Aerodynamic modelling of insect-like flapping flight for micro air vehicles
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McMichael JM, Francis MS. Micro air vehicles—toward a new dimension in flight. World Wide Web 〈http://www.darpa.mil/tto/MAV/mav_auvsi.html〉; August 1997 [accessed: 18/09/2001].
Żbikowski R. Flapping wing autonomous micro air vehicles: research programme outline. In: 14th international conference on unmanned air vehicle systems, vol. Supplementary Papers. 1999a. p. 38.1–.5.
Żbikowski R. Flapping wing micro air vehicle: a guided platform for microsensors. In: Royal aeronautical society conference on nanotechnology and microengineering for future guided weapons, 1999b, p. 1.1–.11.
Żbikowski R. Flapping wing technology. In: European military rotorcraft symposium, Shrivenham, UK, 21–23 March 2000; p. 1–7.
Woods, 2001, Energy requirements for the flight of micro air vehicles, Aeronaut J, 105, 135, 10.1017/S0001924000092058
Knoller, 1909, Die Gesetze des Luftwiderstandes, Flug- und Motortechnik (Wien), 3, 1
Betz, 1912, Ein Beitrag zur Erklärung des Segelfluges, Z Flugtech Motorluftschiffahrt, 3, 269
Ellington, 1984, The aerodynamics of hovering insect flight: II. Morphological parameters, Philos Trans R Soc London Ser B, 305, 17, 10.1098/rstb.1984.0050
Brodsky, 1996
Dudley, 1999
Gullan, 1999
Ellington, 1999, The novel aerodynamics of insect flight: Applications to micro-air vehicles, J Exp Biol, 202, 3439, 10.1242/jeb.202.23.3439
Ansari, 2006, Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: methodology and analysis, Proceedings of the institute of mechanical engineering. Part G: J Aerosp Eng, 220, 10.1243/09544100JAERO50
Ansari, 2006, Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 2: implementation and validation, Proceedings of the institute of mechanical engineering. Part G: J Aerosp Eng, 220, 10.1243/09544100JAERO50
Ansari SA. A Nonlinear, Unsteady, aerodynamic model for insect-like flapping wings in the hover with micro air vehicle applications. PhD thesis, Cranfield University (RMCS Shrivenham); September 2004.
Heppenheimer, 2003
Rozhdestvensky, 2003, Aerohydrodynamics of flapping-wing propulsors, Prog Aerosp Sci, 39, 585, 10.1016/S0376-0421(03)00077-0
Lehmann, 2004, The mechanisms of lift enhancement in insect flight, Naturwissenschaften, 91, 101, 10.1007/s00114-004-0502-3
Wang, 2005, Dissecting insect flight, Ann Revi Fluid Mech, 37, 183, 10.1146/annurev.fluid.36.050802.121940
Ho, 2003, Unsteady aerodynamics and flow control for flapping wing flyers, Prog Aerosp Sci, 39, 635, 10.1016/j.paerosci.2003.04.001
Lian, 2003, Membrane wing aerodynamics for micro air vehicles, Prog Aerosp Sci, 39, 425, 10.1016/S0376-0421(03)00076-9
Marey, 1868, Determination experimentale du mouvement des ailes des insectes pendant le vol, C.R. Acad. Sci. Paris, 67, 1341
Weis-Fogh, 1956, Biology and physics of locust flight. II. Flight performance of the desert locust Schistocerca gregaria, Philos Trans R Soc London Ser B, 239, 459, 10.1098/rstb.1956.0008
Ellington, 1984, The aerodynamics of hovering insect flight: III. kinematics, Philos Trans R Soc London Ser B, 305, 41, 10.1098/rstb.1984.0051
Ennos, 1989, The kinematics and aerodynamics of the free flight of some diptera, J Exp Biol, 142, 49, 10.1242/jeb.142.1.49
Dickinson, 1999, Wing rotation and the aerodynamic basis of insect flight, Science, 284, 1954, 10.1126/science.284.5422.1954
Srygley, 2002, Unconventional lift-generating mechanisms in free-flying butterflies, Nature, 420, 660, 10.1038/nature01223
Azuma, 1992
Ellington, 1984, The aerodynamics of hovering insect flight: IV. Aerodynamic mechanisms, Philos Trans R Soc London Ser B, 305, 79, 10.1098/rstb.1984.0052
Magnan, 1934
Lamb, 1932
Wagner, 1925, Über die Entstehung des Dynamischen Aufftriebes von Tragflügeln, Z Angewandie Math Mech, 5, 17, 10.1002/zamm.19250050103
Dickinson, 1996, Unsteady mechanisms of force generation in aquatic and aerial locomotion, A Zool, 36, 537, 10.1093/icb/36.6.537
Dickinson, 1994, The effects of wing rotation on unsteady aerodynamic performance at low Reynolds numbers, J Exp Biol, 192, 179, 10.1242/jeb.192.1.179
Sane, 2001, The control and flight force by a flapping wing: lift and drag production, J Exp Biol, 204, 2607, 10.1242/jeb.204.15.2607
Pedersen CB. An indicial-Polhamus model of aerodynamics of insect-like flapping wings in hover. PhD thesis, Cranfield University (RMCS Shrivenham); 17 June 2003.
