JP2019030464A - Golf club simulation method, golf club simulation program and golf club simulation apparatus - Google Patents

Abstract

To highly accurately simulate behavior of a golf club when hitting a golf ball on a sandy soil.SOLUTION: A simulation apparatus 10 simulates behavior of a golf club 20 when hitting a golf ball on a sandy soil SP. A movement trajectory acquisition unit 102 acquires movement trajectory data D when the golf club 20 is swung. A discrete processing unit 104 discretizes the golf club 20 and the golf ball B by a finite element method and discretizes the sandy soil SP into aggregation of sand grains S as discrete particles. A dynamic analysis unit 108 calculates the behavior of the golf club 20, the golf ball B, and the sand grains S when the golf club 20 is moved along the movement trajectory data D, by dynamic analysis.SELECTED DRAWING: Figure 11

Description

  The present invention relates to a golf club simulation method, a golf club simulation program, and a golf club simulation apparatus for simulating the behavior of a golf club when hitting a golf ball on sand.

Conventionally, various methods for simulating the behavior of a golf club when hitting a golf ball on the sand have been proposed.
For example, the following Non-Patent Document 1 proposes a method of modeling and simulating golf clubs, golf balls, and sand grains in two dimensions, and the following Non-Patent Document 2 describes golf clubs, golf balls, and sand grains 3 A method of modeling and simulating in a dimension has been proposed.

Kosuke Horii and 5 others, “Evaluation of shape characteristics of sand wedge using particle element method”, Joint Symposium 2004 Proceedings, 2004, No. 04-26, pp. 156-161 Takayuki Aoki, "Development of large-scale simulation method of particle method using GPU supercomputer by dynamic load balancing", Interdisciplinary large-scale information infrastructure joint use / joint research base 2014 joint research final report, May 2015

However, the above-described prior art does not consider a series of swing movements such as address, top, impact, and follow, and therefore there is a problem that a dynamic phenomenon in a bunker (sandy) cannot be accurately reproduced.
In the above-described prior art, the analysis is performed by regarding the swing of the golf club as a circular motion, and the shaft causing the bending is actually handled as a rigid body. Therefore, it is difficult to reproduce and evaluate the behavior of golf clubs, golf balls, sand particles, etc. when a human actually hits a shot.
The present invention has been made in view of such circumstances, and an object of the present invention is to accurately simulate the behavior of a golf club when hitting a golf ball on the sand.

In order to achieve the above object, a simulation method according to the invention of claim 1 is a simulation method for simulating the behavior of a golf club when hitting a golf ball on the sand, and the golf club moves during swinging. A trajectory acquisition step for acquiring trajectory data, a discretization step for discretizing the golf club and the golf ball with a finite element, and discretizing the sand into a set of sand particles which are discrete particles; A dynamic analysis step of calculating behaviors of the golf club, the golf ball, and the sand particles when moving along movement trajectory data by dynamic analysis.
In the simulation method according to the second aspect of the present invention, in the dynamic analysis step, it is possible to set a plurality of vertical relative distances between the golf club and the golf ball at the time of hitting, and the golf club at each relative distance. The behavior of the golf ball and the sand particles is calculated.
The simulation method according to the invention of claim 3 further includes a subsidence amount estimation step of estimating a subsidence amount of the sandy ground due to the weight of the sand grains.
In the simulation method according to the invention of claim 4, in the movement trajectory acquisition step, the movement trajectory data in which position information of the golf club when the measurer swings the golf club is recorded at predetermined intervals is acquired. It is characterized by that.
The simulation method according to claim 5 further includes an evaluation step of evaluating performance of the golf club based on behaviors of the golf club, the golf ball, and the sand particles before and after the hit. .
According to a sixth aspect of the present invention, a simulation program causes a computer to execute the golf club simulation method according to any one of the first to fifth aspects.
A simulation apparatus according to a seventh aspect of the invention is a simulation apparatus for simulating the behavior of a golf club when hitting a golf ball on the sand, and acquiring movement locus data for obtaining movement locus data at the time of swinging the golf club. A discretization processing unit that discretizes the golf club and the golf ball with a finite element and discretizes the sand SP into a set of sand particles that are discrete particles, and moves the golf club along the movement trajectory data. A dynamic analysis unit that calculates behaviors of the golf club, the golf ball, and the sand particles when moved by dynamic analysis.
In the simulation device according to an eighth aspect of the invention, the dynamic analysis unit can set a plurality of vertical relative distances between the golf club and the golf ball at the time of hitting, and the golf club at each relative distance. The behavior of the golf ball and the sand particles is calculated.
The simulation apparatus according to the invention of claim 9 further includes a settlement amount estimation unit that estimates a settlement amount of the sandy ground due to the weight of the sand grains.
In the simulation device according to the invention of claim 10, the movement trajectory acquisition unit acquires the movement trajectory data in which position information of the golf club when the measurer swings the golf club is recorded at predetermined intervals. It is characterized by that.
The simulation apparatus according to the invention of claim 11 further includes an evaluation unit that evaluates the performance of the golf club based on the behavior of the golf club, the golf ball, and the sand particles before and after the hit. .

