selected, the screen of  FIG. 6 or 7  is changed to a screen of  FIG. 8 . A screen lower part illustrated in  FIG. 8  displays a histogram indicating, for example, a distribution of hitting directions on the basis of analysis data from the statistical analysis unit  140  illustrated in  FIG. 2 . As illustrated in  FIG. 8 , a position of a hitting direction measured this time may also be displayed in the histogram. 
     In  FIGS. 6 to 8 , if the column “SQUARE” on the screen upper right is selected, the screen is changed to a screen of  FIG. 9 . In  FIG. 9 , −0.2 degrees is enlarged and displayed in an emphasized manner as the second deviation angle θ 2  (square degree: refer to  FIG. 3B ) of the club head  13   c  during impact on the basis of analysis data from the plan-view direction analysis unit  90  illustrated in  FIG. 2  in the column “SQUARE” on the screen upper right. At the screen center of  FIG. 8 , the angle axis of the polar coordinate system is changed to an angle axis of the square degree 02. A position of the square degree 02=0 in the angle axis of the polar coordinate system becomes a target direction. In  FIG. 9 , a normal line to the face surface of the image indicating the putter  13  is displayed at the position of the square degree 02=−0.2 degrees. Also in this case, as illustrated in  FIG. 9 , coordinate positions (five coordinate positions in  FIG. 9 ) defined by a square degree and a speed specified in the past may be displayed so as to be differentiated from a coordinate position defined by a square degree and a speed specified this time. 
     If “Histogram” on the screen lower left of  FIG. 9  is selected, the screen of  FIG. 9  is changed to a screen of  FIG. 10 . A screen lower part illustrated in  FIG. 10  displays a histogram indicating a distribution of speeds at a square degree on the basis of analysis data from the statistical analysis unit  140  illustrated in  FIG. 2 . As illustrated in  FIG. 10 , a position of a square degree measured this time may also be displayed in the histogram. 
     (3-2-2) Hitpoint 
       FIG. 11  illustrates apart of a screen displayed when “Hitpoint” is selected on the initial screen. The face surface  13   c   1  of the club head  13   c  is displayed on the screen illustrated in  FIG. 11 , and a dot chain line SS which is a vertical line in  FIG. 11  indicates a sweet spot of the golf club  13 . 
     Circular marks illustrated in  FIG. 11  indicate hitting positions of balls at ten swings. A diameter of a single circular mark in the horizontal direction indicates a width of a position where the ball is hit, and is a width of “5 mm” in the example illustrated in  FIG. 11 . In other words, the number of circular marks located on the same vertical line indicates a frequency of hitting positions of balls. For example, in the example illustrated in  FIG. 11 , it can be seen that a frequency of the hitting position “−5±2.5 (mm)” is “twice”. 
     A circular mark indicated by diagonal lines indicates the most recent hitting position of a ball. In the example illustrated in  FIG. 11 , the most recent position of the ball is “+1 mm”, and the circular mark indicated by the diagonal lines is displayed in a grade of “0±2.5 (mm)”. Also regarding a hit point, “Histogram” may be selected, and thus the same histogram as in  FIG. 8  or  FIG. 10  may be displayed. 
     (3-2-3) Stroke 
       FIGS. 12 to 16  illustrate screen examples which are subsequently displayed when “Stroke” is selected on the initial screen.  FIG. 12  illustrates an example of a display screen of stroke analysis data at a single swing when “Stroke” is selected on the initial screen.  FIG. 13  illustrates a screen displayed when “SPAN-BACK” is selected on the screen of  FIG. 12 . In  FIGS. 12 and 13 , 37 cm is enlarged and displayed in an emphasized manner as a stroke (SPAN-BACK) of a backswing of the putter  13  on the basis of analysis data from the stroke (swing width) analysis unit  120  illustrated in  FIG. 2 . If “Histogram” on the screen lower left of  FIG. 12 or 13  is selected, the screen of  FIG. 12 or 13  is changed to a screen of  FIG. 14 . A screen lower part illustrated in  FIG. 14  displays a histogram indicating a distribution of strokes of the backswing on the basis of analysis data from the statistical analysis unit  140  illustrated in  FIG. 2 . As illustrated in  FIG. 14 , a position of a stroke measured this time may also be displayed in the histogram. 
     In  FIGS. 12 to 14 , if “SPEED” on the screen upper right is selected, the screen is changed to a screen of  FIG. 15 . In  FIG. 15 , 4.6 m/s is enlarged and displayed in an emphasized manner as a speed of the club head  13   c  during impact on the basis of analysis data from the speed detection unit  60  illustrated in  FIG. 2  in the column “SPEED” on the screen upper right. A speed display meter is displayed on the right side of the screen center of  FIG. 15 . If “Histogram” on the screen lower left of  FIG. 15  is selected, the screen of  FIG. 15  is changed to a screen of  FIG. 16 . A screen lower part illustrated in  FIG. 16  displays a histogram indicating a distribution of speeds of the club head  13   c  during impact on the basis of analysis data from the statistical analysis unit  140  illustrated in  FIG. 2 . As illustrated in  FIG. 16 , a position of a speed measured this time may be displayed in the histogram. 
     (3-2-4) Rising 
       FIGS. 17 to 21  illustrate screen examples which are subsequently displayed when “Rising” is selected on the initial screen.  FIG. 17  illustrates an example of a display screen of front-view direction analysis data at a single swing when “Rising” is selected on the initial screen.  FIG. 18  illustrates a screen displayed when “DELTA-LOFT” is selected on the screen illustrated in  FIG. 17 . In  FIGS. 17 and 18 , −0.8 degrees is enlarged and displayed in an emphasized manner as the third deviation angle θ 3  (delta-loft angle: DELTA-LOFT) illustrated in  FIG. 4A  on the basis of analysis data from the front-view direction analysis unit  110  illustrated in  FIG. 2 . 
     At the screen center of  FIGS. 17 and 18 , a specified inclined angle is displayed in an angle coordinate system representing a deviation angle relative to a reference inclined angle. In the angle coordinate system, 0 degrees indicate the reference inclined angle. An image indicating the club head  13   c  of the putter  13  in a front view of viewing a golfer (a user using an exercise appliance) from the front side is displayed. In the angle coordinate system, a specified inclined angle is displayed as an extension line of a face surface of the image. In  FIGS. 17 and 18 , the specified inclined angle is displayed so as to match a central line of the angle coordinate system, and a position indicating a reference angle is rotated and displayed by an intersection angle in a direction reverse to a sign of the intersection angle. The central line of the angle coordinate system may match the reference inclined angle (0 degrees), and a line indicating the specified inclined angle may be rotated and displayed in a direction coincident with a sign of the inclined angle by the inclined angle. As mentioned above, if the reference inclined angle and the inclined angle are displayed in the same coordinate system, a difference therebetween can be visually recognized. 
     An angle in the angle coordinate system is exaggerated larger than an actual angle, and an angle range of 1 degree is illustrated to be exaggerated several times to several tens of times. This is so that a deviation of the inclined angle relative to the reference inclined angle can be easily visually recognized. 
     In the angle coordinate system illustrated in  FIGS. 17 and 18 , a target region of, for example, ±1 degree including the reference inclined angle (0 degrees) may be displayed so as to be differentiated from other regions. In the above-described way, since a target is a zone rather than a line, a target achievement ratio is increased, the user feels comfortable, and thus an exercise practice effect can be improved. 
     In the angle coordinate system illustrated in  FIGS. 17 and 18 , inclined angles (five inclined angles in  FIGS. 17 and 18 ) specified in the past may be displayed so as to be differentiated from an inclined angle specified this time. In the above-described manner, in a case where exercise is repeatedly performed, the achievement of a practice effect can be visually recognized. 
     If “Histogram” on the screen lower left in  FIG. 17  or  FIG. 18  is selected, the screen of  FIG. 17 or 18  is changed to a screen of  FIG. 19 . A screen lower part illustrated in  FIG. 19  displays a histogram indicating, for example, a distribution of inclined angles on the basis of analysis data from the statistical analysis unit  140  illustrated in  FIG. 2 . As illustrated in  FIG. 19 , a position of an inclined angle measured this time may also be displayed in the histogram. 
     In  FIGS. 17 to 19 , if the column “ATTACK” on the screen upper right is selected, the screen is changed to a screen of  FIG. 20 . In  FIG. 20 , −7.6 degrees is enlarged and displayed in an emphasized manner as the fourth deviation angle θ 4  (attack angle) of the club head  13   c  during impact illustrated in  FIG. 4B  on the basis of analysis data from the front-view direction analysis unit  110  illustrated in  FIG. 2  in the column “ATTACK” on the screen upper right. At the screen center of  FIG. 20 , an angle in the angle coordinate system is changed to an angle axis of the attack angle. A position of the attack angle=0 degrees in the angle coordinate system is set to a horizontal position on the screen, 0 degrees is the reference inclined angle. In  FIG. 20 , a normal line to a face surface of the image indicating the putter  13  in a front view of viewing the golfer (a user using an exercise appliance) from the front side is displayed at a position of the attack angle=−7.6 degrees. This normal line indicates a specified inclined angle. Also in this case, as illustrated in  FIG. 20 , attack angles (five attack angles in  FIG. 20 ) specified in the past may be displayed so as to be differentiated from an attack angle specified this time. 
     If “Histogram” on the screen lower left of  FIG. 20  is selected, the screen of  FIG. 20  is changed to a screen of  FIG. 21 . A screen lower part illustrated in  FIG. 21  displays a histogram indicating a distribution of attack angles on the basis of analysis data from the statistical analysis unit  140  illustrated in  FIG. 2 . As illustrated in  FIG. 21 , a position of an attack angle measured this time may also be displayed in the histogram. 
     (4) Operation of Swing Position Coordinate Detection Unit 
     A description will be made of calculation performed by the swing position coordinate detection unit  50  illustrated in  FIG. 2 .  FIG. 22  is a flowchart illustrating an example of a procedure of processes of computing attitudes (an initial attitude to an attitude at a time point N) of the sensor unit  12  in the swing position coordinate detection unit  50 . 
     As illustrated in  FIG. 22 , first, the swing position coordinate detection unit  50  specifies the direction of gravitational acceleration on the basis of acceleration data in the three axes during stoppage at the time point t=0 (step S 1 ) and computes a quaternion p( 0 ) indicating an initial attitude (an attitude at a time point t=0) of the sensor unit (step S 2 ). 
     A three-dimensional coordinate position is represented by the following Equation (1) as a quaternion q indicating rotation of a position vector. 
         q =( w,x,y,z )  (1)
 
