Recommendations for Measuring Tennis Racket Parameters

Allen, Tom; Grant, Robyn A.; Sullivan, Matthew; Taraborrelli, Luca; Choppin, Simon; Spurr, James; Haake, Steve

doi:10.3390/proceedings2060263

Cited by 8 publications

(26 citation statements)

References 9 publications

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“…Four rackets were from the International Tennis Federation (ITF), and three were from the Manchester Metropolitan University collection. Measurements of 100 rackets were available from [15]. Only strung rackets were selected in the study, although it was possible to have broken strings in old specimens.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…I x′ and I y were measured using a simple pendulum and bifilar pendulum, respectively, similar to [15]. Both techniques have been shown to measure the MOI of rods to within 2% of theoretical values [15,16]. A frame assembled from aluminium profiles (Rexroth Bosch Group, section 30 × 30 mm) was used for the pendulum tests, and a calibration was performed to check the accuracy of the rig.…”

Section: Methodsmentioning

confidence: 99%

“…Observing historical trends allows us to evaluate how materials and design have changed the racket, and hence the game [8], which could provide useful insights for product development, regulation and injury prevention strategies [12,13], as well as spectator experience and education purposes [14]. Allen et al [15] measured a range of parameters, including I x′ and I z′ , in 100 rackets from different eras employing simple, low-cost and portable tools. They concluded that, since I x′ and I z′ were similar in magnitude, as detailed in Brody [2], measuring both is not always necessary when characterising a large number of rackets.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this research was to assess the accuracy of the models for I x′ used by Allen et al [15], as well as two models of I y . This process identified the parameters that influence these MOIs and quantified their effects, using 416 diverse rackets.…”

Section: Introductionmentioning

confidence: 99%

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Recommendations for estimating the moments of inertia of a tennis racket

et al. 2019

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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.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Recommendations for estimating the moments of inertia of a tennis racket

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Methods for estimating moment of inertia of cricket bats

2021

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Mass moment of inertia is a key inertial property of cricket bats and should be used in selection to optimise performance. Players currently rely on a subjective assessment of how the bat feels when swung supported only by a value for bat mass from the manufacturer. This reliance on a subjective assessment is because the moment of inertia of a bat typically requires a pendulum method to measure with sufficient accuracy. In this study, two methods for estimating moment of inertia were tested. The hypotheses were that (1) an acceptable estimate of moment of inertia could be calculated using a beam model approach, and (2) the inertial property first moment could act as a proxy measure for moment of inertia. Experimental values for moment of inertia were obtained using a pendulum method. The two-section beam model showed an error of 0.43–0.53% between model and experimental values based on a Root Mean Square Error of 0.0017 kg m2. First moment data were generated on 5005 bats spread across eight bat shapes. A correlation was shown between the measured value of first moment and the beam model value of moment of inertia, with an R2 value > 0.992 for all bat shapes. This study showed that a two-section beam model and first moment method for estimating cricket bat moment of inertia could be used to improve bat selection.

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Effect of materials and design on the bending stiffness of tennis rackets

et al. 2021

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Lawn tennis rackets have changed considerably since the origins of the game. Early rackets were wooden, making them heavier and more flexible than modern designs made from fibrepolymer composites. The fundamental frequency of a freely suspended tennis racket is often used as an analogue to stiffness, despite it being dependent on mass. We estimate the bending stiffness of 525 rackets, dating from 1874 to 2017, using a uniform beam model that accounts for mass. The model suggests composite rackets are typically about twice as stiff as their wooden predecessors. Applying typical values of Young's modulus, density and second moment of area, the model was used to demonstrate the benefits of fibre-polymer composites for making lightweight, stiff rackets. Undergraduate students could make use of our large dataset of tennis rackets to explore these patterns themselves. They could also go on to measure the dimensions, mass and fundamental frequency of tennis rackets and model them as a uniform beam. Students could also apply the theory to other implements, like badminton and squash rackets or baseball and cricket bats.

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Recommendations for Measuring Tennis Racket Parameters

Cited by 8 publications

References 9 publications

Recommendations for estimating the moments of inertia of a tennis racket

Recommendations for estimating the moments of inertia of a tennis racket

Methods for estimating moment of inertia of cricket bats

Effect of materials and design on the bending stiffness of tennis rackets

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