Method for determining coefficients of lift and drag of a golf ball

A method of determining a coefficient of lift and a coefficient of drag of a golf ball comprising the steps of

• positioning a plurality of ballistic light screens in a predetermined array of vertical and angularly disposed screens along a longitudinal path for emitting an electronic pulse in response to passage of a ball through a respective screen;
• launching a golf ball from a predetermined launch point at a predetermined speed, a predetermined spin rate and a predetermined trajectory angle through said screens;
• recording the time of passage of the ball through each screen;
• calculating an X coordinate of the ball at each screen relative to said launch point;
• calculating a Y coordinate of the ball at each screen relative to a common horizontal plane;
• thereafter calculating a coefficient of lift (CL) and a coefficient of drag (CD) of the ball in dependence on said speed, spin rate, trajectory angle, times of passage, X coordinates and Y coordinates;
• repeating each of said steps with the ball at different speeds and different spin rates from said launch position to obtain a series of drag and lift coefficients for the ball to form an aerodynamic model of the ball.

A method of determining at least one of the coefficient of lift and the coefficient of drag of a golf ball for a given range of velocities and a given range of spin rates from launch, said method comprising the steps of

• launching a ball from a launch point at a selected velocity within a given range of velocities, at a selected spin rate within a given range of spin rates and at a selected launch angle to a horizontal plane within a range of angles through a series of stations in a longitudinal flight path;
• calculating an X coordinate for the ball at each said station relative to said launch point;
• calculating a Y coordinate for the ball at each said station relative to a horizontal plane common to said launch point;
• mathematically calculating the value of at least one of the coefficient of lift and the coefficient of drag for the ball in dependence on said selected velocity, spin rate and launch angle;
• thereafter launching the ball from said launch point a plurality of times, each at a different velocity setting and a different spin rate setting and repeating said calculating steps to obtain a plurality of mathematically calculated values of at least one of the said coefficients;
• and
• thereafter plotting the plurality of calculated values relative to velocity and spin rate to obtain an aerodynamic model for the flight of the ball.

A method of determining at least one of the coefficient of lift and the coefficient of drag of a golf ball for a given range of velocities and a given range of spin rates from launch, said method comprising the steps of

• launching a ball from a launch point at a selected velocity within a given range of velocities, at a selected spin rate within a given range of spin rates and at a selected launch angle to a horizontal plane within a range of angles through a series of stations in a longitudinal flight path;
• calculating an X coordinate for the ball at each said station relative to said launch point;
• calculating a Y coordinate for the ball at each said station relative to a horizontal plane common to said launch point;
• mathematically calculating the value of at least one of the coefficient of lift and the coefficient of drag for the ball in dependence on said selected velocity, spin rate and launch angle;
• thereafter launching each of a plurality of balls sequentially from said launch point, each at a different velocity setting and a different spin rate setting, and repeating said calculating steps to obtain a plurality of mathematically calculated values of at least one of said coefficients;
• and
• thereafter plotting the plurality of calculated values relative to velocity and spin rate to obtain an aerodynamic model for the flight of said plurality of balls.

A method of determining at least one of the coefficient of lift and the coefficient of drag of a golf ball for a given range of velocities and a given range of spin rates from launch, said method comprising the steps of

• launching a ball from a launch point at a selected velocity, at a selected spin rate and at a selected launch angle to a horizontal plane through a longitudinal flight path;
• calculating an X coordinate for the ball at a plurality of points corresponding to a horizontal distance from said launch point relative to a time of launch;
• calculating a Y coordinate for the ball at said points corresponding to a vertical distance from said horizontal plane relative to said time of launch;
• mathematically calculating the value of at least one of the coefficient of lift and the coefficient of drag for the ball in dependence on said selected velocity, spin rate, launch angle and calculated X and Y coordinates;
• thereafter launching the ball from said launch point a plurality of times, each at a different velocity setting and a different spin rate setting and repeating said calculating steps to obtain a plurality of mathematically calculated values of at least one of the said coefficients;
• and
• thereafter mathematically determining an aerodynamic model for the flight of the ball in dependence on said obtained values of said at least one coefficient relative to said velocity and spin rate.

A method of simulating the flight of a golf ball in a computer, said method comprising the steps of

• launching a ball from a launch point at different sets of launch conditions, each set of launch conditions including at least a selected velocity, a selected spin rate and a selected launch angle to a horizontal plane through a longitudinal flight path;
• calculating an X coordinate for each launched ball at a plurality of points corresponding to a horizontal distance from said launch point relative to a time of launch;
• calculating a Y coordinate for each launched ball at said points corresponding to a vertical distance from said horizontal plane relative to said time of launch;
• mathematically calculating the value of at least one of the coefficient of lift and the coefficient of drag for each launched ball in dependence on said selected velocity, spin rate, launch angle and calculated X and Y coordinates;
• generating an aerodynamic model of the launched balls based on the calculated values for the coefficients of lift and the coefficients of drag at selected launch velocities and spin rates to obtain an equation for at least one of the coefficient of lift and the coefficient of drag;
• and
• thereafter employing said aerodynamic model to simulate the trajectory of the golf ball in a computer.

A method of determining at least one of the coefficient of lift and the coefficient of drag of a golf ball for a given range of velocities and a given range of spin rates from launch, said method comprising the steps of

• launching a ball from a launch point at a selected velocity within a given range of velocities, at a selected spin rate within a given range of spin rates and at a selected launch angle to a horizontal plane within a range of angles through a longitudinal flight path;
• calculating an X coordinate for the ball at a plurality of points in said path relative to said launch point;
• calculating a Y coordinate for the ball at east said point relative to a horizontal plane common to said launch point;
• mathematically calculating the value of at least one of the coefficient of lift and the coefficient of drag for the ball in dependence on said selected velocity, spin rate and launch angle and calculated X and Y coordinates;
• thereafter launching each of a plurality of balls sequentially from said launch point, each at a different velocity setting and a different spin rate setting, and repeating said calculating steps to obtain a plurality of mathematically calculated values of at least one of said coefficients;
• and
• thereafter mathematically determining an aerodynamic model for the flight of the ball in dependence on said obtained values of said at least one coefficient relative to said velocity and spin rate.