     In Equation (1), if a rotation angle of target rotation is θ, and unit vectors of a rotation axis are (r x , r y , r z ) w, x, y, and z are represented by the following Equation (2). 
     
       
         
           
             
               
                 
                   
                     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  12  is stopped at the time point t=0 at the time of starting a swing (address), a quaternion q( 0 ) indicating rotation at θ=0 and the time point t=0 is as in the following Equation (3) on the basis of Equation (1) obtained by assigning θ=0 to Equation (2). 
         q (0)=(1,0,0,0)  (3)
 
     Next, the swing position coordinate detection unit  50  updates the time point t to t+1 (step S 3 ). Here, the time point t=0 is updated to a time point t=1. 
     Next, the swing position coordinate detection unit  50  computes a quaternion Δq(t) indicating rotation per unit time at the time point t on the basis of three-axis angular velocity data at the time point t (step S 4 ). 
     For example, if the three-axis angular velocity data at the time point t is ω(t)=[ω x (t), ω y (t), ω z (t)], the magnitude |ω(t)| of angular velocity per sample measured at the time point t is computed by using the following Equation (4). 
       | w ( t )|=√{square root over (ω x ( t ) 2 +ω y ( t ) 2 +ω z ( t ) 2 )}  (4)
 
     The magnitude |ω(t)| of angular velocity corresponds to a rotation angle per unit time, and thus quaternion Δq(t+1) indicating rotation per unit time at the time point t is computed by using the following Equation (5). 
     
