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The thrust and lift of an ornithopter's membrane wings with simple flapping motion
Aerospace Science and Technology 10 (2006) 111–119 www.elsevier.com/locate/aescte
The thrust and lift of an ornithopter’s membrane wings with simple flapping motion Che-Shu Lin, Chyanbin Hwu, Wen-Bin Young ∗ Department of Aeronautics and Astronautics, National Cheng Kung University, No. 1, DarShei Rd., Tainan, 70101, Taiwan, ROC Received 22 August 2005; received in revised form 7 October 2005; accepted 7 October 2005 Available online 1 December 2005
Abstract Human beings flying with the help of aircrafts of various kinds have been able to fly for about one century. Although the flapping wings of animals served as an inspiration to pioneers of human flight, we don’t really understand how they work. In this study, we employ the concept of four-bar linkage to design a flapping mechanism which simulates a flapping motion of a bird. Wind tunnel tests were performed to measure the lift and thrust of the mechanical membrane flapping wing under different frequency, speed, and angle of attack. It is observed that the flexibility of the wing structure will affect the thrust and lift force due to its deformation at high flapping frequency. The lift force will increase with the increase of the flapping frequency under the corresponding flying speed. For the same flapping frequency, the flying speed can be increased by decrease of the angle of attack with the trade of loosing some lift force. An angle of attack is necessary in a simple flapping motion in order to derive a lift force. The flapping motion generates the thrust to acquire the flying speed. The flying speed and angle of attack combine to generate the lift force for flying. © 2005 Elsevier SAS. All rights reserved. Keywords: Ornithopter; Flapping wing; Membrane wing; Flexible wing
1. Introduction It has been an interesting subject in biology to study the flying mechanism and characteristics of flapping flight of birds [3– 8,11]. Flapping flight is more complicated than the fixed-wing flight. For an aircraft with fixed wings, only forward motion is necessary to sustain the body with the induced aerodynamic lift. For the flapping flight, the wing not only has a forward motion but also the up and down flapping. In the down stroke flapping, the wing is fully extended and produces both lift and thrust at the same time. During the up stroke, some part of the wing is folded to reduce the moment of inertia and the drags of the wings. The wings are also twisted during the flapping to vary the angle of attack for various flying motions. During the hovering, fast forward motion, or slow forward motion, different wing strokes and attack angles are employed. The flapping * Corresponding author. Tel.: (+886) 6 2757575 ext. 63672; fax: (+886) 6 2389940. E-mail address: [email protected] (W.-B. Young).
1270-9638/$ – see front matter © 2005 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2005.10.003
wing flight is also believed to have better maneuverability compared to the fixed wing flight. In biological flight, the wings not only move forward relative to the air, they also couple the motions of flapping up and down, plunge and sweeping [9,10]. In order to attain efficient lift during the flapping motion, the wing will undergo a twist motion to change the angle of incident in the down and up strokes. In general, the down stroke will produce the most lift and thrust with fully extended wings. At the up stroke, additional lift can also be generated by twisting the wing to change the attack angle, especially during the take-off and hovering flight [2]. For small insect flight, the wings flap at high frequency and the unsteady flow mechanism dominates [12]. During the up stroke, the wing surfaces press together at the end for a period of time. As the wings separate for the next down stroke motion, they rotate around the trailing edges first to form a V shape before they begin to move away. This leads to the large circulation and lift on the wing without the negatives of vortex shedding. The flapping-wing aircraft configurations (ornithopter) received great attention to the researchers for a long time. One application of the ornithopter, being a micro air vehicle (MAV),
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C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
has recently attracted much interest. The primary purpose of the MAV currently is surveillance, which requires a slow flight and excellent maneuverability. Early models of rubber powered ornithopters were successful built by Alphonse Penaud [1]. This has been the prototype for many ornithopter models later built as toys. Despite of the flapping wing design, the aerodynamic behaviors of these ornithopters are quite different to those of birds in the cruising flight. The flapping wing of Penaud’s ornithopter is constructed by a stiff leading-edge spar and some flexible ribs attached to the spar. The wing skeleton is covered with a thin sheet of flexible material. This design results in a light flexible membrane wing that may twist and bend during the flapping motion. This study constructs mechanical membrane flapping wings using carbon fiber reinforced epoxy as the skeleton. A four-bar linkage driven by an electric motor was used as the flapping mechanism. The wing surface was formed by covering the skeleton with thin plastic film. Wind tunnel tests were performed to measure the lift and thrust of the mechanical membrane flapping wing under different frequency, speed, and angle of attack. 2. Wing design and kinematics
ω4 =
b sin γ ω2 , d sin ε
and δ = θ2 − θ4 ,
(7)
ε = ψ − β − θ4 ,
(8)
γ = θ2 − ψ + β, −1 b β = sin sin θ2 , s 2 2 2 −1 c + s − d ψ = cos , 2cs c λ = sin−1 sin ψ , d θ4 = 360 − (λ + β),
(9)
OA + AB + BD > OD,
(1)
OA + OD + BD > AB,
(2)
OA + AB − BD < OD,
(3)
AB − OA + BD > OD.
