Engineering tennis - slowing the game down

Abstract

Analysis of results from the four major tennis tournaments shows that the percentage of tie breaks in the men’s game has been increasing over the last 30 years. It is hypothesised that this is due to the increasing speed of the serve in the game. There was found to be a significant difference in tie breaks between slower clay surfaces and faster grass surfaces. The women’s game, on the other hand, showed no increase in tie‐breaks and no difference in the number of tie‐breaks between court surfaces. A larger tennis ball was assessed to see its effect in slowing the game down. Standard and 6% larger pressurised tennis balls were used in experiments to study impacts with a fixed and a freely suspended tennis racket. The coefficient of restitution of the larger ball was found to be larger in the fixed racket tests and analysis of a serve showed that the larger ball would be served marginally faster than a standard sized ball. Drag forces on tennis balls in flight were analysed by mounting tennis balls in a wind tunnel at wind speeds up to 66.6 ms−1 (150 mph). It was found that different brands of standard size tennis ball and a larger tennis ball had a drag coefficient of approximately 0.55. Raising or reducing the nap of the ball changed the drag coefficient by about 10%. Impact experiments of tennis balls on court surfaces showed that the larger and standard tennis balls rebounded at approximately the same speed at 70% of impact speed on acrylic and 64% of impact speed on clay. Both sizes of ball bounced steeper off clay than on acrylic. It appeared that the larger ball rebounded steeper than the standard ball, although evidence for this was clouded by considerable scatter in the data. A computer trajectory program was used to analyse simulated first and second serves at nominally 53.3 ms−1 (120 mph) and 40 ms−1 (90 mph). It was found that a larger ball would increase travel time to the baseline by approximately 10 ms for a first serve and up to 16 ms for a second serve. This increase was found to be just less than half that between acrylic and clay for the same ball. Travel time is increased further if the ball is increased in diameter. It was concluded therefore that the introduction of a larger ball could slow the game of tennis for all strokes and increase the time available for the receiver to return the ball.

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“…on performance indicators should not be underestimated. The current research shows that the duration of a tennis match is related to the surface speed and the type of ball (Hughes & Clarke, 1995;Haake & Coe, 2000;Unierzyski & Wieczorek, 2004;Miller, 2006;Gillet & Leroy, 2009;Takahashi, et al, 2009) , a player's ranking, tactics, game style (Verlinden, et al 2004;Gillet & Leroy, 2009;Reid, et al, 2010) , and the opponent's characteristics. The association between the player and the opponent is important but, to the knowledge of the authors, no study has analysed interdependence between observed subjects.…”

Review of tennis ball aerodynamics

“…The initial measurements gave a C D of approximately 0.52 for a standard tennis ball and it was found to be independent of Re over the range, 200 000oReo270 000. Chadwick and Haake [16] and Haake et al [9] reported that C D ffi0.55 over the same Re range for a standard tennis ball, a pressureless ball and a larger ball. The difference between the two reported C D levels is attributed to the technique used to measure the ball diameter [5].…”

“…Chadwick and Haake [15] used an outer (projected) diameter, which included the nap or fuzz height. Their results also showed that the tennis ball C D could be increased (by raising the fuzz) or decreased (by shaving off the fuzz) by up to 10% [9,15,16].…”

“…It was therefore deduced that for Reynolds numbers normally encountered during a serve, 100 000oReo200 000 (corresponding to a serving velocity range of 26oUo46 m/s [93.6oUo165.5 km/h]), the ball would be in the supercritical regime giving a drag coefficient of approximately 0.3 to 0.4. However, recent measurements on nonspinning tennis balls [9][10][11][12][13][14] showed that the drag coefficient was higher and appeared to be independent of Reynolds number.…”

Understanding the Effect of Seams on the Aerodynamics of an Association Football

“…Previous studies on ball aerodynamics include that by Bearman and Harvey [3] who found that dimples on a golf ball serve to reduce the critical Reynolds number indicating that surface geometry can have a significant effect on ball flight. Studies related to other sports including cricket [1], tennis [4], baseball [5], volleyball [6] have measured the drag and Magnus forces experienced by a ball during flight for varying velocity and spin conditions and examined the effect on transition and boundary layer separation. This work built on ground-breaking research by Achenbach [7,8] on the aerodynamics of smooth and rough spheres, which showed that increased surface roughness encourages transition to occur at low values of Reynolds number.…”