       
         
           
             
               
                 
                   
                     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 is 1, the swing position coordinate detection unit  50  computes Δq( 1 ) by using Equation (5) on the basis of three-axis angular velocity data ω(1)=[ω x ( 1 ), ω y ( 1 ), ω z ( 1 )] at the time point t=1. 
     Next, the swing position coordinate detection unit  50  computes a quaternion q(t) indicating rotation from the time point  0  to the time point t (step S 4 ). The quaternion q(t) is computed by using the following Equation (6). 
         q ( t )= q ( t− 1)·Δ q ( t )  (6)
 
     Here, since t is 1, the swing position coordinate detection unit  50  computes q( 1 ) by using Equation (6) on the basis of q( 0 ) in Equation (3) and Δq( 1 ) computed in step S 4 . 
     Next, the swing position coordinate detection unit  50  repeatedly performs the processes in steps S 3  to S 5  until t becomes N. If t becomes N (YES in step S 6 ), the swing position coordinate detection unit  50  computes a quaternion p(N) indicating an attitude at the time point N on the basis of the quaternion p( 0 ) indicating the initial attitude computed in step S 2  and the quaternion q(N) indicating rotation from time points t=0 to N computed in the previous step S 5  (step S 7 ), and finishes the process. 
     The swing position coordinate detection unit  50  can obtain coordinates (X, Y, Z) in the absolute reference coordinate system of the club head  13   c  of the putter  13  at the time points t=0 to N on the basis of the attitude information acquired in the above-described way, and distance information from the sensor unit  12  to the club head  13   c  (first and second measurement points  13   d  and  13   e  which will be described later). The speed detection unit  60  illustrated in  FIG. 2  can detect a speed at the coordinate position obtained by the swing position coordinate detection unit  50  on the basis of an output signal from the inertial sensor  12 . 
     (5) Analysis Units 
     (5-1) Analysis and Display of First Deviation Angle θ 1 , Second Deviation Angle θ 2 , and Speed V 
     Next, with reference to  FIGS. 23 to 25 , a description will be made of configurations and operations of the address analysis unit  70 , the impact analysis unit  80 , the plan-view direction analysis unit  90 , the statistical analysis unit  140 , and the image processing circuit  18  related to generation of the analysis screens illustrated in  FIGS. 6 to 10 . First, with reference to  FIG. 23 , a description will be made of 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 . As illustrated in  FIG. 23 , in order to specify an attitude and a 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 separated from each other. Here, the first measurement point  13   d  is located on a heel side of the face surface  13   c   1 , and the second measurement point  13   e  is located on a 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 surface and passes through a core (sweet spot) of the face surface  13   c   1 . A line segment  13   f  connecting the first measurement point  13   d  to the second measurement point  13   e  can specify the direction of the face surface  13   c   1  when being projected onto the ground surface. 
     As illustrated in  FIG. 2 , the calculation processing circuit  14  of  FIG. 1  includes the address (stoppage) analysis unit  70  and the impact analysis unit  80 . The address analysis unit  70  includes an attitude specifying portion  71  and a position specifying portion  72 . The attitude specifying portion  71  specifies an attitude of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ during stoppage (that is, during address). When an attitude is specified, for example, as illustrated in  FIG. 24 , the attitude specifying portion  71  connects a coordinate=r h ( 0 ) of the first measurement point  13   d  and a coordinate r t ( 0 ) of the second measurement point  13   e  during stoppage to each other with a first line segment L 1 . An attitude of the face surface  13   c   1  is specified by the first line segment L 1 . In this case, the first line segment L 1  is projected onto a horizontal plane (an X-Z plane: a plane expanding parallel to the ground surface) which is perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ. The swing position coordinate detection unit  50  can specify positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the address time t=0 by using 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  during stoppage. 
     The position specifying portion  72  specifies a second line segment L 2  which is perpendicular to the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ during stoppage. The second line segment L 2  vertically intersects the face surface  13   c   1  at the first measurement point  13   d =r h ( 0 ). The position specifying portion  72  specifies the first line segment L 1  when specifying the second line segment L 2 . The position specifying portion  72  sets the second line segment L 2  in a vertical direction to the first line segment L 1  at the first measurement point  13   d . The second line segment L 2  indicates a so-called target line which is a hitting target direction. In this case, the second line segment L 2  is projected onto the horizontal plane which is perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ in the same manner as the first line segment L 1 . 
     The impact analysis unit  80  includes, as illustrated in  FIG. 2 , an attitude specifying portion  81 , a trajectory specifying portion  82 , and a speed specifying portion  63 . The attitude specifying portion  81  specifies an attitude of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ during impact. When the attitude is specified, for example, as illustrated in  FIG. 24 , the attitude specifying portion  81  connects a coordinate=r h (imp) of the first measurement point  13   d  and a coordinate r t (imp) of the second measurement point  13   e  during impact to each other with a third line segment L 3 . An attitude of the face surface  13   c   1  is specified by the third line segment L 3 . In this case, the third line segment L 3  is projected onto the horizontal plane which is perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ. The swing position coordinate detection unit  50  can specify positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the impact time t=timp during impact by using 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  during impact. For example, considerable acceleration in a specific direction corresponding to an output signal from the inertial sensor  12  is observed at the moment of impact. The impact time t=timp is specified on the basis of a threshold value of the acceleration. 
     The trajectory specifying portion  82  specifies a movement trajectory of the first measurement point  13   d  in the absolute reference coordinate system ΣXYZ during impact. When the movement trajectory is specified, as illustrated in  FIG. 24 , the trajectory specifying portion  82  specifies a first coordinate point P 1  on the absolute reference coordinate system ΣXYZ indicating a position r h (imp) of the first measurement point  13   d  during impact, and a second coordinate point P 2  on the absolute reference coordinate system ΣXYZ indicating a position r h (imp−1) of the first measurement point  13   d  as a sampling point preceding the impact. Here, a sampling point right before the impact time may be allocated 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 via a fourth line segment L 4 . The direction and the length of the fourth line segment L 4  respectively indicate a direction and the magnitude of a movement vector. In this case, in the same manner as described above, the fourth line segment L 4  is projected onto the horizontal plane which is perpendicular to the Y axis in the absolute reference coordinate system ΣXYZ. A direction L 4 ′ (a tangential direction during impact with respect to a movement trajectory) in which the fourth line segment L 4  projected onto the horizontal plane is defined as an accurate hitting direction during impact. 
