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1.
This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple
harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular
amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α
A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play
dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping
are found to be more sensitive to changes in α
A than in Re. In fact, a subtle change in α
A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient
around α
A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a
reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α
A = 30° and a neutral wake structure at α
A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting
an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering
motion only, the unique force characteristics observed here, particularly their strong dependence on α
A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics
to help them to stay aloft and maneuver.
An erratum to this article can be found at 相似文献
2.
Lift and power requirements of hovering insect flight 总被引:6,自引:0,他引:6
Lift and power requirements for hovering flight of eight species of insects are studied by solving the Navier-Stokes equation numerically. The solution provides velocity and pressure fields, from which unsteady aerodynamic forces and moments are obtained. The inertial torque of wing mass are computed analytically. The wing length of the insects ranges from 2 mm (fruit fly) to 52 mm (hawkmoth); Reynolds numbers Re (based on mean flapping speed and mean chord length) ranges from 75 to 3850. The primary findings are shown in the following: (1) Either small (R = 2mm, Re = 75), medium (R ≈ 10 mm, Re ≈ 500) or large (R ≈ 50 mm, Re ≈ 4 000) insects mainly employ the same high-lift mechanism, delayed stall, to produce lift in hovering flight. The midstroke angle of attack needed to produce a mean lift equal to the insect weight is approximately in the range of 25° to 45°, which is approximately in agreement with observation. (2) For the small insect (fruit fly) and for the medium and large insects with relatively small wingbeat frequency (cranefly, ladybird and hawkmoth), the specific power ranges from 18 to 39W·kg^-1 , the major part of the power is due to aerodynamic force, and the elastic storage of negative work does not change the specific power greatly. However for medium and large insects with relatively large wingbeat frequency (hover fly, dronefly, honey bee and bumble bee), the specific power ranges from 39 to 61 W·kg^-1 , the major part of the power is due to wing inertia, and the elastic storage of negative work can decrease the specific power by approximately 33%. (3) For the case of power being mainly contributed by aerodynamic force (fruit fly, cranefly, ladybird and hawkmoth), the specific power is proportional to the product of the wingbeat frequency, the stroke amplitude, the wing length and the drag-to-lift ratio. For the case of power being mainly contributed by wing inertia (hoverfly, dronefly, honey bee and bumble bee), the specific power (without elastic storage) is proportional to the product of the cubic of wingbeat frequency, the square of the stroke amplitude, the square of the wing length and the ratio of wing mass to insect mass. 相似文献
3.
Compliant wing designs have the potential of improving flapping wing Micro-Air Vehicles (MAVs). Designing compliant wings
requires a detailed understanding of the effect of compliance on the generation of thrust and lift forces. The low force and
high-frequency measurements associated with these forces necessitated a new versatile test stand design that uses a 250 g
load cell along with a rigid linear air bearing to minimize friction and the dynamic behavior of the test stand while isolating
only the stationary thrust or lift force associated with drag generated by the wing. Moreover, this stand is relatively inexpensive
and hence can be easily utilized by wing designers to optimize the wing compliance and shape. The frequency response of the
wing is accurately resolved, along with wing compliance on the thrust and lift profiles. The effects of the thrust and lift
force generated as a function of flapping frequency were also determined. A semi-empirical aerodynamic model of the thrust
and lift generated by the flapping wing MAV on the new test stand was developed and used to evaluate the measurements. This
model accounted for the drag force and the effects of the wing compliance. There was good correlation between the model predictions
and experimental measurements. Also, the increase in average thrust due to increased wing compliance was experimentally quantified
for the first time using the new test stand. Thus, our measurements for the first time reveal the detrimental influence of
excessive compliance on drag forces during high frequency operation. In addition, we were also able to observe the useful
effect of compliance on the generation of extra thrust at the beginning and end of upstrokes and downstrokes of the flapping
motion. 相似文献
4.