According to the first and seventh aspects of the invention, the behavior of the golf club at the time of hitting the golf ball on the sand is simulated using the movement trajectory data corresponding to a series of golf swings from the address to the follow-up. The behavior of the golf club, golf ball, and sand particles close to the actual shot can be reproduced, which is advantageous in improving the accuracy of the simulation. In particular, bunker shots are difficult to reproduce and experiments are difficult, but various situations can be reproduced on a desk according to the inventions of claims 1 and 7.
According to the second and eighth aspects of the present invention, since the vertical relative distance between the golf club and the golf ball at the time of hitting can be arbitrarily set, the golf club head having a great influence when hitting the golf ball on the sand is used. Simulation can be performed by changing the degree of dive into the sand, which is advantageous in improving the usefulness of the simulation.
According to the third and ninth aspects of the present invention, the amount of sand subsidence caused by the weight of the sand particles is estimated. Therefore, the initial position of the golf ball and the state of the sand can be calculated more accurately, and the accuracy of the simulation can be improved. Is advantageous.
According to the fourth and tenth aspects of the present invention, the movement trajectory data is generated by recording the position information of the golf club when the measurer actually swings the golf club, so that the actual movement of the golf club is reflected. This is advantageous for simulation.
According to the fifth and eleventh aspects of the invention, since the performance of the golf club is evaluated based on the simulation result, it is advantageous in accurately selecting the golf club and designing the golf club for each user.
According to the invention of claim 6, it is possible to cause a computer to execute the simulation method according to any one of claims 1 to 5.

2 is a block diagram showing a functional configuration of a simulation apparatus 10. FIG. 2 is a block diagram showing a configuration of a computer 30. FIG. It is explanatory drawing which shows a simulation target object typically. It is explanatory drawing which shows the structure of the measurement system 60 which measures the movement locus | trajectory data D. FIG. It is explanatory drawing which shows the structure of the measurement system 60 which measures the movement locus | trajectory data D. FIG. 3 is an explanatory diagram schematically showing a finite element model of a golf club model 20A and a golf ball B. FIG. It is explanatory drawing which shows typically settlement of the sandy ground SP by the dead weight of the sand grain. It is a graph which shows the time series data of head speed. It is explanatory drawing which shows the example of a setting of relative distance diff typically. 4 is a flowchart showing a processing procedure by the simulation apparatus 10. It is a figure which shows the simulation result of the behavior after an impact. It is a graph which shows the time change of the head speed after an impact. It is a table | surface which shows the comparison with a simulation result and a trial hit result.

Exemplary embodiments of a golf club simulation method, a golf club simulation program, and a golf club simulation apparatus according to the present invention will be explained below in detail with reference to the accompanying drawings.
FIG. 1 is a block diagram illustrating a functional configuration of a simulation apparatus 10 that performs the golf club simulation method according to the embodiment.
As shown in FIG. 3, the simulation apparatus 10 simulates the behavior of the golf club 20 when hitting the golf ball B on the sand SP. That is, the simulation apparatus 10 is an apparatus for obtaining the behavior of the golf club 20 mainly by simulation during a bunker shot.

FIG. 2 is a block diagram illustrating a configuration of the computer 30 that functions as the simulation apparatus 10.
As shown in FIG. 2, the computer 30 includes a CPU 32, a ROM 34, a RAM 36, a hard disk device 38, a disk device 40, a keyboard 42, a mouse 44, a display 46, and a printer connected via an interface circuit (not shown) and a bus line. 48, an input / output interface 50, and the like.
The ROM 34 stores a control program and the like, and the RAM 36 provides a working area.

