Wing and body motion and aerodynamic and leg forces during take-off in droneflies

Abstract

Here, we present a detailed analysis of the take-off mechanics in droneflies performing voluntary take-offs. Wing and body kinematics of the insects during take-off were measured using high-speed video techniques. Based on the measured data, the inertia force acting on the insect was computed and the aerodynamic force of the wings was calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. In take-off, a dronefly increases its stroke amplitude gradually in the first 10-14 wingbeats and becomes airborne at about the 12th wingbeat. The aerodynamic force increases monotonously from zero to a value a little larger than its weight, and the leg force decreases monotonously from a value equal to its weight to zero, showing that the droneflies do not jump and only use aerodynamic force of flapping wings to lift themselves into the air. Compared with take-offs in insects in previous studies, in which a very large force (5-10 times of the weight) generated either by jumping legs (locusts, milkweed bugs and fruit flies) or by the 'fling' mechanism of the wing pair (butterflies) is used in a short time, the take-off in the droneflies is relatively slow but smoother.

Keywords: aerodynamic force; body and wing kinematics; flight initiation; insect; leg force.

Figure 1.

Wing model; R, wing length; c, local chord length of wing. (Online version in colour.)

Figure 2.

(a) At time t_n−1, the models of the body and wings were matched with the pictures of the body and wings. (b) At time t_n, the pictures of the body and the wings have moved a little relative to the body and wings models at time t_n−1. (c) After a few adjustments, the body and wings models at time t_n−1 are made to match the pictures of the body and the wings at time t_n. (Online version in colour.)

Figure 3.

Morphological parameters of the wing and body, h₁, distance from the wing-root axis to the long-axis of the body; l₁, distance from the wing-root axis to the centre of mass of the body; l₂, distance from anterior end of the body to the centre of mass; l_r, distance between two wing roots; l_b, body length. (Online version in colour.)

Figure 4.

Angles of a flapping wing that determine the wing orientation. The (X, Y, Z) coordinates are in a system with its origin at the wing root; the Y-axis points to the side of the insect and the X–Y plane coincides with the stroke plane. l, a line that is perpendicular to the wing span and parallel to the stroke plane. ϕ, ψ and θ: positional angle, pitch angle and deviation angle of the wing, respectively. (Online version in colour.)

Figure 5.

Frame (x_E, y_E, z_E) is a right-handed, earth-fixed, inertial frame; the x_E and y_E axes are horizontal and the z_E axis is vertical, pointing downward. Frame (x_b, y_b, z_b) is a right-handed frame fixed on the insect body with its origin at the centre of mass of the wingless body; x_b axis is along the insect body, pointing from tail to head, and y_b axis points to the right side of the insect body.

Figure 6.

(a–z(vi)) Video sequences of a dronefly (DF1) starting flight. Only one of the three camera views is shown. Times noted are ms from the instant when the COM of insect body starts to raise. For complete video sequences, see the electronic supplementary material, movie S1. (Online version in colour.)

Figure 7.

Time histories of wing flapping motion of DF1. ϕ, positional angle; θ, stroke deviation angle; ψ, pitch angle (ψ is related to the angle of attack of the wing, α, as: α = ψ in the downstroke and α = 180°−ψ in the upstroke). Grey bars represent the downstroke. t = 0 is the time when the COM of the insect body starts to raise (wing flapping begins before t = 0). The insect becomes airborne at ‘separating point’. (Online version in colour.)

Figure 8.

Time histories of wing kinematical parameters of the insects. (a) Wingbeat frequency (n). (b) Stroke amplitude (Φ) (the mean of the left and right wings). (c) Mean stroke angle () (the mean of the left and right wings). (d) Time when the insect becomes airborne. DF1a and DF2a denote the second take-off flight of droneflies DF1 and DF2, respectively. t = 0 is the time when the COM of the insect body starts to raise (wing flapping begins before t = 0). (Online version in colour.)

Figure 9.

Measured body motion data of DF1. (a) Displacement of body COM (symbols and curves denote the original and smoothed data, respectively). (b) Orientation of the body (symbols and curves denote the original and smoothed data, respectively). Δx_E, Δy_E and Δz_E, displacements of body COM in x_E, y_E and z_E directions, respectively. ψ_b, θ_b and ϕ_b, heading, elevation and bank angles of the body, respectively. t = 0 is the time when the COM of the insect body starts to raise (wing flapping begins before t = 0). The insect becomes airborne at ‘separating point’. (Online version in colour.)

Figure 10.

Time histories of body motion of DF1. (a) Velocity of body COM. (b) Acceleration of body COM. (c) Angular velocity and acceleration of body. and , horizontal and vertical velocities of body COM, respectively; and , horizontal and vertical accelerations of body COM, respectively; and , pitch angular velocity and acceleration of body, respectively. (Online version in colour.)

Figure 11.

Vertical displacement (Δz_E) versus horizontal displacement (Δx_E) of the body COM during take-off of the droneflies. DF1a and DF2a denote the second take-off flight of droneflies DF1 and DF2, respectively. The insects become airborne at ‘separating point’, denoted by symbols (solid circle) on the curves. (Online version in colour.)

Figure 12.

Time histories of the vertical components of the inertia force (V_i), aerodynamic force (V_a) and leg force (V_leg); the forces are non-dimensionalized by the weight of the insect, mg; = (V_i/mg+1), = V_a/mg and = V_leg/mg. (a) DF1. (b) DF1a (the second take-off flight of dronefly DF1). (c) DF2. (d) DF2a (the second take-off flight of dronefly DF2). (e) DF3. t = 0 is the time when the COM of the insect body starts to raise (wing flapping begins before t = 0). The insect becomes airborne at ‘separating time’. (Online version in colour.)

Figure 13.

Time histories of the horizontal components of the inertia force (H_i), aerodynamic force (H_a) and leg force (H_leg); the forces are non-dimensionalized by the weight of the insect, mg; = H_i/mg, = H_a/mg and = H_leg/mg. (a) DF1. (b) DF1a (the second take-off flight of dronefly DF1). (c) DF2. (d) DF2a (the second take-off flight of dronefly DF2). (e) DF3. t = 0 is the time when the COM of the insect body starts to raise (wing flapping begins before t = 0). The insect becomes airborne at ‘separating time’. (Online version in colour.)

Figure 14.

Time histories of the (a) vertical (V_a) and (b) horizontal (H_a) components of the aerodynamic force of DF1, with and without the ground effect. The forces are non-dimensionalized by the weight of the insect, mg; = V_a/mg and = H_a/mg. t = 0 is the time when the COM of the insect body starts to raise (wing flapping begins before t = 0). The insect becomes airborne at ‘separating time’. (Online version in colour.)

Figure 15.

Averaged time histories of body motion of fruit flies (data points taken from Ref. [4]). (a) Velocity of body COM. (b) Acceleration of body COM. (c) Angular velocity and acceleration of body. and , horizontal and vertical velocities of body COM, respectively; and , horizontal and vertical accelerations of body COM, respectively; q and , pitch angular velocity and acceleration of body, respectively. (Online version in colour.)