Grodnitsky, 1993, Vortex formation during tethered flight of functionally and morphologically two-winged insects, including evolutionary considerations on insect flight, J Exp Biol, 182, 11, 10.1242/jeb.182.1.11
Ennos, 1989, Inertial and aerodynamic torques on the wings of diptera in flight, J Exp Biol, 142, 87, 10.1242/jeb.142.1.87
Ellington, 1984, The aerodynamics of hovering insect flight: V. A vortex theory, Philos Trans R Soc London Ser B, 305, 115, 10.1098/rstb.1984.0053
Sunada, 2000, Approximate added-mass method for estimating induced power for flapping flight, AIAA J, 38, 1313, 10.2514/2.1124
Kramer, 1932, Die Zunahme des Maximalauftriebes von Tragflügeln bei plötzlicher Anstellwinkelvergrösserung (Böeneffekt), Z Flugtech Motorluftschiffahrt, 23, 185
Birch, 2001, Spanwise flow and the attachment of the leading-edge vortex on insect wings, Nature, 412, 729, 10.1038/35089071
Willmott, 1997, Flow visualization and unsteady aerodynamics in the flight of the Hawkmoth, Manduca sexta, Philos Trans R Soc London Ser B, 352, 303, 10.1098/rstb.1997.0022
van den Berg, 1997, The three-dimensional leading-edge vortex of a “Hovering” model hawkmoth, Philos Trans R Soc London Ser B, 352, 329, 10.1098/rstb.1997.0024
van den Berg, 1997, The vortex wake of a “Hovering” model Hawkmoth, Philosl Trans R Soc London Ser B, 352, 317, 10.1098/rstb.1997.0023
Martin, 1977, Flow-visualisation experiments on butterflies in simulated gliding flight, Fortschritte der Zoologie, 24, 307
Maxworthy, 1979, Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1: dynamics of the ‘fling’, J Fluid Mech, 93, 47, 10.1017/S0022112079001774
Brodsky, 1991, Vortex formation in the tethered flight of the peacock butterfly Inachis io L. (Lepidoptera, Nymphalidae) and some aspects of insect flight evolution, J Exp Biol, 161, 77, 10.1242/jeb.161.1.77
Dickinson, 1993, Unsteady aerodynamic performance of model wings at low Reynolds numbers, J Exp Biol, 174, 45, 10.1242/jeb.174.1.45
Sunada, 1993, Performance of a butterfly in take-off flight, J Exp Biol, 183, 249, 10.1242/jeb.183.1.249
Rossow, 1978, Lift enhancement by an externally trapped vortex, J Aircraft, 15, 618, 10.2514/3.58416
Riddle, 1999, An experimental analysis of vortex trapping techniques, Trans ASME: J Fluids Eng, 121, 555, 10.1115/1.2823504
Ellington, 1995, Unsteady aerodynamics of insect flight, Soc Exp Biol, 49, 109
Żbikowski, 2002, On aerodynamic modelling of an insect-like flapping wing in hover for micro air vehicles, Philos Trans R Soc London Ser A, 360, 273, 10.1098/rsta.2001.0930
McCroskey WJ. The phenomenon of dynamic stall. Technical Memorandum TM-81264, NASA, 1981, 1–31.
Liu, 1998, A computational fluid dynamic study of hawkmoth hovering, J Exp Biol, 201, 461, 10.1242/jeb.201.4.461
Birch, 2004, Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers, J Exp Biol, 207, 1063, 10.1242/jeb.00848
Ellington CP. Insects versus birds: the great divide. In: 44th AIAA aerospace sciences meeting and exhibit. No. AIAA-2006-0035. Reno, NV, 2006.
