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Going into the second week of the US Open, we’ve been treated to some incredible tennis, though so far its been more moments of brilliance as opposed to sustained three-hour bouts of amazingness if we’re honest. That said, Danil Medvedev and Nick Kyrgios had some spice and even a decent degree of saltiness.
Most of us are not inclined to consider everything from a deeply analytical and scientific point of view. When we watch a tennis match, we see a struggle between two opponents for dominance and subsequent victory. For the smattering of people more concerned about aerodynamics, a match consists of a bright yellow mystery being swatted back and forth.
It shouldn’t come as a surprise that the world around us and the objects we take for granted is full of scientific wonder. Cascading bubbles in a freshly poured pint of Guinness. A nasty curveball or a free-kick bending toward goal. You can add the flight of a tennis ball to the list of mundane marvels.
Tennis balls measure roughly 63.5mm to 69mm (Wilson Rally balls) in diameter and weigh anywhere between 57 and 59 grams. They are known for their most distinctive feature, the yellow fuzz that is referred to as nap. Like baseballs, they have seams that are indented in relation to the ball’s nap.
Due to their shape and its subsequent effect on air as it cuts a path through it, balls are treated similarly to cylinders in aerodynamics and are considered bluff bodies. What this means is that the flight of the projectile through air is hindered less by friction between the ball and air and more by the various pockets of pressure that form around the ball due to the its motion.
When a ball is in flight, the air next to the surface of the object – the molecules of the air – sticks to the surface. This thin layer of molecules pulls on the surrounding flow of air. The relative strength of the inertial (momentum) and viscous forces in the flow determines how the flow moves around the object and the value of the drag of the object.
The drag on a ball is being generated by the boundary layer separating from the back of the ball. As the flow separates, it creates a viscous wake behind the ball. This causes a pocket of air to form behind the ball containing tiny vortices of air that alters the pressure in the so-called wake of the projectile.
Rather than friction drag, the bulk of the total drag on a tennis ball is accounted for by pressure drag, which in turn is determined solely by the boundary layer separation location on the ball. As the ball punctures the air, a layer forms on the front end that is orderly (called laminar flow). However, it eventually breaks down and separates from the surface and forms the wake of the ball’s flight, as can be seen in the following images. A large, wide wake generates a large amount of drag; a thin wake produces less drag. The thickness of the wake, and the drag on the ball, depends on the conditions in the boundary layer.
For balls with a smooth surface, the separation occurs just before the apex of the ball, causing drag pressure from the wake to form earlier.
For roughened balls and spinning balls (see above) the separation is delayed enough that it forms on the other side of the ball’s apex.
This slight change keeps the ball on course for longer. Experiments have demonstrated that a roughened ball will transition to turbulent flow at a lower Reynolds number (the metric that indicates when laminar flow transitions to turbulent) than a smooth ball. The result is something that is counterintuitive.
For a small range of Reynolds numbers, the drag of a roughened ball is less than the drag of a smooth ball for the same size, velocity and flow conditions. This means that the roughened ball will actually be more aerodynamic than the smooth ball. A good example of this is the size and speed of a golf ball. They fall within this goldilocks zone of Reynolds number range. That is why a golf ball has dimples; the roughened surface causes transition to turbulence that would not occur yet on a smooth golf ball. The lower drag on the dimpled golf ball allows it to fly farther.
Wind tunnel experiments have shown that something similar happens with new tennis balls, only the fuzz acts in place of dimples to disrupt airflow and increase its flight aerodynamics. However, once the balls are used, the fuzz becomes a variable that can work for or against the ball’s drag. Balls that become worn down (loss of nap) experience a decrease in drag while a fluffy ball experiences an increase.
In reality, very few shots in tennis are completely flat (no spin). In fact, spin is the name of the game in tennis. Once spin is introduced into the analysis of a ball’s aerodynamics things get very complicated as Magnus forces come into play. Our earlier models only featured front-to-back drag forces and the perpendicular force exerted by weight. Spinning balls generate sideways pressure that is described by Magnus forces. This causes the ball to deviate from its non-spinning trajectory, the most obvious example being Rafael Nadal’s quick dipping heavy topspin shots.
Before we go, there’s one more thing worth noting. Science being science, there’s always a study that manages to throw a spanner in the works. In this case, a study done by Rod Cross (featured in the video about Magnus forces) and Crawford Lindsey indicated that real-world drag data differs from those collected in wind tunnels and that lift plays a more significant role than drag when it comes to a tennis ball’s trajectory.
The mystery continues…
WORDS: Marc Landas.