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A generic approach to model the kinematics and aerodynamics of flapping wing ornithopter has been followed, to model and analyze a flapping bi- and quad-wing ornithopter and to mimic flapping wing biosystems to produce lift and thrust for hovering and forward flight. Considerations are given to the motion of a rigid and thin bi-wing and quad-wing ornithopter in flapping and pitching motion with phase lag. Basic Unsteady Aerodynamic Approach incorporating salient features of viscous effect and leading-edge suction are utilized. Parametric study is carried out to reveal the aerodynamic characteristics of flapping bi- and quad-wing ornithopter flight characteristics and for comparative analysis with various selected simple models in the literature, in an effort to develop a flapping bi- and quad-wing ornithopter models. In spite of their simplicity, results obtained for both models are able to reveal the mechanism of lift and thrust, and compare well with other work.

Human efforts to mimic flying biosystems such as insects and birds through engineering feat to meet human needs have progressed for hundreds of years as well as motivated mankind creativity, from Leonardo Da Vinci’s drawings to Otto Lilienthal’s gliders, to modern aircraft technologies and present flapping flight research. Recent interest in the latter has grown significantly particularly for small flight vehicles (or Micro- Air-Vehicles) with very small payload carrying capabilities since to allow remote sensing missions where access is restricted due to various hazards. Some of these vehicles may have a typical wingspan of 15 cm, with a weight restriction of less than 100 g [

Among the many potential advantages of flapping flight compared to fixed-wing and rotary-wing flights include increased propulsive efficiency, maneuverability, and stealth. As impressively demonstrated by birds and insects, flapping wings offer potential advantages in maneuverability and energy savings compared with fixed-wing aircraft, particularly in vertical take-off, landing and maneuver dexterity. In comparison to fixed-wing and rotary wing Micro-Air Vehicles, the airfoils of the ornithopter have a flapping or oscillating motion, instead of fixed or in rotary motion, and have a combined function of providing both lift and thrust. The capability of flapping airfoils to produce both lift and thrust minimizes the drag-inducing structures, hence weight. These two advantages potentially allow a high degree of efficiency. As stipulated by Hall and Hall [

and energy efficiency, and increased payload capacity compared to a conventional (flapping wing) MAV.

Within such backdrop, in the present work, a generic approach is followed to understand and mimic the unsteady aerodynamics of biosystem that can be adopted in the present QWAV. To that end, a simple and workable Quad-Wing-Micro-Air-Vehicle (QVMAV) pterosaur-like ornithopter flight model is developed to produce lift and thrust for forward flight. At the present stage, such model will not take into account the more involved leading edge vortex and wake penetration exhibited by insect flight [

The flapping wing motion of ornithopters can be generally grouped into three classes, based on the kinematics of the wing motion and mechanism of forces generation; the horizontal stroke plane, inclined stroke plane and vertical stroke plane [

Following the frame of thought elaborated in the previous section, several generic wing planforms are chosen in the present work as baseline geometries for the ornithopter wing Biomimicry Flapping Mechanism, among others the semi elliptical wing, shown in

The present work resorts to analytical approach to the flapping wing aerodynamic problem, which can be separated into quasi-steady and unsteady models. The quasi-steady model assumes that flapping frequencies are slow enough that shed wake effects are negligible, as in pterosaur and medium- to large-sized birds while the unsteady approach attempts to model the wake like hummingbird and insects. The present aerodynamic approach is synthesized using basic foundations that may exhibit the generic contributions of the motion elements of the bio-inspired quad-wing air vehicle characteristics. These are the strip theory and thin wing aerodynamic approach [

Blade element theory has been utilized for flapping wing analysis by many researchers [

A novel initiative has been introduced by Djojodihardjo and Ramli [

The computational procedure adopted in the present work essentially follows the philosophy outlined in previous section and summarized in

The flapping wing can have three distinct motions with respect to three axes as: a)

Flapping, which is up and down stroke motion of the wing, which produces the majority of the bird’s power and has the largest degree of freedom; b) Feathering is the pitching motion of wing and can vary along the span; c) Lead-lag, which is in-plane lateral movement of wing.

Flapping angle β varies as a sinusoidal function. β and its rate are given by following equations. The degree of freedom of the motion is depicted in

Flapping angle β varies as a sinusoidal function. The angle β and its rate and pitching angle θ are given by

where θ_{0} is the maximum pitch angle,

The vertical and horizontal components of relative wind velocity, as depicted in

For horizontal flight, the flight path angle γ is zero. Also,

The section lift coefficient due to circulation (Kutta-Joukowski condition, flat plate) is given by [

dL_{c} can then be calculated by

which should be integrated along the span to obtain the flapping-wing lift. Here c and dy are the chord length and spanwise strip width of the element of wing under consideration, respectively. The apparent mass effect (momentum transferred by accelerating air to the wing) for the section, is perpendicular to the wing, and acts at mid chord, and can be calculated as [

The drag force has two components, profile drag and induced drag where the values for the drag coefficients are assumed to be similar to those associated with basic geometrical cases (such as flat plate, airfoil with tabulated data and the like). To account for profile drag, a factor K is introduced [_{Di} is induced drag coefficient, and e is the efficiency factor of the wing and is 0.8 for elliptical wing. Total section drag is thus given by

The circulatory lift dL_{c}, non-circulatory force dN_{nc} and drag dD_{d} for each section of the wing changes its direction at every instant during flapping. These forces in the vertical and horizontal directions will be resolved into those perpendicular and parallel to the forward velocity, respectively. The resulting vertical and horizontal components of the forces are given by

and are calculated within one complete cycle, and averaged to get the total average lift and thrust of the ornithopter.

