The self-stabilizing nature of a dart and its low Reynolds number aerodynamic characteristics

Throwing darts is a popular sport today and has also played a significant role as a hunting weapon, yet, the role of aerodynamic forces governing its motion remains unexplored. Our high-speed imaging of dart trajectories illustrates a self-stabilizing behavior in the longitudinal plane, enabling the dart to maintain its orientation mid-flight and pierce the dartboard. We also obtain the aerodynamic characteristics of a dart body estimated using numerical simulations and force measurement. We examined surface pressure and wall shear-stress distribution on flights obtained numerically. Our findings suggest that the aerodynamic performance of a dart is governed by a complex interaction between the multiple vortex pairs emerging over the dart: Primary vortex on horizontal flights, its interaction with Barrel vortex shed by cone-cylinder forebody, and the influence of vertical flights. Smoke flow visualization of the flowfield also substantiates the vortical structures and their mutual interaction in the presence of flights that act like walls, corroborating our findings from the simulations. The combination of a high pitching moment and a long moment arm enables quick pitch stabilization keeping the attitude small and preventing the body from undergoing high side forces, attributed to the axisymmetric bodies at large angles of attack, thus avoiding destabilization. Dart is, therefore, a refined design that evolved over centuries that can serve as an inspiration for self-stabilizing flying vehicles.