(4)
If the angular speed of the driving linkage is ω2 , the angular velocities of the connecting and following linkages can be expressed as ω3 = −
b sin δ ω2 , c sin ε
Fig. 1. The four-bar linkage design for the wing mechanism.
(10) (11) (12) (13)
where ω4 is the angular speed of the following linkage, θ2 and θ4 are the position angles of the driving and following linkages, and the other lengths and angles are defined in Fig. 1. The corresponding angular accelerations can be derived by differentiating with respect to time to have bω22 cos δ + cω32 cos ε + dω42 , c sin ε bω22 cos γ + cω32 + dω42 cos ε α4 = . d sin ε
α3 = A four-bar linkage design was selected as the mechanism for the wing flapping as shown in Fig. 1. The linkage OA is the driving linkage and the linkage BD is connected to the wing structure. The design of the four-bar linkage is a kind of the Crank and Rocker mechanism where the driving linkage can rotate a revolution completely and the following linkage undergoes a rocking motion. The Crank and Rocker mechanism follows some constraints for the member lengths as
(6)
(14) (15)
3. Experimental The selected lengths for each linkages are OA = 8.5 mm, AB = 31.5 mm, BD = 19 mm, and OD = 30.5 mm. The resulting flapping angle for the wing is shown in Fig. 2. The upward flapping angle is about 39 degree and the downward flapping is about 18 degree. In the early stage of the design, several tests were performed to investigate the effect of the flapping upward and downward strokes on the lift force. It was found that large upward angle stroke or larger downward angle stroke do not affect the lift force. In this design, we have a larger upward angle stroke.
(5)
Fig. 2. Flapping angle with respect to the position angle of the driving linkage.
C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
(a)
113
(b)
Fig. 3. (a) Angular flapping velocity and (b) angular flapping acceleration with respect to the position angle of the driving linkage.
Fig. 4. Assembly of the mechanism, motor and the battery set.
Fig. 3 shows the corresponding angular velocity and acceleration of the following linkage. The rotational speed of the motor is assumed to be constant in the analysis. From the velocity and acceleration, it can be assured that the mechanism can operate smoothly without obvious jumps or jerks. The linkages were milled from a titanium alloy plate. Together with the driving motor, the entire assembly of the flapping unit is shown in Fig. 4. It is expected that the wing area will affect the lift force. In order to study the effect of the wing area on the lift force of a flapping wing, two different wings were constructed for the test of the lift force and thrust. The wing aspect ratio is about 2. The two wings with span in 60 cm and 40 cm will be referred as type A and B respectively. Types A and B were constructed by epoxy reinforced carbon fiber composite frames and covered with a PVC plastic film as shown in Fig. 5. The weights and surface areas of the wings are 17.64 g, 0.054 m2 for type A wing and 27.05 g, 0.102 m2 for type B wing.
In the wind tunnel test of the flapping wing, four different attack angles were used, 0, 5, 10, 15 degrees. The angle of attack is formed by attached the wing to the driving mechanism with a specific angle. The angle of attack is defined corresponding to the wind-axes reference frame. The different wind velocities used for the test are 0 to 20 km/hr in a step increase of 5 km/hr. Load cells, MA-SM2, were mounted on the base of the driving unit to measure the lift force or thrust on the wind tunnel test. The capacity of the load cell is 3 kg with an excitation voltage 10 V. Standard weights were used to calibrate the load cell before tests. The signal from the load cell was recorded directly by a Tektronix oscilloscope, TDS 1002. The recording duration is 4 seconds with 2500 digital points that can be downloaded to a personal computer after the test. Before a test, the initial weight of the entire assembly above the load cell was recorded. As the wings start to flap, the oscilloscope will record the load variation during the preset duration. The lift during the flapping motion can be derived by subtracting the measured load from the initial weight. The average lift can be calculated by average
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(a)
(b)
Fig. 5. Different wing constructions: (a) type A, (b) type B.
Fig. 6. Setup of the flapping wings for lift and thrust tests.
the lift along the measured time span. For the measurement of thrust, the data can be collected by direct reading from the load cell. The lift and thrust were measured with respect to the windaxes reference frame. The setups of the flapping wings for lift and thrust tests are shown in Fig. 6.
