Sports Biomechanics

There has been long debate over the exact mechanism responsible for the development of the lift force on spherical objects such as the golf ball. In 1672, Isaac Newton first noted how a tennis ball’s flight was affected by spin (this was real, or royal, tennis, not modern lawn tennis). Seventy years later (1742), Benjamin Robins showed that a rotating sphere, such as a ball, was associated with a sideways (transverse) force. However, the first explanation of the lateral movement of a spinning ball is attributed to H.G. Magnus who, in 1852, showed that the sideways force was proportional to the speed of the air over the ball and the speed of the spin of the ball. Magnus was actually tasked to understand why artillery shells and cannonballs tended to swerve under some conditions, but also had a keen interest in table tennis and noticed that the ball could swing or dip if appropriate spin was placed on it. The most common explanation is that a spinning ball ‘grabs’ the air that flows past it because of the friction between the air and the ball, so these air particles start to spin with the ball (i.e. the boundary layer of air spins). As you can see in Figure 16.1, the collision between the oncoming air and the ball or air spinning with it causes air on one side of the ball to slow down. On the other side of the ball, the air moves past relatively unimpeded. The speed of air on one side of the ball is thus less than the speed on the other side. As you know (from Chapter 15), slow-moving air is associated with higher pressure whereas faster-moving air is associated with lower pressure, according to Bernoulli’s theorem. Thus, we have a pressure differential.

FIG. 16.2 In (A), the club hits the ball straight with an appropriately oriented club face. The ball is hit without side spin and travels straight off the clubface. In (B), the clubface is angled slightly, which puts spin on the ball. Because the angle at which the ball was struck was also altered slightly, the ball started straight, but then swerved in the air due to the Magnus effect.

Life is never quite that simple. More recent studies have shown that only the air that is very close to the ball is dragged around by its spin, so the layer of air trapped against the ball and moving with it (the boundary layer) is also very small; so many believe that the explanations based on the Bernoulli effect are not accurate. However, the collision between the slow-moving air on one side of the ball and the oncoming air causes the air to deflect off the ball sooner, as shown in Figure 16.3. That is, ‘boundary layer separation’, or the separation of the boundary layer from the ball, occurs earlier. The air on the other side of the ball deflects much later and rushes towards the lower pressure area behind the ball. According to Newton’s Third Law, since these masses of air changed their velocities (both magnitude and direction) a force must have been applied. There must therefore be an equal and opposite force, which pushes the ball in the opposite direction (i.e. downwards in Figure 16.3). So the lift force on a spinning ball can be well explained using Newton’s laws.

Regardless of the explanation for the forces created around a spinning object, the problem facing golfers is that spin is imparted on the ball by the club, even though the ball was hit in the right direction. The ball starts off straight but the spin creates a sideways lift force that takes the ball off-line. Depending of the direction of swing, the movement of the ball is called a slice (if it swings to the right for a right-handed golfer) or a hook (if it swings to the left). Golfers have to understand how to manipulate their technique to ensure that spin is not imparted to the ball, unless they deliberately want to swing the ball around an obstacle.

BOX 16.1 THE MATHEMATICS OF THE MAGNUS EFFECT

The mechanisms contributing to the Magnus effect are complex and it would take a massive mathematical effort to predict the effects of changes in ball speed, wind speed or rotation speed on the amount of curve of a ball.

Broadly, the faster a ball travels or spins, the greater will be the Magnus force. Therefore, if the ball is travelling into the wind (i.e. the relative speed of ball and air is greater), the ball will swerve more for less imparted spin. So, in tennis, it might be good to hit into the wind because you can hit with greater horizontal speed and need worry less about trying to apply topspin. But if you were an inexperienced soccer player trying to kick the ball straight, it might be better to kick with the wind, since even a small amount of rotation on the ball will cause it to swerve and miss its target.

Unfortunately, the trajectories of balls are far more complex. For example, you saw in Chapter 13 that drag forces on an object were velocity-dependent, in that drag generally increased with the square of velocity but that at a critical velocity there was a marked reduction. This highlights the fact that the speed of air flow around a ball and the formation and stability of the boundary layer also vary with ball speed. Some examples of how ball speeds influence the movement of balls in sport are briefly described below…

Golf balls: as we have just learned, a spinning golf ball will swerve off-line. In fact, the flight path of a spinning ball is that of a parabola (see Figure 1), so the swerve in the first half of the flight is far less than in the second half. This gives the impression that the ball started travelling straight and then swerved later. As expected, the swerve of the ball is greater for faster spin rates and the magnitude of swerve will increase with ball velocity; however, there is some data showing that the amount of swerve per travel distance is greater for a slower golf ball (Bearman & Harvey, 1976).

