Measuring and testing – Miscellaneous
Reexamination Certificate
1998-04-21
2001-02-13
Raevis, Robert (Department: 2856)
Measuring and testing
Miscellaneous
Reexamination Certificate
active
06186002
ABSTRACT:
This invention relates to a method for determining the coefficients of lift and drag of a golf ball. More particularly, this invention relates to a method for simulating the flight path of a golf ball. Still more particularly, this invention relates to a method of determining the expected trajectory and roll of a golf ball.
As is known, various techniques have been known for obtaining measurements of the aerodynamic lift and drag on golf balls. As described by A. J. Smits (1994) A New Aerodynamic Model of a Golf Ball in Flight, Science and Golf II, (Ed. A. J. Cochran) E&FN SPON, pages 340-347, accurate measurements of the lift and drag characteristics of golf balls are necessary in order to predict the golf ball trajectory and its point of impact. Reference is also made to the use of wind tunnels within which a ball may be dropped to obtain the estimates of the lift and drag of a golf ball. However, one of the problems associated with using a wind tunnel to obtain measurements of the aerodynamic lift and drag of a golf ball is that the wind tunnel provides a very limited height over which a golf ball may be dropped into a horizontal flow of air within the wind tunnel. For example, there are air flow disruptions from the mechanisms used to support a golf ball within a flow of air and there are dynamic imbalances of the balls. In addition, force measurement assumptions have to be made.
Indoor test ranges developed by the research facilities of the Unites States Golf Association have also been used to measure the aerodynamic performance of golf balls. Such indoor testing range utilize spaced apart ballistic light screens through which a golf ball can be propelled at a precisely known initial velocity and spin rate in order to obtain measurements of the aerodynamic performance of the golf ball. Generally, the technics employed have been used to determine the arrival time of a ball at a number of down range stations along with the vertical and horizontal positions of the ball at each station. From this information, a trajectory program has been predicted. This technique is particularly described by M. V. Zagarola (1994) An Indoor Testing Range to Measure the Aerodynamic Performance of Golf Balls, Science and Golf II, (Ed. A. J. Cochran), E. & FN Spon, London, pages 348,354. Typically, the technique has developed aerodynamic coefficients from the information obtained from the flight path of a single ball through the ballistic screens.
U.S. Pat. No. 5,682,230 describes a calibration system for calibrating the position of the ballistic screens in an indoor test range in order to obtain more accurate information to determine the flight path of a ball.
Accordingly, it is an object of the invention to accurately measure the coefficients of lift and drag of a golf ball.
It is another object of the invention to predict and characterize the entire golf ball trajectory for an arbitrably given set of launch conditions.
It is another object of the invention to provide a mathematical model for a ball motion subsequent to landing.
It is another object of the invention to be able to calculate the overall distance, including carry and roll, for a golf ball.
It is another object of the invention to determine the optimum launch conditions that will provide a ball with the greatest overall distance.
It is another object of the invention to determine the optimal conditions for launching a ball without having to exhaust time and man power and tedious outdoor tests.
Briefly, the invention provides a method of obtaining an aerodynamic model of a golf ball. In accordance with the method the coefficient of lift as well as the coefficient of drag of a golf ball are accurately determined to predict optimum conditions for a launch angle and velocity for the golf ball. The techniques used allows a very accurate prediction to be made of the trajectory for a given golf ball. When coupled with a suitable program regarding the ground conditions, the programmed trajectory can be coupled with a program for predicting roll so that the total distance can be predicted for a golf ball under optimum launch conditions.
By being able to more accurately predict the trajectory and roll of a golf ball, a more uniform and accurate standard can be established for all golf balls.
The programs which are used to determine the trajectory of the ball may also be corrected for environment variables such as temperature, humidity, wind and barometric pressure. Further, having an accurate coefficient of lift and coefficient of drag allows for accurate predictions for trajectory and roll for a variety of launch positions. Further, optimization can be obtained for a given velocity to determine the optimum spin and optimum angle for launch.
In accordance with the invention, the technique for determining the coefficients of lift and drag of a golf ball include the basic steps of positioning a plurality of ballistic light screens in a predetermined array of vertical and angularly disposed screens along a longitudinal path with each screen being programmed for emitting an electronic pulse in response to passage of a ball through the respective screens and of launching a ball from a predetermined launch point at a predetermined speed, a predetermined spin rate and a predetermined trajectory angle through the screens.
In accordance with the method, the time of passage of the ball through each screen is recorded and calculations are performed by a suitable computer program in order to calculate an X coordinate of the ball at each screen relative to the launch point and a Y coordinate of the ball at each screen relative to a common horizontal plane.
Thereafter, in a known manner, a coefficient of lift (C
L
) and a coefficient of draft (C
D
) of the ball are calculated in dependence on the initial speed, spin rate, trajectory angle, times of passage through the ballistic screens, X coordinates and Y coordinates of the ball at each screen.
Basically, the above steps have been used in the past in order to calculate a coefficient of lift and a coefficient of drag for a ball. In accordance with the invention, each of the steps is repeated with a plurality of balls being launched from the launch point with each ball being launched at a different speed and different spin rate from the other balls in order to obtain a series of drag and lift coefficients in order to form an aerodynamic model of the ball.
The series of balls which are launched through the series of ballistic screens should be of the same make and model in order to obtain a coefficient and a coefficient of drag for that make and model of ball.
The results of the data gathered as a result of the series of launches through the ballistic screens is used to determine the proper lift and draft coefficient parameters using least squares identification. The resulting parameters are then used to calculate the lift and drag force for every condition of velocity and spin rate along the flight of the ball keeping in mind that the speed of the ball varies along its trajectory as does the spin rate. Having correct mathematical descriptions of the lift and drag allows one to accurately predict the flight of a golf ball. In addition, the ease of repetitive simulations allows one to determine the optimum launch conditions for the ball being tested.
REFERENCES:
patent: 5489099 (1996-02-01), Rankin et al.
patent: 5682230 (1997-10-01), Anfinsen et al.
patent: 5700204 (1997-12-01), Teder
patent: 5935023 (1999-08-01), Machara et al.
Lieberman Burton B.
Quintavalla Steven J.
Smits Alexander J.
Thomas Frank W.
Winfield Douglas
Carella Byrne Bain Gilfillan Cecchi Stewart & Olstein
Hand Francis C.
Raevis Robert
United States Golf Associates
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