4. Results and discussions The lift forces for different flapping frequencies and wind speeds are shown in Fig. 7 using the wing type A. The figure also shows the lift forces for different angles of attack. It
C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
(a)
115
(b)
Fig. 7. The lift forces under different flapping frequencies and wind speeds at (a) angle of attack = 0, (b) angle of attack = 15 degree using the type A wing.
(a)
(b)
Fig. 8. The lift forces under different flapping frequencies and wind speeds at an angle of attack = 15 degree using (a) the type A wing and (b) the type B wing.
(a)
(b)
Fig. 9. The lift forces under different attack angles and wind speeds using (a) type A wing at 5 Hz and (b) type B wing at 7 Hz.
is shown that there is no lift force without the relative wind speed. Although the flapping angles are different in upstroke and down stroke, the upward force and downward force are about the same during the entire flapping cycle and tend to cancel each other in this situation. Increase of the flapping frequency does not induce any lift force also. With a relative wind speed, a lift force can be generated and higher lift force is induced in a higher angle of attack. It is demonstrated that the relative wind speed and the angle of attack are the major factors for the lift force of an ornithopter under a simple flapping motion. For 15 degree of angle of attack, the lift force increases with the increase of flapping frequency up to about 5 Hz. Notice that for zero angle of attack, the lift will increase with the wind speed in Fig. 7. Actually, in installation of the wing mechanism, the leading edge of the wing is set to parallel to the wind direction. However, due to the weight of the wing itself, slight sag
of the trailing edge will occur, leading to certain lift readings in the test. The lift force is also shown to increase with respect to the wind speed and flapping frequency in the wind tunnel tests as in Fig. 8. The angle of attack for the wing under tests is set to 15 degree. Most of the data for type A wing is measured at the frequency below 5 Hz. Due to the flexibility of type A wing, the second mode deformation is induced for a higher flapping frequency. Under this situation of second mode deformation, the lift force is saturated or even decreases. The interesting thing is that the lift force for type B wing is about the same as type A wing for the same flapping frequency. Notice that the wing span for type B wing is about 40 cm while it is 60 cm for type A wing. The lift force is not directly proportional to the wing area for a flapping wing under the same flapping frequency and wind speed. The possible cause will be that the flexibilities of
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(a)
(b)
Fig. 10. The thrusts under different flapping frequencies and wind speeds at an angle of attack = 15 degree using (a) the type A wing and (b) the type B wing.
(a)
(b)
Fig. 11. The lift forces generated by different flapping frequencies and angles of attack using the type A wing.
(a)
(b)
Fig. 12. The lift forces generated by different flapping frequencies and angles of attack using the type B wing.
C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
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(a)
(b) Fig. 13. Schematic diagram of the lift and drag forces near the root of the wing for the up and down strokes. (a) Angle of attack = 0; (b) angle of attack > 0.
the two wings are different. Large deformation along the wing span will disturb the air flow, causing the reduction of the lift force. At a higher frequency, the deformation of type A wing becomes larger and the lift force curve with respect to the flapping frequency starts to level off as in Fig. 8. The effect of wind speed on the lift force is shown in Fig. 9. The lift force increases substantially at the high wind speed. That means flying at higher speed is a more effective way in obtaining the required lift force rather than increasing the flapping frequency. In the experimental wind tunnel tests, the wind speed and flapping frequency are kept as separated independent variables. However, in the actual flying, the flying speed that can be reached depends on the flapping frequency of the wings. In order to increase the flying speed, the flapping frequency must be increased also. The flying speed depends on the thrust of the flapping wings. During the flying motion, the generated thrust can overcome the
drags and accelerate the ornithopter. In the wind tunnel tests, the wind speed is set by the wind tunnel. However, the actual flying speed that an ornithopter can reach depends on the thrust and the drag. The drag force is a function of the flying speed and the angle of attack. Fig. 10 shows the net thrust in a wind tunnel test under different flapping frequency and angle of attack = 15 degree. The curve with diamond symbols is corresponding to thrust force for flapping with no wind. The thrust force becomes saturated at higher frequency for type A wing as shown in Fig. 10(a). This is suspected to be caused by the large deformation of the wing shape during high frequency flapping. The data shows that the net thrust may become negative in some wind speeds and frequencies. The negative net thrust means that the flapping motion at the specified frequency can not reach the preset speed under this angle of attack. Since the type B wing is smaller, most of the net thrust data for type B wing is at the negative region. The largest obtainable speed is about 10 km/hr
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(a)
(b) Fig. 14. Schematic diagram of the lift and drag forces near the tip of the wing for the up and down strokes. (a) Angle of attack = 0; (b) angle of attack > 0.
