Peak Compression Force Physics in Rugby Union Scrum

: Scrums play a major role in Rugby Union games, and are historically known as a showdown between the two packs of opposing teams, composed of their eight forwards players organized in a 3-4-1 configuration, respectively. We investigate scrum mechanics by working with professional male forward players from Racing 92, a high-level French Rugby club, and measuring the forces they apply on the French Rugby Federation instrumented scrum machine. Signal analysis reveals two major phases in the force production during a scrummaging effort: an impulsive engagement force, and then a force sustained for a few seconds. We experimentally compare individual performances of the engagement phase. We discuss the influence of the mass and the engagement speed of the players, and we introduce the model we are investigating to describe the individual impact on a scrum machine. We expect this model to be the elementary component of a collective model of a pack.


Introduction
In Rugby Union, the 'scrum' is a trial of strength and a strategic opposition between the two teams' eight forwards. These two packs, pushing against each other, are composed of three rows, in a 3-4-1 configuration, as shown in Figure 1a. Nowadays, a scrum is directed by the Crouch-Bind-Set (CBS) referee's calls [1]: • "Crouch"-front rows are crouching to face the opponents at the same height; • "Bind"-each prop binds to her/his opponent who is in front of her/him; • "Set"-when both sides are stable, packs engage.
Then, when the scrum is stable again, the scrum-half introduces the ball between the two packs, and the pushing phase follows.
The scrum is an important part of a rugby game that has constantly changed throughout decades. The last thirty years' evolution results from studies made in order to reduce the number of spine injuries [2][3][4]. Until the nineties, front row players were starting to engage in a standing position really far from each other (more than 2 m), as we can see in Figure 1b. Then, the rows started to crouch before engaging, but the space between the first rows remained large (more than 1 meter) until mid-2000s, as we observe in Figure 1c. Then, with the introduction of a touch phase, we observed a tendency to put the first rows closer to each other before the engagement. Nowadays, front rows are practically touching opponents with their heads (cf. Figure 1d). Milburn [5] described engagement force as an impulsive force that becomes larger with higher front rows' engagement speed and larger player's weight. As the mass of rugby forwards increased of 26% through these last forty years [6,7], we show in Table 1 the correlation between pack's weight increase and engagement compression  force (expressed in kilogram-force), from 800 kg in the nineties to 1600 kg in the 2010s.  The second main parameter involved in magnitude is engagement speed. This influence of impact speed is represented in the last column of Table 1 with data from [9] for a pack using different engagement techniques. CTPE refers to Crouch-Touch-Pause-Engage 2011/2012 engagement process, CTS refers to Crouch-Touch-Set 2012/2013 engagement process, and FoldIn consists in a CTPE process with an instruction given to the players to not generate momentum before the scrum machine's contact. In this latter case, the impact speed is reduced a lot thanks to space reduction between front rows, and so too [9,10]. Thus, the referee's calls are here to reduce peak compression force in the engagement phase by reducing the space, and so speed between front rows [11].
We conducted an experimental study with professional rugby players to study force production and transmission in scrums. After introducing the experimental setup, we show the individual peak compression forces obtained and discuss the results in terms of the influence of engagement speed. Finally, we investigate a mass-spring-damper (MSD) model to learn about players' parameters through impact force analysis.

Experimental Study
"L'Atelier de la mêlee" is the instrumented scrum machine of the French National team we used to conduct our experiments thanks to the French Rugby Federation. This tool is able to simulate an adverse pack and to measure simultaneously the different forces applied to it [12,13]. The experimental setup is shown in Figure 2a. In our study, we only focus on compression force which corresponds to the force developed along the scrum's main axis , defined in Figure 2a. We studied individually 11 professional forward players of Racing 92 (mean mass = 117 ± 14 kg). Each player volunteered and signed an informed consent form. Players were asked to adopt a position that corresponds to the one they have in a complete scrum. They first impacted the scrum machine in the same way they are doing during a complete scrum engagement phase, and after a coach instruction, were asked to produce three seconds of maximal effort push.