FIG. 1 The sideways deviation of a golf ball influenced by the Magnus force is parabolic.

Baseballs: the curveball is pitched with side spin on the ball so that a sideways Magnus force is generated. A faster spin rate or pitch speed causes a greater sideways movement. In fastball pitches, backspin is placed on the ball. This creates an upward Magnus force which, if of sufficient spin speed, is thought to be responsible for the ball tending to rise as it nears the batter (the so-called rising fastball). In fact, research has shown that the upward force is probably only about half that required to overcome the weight of the ball so, while the pitch may not dip as far as expected, it does not actually rise (Alaways, 1998). For all pitches the seams on the ball increase the Magnus force because the roughened surface reduces the velocity at which the boundary layer is tripped towards turbulence. Pitchers may throw the ball such that either two or four seams tend to rotate to the front of the ball; the four-seam pitches produce more dramatic changes in trajectory although this is probably less pronounced at higher ball spin rates.

Soccer (football) balls and volleyball s: clearly, imparting spin on these balls will cause a Magnus effect. But, in fact, slower-moving balls have been shown to produce greater swerve (Asai et al., 2007). So curvature of a ball may increase later in the ball flight when the effects of drag slow the ball. Asai and colleagues also showed the drag increased when the spin rate of the ball was increased. An interesting flight path can be obtained with soccer balls and volleyballs because the panels that comprise the ball ensure that the surface roughness varies as the ball rotates during flight. This allows the so-called ‘floater’ to be produced, whereby projecting the ball without spin can cause unpredictable swerving that varies during flight. As the ball is first projected the uneven surface causes flow variations that cause swerve. The surface friction variability also causes the ball to rotate slightly and for a different region of the ball to face the oncoming air. This will cause a new swerve of the ball, dependent on the variability in roughness, and a further rotation of the ball. This continuing effect through the flight path causes the inconsistency in flight. Another important phenomenon is the ability to project these balls at speeds faster than the critical speed, where the coefficient of drag (and therefore the drag force) decreases rapidly (see Box 13.1 again). In this case the ball continues to move very rapidly through the air without slowing substantially. The ability to hit or kick a ball fast enough, especially without spin where the flight path is unpredictable, is a good one to have.

Cricket balls: while spin bowlers can see significant swerve as the ball travels down the pitch, the greatest swerve (or swing as it is called in cricket) occurs when fast bowlers bowl the ball with its seam appropriately angled. When a ball is new it can swing if the seam remains perfectly upright during ball travel. This is because irregularities on the ball (usually the manufacturer’s printed logo) cause a greater roughness on one side and thus an imbalance in air pressure s (the ball swings towards the rough side). Because there is little roughness, swing is obtained only by the fastest bowlers because the aerodynamic effects are amplified at high speeds. As the ball becomes rougher during play it becomes more likely to swing at slower speeds, as long as one side remains smoother than the other. This type of swing is often referred to as ‘contrast swing’.

It is also possible to increase the swing by bowling the ball with the seam pointed about 20° to one side. The seam acts to trip the boundary layer towards turbulence, thus reducing air pressure on that side. The ball swings to the side that the seam was pointing (what is called ‘traditional swing’). Bowlers often impart a backspin on the ball as it’s bowled. This would not only stabilise the orientation of the ball in flight (as described in Chapter 13) but also increase the magnitude of the effect: swing is greater when backspin is placed on the ball (Mehta, 2005). As the ball gets even rougher the boundary layer is tripped more easily. The roughest side can then cause enough turbulence that drag is reduced (much like the dimples on a golf ball); in this case the drag on the smooth side is actually greater than the drag on the rough side. At fast ball speeds, an effect can be created where the ball swings away from the rough side. To increase the amount of the smooth side facing the oncoming air, the ball is often bowled with the seam angled (much like ‘traditional swing’); however, instead of the ball swinging towards the angled seam the ball swings away from it, towards the smooth side of the ball. This unexpected direction of swing is often referred to as ‘reverse swing’. Despite some anecdotal accounts, it is not necessary to wet the rougher side of the ball to obtain this effect. Another point of interest is that sometimes the ball appears to swing late. This might happen in some instances when the slowing of the ball is associated with a greater swing (e.g. traditional swing); however, the decrease in ball velocity is not great enough to have a large effect. More likely, the observation simply reflects the typical parabolic trajectory of the swinging ball, as shown in Figure 1.