at this angle attack. Notice that the data (zero net thrust force) derived in this study is based on the measurement of the flapping mechanism only. The actual drag in the ornithopter must include the entire body and the tail structures. The flying speeds for different flapping frequencies can be constructed based on Fig. 10. For each flapping frequency, the wind speed approaching the zero net thrust force can be considered as the corresponding flying speed. The relations are shown in Fig. 11(a) for different angles of attack for type A wing. With specified frequency and wind speed, the corresponding lift force
can be derived from the previous experimental data. The lift force for different frequencies and angles of attack is shown in Fig. 11(b). For the same frequency, the flying speed is lower for high angle of attack, but the lift force is higher. The lift force and flying speed are shown to increase with the flapping frequency. From the experiments, it was observed that the maximum flapping frequency was limited by the wing structure. As the frequency is high enough to induce the second mode wing deformation, the wing performance will decrease. It should be noticed that the limitation of the driving system is not consid-
C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
ered in the above discussion. The corresponding flying speed and lift force for type B wing are shown in Fig. 12. 5. Conclusions This study constructs mechanical membrane flapping wings using carbon fiber reinforced epoxy as the skeleton. A fourbar linkage driven by an electric motor was used as the flapping mechanism. The wing surface was formed by covering the composite skeleton with thin plastic film. Wind tunnel tests were performed to measure the lift and thrust of the mechanical membrane flapping wing under different frequency, speed, and angle of attack. It is observed that the flexibility of the wing structure will affect the thrust and lift force due to its deformation at high flapping frequency. The lift force will increase with the increase of the flapping frequency under the corresponding flying speed. For the same flapping frequency, the flying speed can be increased by decrease of the angle of attack with the trade of loosing some lift force as shown in Figs. 11 and 12. The mechanism of the thrust and lift forces generated by the simple flapping motion are also shown in Figs. 13 and 14 schematically. For the wing cross section near the root, the speed of the wing is low. The corresponding speed is most due to the flying speed, resulting in more lift force due to the aerodynamic effect. Notice that the trailing edge of the wing section will deform up and down during the duty flapping cycle because of its flexibility. For wing section far from the root, the flapping speed is higher and comparable to the wind speed. For zero angle of attack, the lift forces during the up and down strokes will cancel each other. An angle of attack is necessary in this situation in order to derive a lift force. The flapping motion generates the thrust to acquire the flying speed. The flying speed and angle of attack combines to generate the lift force for flying.
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Acknowledgements The authors would like to thank for the financial support from National Science Council in Republic of China under the contract number of NSC 93-2212-E006-067. References [1] J.D. Delaurier, An ornithopter wing design, Canadian Aeronautics Space J. 40 (1) (1994) 10–18. [2] T. Hedrick, B. Tobalske, A. Biewener, Estimate of circulation and gait change based on a three-dimensional kinematic analysis of flight in cockatiels (Nymphius hollandicus) and ringed turtle-doves (Streptopelia risoria), J. Exp. Biol. 205 (2002) 1389–1409. [3] C.J. Pennycuick, A wind-tunnel study of gliding flight in the pigeon Columbia livia, J. Exp. Biol. 49 (1968) 509–526. [4] C.J. Pennycuick, Predicting wingbeat frequency and wavelength of birds, J. Exp. Biol. 165 (1990) 171–185. [5] J.M.V. Rayner, Bounding and undulating flight in birds, J. Theoret. Biol. 117 (1985) 47–77. [6] J.M.V. Rayner, Aerodynamic corrections for the flight of birds and bats in wind tunnels, J. Zool. Lond. 234 (1994) 537–563. [7] J.M.V. Rayner, Mathematical modeling of the avian flight power curve, Math. Meth. Appl. Sci. 24 (2001). [8] W. Shyy, M. Berg, D. Ljungqvist, Flapping and flexible wings for biological and micro air vehicles, Progr. Aerospace Sci. 35 (1999) 455–505. [9] G.R. Spedding, J.M.V. Rayner, C.J. Pennycuick, Momentum and energy in the wake of a pigeon (Columbia) in slow flight, J. Exp. Biol. 111 (1984) 81–102. [10] G.R. Spedding, The wake of a kestrel (Falco tinnunculus) in flapping flight, J. Exp. Biol. 127 (1987) 59–78. [11] V.A. Tucker, G. Heine, Aerodynamics of gliding flight in a Harris’ hawk, Parabuteo unicinctus, J. Exp. Biol. 165 (1990) 469–489. [12] T. Weis-Fogh, Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production, J. Exp. Biol. 59 (1973) 169–230.