C'(k), F'(k) and G'(k) relate to the Theodorsen function [_{0}/U which causes a local induced angle of attack, where it reduces lift [

The results below are obtained using the following wing geometry and parameters: the wingspan 40 cm, aspect ratio 6.2, flapping frequency 7 Hz, total flapping angle 60˚, forward speed 6 m/s, maximum pitching angle 20˚, and incidence angle 6˚. The computational scheme developed has been validated satisfactorily. Two methods (procedures); first method and second method are shown for insight purpose on force production tolerance. A sample of such validation is shown in

The following assumptions were made: the pitching and flapping motions are in sinusoidal motion, and the upstroke and downstroke phases have equal time duration. There is incidence angle, which is 6˚ and there is no flight path angle.

The phase lag was assumed to be fixed at 90˚. The Computational Procedure did not incorporate the leading edge suction, wake capture and dynamic stall.

The Average values for lift per flapping cycle calculated using the first and second Computational Procedure are comparable, both for rectangular and semi-elliptical planform. Agreement with Byl’s [

Companion studies is carried out to investigate the influence of individual contributions of the pitching-flapping motion and their phase lag on the flight performance [

A parametric study is carried out to assess the influence of some flapping wing motion parameters to the flight performance desired. The study considers the following parameters: the Effect of Forward speed, the Effect of Flapping Frequency, the Effect of Lag Angle, the Effect of Angle of Incidence and the Effect of Total Flapping Angle.

The results are exhibited in

Following similar kinematic and aerodynamic model and aerodynamic computational

scheme as elaborated in previous sections, a computational study is carried out for a quad-wing flapping ornithopter, using similar dimensions as the bi-wing flapping ornithopter. The wing dimensions are such that performance comparison between the bi-wing and quad-wing ornithopter can be made, such as the total wing area should be similar for both. The influence of individual contributions of the pitching-flapping motion and their phase lag on the flight performance is carefully modelled and investigated. Without loss of generality, for simplicity the calculation is also performed on rectangular wing.

Results obtained as exhibited in

Average Force | Bi-Wing (Baseline Computational Procedure) | Quad-Wing (Fore-and Hind-Wings, simultaneous | Quad-Wing Flapping 90^{o} Phase Difference | Quad-Wing Pitching 90˚ Phase Difference | Quad-Wing Flapping & Pitching 90˚ Phase Difference | Quad-Wing Flapping & Pitching 180˚ Phase Difference |
---|---|---|---|---|---|---|

Lift (N) | 0.2108 | 0.3503 | 0.4391 | 0.4378 | 0.4096 | 0.4613 |

Drag (N) | 0.090 | 0.1629 | 0.4270 | 0.2817 | 0.1928 | 0.4882 |

Thrust (N) | 0.2768 | 0.7902 | 0.8770 | 0.4793 | 0.5580 | 0.7753 |

The computational results for simplified modelling of both bi-wing and quad-wing ornithopters are meant for better understanding of the key elements that produce Lift and Thrust Forces for these ornithopters, as well as a guideline for developing a simple experimental model that can easily be built. More sophisticated computational and experimental model can be built in a progressive fashion, by superposing other key features. To gain better insight into the kinematic and aerodynamic modelling of bi-wing and quad-wing ornithopters, comparison will be made on the basic characteristics and performance of selected ornithopter models with those of selected real birds and insects.

The most noticeable of these changes is the phase difference between forewing and hind wings, defined as the phase angle by which hindwing leads the forewing. When hovering, dragonflies employ a 180˚ phase difference (out of phase), while 54˚ - 100˚ is used for forward flight. When accelerating or performing aggressive maneuvers, there is no phase difference between the two wings (0˚ in phase) [

^{o} phase difference between the fore- and hind-wings is the highest among other flight cases, giving the best performance attitude for forward flight mode.

Wang and Russel [

Although quantitatively the comparison shows some discrepancies, qualitatively both results show similar behaviour. Such result could lend support to the present kinematic and aerodynamic modeling of quad-wing ornithopter with non-deforming wing, which can progressively be refined to approach the real biosystem flight characteritics, such as those of dragonfly and other related entomopters.

For this purpose, ^{4} to 1.0 ´ 10^{4}. Shyy et al. [_{L}/C_{D} ratio exhibits a clear Reynolds number dependency. For Re varying between 7.5 ´ 10^{4} and 2.0 ´ 10^{6}, C_{L}/C_{D} changes by a factor of 2 to 3 for the airfoils tested.

