Chapter 2 is devoted to the aerodynamics of a golf ball flight. However, it is fitting to provide a short historical introduction to this work here.
From the substantial literature on golf ball flight, two papers are of particular interest for the combination of careful experimentation and extensive databases they provide. The first is an exhaustive experimental assessment of the performance of golf balls, carried out in 1976 at Imperial College, London, by Bearman and Harvey (B&H; 1976). They carried out a series of wind-tunnel tests of dimpled balls, equipped with internal motors to provide varying spin rates. The authors measured lift and drag forces and produced tables of lift and drag data covering the range of golf ball speeds and spin rates experienced in play.
They tested two different 1976Uniroyal brand balls: one with circular and one with hexagonal dimples. They demonstrated close agreement between ball flight distances of the hexagonal-dimple balls, as predicted using their wind-tunnel data, and measured sets of launch angle, ball velocity, initial ball spin, and flight distance. Because of the distance validation, this extensive data set provides a benchmark in time against which to compare the aerodynamic performance of the modern golf ball. Two decades later, Smits and Smith (S&S; 1994) used a higher-speed wind tunnel, mounted golf balls on slender spindles, and measured lift and drag forces and the rate of spin decay, for a wide range of airspeed and spin rates applicable to the driver through short-iron shots. Smits and Smith obtained lift data that “in all respects are similar to the data obtained by Bearman and Harvey,” although their values were higher than the hexagonally dimpled ball data of B&H by a constant increment of 0.04. S&S also obtained “broad agreement” with the drag coefficient data of B&H, although their results indicated a “stronger dependence on spin-rate.” This is to be expected; if golf ball designers had managed to tweak the dimple spacing and profiles to achieve greater lift, then it is likely this would have been accompanied by an added amount of induced drag. For the present study, the B&H lift and drag data were incrementally adjusted by the
Figure 1C Trackman measurements of the robot driving tests with predictions using the Bearmanand Harvey (1976) lift and drag coefficients and the Smits and Smith (1994) ball aerodynamic drive model; data on the Great Big Bertha II courtesy of Callaway Corporation.
Writer until the best agreement was obtained over the range of PGA and LPGA Tour player trajectories. For the drive, the S&S model was found to give better agreement with current premium balls. The nature of the lift and drag forces acting on the ball is explained in Chapter 2.
Figure 1C shows the actual ball flight from robot testing, as monitored by the Trackman radar system. The tests were carried out, as a demonstration for the writer and one of his colleagues, by the Callaway Golf Corporation using a conforming golf ball and the Great Big Bertha II titanium driver. From an average of ten 100 miles per hour hits, the measured results of the drive were: initial ball speed = 154.3 miles per hour; launch angle = 12.9 degrees; initial backspin = 3,106revolutions per minute; maximum height = 38.3 yards; and carry distance = 245.1 yards. The dashed line (in Figure 1C) shows the predicted trajectory obtained by the writer, using the original Bearman and Harvey lift and drag data for the hexagonal-dimple, 1976 Uniroyal balls. Calculations were carried out as described by Bearman and Harvey (1976), but using a spin decay rate as later determined experimentally by Smits and Smith (1994).
With very minor adjustments, the S&S aerodynamic model simulated the Trackman trajectory almost perfectly as shown by the square symbols in Figure 1C.
Before concluding this chapter, it is difficult to overlook the quite amazing performance of the 1977 Uniroyal hexagonal-dimple ball. With all of the advances in the understanding of fluid flows and the development of sophisticated computational fluid dynamics software systems for advanced aerospace design over the last two decades, it would have been natural to expect a little more. However, this comparison does not tell us anything about the ball-striking behavior of the Uniroyal ball compared to the modern premium ball. It would be wrong to assume from these flight comparisons that the Uniroyal ball would perform as well in actual play, and there is ample evidence to show that it certainly would not. Likewise, the robot testing, with ten perfectly centered face strikes, gives no indication of its performance in the actual play, particularly with a high-handicap player whose ball strikes would be scattered quite widely from the face center. Dealing with issues such as these and of course different issues arising for every aspect of the game, is the goal of this work.
As mentioned at the beginning of this Introduction, Trackman data on PGA and LPGA Tour players will be used as the science “examples” throughout the text. This
Table 1A Average Trackman test results and modeling for PGA tour players
Table 1B Average Trackman test results and modeling for LPGA tour players
data are presented here in Tables 1A and 1B as an easy to find a reference for recurring discussions of Tour player performance.
Ball flight or “carry” distances shown in the tables are not as large as might have been expected. This suggests that for a player to be “on Tour,” the peak level of achievement in the game, the major requirement is not ultra-long hitting, so it can only be the consistency of ball striking, coupled with accuracy on the putting surface and of course a high tolerance for stress. However, we should certainly not underestimate the importance of distance combined with accuracy off the tee, for separating the very good from the very best.
On to the ball that actually does fly by creating its own propulsion system.
BALL FLIGHT
As we know, golf ball velocities are high. They fly off the golf club face at speeds ranging from about 50 miles per hour for partial wedge shots to 180 miles per hour for the longest drives. They descend back to earth at speeds up to 70 miles per hour. However, these high speeds do not explain for the amazing distances a golf ball can be driven, the ease with which the same ball can be lofted over high trees, or the manner in which they can be stopped on fast greens in a single bounce. A ball without the elastic resilience of the modern ball, and particularly without its complex dimple pattern, would do none of these things. How it is achieved is the subject of this chapter and Chapter 3. Before explaining the science underlying the flight performance of the modern ball, a preview of the game of golf without dimples might be useful.