The hard disk device 38 simultaneously performs a finite element analysis of the golf club 20 and the golf ball B and a discrete element analysis of the sand grains S constituting the sandy ground SP, and uses the simulation result obtained by this analysis program to use the golf club 20. A simulation program for calculating evaluation data is stored.
This kind of calculation program is arbitrary, such as using a dedicated program, or using commercially available spreadsheet software (application program) and its macro program.

As a simulation program, various conventionally known commercially available analysis software that performs finite element analysis and discrete element analysis, for example, Abaqus (registered trademark of United States and / or other countries subsidiary of Dassault Systems) is used. Can do.
The analysis program includes the following programs.
1) A program for creating a finite element model:
In the present embodiment, the program is for creating a finite element model of the golf club 20 and a finite element model of the golf ball B.
2) A program for creating a discrete element model:
In the present embodiment, the program is for creating a discrete element model of sand grains S constituting the sand where the golf ball B is placed.
3) A program for performing simulation (analysis) using a finite element model and a discrete element model:
The present embodiment is a program for analyzing the behavior of the golf club 20, the golf ball B, and the sand particles S using the finite element model and the discrete element model.
4) Program for outputting simulation results:
It is a program for visualizing and outputting simulation results as figures and numerical tables in various forms including contour diagrams.

The disk device 40 records and / or reproduces data on a recording medium such as a CD or a DVD.
The keyboard 42 and the mouse 44 receive an operation input by the operator.
The display 46 displays and outputs data, and the printer 48 prints and outputs data. The display 46 and the printer 48 output data.
The input / output interface 50 exchanges data with an external device.

As shown in FIG. 1, the computer 30 causes the movement locus acquisition unit 102, the discretization processing unit 104, the settlement amount estimation unit 106, the dynamic analysis unit 108, and the evaluation unit 110 to be executed when the CPU executes the simulation program. It functions as a simulation apparatus 10 provided with.
The movement locus acquisition unit 102 acquires movement locus data D when the golf club 20 swings. The movement trajectory data D is data in which position information of the golf club 20 when the measurer (human being) actually swings the golf club 20 is recorded at predetermined intervals. In the present embodiment, the movement trajectory data D is measured and recorded in advance, and is read by the movement trajectory acquisition unit 102 as necessary.

4 and 5 are explanatory diagrams showing the configuration of the measurement system 60 that measures the movement trajectory data D. FIG.
As shown in FIGS. 4 and 5, the measurement system 60 measures time-series data indicating the three-dimensional positions and directions (directions) of the grip portion 23 and the golf club head 24 of the golf club 20.
The measurement system 60 includes a transmitter 62, a three-dimensional magnetic sensor 64, a controller / data processing device 66, and a personal computer 68.

The transmitter 62 is installed at a predetermined position. As shown in FIG. 5, the transmitter 62 is wound in a loop shape in directions of three axes (X axis, Y axis, Z axis) orthogonal to each other. It is composed of three coils.
The transmitter 62 is installed such that the X axis and the Y axis extend on a horizontal plane, and the Z axis faces the vertical direction.
As shown in FIG. 4, the center position of the transmitter 62 is defined as a predetermined reference position 6202, and the Y-axis direction passing through the reference position 6202 is defined as a predetermined reference direction 6204.
The transmitter 62 generates a magnetic field whose distribution with respect to strength and direction is known by a drive signal supplied from the controller / data processor 66.

As shown in FIG. 5, the three-dimensional magnetic sensor 64 is constituted by three coils wound in a loop shape in the directions of three axes (X axis, Y axis, Z axis) orthogonal to each other.
As shown in FIG. 5, the three-dimensional magnetic sensor 64 has a measurement point 6402 and a measurement direction 6404.
The three-dimensional magnetic sensor 64 senses the magnetism around the measurement point 6402 in the three axis directions of the X axis, the Y axis, and the Z axis that are orthogonal to each other, and the three-dimensional position and the reference direction 6204 of the measurement point 6402 with respect to the reference position 6202. The detection signal S1 is output according to the direction of the measurement direction 6404 with respect to.
A measurement point 6402 is a center position of the three-dimensional magnetic sensor 64, and a measurement direction 6404 is a Y-axis direction passing through the measurement point 6402.
The three-dimensional magnetic sensor 64 is fixed to the end of the grip part 23 of the golf club 20.
The three-dimensional magnetic sensor 64 has the Y axis (measurement direction 6404) parallel to the striking direction of the golf club 20 and the Z axis parallel to the shaft axis.
An example of such a measurement system 60 is LIBERTY (manufactured by Polhemus).

