Recommendations for estimating the moments of inertia of a tennis racket

Tennis racket properties are of interest to sports engineers and designers as it allows them to evaluate performance, review trends and compare designs. This study explored mathematical models that correlated to the mass moments of inertia of a tennis racket, both about an axis through the butt and about the longitudinal axis, using its dimensions, mass and centre of mass location. The models were tested on 416 rackets, dating from 1874 to 2017. Results showed that moments of inertia about the butt and longitudinal axis can be estimated to within − 4 to 5% and − 11 to 12% of measured values, respectively, using the proposed models on original rackets. When rackets were customised, with 30 g of additional mass, moment of inertia about the butt could be estimated within 6%, but the model for moment of inertia about the longitudinal axis was less accurate (largest error at 25%). A Stepwise Linear Regression model indicated that racket mass and then centre of mass location had the largest effect on moment of inertia about the handle, with head width having the largest effect on moment of inertia about the longitudinal axis.

[1]  David James,et al.  Effects of moment of inertia on restricted motion swing speed , 2015, Sports biomechanics.

[2]  Rod Cross.  Impact of sports balls with striking implements , 2014 .

[3]  D. Altman,et al.  STATISTICAL METHODS FOR ASSESSING AGREEMENT BETWEEN TWO METHODS OF CLINICAL MEASUREMENT , 1986, The Lancet.

[4]  Howard Brody.  The moment of inertia of a tennis racket , 1985 .

[5]  Simon Richard Goodwill.  The dynamics of tennis ball impacts on tennis rackets. , 2002 .

[6]  Steve Haake,et al.  Comparison of a finite element model of a tennis racket to experimental data , 2009 .

[7]  J M Bland,et al.  Statistical methods for assessing agreement between two methods of clinical measurement , 1986 .

[8]  Steve Haake,et al.  Recommendations for Measuring Tennis Racket Parameters , 2018 .

[9]  John Eric Goff,et al.  Resources for sports engineering education , 2018 .

[10]  Crawford Lindsey,et al.  The physics and technology of tennis , 2004 .

[11]  Rod Cross.  Customising a tennis racket by adding weights , 2001 .

[12]  Rod Cross,et al.  Performance versus moment of inertia of sporting implements , 2009 .

[13]  Rod Cross,et al.  Technical Tennis: Racquets, Strings, Balls, Courts, Spin, and Bounce , 2005 .

[14]  Simon Goodwill,et al.  ScienceDirect The 2014 conference of the International Sports Engineering Association Measuring the inertial properties of a tennis racket , 2014 .

[15]  Simon Choppin,et al.  A review of tennis racket performance parameters , 2016 .

[16]  Simon Choppin.  An investigation into the power point in tennis , 2013 .

[17]  Sean R. Mitchell,et al.  Head speed vs. racket inertia in the tennis serve , 2000 .

[18]  Steve Haake,et al.  The evolution of the tennis racket and its effect on serve speed , 2007 .

[19]  S. Miller,et al.  Modern tennis rackets, balls, and surfaces , 2006, British Journal of Sports Medicine.

[20]  Marcus Dunn,et al.  Tennis Equipment and Technique Interactions on Risk of Overuse Injuries , 2018 .

[21]  R. Cross,et al.  Performance versus moment of inertia of sporting implements , 2009 .

[22]  98.08 The moment of inertia of an elliptical wire , 2014, The Mathematical Gazette.

[23]  Brendan Lay,et al.  The effect of racquet swing weight on serve kinematics in elite adolescent female tennis players. , 2014, Journal of science and medicine in sport.