Sun, 2002, Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion, J Exp Biol, 205, 55, 10.1242/jeb.205.1.55
Sun, 2004, A computational study of the aerodynamic forces and power requirements of dragon fly (Aeschna juncea) hovering, J Exp Biol, 207, 1887, 10.1242/jeb.00969
Sun, 2003, Aerodynamic forces generation and power requirements in forward flight in a fruit fly with modeled wing motion, J Exp Biol, 206, 3065, 10.1242/jeb.00517
Sun, 2005, Dynamic flight stability of a hovering bumblebee, J Exp Biol, 208, 447, 10.1242/jeb.01407
Sun, 2005, High-lift generation and power requirements of insect flight, Fluid Dyn Res, 37, 21, 10.1016/j.fluiddyn.2004.04.006
Wang, 2005, A computational study of the aerodynamics and forewing–hindwing interaction of a model dragonfly in forward flight, J Exp Biol, 208, 3785, 10.1242/jeb.01852
Taylor, 2005, Non-linear time-periodic (NLTP) models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria, J R Soc Interface, 2, 197, 10.1098/rsif.2005.0036
Ramamurti, 2002, A three-dimensional computational study of the aerodynamic mechanisms of insect flight, J Exp Biol, 205, 1507, 10.1242/jeb.205.10.1507
Isogai, 2004, Unsteady three-dimensional viscous flow simulation of a dragonfly hovering, AIAA J, 42, 2053, 10.2514/1.6274
Yamamoto, 2005, Measurement of unsteady fluid dynamic forces for a mechanical dragonfly model, AIAA J, 43, 2475, 10.2514/1.15899
Kurtulus DF, Farcy A, Alemdaroglu N. Numerical calculation and analytical modelization of flapping motion in hover. In: First european micro air vehicle conference (EMAV 2004). Braunschweig, Germany; 2004. p. 1–19.
Kurtulus DF, Farcy A, Alemdaroglu N. Unsteady aerodynamics of flapping airfoil in hovering flight at low Reynolds numbers. In: 43rd AIAA aerospace sciences meeting and exhibit. No. AIAA 2005-1356. AIAA, Reno, NV; 2005. p. 1–15.
Żbikowski R, Pedersen CB, Ansari SA, Galiński C. Flapping wing micro air vehicles. Lecture series: low Reynolds number aerodynamics on aircraft including applications in emerging UAV technology RTO/AVT 104, von Kármán Institute, Belgium, 24–28 November 2003.
Küssner, 1936, Zusammenfassender Bericht über den instationären Auftrieb von Flügeln, Luftfahrtforschung, 13, 410
Eldridge JD. Efficient tools for the simulation of flapping wing flows. In: 43rd aerospace sciences meeting. No. 2005-0085. AIAA, Reno, NV; 10–13 January 2005. p. 1–11.
Conway, 1978
Conway, 1995
Theodorsen T. General theory of aerodynamic instability and the mechanism of flutter. Report 496, NACA; 1935. p. 413–33.
Keldysh MV, Lavrent’ev MA. K teorii kolebliushchevosya kryla. Technical Note Tsent 45, Aero-Gidrodin. Inst. (On the theory of oscillating wings); 1935.
Sedov LI. Teoriya nestatsionarnovo glissirovanya i dvizheniya kryla so sbegayu shchimi vikhryami. Tr. Tsent 252, Aero-Gidrodin. Inst., (The theory of unsteady hydrodynamic planning and wing motion with shed vorticity); 1936.
Garrick IE. Propulsion of a flapping and oscillating airfoil. Report 567, NACA; 1937. p. 419–27.
Garrick IE. On some reciprocal relations in the theory of nonstationary flows. Report 629, NACA, 1938. p. 347–50.
Jones RT. Operational treatment of the nonuniform-lift theory. Report 667, NACA; 1938.
Jones RT. The unsteady lift of a wing of finite aspect ratio. Report 681, NACA; 1940. p. 31–38.
Leishman, 2000
Thwaites B. (Ed.). Incompressible aerodynamics: an account of the theory and observation of the steady flow of incompressible fluid past aerofoils, wings, and other bodies. Fluid motion memoirs. New York: Oxford University Press; 1960.