     The speed specifying portion  63  specifies a speed of the face surface  13   c   1  during impact, displayed along with the absolute face angle θ 1  or the square degree θ 2  in the polar coordinate system. The speed of the face surface  13   c   1  during impact may be obtained on the basis of information regarding acceleration or the like at an impact position. 
     The plan-view direction analysis unit  90  includes, as illustrated in  FIG. 2 , a first deviation angle analysis portion  91  and a second deviation angle analysis portion  92 . The first deviation angle analysis portion  91  is connected to the position specifying portion  72  of the address analysis unit  70  and the trajectory specifying portion  82  of the impact analysis unit  80 . In this case, the first deviation angle analysis portion  91  specifies, for example, the extension line L 4 ′ of the fourth line segment L 4  specified by the trajectory specifying portion  82  as a hitting direction. The first deviation angle analysis portion  91  calculates an intersection angle (the first deviation angle or the absolute face angle) θ 1  between the second line segment L 2  (which is parallel to a hitting target direction or a target line) which is perpendicular to the face surface  13   c   1  at the first measurement point  13   d  on the face surface  13   c   1  during address, and the extension line L 4 ′ (accurate hitting direction) of the fourth line segment L 4  which is perpendicular to the face surface  13   c   1  at the first measurement point  13   d  on the face surface  13   c   1  during impact. The first deviation angle analysis portion  91  may be connected to the position specifying portion  72  of the address analysis unit  70  and the attitude specifying portion  81  of the impact analysis unit  80 . In this case, the first deviation angle analysis portion  91  temporarily specifies a hitting direction L 5  to a vertical direction to the third line segment L 3  specified by the attitude specifying portion  81 . The first deviation angle analysis portion  91  calculates an intersection angle (the first deviation angle or the absolute face angle)  01  between the second line segment L 2  (which is parallel to a hitting target direction or a target line) which is perpendicular to the face surface  13   c   1  at the first measurement point  13   d  on the face surface  13   c   1  during address, and the hitting direction L 5  which is perpendicular to the face surface  13   c   1  during impact. 
     The second deviation angle analysis portion  92  is connected to the attitude specifying portion  81  and the trajectory specifying portion  82  of the impact analysis unit  80 . The second deviation angle analysis portion  92  temporarily specifies the hitting direction L 5  to a vertical direction to the third line segment L 3  specified by the attitude specifying portion  81 . In other words, as described above, the accurate hitting direction L 4 ′ is set on the extension line (a tangential direction during impact with respect to a movement trajectory) of a movement vector (the fourth line segment L 4 ), but the face surface  13   c   1  in an actual attitude may not necessarily be perpendicular to the accurate hitting direction L 4 ′. This is because the face surface  13   c   1  is closed or opened during impact and thus is not perpendicular to the accurate hitting direction L 4 ′. The second deviation angle analysis portion  92  specifies the intersection angle θ 2  between the accurate hitting direction L 4 ′ and the virtual hitting direction L 5  as a square degree. The square degree θ 2  indicates a deviation angle between a virtual vertical plane with respect to the accurate hitting direction L 4 ′ and the face surface  13   c   1  measured during impact. 
     The statistical analysis unit  140  calculates a statistical value indicating variation in the absolute face angle θ 1 , the square degree θ 2 , or the speed V during impact. The statistical analysis unit  140  includes a histogram generation portion  141 . The histogram generation portion  141  sorts the absolute face angle θ 1 , the square degree θ 2 , or the speed V measured as data for the histogram illustrated in  FIG. 8 or 10  into a plurality of zones, and counts the number of samples included in each zone. The statistical analysis unit  140  also includes a variation analysis portion  142 . The variation analysis portion  142  calculates an average value, a standard deviation, and the like of the whole number of samples of the absolute face angle θ 1 , the square degree θ 2 , or the speed V. In the above-described way, a statistical value indicating the absolute face angle θ 1 , the square degree θ 2 , or the speed V is displayed, and thus it is possible to estimate reproducibility of the directionality and the perception of distance of a hit ball. 
     The image processing circuit  18  may generate display information illustrated in  FIGS. 6 to 10  displayed on the display device  19  on the basis of information from the plan-view direction analysis unit  90  and the statistical analysis unit  140 . In addition, the image processing circuit  18  may display the extent to which a hitting direction is deviated relative to a target region by using a multiple of the unit indicating a region corresponding to the target region on the basis of information from the plan-view direction analysis unit  90 . For example, as illustrated in  FIG. 25 , the unit indicating a region corresponding to the target region of the golf putter  13  is a size of a cup, and, for example, it is displayed that deviation occurs by two cups, and thus it becomes easier to recognize a deviation relative to the target. 
     The image processing circuit  18  may display a ratio (for example, 46%) of the number of times in which a hitting direction enters a target region to the number of exercises in which the hitting direction is specified on the basis of information from the statistical analysis unit  140 . In the above-described manner, a target achievement ratio can be recognized as a numerical value, and thus notification of an exercise practice effect can be performed in a quantitative manner. 
     (5-2) Analysis and Display of Deviation Amount δ Relative to Sweet Spot 
     The hit point analysis unit  100  illustrated in  FIG. 2  includes an impact angular velocity acquisition portion  101  and a deviation amount analysis portion  102 . The impact angular velocity acquisition portion  101  acquires angular velocity around a long axis (the z axis of the sensor coordinate system) of the club shaft  13   a  during impact on the basis of an output signal from the inertial sensor  12 . The deviation amount analysis portion  102  analyzes a deviation amount  3  relative to the hit point illustrated in  FIG. 3C  on the basis of the acquired angular velocity. 
     Here,  FIG. 26  illustrates a relationship between angular velocity GyroZ around the long axis (the Z axis of the sensor coordinate system) of the club shaft  13   a , and a deviation amount  3  of a hitting position relative to the sweet spot in the horizontal direction of the face surface  13   c   1 . It can be seen from  FIG. 26  that, when illustrated GyroZ is “−114.6 rad/s”, a deviation amount of a hitting position relative to the sweet spot is “8 mm”.  FIG. 27  is a diagram illustrating the relationship illustrated in  FIG. 26  as a graph. A transverse axis of the graph illustrated in  FIG. 27  expresses angular velocity, and a longitudinal axis thereof expresses a deviation amount of a hitting position. The correspondence relationship in  FIG. 27  may be expressed in a linear expression. A coefficient and an intercept of a linear expression may be obtained through retrogression analysis, and, in a case of the example illustrated in  FIG. 27 , the linear expression is represented by the following Equation (7). 
         y=− 0.0604 x+ 2.4944  (7)
 
