The Ball in Flight Model

Abstract

This chapter is independent of the rest of this book. It derives equations for the three forces that affect the flight of the ball: the force of gravity, the drag force and the lift force due to the Magnus effect (the force due to a spinning object moving in an airflow). The lift and drag forces depend on air density. Altitude and weather affect air density, which in turn affects how far a batted baseball or softball travels. This chapter shows that air density is inversely related to altitude, temperature and humidity, and is directly related to barometric pressure. Regression analysis is used to show the relative importance of each of the four factors (altitude, temperature, humidity and barometric pressure) and to look for interactions between them. As shown by this model, on a typical July afternoon in a major-league baseball stadium, altitude is easily the most important factor, explaining 80% of the variability. This is followed by temperature (13%), barometric pressure (4%) and relative humidity (3%). A simple linear algebraic equation presented in this chapter predicts air density well. A different model shows how the batted-ball’s range depends on both the drag force and the Magnus force and considers the relative importance of the drag and Magnus forces. As asides, this chapter shows that a home run ball might go 26 feet farther in San Francisco then in Denver and it answers the question, “Can a tennis ball be thrown farther that a baseball?”