MAJOR QUESTION

What are the optimal biomechanics for scoring a top corner penalty kick in soccer?

Soccer is one of the most popular sports in the world, and the objective of the sport is to win by scoring goals.  One way to score a goal is from a penalty kick.  A penalty kick occurs under two circumstances in soccer.  If there is a foul inside the 18 yard box, the opposing team (who did not commit the foul) will be awarded a penalty kick.  A penalty shootout will also occur in a knock out game or a final if it is a draw after full time and extra time, to determine the winner of the match.  Penalty kicks are taken from the penalty spot, which is 11.005m directly in front of the goals (Figure 1) (Bauer, Fryer, Levesque & O’Brien, n.d.).  The aim of a penalty kick is to kick the ball past the goal keeper and into the net to score a goal.  A curved ball that is moving at a high velocity means the goal keeper has minimal time to react, and may be deceived by the swing on the ball; therefore, the kicker is more likely to score.  Aiming towards the top corner of the goals also creates a higher chance of scoring, as it is harder for the goal keeper to reach the ball. 

Figure 1: The Penalty Spot (Shergold, 2013).

To successfully complete a penalty kick, the following movements must occur consecutively; the approach, the foot plant and swing-limb loading, hip flexion and knee extension, ball contact, and the follow through (Figure 2).  This is called the kinetic chain, and the penalty kick is an example of a throw-like movement, where all joints of the kinetic chain extend sequentially, to allow a greater summation of forces which translates into a more powerful kick.  Newton’s first law of motion states that a stationary object will remain at rest, unless acted on by an unbalanced force.  In the case of the penalty kick, the ball is the object at rest, and the foot is the force that acts upon it.  Newton’s second law states that the acceleration of an object is proportional to the net force applied to it, and inversely proportional to the mass of the object.  Therefore, the ball will have greater acceleration and velocity if the foot applies a greater force to it.  The optimal biomechanics that will enhance kinetic linking, maximise foot velocity and result in a powerful, curved, accurate penalty kick will be explored throughout this blog. 

Figure 2: The Stages of a Penalty Kick (Barfield, 1998).

THE ANSWER

The Approach

When taking a penalty kick the approach is important for the player to overcome their moment of inertia.   The approach should be between 3-5 steps; this enough to gain a reasonable amount of speed and overcome the moment of inertia, however it would not be functional to approach the ball from much further away and reach an extremely high speed, as this could have a negative effect on balance and control upon reaching the ball (Lees et al., 2010).  The approach is the beginning of the kinetic chain, and a foundation to build momentum which is later translated into the kick, having an effect on ball velocity.  Novice players often begin their approach directly behind the ball, however this method is not effective as it inhibits swing limb angular velocity and leads to a less powerful kick (Lees et al., 2010).  Instead, the approach should be curved and begin on a 45 degree angle on the non-kicking side; this can be seen in Figure 3 (Kellis & Katis, 2007).  Studies have shown that a curved approach is more effective as it produces greater swing limb velocity and encourages a centre of rotation upon reaching the ball, creating angular velocity and torque.  This in turn leads to a faster, curved ball that is harder for the keeper to save (Lees et al., 2010).  The final stride in the approach before the foot plant has an effect on the penalty kick itself.  A lengthier final stride enables more pelvic rotation to occur during the swing through stage, which creates greater angular velocity and torque, and hence increased ball velocity (Bauer et al, n.d.).  These biomechanical aspects will be discussed in more detail in their relevant stages.

Figure 3: Curved 45 degree approach to penalty kick (LSM, 2014).