     A contribution ratio is “R 2 =0.8954”. 
     The above Equation (7) is calculated in advance and is stored in the storage device  16 . Consequently, the deviation amount analysis portion  102  can calculate the deviation amount δ of a hitting position relative to the sweet spot on the basis of information from the inertial sensor  12  and the storage device  16 . 
     The statistical analysis unit  140  may calculate a statistical value indicating variation in the deviation amount δ. The histogram generation portion  141  sorts the measured deviation amount δ into a plurality of zones, and counts the number of samples of the deviation amount δ included in each zone in the same manner as in  FIG. 8 or 10 . The variation analysis portion  142  calculates an average value, a standard deviation, and the like of the whole number of samples of the deviation amount δ. In the above-described way, it is possible to display a statistical value indicating variation in the deviation amount δ. 
     The image processing circuit  18  may generate the display information illustrated in  FIG. 11  displayed on the display device  19  on the basis of information from the hit point analysis unit  100  and the statistical analysis unit  140 . 
     The image processing circuit  18  may display a ratio (for example, ±5 mm from the sweet spot) of the number of times in which the deviation amount δ enters a target region to the number of exercises in which the deviation amount δ is specified on the basis of information from the statistical analysis unit  140 . In the above-described manner, a target achievement ratio can be recognized as a numerical value, and thus notification of an exercise practice effect can be performed in a quantitative manner. 
     (5-3) Analysis and Display of Swing Width 
     Next, a description will be made of analysis and display of the stroke (swing width) L illustrated in  FIGS. 12 to 16 . The stroke (swing width) analysis unit  120  may include a position determination portion  121  and a stroke (swing width) determination portion  122  as illustrated in  FIG. 2 . The position determination portion  121  determines a first position which is a start point of a swing width and a second position which is an end point of the swing width on the basis of an output signal or the like from the inertial sensor  12 . In the present embodiment, the first position is an address position, and thus a position corresponding to t=0 may be designated. The second position is a swing turning position, and, for example, a position where a sign of acceleration in the X-axis direction (a backswing direction) of the absolute reference coordinate system is switched may be designated. The position determination portion  121  may also determine a hitting position (impact position). Considerable acceleration in a specific direction corresponding to an output signal from the inertial sensor  12  is observed at the moment of impact. The moment of impact is specified on the basis of a threshold value of the acceleration. The speed detection unit  60  may obtain a speed of the club head  13   c  at each position on the basis of positions from the first position to the second position, acceleration information at the impact position, and the like. 
     The stroke (swing width) determination portion  122  may calculate the length of a route following a swing trajectory from the first position (address position) to the second position (swing turning position) as the swing width L. Since a plurality of sampled coordinate positions from the first position to the second position are acquired, it is possible to substantially accurately calculate the length of the route by integrating a distance in a three-dimensional space between coordinate positions adjacent to each other, sampled with a fine pitch. 
     Alternatively, the stroke (swing width) determination portion  122  may obtain the swing width L from the first position to the second position by obtaining a distance between coordinates on a horizontal axis X of the first position and the second position projected onto a projection plane (for example, the vertical X-Y plane in the absolute reference coordinate system). This is because, for a golfer, as the swing width L during a backswing, it is sufficient to acquire a pulled length (that is, a distance between projected coordinates) in a backswing direction rather than a swing width of a more accurate route. In  FIG. 28 , a distance between coordinates on the horizontal axis X of the first position and the second position is expressed on a transverse axis. In  FIG. 28 , a distance between coordinates on a vertical axis Y of the first position and the second position, projected onto the vertical X-Y plane in the absolute reference coordinate system, is expressed on a longitudinal axis. However, a distance between coordinates on the vertical axis Y may be omitted. 
     The statistical analysis unit  140  may calculate a statistical value indicating variation in the swing width L. The histogram generation portion  141  sorts a swing width or a speed measured as data for the histogram illustrated in FIG.  14  or  16  into a plurality of zones, and counts the number of samples included in each zone. The variation analysis portion  142  of the statistical analysis unit  140  calculates an average value, a standard deviation, and the like of the whole number of samples of the swing width L or the speed V. In the above-described way, a statistical value indicating the swing width L or the speed V is displayed, and thus it is possible to estimate reproducibility of the swing width L or the speed V of an exercise appliance according to a traveled distance of a hit ball. 
     The image processing circuit  18  may generate the display information illustrated from  FIGS. 17 to 21  displayed on the display device  19  on the basis of the front-view direction analysis unit  110  and the statistical analysis unit  140 . In addition, the image processing circuit  18  may display a ratio (for example, 48%) of the number of times in which the third deviation angle θ 3  or the fourth deviation angle θ 4  enters a target region (for example, θ 3 =θ 4 =±1° to the number of exercises in which the third deviation angle θ 3  or the fourth deviation angle θ 4  is specified on the basis of information from the statistical analysis unit  140 . In the above-described manner, a target achievement ratio can be recognized as a numerical value, and thus notification of an exercise practice effect can be performed in a quantitative manner. 
     The image processing circuit  18  may generate the display information illustrated from  FIGS. 4A to 7  displayed on the display device  19  on the basis of the stroke (swing width) analysis unit  120  and the statistical analysis unit  140 . Particularly, in  FIG. 13 , a display pitch of images indicating the putter  13  displayed at a plurality of positions may be made short in a period in which a swing speed obtained by the speed detection unit  60  is high, and may be made long in a period in which the swing speed is low. A single image indicating the putter  13  may be displayed for each predetermined time (every plural sampling data items). Consequently, it is possible to visually recognize both a swing width and a swing speed of the putter  13 . 
     The image processing circuit  18  may sequentially display the images indicating the putter  13  displayed at a plurality of positions in  FIG. 13  according to swing movement of the putter  13  in synchronization with the swing movement. Consequently, it is possible to visually recognize a dynamic swing width of the putter  13 . 
     The first position which is a start point of the swing width L and the second position are not limited to setting to the above-described address position and swing turning position. As a combination of the first position and the second position, a combination of a swing turning position and an impact position for defining a swing width L of a downswing, a combination of an impact position and a swing end position for defining a swing width of follow-through, or a combination of a swing start position and a swing end position for defining a swing width L of the entire swing may be employed. Such a swing width L has a relation to a swing width of a backswing, and can contribute to gaining good reproducibility of the perception of distance, for example, in a half swing of a golf putter or iron. 
     (5-4) Analysis and Display of Third Deviation Angle θ 3  and Fourth Deviation Angle θ 4   
     Next, with reference to  FIGS. 29 and 30 , a description will be made of configurations and operations of the front-view direction analysis unit  110 , the statistical analysis unit  140 , and the image processing circuit  18  related to generation of the analysis screens for the third deviation angle θ 3  (delta-loft angle) or the fourth deviation angle θ 4  (attack angle) illustrated in  FIGS. 17 to 21 . First, with reference to  FIG. 29 , a description will be made of 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 . As illustrated in  FIG. 29 , in order to specify an attitude and a 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 separated from each other. Here, the first measurement point  13   d  is located on the upper side in the face surface  13   c   1 , and the second measurement point  13   e  is located on a lower side in 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 passes through a core (sweet spot) of the face surface  13   c   1  vertically to the ground surface. A line segment  13   f  connecting the first measurement point  13   d  to the second measurement point  13   e  can specify an inclined angle of the face surface  13   c   1  relative to the vertical surface when being projected onto the ground surface. 
