Torque:

In relation to moment of force, or torque, it can be said that “the angular acceleration of an object is proportional to the net torque acting on it and inversely proportional to the object t=Ia” (Blazevich, 2010). This means that torque is equal to inertia multiplied by angular acceleration. Greater torque can be generated by quicker rotation at the joint, which, in the case of the tennis serve, is located at the shoulder. To generate greater torque a tennis player must reach right back behind their back with their racquet. The quicker they are able to snap their arm back around and through the ball the more force will be generated. Whilst muscle plays a role in generating greater torque, it can somewhat be dependent on a person’s arm length (Blazevich, 2010).

Projectile motion:

In order to complete the perfect serve, the player must take into account some key elements; angle of contact, projection speed and relative height of the projection.

The angle of contact, or the projection angle, greatly affects the projectile range (Blazevich, 2010). Obviously if the player was to hit the tennis ball straight up in the air it will land next to him or her, and similarly if the angle is too horizontal the ball will not make it over the net (Blazevich, 2010). In order to achieve maximum distance, the angle of projection should be forty five degrees to the horizontal. This is because at forty five degrees the ball is projected equally both vertically and horizontally (Blazevich, 2010). However, with the tennis serve the player must take into consideration that the ball has been tossed in the air and is on its way back down to Earth due to the force of gravity. The player must contact the ball at the player’s highest point in order to get optimal angle over the net.

Contact height, or relative height of projection, stays the same for all tennis players (Grimshaw et al, 2007). The optimal height of contact for the standard flat tennis serve is three metres off the ground (Grimshaw et al, 2007). Achieving this has varying difficulties for players due to individual factors such as a person’s height and arm length. Players struggling to contact the ball at the optimal contact height will change the angle of projection. The compensation of this height is usually at and angle of between four to seven degrees different (Grimshaw et al, 2007). Tennis players must aim to minimise this angle of compensation, and contact the ball as close as possible to three metres above the ground.

Figure 4. The action of an elite tennis server, demonstrating the contact height position and ball contact angle. (Image credit: Grimshaw et al.)

Projection speed is the final element. Projection speed will allow the ball to travel over the net and into the service court without being a fault. With too little projection speed the ball will not travel over the net. Similarly, if the projection speed is too great there is a risk the ball will go out of play, and therefore not be a legal serve.

In order to achieve a perfect serve the player must consider these three factors and incorporate them in equal proportion when serving, to produce a serve that maximises power and maintains accuracy.

Newton's Laws

The tennis serve relates directly to Newton’s third law of motion. Newton’s third law of motion states, “for every action there is an equal and opposite reaction” (Blazevich, 2010). When looking at the tennis serve, the primary force is the impact of the racquet on the tennis ball. The impact of the racquet onto the ball propels the ball over the net and across the court to the opponent. The reactant force is the ball on the racquet, which causes the strings to move. This is confirmed when watching a slow motion video (click the link below) of a tennis ball making contact with the racquet. You can clearly see the impact of both the racquet onto the ball and the opposite force of the ball onto the racquet.


http://www.youtube.com/watch?v=pufedQgGYzg

The tennis serve also links to Newton’s second law of motion. The second law of motion states “The acceleration (a) of a body is parallel and directly proportional to the net force (F) acting on the body, is in the direction of the net force, and is inversely proportional to the mass (m) of the body, i.e., F = ma” (Blazevich, 2010). This means that the force exerted, measured in Newton’s, is equal to the mass of an object multiplied by it’s acceleration. Assuming that all tennis balls are equal in mass, what separates different players’ serves is the acceleration that each individual can place on the ball, while still maintaining accuracy. The greater the force of the tennis serve, the more difficult for the opponent to return the serve.