Early Research on Physics of Heading (Part 2 of 3)

Part 2 of 3 of this article on Charles Babbs’ experiment on the underlying mechanism of heading discusses the biomechanics of heading and head acceleration. Equations to understand ball collision with the player, effective body mass, ideal heading technique for grounded and jumping player, and mediocre heading technique are explained. Babbs discussion on Newton’s second law of motion, horizontal motion of the head, and the impact of the header is defined.

Biomechanics of Heading

• The biomechanics of heading were presented as a one-dimensional equation. A player moving eastward is assumed to collide with a ball moving west to change its direction. The player’s effective mass opposes the horizontal acceleration of the head and body to the same degree as the three dimensional body of the player. Effective mass is defined as the ratio of horizontal force to horizontal acceleration (m’=Fx /ax). The effective mass is dependent on the angle of inclination of the player with respect to the ground, the theta angle (θ).
• Assuming that the player uses the ideal heading technique with strong and stiff neck muscles, preventing the head from wobbling backward, and entire body mass connected to ball on impact:
• The effective mass of the grounded player inclined at an angle of θ is defined as m’ = m / 2sin2θ.
• The effective mass of the jumping player is defined as m’ = m / 2sin2θ + cos2θ
• When a player is standing vertically, θ = 90 degrees and sin(θ) = 1. The effective mass is one half body mass for grounded or jumping player
• Effective mass for perfectly diving horizontal header (with feet off the ground) is 100% body mass. Here, θ = 0 degrees, sin (θ) = 0 and cos (θ) = 1
• When the player is head unawares by the ball, the mass of the head alone is used i.e. 2 to 5 kgs, corresponding to the sex and age of the player, making the head susceptible to acceleration during head-ball contact when compared to the effective mass of player using the good technique.
• A mediocre technique is one where the head is allowed to wobble slightly, the effective mass is the intermediate between the head and one half of the total body mass.
• All techniques described assume heading as a collision between the ball and the forehead with effective mass moving in the opposite direction. It must be noted that young players have a smaller effective mass and the use of an appropriate technique decreases the effective mass further. Effective mass is the major determinant of the head acceleration on impact. Higher effective mass results in smaller acceleration of the head.

Head Acceleration

The horizontal motion of the head and ball is a function of time in adult heading impact. The horizontal head and ball positions are calculated using Newton’s second law of motion:

• soccer ball size 5 colliding with 70 kg adult player and effective body mass 35 kg
• Head ball contact is recorded at time zero
• Positive values of position in meters are plotted on Y axis and represent forward progress in the direction faced by the player.
• At the instant of contact and separation, the center of the ball is one radius away.
• U-shape curve shows ball position and a slant line superimposed on it shows the head position.
• At instances of contact and separation, curves cross.
• Position of the ball plotted below the head indicates the head indenting the ball.
• The example indicates that the plater is moving at one meter per second towards the ball, and the ball is moving at five meters per second.
• Curvatures of head and ball tracings indicating acceleration are a relation of ball to player mass (effective body mass)

a1 / a2 = -m1 / m2

• Instantaneous head acceleration versus time is plotted as a U-shape curve. Negative values indicate backward head acceleration.
• Harmful effects of acceleration are functions of duration of acceleration and mean value of acceleration during the interval, represented as a point in mean acceleration — duration space.
• Heading safety is interpreted by curves showing HIC for “clearly harmful” and “potentially fatal” single impacts. Safe values of HIC are plotted towards the bottom (acceleration experienced during normal movement — HIC value 0.2 g2.5/sec

Scientists calculated 100 random ball impacts using Monte Carlo simulation. Data collected for every impact includes total duration of impact and head acceleration during impact, through data points in the acceleration — duration space. Ball inflation pressures ranged from 0.3 to 1.1 atmospheres (soft, medium, hard balls). Different scenarios were plotted such as 70 kg heading size 5 balls and 40 kg heading size 4 balls.

The average impact of a header performed with a good heading technique lasts 0.0085 seconds and has mean head acceleration of 2.4g. HIC is measured as 0.07 g2.5/sec

Heading varies as the 2,5th power of a head acceleration. Small increases in head acceleration produce large increases in HIC. Adults with normal size 5 ball inflated to any of the three pressures, most combinations of technique and ball speed produced impacts of HIC values less than 0.2 g2.5/sec

For a long life soccer player, few safe headers occur during normal play. HIC values between 0.2 to 0.5 were recorded for a small number of players, which was slightly above the normal activity threshold. Normal reading by adults appears to be as safe as jumping or head nodding as per HIC.

In youth players, the effective body mass values in a normal distribution had a mean of 15.4 kg and standard deviation of 4.6 kg. These values measure 40/70 times those of adults (mean weight only 40 kg for a 10.5 year old or 11 year old boy). Horizontal ball velocity is selected at random with mean 7.1 meters per second and standard deviation 2.2 meters per second (which closely represents distance of youth players between 9 and 13 years. Overall range of possible accelerations during heading of legally inflated balls is greater in youth when compared to adults. A smaller size ball (size 4) does not compensate for smaller effective mass of younger players. For an inflation pressure between 0.6 to 1.1 atm, acceleration distributions for size 4 balls on both sides of safe level 0.2 g2.5/sec

Higher accelerations for youth were in the range 15 to 20 grams rage with unfavorable conditions (high ball velocity, bad technique, high inflation pressure)

References

Babbs, C. F. (2001). Biomechanics of Heading a Soccer Ball: Implications for Player Safety. The Scientific World JOURNAL, 1, 281–322. https://doi.org/10.1100/tsw.2001.56