     As illustrated in  FIG. 2 , the calculation processing circuit  14  includes the address (stoppage) analysis unit  70  and the impact analysis unit  80 . The attitude specifying portion  71  of the address analysis unit  70  specifies an attitude of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ during stoppage (that is, during address). When an attitude is specified, for example, as illustrated in  FIG. 30 , the attitude specifying portion  71  connects a coordinate=r h ( 0 ) of the first measurement point  13   d  and a coordinate r t ( 0 ) of the second measurement point  13   e  during stoppage to each other with a first line segment L 1 . An attitude of the face surface  13   c   1  is specified by the first line segment L 1 . In this case, the first line segment L 1  is projected onto a vertical plane (an X-Y plane: a surface perpendicular to the ground surface) which is perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ. The swing position coordinate detection unit  50  can specify positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the address time t=0 by using 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  during stoppage. 
     The position specifying portion  72  specifies a second line segment L 2  which is perpendicular to the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ during stoppage. The second line segment L 2  vertically intersects the face surface  13   c   1  at the first measurement point  13   d =r h ( 0 ). The position specifying portion  72  specifies the first line segment L 1  when specifying the second line segment L 2 . The position specifying portion  72  sets the second line segment L 2  in a vertical direction to the first line segment L 1  at the first measurement point  13   d . The second line segment L 2  indicates a so-called target line which is a hitting target direction. In this case, the second line segment L 2  is projected onto the horizontal plane which is perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ in the same manner as the first line segment L 1 . 
     The attitude specifying portion  81  of the impact analysis unit  80  specifies an attitude of the face surface  13   c   1  in the absolute reference coordinate system ΣXYZ during impact. When the attitude is specified, for example, as illustrated in  FIG. 30 , the attitude specifying portion  81  connects a coordinate=r h (imp) of the first measurement point  13   d  and a coordinate=r t (imp) of the second measurement point  13   e  during impact to each other with a third line segment L 3 . An attitude of the face surface  13   c   1  during impact is specified by the third line segment L 3 . In this case, the third line segment L 3  is projected onto the vertical plane which is perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ. The swing position coordinate detection unit  50  can specify positions of the first measurement point  13   d  and the second measurement point  13   e  corresponding to the impact time t=timp during impact by using 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  during impact. For example, considerable acceleration in a specific direction corresponding to an output signal from the inertial sensor  12  is observed at the moment of impact. The impact time t=timp is specified on the basis of a threshold value of the acceleration. 
     The trajectory specifying portion  82  specifies a movement trajectory of the first measurement point  13   d  in the absolute reference coordinate system ΣXYZ during impact. When the movement trajectory is specified, as illustrated in FIG.  30 , the trajectory specifying portion  82  specifies a first coordinate point P 1  on the absolute reference coordinate system ΣXYZ indicating a position r h (imp) of the first measurement point  13   d  during impact, and a second coordinate point P 2  on the absolute reference coordinate system ΣXYZ indicating a position r h (imp−1) of the first measurement point  13   d  as a sampling point preceding the impact. Here, a sampling point right before the impact time may be allocated 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 via a fourth line segment L 4 . The direction and the length of the fourth line segment L 4  respectively indicate a direction and the magnitude of a movement vector. In this case, in the same manner as described above, the fourth line segment L 4  is projected onto the vertical plane which is perpendicular to the Z axis in the absolute reference coordinate system ΣXYZ. A direction L 4 ′ (a tangential direction during impact with respect to a movement trajectory projected onto the vertical plane) in which the fourth line segment L 4  projected onto the vertical plane is defined as a hitting direction during impact. 
     The front-view direction analysis unit  110  includes, as illustrated in  FIG. 9 , a third deviation angle analysis portion  111  and a fourth deviation angle analysis portion  112 . The third deviation angle analysis portion  111  is connected to the position specifying portion  72  of the address analysis unit  70  and the attitude specifying portion  81  of the impact analysis unit  80 . In this case, the third deviation angle analysis portion  111  specifies an intersection angle between the first line segment L 1  (a line segment indicating a reference inclined angle) specified by the position specifying portion  72  and the third line segment L 3  (a line segment indicating an inclined angle) specified by the attitude specifying portion  81 , as the third deviation angle θ 3  (delta-loft angle). 
     The fourth deviation angle analysis portion  112  is connected to the attitude specifying portion  71  of the address analysis unit  70  and the trajectory specifying portion  82  of the impact analysis unit  80 . The fourth deviation angle analysis portion  112  specifies, for example, the extension line L 4 ′ of the fourth line segment L 4  specified by the trajectory specifying portion  82  as a hitting direction. The fourth deviation angle analysis portion  112  calculates an intersection angle between the second line segment L 2  (which is parallel to a hitting target direction or a target line) which is perpendicular to the face surface  13   c   1  at the first measurement point  13   d  on the face surface  13   c   1  during address, and the extension line L 4 ′ (accurate hitting direction) of the fourth line segment L 4  which is perpendicular to the face surface  13   c   1  at the first measurement point  13   d  on the face surface  13   c   1  during impact, as the fourth deviation angle θ 4  (attack angle). 
     The statistical analysis unit  140  calculates a statistical value indicating variation in the third deviation angle θ 3  or the fourth deviation angle θ 4 . The statistical analysis unit  140  sorts the third deviation angle θ 3  or the fourth deviation angle θ 4  measured as data for the histogram illustrated in  FIG. 19  or  FIG. 21  into a plurality of zones, and counts the number of samples included in each zone. In addition, the statistical analysis unit  140  may calculate an average value, a standard deviation, and the like of the whole number of samples of the third deviation angle θ 3  or the fourth deviation angle θ 4 . In the above-described way, a statistical value indicating variation in the third deviation angle θ 3  or the fourth deviation angle θ 4  is displayed, and thus it is possible to estimate reproducibility of the directionality and the perception of distance of a hit ball. 
     The image processing circuit  18  may generate the display information illustrated from  FIGS. 17 to 21  displayed on the display device  19  on the basis of the front-view direction analysis unit  110  and the statistical analysis unit  140 . In addition, the image processing circuit  18  may display a ratio (for example, 48%) of the number of times in which the third deviation angle θ 3  or the fourth deviation angle θ 4  enters a target region (for example, θ 3 =θ 4 =±1° to the number of exercises in which the third deviation angle θ 3  or the fourth deviation angle θ 4  is specified on the basis of information from the statistical analysis unit  140 . In the above-described manner, a target achievement ratio can be recognized as a numerical value, and thus notification of an exercise practice effect can be performed in a quantitative manner. 
     (6) Scoring 
     Next, a description will be made of the score analysis unit  130  which scores swings on the basis of the above-described plurality of analysis data items. The scoring is roughly classified into scoring of analysis items (the first to fourth deviation angles θ 1  to θ 4 , the swing width L, the deviation amount δ relative to a sweet spot, and the speed V during impact) and scoring of the total point obtained by weighting a plurality of analysis items. 
     (6-1) Scoring of Each Analysis Item 
     The performance score (PS) is represented by the following equation. 
       PS= P −(1−Ta)× S   (8)
 
