Optimum projection angle for attaining maximum distance in a rugby place kick.

Author:Linthorne, Nicholas P.


The place kick is an important skill in rugby union as it can contribute to the team's score through a penalty kick at goal (3 points) and through converting a try (2 points). A player who can produce a longer kick distance is able to attempt a penalty kick or try conversion from a greater fraction of the field of play and hence has a greater opportunity to score. The kick distance in a rugby place kick is determined mainly by the projection velocity and projection angle of the ball. It is well known that a higher projection velocity produces a longer kick distance and that players with greater muscular strength can produce a higher ball projection velocity (Cabri et al., 1988). Video analysis has shown that top-level rugby union players use a projection angle of around 30[degrees] (Holmes et al., 2006). However, the biomechanical rationale for this projection angle is not clear.

The optimum projection angle for achieving the greatest distance in a rugby place kick is not expected to be 45[degrees]. Previous studies of throwing, jumping, and kicking events have shown that projection velocity and projection angle can be inter-related (Hubbard et al., 2001; Leigh et al., 2010; Linthorne, 2001; Linthorne and Everett, 2006; Linthorne et al., 2005; Linthorne and Patel, 2011; Red and Zogaib, 1977; Wakai and Linthorne, 2005). In almost all the events studied previously the projection velocity that the athlete can produce decreases as the projection angle is increased. Because the range of a sports projectile is strongly dependent on its projection velocity, this negative relationship between projection velocity and projection angle means that the athlete's optimum projection angle is substantially less than 45[degrees]. An exception is the punt kick by a soccer goalkeeper. In a punt kick the projection velocity of the ball is the same at all projection angles and so the optimum projection angle is about 45[degrees] (Linthorne and Patel, 2011). Here, we suggest that the low projection angle that is used in a rugby place kick (about 30[degrees]) arises because there is a strong negative relationship between projection velocity and projection angle.

The aim of the study reported here was to quantify the relationship between projection velocity and projection angle in a rugby place kick and to see whether this relationship could account for the projection angle that is used (about 30[degrees]). We used a video camera to obtain the projection velocity and projection angle of maximum-effort kicks by a male rugby player when performing kicks over a wide range of projection angles. The player's optimum projection angle for attaining the greatest kick distance was calculated by substituting a mathematical expression for the relationship between projection velocity and projection angle into the equations for the aerodynamic flight of a rugby ball. Our hypothesis was that the player's calculated optimum projection angle would be in close agreement with his preferred projection angle when kicking for maximum distance. The player's projection velocity was expected to decrease substantially with increasing projection angle and so his optimum projection angle was expected to be considerably less than 45[degrees]. Aerodynamic forces and the requirement to clear the crossbar were expected to have only a small influence on the player's optimum projection angle (Linthorne and Everett, 2006; Linthorne and Patel, 2011).


In a common place kick technique the ball is placed on the ground (supported by a kicking tee, earth, or sand) with its long axis pointing upwards. The kicker uses an approach of about three steps and strikes the ball with the instep of the foot. Many coaches recommend that the goal kicker use the same kicking technique, with nearmaximum effort, regardless of the player's kicking position on the field. For a penalty kick or conversion kick to be successful the ball must pass between the goal posts and over the crossbar. The maximum achievable kick distance is the horizontal distance the centre of mass of the ball travels from the instant of leaving the foot to the instant of reaching the height of the crossbar (Figure 1). The projection variables that determine the kick distance are the projection velocity, v, the projection angle, 9, and the height of the crossbar, h (3.0 m; IRB, 2013).



One male semi-professional rugby union player (age 21 years, height 1.76 m, body mass 82 kg) volunteered to participate in the study. The study was approved by the Human Ethics Committee of Brunel University, the participant was informed of the protocol and procedures prior to his involvement, and written consent to participate was obtained. The participant wore his own athletic training clothes and football boots.


The kicks were conducted in still-air conditions in an outdoor football facility using an IRB-approved match ball (Synergie; Gilbert Rugby, Robertsbridge, East Sussex, UK). All kicks were performed from a flat artificial grass surface using a standard kicking tee. The participant used three walking steps into the kicking action and performed the kick using the 'round-the-corner' style, with the ball making contact with his foot between the toe and the ankle (similar to an instep kick in soccer). A wide range of projection angles was deliberately induced so as to minimize the uncertainty in the mathematical expression that was obtained to describe the relationship between projection velocity and projection angle. The participant performed 18 maximum-effort kicks at his preferred projection angle for attaining maximum distance, and 31 maximum-effort kicks at other projection angles that were 'higher' and 'lower' than his preferred projection angle. The order of the projection angles was altered to preclude any effect resulting from the order, and an unlimited rest interval was given between kicks to minimize the effects of fatigue on kicking performance. For each kick the horizontal flight distance was measured to the nearest 0.1 m using a fiberglass tape measure.

A JVC GR-DVL 9600 video camera (Victor Company...

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