The Foot Plant and Swing-Limb Loading

During stage two, the non-kicking foot is planted adjacent to the ball.  Simultaneously, the kicking leg is flexed in preparation for the swing through to kick the ball.  The foot plant is a crucial aspect of the penalty kick as it determines accuracy and transfer of momentum from the approach into the kick.  Therefore, a good foot plant provides a good foundation or a link in the kinetic chain.  When the support foot is planted, it supports the total body weight.  To maintain stability the foot should be planted adjacent to, and in line with the ball, approximately 5-10cm away (The Sports Injury Doctor, n.d.).  The aim is to plant the foot as close as possible to maintain a stable centre of gravity and hence produce a more accurate kick, but not to plant it so close that it is in the path of the kicking leg (Barfield, 1998; Bauer et al., n.d.).  A close foot plant also allows the kicking foot to make better contact with the underside of the ball; the importance of this will be discussed in the ‘ball contact’ stage.  There should be a slight knee bend in the plant leg to absorb kinetic energy and maintain balance, and the plant foot should be facing the direction the player wishes the ball to go for accuracy purposes.  Expert players can sometimes face their plant foot away from where they are kicking to deceive the goal keeper, however this requires a rapid last minute hip rotation to produce adequate angular velocity and torque, and an accurate kick.  Whilst the non-kicking foot is planted, the kicking leg is flexed and close to the hip.  This is known as the swing-limb loading phase (Lees et al., 2010).  During this phase, elastic energy is stored in the kicking leg and this allows for the transfer of more force onto the ball in the swing through phase.  In this phase the centre of mass should be located as close to the hip as possible.  This decreases the radius of gyration and moment of inertia about the hip joint, and produces greater angular velocity in the swing phase, which is important for producing a more powerful kick.  Figures 4 and 5 highlight the importance of a good foot plant; Figure 4 shows a novice player who plants her foot too far away, resulting in an unstable centre of gravity and less transfer of momentum, whereas Figure 5 shows an ideal foot plant for producing power and accuracy.

Figure 4: Novice player plants foot too far back and loses balance and momentum (Bauer et al., n.d.).

Figure 5: Good foot plant maintains centre of gravity and enables transfer of momentum into kick (Bauer et al., n.d.).

Hip Flexion and Knee Extension

This phase incorporates the downward swing of the leg towards the ball.  Because the moment of inertia about the hip is decreased from the previous stage, there will be greater angular velocity produced at the hip during the swing through stage.  This leads to greater acceleration and linear velocity of the foot, hence producing a greater force acting upon the ball and greater ball velocity, which is the aim of the penalty kick (Bauer et al., n.d.).  Angular velocity and torque are important in this phase for translating momentum and producing maximum ball speed (Figure 6).  The curved approach at the beginning facilitates torso rotation simultaneous with the downswing of the kicking leg.  Torque is produced by the rotation of the torso about the hip of the plant leg (Bauer et al., n.d.).  The torques and angular momentum produced in this phase are transferred down the leg and into the foot, resulting in a more powerful kick; this can be seen in Figure 6 below.

Figure 6: Angular velocity and torque produced in swing through to ball (Bauer et al., n.d.).

Ball Contact

To produce an accurate penalty kick, a controlled stable body position is important in the ball contact stage.  The close foot plant discussed earlier allows the player to contact the underside of the ball with the kicking foot.  Projectile motion is relevant when considering the path of the ball.  Contacting the underside of the ball facilitates the lift of the ball which is necessary when aiming for the top corner of the net.  To contact the underside of the ball and produce more force, players lean backwards during ball contact (Bauer et al., n.d.).  Newton’s third law of motion states that for every action there is an equal and opposite reaction; therefore, players may extend the non-kicking side arm to account for this backwards lean, distribute mass evenly and maintain their centre of gravity (Lees et al., 2010).  The backwards lean also allows for the kicking leg, which is acting as a lever/force upon the ball, to fully extend.  Full extension of the lever/leg produces greater angular velocity and torque, and a greater force acting upon the ball, therefore due to Newton’s first law this leads to a faster and more powerful kick. 

Figure 7: Foot should contact underside of ball for lift and spin (Bauer et al., n.d.).

Figure 8: Foot should contact ball in this area to produce power and spin (Bauer et al., n.d.).

Figure 9 shows a right angled triangle formed between the penalty spot, the top corner of the goals, and the desired flight path.  To score a goal in the top corner, the optimal flight path would see the apex of the ball’s arc (where the vertical velocity is zero) occurring just before the crossbar; the ball will dip into the goals just out of reach of the goal keeper’s hands, because gravity is increasing friction, which becomes the opposite force (Newton’s third law) that begins to pull the ball back towards the ground.  Because it is known that the distance between the penalty spot and the goals is 11.005m, and that the goals are 2.44m high, trigonometry can be used to calculate the optimal angle of projection which is approximately 13°, and this is relevant for a maximal ball speed of 25m.s^-1.  During ball contact, 15% of kinetic energy is transferred to the ball, whist the remaining 85% is dispersed through up the leg which slows it down during the follow through stage (Gainor, Pitrowski & Puhl, 1978).  The coefficient of restitution refers to the proportion of total energy that remains in the ball after the kick.  It is represented by a number between zero one one; zero meaning all energy is lost, and one meaning all energy is retained.  FIFA regulations state the coefficient of restitution must be between 0.82-0.88 at 20°c (Wiart et al., 2011).  A higher coefficient of restitution has been suggested to lead to a faster ball speed, and the coefficient of restitution can be affected by the mechanical properties of the ball, the temperature and the soccer boot material (Kellis & Katis, 2007; Wiart et al., 2011).

