GOLF BALL TRAJECTORY SIMULATION METHOD

• US 20110257945A1
• Filed: 12/20/2010
• Published: 10/20/2011
• Est. Priority Date: 04/20/2010
• Status: Active Grant

• Current Assignee: Bridgestone Sports Co Limited (Bridgestone Corporation)
• Original Assignee: Bridgestone Sports Co Limited (Bridgestone Corporation)
• Inventors: SATO, Katsunori
• Granted Patent: US 8,452,577 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: A63B 2102/32 Golf
• CPC Class Codes: A63B 45/00 Apparatus or methods for manufacturing balls working of plastics or substances in a plastic state B29
• CPC Class Codes: A63B 69/36 for golf
• CPC Class Codes: A63B 69/3691 Golf courses; Golf practising terrains having a plurality of driving areas, fairways, greens special golf games, e.g. miniature golf, A63B67/02; mats for simulating golf greens A63B69/3661
• CPC Class Codes: G06F 2111/10 Numerical modelling
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]
• CPC Class Codes: G06F 30/28 using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
• CPC Class Codes: G06T 13/20 3D [Three Dimensional] animation

Abstract

The invention is directed at a golf ball trajectory simulation method which sets up a golf ball model within a virtual airflow space where a grid has been generated, sets a weight for the ball model and applies initial conditions (initial velocity, launch angle, spin rate) to the ball model so as to cause the model to fly within the virtual airflow space, then calculates the lift coefficient and the drag coefficient for the golf ball from the air stream velocity, direction and pressure calculated in each grid cell, and calculates the flight distance and left-to-right dispersion for the golf ball from launch until landing by calculating the change in height, change in lateral direction, change in velocity and change in spin rate for the golf ball during flight. The trajectory simulation method divides the flight path of the golf ball model into two or three regions based on the criteria that Re=250,000 to 170,000 is a high-velocity region, Re=170,000 to 100,000 is a medium-velocity region and Re=100,000 and below is a low-velocity region, and sets up a height for the grid adjacent to the golf ball model surface in the high-velocity region (grid height A), a height for the grid adjacent to the golf ball model surface in the medium-velocity region (grid height B) and a height for the grid adjacent to the golf ball model surface in the low-velocity region (grid height B) such that grid height A<grid height B<grid height C.

Claims

1. A golf ball trajectory simulation method which employs arithmetic operations executed by a computer to analyze and estimate the trajectory of a golf ball having a plurality of dimples on a surface thereof when the ball is launched into flight, comprising the steps of:

(A) generating a grid within a virtual airflow space (field) where the ball is to be launched;

(B) setting up within the virtual airflow space (field) a substantially spherical golf ball model having a plurality of dimples formed on a surface thereof;

(C) dividing the grid into cells in such a way as to make the grid near the golf ball model finer than the grid within the virtual space (field) and to have the grid gradually increase in size in a direction leading away from the surface of the ball model;

(D) setting a weight for the golf ball model;

(E) applying initial conditions (initial velocity, launch angle, spin rate) to the golf ball model;

(F) initiating movement of the golf ball model under the initial conditions, regenerating in an area of movement the grid near the ball in such a way as to follow the movement of the ball model without disturbing the originally set grid size, and restoring the grid after the ball has passed therethrough to the grid within the virtual airflow space (field);

(G) calculating a lift coefficient and a drag coefficient for the golf ball in flight within the virtual airflow space (field) by integrating an air stream velocity, direction and pressure calculated in each grid cell within the virtual airflow space (field); and

(H) calculating a flight distance and a left-to-right dispersion for the golf ball from launch until landing by calculating a change in height, a change in lateral direction, a change in velocity and a change in spin rate for the golf ball during flight,

wherein the simulation method, when estimating the trajectory, calculates the Reynolds number (Re) around the golf ball model in flight, divides a flight path of the golf ball model into two or three regions based on the criteria that Re=250,000 to 170,000 is a high-velocity region, Re=170,000 to 100,000 is a medium-velocity region and Re=100,000 and below is a low-velocity region, and sets up a height for the grid adjacent to the golf ball model surface in the high-velocity region (grid height A), a height for the grid adjacent to the golf ball model surface in the medium-velocity region (grid height B) and a height for the grid adjacent to the golf ball model surface in the low-velocity region (grid height B) such that grid height A<

grid height B<

grid height C.

