Physics of knuckleballs

Abstract

Zigzag paths in sports ball trajectories are exceptional events. They have been reported in baseball (from where the word knuckleball comes from), in volleyball and in soccer. Such trajectories are associated with intermittent breaking of the lateral symmetry in the surrounding flow. The different scenarios proposed in the literature (such as the effect of seams in baseball) are first discussed and compared to existing data. We then perform experiments on zigzag trajectories and propose a new explanation based on unsteady lift forces. In a second step, we exploit wind tunnel measurements of these unsteady lift forces to solve the equations of motion for various sports and deduce the characteristics of the zigzags, pointing out the role of the drag crisis. Finally, the conditions for the observation of such trajectories in sports are discussed.

Surface Patterns for Drag Modification in Volleyballs

“…The presence of two panel directions is supposed to be important for the anisotropic aerodynamic performance of volleyballs. The critical Reynolds numbers Re c = dU c /ν for the onset of the drag crisis are measured in Figure 2, where U c is the critical ball velocity and ν is the kinematic viscosity of the air (ν = 1.5 × 10 −5 m/s 2 at 20 • C [1,15]). Figure 3 shows the flight characteristics of each ball taken from the lateral and horizontal landing positions.…”

“…In ball sports, the well-controlled flight trajectory of a ball would be useful to lure opponents and score [15]. For instance, float serves are important skills for ace players and they utilize the knuckle effect of a ball, allowing a ball to fall suddenly or to have irregular flight paths using noor slow-rotating while flying [25].…”

“…The aerodynamic coefficients of the drag coefficient (C d ), the lift force coefficient (C l ) and the side force coefficient (C s ) were calculated as C d = 2D ρU 2 A , C l = 2L ρU 2 A and C s = 2S ρU 2 A , respectively. Here ρ is the density of air (ρ = 1.2 kg/m 3 ), A is the cross-sectional area of the volleyball (A = πd 2 /4 ≈ 0.0346 m 2 for the diameter of the volleyball d = 0.21 m [15]), and the D, L, and S quantities are the longitudinal, transverse and side components of the aerodynamic forces [6].…”

“…The drag force can be smaller on a rough ball than a smooth ball, especially at speeds in ball sports [14]. Zigzag paths (knuckleballs) have been reported for volleyballs with the typical ball velocity and the corresponding Reynolds number ∼4 ×10 5 [15]. Practically, aerodynamic modification through pattering surfaces is a plausible task to scientists and engineers [5,[16][17][18][19][20][21][22][23][24]..…”

A Computational Fluid Dynamics (CFD) Analysis of the Aerodynamic Effects of the Seams on a Two-Dimensional Representation of a Soccer Ball

“…Over the past decade, there have been extensive wind tunnel testing and flow visualization of various ball designs, surface geometry, and surface roughness [8][9][24][25][29][30][31][32] . The conclusions largely converged on the hypothesis that overall surface geometry of soccer balls alter the drag crisis to a lower Reynolds number in comparison to a smooth sphere, consistent with established work on surface roughening [4][5] .…”