John Eric Goff

Trajectory analysis of a soccer ball

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.

Soccer Ball Lift Coefficients via Trajectory Analysis.

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 todays 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.

Parameter space for successful soccer kicks

A computational model of two important types of soccer kicks, the free kick and the corner kick, is developed with the goal of determining the success rate for each type of kick. What is meant by ‘success rate’ is the probability of getting an unassisted goal via a free kick and the probability of having a corner kick reach an optimum location so that a teammate’s chance of scoring a goal is increased. Success rates are determined through the use of four-dimensional parameter space volumes. A one-in-ten success rate is found for the free kick while the corner-kick success rate is found to be one in four.

Model of the 2003 Tour de France

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%.

A comparison of Jabulani and Brazuca non-spin aerodynamics

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.

Inclined-plane model of the 2004 Tour de France

We make modifications to a model we created to predict the stage-winning times of the 2003 Tour de France. With the modifications in place, we model the 2004 Tour de France. We demonstrate here the utility of our 2003 model with its successful application to the 2004 race; our total of all stage-winning times is just 0.05% different from the actual total. We also apply our 2004 model to the 2003 Tour de France and compare our results with our 2003 model. Our 2004 model misses the actual sum of stage-winning times in the 2003 race by just 1.77%.

Golden ratio in a coupled-oscillator problem

The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.

Predicting Tour de France stage-winning times with continuous power and drag area models and high speeds in 2013

We present comparisons between our predicted stage-winning times and actual stage-winning times for the 2012 and 2013 Tour de France races. The former race represented our last use of a decade-old discrete power and drag area models; the continuous power and drag area models used for the latter race represent significant changes in our modeling. Although our new model worked well when applied to the 2012 Tour de France, it did not fare so well in 2013, especially during the second week of the race when speeds were quite high.

Improving Tour de France modeling with allometric scaling

We describe improvements we have made to the model our research group employs to predict stage-winning times of the Tour de France. Accounting for different stage-winning cyclist masses associated with different stage types, we use allometric scaling to modify our model’s cyclist power output. We show definitively that such a change to our model improved our prediction capabilities over what we were able to predict using the model we employed for the 2013 Tour de France. Excluding three tailwind-dominated stages, where our worst error was 7.79%, we predicted all other stages to better than 5%, including five stages that we predicted to better than 1%. We also show how to improve our model further with a different type of scaling.

Critical shoe contact area ratio for sliding on a tennis hard court

Dimples have been used in the design of some modern tennis shoe outsoles to enhance sliding ability on hard courts. Experiments were performed with bespoke rubber samples possessing various numbers of holes, which served to simulate dimples in tennis shoe treads. The aim of the research was to assess the effect of contact area on sliding friction. As the ratio of holes to solid rubber increased, a critical ratio was reached whereby the static friction coefficient decreased by more than 11% for tread-to-court pressures comparable to real tennis play. Although this study analyzed bespoke rubber samples and not actual tennis shoe treads, shoe manufacturers should be interested in the existence of a critical dimple ratio that could aid them in the creation of tennis shoes suited for sliding on hard courts.