Experimental investigation of the effect of chordwise flexibility on the aerodynamics of flapping wings in hovering flight 总被引:1,自引:0,他引:1
Ornithopters or mechanical birds produce aerodynamic lift and thrust through the flapping motion of their wings. Here, we use an experimental apparatus to investigate the effects of a wing's twisting stiffness on the generated thrust force and the power required at different flapping frequencies. A flapping wing system and an experimental set-up were designed to measure the unsteady aerodynamic and inertial forces, power usage and angular speed of the flapping wing motion. A data acquisition system was set-up to record important data with the appropriate sampling frequency. The aerodynamic performance of the vehicle under hovering (i.e., no wind) conditions was investigated. The lift and thrust that were produced were measured for different flapping frequencies and for various wings with different chordwise flexibilities. The results show the manner in which the elastic deformation and inertial flapping forces affect the dynamical behavior of the wing. It is shown that the generalization of the actuator disk theory is, at most, only valid for rigid wings, and for flexible wings, the power P varies by a power of about 1.0 of the thrust T. This aerodynamic information can also be used as benchmark data for unsteady flow solvers. 相似文献
5.
昆虫拍翼方式的非定常流动物理再探讨 总被引:5,自引:0,他引:5
基于提出的理论模化方法来探讨昆虫拍翼方式的非定常流动物理. 以悬停飞行为
例,通过对拍翼运动的分析,不仅解释了昆虫利用高频拍翼的方式为何能够克服低雷诺数带
来的气动局限性(St \gg 1/Re),而且还指出高升力产生和调节的3个流动
控制因素:(1) 由于拍翼的变速运动即时引起了流体动力响应,这种附加惯性效应
可产生瞬时的高升力; (2) 保持前缘涡不脱离翼面有助于减少升力的下降;
(3) 增大后缘涡的强度并加速其脱离后缘能够有效地提高升力. 相似文献
6.
This paper is motivated by the works of Dickinson et al. (Science 284:1954–1960, 1999) and Sun and Tang (J Exp Biol 205:55–70, 2002) which provided two different perspectives on the influence of wing–wake interaction (or wake capture) on lift generation
during flapping motion. Dickinson et al. (Science 284:1954–1960, 1999) hypothesize that wake capture is responsible for the additional lift generated at the early phase of each stroke, while Sun
and Tang (J Exp Biol 205:55–70, 2002) believe otherwise. Here, we take a more fundamental approach to study the effect of wing–wake interaction on the aerodynamic
force generation by carrying out simultaneous force and flow field measurements on a two-dimensional wing subjected to two
different types of motion. In one of the motions, the wing at a fixed angle of attack was made to follow a motion profile
described by “acceleration-constant velocity-deceleration”. Here, the wing was first linearly accelerated from rest to a predetermined
maximum velocity and remains at that speed for set duration before linearly decelerating to a stop. The acceleration and deceleration
phase each accounted for only 10% of the stroke, and the stroke covered a total distance of three chord lengths. In another
motion, the wing was subjected to the same above-mentioned movement, but in a back and forth manner over twenty strokes. Results
show that there are two possible outcomes of wing–wake interaction. The first outcome occurs when the wing encounters a pair
of counter-rotating wake vortices on the reverse stroke, and the induced velocity of these vortices impinges directly on the
windward side of the wing, resulting in a higher oncoming flow to the wing, which translates into a higher lift. Another outcome
is when the wing encounters one vortex on the reverse stroke, and the close proximity of this vortex to the windward surface
of the wing, coupled with the vortex suction effect (caused by low pressure region at the center of the vortex), causes the
net force on the wing to decrease momentarily. These results suggest that wing–wake interaction does not always lead to lift
enhancement, and it can also cause lift reduction. As to which outcome prevails depend very much on the flapping motion and
the timing of the reverse stroke. 相似文献
7.
