Physics of bicycle kick (scissors kick) in football soccer

In soccer, the bicycle kick has provided viewers moments of breathtaking spectacle that seem virtuosic in scope. The novelty of such moments is underscored by the rarity with which players have performed this complex skill during national or international tournaments.

The rarity of these occurrences is both a product of perceptions that it is a high-risk, low return skill and by the fact that there is a dearth of scientific research on the biomechanics of the technique. Pelé, Cristiano Ronaldo (CR7), Ronaldinho, Messi, all the best players have performed at least once a bicycle kick.

This magic skill has captivated fans and also the scientific community. Some studies such as Shan et al., (2015) applied 3D motion capture and numerical simulations to better analyze and understand this movement.

In this post we will summarize the physics processes involved in bicycle kick (or scissor kick) taking as example the famous kick from Pele, the greatest player of all times. This movement of less than 1 second will always amaze soccer fans and physics fans.

Bicycle kick movements

The movements of the bicycle kick can be described in three phases:

1. The jumping: The player (Pelé) places himself back to the intended direction of the kicked ball and to jump, his center of gravity (CG), defined as a point where the resultant of all the weight forces can be considered acting upon, projects a little behind of his impulse foot. This allows him to gain rotational momentum when he applies force on the ground that passes within a certain distance from the CG to jump like in a back somersault.

2. The scissors: Once completely in the air, Pelé, in astonishing synchrony with the ball trajectory, elevates the leg which is going to hit the ball and moves the other leg in the opposite direction; like the movement of a scissors, as can be seen by the angles between the thigh and the trunk for each leg shown in Figure1c.

While the movement is performed, the head is kept in a very stable posture because he must gaze at the ball. To facilitate the rotational movement of the kicking leg at the beginning, he bends the knee of this leg, approximating his limbs to the hip, and fully extends this leg just before the kick to hit the ball as high as possible, like the divers do to rotate faster during a dive.

The physical property being altered is called the rotational inertia, the property of a body to resist change in its state of angular movement. The rotational inertia is calculated as the product between the body mass and the squared distance from the body to the center of rotation.

Decreasing the distances of each segment to the hip joint decreases the total rotational inertia of the lower limb. In the air, the arms stabilize the body position: the arms are kept away from the trunk in the frontal plane to intentionally increase the body’s rotational inertia in the longitudinal direction to diminish any rotational perturbation in this direction, like a circus acrobat walking on a rope with a balancing beam in the hands.

3. The ball striking: The leg, at high speed, intercepts the ball above the height of a standing person, and changes its movement. Then, for a moment (see the video), it seems as if his body stops in the air and only the legs rotate around the hip.

This phenomenon is due to the movement of other segments of the body that move faster than the trunk: although the entire body CG is in a parabolic trajectory, as predicted by the classical laws of motion, the trunk vertical trajectory (trunk CG) actually slows down in its apex.