Figure 9: The optimal angle of projection for the ball to dip under the crossbar is 13 degrees (Bauer et al., n.d.).

Although this blog is exploring the optimal biomechanics for a top corner penalty, if the goal keeper was extremely tall, it could be more efficient to aim for the bottom corner, as it may be harder for the keeper to dive low enough to save the ball in time.  When aiming for the bottom corner, the optimal projection angle would be closer to zero; this could be achieved by striking the ball closer to the centre rather than underneath, and producing less backwards lean of the torso in the follow through as this also contributes to the lift of the ball.

Follow Through

The follow through is crucial for maximising the time the foot is in contact with the ball (which is generally only 10 milliseconds), and for reducing the risk of injury (Bauer et al., n.d.; Lees et al., 2010).  Studies have shown that with optimum force production, ball velocity can range from 18-35m.s^-1 however for accuracy purposes an effective penalty would be around 25m.s^-1 (Asai, Carre, Akatsuka & Haake, 2002; Kellis & Katis, 2007; Lees et al., 2010).  Maximising foot ball contact time by fully extending the kicking leg produces greater force and speed on the ball.  This is because it allows for the transfer of momentum and kinetic energy that has been produced as a result of the kinetic chain in the lead up to the kick.  The full extension of the leg also enhances accuracy as the ball is inclined to follow the path of the leg.  During the follow through, the hip continues to flex and the torso rotates as the opposite force to maintain a stable centre of gravity (Newton’s third law).  Newton’s third law is also relevant to the injury prevention component of the follow through.  The follow through allows the body to disperse the remaining 85% of the build-up of elastic and kinetic energy; if the player came to a sudden stop instead, there would be an increased risk of injury to the hamstring or surrounding muscles due to equal and opposite reactions (Gainor, Pitrowski & Puhl, 1978). 

Figure 10: Follow through is important for accuracy and injury risk reduction (GBDCT, 2015).

The Magnus Effect

Figure 11: The Magnus effect (Aviation for Kids, n.d.).

Figure 12: The Magnus effect (Wander, n.d.).

Whilst the follow through is occurring, the ball is a projectile in motion.  The curved approach paired with the underside ball contact creates torque on the ball, and it spins about its own axis in the air; this results in a sideways lift force called the Magnus effect (Bauer et al., n.d.).  Because of the friction between the air and the ball, a spinning ball will ‘grab’ the air that flows past it.  The oncoming air deflects off the ball sooner, whereas the air on the other side of the ball deflects later and is drawn behind the ball to the low pressure air (Figure 11 & Figure 12).  Therefore there is greater airflow acceleration at the front of the ball than the back, and this imbalance causes the ball to curve through its projectile.  This can be explained by Newton’s third law of equal and opposite reactions, and conservation of momentum; the deflection of airflow around the ball due to the spin creates the curve of the ball, and this can deceive the goal keeper in a penalty kick as the curve is unexpected and harder to read.  The following videos show the Magnus effect in action, and provide further explanations of the biomechanical principles behind it.  

HOW ELSE CAN WE USE THIS INFORMATION?

