Flow analysis and aerodynamic characteristics of a badminton shuttlecock with spin at high Reynolds numbers

Abstract

A badminton shuttlecock flies in a high-drag, and thus, the sport has been a subject of research from the point of view of aerodynamics. A badminton shuttlecock generates significant aerodynamic drag and has a complex flight trajectory. It also has the smallest ballistic coefficient and exhibits the largest in-flight deceleration of any airborne sporting projectile. The ballistic coefficient of a projectile is a measure of its ability to overcome air resistance in flight and is inversely proportional to deceleration. The primary objectives of this study were to measure the aerodynamic properties of feather shuttlecocks under a range of the wind speed (10–60 m/s) and pitch angle (0°–25°). In particular, measurements of aerodynamic forces were performed at high Reynolds numbers (more than Re = 210,000), and the effect of shuttlecock deformation on aerodynamic properties was also investigated, because it is presumed that the flight dynamics is affected by the deformation of the shuttlecock skirt. A shuttlecock skirt is composed of an array of diverging stems, the ends of which are at the convergent end of the skirt, joined together in an end ring. The shuttlecock rotates about its major axis in actual flight, and thus, the experiments were performed on shuttlecocks with and without rotation (spin). Furthermore, the effect of the flow passing through the gaps between the slots (stiffeners) located at the leg portion of the shuttlecock skirt on aerodynamic characteristics is demonstrated by means of a shuttlecock model without gaps, which was completely covered with cellophane tape. The free rotation rate of a shuttlecock increased with an increase in the Reynolds number, and the drag coefficient gradually decreased above Re = 86,000 for a non-rotating shuttlecock. The reduction of drag can be explained by the deformation of the skirt observed in wind tunnel experiments at high speed. In this study, for a rotating shuttlecock, a reduction of drag was not observed over a whole range of Reynolds numbers, because deformation of the skirt for a rotating shuttlecock becomes smaller than that for a non-rotating shuttlecock. However, there was no significant difference in drag coefficient between rotating and non-rotating shuttlecocks, in contrast to the difference in drag coefficient between shuttlecocks with and without gaps. The drag coefficient for a shuttlecock without gaps was significantly smaller than that for a standard shuttlecock (with gaps). For a standard shuttlecock, the air flowed through the gaps into the shuttlecock skirt, and this flow was related to high aerodynamic drag.