     Here, P indicates a perfect score (100 points), and Ta indicates target zone estimation and is represented by the following equation. 
       Ta=(Tz−(| T−R |))/Tz  (9)
 
     Here, Tz indicates a target zone, T indicates a target value, and R indicates analysis data. If (1−Ta) is 0 to 1, this indicates that convergence to the target zone occurs. It is indicated that (1−Ta) coming closer to 0 approaches the target value. If (1−Ta) is equal to or greater than 1, this indicates a deviation relative to the target zone. In addition, S indicates a scale number and is used for scale matching between a point and a data numerical value. S is represented by P/A, and, here, A indicates an analysis possible range. 
     (6-1-1) Performance Score PsF of First Deviation Angle θ 1   
     If a square impact is applied toward a target line, the first deviation angle θ 1  is 0, and, in this case, 100 points are given as PsF. A score of the first deviation angle θ 1  is computed by assigning, for example, P=100, T=0, Tz=1°, A=30, and R=θ1 to Equations (8) and (9). In this case, the target zone Tz is a variable value which may be set to ±arcsin (R/L) by using the radius R of the cup and a distance L from the address position to the cup center as described above. 
     (6-1-2) Performance Score PsS of Second Deviation Angle θ 2   
     If a square impact is applied on a club path, the second deviation angle θ 2  is 0, and, in this case, 100 points are given as PsS. A score of the second deviation angle θ 2  is computed by assigning, for example, P=100, T=0, Tz=1°, A=30, and R=θ2 to Equations (8) and (9). 
     (6-1-3) Performance Score PsH of Deviation Amount δ Relative to Sweet Spot 
     If hitting is performed at the sweet spot, the as deviation amount δ is 0, and, in this case, 100 points are given as PsH. A score of the deviation amount δ is computed by assigning, for example, P=100, T=0, Tz=5°, A=100, and R=δ to Equations (8) and (9). 
     (6-1-4) Performance Score PsB of Swing Width L 
     It is targeted that the swing width L is put in a standard deviation of 1σ. A score of the swing width L is computed by assigning, for example, P=100, T=0, Tz=1σ°, A=100, and R=L to Equations (8) and (9). 
     (6-1-5) Performance Score PsI of Impact Speed V 
     It is targeted that the impact speed V is also put in a standard deviation of 1τ. A score of the impact speed V is computed by assigning, for example, P-100, T=0, Tz=1τ°, A=10, and R=V to Equations (8) and (9). 
     (6-1-6) Performance Score PsL of Third Deviation Angle θ 3   
     If an impact is applied according to a standard loft angle or an actually measured loft angle during address, the third deviation angle θ 3  is 0, and, in this case, 100 points are given as PsL. A score of the third deviation angle θ 3  is computed by assigning, for example, P=100, T=0, Tz=1°, A=15, and R=θ 3  to Equations (8) and (9). 
     (6-1-7) Performance Score PsA of Fourth Deviation Angle θ 4   
     If an impact which is parallel to a target line is applied, the fourth deviation angle θ 4  is 0, and, in this case, 100 points are given as PsA. A score of the fourth deviation angle θ 4  is computed by assigning, for example, P=100, T=0, Tz=1°, A=15, and R=θ 4  to Equations (8) and (9). 
     The performance score PS of each analysis item is displayed as a numerical value in the PS column of the above-described analysis screen of the analysis item. 
     (6-2) Scoring of Total Point 
     The above-described analysis items are roughly classified into the analysis items (the first deviation angle θ 1 , the second deviation angle θ 2 , and the deviation amount δ relative to the sweet spot) regarding the directionality and the analysis items (the impact speed V, the swing width L, the third deviation angle θ 3 , and the fourth deviation angle θ 4 ) regarding the perception of distance. Therefore, as total points obtained by weighting the analysis items, three types of total points are useful, including 1) a total point regarding the directionality, 2) a total point regarding the perception of distance, and 3) a total point regarding the directionality and the perception of distance. 
     (6-2-1) Scoring of Total Point of Analysis Item Regarding Directionality of Hit Ball 
     Weighting factors when the three analysis items (the first deviation angle θ 1 , the second deviation angle θ 2 , and the deviation amount δ relative to the sweet spot) regarding the directionality are defined as follows. A weighting factor of the performance score PsS regarding the first deviation angle θ 1  (absolute face angle) is set to WS, a weighting factor of the performance score PsF regarding the second deviation angle θ 2  (square degree) is set to WF, and a weighting factor of the performance score PsH regarding the deviation amount δ relative to the sweet spot is set to WH. 
     When an extent of an influence on the directionality of a hit ball is taken into consideration, the weighting factor WS for the first deviation angle θ 1  is higher than the weighting factor WH for the deviation amount δ (WS&gt;WH). The weighting factor WH for the deviation amount δ is higher than the weighting factor WF for the second deviation angle θ 2  (WH&gt;WF). Therefore, the three weighting factors have the following relationship. 
       WS&gt;WH&gt;WF  (10)
 
