Experimental and theoretical study of the oblique impact of a tennis ball with a racket

Abstract

The normal and the oblique impact of a tennis ball with a racket has been studied. An accurate setup has been built in order to provide consistent initial conditions for the impacts. Experiments have been done for a wide range of impact angles and initial velocities. The motion of the ball before, during and after the impact has been recorded using a high-speed camera with 10,000 frames per second. The impact has been divided into two phases, compression and restitution. An expression for the contact force has been provided. The coefficient of restitution and effective coefficient of friction have been analyzed experimentally. For low impact velocities, the coefficient of restitution is constant at different impact angles. The effective coefficient of friction changes as a function of the impact angle. The contact force expression has been determined for the compression and the restitution phases using the experimental data from normal impact experiments. The simulation and experimental results are compared and verified for the normal and the oblique impacts.

Keywords

Impact tennis ball friction image processing string bed contact force

Get full access to this article

View all access options for this article.

References

Garwin

. Kinematics of an ultraelastic rough ball. Am J Phys 1969; 37(1): 88–92.

Brody

. That’s how the ball bounces. Phys Teach 1984; 22(8): 494–497.

Cross

. Dynamic properties of tennis balls. Sports Eng 1999; 2: 23–34.

Haake

Carre

Goodwill

. The dynamic impact characteristics of tennis balls with tennis rackets. J Sport Sci 2003; 21(10): 839–850.

Dignall

Haake

. Analytical modelling of the impact of tennis balls on court surface. In: Haake

Coe

(eds) Tennis science and technology. Oxford: Blackwell, 2000, pp.155–162.

Cross

. Measurements of the horizontal and vertical speeds of tennis courts. Sports Eng 2003; 6(2): 95–111.

Goodwill

Kirk

Haake

. Experimental and finite element analysis of a tennis ball impact on a rigid surface. Sports Eng 2005; 8(3): 145–158.

Cross

. Measurements of the horizontal coefficient of restitution for a superball and a tennis ball. Am J Phys 2002; 70(5): 482–489.

Cross

. Effects of friction between the ball and strings in tennis. Sports Eng 2000; 3(2): 85–97.

10.

Cross

. Grip-slip behavior of a bouncing ball. Am J Phys 2002; 70(11): 1093–1102.

11.

Cross

. Oblique impact of a tennis ball on the strings of a tennis racket. Sports Eng 2003; 6(4): 235–254.

12.

Goodwill

Haake

. Spring damper model of an impact between a tennis ball and racket. Proc IMechE, Part C: J Mechanical Engineering Science 2001; 215(11): 1331–1341.

13.

Goodwill

Haake

. Modelling of tennis ball impacts on a rigid surface. Proc IMechE, Part C: J Mechanical Engineering Science 2004; 218(10): 1139–1153.

14.

Païdoussis

Botez

. Chaotic dynamics of articulated cylinders in confined axial flow. J Fluid Struct 1993; 7(7): 719–750.

15.

Botez

Païdoussis

. Dynamics of an articulated cylinder in annular flow via non-linear and partially linearized versions of an analytical model. J Sound Vib 1996; 192(3): 645–668.

16.

Yang

Fafitis

Wiezel

. Nonlinear impact model of a tennis racket and a ball. J Mech Sci Technol 2012; 26(2): 315–321.

17.

Allen

Goodwill

Haake

. Experimental validation of a finite-element model of a tennis racket string-bed (P21). The Engineering of Sport 7. Springer Paris 2008; 115–123.

18.

Allen

Haake

Goodwill

. Comparison of a finite element model of a tennis racket to experimental data. Sports Eng 2009; 12(2): 87–98.

19.

Allen

Haake

Goodwill

. Effect of friction on tennis ball impacts. Proc IMechE, Part P: J Sports Engineering and Technology 2010; 224(3): 229–236.

20.

Maeda

Okauchi

. Properties of friction during the impact between tennis racket surface and ball. Procedia Eng 2010; 2(2): 2973–2978.

21.

Stronge

. Rigid body collisions with friction. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 1990; 431(1881): 169–181.

22.

Kogut

Etsion

. Elastic-plastic contact analysis of a sphere and a rigid flat. J Appl Mech: T ASME 2002; 69(5): 657–662.

23.

Jackson

Chusoipin

Green

. A finite element study of the residual stress and strain formation in spherical contacts. J Tribol: T ASME 2010; 60(3): 217–229.

24.

Kogut

Komvopoulos

. Analysis of the spherical indentation cycle for elastic-perfectly plastic solids. J Mater Res 2002; 19(12): 3641–3653.

25.

Goldsmith

. Impact. Courier Dover Publications, 2001. New York, USA

26.

Shapiro

Stockman

. Computer vision. Englewood Cliffs, NJ: Prentice Hall, 2001.

27.

Stockman

Agrawala

. Equivalence of Hough curve detection to template matching. Commun ACM 1977; 20(11): 820–822.

28.

Brody

Cross

Lindsey

. The physics and technology of tennis. Solana Beach, CA: Racquet Tech Publishing, 2002.