As shown in FIG. 5, the controller / data processing device 66 includes a drive circuit 6602, a detection circuit 6604, and a computer 6606.
The drive circuit 6602 generates a drive signal for causing the transmitter 62 to sequentially generate predetermined three types of magnetic fields, and supplies the drive signal to the transmitter 62.
The detection circuit 6604 detects the first detection signal S1 supplied from the three-dimensional magnetic sensor 64.

The computer 6606 implements the following functions by executing data processing software.
That is, the computer 6606 controls the drive circuit 6602 and the detection circuit 6604, performs data processing from the output voltage obtained from the detection circuit 6604, and generates data indicating the position and orientation of the three-dimensional magnetic sensor 64.
The computer 6606 uses the position of the transmitter 62 as a reference position 6202, calculates and outputs time-series data of three-dimensional position coordinates (x, y, z) with reference to three axes X, Y, and Z orthogonal to each other. .
Further, the computer 6606 sets the Y-axis direction centering on the transmitter 62 as the reference direction 6204, and the posture angle representing the direction of the three-dimensional magnetic sensor 64 with respect to the reference direction 6204, that is, the yaw angle, the pitch angle, and the roll angle (hereinafter, , (Represented as [theta] y, [theta] p, [theta] r)) is calculated and output.
Therefore, the time-series data of the three-dimensional position coordinates (x, y, z) is data indicating the position of the three-dimensional magnetic sensor 64, and the time-series data of the yaw angle θy, the pitch angle θp, and the roll angle θr is three-dimensional magnetic. This is data indicating the orientation of the sensor 64.

Next, a time series of the three-dimensional position coordinates (x, y, z) with respect to the reference position 6202 of the measurement point 6402 of the three-dimensional magnetic sensor 64 and the posture angle (θy, θp, θr) of the measurement direction 6404 with respect to the reference direction 6204. Data generation will be described.
The drive circuit 6602 outputs the same signal whose frequency and phase are always constant according to the command signal of the computer 6606, and sequentially excites the three loop coils wound around the three axes of the transmitter 62.
Each loop-like coil generates a different magnetic field each time it is excited, and based on this, an independent output voltage V is generated in each of the three loop-like coils wound in the three-axis direction of the three-dimensional magnetic sensor 64.
This output voltage V is obtained in accordance with the three magnetic fields excited by the three loop coils of the transmitter 62, so that three output voltages V generated in the three loop coils of the three-dimensional magnetic sensor 64 are obtained. Nine (3 × 3) output voltages V are obtained.

On the other hand, since the transmitter 62 for forming the magnetic field is fixedly installed at a predetermined position, the distribution regarding the strength and direction of the generated magnetic field is known with respect to the reference position 6202 where the transmitter 62 is installed and the reference direction 6204. .
By using the nine output voltages V generated by the formed magnetic field, the three-dimensional position coordinates (x, y, z) of the three-dimensional magnetic sensor 64 with respect to the reference position 6202 and the posture angle (θy with respect to the reference direction 6204). , Θp, θr) can be obtained.
The computer 6606 of the controller / data processor 66 uses the nine output voltages V sent from the detection circuit 6604 to change the three-dimensional position coordinates (x, y, z) and the posture angle (θy, θp, θr). Calculate the data.

The three-dimensional position coordinates (x, y, z) and the posture angles (θy, θp, θr) obtained by the controller / data processing device 66 are taken into the personal computer 68, AD-converted, and the grip portion 23 is being swung. Time-series data (movement trajectory data) of the behavior can be obtained.
The personal computer 68 and the computer 30 functioning as the simulation device 10 may be the same device or different devices.
In the above description, the movement trajectory data is measured using a magnetic sensor. However, the present invention is not limited to this. For example, the movement trajectory data is measured by attaching a small acceleration sensor to the golf club 20. Various movement trajectory data measurement methods can be applied.