Osborne, 1951, Aerodynamics of flapping flight with application to insects, J Exp Biol, 28, 221, 10.1242/jeb.28.2.221
Weis-Fogh, 1956, Biology and physics of locust flight. I. Basic principles in insect flight. A critical review, Philos Trans R Soc London Ser B, 239, 415, 10.1098/rstb.1956.0007
Weis-Fogh, 1972, Energetics of hovering flight on hummingbirds and Drosophila, J Exp Biol, 56, 79, 10.1242/jeb.56.1.79
Rayner, 1979, A vortex theory of animal flight: part 1. The vortex wake of a hovering animal, J Fluid Mech, 91, 697, 10.1017/S0022112079000410
Ramasamy M, Leishman JG, Singh B. Wake structure diagnostics of a flapping wing MAV. In: SAE international powered lift conference. No. IPLC 2005-01-3198. Texas; 3–6 October 2005. p. 1–13.
Milne-Thomson, 1973
Ellington, 1978, The aerodynamics of normal hovering flight: three approaches, 327
Brackenbury, 1995
Sunada, 2001, A new method for explaining the generation of aerodynamic forces in flapping flight, Math Meth Appl Sci, 24, 1377, 10.1002/mma.186
Weis-Fogh, 1973, Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production, J Exp Biol, 59, 169, 10.1242/jeb.59.1.169
Pringle, J.W.S. Insect flight. Oxford biology readers, vol. 52, Glasgow: Oxford University Press; 1975.
Ellington, 1984, The aerodynamics of hovering insect flight: I. The quasi-steady analysis, Philos Trans R Soc London Ser B, 305, 1, 10.1098/rstb.1984.0049
Ellington, 1984, The aerodynamics of hovering insect flight: VI. Lift and power requirements, Philos Trans R Soc London Ser B, 305, 145, 10.1098/rstb.1984.0054
Fung, 1955
van der Wall, 1994, On the influence of time-varying flow velocity on unsteady aerodynamics, J Am Helicopter Soc, 39, 25, 10.4050/JAHS.39.25
Ansari SA, Knowles K, Żbikowski R. Design guidelines for flapping-wing micro UAVs. In: SAE international powered lift conference. No. IPLC 2005-01-3197. Houston, Texas; 3–6 October 2005. p. 1–10.
Azuma A, Okamoto M, Yasuda K. Aerodynamic characteristics of wings at low Reynolds number. In: Mueller TJ. editor. Fixed and flapping wing aerodynamics for micro air vehicle applications. Progress in Astronautics and Aeronautics, vol. 195. American Institute of Aeronautics and Astronautics; 2001. p. 341–98 (Chapter 17).
Michelson RC, Naqvi MA. Extraterrestrial flight–entomopter-based mars surveyor. In: Low Re aerodynamics on aircraft including applications in emerging UAV technology. RTO-AVT/VKI Lecture Series 2004. von Kármán Institute for Fluid Dynamics; 24–28 November 2003. p. 1–17.
Glauert, 1959
Sane, 2002, The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight, J Exp Biol, 205, 1087, 10.1242/jeb.205.8.1087
Walker, 2002, Rotational lift: something different or more of the same?, J Exp Biol, 205, 3783, 10.1242/jeb.205.24.3783
Traub, 2004, Analysis and estimation of the lift components of hovering insects, J Aircraft, 41, 284, 10.2514/1.9323
Dudley, 1990, Mechanics of forward flight in bumblebees. II. Quasi-steady lift and power requirements, J Exp Biol, 148, 53, 10.1242/jeb.148.1.53
Wakeling, 1997, Dragonfly flight: III. Lift and power requirements, J Exp Biol, 200, 583, 10.1242/jeb.200.3.583
Pedersen CB. Żbikowski R. An indicial-Polhamus aerodynamic model of insect-like flapping wings in hover. In: Flow phenomena in nature: a challenge to engineering design. Billerica, MA: WIT Press; 2006.
Willmott, 1997, The mechanics of flight in the Hawkmoth Manduca Sexta: II. Aerodynamics consequences of kinematic and morphological variation, J Exp Biol, 200, 2723, 10.1242/jeb.200.21.2723
Lighthill MJ. Mathematical biofluiddynamics. CBMS-NSF regional conference series in applied mathematics, vol. 17. Philadelphia, PA: SIAM; 1975.
