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An Aerodynamic Analysis of Recent FIFA World Cup Balls
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Abstract
Drag and lift coefficients of recent FIFA world cup balls are examined. We fit a novel functional form to drag coefficient curves and in the absence of empirical data provide estimates of lift coefficient behaviour via a consideration of the physics of the boundary layer. Differences in both these coefficients for recent balls, which result from surface texture modification, can significantly alter trajectories. Numerical simulations are used to quantify the effect these changes have on the flight paths of various balls. Altitude and temperature variations at recent world cup events are also discussed. We conclude by quantifying the influence these variations have on the three most recent world cup balls, the Brazuca, the Jabulani and the Teamgeist. While our paper presents findings of interest to the professional sports scientist, it remains accessible to students at the undergraduate level.
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Aerodynamic forces act on a golf ball during flight. For that purpose in order to develop a golf ball with high performance, it is important to analyze aerodynamic characteristics of the golf ball. On the other hand, dimple pattern of a golf ball is complicate and the influence of dimples hasn’t been investigated in detail. Therefore the influence of golf ball dimples on aerodynamic characteristics was investigated using a wind tunnel and rotating device. Some golf balls whose dimples have different depths were measured. As a result, it was found that the shallower the dimple was, the larger the lift coefficient was. However, when the depth of the dimples was much shallower, the lift coefficient was extremely-little on the slow velocity, i.e. under 30m/s. When the golf ball trajectory which was launched with a driver was calculated under various initial conditions, the ball velocity became under 30 m/s over the vertex of the trajectory in many cases, including professional male golfers and female golfers. Therefore, if the lift coefficient of the velocity of 30m/s becomes smaller, distances will become shorter. Dimple patterns that had a high lift coefficient at all velocities was researched. As a result, it was found that a golf ball with a dimple pattern that has extremely small dimples between large shallow dimples has a high lift coefficient at all velocities, including under 30m/s. In order to investigate the cause of the results, a flow visualization experiment was conducted. Visualization of flow around a golf ball was conducted by generating smoke. Moreover pictures of flow were taken by high-speed video and analyzed by PIV (Particle Image Velocimetry). As a result, there was the difference in the streamline distribution between golf balls.
Wind-tunnel experimental measurements of drag coefficients for non-spinning Jabulani and Brazuca balls are presented. The Brazuca ball's critical drag speed is lower than that of the Jabulani ball, and the Brazuca ball's super-critical drag coefficient is larger than that of the Jabulani ball. Compared to the Jabulani ball, the Brazuca ball suffers less instability due to knuckle-ball effects. Using drag data, numerically determined ball trajectories are created, and it is postulated that although power shots are too similar to note flight differences, goalkeepers are likely to note the differences between Jabulani and Brazuca ball trajectories for intermediate-speed ranges. This latter result may appear in the 2014 World Cup for goalkeepers used to the flight of the ball used in the 2010 World Cup.
Baseball and softball are popular sports in many parts of the world especially in North America. These games are enjoyed both by participants and spectators. The flight trajectory of a baseball and softball largely depends on their aerodynamic characteristics. Despite the popularity of the game, it appears that little information on the aerodynamic force experienced by a baseball and softball is available. Having curved stitches, complex seams and their orientation, the airflow around these balls are believed to be significantly complex and little understood. The primary objective of this study was to measure aerodynamic drag of a series of baseballs and softballs. The aerodynamic forces and moments were measured experimentally for a range of wind speeds and seam orientations. The aerodynamic forces and their non-dimensional coefficients were analysed. The results indicate that the drag coefficients of a baseball and softball did not undergo a distinctive drag crisis as a smooth sphere due to their complex seams and their orientation. The findings also indicate that the seam orientation had profound impact on aerodynamic characteristics of both balls.
The purpose of this study is to analyze the fluid mechanics and frequency of forces acting on a knuckleball, specifically a soccer ball that was kicked and was in flight, was visualized using a smoke agent (titanium tetrachloride), and its unsteady aerodynamics were investigated. In the case of the knuckleball, the peak value of the vortex lift reached approximately 2.0 N, and the average vortex lift force frequency of approximately 3.5 Hz. A comparison of this vortex lift frequency and vortex oscillation frequency indicated that these frequencies tended to act in unison with a high statistical correlation (r=0.83,p<0.01)(r=0.83,p<0.01).
