The term “ball flight” was deliberately omitted in the last section. In this section, we see that the golf ball, struck by a lofted club, really does fly, and by virtue of the same principles that allow aircraft to fly. In the case of a golf ball, it results from backspin and is enhanced by dimples. The discussion of drag in the last section did not take account of the effect of the spinning ball. The intention was to explain in the simplest way the basis for aerodynamic drag and the mechanism by which dimples reduce drag. However, in all golf shots, the ball is launched with quite amazing amounts of backspin. This section is concerned with the fact that backspin changes the ball into a flying object, rather than just a passive projectile moving through the air.
For the average driver, the ball is spinning at about the speed of a car engine cruising at 55 miles per hour on the highway. In a full wedge shot, it’s spinning at the rotational speed of a race-car engine at top speed on the track. This high backspin is produced by the glancing blow of the lofted (wedge-shaped) club.
It is absolutely Figure 2D Rotating golf ball acting as a spherical fan.
central to the game of golf. It is the combination of backspin and dimples that create the special excitement of the game. The next time you hear a golf commentator say “he must have put a lot of topspin on that one,” just smile. An almost miss-hit, glancing blow across the top of the ball is the only way to create topspin.
The backspin of the ball speeds up the layer of air flowing up and over the top of the ball surface. The ball thus acts as a spherical fan, driving the layer of air, through which it is passing, slightly downward. This action is greatly enhanced by the presence of the dimples. Because by Newton’s laws, action and reaction are equal and opposite, this downward push on the air must be accompanied by an equal and opposite upward push on the ball. This is the aerodynamic lift that keeps the ball airborne much longer than would be the case if it was merely a projectile. This process is illustrated in Figure 2D. The source of this lifting force is easily defined from our previous discussion. We know that the air must speed up as it is forced to move around the ball. The rotating ball causes the air layer above the ball, assisted by the moving upper surface, to have higher speed than the air layer below the ball, which is resisted by the forward-moving lower surface. Since speed increase causes pressure drop, the pressure on top of the ball must, therefore, be lower than the pressure below the ball. The net force on the ball is thus upward, or more correctly, at right angles to the ball’s direction of travel.
This effect is precisely analogous to the effect of an aircraft wing, which bulges upward on the top surface, forcing the air to go faster over the top than across the bottom. This causes a larger pressure drop on top and a net upward pressure on the wing from the higher pressure below.
Data from wind-tunnel testing was used to illustrate the relationship between the lifting force for a dimpled ball compared to a smooth ball. Just as for the drag force, the lifting force varies with the speed squared. However, it also increases with the ratio of the rotational surface speed of the ball to the forward speed. Because we are considering a fixed ball size, we can represent this ratio in the golf units of rpm/mph, as shown in Figure 2E. This ratio increases with club loft, with the highest ratio for loftiest wedge shots. From published data on PGA players, the average
Figure 2E Relative lift of a golf ball and same-diamet
er smooth ball.
value for a 7-iron shot as the ball leaves the face is 7,000 rpm/120 mph = 58. For this case, the relative lift force from Figure 2E is approximately 0.6. In contrast, for PGA players, the average drive ratio is 2,700/165 = 16, with a relative lift factor from Figure 2E of approximately 0.3.
With a smooth ball, the 7-iron shot would produce a relative aerodynamic lift of only about 0.15; for the drive, the “lifting” force can actually become negative and pull the ball downward, considerably shortening the flight. The reason for this unlikely behavior can be seen in Figure 2B, where the relative drag can be seen to start decreasing slowly around the 165 miles per hour ball speed of the PGA Tour average drive. With backspin, the bottom surface is traveling faster through the air than the lower surface, so more favorable air flow conditions exist underneath the ball. In particular, the airflow below can now separate later than above, the opposite of that shown in Figure 2D.