Walker, 2000, Mechanical performance of aquatic rowing and flying, Proc R Soc London Ser B, 267, 1875, 10.1098/rspb.2000.1224
Swanson, 1961, The Magnus effect: a summary of investigations to date, Trans ASME J Basic Eng, 60, 461, 10.1115/1.3659004
Sedov, 1965
McCune, 1990, Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver, AIAA J, 28, 385, 10.2514/3.10403
Wang, 2004, Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments, J Exp Biol, 207, 449, 10.1242/jeb.00739
Maybury, 2004, The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings, J Exp Biol, 207, 4707, 10.1242/jeb.01319
Polhamus EC. A concept of the vortex lift of sharp-edge delta wings based on a leading-edge suction analogy. Technical note TN D-3767, NASA; December 1966. p. 1–15.
Tarascio, 2005, Flow visualization of micro air vehicle scaled insect-based flapping wings, J Aircraft, 42, 385, 10.2514/1.6055
Chorin, 1973, Numerical study of slightly viscous flow, J Fluid Mech, 57, 785, 10.1017/S0022112073002016
Sears, 1940, Operational methods in the theory of airfoils in non-uniform motion, J Franklin Inst, 230, 95, 10.1016/S0016-0032(40)90651-2
Loewy, 1957, A two-dimensional approximation to the unsteady aerodynamics of rotary wings, J Aeronaut Sci, 24, 81, 10.2514/8.3777
Wu TY. Advances. In: On theoretical modeling of aquatic and aerial animal locomotion. Applied mechanics, vol. 38. New York: Academic Press; 2001. p. 291–353.
Tavares, 1993, Aerodynamics of maneuvering slender wings with leading-separation, AIAA J, 31, 977, 10.2514/3.49043
Munk MM. General theory of thin wing sections. Report 142, NACA; 1923. p. 243–61.
Polhamus, 1971, Predictions of vortex-lift characteristics by a leading-edge suction analogy, J Aircraft, 8, 193, 10.2514/3.44254
Bradley, 1973, Vortex-lift prediction for complex wing planforms, J Aircraft, 10, 379, 10.2514/3.44375
Lamar, 1976, Prediction of vortex flow characteristics of wings at subsonic and supersonic speeds, J Aircraft, 13, 490, 10.2514/3.58681
von Kármán, 1940
Bisplinghoff, 1955
Żbikowski, 2005, A four-bar linkage mechanism for insect-like flapping wings in hover: concept and an outline of its realisation, Trans ASME: J Mech Design, 127, 817, 10.1115/1.1829091
Żbikowski, 2005, Some aeromechanical aspects of insect-like flapping wings in hover, Proceedings of the institution of mechanical engineers: J Aerosp Eng, 218, 389
Minotti, 2002, Unsteady two-dimensional theory of a flapping wing, Phys Rev E, 66, 1
Minotti, 2005, Leading-edge vortex stability in insect wings, Phys Rev E, 71, 1
Jones, 2003, The separated flow of an inviscid fluid around a moving flat plate, J Fluid Mech, 496, 405, 10.1017/S0022112003006645
Rott, 1956, Diffraction of a weak shock with vortex generation, J Fluid Mech, 1, 111, 10.1017/S0022112056000081
Birkhoff G. Helmholtz and Taylor Instability. In: Proceedings of the symposium on applied mathematics, vol. 13. Rhode Island; 1962. p. 55–76.
Keulegan, 1958, Forces on cylinders and plates in an oscillating fluid, J Res National Bureau Standards, 60, 423, 10.6028/jres.060.043
Pullin, 2004, Unsteady forces on an accelerating plate and application to hovering insect flight, J Fluid Mech, 509, 1, 10.1017/S0022112004008821
Graham, 1983, The lift on an aerofoil in starting flow, J Fluid Mech, 133, 413, 10.1017/S0022112083001986
Edwards RH. Leading-edge separation from delta wings. J Aeronaut Sci 1954, 134–135.
Legendre R, Écoulement au voisinage de la pointe avant d’une aile à la forte flèche aux incidences moyennes. La Recherche Aéronautique (ONERA) (31), 3–6, translated as ARC 16976; January–February 1953.
Cheng HK. Remarks on nonlinear lift and vortex separation. J Aeronaut Sci Readers’ Forum 1954; 212–4.
