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Effects of unsteady deformation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid. Aerodynamic forces on the flapping wing are not much affected by considerable twist, but affected by camber deformation. The effect of combined camber and twist deformation is similar to that of camber deformation. With a deformation of 6% camber and 20° twist (typical values observed for wings of many insects), lift is increased by 10% ∼ 20% and lift-to-drag ratio by around 10% compared with the case of a rigid flat-plate wing. As a result, the deformation can increase the maximum lift coefficient of an insect, and reduce its power requirement for flight. For example, for a hovering bumblebee with dynamically deforming wings (6% camber and 20° twist), aerodynamic power required is reduced by about 16% compared with the case of rigid wings. [ABSTRACT FROM AUTHOR]

The control of flight forces and moments by flapping wings of a model bumblebee is studied using the method of computational fluid dynamics. Hovering flight is taken as the reference flight: Wing kinematic parameters are varied with respect to their values at hovering flight. Moments about (and forces along) x, y, z axes that pass the center of mass are computed. Changing stroke amplitude (or wingbeat frequency) mainly produces a vertical force. Changing mean stroke angle mainly produces a pitch moment. Changing wing angle of attack, when down-and upstrokes have equal change, mainly produces a vertical force, while when down-and upstrokes have opposite changes, mainly produces a horizontal force and a pitch moment. Changing wing rotation timing, when dorsal and ventral rotations have the same timing, mainly produces a vertical force, while when dorsal and ventral rotations have opposite timings, mainly produces a pitch moment and a horizontal force. Changing rotation duration has very small effect on forces and moments. Anti-symmetrically changing stroke amplitude (or wingbeat frequency) of the contralateral wings mainly produces a roll moment. Anti-symmetrically changing angles of attack of the contralateral wings, when down-and upstrokes have equal change, mainly produces a roll moment, while when down-and upstrokes have opposite changes, mainly produces a yaw moment. Anti-symmetrically changing wing rotation timing of the contralateral wings, when dorsal and ventral rotations have the same timing, mainly produces a roll moment and a side force, while when dorsal and ventral rotations have opposite timings, mainly produces a yaw moment. Vertical force and moments about the three axes can be separately controlled by separate kinematic variables. A very fast rotation can be achieved with moderate changes in wing kinematics. [ABSTRACT FROM AUTHOR]

The longitudinal stabilization control of a hovering model insect was studied using the method of computational fluid dynamics to compute the stability and control derivatives, and the techniques of eigenvalue and eigenvector analysis and modal decomposition, for solving the equations of motion (morphological and certain kinematical data of hoverflies were used for the model insect). The model insect has the same three natural modes of motion as those reported recently for a hovering bumblebee: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. Controllability analysis shows that although unstable, the flight is controllable. For stable hovering, the unstable oscillatory mode needs to be stabilized and the slow subsidence mode needs stability augmentation. The former can be accomplished by feeding back pitch attitude, pitch rate and horizontal velocity to produce δϕ or δα2; the latter by feeding back vertical velocity to produce δΦ or δα1 (δΦ, δϕ, δα1 and δα2 denote control inputs: δΦ and δϕ represent changes in stroke amplitude and mean stroke angle, respectively; δα1 represents an equal change whilst δα2 a differential change in the geometrical angles of attack of the downstroke and upstroke). [ABSTRACT FROM AUTHOR]

The longitudinal dynamic flight stability of a hovering bumblebee was studied using the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. For the longitudinal disturbed motion, three natural modes were identified: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. The unstable oscillatory mode consists of pitching and horizontal moving oscillations with negligible vertical motion. The period of the oscillations is 0.32 s (approx. 50 times the wingbeat period of the bumblebee). The oscillations double in amplitude in 0.1 s; coupling of nose-up pitching with forward horizontal motion (and nose-down pitching with backward horizontal motion) in this mode causes the instability. The stable fast subsidence mode consists of monotonic pitching and horizontal motions, which decay to half of the starting values in 0.024 s. The stable slow subsidence mode is mainly a monotonic descending (or ascending) motion, which decays to half of its starting value in 0.37 s. Due to the unstable oscillatory mode, the hovering flight of the bumblebee is dynamically unstable. However, the instability might not be a great problem to a bumblebee that tries to stay hovering: the time for the initial disturbances to double (0.1 s) is more than 15 times the wingbeat period (6.4 ms), and the bumblebee has plenty of time to adjust its wing motion before the disturbances grow large. [ABSTRACT FROM AUTHOR]

Aerodynamic force generation and mechanical power requirements of a dragonfly (Aeschna juncea) in hovering flight are studied. The method of numerically solving the Navier-Stokes equations in moving overset grids is used. When the midstroke angles of attack in the downstroke and the upstroke are set to 52° and 8°, respectively (these values are close to those observed), the mean vertical force equals the insect weight, and the mean thrust is approximately zero. There are two large vertical force peaks in one flapping cycle. One is in the first half of the cycle, which is mainly due to the hindwings in their downstroke; the other is in the second half of the cycle, which is mainly due to the forewings in their downstroke. Hovering with a large stroke plane angle (52°), the dragonfly uses drag as a major source for its weight-supporting force (approximately 65% of the total vertical force is contributed by the drag and 35% by the lift of the wings). The vertical force coefficient of a wing is twice as large as the quasi-steady value. The interaction between the fore- and hindwings is not very strong and is detrimental to the vertical force generation. Compared with the case of a single wing in the same motion, the interaction effect reduces the vertical forces on the fore- and hindwings by 14% and 16%, respectively, of that of the corresponding single wing. The large vertical force is due to the unsteady flow effects. The mechanism of the unsteady force is that in each downstroke of the hindwing or the forewing, a new vortex ring containing downward momentum is generated, giving an upward force. The body-mass-specific power is 37 W kg-1, which is mainly contributed by the aerodynamic power. [ABSTRACT FROM AUTHOR]

We have examined the aerodynamic effects of corrugation in model insect wings that closely mimic the wing movements of hovering insects. Computational fluid dynamics were used with Reynolds numbers ranging from 35 to 3400, stroke amplitudes from 70 to 180 deg and mid-stroke angles of incidence from 15 to 60 deg. Various corrugated wing models were tested (care was taken to ensure that the corrugation introduced zero camber). The main results are as follows. At typical mid-stroke angles of incidence of hovering insects (35-50 deg), the time courses of the lift, drag, pitching moment and aerodynamic power coefficients of the corrugated wings are very close to those of the flat-plate wing, and compared with the flat-plate wing, the corrugation changes (decreases) the mean lift by less than 5% and has almost no effect on the mean drag, the location of the center of pressure and the aerodynamic power required. A possible reason for the small aerodynamic effects of wing corrugation is that the wing operates at a large angle of incidence and the flow is separated: the large angle of incidence dominates the corrugation in determining the flow around the wing, and for separated flow, the flow is much less sensitive to wing shape variation. The present results show that for hovering insects, using a flat-plate wing to model the corrugated wing is a good approximation. [ABSTRACT FROM AUTHOR]