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.

We derive and evaluate a hydrodynamic theory of photon-drag effects in simple metals. Considering a jellium surface obliquely illuminated by monochromatic light, we calculate both the steady surface-parallel current and the emf induced along the surface normal. The sizes of these effects are estimated with a variety of approaches, ranging from momentum-balance arguments, through sum rules, to detailed microscopic calculations using a hydrodynamic description of the electrons’ dynamics. Comparisons between the sometimes different results help clarify the physical origin of the phenomena, in particular, the extent to which effects are surface sensitive. We also outline a calculational approach that should allow a tractable incorporation of quantum-mechanical dynamics.

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.

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.