A new analysis is presented of the major findings in sports ball aerodynamics over the last 20 years, leading to a new method for defining surface roughness and its effects on the aerodynamic performance of sports balls. It was shown that the performance of balls in soccer, tennis, and golf are characterized by the position of the separation points on the surface of the ball, and that these are directly influenced by the roughness of the surface at a given Reynolds number and spin rate. The traditional measure of roughness k/D (the ratio of surface asperity dimension to diameter) was unable to predict the transition from laminar to turbulent flow for different sports balls. However, statistical measures of roughness commonly used in tribology were found to correlate well with the Reynolds number at transition and the minimum Cd after transition. It was concluded that this new measure and a further one of dimension should allow the complete characterization of the aerodynamic performance of sports balls. The effects of surface roughness on spin rate decay were also considered, and it was found that tennis balls had spin decay over six times that of golf balls and was due to the increased skin friction of the nap.
We performed experiments in which a soccer ball was launched from a machine while two cameras recorded portions of its trajectory. Drag coefficients were obtained from range measurements for no-spin trajectories, for which the drag coefficient does not vary appreciably during the ball's flight. Lift coefficients were obtained from the trajectories immediately following the ball's launch, in which Reynolds number and spin parameter do not vary much. We obtain two values of the lift coefficient for spin parameters that had not been obtained previously. Our codes for analyzing the trajectories are freely available to educators and students.
The nature of the forces causing the erratic motion of a knuckleball has been investigated by measuring the lateral force on a baseball in a wind tunnel. We have identified two possible sources of a lateral force imbalance that can give rise to the observed erratic changes in the direction of a knuckleball as it moves through the air. One of these results because the nonsymmetrical location of the roughness elements (strings) gives rise to a nonsymmetrical lift (lateral) force. A very slowly spinning knuckleball will have imposed upon it a lateral force that changes as the positions of the strings change. A knuckleball whose spin is identically zero has a constant lateral force unless a portion of the strings is precisely at a location where boundary layer separation occurs. If this happens, the point of boundary layer separation switches alternatively from the front to the rear of the strings, shifting the wake from one position to another, and thereby giving rise to a second possible alternating force imbalance. A two-dimensional analysis of the trajectory of the baseball indicates that the measured force can cause a deflection of the baseball's trajectory of more than a foot. An effective knuckleball should be thrown so that it rotates substantially less than once on its path to home plate.
The aerodynamic properties of an association football were measured using a wind tunnel arrangement. A third scale model of a generic football (with seams) was used in addition to a 'mini-football'. As the wind speed was increased, the drag coefficient decreased from 0.5 to 0.2, suggesting a transition from laminar to turbulent behaviour in the boundary layer. For spinning footballs, the Magnus effect was observed and it was found that reverse Magnus effects were possible at low Reynolds numbers. Measurements on spinning smooth spheres found that laminar behaviour led to a high drag coefficient for a large range of Reynolds numbers, and Magnus effects were inconsistent, but generally showed reverse Magnus behaviour at high Reynolds number and spin parameter. Trajectory simulations of free kicks demonstrated that a football that is struck in the centre will follow a near straight trajectory, dipping slightly before reaching the goal, whereas a football that is struck off centre will bend before reaching the goal, but will have a significantly longer flight time. The curving kick simulation was repeated for a smooth ball, which resulted in a longer flight time, due to increased drag, and the ball curving in the opposite direction, due to reverse Magnus effects. The presence of seams was found to encourage turbulent behaviour, resulting in reduced drag and more predictable Magnus behaviour for a conventional football, compared with a smooth ball. © IMechE 2005.
