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Most hovering insects flap their wings in a horizontal plane (body having a large angle from the horizontal), called 'normal hovering'. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane (body being approximately horizontal). In the present paper, wing and body kinematics of four freely hovering true hoverflies were measured using three-dimensional high-speed video. The measured wing kinematics was used in a Navier-Stokes solver to compute the aerodynamic forces of the insects. The stroke amplitude of the hoverflies was relatively small, ranging from 65 to 85 deg, compared with that of normal hovering. The angle of attack in the downstroke (~50 deg) was much larger that in the upstroke (~20 deg), unlike normal-hovering insects, whose downstroke and upstroke angles of attack are not very different. The major part of the weight-supporting force (approximately 86%) was produced in the downstroke and it was contributed by both the lift and the drag of the wing, unlike the normal-hovering case in which the weight-supporting force is approximately equally contributed by the two half-strokes and the lift principle is mainly used to produce the force. The mass-specific power was 38.59-46.3 and 27.5-35.4 W kg-1 in the cases of 0 and 100% elastic energy storage, respectively. Comparisons with previously published results of a normal-hovering true hoverfly and with results obtained by artificially making the insects' stroke planes horizontal show that for the true hoverflies, the power requirement for inclined stroke-plane hover is only a little (<10%) larger than that of normal hovering. [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]

We studied the effects of wing deformation on the aerodynamic forces of wings of hovering hoverflies by solving the Navier-Stokes equations on a dynamically deforming grid, employing the recently measured wing deformation data of hoverflies in free-flight. Three hoverf lies were considered. By taking out the camber deformation and the spanwise twist deformation one by one and by comparing the results of the deformable wing with those of the rigid flat-plate wing (the angle of attack of the rigid flatplate wing was equal to the local angle of attack at the radius of the second moment of wing area of the deformable wing), effects of camber deformation and spanwise twist were identified. The main results are as follows. For the hovering hoverf lies considered, the time courses of the lift, drag and aerodynamic power coefficients of the deformable wing are very similar to their counterparts of the rigid flat-plate wing, although lift of the deformable wing is about 10% larger, and its aerodynamic power required about 5% less than that of the rigid flat-plate wing. The difference in lift is mainly caused by the camber deformation, and the difference in power is mainly caused by the spanwise twist. The main reason that the deformation does not have a very large effect on the aerodynamic force is that, during hovering, the wing operates at a very high angle of attack (about 5odeg) and the flow is separated, and separated flow is not very sensitive to wing deformation. Thus, as a first approximation, the deformable wing in hover flight could be modeled by a rigid flat-plate wing with its angle of attack being equal to the local angle of attack at the radius of second moment of wing area of the deformable wing. [ABSTRACT FROM AUTHOR]

When an insect hovers, the centre of mass of its body oscillates around a point in the air and its body angle oscillates around a mean value, because of the periodically varying aerodynamic and inertial forces of the flapping wings. In the present paper, hover flight including body oscillations is simulated by coupling the equations of motion with the Navier-Stokes equations. The equations are solved numerically; periodical solutions representing the hover flight are obtained by the shooting method. Two model insects are considered, a dronefly and a hawkmoth; the former has relatively high wingbeat frequency (n) and small wing mass to body mass ratio, whilst the latter has relatively low wingbeat frequency and large wing mass to body mass ratio. The main results are as follows. (i) The body mainly has a horizontal oscillation; oscillation in the vertical direction is about 1/6 of that in the horizontal direction and oscillation in pitch angle is relatively small. (ii) For the hawkmoth, the peak-to-peak values of the horizontal velocity, displacement and pitch angle are 0.11 U (U is the mean velocity at the radius of gyration of the wing), 0.22=4mm (c is the mean chord length) and 4 deg., respectively. For the dronefly, the corresponding values are 0.02U, 0.05c=0.15mm and 0.3 deg., much smaller than those of the hawkmoth. (iii) The horizontal motion of the body decreases the relative velocity of the wings by a small amount. As a result, a larger angle of attack of the wing, and hence a larger drag to lift ratio or larger aerodynamic power, is required for hovering, compared with the case of neglecting body oscillations. For the hawkmoth, the angle of attack is about 3.5 deg. larger and the specific power about 9% larger than that in the case of neglecting the body oscillations; for the dronefly, the corresponding values are 0.7 deg. and 2%. (iv) The horizontal oscillation of the body consists of two parts; one (due to wing aerodynamic force) is proportional to 1/cn2 and the other (due to wing inertial force) is proportional to wing mass to body mass ratio. For many insects, the values of 1/cn2 and wing mass to body mass ratio are much smaller than those of the hawkmoth, and the effects of body oscillation would be rather small; thus it is reasonable to neglect the body oscillations in studying their aerodynamics. [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 aerodynamics and forewing-hindwing interaction of a model dragonfly in forward flight are studied, using the method of numerically solving the Navier-Stokes equations. Available morphological and stroke-kinematic parameters of dragonfly (Aeshna jancea) are used for the model dragonfly. Six advance ratios (J; ranging from 0 to 0.75) and, at each J, four forewing-hindwing phase angle differences (γd; 180°, 90°, 60° and 0°) are considered. The mean vertical force and thrust are made to balance the weight and body-drag, respectively, by adjusting the angles of attack of the wings, so that the flight could better approximate the real flight. At hovering and low J (J=0, 0.15), the model dragonfly uses separated flows or leading-edge vortices (LEV) on both the fore- and hindwing downstrokes; at medium J (J=0.30, 0.45), it uses the LEV on the forewing downstroke and attached flow on the hindwing downstroke; at high J (J=0.6, 0.75), it uses attached flows on both fore- and hindwing downstrokes. (The upstrokes are very lightly loaded and, in general, the flows are attached.) At a given J, at γd=180°, there are two vertical force peaks in a cycle, one in the first half of the cycle, produced mainly by the hindwing downstroke, and the other in the second half of the cycle, produced mainly by the forewing downstroke; at γd=90°, 60° and 0°, the two force peaks merge into one peak. The vertical force is close to the resultant aerodynamic force [because the thrust (or body-drag) is much smaller than vertical force (or the weight)]. 55–65% of the vertical force is contributed by the drag of the wings. The forewing-hindwing interaction is detrimental to the vertical force (and resultant force) generation. At hovering, the interaction reduces the mean vertical force (and resultant force) by 8–15%, compared with that without interaction; as J increases, the reduction generally decreases (e.g. at J=0.6 and γd=90°, it becomes 1.6%). A possible reason for the detrimental interaction is as follows: each of the wings produces a mean vertical force coefficient close to half that needed for weight support, and a downward flow is generated in producing the vertical force; thus, in general, a wing moves in the downwash-velocity field induced by the other wing, reducing its aerodynamic forces. [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]

Aerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion were studied using the method of computational fluid dynamics. The Navier-Stokes equations were solved numerically. The solution provided the flow velocity and pressure fields, from which the vorticity wake structure and the unsteady aerodynamic forces and torques were obtained (the inertial torques due to the acceleration of the wing-mass were computed analytically). From the flowstructure and force information, insights were gained into the unsteady aerodynamic force generation. On the basis of the aerodynamic and inertial torques, the mechanical power was obtained, and its properties were investigated. The unsteady force mechanisms revealed previously for hovering (i.e. delayed stall, rapid acceleration at the beginning of the strokes and fast pitching-up rotation at the end of the strokes) apply to forward flight. Even at high advance ratios, e.g. J=0.53-0.66 (J is the advance ratio), the leading edge vortex does not shed (at such advance ratios, the wing travels approximately 6.5 chord lengths during the downstroke). At !ow speeds (J≈0.13), the lift (vertical force) for weight support is produced during both the down- and upstrokes (the downstroke producing approximately 80% and the upstroke producing approximately 20% of the mean lift), and the lift is contributed mainly by the wing lift; the thrust that overcomes the body drag is produced during the upstroke, and it is contributed mainly by the wing drag. At medium speeds (J≈0.27), the lift is mainly produced during the downstroke and the thrust mainly during the upstroke; both of them are contributed almost equally by the wing lift and wing drag. At high speeds (J≈0.53), the lift is mainly produced during the downstroke and is mainly contributed by the wing drag; the thrust is produced during both the down- and upstrokes, and in the downstroke, is contributed by the wing lift and in the upstroke, by the wing drag. In forward flight, especially at medium and high flight speeds, the work done during the downstroke is significantly greater than during the upstroke. At advance ratios J≈0.13, 0.27 and 0.53, the work done during the downstroke is approximately 1.6, 2.8 and 4.2 times as much as that during the upstroke, respectively. At J=O (hovering), the body-mass-specific power is approximately 29 W kg[sup -1]; at J=0.13 and 0.27, the power is approximately 10% less than that of hovering; at J=0.40, the power is approximately the same as that of hovering; when J is further increased, the power increases sharply. The graph of power against flying speeds is approximately J -shaped. From the graph of power against flying speeds, it is predicted that the insect usually flies at advance ratios between zero and 0.4, and for fast flight, it would fly at an advance ratio between 0.4 and 0.53. [ABSTRACT FROM AUTHOR]

The lift and power requirements for hovering flight in Drosophila virilis were studied using the method of computational fluid dynamics. The Navier-Stokes equations were solved numerically. The solution provided the flow velocity and pressure fields, from which the unsteady aerodynamic forces and moments were obtained. The inertial torques due to the acceleration of the wing mass were computed analytically. On the basis of the aerodynamic forces and moments and the inertial torques, the lift and power requirements for hovering flight were obtained. For the fruit fly Drosophila virilis in hovering flight (with symmetrical rotation), a midstroke angle of attack of approximately 37° was needed for the mean lift to balance the insect weight, which agreed with observations. The mean drag on the wings over an up- or downstroke was approximately 1.27 times the mean lift or insect weight (i.e. the wings of this tiny insect must overcome a drag that is approximately 27 % larger than its weight to produce a lilt equal to its weight). The body-mass-specific power was 28.7Wkg[sup -1], the muscle-mass-specific power was 95.7Wkg[sup -1] and the muscle efficiency was 17 %. With advanced rotation, larger lift was produced than with symmetrical rotation, but it was more energy-demanding, i.e. the power required per unit lift was much larger. With delayed rotation, much less lilt was produced than with symmetrical rotation at almost the same power expenditure; again, the power required per unit lift was much larger. On the basis of the calculated results for power expenditure, symmetrical rotation should be used for balanced, long-duration flight and advanced rotation and delayed rotation should be used for flight control and manoeuvering. This agrees with observations. [ABSTRACT FROM AUTHOR]

Examines the unsteady aerodynamic force process of a model fruit fly wing in flapping motion. Acceleration of the wing at the beginning of a stroke; Increase of pitching-up rotation of the wing; Absence of stall during the stroke.