2. The golf ball trajectory simulation method of claim 1 which sets the grid height A in the high-velocity region in a range of from 0.001 to 0.015 mm, the grid height B in the medium-velocity region in a range of from 0.005 to 0.02 mm, and the grid height C in the low-velocity region in a range of from 0.01 to 0.025 mm.

3. The golf ball trajectory method of claim 1 which sets up, on a bottom side of the virtual airflow space (field), a wall representing a ground surface, thereby making the bottom side of the virtual airflow space (field) a closed side.

4. The golf ball trajectory method of claim 3, wherein a ball striking height, defined as the distance from the bottom side of the virtual airflow space (field) representing the ground surface to a bottommost point of the golf ball model, is added to the initial conditions set up in step (E).

5. The golf ball trajectory simulation method of claim 1, wherein the grid is shaped as an adaptive Cartesian mesh.

6. The golf ball trajectory simulation method of claim 1, wherein the grid is shaped as an unstructured mesh.

7. The golf ball trajectory simulation method of claim 1 which calculates, from a velocity, angle and spin rate calculated for the golf ball on landing, the distance traveled by the golf ball after landing until the ball comes to rest, and thereby calculates the distance traveled by the golf ball from launch until coming to rest.

8. A golf ball trajectory simulation method that employs arithmetic operations executed by a computer to analyze and estimate a trajectory of a golf ball having a plurality of dimples on a surface thereof when the ball is launched into flight, comprising the steps of:

(A) generating a grid within a virtual airflow space (field) where the ball is to be launched;

(B) setting up within the virtual airflow space (field) a substantially spherical golf ball model having a plurality of dimples formed on a surface thereof;

(C) dividing the grid into cells in such a way as to make the grid near the golf ball model finer than the grid within the virtual space (field) and to have the grid gradually increase in size in a direction leading away from the surface of the ball model;

(D) setting a weight for the golf ball model;

(D-2) setting up within the virtual airflow space a state wherein an air stream of a given velocity flows into the golf ball model;

(E) applying initial conditions (initial velocity, launch angle, spin rate) to the golf ball model;

(F) initiating movement of the golf ball model under the initial conditions, regenerating in an area of movement the grid near the ball in such a way as to follow the movement of the ball model without disturbing the originally set grid size, and restoring the grid after the ball has passed therethrough to the grid within the virtual airflow space (field);

(G) calculating a lift coefficient and a drag coefficient for the golf ball in flight within the virtual airflow space (field) by integrating an air stream velocity, direction and pressure calculated in each grid cell within the virtual airflow space (field); and

(H) calculating a flight distance and a left-to-right dispersion for the golf ball from launch until landing by calculating a change in height, a change in lateral direction, a change in velocity and a change in spin rate for the golf ball during flight,

wherein the simulation method, when estimating the trajectory, calculates the Reynolds number (Re) around the golf ball model in flight, divides a flight path of the golf ball model into two or three regions based on the criteria that Re=250,000 to 170,000 is a high-velocity region, Re=170,000 to 100,000 is a medium-velocity region and Re=100,000 and below is a low-velocity region, and sets up a height for the grid adjacent to the golf ball model surface in the high-velocity region (grid height A), a height for the grid adjacent to the golf ball model surface in the medium-velocity region (grid height B) and a height for the grid adjacent to the golf ball model surface in the low-velocity region (grid height B) such that grid height A<

grid height B<

grid height C.

9. The golf ball trajectory simulation method of claim 8 which sets the grid height A in the high-velocity region in a range of from 0.001 to 0.015 mm, the grid height B in the medium-velocity region in a range of from 0.005 to 0.02 mm, and the grid height C in the low-velocity region in a range of from 0.01 to 0.025 mm.

10. The golf ball trajectory method of claim 8 which sets up, on a bottom side of the virtual airflow space (field), a wall representing a ground surface, thereby making the bottom side of the virtual airflow space (field) a closed side.

11. The golf ball trajectory method of claim 10, wherein a ball striking height, defined as the distance from the bottom side of the virtual airflow space (field) representing the ground surface to a bottommost point of the golf ball model, is added to the initial conditions set up in step (E).

12. The golf ball trajectory simulation method of claim 8, wherein the grid is shaped as an adaptive Cartesian mesh.

13. The golf ball trajectory simulation method of claim 8, wherein the grid is shaped as an unstructured mesh.

14. The golf ball trajectory simulation method of claim 8 which calculates, from a velocity, angle and spin rate calculated for the golf ball on landing, the distance traveled by the golf ball after landing until the ball comes to rest, and thereby calculates the distance traveled by the golf ball from launch until coming to rest.