Figure 1 — Trajectories in a vacuum and in air — (a) results of altering the drag coefficient (CD) for identical launch conditions and no spin (CL = 0) — CD is typically about 0.5-0.6, so the trajectory doesn't depend very much on CD in practice; (b) results of altering the lift coefficient (CL) for the same initial launch conditions and the CD = 0.5 — CL is varied by varying the ball spin. Engineering of Sport, Research, Development and Innovation: Proceedings of the 3rd International Conference on the Engineering of Sport; Sydney, Australia. The WIRED conversation illuminates how technology is changing every aspect of our lives—from culture to business, science to design. (He later introduced graphite frames, which are even lighter and stronger.) It is the essential source of information and ideas that make sense of a world in constant transformation. As this process progresses over the surface of the ball, it is like dominoes falling on each other, such that the fuzz becomes compacted and forms a fuzz ramp as you move toward the apex of the ball. At each camera location, the ball speed is calculated from the two ball centers located by the above procedure. The drag and lift coefficients are the result of the type of air flow around the ball.

Each layer up from the surface has a higher relative velocity to the ball until a layer is reached that is no longer influenced by the frictional and viscous effects caused by the ball (known as the free stream flow). The distinguishing feature of a tennis ball is its filament surface that manifests as "fuzz" to the player.

Cross hairs were drawn at two locations on the back wall and front glass wall, all at the same height. As air streams over the ball, it no longer flows through the fibers and it is forced up the ramp and separates from the ball. Figure 25 shows an example of balls traveling about 19 m/s (43 mph). Kensrud J, Smith L (2011) In situ lift measurement of sports balls. Lindsey and Cross are science buddies, and meet every year to do new experiments---testing things like hybrid strings, racquet vibration, and the way different strings behave under stress. The lower CL indicates that there is less asymmetric wake diversion than indicated by the wind tunnel. Physics of the Tennis Kick Serve.

In the supercritical region, even though the flow is turbulent, there is a bit more friction drag due to the greater distance of attachment of the flow so the CD starts increasing. $\begingroup$ In cricket, measurement of spin bowling speed is done using Doppler radar, not high speed cameras. Tennis is a game of spin, and much attention is devoted to the mechanics and equipment for producing it. As the boundary layer develops from the front to back of the ball, it grows thicker and effectively changes the shape of the ball because the free stream flow behaves as if the edge of the boundary layer were the surface of the ball. Table 1 — Tennis ball aerodynamics research summary. One of the best ways to achieve depth of placement is to aim groundstrokes high over the net. Filming a second hand at 300 fps for exactly 10 seconds should be 3000 frames. Several wind tunnel experiments have been performed [2-7], but there is little literature regarding the actual flight of a tennis ball. This creates the "heavy ball… Straight away, I was pretty skeptical, but definitely noticed a difference. All these adverse effects can be controlled, calibrated or calculated out, but the bottom line effect may still be unknown. Figure 21 shows the setup. The variables include squishy balls, stiff racquets, taut strings, thrusting knees, twisting hips, swinging shoulders, and rotating elbows. Figure 8 — Measured results of CD vs Re (left) CD and CL vs the spin parameter S = Rω/v (right) for new tennis balls. The fuzz tries to lie down on the advancing side, gets squashed in the front, and tends to stand on the retreating side. Springer: Hoboken, 2004; 35-41. But all those mechanics are made possible by a pair of equipment innovations. However, tufts of fuzz can dislodge, standup, or otherwise protrude into the airflow, even on the forward moving side of the ball, as seen on the top of the ball in Figure 12a. 9.

At any of these 9 locations, a horizontal or vertical 5-box section should be 5 cm long if there is no distortion (though there will be some digitizing error).

A few decades later, Head sold his company, retired, and took up tennis. It may indeed be correct, but further experiments would be needed to investigate the phenomena in more detail. But, as Figure 1 shows, the presence of air introduces additional forces that alter the trajectory, namely the drag force and, for spinning balls, the lift force (aka the Magnus force). 4. "For a good topspin, you have to tilt the racquet at a good angle, too," says Crawford Lindsey, head tester at the Tennis Warehouse University, a tennis testing website (with some seriously awesome studies). Viscosity is a measure of how a fluid flows. It would be even more obvious if you tried to serve a table tennis ball or a shuttlecock over the net. The two methods agree on this. Movie Screen 1 shows an exaggerated simulation of the fuzz effect for topspin and no spin. The change in horizontal speed determines CD and the change in vertical position determines CL.