Returning to the description of FIG. 1, the discretization processing unit 104 discretizes the golf club 20 and the golf ball B with finite elements and discretizes the sand SP into a set of sand particles S that are discrete particles.
First, the discretization processing unit 104 creates a golf club head model that is a finite element model of the golf club 20 and a golf ball model that is a finite element model of the golf ball B.
These finite element models are created based on a conventionally known finite element method.
Specifically, the three-dimensional shape data of the golf club 20 and the golf ball B created using a three-dimensional CAD program, that is, design data (CAD data) is input to the computer 30.
Various data including constraint conditions and material constants necessary for creating the finite element models of the golf club 20 and the golf ball B are input to the computer 30.
When the computer 30 executes the finite element analysis program, the three-dimensional shape data of the golf club 20 and the golf ball B are divided into meshes.
As the finite element, either a shell element or a solid element may be used. However, using a shell element is advantageous in that the time required for calculation is shortened as compared with a solid element.
As a result, a golf club model 20A as a finite element model of the golf club 20 and a golf ball model BA as a finite element model of the golf ball B are created as shown in FIG. In FIG. 6, only the portion corresponding to the golf club head 24 in the golf club model 20A is shown.

Secondly, the discretization processing unit 104 discretizes the sand ground SP into a set of sand grains S that are discrete particles.
The sand grain S is modeled as a hard sphere-shaped single node element having a specified radius.
These discrete element models are created based on a conventionally known discrete element method.
Specifically, the radius (shape), weight, etc. of the sand particles S constituting the sand ground SP are input to the computer 30.
When the computer 30 executes the discrete element analysis program, the sand ground SP is modeled into a set of sand grains S which are discrete particles.
Note that the sand SP is different from an object such as the golf club 20 and its boundary is not clear. For this reason, a rigid frame 28 as shown in FIG. 3 is defined to determine the area of the sand SP.

The settlement amount estimation unit 106 estimates the settlement amount of the sand land SP due to the weight of the sand particles S.
As described above, the discretization processing unit 104 models the sand ground SP into the sand particles S, but at the initial stage, as shown in FIG. 7A, the sand particles S are arranged uniformly and the top surface is also flat. However, in the actual sand SP, the sand particles S are not evenly arranged as shown in FIG. 7A due to their own weight. That is, as shown in FIG. 7B, each sand particle S enters a gap between adjacent sand particles S and is displaced downward.
The settlement amount estimation unit 106 simulates the displacement of the sand grains S due to the influence of its own weight, and brings the state of the sand land SP on the model closer to the state of the actual sand land SP. For example, if the sand depth H0 in the initial state shown in FIG. 7A is 100, the sand depth H1 in the settled state shown in FIG. 7B is 95.2.
By such processing, the reproduction accuracy of the initial position of the golf ball B can be improved.

The dynamic analysis unit 108 includes the golf club 20 (golf club model 20A) and the golf ball B (golf ball model) when the golf club 20 (more specifically, the golf club model 20A) is moved along the movement trajectory data D. BA) and the behavior of sand grains S are calculated by dynamic analysis.
That is, the dynamic analysis unit 108 includes the golf club model 20A, the golf ball model BA, the sand model (a set of sand grains S) created by the discretization processing unit 104, and the movement track data acquired by the movement track acquisition unit 102. It is a part which performs the calculation process of the simulation calculation which reproduced golf swing using D. Specifically, by giving movement trajectory data (three-dimensional time-series data) as a boundary condition to a portion corresponding to the grip portion 23 of the golf club model 20A, the dynamic behavior of the golf club model 20A and the golf club model 20A The dynamic behavior of the hit golf ball model BA and the dynamic behavior of the sand particles S scattered by the golf club model 20A are calculated. Specifically, the calculation is performed by a known method that sequentially solves over time by an explicit method using a time difference scheme of the equation of motion.

Further, the dynamic analysis unit 108 calculates a characteristic physical quantity indicating the behavior of the golf club model 20A, the golf ball model BA, and the sand ground SP from the calculation result obtained by the simulation calculation.
The dynamic analysis unit 108 is, for example, a moving speed (head speed) of a portion corresponding to the golf club head 24 in the golf club model 20A, a head speed difference before and after impact (hitting), and a positional relationship between the golf club head 24 and the shaft 22 ( The degree of head advance) and the like, the launch speed of the golf ball model BA, the launch angle, the spin amount, and the like, the degree of scattering of the sand particles S, and the like are calculated as characteristic physical quantities.

FIG. 8 shows time-series data of the head speed, which is an example of the characteristic physical quantity calculated by the dynamic analysis unit 108. The vertical axis represents the speed of the golf club head 24, and the horizontal axis represents time.
In FIG. 8, the head speeds up to the address (reference A), top (return: reference B), impact (reference C), and follow (reference D) are shown in time series. From such data, for example, the head speed immediately before the impact and the head speed difference before and after the impact can be calculated.

