Golf balls curve in flight for one principal reason: Namely that the golf club face is not square to the path being followed by the club head as it impacts the ball. This is illustrated in the figure where the club face is “open” to the club path by about four degrees. This is sufficient to produce a significant slice to the right. The club face dictates about 75% of the initial launch direction, so the ball will start out three degrees to the right and then curve away further during its flight. It can easily be appreciated that the sideways angled club face will, with the slightly glancing blow, impart a side spin to the ball — as shown by the counter-clockwise arrow. At the same time, the loft of the club produces a large backspin. Of course these cannot be two separate spins. If the loft angle is 30 degrees, then we can imagine that the ball starts turning on the face in a direction that gives the ratio of four degrees of sideways turn to 30 degrees of backwards turn; that is, it turns in an angled direction up the face. This tilts the axis of spin of the ball.
The next illustration is of a ball flying into the page, which has been struck with a club angled the opposite way with respect to the club path; i.e. the face was closed. The tilted spin axis causes the lifting force resulting from the back spin, to tilt by the same amount. This picture of the ball remains unchanged throughout the flight; that is, it keeps moving and facing forwards while the angled lift force pulls it sideways. It does this according to the principle of gyroscopic stability — just like the horizontally spinning rotors behind aircraft instruments panels fix the unchanged horizon as the plane banks.
In an aircraft, we get exactly the same flight conditions by applying left ailerons and just enough opposite rudder to keep the craft pointing forwards. We might do that to slip sideways to a runway over to the left, while losing altitude quickly with the high sideways drag. When aligned with the runway, returning the ailerons and rudder to the neutral position will straighten the plane up for landing. Unfortunately, golf balls with an internal control system are not yet available! So too often we watch helplessly as the ball continues to slip sideways past the grass landing strip to a crash site deep in the woods or the water.
Avoiding slices and hooks in the modern game is extremely difficult. Fredrick Tuxen, the inventor of the Trackman radar ball monitoring system, estimated empirically that for the driver, a golf ball with a five degree spin axis tilt will move 4.5 yards sideways for each 100 yards of travel. In my own research, I was able to determine from the impact mechanics that a five degree tilt is produced when the ratio of the face angle to the club loft angle is approximately 1/10. So a drive of 200 yards using a ten degree lofted driver, with the face just one degree open or closed, will give approximately 2 x 4.5 = 9 yards of slice or hook. Using, say, a 6-iron with 30 degrees of loft, two beneficial changes occur. The first is that, all things being the same, aerodynamic modeling showed that grooved clubs produce slightly less sideways movement because the higher spin rates increase drag, and so reduce both speed and lifting force more quickly – the “normalized” side movement becomes nearer to 3.5 yards. One degree of open or closed face with a six iron gives a side angle to loft ratio of 1/30, and so produces one third of the ball axis tilt compared to the driver. A 150 yard shot in this case would give 3.5/3 yards for each 100 yards, and so just under two yards sideways for the shot. The main lesson here with regard to equipment is that loft is the golfers friend, particularly with the driver. Tour players resort to hitting fairway woods into tight landing areas precisely because the extra loft improves directional control.
Because driver heads extend behind the shaft, the shaft is actually bent forward at impact, which further increases loft. The average loft at impact of PGA Tour pros is 14.4 degrees, resulting from about five degrees of forward shaft bending. From the above calculation, we can estimate that for their average flight distance of 269 yards a one degree open or closed face will put the ball 8.4 yards sideways from the launch direction. Compare this to a typical PGA fairway width of 30 yards and we conclude that while swinging with an average club speed of 112 mph, they must keep the face square to within about plus or minus three degrees to stay on the flat stuff.
Featured image credit: A hot headed golfer taking a tee shot to begin a round of golf by Lilrizz. CC0 via Wikimedia Commons.