Fig 1.
Frames to describe the wing and body kinematics: the reference frame with origin at the wing base (X, Y, Z).
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; the Earth-fixed frame (xE, yE, zE); the insect’s body-fixed frame (xb, yb, zb).
Fig 2.
Experimental setup used to film the maneuver flights.
Table 1.
Morphological parameters of the fruitflies.
Fig 3.
(A) Video sequences of the flight after take-off for fruitfly FF1. (B) Time histories of body pitch motion (pitch angle θ’b = θb+β0, angular velocity qb and angular acceleration respectively). (C) Time histories of wing flapping motion. 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 upstroke.
Fig 4.
(A) The inertia pitch moment (Mi) and aerodynamic pitch moment (Ma) of FF1. The moments are non-dimensionalized by the mgc, where c is the mean chord length of wing: Mi+ = Mi/mgc and Ma+ = Ma/mgc. The stroke average moment of cycle a is approximately zero, and positive in cycle b, negative in cycle c and d. (B) Aerodynamic moment coefficient CM of cycle a, b and c, and the horizontal axis normalized by the cycle period.
Fig 5.
(A) Wing tip trajectory of cycle a. The red solid circle denotes the body mass center. (B) Aerodynamic force in the downstroke of cycle a. The reference vector denotes the magnitude of the insect weight. (C) Aerodynamic force in the upstroke of cycle a.
Fig 6.
(A) Wing tip trajectory of cycle b. The dash line indicates the wing tip trajectory of cycle a. (B) Aerodynamic force in the downstroke of cycle b. (C) Aerodynamic force in the upstroke of cycle b.
Fig 7.
(A) Wing tip trajectory of cycle c. The dash line indicates the wing tip trajectory of cycle a. (B) Aerodynamic force in the downstroke of cycle c. (C) Aerodynamic force in the upstroke of cycle c.
Fig 8.
The pitch angle of cycle a, b and c.
The horizontal axis is normalized with wingbeat cycle.
Fig 9.
The time histories of the pitch moment coefficients in a cycle for each case.
The horizontal axis is normalized with wingbeat cycle. (A) cycle b; (B) cycle c.
Table 2.
Difference in cycle-average moment coefficients compared with cycle a.
Table 3.
Difference in the angular displacement of pitch compared with cycle a.