Here, in the dynamic analysis unit 108, the vertical relative distance between the golf club 20 (golf club model 20A) and the golf ball B (golf ball model BA) at the time of hitting, more specifically, the golf club model 20A. A plurality of vertical relative distances between the center of gravity of the head and the center point of the golf ball model BA can be set, and the golf club 20 (golf club model 20A), golf ball B (golf ball model BA), and The behavior of the sand grain S is calculated.
That is, as shown in FIG. 9, the relative distance diff in the vertical direction between the center point O1 of the golf ball model BA and the center of gravity O2 of the golf club head model is set, and a plurality of relative distances diff can be set. FIG. 9A schematically shows a state in which the relative distance diff is relatively large, and FIG. 9B schematically shows a state in which the relative distance diff is relatively small. In FIG. 9, the illustration of the sand ground SP (sand particles S) is omitted.

The reason why the relative distance diff can be set in this way is that the magnitude of the sand resistance varies depending on the magnitude of the relative distance diff. That is, when the relative distance diff is relatively large, the golf club 20 is deeply submerged in the sand, and the resistance of the sand is also relatively large. If the relative distance diff is relatively small, the golf club 20 will dive shallowly in the sand, and the resistance of the sand will be relatively small.
Due to such a difference, a difference occurs in the behavior of the golf club model 20A, the golf ball model BA, and the sand SP. For example, when the resistance of sand is large, the bending of the shaft 22 of the golf club 20 becomes small, leading of the head is suppressed, and the head speed is reduced. For example, when the resistance of sand is large, the golf ball B is prevented from flying. Moreover, when the resistance of sand is large, the amount of sand particles S scattered increases.
The dynamic analysis unit 108 can set a plurality of relative distances diff during simulation in order to reflect the differences in the behavior of the golf club model 20A, the golf ball model BA, and the sand SP due to the difference in the relative distance diff.

In the present embodiment, the relative distance diff is a vertical distance between the center point O1 of the golf ball model BA and the head center-of-gravity point O2 of the golf club model 20A.
Among these, the head center-of-gravity point O2 of the golf club model 20A is the center of mass (gravity action point) of the golf club 20 that can be detected by a conventionally known method. Normally, the center of gravity of a hollow structure such as a driver is inside the head, but since the sand wedge used for shots in the sand SP is a solid structure, the center of gravity O2 is not necessarily inside the head. In some cases, the position is off the center.
Further, since the shapes of the golf ball B and the golf club 20 are known, the position serving as a reference for the relative distance diff can be arbitrarily changed. For example, the distance between the ground point of the golf ball B and the lower end point of the golf club 20 may be set as the relative distance diff.

The evaluation unit 110 evaluates the performance of the golf club 20 based on the behavior of the golf club 20 (golf club model 20A), golf ball B (golf ball model BA), and sand ground SP (sand particles S) before and after hitting. In other words, the evaluation unit 110 evaluates the golf club 20 based on the characteristic physical quantity calculated by the dynamic analysis unit 108.
For example, the evaluation unit 110 evaluates the performance of the golf club 20 under a predetermined environment.
As an example of the environment, for example, the distance from the bunker (the initial position of the golf ball B) to the pin will be described. When the distance is short, the golf club head is generally deeply inserted into the sand to increase the ball launch angle. Thus, it is preferable to hit the ball so as to suppress the momentum of the ball and lift it up with the sand to escape from the bunker. On the other hand, when the distance is long, it is generally preferable to put the head shallowly in the sand, lower the launch angle of the ball, and increase the flight distance by applying momentum to the ball. Note that the above-described evaluation index is a general example and does not apply to all cases. The evaluation index in the evaluation unit 110 is appropriately set according to the simulation contents.
Thus, even if the same golf club moves along the same movement locus, the evaluation for the shot varies depending on the surrounding environment (the distance from the bunker to the pin in the above example). The evaluation unit 110 applies the behavior of each part before and after hitting to different environments and evaluates each simulation result.