Trajectory analysis is an alternative to using wind tunnels to measure a soccer ball's aerodynamic properties. It has advantages over wind tunnel testing such as being more representative of game play. However, previous work has not presented a method that produces complete, speed-dependent drag and lift coefficients. Four high-speed cameras in stereo-calibrated pairs were used to measure the spatial co-ordinates for 29 separate soccer trajectories. Those trajectories span a range of launch speeds from 9.3 to 29.9 m s⁻¹. That range encompasses low-speed laminar flow of air over a soccer ball, through the drag crises where air flow is both laminar and turbulent, and up to high-speed turbulent air flow. Results from trajectory analysis were combined to give speed-dependent drag and lift coefficient curves for the entire range of speeds found in the 29 trajectories. The average root mean square error between the measured and modelled trajectory was 0.028 m horizontally and 0.034 m vertically. The drag and lift crises can be observed in the plots of drag and lift coefficients respectively.
The Magnus effect on a prototype model soccer ball rotating perpendicular to the flow direction at Reynolds numbers in the range of 0.96×510<ReD<4.62×5100.96×105<ReD<4.62×105 was investigated by means of aerodynamic force measurements and of a flow field survey. Experiments were performed using a rear sting support where the soccer ball was split into two halves that were driven by a motor inside of them. In the non-rotating state the variation of force coefficients with Reynolds number and boundary layer separation points are within the range that is found for real soccer balls. In the rotating-state, considerable changes of the mean force coefficients with Reynolds number ReDReD and spin parameter SPSP occurred, which can be attributed to the altered boundary layer separation. These changes also lead to significant changes of size and deflection of the wake zones in the lateral direction. A negative Magnus effect occurs in the critical Reynolds number range. Positive Magnus force is induced when the boundary layer is either laminar or turbulent on both sides of the rotating model soccer ball.
The present work is concerned with the flow past spheres in the Reynolds number range 5 × 104 [less-than-or-eq, slant] Re [less-than-or-eq, slant] 6 × 106. Results are reported for the case of a smooth surface. The total drag, the local static pressure and the local skin friction distribution were measured at a turbulence level of about 0·45%. The present results are compared with other available data as far as possible. Information is obtained from the local flow parameters on the positions of boundary-layer transition from laminar to turbulent flow and of boundary-layer separation. Finally the dependence of friction forces on Reynolds number is pointed out.
The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 10 ⁴ < Re < 6 × 10 ⁶ . The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.
The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.
The drag coefficient of a sphere under the blockage conditions 0·5 < d s / d t < 0·92 has been determined over the Reynolds number range 3 × 10 ⁴ < Re < 2 × 10 ⁶ . Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.
This paper describes experiments performed on stationary and rotating cricket balls to determine the aerodynamic forces acting on the ball over a range of bowling speeds and seam angles. Lift, drag and side forces were measured directly and it was found they exhibited magnitudes in the order of 1.4, 1 and 0.4 N, respectively, for the stationary ball. At air velocities above 20 m/s, the lift force increased with increasing air speed being weakly influenced by the vertical seam angle. At 10 m/s air speed, the side force began to increase steadily with air speed for seam angles up to 70°. At 80° the side force direction reversed due to the sudden movement of the separation point on the surface of the ball. Roughening one side of the ball increased the side force but delayed its reversal at 80° seam angle until a marginally higher velocity was reached. When top spin was applied to the smooth ball, the lift force increased almost linearly in the negative direction but there was no resultant side force. When a roughened ball was spun, the negative lift force was constant at all air speeds over a range of rotational speeds. The development of the measured forces are discussed in terms of boundary layer flow and Magnus effect.
The purpose of this study is to assess the fundamental characteristics that cause a football to spin in a curve ball kick due to impact conditions, and then to examine how the change in spin affects the flight of the ball.
Two experimental trials were carried out to examine the aerodynamic properties of footballs during flight. In the first trial, a football was projected with no spin at varying launch velocities and the trajectory of each flight measured and analysed. A drag coefficient was calculated for each test, based on a trajectory model. The second trial involved a football being fired with the same launch velocity, but varying spin conditions (spin axis horizontal in all cases). Again, the trajectory of each flight was measured and drag and lift coefficients were calculated. This information was used to simulate three typical game situations and the effects of foot impact offset distance and weather conditions were examined.
This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m x s(-1), the ball's initial elevation must be constrained between 16.5 degrees and 17.5 degrees and the ball kicked with almost perfect sidespin.
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Soccer ball lift coefficients via trajectory analysis
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Mathematical Tracts, 1 & 2
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