Karim Mazaheri Abbas Ebrahimi 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(11):1255-1269
Flapping wings are promising lift and thrust generators, especially for very low Reynolds numbers. To investigate aeroelastic
effects of flexible wings (specifically, wing’s twisting stiffness) on hovering and cruising aerodynamic performance, a flapping-wing
system and an experimental setup were designed and built. This system measures the unsteady aerodynamic and inertial forces,
power usage, and angular speed of the flapping wing motion for different flapping frequencies and for various wings with different
chordwise flexibility. Aerodynamic performance of the vehicle for both no wind (hovering) and cruise condition was investigated.
Results show how elastic deformations caused by interaction of inertial and aerodynamic forces with the flexible structure
may affect specific power consumption. This information was used here to find a more suitable structural design. The best
selected design in our tests performs up to 30% better than others (i.e., less energy consumption for the same lift or thrust
generation). This measured aerodynamic information could also be used as a benchmarking data for unsteady flow solvers. 相似文献
8.
A new bionic MAV's flapping motion based on fruit fly hovering at low Reynolds number 总被引:1,自引:0,他引:1
On the basis of the studies on the high unsteady aerodynamic mechanisms of the fruit fly hovering the aerodynamic advantages
and disadvantages of the fruit fly flapping motion were analyzed. A new bionic flapping motion was proposed to weaken the
disadvantages and maintain the advantages, it may be used in the designing and manufacturing of the micro air vehicles (MAV’s).
The translation of the new bionic flapping motion is the same as that of fruit fly flapping motion. However, the rotation
of the new bionic flapping motion is different. It is not a pitching-up rotation as the fruit fly flapping motion, but a pitching-down
rotation at the beginning and the end of a stroke. The numerical method of 3rd-order Roe scheme developed by Rogers was used
to study these questions. The correctness of the numerical method and the computational program was justified by comparing
the present CFD results of the fruit fly flapping motion in three modes, i.e., the advanced mode, the symmetrical mode and
the delayed mode, with Dickinson’s experimental results. They agreed with each other very well. Subsequently, the aerodynamic
characteristics of the new bionic flapping motion in three modes were also numerically simulated, and were compared with those
of the fruit fly flapping. The conclusions could be drawn that the high unsteady lift mechanism of the fruit fly hovering
is also effectively utilized by this new bionic flapping. Compared with the fruit fly flapping, the unsteady drag of the new
flapping decreases very much and the ratio of lift to drag increases greatly. And the great discrepancies among the mean lifts
of three flapping modes of the fruit fly hovering are effectively smoothed in the new flapping. On the other hand, this new
bionic flapping motion should be realized more easily. Finally, it must be pointed out that the above conclusions were just
drawn for the hovering flapping motion. And the aerodynamic characteristics of the new bionic flapping motion in forward flight
are going to be studied in the next step.
The project supported by the National Natural Science Foundation of China (10232010, 10032060, 90605005). 相似文献
9.
A growing body of evidence indicates that a majority of insects experience some degree of wing deformation during flight.
With no musculature distal to the wing base, the instantaneous shape of an insect wing is dictated by the interaction of aerodynamic
forces with the inertial and elastic forces that arise from periodic accelerations of the wing. Passive wing deformation is
an unavoidable feature of flapping flight for many insects due to the inertial loads that accompany rapid stroke reversals—loads
that well exceed the mean aerodynamic force. Although wing compliance has been implicated in a few lift-enhancing mechanisms
(e.g., favorable camber), the direct aerodynamic consequences of wing deformation remain generally unresolved. In this paper,
we present new experimental data on how wing compliance may affect the overall induced flow in the hawkmoth, Manduca sexta. Real moth wings were subjected to robotic actuation in their dominant plane of rotation at a natural wing beat frequency
of 25 Hz. We used digital particle image velocimetry at exceptionally high temporal resolution (2,100 fps) to assess the influence
of wing compliance on the mean advective flows, relying on a natural variation in wing stiffness to alter the amount of emergent
deformation (freshly extracted wings are flexible and exhibit greater compliance than those that are desiccated). We find
that flexible wings yield mean advective flows with substantially greater magnitudes and orientations more beneficial to lift
than those of stiff wings. Our results confirm that wing compliance plays a critical role in the production of flight forces.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
10.