FIG. 10 is a flowchart illustrating a processing procedure performed by the simulation apparatus 10.
Prior to processing by the simulation apparatus 10, the movement trajectory data D is measured and recorded by the measurement system 60 (step S100). At this time, a plurality of movement trajectory data D are measured, for example.
When the simulation is executed, the simulation worker first designates desired movement trajectory data D to the simulation apparatus 10. The movement locus acquisition unit 102 reads the designated movement locus data D (step S102).
Next, the simulation worker determines the specifications (shape, material, weight) of the golf club 20 and the golf ball B (step S104). In this step, for example, the simulation operator designates the model numbers of the golf club 20 and the golf ball B, and the simulation apparatus 10 reads out the three-dimensional shape data of the golf club 20 and the golf ball B of the model number stored in advance. Executed.
Subsequently, the simulation worker determines the specifications (shape / weight) of the sand particles S and the area of the sand SP (range of the rigid frame 28) (step S106).
Also, the simulation worker sets a vertical relative distance diff between the center of gravity of the golf club 20 and the center of the golf ball B (step S108).

The discretization processing unit 104 discretizes the golf club 20 and the golf ball B with finite elements to generate the golf club model 20A and the golf ball model BA, and discretizes the sand ground SP into a set of sand particles S that are discrete particles. (Step S110).
Next, the settlement amount estimation unit 106 estimates the settlement amount due to the weight of the sand particles S in the modeled sandy ground SP (step S112).

The dynamic analysis unit 108 dynamically analyzes the behavior of the golf club model 20A, the golf ball model BA, and the sand particles S when the golf club model 20A is moved along the movement trajectory data D, and calculates various characteristic physical quantities. (Step S114).
The evaluation unit 110 evaluates the performance of the golf club 20 based on various characteristic physical quantities (behavior of the golf club model 20A, golf ball model BA, and sand particles S before and after hitting), and outputs the result (step S116). Then, the process according to this flowchart is terminated.

<Example>
A simulation result using the simulation apparatus 10 according to the embodiment is shown below.
The golf club 20 used in the simulation has a length of 35 inches, a mass of 446.6 g, a club balance indicating the ratio of the head mass to the total mass of the golf club 20 is D-1.6, and the club frequency is 348 cpm. .
In this example, the vertical relative distance diff between the center of gravity of the golf club 20 and the center of the golf ball B was set to four conditions of 15.50 mm, 10.00 mm, 5.00 mm, and 0.26 mm.

FIG. 11 is a diagram illustrating simulation results of behaviors of the golf club 20, the golf ball B, and the sand particles S after 1.100e-02 seconds from the impact.
11A shows a relative distance diff of 15.50 mm, FIG. 11B shows a relative distance diff of 10.00 mm, FIG. 11C shows a relative distance diff of 5.00 mm, and FIG. 11D shows a relative distance diff of 0. .26 mm.
The larger the relative distance diff, the deeper the head of the golf club 20 is submerged in the sand and the greater the resistance of the sand. For this reason, as the relative distance diff is larger, the bending of the shaft 22 of the golf club 20 becomes smaller, and the leading of the head is suppressed. Further, the larger the relative distance diff, the more the golf ball B is prevented from flying. Further, the larger the relative distance diff, the greater the amount of sand particles S scattered.

FIG. 12 is a graph showing the temporal change in head speed after impact.
The head speed at the time of impact (0 seconds) is the same regardless of the relative distance diff, but thereafter, as the relative distance diff increases, the decrease in the head speed increases. That is, it can be seen that the larger the relative distance diff, the more the head speed decreases due to sand resistance.

FIG. 13 is a table showing a comparison between a simulation result and a test hit result using an actual golf club 20.
FIG. 13 shows the difference in head speed before and after impact when the relative distance diff is 15.50 mm, 10.00 mm, and 0.26 mm, and the relative distance diff is 23.00 mm, 9.00 mm, and 5.00 mm by trial hitting. This shows the head speed difference before and after impact.
Note that the trial hits were made by human hits, and the values of the relative distance between the head and the ball and the head speed difference show the average values when three test hits were made under each condition. Measurement data was obtained using a high-speed camera.
The head speed difference in the simulation was 12.02 m / s at diff15.50 mm, 10.02 m / s at diff10.00 mm, and 6.61 m / s at diff0.26 mm. Further, the head speed difference in the test hit was 13 m / s at diff 23.00 mm, 8 m / s at diff 9.00 mm, and 7 m / s at diff 5.00 mm.
In both simulation and trial hits, the larger the diff, the larger the head speed difference, and it can be seen that the simulation can reproduce the tendency in the actual shot.

