Curved ball flight has just a single cause, and that is a tilt from the horizontal of the ball spin axis. This, in turn, has only one major cause for almost all golf shots, and that is the inclination of the club face to the club head direction at impact in the horizontal plane. This gives a sideways glancing blow to the ball, which produces a
Figure 2M Short 5-iron shot with 10 mph head- and tailwind.
sideways component of spin, thereby tilting the spin axis. The direction in which the clubhead is traveling at impact is usually referred to as the “club path.”
For drivers, a tilted spin axis is also caused by striking the ball at a position on the face offset horizontally from the face center. This causes the clubhead to rotate sideways during the impact, which in turn, like a pair of mating gears, causes the ball to rotate sideways in the opposite direction; together with the backspin caused by the club loft, this tilts the spin axis. The curved face of the driver from heel to toe is designed to minimize this effect by starting the curved trajectory away from the target line. This is discussed fully in Chapter 6.
If we address only the major cause of an angled face to the club path, then the tilt of the spin axis is easy to estimate. If, for example, the clubface is angled to the club path by 3 degrees, and the club has 34 degrees of loft, then the spin axis tilt is given approximately by tilt angle = 57 × (3/34) = 5.0 degrees. If the same face angle error was made with a driver lofted at 10 degrees, the tilt of the spin axis becomes 57 × (3/10) = 17.0 degrees. For the latter, it would produce a large slice if the face was 3 degrees open to the club path, or a large hook if it was closed. The multiplier 57, approximately equal to 180 divided by pi, comes from the conversion of the scientific radian measure of angle to degrees.
These calculations raise a very important point. With a low-lofted driver, quite amazing precision is needed to keep the ball in the fairway. In this regard, most amateur players use drivers with far too little loft, resulting in too much difficulty with direct control. This issue is pursued fully in Chapter 5.
These simple relationships between the face angle and the spin axis tilt arise from the fact that the ball will separate in a spinning condition from the face along the direction angled across the face by the club path, which in the driver case is 3 degrees sideways and 10 degrees upward. The spin axis thus starts out parallel to the face but angled with respect to the edge of the sole. Moreover, because of the high spin rate, it flies through the air with the spin axis fixed in that orientation. This stems from the principle of gyroscopic stability, which allows us to ride bicycles with ease and keeps the gyroscopic instruments in aircraft panels aligned with the horizontal as the aircraft banks and turns. One other property of golf balls that leads to gyroscopic stability is their very high level of spherical symmetry, sufficient enough that they fly precisely the same from whichever orientation they are placed on a tee.
Thus, while following a curved path, the ball slips through the air, exposing more of the “side” of the ball toward the direction of flight as it turns.
Figure 2N Inclination of the spin axis and forces acting on the ball in flight.
In Chapter 4, we will learn that the curve in the ball flight of a drive will produce approximately 3.5 yards of sideways movement, for every 5 degrees of spin axis tilt, per 100 yards of carrying. Thus, a 200-yard drive with the 10 degrees lofted driver, having the face 3 degrees open, would, because of the 17-degree inclination of the spin axis, slice: to give a total sideways movement of approximately (17/5) × (200/100) × 3.5 = 24 yards.
The stability of the spin axis in flight allows us to calculate the direction of the forces throughout the flight, as the ball climbs then descends while continuing on a curved sideways path. As illustrated in Figure 2N, the lift force always acts at right angles to the spin axis and therefore is tilted to the vertical by exactly the same amount. This provides a horizontal component of the lift force, which, exactly as for a banked aircraft, produces a turn. Unlike a banked aircraft, however, which uses the coordinated effect of the rudder to keep the plane pointing in the direction of the turn, the ball continues to face in the same direction in which it left the face.
In aircraft flight terms, the ball is “slipping” sideways through the air and will strike the ground with the ball spinning backward at an angle to the direction in which it landed. This can cause balls to spin back to the side of the landing direction, a condition that can be reduced or exaggerated if the landing is on a side slope, depending on whether the tilted axis is aligned with or against the slope.
Consider the effect of a 5-degree spin axis tilt on the average PGA professional drive with a carry of 269 yards. The lifting force at the start of the flight is 1.5 times the ball weight or 0.15 pounds. The horizontal component of this force is only 0.013 pounds; and during the flight, it decreases to 0.003 pounds. However, whereas the vertical component of lift has to overcome gravity, the horizontal component has very little resistance to contend with, and so such a tiny and decreasing force can carry the ball almost 10 yards sideways. Moreover, for the
Figure 2P Effect on a slice of 17 mph tail- and headwinds.
average PGA Tour player drive, this is caused by having the face only 1 degree open or closed!