Lift generation with optimal elastic pitching for a flapping plate

Peng, Diing-wen; Milano, Michele

doi:10.1017/jfm.2012.614

Cited by 11 publications

(10 citation statements)

References 22 publications

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“…A dashed black line on each plot in (a-c) indicates the mean stroke amplitude before the maneuver Φmean=156 • ± 2. late their wing pitch and perform yaw turns [73]. Here, we highlight that fruit flies can also modulate the effective spring damping coefficient c and elastic coefficient k. This work builds on previous studies that used a damped torsional spring model [62,64,65,73,78] and on studies that showed that the torques exerted by the hinge can be approximated by a such a spring by analytically recovering the spring-torque from measured kinematic data [56,73]. Here, we use this torsional spring model to directly solve the equation of motion for the wing-pitch and reproduce its intricate kinematics.…”

Section: Fig 10 (Color Online) (A-c)supporting

confidence: 58%

“…Several pioneering studies have suggested that wingpitch kinematics are passively determined by a balance between aerodynamic and elastic torques, as well as the inertia of the moving wing [49][50][51][52][53][54][55][56]. Subsequently, a number of studies have used torsional-spring models to describe wing-pitch kinematics in mechanical [57][58][59][60][61][62][63][64] and computational [63,[65][66][67][68][69][70][71][72] models of flapping wings, as well as to describe wing-pitch kinematics of free-flying fruit flies [73]. For example, the latter study showed that the torques produced by the wing hinge to control wingpitch can be effectively modeled as those arising from a damped torsional spring.…”

Section: Introductionmentioning

confidence: 99%

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Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring

Beatus

Cohen

2015

Phys. Rev. E

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While the wing kinematics of many flapping insects have been well characterized, understanding the underlying sensory, neural, and physiological mechanisms that determine these kinematics is still a challenge. Two main difficulties in understanding the physiological mechanisms arise from the complexity of the interaction between a flapping wing and its own unsteady flow, as well as the intricate mechanics of the insect wing hinge, which is among the most complicated joints in the animal kingdom. These difficulties call for the application of reduced-order approaches. Here this strategy is used to model the torques exerted by the wing hinge along the wing-pitch axis of maneuvering fruit flies as a damped torsional spring with elastic and damping coefficients as well as a rest angle. Furthermore, we model the air flows using simplified quasistatic aerodynamics. Our findings suggest that flies take advantage of the passive coupling between aerodynamics and the damped torsional spring to indirectly control their wing-pitch kinematics by modulating the spring parameters. The damped torsional-spring model explains the changes measured in wing-pitch kinematics during roll correction maneuvers through modulation of the spring damping and elastic coefficients. These results, in conjunction with the previous literature, indicate that flies can accurately control their wing-pitch kinematics on a sub-wing-beat time scale by modulating all three effective spring parameters on longer time scales.

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Section: Fig 10 (Color Online) (A-c)supporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring

Beatus

Cohen

2015

Phys. Rev. E

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“…(22) and (24) with numerical or experimental results, it is convenient to define the amplitude ratios …”

Section: ) American Institute Of Aeronautics and Astronauticsmentioning

confidence: 99%

“…(14), (17), (22) and, (24), for the special case when the pitching angle, α(t), is in phase with the upward quarter-chord y-velocity component, V y (t), the coefficient for the instantaneous power required is obtained from the relation …”

Section: ) American Institute Of Aeronautics and Astronauticsmentioning

confidence: 99%

Propulsion Theory of Flapping Airfoils, Comparison with Computational Fluid Dynamics

Hunsaker

Phillips

2015

53rd AIAA Aerospace Sciences Meeting

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The thrust, required power, and propulsive efficiency of a flapping airfoil as predicted by the well-known Theodorsen model are compared with solutions obtained from gridresolved inviscid computational fluid dynamics.A straight-forward summary of Theodorsen's flapping airfoil model is presented using updated terminology and symbols. This shows that both axial and normal reduced frequencies are of significant importance. The axial reduced frequency is based on the chord length and the normal reduced frequency is based on the plunging amplitude. Computational fluid dynamics solutions are presented over the range of both reduced frequencies typically encountered in the forward flight of birds. It is shown that computational results agree reasonably well with those predicted by Theodorsen's model at low flapping frequencies. An alternate model is also developed, which shows that the time-dependent aerodynamic forces acting on a flapping airfoil can be related to two unknown Fourier coefficients. The computational results are correlated with algebraic relations for these Fourier coefficients, which can be used to predict the thrust, required power, and propulsive efficiency for airfoils with sinusoidal pitching and plunging motion.

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“…2013; Farrell Helbling & Wood 2018). Passive pitching during a flapping stroke is a consequence of flexibility and mediated by the interplay of elastic restoring, wing inertial and aerodynamic forces, associated with energy transfer between the fluid and structural kinetic and elastic energies (Peng & Milano 2013; Tian et al. 2013; Ishihara & Horie 2016; Kolomenskiy et al.…”

Section: Introductionmentioning

confidence: 99%

Power synchronisations determine the hovering flight efficiency of passively pitching flapping wings

Huang,

Bhat,

Yeo

et al. 2023

J. Fluid Mech.

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The power exchange between fluid and structure plays a significant role in the force production and flight efficiency of flapping wings in insects and artificial flyers. This work numerically investigates the performance of flapping wings by using a high-fidelity fluid–structure interaction solver. Simulations are conducted by varying the hinge flexibility (measured by the Cauchy number, $Ch$ , i.e. the ratio between aerodynamic and torsional elastic forces) and the wing shape (quantified by the radius of the first moment of area, $\bar {r}_1$ ). Results show that the lift production is optimal at $0.05 < Ch \leq 0.2$ and larger $\bar {r}_1$ where the minimum angle of attack is around $45^\circ$ at midstroke. The power economy is maximised for wings with lower $\bar {r}_1$ near $Ch=0.2$ . Power analysis indicates that the optimal performance measured by the power economy is obtained for those cases where two important power synchronisations occur: anti-synchronisation of the pitching elastic power and the pitching aerodynamic and inertial powers and nearly in-phase synchronisation of the flapping aerodynamic power and the total input power of the system. While analysis of the kinematics for the different wing shapes and hinge stiffnesses reveals that the optimal performance occurs when the timing of pitch and stroke reversals are matched, thus supporting the effective transfer of input power from flapping to passive pitching and into the fluid. These results suggest that careful optimisation between wing shapes and hinge properties can allow insects and robots to exploit the passive dynamics to improve flight performance.

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Lift generation with optimal elastic pitching for a flapping plate

Cited by 11 publications

References 22 publications

Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring

Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring

Propulsion Theory of Flapping Airfoils, Comparison with Computational Fluid Dynamics

Power synchronisations determine the hovering flight efficiency of passively pitching flapping wings

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