柔性扑翼的气动特性研究 总被引:6,自引:0,他引:6
以往扑翼的气动力计算研究都很少考虑扑翼的柔性,而在鸟的扑翼动作中,在外加气动力和鸟自身的扑动力作用下,扑翼的柔性变形相当大。本文在原有匀速刚性模型的基础上,提出考虑了扑翼扑动速率变化和形状变化的扑翼分析模型,使之更接近鸟翼柔性扑动真实情况。通过计算分析气动特性发现,控制适当的话,柔性变形能大大改善扑翼的气动性能。本文通过模拟鸟扑翼的柔性运动,计算了时柔性扑翼气动力以及平均升力系数和平均推力系数随着扑动角、倾斜角等参数变化的情况,从而从气动的角度解释了为什么鸟在不同的飞行阶段扑翼规律各不相同,并为柔性扑翼飞行器的设计提供了理论依据。 相似文献
11.
Near wake vortex dynamics of a hovering hawkmoth 总被引:1,自引:0,他引:1
Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wingbased micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventu- ally break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time- varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle. 相似文献
12.
To examine the effects of wing morphing on unsteady aerodynamics, deformable flapping plates are numerically studied in a low-Reynolds-number flow. Simulations are carried out using an in-house immersed-boundary-method-based direct numerical simulation (DNS) solver. In current work, chord-wise camber is modeled by a hinge connecting two rigid components. The leading portion is driven by a biological hovering motion along a horizontal stroke plane. The hinged trailing-edge flap (TEF) is controlled by a prescribed harmonic deflection motion. The effects of TEF deflection amplitude, deflection phase difference, hinge location, and Reynolds number on the aerodynamic performance and flow structures are investigated. The results show that the unsteady aerodynamic performance of deformable flapping plates is dominated by the TEF deflection phase difference, which directly affects the strength of the leading-edge vortex (LEV) and thus influences the entire vortex shedding process. The overall lift enhancement can reach up to 26% by tailoring the deflection amplitude and deflection phase difference. It is also found that the role of the dynamic TEF played in the flapping flight is consistent over a range of hinge locations and Reynolds numbers. Results from a low aspect-ratio (AR=2) deformable plate show the same trend as those of 2-D cases despite the effect of the three-dimensionality. 相似文献
13.
K. MazaheriA. Ebrahimi 《Journal of Fluids and Structures》2011,27(4):586-595
The aerodynamic performance of a flexible membrane flapping wing has been investigated here. For this purpose, a flapping-wing system and an experimental set-up were designed to measure the unsteady aerodynamic forces of the flapping wing motion. A one-component force balance was set up to record the temporal variations of aerodynamic forces. The flapping wing was studied in a large low-speed wind tunnel. The lift and thrust of this mechanism were measured for different flapping frequencies, angles of attack and for various wind tunnel velocities. Results indicate that the thrust increases with the flapping frequency. An increase in the wind tunnel speed and flow angle of attack leads to reduction in the thrust value and increases the lift component. The aerodynamic and performance parameters were nondimensionalized. Appropriate models were introduced which show its aerodynamic performance and may be used in the design process and also optimization of the flapping wing. 相似文献
14.
仿生扑翼飞行机器人翅型的研制与实验研究 总被引:6,自引:0,他引:6
模仿昆虫和小鸟飞行的扑翼飞行机器人将举升、悬停和推进功能集于一个扑翼系统,与固定翼和旋翼完全不同,因此研究只能从生物仿生开始。生物飞行的极端复杂性使得进行完整和精确的扑翼飞行分析非常复杂,因此本文在仿生学进展基础上,通过一些合适的假设和简化,建立了仿生翅运动学和空气动力学模型,并以此为基础研制了多种翅型。研制了气动力测量实验平台,对各种翅型进行了实验研究。实验结果表明,研制的翅型都能产生一定的升力,其中柔性翅具有较好的运动性能和气动性能,并且拍动频率和拍动幅度对升力有较大影响。 相似文献
15.
