A mathematical model of the environmental effects on long jump performance of world class athletes

A model is presented that combines experimental data on the relationship between approach velocity and takeoff angle with a five-parameter model to approximate environmental effects on approach velocity and in-flight travel. Results indicate that wind speed provides the greatest influence on jump distance, followed by air density which itself is a product of altitude, temperature, air pressure, and humidity. Local fluctuations in the Earth's surface gravitational field strength are shown to have a slight effect on performance. Previously, analysis attributed the majority of performance increase to faster approach speed and takeoff velocity. These new results suggest a diminishing return to performance from an increase in approach speed.