The optimal biomechanics for a penalty kick can be transferable to other techniques of a similar nature.  The movement sequence for a penalty kick is similar to point scoring in rugby or NFL, and the AFL football kick; these skills are other examples of throw like kinetic chain movements, therefore the optimal biomechanics for each of the stages discussed in this blog could be adapted to enhance performance in these sports too.  The AFL drop punt particularly closely replicates the kinetic chain of a penalty kick.  There are similarities with the swing-limb loading, hip flexion and knee extension, and follow through to produce power and accuracy, and reduce injury, and these can be seen in Figure 13.  Therefore, a coach could apply a similar training strategy for encouraging optimal performance in both skills.  Predicting optimal release angles for projectiles to meet a required distance can also be relevant to many skills such as shotput, javelin, or simply throwing a ball.  The coefficient of restitution is relevant to any skill that involves striking; in soccer, the players can modify their boots, however in other sports such as cricket or baseball, the batsmen may do similar things.  Finally, the Magnus effect is transferable to any skill where a person aims to put spin on the ball to deceive the opposition.  These include but are not exclusive to bowling in cricket, pitching in baseball or softball, or hitting topspin in tennis.

Figure 13: AFL drop punt consists of a similar movement pattern (Gleeson, 2009).

The following video provides an excellent summary of the optimal biomechanics for a soccer instep kick, and it is included as an additional resource to further explain and demonstrate each of the stages discussed in this blog.

REFERENCES

Asai, T., Carré, M. J., Akatsuka, T., & Haake, S. J. (2002). The curve kick of a football I: impact with the foot. Sports Engineering, 5(4), 183-192.

Aviation for Kids. (n.d.). The Magnus Force. Retrieved from http://www.aviation-for-kids.com/the-magnus-force.html

Blazevich, A. (2012). Sports Biomechanics The Basics, Optimising Human Performance (2^nd ed). London: Bloomsbury.

Barfield, B. (1998). The biomechanics of kicking in soccer. Clinics in Sports Medicine. 17(4): 711-728.

Bauer, L., Fryer, E., Levesque, C., & O’Brien, S. (n.d.). Qualitative Biomechanical Analysis of a Penalty Kick in Soccer. Retrieved from folioz.ca/artefact/file/download.php?file=24233&view=3153

Gainor, B., Pitrowski, G., and Puhl, J. (1978). The kick. Biomechanics and collision injury. Am J Sports Med.6. 185-193.

GBDCT. (2015). GBDCT Notebook: Using Photoshop Layers to Simulate Fluid Motion. Retrieved from http://www.granitebaydesign.com/2602/photoshop-layers-fluid-motion/

Gleeson, M. (2009). Kicking On. Retrieved from http://www.foxsportspulse.com/assoc_page.cgi?c=1-4712-0-0-0&sID=85584&news_task=DETAIL&articleID=9858665

Hale, C. (2014). Biomechanics of the Instep Kick. [Video File]. Retrieved from https://www.youtube.com/watch?v=PQjoSNaFf5c

Kellis, E., & Katis, A. (2007). Biomechanical characteristics and determinants of instep soccer kick. Journal of Sports Science & Medicine, 6(2),154.

Lees, A., Asai, T., Andersen, T. B., Nunome, H., & Sterzing, T. (2010). The biomechanics of kicking in soccer: A review. Journal of Sports Sciences, 28(8), 805-817.

LSM. (2014). A Little Secret about Taking Penalty Kicks. Retrieved from http://www.lifesomundane.net/2014/04/penalties.html

Physics Girl. (2014). The Physics Behind a Curveball - The Magnus Effect. [Video File]. Retrieved from https://www.youtube.com/watch?v=YIPO3W081Hw

RayperEnglishKnight. (2015). Roberto Carlos best goals ever. [Video File]. Retrieved from https://www.youtube.com/watch?v=vnB_4Jtfy6A

Shergold, A. (2013). Can we beat the Germans on penalties? Retrieved from  http://www.dailymail.co.uk/sport/football/article-2480025/Sportsmail-Rene-Adler-science-penalty-shootout.html#ixzz3dQ1XC32C 

The Sports Injury Doctor. (n.d.) Biomechanics of Soccer: The soccer-style kick - a slow-motion commentary on one of the most common sporting actions in the world. Retrieved from http://www.sportsinjurybulletin.com/archive/biomechanics-soccer.htm

Veritasium. (2011). What is the Magnus force? [Video File]. Retrieved from https://www.youtube.com/watch?v=23f1jvGUWJs

Wander, L. (n.d.). What’s really happening when you ‘bend it like Beckham’. Retrieved from http://www.unc.edu/~lwander/Group%20Project.html

Wiart, N., Kelley, J., James, D., & Allen, T. (2011). Effect of temperature on the dynamic properties of soccer balls. Journal of Sports Engineering and Technology, 225(4) 189-198.