The effects of lift and drag described in the previous section may be surprising to anyone unfamiliar with aerodynamic forces. To put these in some context, the average automobile, under full braking, takes at least 120 feet to stop from 60 miles per hour, which is a deceleration of approximately 1 “g.” The explanation, for decelerations as high as 2.5 g acting on a driven golf ball, is simply the surprising density of the air. To obtain the actual forces, the relative force values in Figures 2E and 2F are multiplied by the cross-sectional area of the ball, the ball speed squared, and the density of air. The density of air under standard atmospheric conditions at sea level is 1.2 kilograms per cubic meter. In more familiar terms, a 3 × 3 × 3 foot cardboard box contains 2 pounds of air; or in more appropriate terms, the weight of air that is displaced by a 0.1 pound, 1.68 inch diameter golf ball, over the trajectory length of a 269 yard drive, is 1.2 pounds. Two things are immediately obvious from these calculations. First, a golf ball with the same launch conditions in thinner, less dense, air will no doubt fly further. Second, a lighter ball of the same diameter will be subject to the same aerodynamic forces and so will be influenced more by them.
To see the effects of atmospheric changes, the trajectory using the average PGA Tour launch conditions was modeled with the same ball strike conditions but in the mile-high city of Denver, Colorado. The air density there is 12 percent less on average than at golf courses much nearer to sea level. So all that is needed is to reduce the lift and drag forces by 12 percent.
To test the effect of using a lighter ball, we assume the use of the floating balls at some golf resorts for driving out over water. These have a weight of 39 grams compared to 45 grams for the regular ball. They are also typical range balls, which have hard rugged covers for long life and do not grip the face to provide the spin rates of the premium golf balls. For this exercise, they are assumed to have the performance of the modern premium ball. However, we do need to step ahead to some of the results from Chapter 3. If a 39-gram ball is struck with the same club head speed and club loft as a 45-gram ball, it will launch at a lower angle with a higher speed and spin rate. The new launch values in this case will be: ball speed = 168.5 miles per hour; spin rate = 2,973 revolutions per minute; and launch angle = 11.0 degrees. The reason for these changes will be evident in the descriptions of ball striking in Chapter 3. For now, all that is needed is a re-run of the six steps used to determine ball trajectory, for the changed launch conditions and ball weight. The results of these calculations are given in Figure 2J.
It is evident that the lighter ball is influenced to a significantly higher degree by the lift and drag forces. The trajectory can be seen to curve slightly upward over the first third or so of the carry distance. Also, the increased efficiency of the drag force, combined with the higher climb, has resulted in the ball dropping 18 yards shorter than the regular weight ball. The use of a lighter ball has been suggested in the past as a means of limiting the distance of touring professional drives. These calculations would seem to support the validity of that proposal. However, as discussed in a later
Figure 2J Effects of an average PGA Tour player drive using a 39 g floating ball or playing a
standard ball in Denver, Colorado, standard atmospheric conditions.
section, hooks, and slices also result from the aerodynamic forces, and a lighter ball would make direction control considerably more difficult for the average golfer.
The 12 percent lower air density in Denver lowers both lift and drag. It can be seen that as a result, the ball climbs about 9 feet less but still carries 13 yards further. Teeing the ball up further to increase the launch angle and flight time would be a good strategy there.
THE EFFECTS OF HEAD- AND TAILWINDS:
As we have discussed, a golf ball flying through the air is subjected only to gravity and the aerodynamic forces of drag and lift. The latter two forces depend on the square of the ball speed with respect to the air. So when subjected to a headwind, the wind does not blow the ball in the everyday sense. It simply increases the ball speed with respect to the air, as illustrated in Figure 2K. Because of this, it will be subjected to increased lift and drag. The increased lift will make it fly higher, and the increased drag will make it fall shorter.
Conversely, if the ball is struck into a tailwind, its speed with respect to the air is decreased. Drag and lift will then be reduced, and the ball will fly lower but generally go further.
Consider a 7-iron shot, with a club head speed of 85 miles per hour and a ball launch speed of 110 miles per hour, played into a 10 miles per hour headwind. At launch, the ball speed with respect to the air is increased to 120 miles per hour. Since the aerodynamic forces increase by the square of the velocity, they will increase compared to still air by the factor (120/110)2 = 1.19. So the lift and drag will increase by 19 percent. Conversely, in the 10 miles per hour tailwind, the factor will be(100/110)2 = 0.83, so lift and drag will decrease by 17 percent.
Figure 2K Effect of a headwind on ball flight.
Figure 2L Effect of 10 mph head- and tailwinds on a 145 yd., 7-iron shot; with the headwind, 126
yd.; with the tailwind, 162 yds.
A simulation of this 7-iron shot in the still air, and with 10 miles per hour head- and tailwinds are given in Figure 2L. In this case, the changes in carrying are +17 yards for the tailwind and −19 yards for the headwind. The middle trajectory is the ball path in the still air.
These differences are clearly of great significance when making approach shots into a green. Since the differences in carrying are caused by the changes in the aerodynamic forces, the time of flight is a large determining factor. For this reason, in high winds a lower trajectory approach shot with a lower-lofted club, resulting in a shorter flight time, is often a safer selection. Note that at the bottom of Figure 2L, the “attack angle” value is given as −4.7 degrees. This means that the club has struck the ball on a downward club path, inclined at −4.7 degrees to the fairway surface. This negative attack of the ball is standard procedure for elite players. It allows them to lower the trajectory of the ball for more penetrating shots while still getting a high backspin rate. The follow-through of this, after the ball has flown, is the taking of a divot. If the ball had been struck with a horizontal attack, the launch angle would have been higher, the flight longer, and the effect of the head- and tailwinds even more pronounced.
Figure 2M shows the trajectories for the same nominal distance with a 5-iron using a reduced swing speed. The distances, in this case, are 145 yards in the still air as for the 7-iron shot, 132 yards with a 10 miles per hour headwind, and 154 yards with a 10 miles per hour tailwind. The differences are +9 yards for the tailwind and −13 yards for the headwind. This means that with only rough estimates of wind speed available to the player, the low 5-iron shots have the potential for significantly less error than the much higher, longer-flying-time, 7-iron ones. This is no doubt the reason why the “bump and run” approach shots are so often seen on the windblown links courses of Scotland and Ireland.