As described above, the simulation apparatus 10 according to the embodiment hits the golf ball B on the sandy ground SP using the movement trajectory data D corresponding to a series of golf swings from the address to the follow. Since the behavior of the golf club 20 is simulated, the behavior of the golf club 20, the golf ball B, and the sand particles S close to the actual shot can be reproduced, which is advantageous in improving the accuracy of the simulation.
Further, since the simulation apparatus 10 can arbitrarily set the vertical relative distance diff between the golf club 20 and the golf ball B at the time of hitting, the golf club head having a great influence when hitting the golf ball B on the sand SP. It is advantageous to improve the usefulness of the simulation by changing the degree of dive into the sand.
Moreover, since the simulation apparatus 10 estimates the amount of settlement of the sand SP due to the weight of the sand particles S, the initial position of the golf ball B and the state of the sand SP can be calculated more accurately, and the simulation accuracy can be improved. Is advantageous.
Further, the simulation apparatus 10 generates the movement trajectory data D by recording the position information of the golf club 20 when the measurer actually swings the golf club 20, and thus reflects the actual movement of the golf club 20. This is advantageous for simulation.
Further, since the simulation apparatus 10 evaluates the performance of the golf club 20 based on the simulation result, it is advantageous in accurately selecting the golf club 20 and designing the golf club 20 for each user.

DESCRIPTION OF SYMBOLS 10 Simulation apparatus 102 Moving locus | trajectory acquisition part 104 Discretization process part 106 Settling amount estimation part 108 Dynamic analysis part 110 Evaluation part 20 Golf club 20A Golf club model 22 Shaft 23 Grip part 24 Golf club head 28 Rigid body frame 30 Computer B Golf ball BA Golf Ball Model D Movement Trajectory Data S Sand Grain SP Sand

Claims (11)

A simulation method for simulating the behavior of a golf club when hitting a golf ball on the sand,
A movement locus acquisition step for obtaining movement locus data at the time of swing of the golf club;
Discretizing the golf club and the golf ball with a finite element and discretizing the sand into a set of sand particles that are discrete particles;
A dynamic analysis step of calculating behaviors of the golf club, the golf ball, and the sand particles when the golf club is moved along the movement trajectory data by dynamic analysis;
A golf club simulation method comprising: In the dynamic analysis step, a plurality of vertical relative distances between the golf club and the golf ball at the time of hitting can be set, and the behavior of the golf club, the golf ball, and the sand particles at each relative distance is calculated. To
The golf club simulation method according to claim 1, wherein: A subsidence amount estimating step for estimating a subsidence amount of the sandy ground due to the weight of the sand particles;
3. The golf club simulation method according to claim 1, wherein the golf club is simulated. In the movement locus acquisition step, the movement locus data obtained by recording position information of the golf club at a predetermined interval when the measurer swings the golf club is obtained;
4. The golf club simulation method according to claim 1, wherein the golf club is simulated. An evaluation step of evaluating the performance of the golf club based on the behavior of the golf club, the golf ball, and the sand particles before and after the hitting;
5. The golf club simulation method according to claim 1, wherein the golf club is simulated.   A golf club simulation program that causes a computer to execute the golf club simulation method according to claim 1. A simulation device for simulating the behavior of a golf club when hitting a golf ball on the sand,
A movement locus acquisition unit for obtaining movement locus data at the time of swing of the golf club;
A discretization processing unit that discretizes the golf club and the golf ball with a finite element, and discretizes the sand into a set of sand particles that are discrete particles;
A dynamic analysis unit that calculates the behavior of the golf club, the golf ball, and the sand particles when the golf club is moved along the movement trajectory data by dynamic analysis;
A golf club simulation apparatus comprising: The dynamic analysis unit can set a plurality of vertical relative distances between the golf club and the golf ball at the time of hitting, and calculates the behavior of the golf club, the golf ball, and the sand particles at each relative distance. To
The golf club simulation apparatus according to claim 7, wherein: A subsidence amount estimation unit for estimating a subsidence amount of the sandy ground due to the weight of the sand particles;
9. The golf club simulation apparatus according to claim 7 or 8, wherein the golf club simulation apparatus according to claim 7 is used. The movement trajectory acquisition unit acquires the movement trajectory data in which position information of the golf club when the measurer swings the golf club is recorded at predetermined intervals.
The golf club simulation apparatus according to claim 7, wherein the golf club simulation apparatus is a golf club simulation apparatus. An evaluation unit that evaluates the performance of the golf club based on the behavior of the golf club, the golf ball, and the sand particles before and after the hitting;
The golf club simulation apparatus according to claim 7, wherein the golf club simulation apparatus is a golf club simulation apparatus.

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