Recall that the actual lift force increases with the ball speed squared; so, to compare the lifting force for the drive and the 7-iron shots, we need to take the ratio of 0.3 × (1652) to 0.6 × (1202), which gives 0.95. The actual lift force acting on the ball as it launched in the PGA average drive can be calculated from wind-tunnel testing data to be 0.153 pounds. For the PGA 7-iron shot, the calculated value is 0.166 pounds. The ratio of these two values is 0.92, in close agreement to our approximate estimate from Figure 2E. The weight of a golf ball is 0.10 pounds, so these lift forces are approximately 1.5 times the ball weight. Thus, in the initial phase of ball flight, the ball is actually climbing at a progressively higher rate. This can be seen very clearly in the long iron shots of powerful players when viewed from behind. The ball can be seen to curve upward slightly in the first half or so of the flight.
It will be shown later in the chapter that the relative drag force, like the life force, is also very strongly dependent on the ball’s backspin/speed ratio. That is, a golf ball traveling at 100 miles per hour with a backspin rate of 4,000 revolutions per minute will experience approximately the same relative drag force as a ball at 50 miles per hour with 2,000 revolutions per minute backspin. This is interesting from a physics perspective, but for our present purposes, it allows us to present all of the necessary
It is absolutely Figure 2D Rotating golf ball acting as a spherical fan.
central to the game of golf. It is the combination of backspin and dimples that create the special excitement of the game. The next time you hear a golf commentator say “he must have put a lot of topspin on that one,” just smile. An almost miss-hit, glancing blow across the top of the ball is the only way to create topspin.
This effect is precisely analogous to the effect of an aircraft wing, which bulges upward on the top surface, forcing the air to go faster over the top than across the bottom. This causes a larger pressure drop on top and a net upward pressure on the wing from the higher pressure below.
Data from wind-tunnel testing was used to illustrate the relationship between the lifting force for a dimpled ball compared to a smooth ball. Just as for the drag force, the lifting force varies with the speed squared. However, it also increases with the ratio of the rotational surface speed of the ball to the forward speed. Because we are considering a fixed ball size, we can represent this ratio in the golf units of rpm/mph, as shown in Figure 2E. This ratio increases with club loft, with the highest ratio for loftiest wedge shots. From published data on PGA players, the average
er smooth ball.value for a 7-iron shot as the ball leaves the face is 7,000 rpm/120 mph = 58. For this case, the relative lift force from Figure 2E is approximately 0.6. In contrast, for PGA players, the average drive ratio is 2,700/165 = 16, with a relative lift factor from Figure 2E of approximately 0.3.
With a smooth ball, the 7-iron shot would produce a relative aerodynamic lift of only about 0.15; for the drive, the “lifting” force can actually become negative and pull the ball downward, considerably shortening the flight. The reason for this unlikely behavior can be seen in Figure 2B, where the relative drag can be seen to start decreasing slowly around the 165 miles per hour ball speed of the PGA Tour average drive. With backspin, the bottom surface is traveling faster through the air than the lower surface, so more favorable air flow conditions exist underneath the ball. In particular, the airflow below can now separate later than above, the opposite of that shown in Figure 2D.
Recall that the actual lift force increases with the ball speed squared; so, to compare the lifting force for the drive and the 7-iron shots, we need to take the ratio of 0.3 × (1652) to 0.6 × (1202), which gives 0.95. The actual lift force acting on the ball as it launched in the PGA average drive can be calculated from wind-tunnel testing data to be 0.153 pounds. For the PGA 7-iron shot, the calculated value is 0.166 pounds. The ratio of these two values is 0.92, in close agreement to our approximate estimate from Figure 2E. The weight of a golf ball is 0.10 pounds, so these lift forces are approximately 1.5 times the ball weight. Thus, in the initial phase of ball flight, the ball is actually climbing at a progressively higher rate. This can be seen very clearly in the long iron shots of powerful players when viewed from behind. The ball can be seen to curve upward slightly in the first half or so of the flight.