The thrust and lift of an ornithopter’s membrane wings with simple flapping motion Che-Shu Lin, Chyanbin Hwu, Wen-Bin Young ∗ Department of Aeronautics and Astronautics, National Cheng Kung University, No. 1, DarShei Rd., Tainan, 70101, Taiwan, ROC Received 22 August 2005; received in revised form 7 October 2005; accepted 7 October 2005 Available online 1 December 2005
Abstract Human beings flying with the help of aircrafts of various kinds have been able to fly for about one century. Although the flapping wings of animals served as an inspiration to pioneers of human flight, we don’t really understand how they work. In this study, we employ the concept of four-bar linkage to design a flapping mechanism which simulates a flapping motion of a bird. Wind tunnel tests were performed to measure the lift and thrust of the mechanical membrane flapping wing under different frequency, speed, and angle of attack. It is observed that the flexibility of the wing structure will affect the thrust and lift force due to its deformation at high flapping frequency. The lift force will increase with the increase of the flapping frequency under the corresponding flying speed. For the same flapping frequency, the flying speed can be increased by decrease of the angle of attack with the trade of loosing some lift force. An angle of attack is necessary in a simple flapping motion in order to derive a lift force. The flapping motion generates the thrust to acquire the flying speed. The flying speed and angle of attack combine to generate the lift force for flying. © 2005 Elsevier SAS. All rights reserved. Keywords: Ornithopter; Flapping wing; Membrane wing; Flexible wing
1. Introduction It has been an interesting subject in biology to study the flying mechanism and characteristics of flapping flight of birds [3– 8,11]. Flapping flight is more complicated than the fixed-wing flight. For an aircraft with fixed wings, only forward motion is necessary to sustain the body with the induced aerodynamic lift. For the flapping flight, the wing not only has a forward motion but also the up and down flapping. In the down stroke flapping, the wing is fully extended and produces both lift and thrust at the same time. During the up stroke, some part of the wing is folded to reduce the moment of inertia and the drags of the wings. The wings are also twisted during the flapping to vary the angle of attack for various flying motions. During the hovering, fast forward motion, or slow forward motion, different wing strokes and attack angles are employed. The flapping * Corresponding author. Tel.: (+886) 6 2757575 ext. 63672; fax: (+886) 6 2389940. E-mail address: [email protected] (W.-B. Young).
1270-9638/$ – see front matter © 2005 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2005.10.003
wing flight is also believed to have better maneuverability compared to the fixed wing flight. In biological flight, the wings not only move forward relative to the air, they also couple the motions of flapping up and down, plunge and sweeping [9,10]. In order to attain efficient lift during the flapping motion, the wing will undergo a twist motion to change the angle of incident in the down and up strokes. In general, the down stroke will produce the most lift and thrust with fully extended wings. At the up stroke, additional lift can also be generated by twisting the wing to change the attack angle, especially during the take-off and hovering flight [2]. For small insect flight, the wings flap at high frequency and the unsteady flow mechanism dominates [12]. During the up stroke, the wing surfaces press together at the end for a period of time. As the wings separate for the next down stroke motion, they rotate around the trailing edges first to form a V shape before they begin to move away. This leads to the large circulation and lift on the wing without the negatives of vortex shedding. The flapping-wing aircraft configurations (ornithopter) received great attention to the researchers for a long time. One application of the ornithopter, being a micro air vehicle (MAV),
112
C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
has recently attracted much interest. The primary purpose of the MAV currently is surveillance, which requires a slow flight and excellent maneuverability. Early models of rubber powered ornithopters were successful built by Alphonse Penaud [1]. This has been the prototype for many ornithopter models later built as toys. Despite of the flapping wing design, the aerodynamic behaviors of these ornithopters are quite different to those of birds in the cruising flight. The flapping wing of Penaud’s ornithopter is constructed by a stiff leading-edge spar and some flexible ribs attached to the spar. The wing skeleton is covered with a thin sheet of flexible material. This design results in a light flexible membrane wing that may twist and bend during the flapping motion. This study constructs mechanical membrane flapping wings using carbon fiber reinforced epoxy as the skeleton. A four-bar linkage driven by an electric motor was used as the flapping mechanism. The wing surface was formed by covering the skeleton with thin plastic film. Wind tunnel tests were performed to measure the lift and thrust of the mechanical membrane flapping wing under different frequency, speed, and angle of attack. 2. Wing design and kinematics
ω4 =
b sin γ ω2 , d sin ε
and δ = θ2 − θ4 ,
(7)
ε = ψ − β − θ4 ,
(8)
γ = θ2 − ψ + β, −1 b β = sin sin θ2 , s 2 2 2 −1 c + s − d ψ = cos , 2cs c λ = sin−1 sin ψ , d θ4 = 360 − (λ + β),
(9)
OA + AB + BD > OD,
(1)
OA + OD + BD > AB,
(2)
OA + AB − BD < OD,
(3)
AB − OA + BD > OD.
