A novel mathematical model of the badminton smash: simulation and modeling in biomechanics

Abstract

Applied physics and computer methods in biomechanics have been extensively used in sports science research, including performance and biomechanics analysis. The Brachistochrone problem, which expresses the curve that an object draws quickly under gravitational forces in a vertical position, is one of the most widely used studies in classical mechanics. A similar problem arises when a badminton player intends to hit a smash with the shortest shot time. This paper aims to determine the optimal stroke trajectory for a shuttlecock smash in the shortest time. We simulate the badminton smash movement using a computer program after analyzing the shuttlecock smash analytically and numerically for several conditions. The modeling results show that a cycloid trajectory allows badminton players to smash the shuttlecock in the shortest time. Based on the experimental findings of Tsai, Huang, and Jih’s study and our models, the ratio of clear speed to smash speed is 0.75, which is still in the range of 0.71 to 0.76, and we find that a cycloid trajectory gives the shortest shuttlecock smash time. We concluded that the experimental data from this study’s literature supported our model. The novelty of this study is that we found the first powerful model and simulation of conventional Brachistochrone in the case of a badminton smash of badminton players. For badminton coaches and players, this model formulation is intended as a reference for optimizing shuttlecock shots. Furthermore, another novelty of this research is that it may lead to software that can be used to analyze the muscle strength of badminton players based on their cycloid hand trajectory and shuttlecock speed.

Keywords:

• Brachistochrone problem
• badminton
• simulation
• smash

Acknowledgments

The authors thank the Ministry of Industry of the Republic of Indonesia for providing adequate facilities. We also thank our colleagues who helped us with the research and analysis.

Authors’ contributions

Valentinus Galih Vidia Putra, Juliany Ningsih Mohamad, and Irwan conducted the simulations and the calculations. Valentinus Galih Vidia Putra and Juliany Ningsih Mohamad wrote and revised the manuscript. All authors agreed to the final version of this manuscript.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.