Indeterminacy of drag exerted on an arrow in free flight: arrow attitude and laminar-turbulent transition

Abstract

The aerodynamic properties of an arrow (A/C/E; Easton) were investigated in an extension of our previous work, in which the laminar-turbulent transition of the boundary layer on the arrow shaft was found to take place in the Re number range of 1.2 × 104 < Re < 2.0 × 104. In this paper, we focus on the influence of the arrow’s attitude on the transition. Two types of vane (Spin Wing vane and Gas Pro vane) are fletched, and their stabilizing effects are compared. Two support-interference-free tests are performed to provide aerodynamic properties such as the drag, lift and pitching moment coefficients. The static aerodynamic properties are measured in a wind tunnel with JAXA’s 60 cm magnetic suspension and balance system. When the arrow is aligned with the flow, the boundary layer remains laminar for Re < 1.5 × 104, and the drag coefficient is approximately 1.5 for 1.0 × 104 < Re < 1.5 × 104. If the arrow has an angle of attack of 0.75 ° with the flow, the transition to turbulence takes place at approximately Re = 1.1 × 104, and the drag coefficient increases to approximately 3.1. In addition, free flight experiments are performed. The arrow’s velocity and angular velocity are recorded using five high-speed video cameras. By analysing the recorded images, we obtain the initial and final velocities from which the drag coefficient is determined. The trajectory and attitude of the arrow in free flight are computed numerically by integrating the equations of motion for a rigid body using the initial data obtained from the video images. The laminar-turbulent transition of the boundary layer is shown to take place, if the maximum angle of attack exceeds about 0.4° at Re = 1.75 × 104. The crucial influence of the initial angular velocity on the angle of attack is also examined.