(4)
If the angular speed of the driving linkage is ω2 , the angular velocities of the connecting and following linkages can be expressed as ω3 = −
b sin δ ω2 , c sin ε
Fig. 1. The four-bar linkage design for the wing mechanism.
(10) (11) (12) (13)
where ω4 is the angular speed of the following linkage, θ2 and θ4 are the position angles of the driving and following linkages, and the other lengths and angles are defined in Fig. 1. The corresponding angular accelerations can be derived by differentiating with respect to time to have bω22 cos δ + cω32 cos ε + dω42 , c sin ε bω22 cos γ + cω32 + dω42 cos ε α4 = . d sin ε
α3 = A four-bar linkage design was selected as the mechanism for the wing flapping as shown in Fig. 1. The linkage OA is the driving linkage and the linkage BD is connected to the wing structure. The design of the four-bar linkage is a kind of the Crank and Rocker mechanism where the driving linkage can rotate a revolution completely and the following linkage undergoes a rocking motion. The Crank and Rocker mechanism follows some constraints for the member lengths as
(6)
(14) (15)
3. Experimental The selected lengths for each linkages are OA = 8.5 mm, AB = 31.5 mm, BD = 19 mm, and OD = 30.5 mm. The resulting flapping angle for the wing is shown in Fig. 2. The upward flapping angle is about 39 degree and the downward flapping is about 18 degree. In the early stage of the design, several tests were performed to investigate the effect of the flapping upward and downward strokes on the lift force. It was found that large upward angle stroke or larger downward angle stroke do not affect the lift force. In this design, we have a larger upward angle stroke.
(5)
Fig. 2. Flapping angle with respect to the position angle of the driving linkage.
C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
(a)
113
(b)
Fig. 3. (a) Angular flapping velocity and (b) angular flapping acceleration with respect to the position angle of the driving linkage.
Fig. 4. Assembly of the mechanism, motor and the battery set.
Fig. 3 shows the corresponding angular velocity and acceleration of the following linkage. The rotational speed of the motor is assumed to be constant in the analysis. From the velocity and acceleration, it can be assured that the mechanism can operate smoothly without obvious jumps or jerks. The linkages were milled from a titanium alloy plate. Together with the driving motor, the entire assembly of the flapping unit is shown in Fig. 4. It is expected that the wing area will affect the lift force. In order to study the effect of the wing area on the lift force of a flapping wing, two different wings were constructed for the test of the lift force and thrust. The wing aspect ratio is about 2. The two wings with span in 60 cm and 40 cm will be referred as type A and B respectively. Types A and B were constructed by epoxy reinforced carbon fiber composite frames and covered with a PVC plastic film as shown in Fig. 5. The weights and surface areas of the wings are 17.64 g, 0.054 m2 for type A wing and 27.05 g, 0.102 m2 for type B wing.
In the wind tunnel test of the flapping wing, four different attack angles were used, 0, 5, 10, 15 degrees. The angle of attack is formed by attached the wing to the driving mechanism with a specific angle. The angle of attack is defined corresponding to the wind-axes reference frame. The different wind velocities used for the test are 0 to 20 km/hr in a step increase of 5 km/hr. Load cells, MA-SM2, were mounted on the base of the driving unit to measure the lift force or thrust on the wind tunnel test. The capacity of the load cell is 3 kg with an excitation voltage 10 V. Standard weights were used to calibrate the load cell before tests. The signal from the load cell was recorded directly by a Tektronix oscilloscope, TDS 1002. The recording duration is 4 seconds with 2500 digital points that can be downloaded to a personal computer after the test. Before a test, the initial weight of the entire assembly above the load cell was recorded. As the wings start to flap, the oscilloscope will record the load variation during the preset duration. The lift during the flapping motion can be derived by subtracting the measured load from the initial weight. The average lift can be calculated by average
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(a)
(b)
Fig. 5. Different wing constructions: (a) type A, (b) type B.
Fig. 6. Setup of the flapping wings for lift and thrust tests.
the lift along the measured time span. For the measurement of thrust, the data can be collected by direct reading from the load cell. The lift and thrust were measured with respect to the windaxes reference frame. The setups of the flapping wings for lift and thrust tests are shown in Fig. 6.
