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.

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.

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We performed experiments in which a soccer ball was launched from a machine while two high-speed cameras recorded portions of the trajectory. Using the trajectory data and published drag coefficients, we extracted lift coefficients for a soccer ball. We determined lift coefficients for a wide range of spin parameters, including several spin parameters that have not been obtained by today's wind tunnels. Our trajectory analysis technique is not only a valuable tool for professional sports scientists, it is also accessible to students with a background in undergraduate-level classical mechanics.

We modeled the 2003 Tour de France bicycle race using stage profile data for which elevations at various points in each stage are known. Each stage is modeled as a series of inclined planes. We accounted for the forces on a bicycle-rider combination such as aerodynamic drag and rolling resistance and calculated the winning stage times for an assumed set of bicycle and rider parameters. The calculated total race time differed from the sum of all actual winning stage times by only 0.03%.

We derive and evaluate a quantum mechanical, self-consistent field theory of the photon-drag effect in simple metals. The calculation of the induced voltage across a flat surface illuminated with light is based on a scheme that allows the separate treatment of contributions that depend on bulk or surface response properties. The microscopic theory uses the time-dependent local density-functional approach in a numerical formulation similar to that for second harmonic generation, but incorporates finite damping. The results show a considerable sensitivity to the surface behavior of the responding electrons, with the strength of the surface contribution increased by two orders of magnitude compared to an earlier hydrodynamic estimate.

Aerodynamic coefficients were determined for Telstar 18 and Brazuca, match balls for the 2018 and 2014 World Cups, respectively. Experimental determination of aerodynamic coefficients prompted the development of computationally determined soccer ball trajectories for most launch speeds experienced in actual play. Although Telstar 18's horizontal range will be nearly 10% shorter than Brazuca's horizontal range for high-speed kicks, both Telstar 18 and Brazuca have similar knuckling effects due to nearly equal critical speeds and high-speed drag coefficients that differ by less than 10%. Surface comparisons suggest why aerodynamic properties for the two World Cup balls are so similar.

The effect of a soccer ball’s surface texture on its aerodynamics and flight trajectory is not definitively known. For this study, five soccer balls were used, each having 32 panels with different surface textures. Their aerodynamics were examined via wind-tunnel experiments and then several non-spin trajectories were calculated for each ball. The results showed that the aerodynamic forces acting on a soccer ball change significantly depending on the surface texture of the ball, which in turn influences flight trajectories. The study contributes to an understanding of how a soccer ball’s surface influences the aerodynamics, which may impact the future design and development of soccer balls.