THE MAGNUS EFFECT - Online International...
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Curving Trajectories in Football 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. 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 off- centre, 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. The Magnus Effect in Ball Design 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. The Knuckleball 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. 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? 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 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 •Ball design : Different balls knuckle at different speeds 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. The Curveball 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. 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. The Magnus force can be described with the following equation: 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. || THE MAGNUS EFFECT = = ℎ = = = =
Transcript of THE MAGNUS EFFECT - Online International...
Curving Trajectories in Football 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.
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 off-centre, 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. The Magnus Effect in Ball Design 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.
The Knuckleball 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. 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? 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 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 •Ball design : Different balls knuckle at different speeds 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.
The Curveball 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. 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. The Magnus force can be described with the following equation: 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. ||
THE MAGNUS EFFECT
𝑭 = 𝟐𝝅𝑹𝟑𝝆𝝎𝝂
𝐹 = 𝑇ℎ𝑒 𝑀𝑎𝑔𝑛𝑢𝑠 𝐹𝑜𝑟𝑐𝑒
𝑅 = 𝑅𝑎𝑑𝑖𝑢𝑠
𝜌 = 𝑎𝑖𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦
𝜔 = 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝜈 = 𝑓𝑙𝑜𝑤 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