4. Results and discussions The lift forces for different flapping frequencies and wind speeds are shown in Fig. 7 using the wing type A. The figure also shows the lift forces for different angles of attack. It
C.-S. Lin et al. / Aerospace Science and Technology 10 (2006) 111–119
(a)
115
(b)
Fig. 7. The lift forces under different flapping frequencies and wind speeds at (a) angle of attack = 0, (b) angle of attack = 15 degree using the type A wing.
(a)
(b)
Fig. 8. The lift forces under different flapping frequencies and wind speeds at an angle of attack = 15 degree using (a) the type A wing and (b) the type B wing.
(a)
(b)
Fig. 9. The lift forces under different attack angles and wind speeds using (a) type A wing at 5 Hz and (b) type B wing at 7 Hz.
is shown that there is no lift force without the relative wind speed. Although the flapping angles are different in upstroke and down stroke, the upward force and downward force are about the same during the entire flapping cycle and tend to cancel each other in this situation. Increase of the flapping frequency does not induce any lift force also. With a relative wind speed, a lift force can be generated and higher lift force is induced in a higher angle of attack. It is demonstrated that the relative wind speed and the angle of attack are the major factors for the lift force of an ornithopter under a simple flapping motion. For 15 degree of angle of attack, the lift force increases with the increase of flapping frequency up to about 5 Hz. Notice that for zero angle of attack, the lift will increase with the wind speed in Fig. 7. Actually, in installation of the wing mechanism, the leading edge of the wing is set to parallel to the wind direction. However, due to the weight of the wing itself, slight sag
of the trailing edge will occur, leading to certain lift readings in the test. The lift force is also shown to increase with respect to the wind speed and flapping frequency in the wind tunnel tests as in Fig. 8. The angle of attack for the wing under tests is set to 15 degree. Most of the data for type A wing is measured at the frequency below 5 Hz. Due to the flexibility of type A wing, the second mode deformation is induced for a higher flapping frequency. Under this situation of second mode deformation, the lift force is saturated or even decreases. The interesting thing is that the lift force for type B wing is about the same as type A wing for the same flapping frequency. Notice that the wing span for type B wing is about 40 cm while it is 60 cm for type A wing. The lift force is not directly proportional to the wing area for a flapping wing under the same flapping frequency and wind speed. The possible cause will be that the flexibilities of
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(a)
(b)
Fig. 10. The thrusts under different flapping frequencies and wind speeds at an angle of attack = 15 degree using (a) the type A wing and (b) the type B wing.
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(b)
Fig. 11. The lift forces generated by different flapping frequencies and angles of attack using the type A wing.
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(b)
Fig. 12. The lift forces generated by different flapping frequencies and angles of attack using the type B wing.
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(a)
(b) Fig. 13. Schematic diagram of the lift and drag forces near the root of the wing for the up and down strokes. (a) Angle of attack = 0; (b) angle of attack > 0.
the two wings are different. Large deformation along the wing span will disturb the air flow, causing the reduction of the lift force. At a higher frequency, the deformation of type A wing becomes larger and the lift force curve with respect to the flapping frequency starts to level off as in Fig. 8. The effect of wind speed on the lift force is shown in Fig. 9. The lift force increases substantially at the high wind speed. That means flying at higher speed is a more effective way in obtaining the required lift force rather than increasing the flapping frequency. In the experimental wind tunnel tests, the wind speed and flapping frequency are kept as separated independent variables. However, in the actual flying, the flying speed that can be reached depends on the flapping frequency of the wings. In order to increase the flying speed, the flapping frequency must be increased also. The flying speed depends on the thrust of the flapping wings. During the flying motion, the generated thrust can overcome the
drags and accelerate the ornithopter. In the wind tunnel tests, the wind speed is set by the wind tunnel. However, the actual flying speed that an ornithopter can reach depends on the thrust and the drag. The drag force is a function of the flying speed and the angle of attack. Fig. 10 shows the net thrust in a wind tunnel test under different flapping frequency and angle of attack = 15 degree. The curve with diamond symbols is corresponding to thrust force for flapping with no wind. The thrust force becomes saturated at higher frequency for type A wing as shown in Fig. 10(a). This is suspected to be caused by the large deformation of the wing shape during high frequency flapping. The data shows that the net thrust may become negative in some wind speeds and frequencies. The negative net thrust means that the flapping motion at the specified frequency can not reach the preset speed under this angle of attack. Since the type B wing is smaller, most of the net thrust data for type B wing is at the negative region. The largest obtainable speed is about 10 km/hr
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(a)
(b) Fig. 14. Schematic diagram of the lift and drag forces near the tip of the wing for the up and down strokes. (a) Angle of attack = 0; (b) angle of attack > 0.