Except for a very thin airfoil UF developed by Shyy [^{4}, the situation is quite different. UF, the thinner airfoil with identical camber, exhibits substantially better aerodynamic performance while maintaining

a comparable range of acceptable angles-of-attack. However, in the present study, viscosity effects are taken into account following the approach and results of DeLaurier [

The present work has been performed to assess the effect of flapping-pitching motion with pitch-flap phase lag in the flight of ornithopter. In this conjunction, a computational model has been considered, and a generic computational method has been adopted, utilizing two-dimensional unsteady theory of Theodorsen with modifications to account for three-dimensional and viscous effects, leading edge suction and post-stall behavior. The study is carried out on rectangular and semi-elliptical wing planforms. The results have been compared and validated with others within similar unsteady aerodynamic approach and general physical data, and within the physical assumptions limitations; encouraging qualitative agreements or better have been indicated, which meet the proof of concept objectives of the present work. For the bi-wing flapping ornithopter, judging from lift per unit span, the present flapping-wing model performance is comparable to those studied by Byl [

The analysis and simulation by splitting the flapping and pitching motion shows that: (a) the lift is dominantly produced by the pitching motion, since the relative airflow effect prevailed along 75% of the chord length. (b) The thrust is dominated by flapping motion. The vertical component of relative velocity increases significantly as compared to the horizontal components, which causes the force vector produced by the flapping-pitching motion to be directed towards the horizontal axis (thrust axis). (c) The drag is dominated by the flapping motion, due to higher relative velocity as well as higher induced drag due to circulation.

For the quad-wing ornithopter, at the present stage, the simplified computational model adopted verified the gain in lift obtained as compared to bi-wing flapping ornithopter, in particular by the possibility of varying the phase lag between the flapping and pitching motion of individual wing as well as between the fore-and hind-wings.

A structured approach has been followed to assess the effect of different design parameters on lift, thrust, and drag of an ornithopter, as well as the individual contribution of the component of motion. These results lend support to the utilization of the generic modelling adopted in the synthesis of a flight model, although more refined approach should be developed. Various physical elements could be considered in developing ornithopter kinematic and aerodynamic model. More refined aerodynamic computational methods, such as CFD or lifting surface methods can be utilized for refined modeling. In retrospect, a generic physical and computational model based on simple kinematics and basic aerodynamics of a flapping-wing ornithopter has been demonstrated to be capable of revealing its basic characteristics and can be utilized for further development of a flapping-wing MAV. Application of the present kinematic, aerodynamic and computational approaches shed some light on some of the salient aerodynamic performance of the quad-wing ornithopter.

The authors would like to thank Universiti Putra Malaysia (UPM) for granting Research University Grant Scheme (RUGS) Project Code: 9378200, under which the present research is carried out.

Djojodihardjo, H., Ramli, A.S.S., Wiriadidjaja,^{ }S. and Rafie, A.S.M. (2016) Kinematic and Aerodynamic Modelling of Bi- and Quad-Wing Flapping Wing Micro-Air-Vehicle. Advances in Aerospace Science and Technology, 1, 83-101. http://dx.doi.org/10.4236/aast.2016.13008

AR = aspect ratio

B = semi-wingspan

c = chord

C_{L} = Lift Coefficient

C_{D} = Drag Coefficient

C_{Di} = induced Drag Coefficient

C(k) = Theodorsen function

C(k)_{jones} = modified Theodorsen function

C_{df} = drag coefficient due to skin friction

dD_{camber} = sectional force due to camber

dD_{f} = sectional friction drag

dF_{x} = sectional chordwise force

F_{x} = x (horizontal) component of the resultant pressure force acting on the vehicle

F_{z} = z (vertical) component of the resultant pressure force acting on the vehicle

f, g = generic functions

h = height

i = time index during navigation

j = waypoint index

dL = sectional lift

dy = width of sectional strip under consideration

dN = sectional total normal force

dN_{c} = sectional circulatory normal force

dN_{nc} = sectional apparent mass effect

dt = time step

dT = sectional thrust

dT_{s} = leading edge suction force

F(k) = Theodorsen function real component

G(k) = Theodorsen function imaginary component

k = reduced frequency

L = total lift

L_{fore} = lift force of fore-wing

t = time

T = total thrust

U = flight velocity

V = relative velocity at quarter chord point

V_{x} = flow speed tangential to section

V_{rel} = relative velocity

V_{i} = induced velocity

w_{0} = downwash velocity at ¾-chord point

Г = circulation

ρ = air density

β = flapping angle

β_{0} = maximum flapping angle

θ = pitching angle

θ_{0} = maximum pitch angle

θ_{hindwing} = effective pitching angle of hind-wing

f = lag angle between pitching and flapping angle

δ = incidence angle

α = relative angle of attack

α’ = flow’s relative angle of attack at three-quarter chord point (DeLaurier)

α_{0} = zero-lift angle

α_{Theodorsen} = phase angle of Theodorsen function

η_{s} = efficiency coefficient

ω = flapping frequency

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