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Soccer Kicks to Understand the Physics Behind Them

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Soccer Kicks to Understand the Physics Behind Them Analyzing the Use of the Magnus Effect in Soccer Goals Evamvid Sharma, Ifedayo Ajasa Summer Ventures in Math and Science 2015 Visual and Image Processing Dr. Rahman Tashakkori, David Kale, Sina Tashakkori, Grayson Fenwick Appalachian State University Abstract – The goal of this research was to analyze some of the most famous soccer kicks to understand the physics behind them. The research examined in particular each player’s use of the Magnus Effect to create opportunities that may not have been possible without utilization of the Effect. 1.0 Introduction This research studies one of the 2015 goals from the FIFA Women’s World Cup, as well as several other famous goals. All goals relate to the Magnus Effect, and several other research studies that explains its purpose. The first step was to review pre-existing literature on the subject. A paper that specifically relates to any of the goals we selected was Depeux 2010[2], which asserted that the path of a curving soccer ball was a spiral rather than a circle, and used the goal by Roberto Carlos from the Tournoi de France to demonstrate this. Other related literature includes several papers on the Magnus effect, some of those describing it in sports, and two analyses of drag coefficients for soccer balls [3, 4, and 6]. Although it is simple to view these goals on the most basic level, there was plenty more going on in the background that was not so easy to understand but worth studying. For each goal, we looked at the factors that made the shot into a goal. Most had in common human error and the Magnus Effect. After reading several articles discussing the effects of a spinning ball, we came across a theorem that explains the dramatic movement of soccer balls – The Magnus Effect. We wanted to examine the physics behind each goal in-depth. For the goals we chose, the common thread was the Magnus Effect. 2.0 Methodology Many Americans watched the final of the 2015 FIFA Women’s World Cup. The American women were set to face the Japanese national team, in a rematch of the 2011 World Cup Final. The teams were widely considered to be equals, so it was a pleasant surprise for the American fans when Carli Lloyd scored two goals in the first five minutes. Then, in the 11th minute, her teammate Lauren Holliday scored to put the USA up 3-0. When Lloyd scored again, in the 15th minute, she did so in spectacular fashion by shooting from the midfield line. She took the shot from almost directly on the midfield line during the final match of the FIFA Women’s World Cup. The Japanese goalkeeper, Ayumi Kaihori, allowed the ball into the goal after being caught looking into the sun as she moved back from the 18-yard goal box. She tripped on her own foot, but still managed to tip the ball to the side as she fell. However, it wasn’t enough to knock it wide, and the ball went in and hit the side netting of the goal. 1 Figure 2-1: Carli Lloyd's Half Field Goal Roberto Carlos is well known in the soccer community for his skill on set pieces. We examined two of his most famous goals. The first goal by Roberto Carlos that we examined is commonly known as the “banana kick”. A “banana kick” can be any kick that curves dramatically, but this goal in particular, scored in the opening match of the 1997 Tournoi de France, has acquired the name. This goal was scored off of a free kick where Carlos’ shot bent several yards around the “wall” (a group of players standing between the ball and the goal with the object of stopping the shot) and back to bounce off the inside of the post. The curve of the shot was so dramatic that the keeper, Fabian Barthez, didn’t even make an attempt for it, as he thought the ball would go wide. Figure 2-2: Roberto Carlos’ Banana Kick Goal 2 The second goal by Roberto Carlos, colloquially known as the “Impossible Goal”, was for Real Madrid against Tenerife on the 21st of February 1998. Carlos took the shot from the corner just before the ball would have gone out of bounds across the goal line. Carlos kicked the ball with an anticlockwise spin that tricked the goalkeeper, Bengt Andersson, into stepping off the line, leaving him unable to reach the ball when it subsequently curved back towards the goal. The easiest way for Carlos to kick it would have put a clockwise spin that would have curved away from the goal. However, by putting an anticlockwise spin on the ball, Carlos caused it to spin towards the goal. The shot was even more deceptive for the keeper because the initial force of the ball moved back towards the goal. This goal was not subject to the analysis that the others were, but presented as an example of some of the principles that were discussed. Figure 2-3: Roberto Carlos’ Impossible Goal The fourth goal that was analyzed in this research was David Beckham’s famous 2001 free kick against Greece that sealed England’s trip to the 2002 World Cup. 2 minutes and 40 seconds into stoppage time, England was awarded a free kick from just over 10 yards outside the goal box. Beckham’s kick curved within a couple of feet of the head of the closest member of the wall before swerving outwards to the top left corner of the Greek goal. This leveled Greece and England at 2 - 2. This tie and the result of the concurrent Germany-Finland game, also a tie, meant that England won the Qualification Group and advanced to the World Cup proper. 3 Figure 2-4: Beckham’s Free Kick The fifth goal we worked with was by Papiss Demba Cissé for Newcastle, against Chelsea on the 2nd of May, 2012. A teammate brought down a long throw in off of his chest near the top left corner of the goal box. It bounced towards Cissé, who struck it mid-bounce, imparting a spin that caused it to go towards the goal before flattening to go into the right side netting of the goal, over the head and outstretched arm of the Chelsea keeper, Peter Cech. Figure 2-5: Papiss Dempa Cissé’s shot In order to clearly understand these topics we needed to study several theories that proved the physics behind Carli Lloyd’s, Roberto Carlos’, and several other goals - Reynolds Number, Drag, and Magnus Effect. Reynolds Number is a dimensionless number governed by wind speed, air density, and the shape of the object. The coefficient of drag for any object in a given environment 4 varies with Reynolds Number. The drag and surface friction of the object create a so-called boundary layer across the surface, which consists of a layer of fluid being pulled by the surface of the ball in the direction of its spin. Drag is created as an object flows through the air, creating a viscous wake from behind. The larger the wake the larger the drag. The size of the boundary layer, which is itself affected by Reynolds’ Number can affect the size of the wake. Overall, drag increases with faster speed, a large Reynold Number, and a thick wake. The Magnus Effect is a principle that specifically explains the curve of a soccer ball. As a ball with continual rotation moves through the air, surface friction causes a boundary layer of air that is dragged in the direction of the spin to form. On one side, the boundary layer follows the same direction as the air passing. This interaction results in no collision, meaning the air flows faster by the ball and creating a low-pressure. On the other side, the boundary layer of air flows against the air passing by. This collision reduces the speed of the air around the ball, creating a high-pressure zone. Just like the concentration differential in diffusion – high-concentration to low-concentration, the high-pressure zone forces itself onto the low-pressure zone, forcing the object in the direction of the low pressure zone [1, 5]. 2.1 Lloyd Goal Physics To get data about the projectile motion variables of Carli Lloyd’s half field strike, we used ImageJ to measure some attributes of the shot, including Lloyd’s distance from the midfield line at the time of the shot, the height of the goalkeepers hand at the time of the tip, and the distance of the ball from the 6-yard goal box at the time of the tip. Using this data, we used some standard physics equations to find distance and time data for an idealized version of the shot. 2.2 Magnus Demonstration After seeing a video of a person utilizing the Magnus Effect by dropping basketballs off a dam with backspin and watching them be pushed away from a 650 ft. dam by the Magnus Force, we were inspired to do our own demonstration. We used the staircase in the Anne Belk Hall of Appalachian State University to perform several drop tests with a miniature foam soccer ball spinning in the air. We used two camera angles to properly show the movement of the spinning ball as it fell through the air. One of these cameras generated high framerate footage, at 124 frames per second, that was converted to slow motion to show in greater detail the flight of the ball. Once we had enough footage, we used Windows Live Movie Maker to create a video presentation to show the bend of the ball.
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