THE MAGNUS EFFECT
Curving Trajectories in Football
The Knuckleball
The Curveball
The behaviour of objects passing through fluids fascinates and intrigues the
scientific community. We see this in areas of our lives from commercial
aviation to sport. In leisure, ball sports reveal interesting dynamics that
scientists are keen to understand. The most popular sport in the world,
football, continues to amaze with free-kicks and the trajectories it produces.
Here, set-piece specialists such as David Beckham, Roberto Carlos and
Cristiano Ronaldo bamboozle goalkeepers with the complex curvature of their
free-kicks. Following his 1852 breakthrough in the observed effect, German
physicist Gustav Magnus unravelled these mysteries.
Striking a football so that little spin is applied is a skill that few have mastered. 3 time
Ballon D’or winner Cristiano Ronaldo uses this technique to devastating effect from his
set-pieces.
Bending it like Beckham. Professional footballers alike impart spin on a ball
and use the Magnus Effect to achieve fantastic footballing feats. A notable
example is the free-kick scored by Roberto Carlos in the 1997 World Cup.
Coined in 1909 after a style of baseball pitch, the knuckleball is an unpredictable ball
motion that shifts and flutters erratically in flight. Cristiano’s ability to strike the ball
using the knuckleball technique leaves goalkeepers defenceless. So just what is the
science behind such a punishing strike?
As discussed, striking the ball off centre creates a pressure differential that
produces contrasting airflows on either side of the ball. The induced spin
causes the Magnus Effect to influence the flight path and the ball curves in the
air.
During flight, air flowing past the ball grabs at the seams and at the surface of the ball.
When the ball spins, there is little effect caused by the seams. However, when the ball
is barely spinning, the difference in textures produces an asymmetric flow. This means
that the ball may travel straight for a period of time, before rapidly veering to the left
or right or dipping violently.
The Magnus force can be described with the following equation:
What is the Magnus Effect?
The Magnus effect is the observed effect in which a spinning ball curves away
from its principal flight path. In football, when a footballer strikes a ball offcentre, a spin force is applied. From the side the ball was struck, the motion of
the ball is opposed by a drag force. Now, if we consider the opposite side of
the ball, the result of the spin and drag force is the sum of their magnitude as
both travel in the same direction. The asymmetry of force creates a pressure
differential. This causes the ball to veer towards the region of low pressure;
the side of the ball opposing the initial contact point.
𝑭 = 𝟐𝝅𝑹𝟑 𝝆𝝎𝝂
𝐹 = 𝑇ℎ𝑒 𝑀𝑎𝑔𝑛𝑢𝑠 𝐹𝑜𝑟𝑐𝑒
𝑅 = 𝑅𝑎𝑑𝑖𝑢𝑠
𝜌 = 𝑎𝑖𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦
The effects in flight depend on different factors. This includes:
•Air density :
Denser air helps the ball to deviate
•Air temperature:
Knuckleballs are less deceptive at higher temperatures
The Magnus Effect in Ball Design
•Ball design :
Different balls knuckle at different speeds
The impact of the Magnus effect must be taken into account in the industrial
design of footballs. History has already demonstrated the consequences of
experimental football design, for instance, the FIFA World Cup 2010 Adidas
Jabulani ball. With 8 thermally fused panels as opposed to the traditional 32
stitched panels, the ball’s surface was textured with grooves and bumps and
was found to knuckle at speeds 10-20mph greater than traditional balls. As a
result, the World Cup witnessed a number of shots that behaved chaotically
and often left goalkeepers clueless.
Hence, it is the lack of a Magnus force that produces a trajectory that is dictated almost
entirely by environmental factors; creating an interesting dynamic of uncertainty.
𝜔 = 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝜈 = 𝑓𝑙𝑜𝑤 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
For Roberto Carlos’ wonder goal, the pressure created on the right side of the
ball caused it to spin back towards the net from right to left. In flight, the
airflow around the ball changed from turbulent to laminar. Under laminar
flow, ball speed is reduced by drag and the Magnus Effect dominates. This
makes the ball curve late on in flight, keeping goalkeepers guessing until the
very last second.
An interesting feature of the Magnus Effect is seen in the case of no gravity.
Without obstacles or gravity, a spinning ball still obeys the Magnus Effect;
producing a spiral flight path.
JAMES BRINDLEY, RYAN MEADEN, ROBERT NAISH, DANIEL VINCENT, DARYA KARELINA.
Blazevich, A. (2012) Sports Biomechanics: The Basics. 2nd ed. London: A&C Black Publishers || Mendes, R., Malacarne, L., and Anteneodo, C. (2007) ‘Statistics of Football Dynamics’. Eur. Phys. J. B 57, 357 || Seifert, J. (2012) ‘A review of the Magnus Effect in Aeronautics’. Progress in Aerospace Sciences 55, 17 ||
Mail Online (2009) The List: The Top 10 Free-kick Kings in History [online] available from <http://www.dailymail.co.uk/sport/football/article-1168803/THE-LIST-The-10-free-kick-kings-history.html> [07 February 2015] || Harper, D. (2014) Online Etymology Dictionary “Knuckleball” [Online] Available at
<http://www.etymonline.com/index.php?allowed_in_frame=0&search=knuckleball&searchmode=none> (Accessed: 26 February 2015) || Chartier, T. (2010) Bending a soccer ball with math. Available at: http://www.mathaware.org/mam/2010/essays/ChartierSoccer.pdf (Accessed: 5 March 2015) ||
Hyperspace (2012) Physics Buzz: The ‘Perfect’ Free Kick and the Magnus Effect, Physics Buzz. Available at: http://physicsbuzz.physicscentral.com/2012/06/perfect-free-kick-and-magnus-effect.html (Accessed: 5 March 2015) ||Discovery (2010) World Cup Ball: What’s Wrong With It?, YouTube. YouTube. Available at:
https://www.youtube.com/watch?v=NWjKVeH1QUQ (Accessed: 8 March 2015). || Sandhu, J et al. (2011). How to score a goal. Journal of Physics Special Topics. 10 (1), 1-2. ||