Kite festival: the physics behind the oscillations of a kite’s long tail

Abstract

When we watch a flying kite with a long tail hanging beneath, the tail sometimes oscillates and sometimes maintains a static shape. Generally, the tail portion deviates more when moving toward the free (bottom) end. The shape of the tail is described by a zeroth-order Bessel function where the coordinate origin locates at the tail’s bottom. In this paper, we derive simple equations to qualitatively explain the tail profile under a horizontal wind. We discuss three possible states: static bending, oscillations with small displacements around the vertical axis, and oscillations with small displacements around the static bending state. We find that the deviations of the small oscillations satisfy the zeroth-order Bessel function of the first kind. Since this work is aimed as reading material for teachers or undergraduate students, some approximations were performed for the sake of simplicity so that the solution can be obtained from standard mathematical procedures taught at the undergraduate level.