On the size of sports fields

Abstract

The size of sports fields considerably varies from a few meters for table tennis to hundreds of meters for golf. We first show that this size is mainly fixed by the range of the projectile, that is, by the aerodynamic properties of the ball (mass, surface, drag coefficient) and its maximal velocity in the game. This allows us to propose general classifications for sports played with a ball.One could think that the size of a sports field is a function of the number of players, of the rules, of the ball shape, or of the way of launching the ball [1]. We focus here on the role of the ball range, that is, the maximal distance that the ball can travel in one shot. Due to its application in the military context [2], and more recently in sports [3], this ballistic problem has been studied in detail for a long time, and geometrical constructions [4], numerical solutions [5] and theoretical discussions [6,7] have been proposed for approaching the actual trajectory.One famous early work on the subject is 'Dialogues Concerning Two New Sciences' [8] published in 1638 by Galileo, one century after 'triangular trajectories' were reported by Tartaglia [9, 10]. Here, we revisit the problem with a special focus on the maximal range and then study its correlation with the size of sports fields. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New J. Phys. 16 (2014) 033039 B D Texier et al 2 New J. Phys. 16 (2014) 033039 B D Texier et al 6 Figure 2. Correlation between the size of the sports field L field for the different sports and the associated ballʼs maximum range, x max . The data are extracted from table 1. The solid line represents the equality between those two distances. New J. Phys. 16 (2014) 033039 B D Texier et al 9

The physics of badminton

“…For clear strokes, section 2.1 shows that the range 'saturates' with the initial velocity at a maximal value which depends on the aerodynamical length . For the maximal initial speed ever recorded (U 137 m s max 1 = − ), the shuttlecock maximum range x max is 13.8 m [14]. This distance compares to the court length (L 13.4 m field = ), which implies that the projectile rarely leaves the field and may explain why the mean number of shots per rally (13.5) is so large in top level badminton competitions [15].…”

Physics of knuckleballs

“…So far, the characteristics time over which knuckleballs occur have not been discussed. Such a time can be estimated as t l = U knuckle shot and compared with the typical reaction time of a player  t 1 s as introduced earlier by Darbois Texier et al [11]. One expects that if t t > knuckle , players can react to ball motions and catch zigzagging paths.…”

“…For sports where zigzag paths are reported (in red), the range of ball velocity U for which knuckleballs are obtained is reported in column 7 together with the typical length λ of a zigzag (column 8) and the range of normalized lateral deviation d D (column 9). Data are extracted from [2,[5][6][7][8]11]. , on the order of the ball diameter.…”

Physics of ball sports

“…Indeed, it's no use playing on a 100 m-long field, if the maximal range of the ball is 10 m. Figure 4(d) shows a strong correlation between the size of sports fields and the maximal range, x max , of the associated balls, from table tennis to golf. We conclude that the size of sports fields is mainly imposed by the physics of the ball flight [6].…”