We discuss several potential error sources and how to identify or prevent them below. Free-standing vs Hand-held Racquet Testing. To do that, at each camera we filmed an object of known length in the plane of the desired trajectory (Figure 17). But today, the best strings for inducing spin are polyester. It's fairly easy to figure out what spin does: It wins tennis matches. Several surprising results were obtained: The average drag coefficient for new tennis balls was 0.507 +/- 0.024 and did not vary with spin or speed. The most comprehensive of these methods is shown in Figure 26. The fuzzy filament surface is primarily responsible for the turbulent flow around a tennis ball at all speeds of interest. Down-the-line shots are often more effective offensively but are more difficult. All tennis shots are made with some ball spin; even “flat” serves and groundstrokes have some spin. Thinner strings bury themselves deeper into the ball, and as a result, “grab” the ball, which results in more spin. A laminar boundary layer separates earlier, resulting in a larger wake. Thus, boundary layer separation will occur at different locations on the top and bottom of the ball, diverting the wake in a direction depending on the spin direction. Not only were significant quantitative differences found, but there were also qualitative differences. The net aerodynamic force is equal to the vector sum of the drag and lift forces. All spins, S ratios, and CL have been made positive. His frustration became the first aluminum skis, which he patented and used to form the Head Ski Company. CL is normally taken to be positive for backspin and negative for topspin. Even if the explanation for each behavior makes sense, why are we seeing two different behaviors needing separate explanations? Figure 16 — Measuring equal heights. Figure 17 — Distance calibrating of the camera. Ad Choices, The Mind-Bending Physics of a Tennis Ball's Spin. It is the vector summation of the the drag and lift forces, or comparably, the summation of all the aforementioned components. This is known as the drag crisis. As discussed in the setup, great care was taken to make sure the cameras were at the same height and tilt and focused in the same plane. Spin causes one side of the ball to be moving faster than the other with respect to the surrounding air, influencing transition points and boundary layer thickness. So he bought the company the made it---Prince---and invented a better version. Similarly, any combination of spin and speed that results in the same S ratio will have similar rotational air flow. Howard Head's big headed racquets let players attack the ball with more angle on their swings. Drag force increases with velocity, but at a characteristic velocity for each ball (the "critical" velocity), the drag force and drag coefficient suddenly decrease, sometimes by as much as half or more. Both topspin and backspin shots are shown. Figure 19 shows the geometry to determine this. A grid was drawn on the end wall and filmed by camera 3 to measure out-of-plane (z-axis) movement. Even though the shutter speed was 1/5000 second, by the time the bottom of the ball was exposed, the ball had moved to the right, so in effect, top and bottom were shot at slightly different locations, stretching the ball's appearance (see more examples in Appendix: Rolling Shutter and Zoom Distortion). Why then did the CD decrease at low Re in the free flight experiment?

Go to any court in any city and you will find players at every level squatting, twisting, grunting---trying to find that spin. Camera 1 will say the ball passed over the line. For that reason, if there is known distortion, it is best to limit measurements to the center of the image and to zoom in, which narrows the view to the center. Figure 25 — Rolling Shutter and Zoom distortion. Free flight study is inherently problematic due to the difficulty in accurately pin-pointing position during flight.

In: Hubbard M, Mehta RD, Pallis JM, eds. The ability to change shot direction and the understanding of the tactical advantage, or percentages, of so doing is important to overall success. Both the magnitude and behavior of the coefficients differed between the methods as Re and S varied.

From the Re equation (Equation 4), two balls, one with twice the diameter as the other, will have the same Re if the larger ball also travels at half the velocity. 13.

The main difference may be that a ball in flight is subject to variable acceleration and spin change whereas a ball in a wind tunnel is subjected to steady, stabilized air flow and speed (though unwanted vortices can occur in the test section also). (The sensor's spin scale is pretty arbitrary, so I don't have actual RPMs. "We’ve tested about 2,000 different strings," says Cross. Another mechanism is offered here to explain the low CD findings — the "fuzz ramp" effect. These numbers are essential to predicting flight path, velocity, time, and bounce of the ball. Triangles abc and ade are similar triangles so the ratio of their sides is the same.

Because the ball is a three-dimensional object, there is always part of it that is in front of the calibrated plane of motion and part of it behind. Experiments labeled as "wind tunnel drop" indicate research done by dropping a ball into the wind tunnel air flow as opposed to mounting it on a stationary sting. Figure 26 — Digitizing method to normalize for optical ball distortions and edge uncertainty.

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