     A total point of the analysis items regarding the directionality of a hit ball is as follows in a case of using the three data items θ 1 , θ 2 , and δ. 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsF×WF+PsS×WS+PsH×WH)/(WF+WS+WH)  (11)
 
     A total point of the analysis items regarding the directionality of a hit ball is as follows in a case of using the two data items θ 1  and δ. 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsF×WF+PsH×WH)/(WF+WH)  (12)
 
     A total point of the analysis items regarding the directionality of a hit ball is as follows in a case of using the two data items θ 2  and δ. 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsS×WS+PsH×WH)/(WS+WH)  (13)
 
     A total point of the analysis items regarding the directionality of a hit ball is as follows in a case of using the two data items θ 1  and θ 2 . 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsF×WF+PsS×WS)/(WF+WS)  (14)
 
     (6-2-2) Scoring of Total Point of Analysis Item Regarding Perception of Distance of Hit Ball 
     Weighting factors when 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 ) regarding the perception of distance are defined as follows. A weighting factor of the performance score PsI regarding the impact speed V is set to WI, a weighting factor of the performance score PsB regarding the swing width L is set to WB, a weighting factor of the performance score PsL regarding the third deviation angle θ 3  (delta-loft angle) is set to WL, and a weighting factor of the performance score PsA regarding the fourth deviation angle θ 4  (attack angle) is set to WA. 
     When the extent of the influence on the perception of distance of a hit ball is taken into consideration, the weighting factor WI for the impact speed V is higher than the weighting factor WB for the swing width L (WI&gt;WB). The weighting factor WB for the swing width L is higher than the weighting factor WL for the third deviation angle θ 3  and the weighting factor WA for the fourth deviation angle θ 4  (WI&gt;WB&gt;WL, and WI&gt;WB&gt;WA). The weighting factor WL for the third deviation angle θ 3  and the weighting factor WA for the fourth deviation angle θ 4  may set to be equal to each other since the weighting factor WL for the third deviation angle θ 3  and the weighting factor WA for the fourth deviation angle θ 4  have a correlation to each other (WL=WA). Therefore, the four weighting factors have the following relationship. 
       WI&gt;WB&gt;WL=WA  (15)
 
     A total point of the analysis items regarding the perception of distance of a hit ball is as follows in a case of using the four data items V, L, θ 3 , and θ 4 . 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsI×WI+PsB×WB+PsL×WL+PsA×WA)/(WI+WB+WL+WA)  (16)
 
     A total point of the analysis items regarding the perception of distance of a hit ball is as follows in a case of using the three data items V, L, and θ 3 . 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsI×WI+PsB×WB+PsL×WL)/(WI+WB+WL)  (17)
 
     A total point of the analysis items regarding the perception of distance of a hit ball is as follows in a case of using the three data items V, L, and θ 4 . 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsI×WI+PsB×WB+PsA×WA)/(WI+WB+WA)  (18)
 
     A total point of the analysis items regarding the perception of distance of a hit ball is as follows in a case of using the two data items V and L. 
       SUM(respective PSs×weighting factors)/SUM(respective weighting factors)=(PsI×WI+PsB×WB)/(WI+WB)  (19)
 
     (6-2-3) Scoring of Total Point of Analysis Item Regarding Directionality and Perception of Distance of Hit Ball 
     Of the directionality and the perception of distance of a hit ball, the directionality of a hit ball is emphasized when taking into consideration the extent of the influence on swing improvement or sports. An analysis item (for example, V or L) which has a great influence among the analysis items regarding the perception of distance of a hit ball may be emphasized more than an analysis item (for example, θ 2 ) which has a small influence among the analysis items regarding the directionality of a hit ball. Therefore, the weighting factors for the seven analysis items (θ 1 , θ 2 , δ, V, L, θ 3 , and θ 4 ) regarding the directionality and the perception of distance of a hit ball have the following relationship on the basis of Equations (10) and (15). 
       WS&gt;WH&gt;WI&gt;WB&gt;WF&gt;WL=WB  (20)
 
     A comprehensive performance score Ps (directionality+perception of distance) of the performance score Ps (directionality) regarding the directionality represented by any one of Equations (11) to (14) and the performance score Ps (perception of distance) regarding the perception of distance represented by any one of Equations (16) to (18) is as follows. 
       Performance score Ps(directionality+perception of distance)= a ×performance score Ps(directionality)+ b ×performance score Ps(perception of distance)  (21)
 
     Here, the weighting factors a and b may be a=b=1, and, in other cases, may be a&gt;b so that the directionality is emphasized. 
     The performance score Ps (directionality+perception of distance) and a×performance score Ps (directionality) or b×performance score Ps (perception of distance) may be displayed as scores, and analysis data of the plurality of analysis items used for the displayed performance scores may also be displayed with, for example, a radar chart. 
     Although the present embodiment has been described in detail, it is easily understood by a person skilled in the art that various modifications may occur without substantially departing from the novel matters and effects of the invention. Therefore, such modification examples are all intended to be included in the scope of the invention. For example, in the specification or the drawings, a terminology which is described at least once along with another terminology which has a broader meaning or the same meaning may be replaced with another terminology in any location of the specification or the drawings. In addition, configurations and operations of the inertial sensor  12 , the golf club  13 , the calculation processing circuit  14 , and the like are not limited to those described in the present embodiment and may be variously modified. For example, the invention is not limited to golf, and is applicable to exercise appliances of baseball or tennis. 
     The entire disclosure of Japanese Patent Application No. 2015-025694, filed Feb. 12, 2015 is expressly incorporated by reference herein.