at this angle attack. Notice that the data (zero net thrust force) derived in this study is based on the measurement of the flapping mechanism only. The actual drag in the ornithopter must include the entire body and the tail structures. The flying speeds for different flapping frequencies can be constructed based on Fig. 10. For each flapping frequency, the wind speed approaching the zero net thrust force can be considered as the corresponding flying speed. The relations are shown in Fig. 11(a) for different angles of attack for type A wing. With specified frequency and wind speed, the corresponding lift force
can be derived from the previous experimental data. The lift force for different frequencies and angles of attack is shown in Fig. 11(b). For the same frequency, the flying speed is lower for high angle of attack, but the lift force is higher. The lift force and flying speed are shown to increase with the flapping frequency. From the experiments, it was observed that the maximum flapping frequency was limited by the wing structure. As the frequency is high enough to induce the second mode wing deformation, the wing performance will decrease. It should be noticed that the limitation of the driving system is not consid-
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ered in the above discussion. The corresponding flying speed and lift force for type B wing are shown in Fig. 12. 5. Conclusions This study constructs mechanical membrane flapping wings using carbon fiber reinforced epoxy as the skeleton. A fourbar linkage driven by an electric motor was used as the flapping mechanism. The wing surface was formed by covering the composite skeleton with thin plastic film. Wind tunnel tests were performed to measure the lift and thrust of the mechanical membrane flapping wing under different frequency, speed, and angle of attack. It is observed that the flexibility of the wing structure will affect the thrust and lift force due to its deformation at high flapping frequency. The lift force will increase with the increase of the flapping frequency under the corresponding flying speed. For the same flapping frequency, the flying speed can be increased by decrease of the angle of attack with the trade of loosing some lift force as shown in Figs. 11 and 12. The mechanism of the thrust and lift forces generated by the simple flapping motion are also shown in Figs. 13 and 14 schematically. For the wing cross section near the root, the speed of the wing is low. The corresponding speed is most due to the flying speed, resulting in more lift force due to the aerodynamic effect. Notice that the trailing edge of the wing section will deform up and down during the duty flapping cycle because of its flexibility. For wing section far from the root, the flapping speed is higher and comparable to the wind speed. For zero angle of attack, the lift forces during the up and down strokes will cancel each other. An angle of attack is necessary in this situation in order to derive a lift force. The flapping motion generates the thrust to acquire the flying speed. The flying speed and angle of attack combines to generate the lift force for flying.
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Acknowledgements The authors would like to thank for the financial support from National Science Council in Republic of China under the contract number of NSC 93-2212-E006-067. References [1] J.D. Delaurier, An ornithopter wing design, Canadian Aeronautics Space J. 40 (1) (1994) 10–18. [2] T. Hedrick, B. Tobalske, A. Biewener, Estimate of circulation and gait change based on a three-dimensional kinematic analysis of flight in cockatiels (Nymphius hollandicus) and ringed turtle-doves (Streptopelia risoria), J. Exp. Biol. 205 (2002) 1389–1409. [3] C.J. Pennycuick, A wind-tunnel study of gliding flight in the pigeon Columbia livia, J. Exp. Biol. 49 (1968) 509–526. [4] C.J. Pennycuick, Predicting wingbeat frequency and wavelength of birds, J. Exp. Biol. 165 (1990) 171–185. [5] J.M.V. Rayner, Bounding and undulating flight in birds, J. Theoret. Biol. 117 (1985) 47–77. [6] J.M.V. Rayner, Aerodynamic corrections for the flight of birds and bats in wind tunnels, J. Zool. Lond. 234 (1994) 537–563. [7] J.M.V. Rayner, Mathematical modeling of the avian flight power curve, Math. Meth. Appl. Sci. 24 (2001). [8] W. Shyy, M. Berg, D. Ljungqvist, Flapping and flexible wings for biological and micro air vehicles, Progr. Aerospace Sci. 35 (1999) 455–505. [9] G.R. Spedding, J.M.V. Rayner, C.J. Pennycuick, Momentum and energy in the wake of a pigeon (Columbia) in slow flight, J. Exp. Biol. 111 (1984) 81–102. [10] G.R. Spedding, The wake of a kestrel (Falco tinnunculus) in flapping flight, J. Exp. Biol. 127 (1987) 59–78. [11] V.A. Tucker, G. Heine, Aerodynamics of gliding flight in a Harris’ hawk, Parabuteo unicinctus, J. Exp. Biol. 165 (1990) 469–489. [12] T. Weis-Fogh, Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production, J. Exp. Biol. 59 (1973) 169–230.