Flight agility, resistance to gusts, capability to hover coupled with a low noise generation might have been some of the reasons
why insects are among the oldest species observed in nature. Biologists and aerodynamicists focused on analyzing such flight
performances for diverse purposes: understanding the essence of flapping wings aerodynamics and applying this wing concept
to the development of micro-air vehicles (MAVs). In order to put into evidence the fundamentally non-linear unsteady mechanisms
responsible for the amount of lift generated by a flapping wing (Dickinson et al. in Science 284:1954–1960, 1999), experimental and numerical studies were carried out on typical insect model wings and kinematics. On the other hand, in
the recent context of MAVs development, it is of particular interest to study simplified non-biological flapping configurations
which could lead to lift and/or efficiency enhancement. In this paper, we propose a parametrical study of a NACA0012 profile
undergoing asymmetric hovering flapping motions at Reynolds 1000. On the contrary to normal hovering, which has been widely
studied as being the most common configuration observed in the world of insects, asymmetric hovering is characterized by an
inclined stroke plane. Besides the fact that the vertical force is hence a combination of both lift and drag (Wang in J Exp
Biol 207:1137–1150, 2004), the specificity of such motions resides in the vortex dynamics which present distinct behaviours, whether the upstroke
angle of attack leads to a partially attached or a strong separated flow, giving more or less importance to the wake capture
phenomenon. A direct consequence of the previous remarks relies on the enhancement of aerodynamic efficiency with asymmetry.
If several studies reported results based on the asymmetric flapping motion of dragonfly, only few works concentrated on parametrizing
asymmetric motions (e.g. Wang in Phys Rev Lett 85:2216–2219, 2000). The present study relies on TR-PIV measurements which allow determination of the vorticity fields and provide a basis to
evaluate the resulting unsteady forces through the momemtum equation approach. 相似文献
16.
The aerodynamic mechanism of the bat wing membrane Mong the lateral border of its body is studied. The twist-morphing that alters the angle of attack (AOA) along the span-wise direction is observed widely during bat flapping flight. An assumption is made that the linearly distributed AOA is along the span-wise direction. The plate with the aspect ratio of 3 is used to model a bat wing. A three-dimensional (3D) unsteady panel method is used to predict the aerodynamic forces generated by the flapping plate with leading edge separation. It is found that, relative to the rigid wing flapping, twisting motion can increase the averaged lift by as much as 25% and produce thrust instead of drag. Furthermore, the aerodynamic forces (lift/drag) generated by a twisting plate-wing are similar to those of a pitching rigid-wing, meaning that the twisting in bat flight has the same function as the supination/pronation motion in insect flight. 相似文献
17.
In this paper, the decade of numerical and experimental investigations leading to the development of the authors’ unique flapping-wing
micro air vehicle is summarized. Early investigations included the study of boundary layer energization by means of a small
flapping foil embedded in a flat-plate boundary layer, the reduction of the recirculatory flow region behind a backward-facing
step by means of a small flapping foil, and the reduction or suppression of flow separation behind blunt or cusped airfoil
trailing edges by flapping a small foil located in the wake flow region. These studies were followed by systematic investigations
of the aerodynamic characteristics of single flapping airfoils and airfoil combinations. These unsteady flows were described
using flow visualization, laser-Doppler velocimetry in addition to panel and Navier–Stokes computations. It is then shown
how this flapping-wing database was used to conceive, design and develop a micro air vehicle which has a fixed wing for lift
and two flapping wings for thrust generation. While animal flight is characterized by a coupled force generation, the present
design appears to separate lift and thrust. However, in fact, the performance of one surface is closely coupled to the other
surfaces. 相似文献
18.