Results
An example of individual experiment is featured in Figure 2. In Figure 2a, we show a snapshot from the zenithal and side point of view of a Number-5 lock's experiment. Figure 2b shows the time evolution associated compression force. There are two interesting phases on the curve: the engagement phase which enables us to define , and a second phase with a plateau at an average value . In Figure 2b, between these two phases (from t = 4 s and t = 5 s), we observe twice a 30% decrease of force, which correspond on the synchronized video to the moments when the player moves his feet. In Table 2, we sum up the individual results. We see that, on average, hookers and tighthead props are the players that can develop the higher forces. In Table 3, we gather the individual results. For each player, we determine the initial speed of engagement by manual tracking on the video. It corresponds to the speed reached by the players are reaching when they hit the scrum machine. Table 2. Individual mean forces on the scrum machine.

Hookers Tighthead Props (3) Locks (3) Flankers * (2) Number-8 (1)
Weight (  In this table, we only chose the players who are pushing with two shoulders in order to have an equivalent surface of contact. We observe the higher the engagement speed, the higher results (excluding locks results) are.

MacMahon Look-Alike Model for a Single Player and Discussion
In this section, we propose a model inspired from the MacMahon's model for muscle [14] to simulate a player that hits a scrum machine. We are focusing our study on the impact phase. We introduce the schematic drawing of the model in Figure 3a. We consider that the scrum machine is not moving. The player is modelized by a mass , a spring of stiffness , a damper of damping coefficient and a force generator . We define and in Figure 3a such that the player's total length is given by and the force the player is applying on the scrum machine can be expressed as In Figure 3a, we represent the system at = 0 when the player hits the scrum machine with an initial speed . The force model equations can be written as For a simplification purpose, we use the approximation ( ) = 0, that signifies player's length does not change during the impact: player is staying on his feet. By nondimensionalization of Equation (3), we simplify the force model equation by introducing a dimensionless parameter A = .
An individual attempt on the scrum machine is fully described by , (0) = and Equation (4).
We developed a method to an analyze players' experimental curves in order to determine parameters values. The engagement speed is manually determined by video analysis. After the impact, the force is converging towards regarding to Equation (3). On the experimental curves, is determined by reading the force value after the impact and just before the player is doing is muscular effort to push the scrum machine. Then, the process consists in measuring global characteristics of the curve such as , and enables us to find parameters , , and step by step. In Figure 3b, we plot an example of experimental curve on which we applied this method. The dashed orange curve is obtained thanks to Equation (4) and parameters determined by this process. For this example, = 0.73, = 3.1 × 10 . , = 6.1 × 10 . , = 1250 and = 115 . In the model, is an effective mass which is in motion during the impact.
(4) Thanks to this model, we can easily discuss engagement speed and player mass influences on . In Figure 4a, we plot different peak force time evolutions for different masses , which represents player weight influence. In Figure 4b, we have the same kind of plot with different engagement speeds. All the other parameters are fixed to the values mentioned earlier. For a single player, we observe that the maximal force at impact increases when the mass in motion increases, the same tendency that we presented in Section 1 for real scrums. This evolution is quasi-linear. We also observe the increase of with the engagement speed. As the player mass is difficult to control and has shown in past to constantly increased, we understand that engagement speed is a key parameter to control the compression force peak and to reinforce players' safety. . We observe that the peak force increases both with engagement speed and mass.

Conclusions
As the weight of rugby players has constantly increased these last decades, we understand the evolutions of the scrum engagement process: by reducing engagement speed, which plays a main role in value, we observe a decrease in peak compression force applied by players. The featured model, which simulates one player pushing against a scrum machine, describes the same influences of player mass and initial speed on . The perspectives of this work is to use this model to determine the stiffness and damping coefficient for different players professional and nonprofessional. Finally, we will implement several units of this model to simulate a complete scrum.