Kinematic and Aerodynamic Analysis of a Coccinella septempunctata Performing Banked Turns in Climbing Flight

Abstract

Many Coccinella septempunctata flights, with their precise positioning capabilities, have provided rich inspiration for designing insect-styled micro air vehicles. However, researchers have not widely studied their flight ability. In particular, research on the maneuverability of Coccinella septempunctata using integrated kinematics and aerodynamics is scarce. Using three orthogonally positioned high-speed cameras, we captured the Coccinella septempunctata's banking turns in the climbing flight in the laboratory. We used the measured wing kinematics in a Navier-Stokes solver to compute the aerodynamic forces acting on the insects in five cycles. Coccinella septempunctata can rapidly climb and turn during phototaxis or avoidance of predators. During banked turning in climbing flight, the translational part of the body, and the distance flown forward and upward, is much greater than the distance flown to the right. The rotational part of the body, through banking and manipulating the amplitude of the insect flapping angle, the stroke deviation angle, and the rotation angle, actively creates the asymmetrical lift and drag coefficients of the left and right wings to generate right turns. By implementing banked turns during the climbing flight, the insect can adjust its flight path more flexibly to both change direction and maintain or increase altitude, enabling it to effectively avoid obstacles or track moving targets, thereby saving energy to a certain extent. This strategy is highly beneficial for insects flying freely in complex environments.

Keywords: Coccinella septempunctata; aerodynamic forces; banked turns; climbing flight; wing kinematics.

Figure 1

Trinocular Stereo Vision System Model.

Figure 2

Videos of Coccinella septempunctata in climbing motion, presented from the perspectives of three cameras. The time notations are non-dimensionalized for the cycle.

Figure 3

Reference coordinate system (x_E, y_E, z_E) and the body angular velocity components along the three axes of the body-fixed frame (x_b, y_b, z_b): p (roll rate), q (pitch rate), r (yaw rate).

Figure 4

Wing kinematics parameters and coordinates.

Figure 5

Turning radius of a Coccinella septempunctata on the XY plane.

Figure 6

Portions of a computational grid system.

Figure 7

Illustrates the temporal evolution of the lift coefficient (CL) during the banked turn in the climbing flight for Coccinella septempunctata across different grid numbers within one cycle.

Figure 8

Variations in Euler angles (a) and center of mass displacement (b) of a Coccinella septempunctata during a banking turn.

Figure 9

Temporal records of the movements of the Coccinella septempunctata’s body, illustrated as the (a) rates of Euler angles; (b) rates of roll, pitch, and yaw movements; and (c) movement speed of the body’s center of mass, detailing u_c, v_c, and w_c for the translational velocity components and x_E, y_E, z_E for the spatial velocity components of the body’s mass center.

Figure 9

Temporal records of the movements of the Coccinella septempunctata’s body, illustrated as the (a) rates of Euler angles; (b) rates of roll, pitch, and yaw movements; and (c) movement speed of the body’s center of mass, detailing u_c, v_c, and w_c for the translational velocity components and x_E, y_E, z_E for the spatial velocity components of the body’s mass center.

Figure 10

Instantaneous wing kinematics of Coccinella septempunctata, (a) ϕ_w, the flapping angle; (b) θ_w, the deviation angle; and (c) α_w, the pitching angle.

Figure 11

Diagram illustrating insects performing inclined turns at the center of mass.

Figure 12

Diagram illustrating insects performing inclined turns at the center of mass.

Figure 13

The progression of the coefficients for wing lift and F force over five cycles.