The development of Micro Air Vehicles with flapping wings is inspired from the observation and study of natural flyers such
as insects and birds. This article explores the rotational power consumption of a flapping wing using a mechanical flapper
at Re ≃ 4,500. This mechanical flapper is simplified to a 2D translation and a rotation in a water tank. Moreover, the wing kinematics
are reduced to a linear translation and a rotation for the purpose of our study. We introduce the notion of non-ideal flapper
and associated non-ideal rotational power. Such non-ideal devices are defined as consuming power for adding and removing mechanical
power to and from the flow, respectively. First, we use a traditional symmetrical wing kinematic which is a simplified kinematic
inspired from natural flyers. The lift coefficient of this flapping is about C
L ≃ 1.5. This symmetrical wing kinematic is chosen as a reference. Further, wing kinematics with asymmetric rotations are then
compared with this one. These new kinematics are built using a differential velocity defined according to the translational
kinematics, a time lag and a distance, r
kp. The analogy of this distance is discussed as a key point to follow along the chord. First, the wing kinematics are varied
keeping a similar shape for the profiles of the angular velocity. It is shown that when compared to the reference wing kinematic,
a 10% reduction in the rotational power is obtained whilst the lift is reduced by 9%. Second, we release the limitation to
a similar shape for the profiles of the angular velocity leading to a novel shape for the angular velocity profile named here
as “double bump” profile. With these new wing kinematics, we show that a 60% reduction in the non-ideal rotational power can
be achieved whilst the lift coefficient is only reduced by 1.7%. Such “double bump kinematics” could then be of interest to
increase the endurance of Micro Air Vehicles. 相似文献
19.
A study on the mechanism of high-lift generation by an airfoil in unsteady motion at low reynolds number 总被引:3,自引:0,他引:3
The aerodynamic force and flow structure of NACA 0012 airfoil performing an unsteady motion at low Reynolds number (Re=100) are calculated by solving Navier-Stokes equations. The motion consists of three parts: the first translation, rotation
and the second translation in the direction opposite to the first. The rotation and the second translation in this motion
are expected to represent the rotation and translation of the wing-section of a hovering insect. The flow structure is used
in combination with the theory of vorticity dynamics to explain the generation of unsteady aerodynamic force in the motion.
During the rotation, due to the creation of strong vortices in short time, large aerodynamic force is produced and the force
is almost normal to the airfoil chord. During the second translation, large lift coefficient can be maintained for certain
time period and
, the lift coefficient averaged over four chord lengths of travel, is larger than 2 (the corresponding steady-state lift coefficient
is only 0.9). The large lift coefficient is due to two effects. The first is the delayed shedding of the stall vortex. The
second is that the vortices created during the airfoil rotation and in the near wake left by previous translation form a short
“vortex street” in front of the airfoil and the “vortex street” induces a “wind”; against this “wind” the airfoil translates,
increasing its relative speed. The above results provide insights to the understanding of the mechanism of high-lift generation
by a hovering insect.
The project supported by the National Natural Science Foundation of China (19725210) 相似文献
20.
Dynamic flight stability of hovering insects 总被引:2,自引:3,他引:2
The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the
“rigid body” assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of
four insects (hoverfly, cranefly, dronefly and hawkmoth) in hovering flight is studied (the mass of the insects ranging from
11 to 1,648 mg and wingbeat frequency from 26 to 157 Hz). The method of computational fluid dynamics is used to compute the
aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion.
The validity of the “rigid body” assumption is tested and how differences in size and wing kinematics influence the applicability
of the “rigid body” assumption is investigated. The primary findings are: (1) For insects considered in the present study
and those with relatively high wingbeat frequency (hoverfly, drone fly and bumblebee), the “rigid body” assumption is reasonable,
and for those with relatively low wingbeat frequency (cranefly and howkmoth), the applicability of the “rigid body” assumption
is questionable. (2) The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e.,
one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. (3) Approximate analytical
expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived.
The expressions identify the speed derivative M
u (pitching moment produced by unit horizontal speed) as the primary source of the unstable oscillatory mode and the stable
fast subsidence mode and Z
w (vertical force produced by unit vertical speed) as the primary source of the stable slow subsidence mode.
The project supported by the National Natural Science Foundation of China (10232010 and 10472008). 相似文献