Bryson, 1959, Symmetric vortex separation on circular cylinders and cones, Trans ASME: J Appl Mech, 81, 643, 10.1115/1.4012127
Yu, 2003, An analytic approach to theoretical modeling of highly unsteady viscous flow excited by wing flapping in small insects, Acta Mech Sin, 19, 508, 10.1007/BF02484543
Kelvin, Lord (W.H. Thomson), On vortex motion. Trans R Soc Edinburgh 1869;25:217–60.
Yu, 2005, A flow control mechanism in wing flapping with stroke asymmetry during insect forward flight, Acta Mech Sin, 21, 218, 10.1007/s10409-005-0032-z
Hess JL. Calculation of potential flow about bodies of revolution having axes perpendicular to the free stream direction. Technical Report ES 29812, Douglas Aircraft Company, Inc. (El Segundo Division), El Segundo, CA; 1960.
Hess JL, Smith AMO. Calculation of Non-lifting potential flow about arbitrary three-dimensional bodies. Technical Report ES 40622, Douglas Aircraft Company, Inc. (Aircraft Division), Longbeach, CA; 1962.
Zdunich P. A discrete vortex model of unsteady separated flow about a thin aerofoil for application to hovering flapping-wing flight. Master's thesis, University of Toronto; 2002.
Katz, 2001
Smith, 1996, The advantages of an unsteady panel method in modelling the aerodynamic forces on rigid flapping wings, J Exp Biol, 199, 1073, 10.1242/jeb.199.5.1073
Smith, 1996, Simulating moth wing aerodynamics: towards the development of flapping-wing technology, AIAA J, 34, 1348, 10.2514/3.13239
Fritz, 2004, Object-oriented unsteady vortex lattice method for flapping flight, J Aircraft, 41, 1275, 10.2514/1.7357
Raviart PA. An analysis of particle methods. In: Brezzi, F. (editor). Numerical methods in fluid dynamics. Lecture Notes in Mathematics, vol. 1127. Springer; New York/Berlin; 1985. p. 243–324.
Lighthill, 1973, On the Weis-Fogh mechanism of lift generation, J Fluid Mech, 60, 1, 10.1017/S0022112073000017
Edwards, 1982, The separation vortex in the Weis-Fogh circulation-generation mechanism, J Fluid Mech, 120, 463, 10.1017/S0022112082002857
Iima, 2005, Asymmetric motion of a two-dimensional symmetric flapping model, Fluid Dyn Res, 36, 407, 10.1016/j.fluiddyn.2004.07.005
Morris, 1937, The two-dimensional hydrodynamical theory of moving aerofoils—I, Proc R Soc London Ser A, 161, 406, 10.1098/rspa.1937.0152
Morris, 1938, The two-dimensional hydrodynamical theory of moving aerofoils—II, Proc R Soc London Ser A, 164, 346, 10.1098/rspa.1938.0022
Wakeling, 1997, Dragonfly flight: II. Velocities, accelerations and kinematics of flapping flight, J Exp Biol, 200, 557, 10.1242/jeb.200.3.557
Ansari SA, Knowles K, Żbikowski R. Aerodynamic modelling of some planforms for insect-like flapping wings, In: CEAS Aerospace Aerodynamics Conference. London; 10–12 June 2003. p. 38.1–.14.
Benson HAO. Apparent-mass and on-board circulation of Joukowski airfoils and cascades in severe unsteady motion, Master's thesis, Massachusetts Institute of Technology; May 1989.
Karamcheti, 1966
Betz, 1932, Verhalten is von Wirbelsystemen, Z Angewandte Math Mech, 12, 164, 10.1002/zamm.19320120307
Oseen, 1911, Über die Stokes'sche Formel und über eine verwandte Aufgabe in der Hydrodynamik, Arkiv för Matematik, Astronomi och Fysik, 7, 1
Spallart PR. Vortex Methods for Separated Flows. Technical Memorandum 100068, N88-26342, NASA; 1988.
Sarpkaya, 1989, Computational methods with vortices—the 1988 freeman scholar lecture, Trans ASME: J Fluids Eng, 111, 5, 10.1115/1.3243601
Ting L, Klein R. Viscous vortical flows. Lecture Notes in Physics. vol. 374. Berlin: Springer; 1991.
Crighton, 1985, The Kutta condition in unsteady flow, Ann Rev Fluid Mech, 17, 411, 10.1146/annurev.fl.17.010185.002211
Silverstein A, Joyner UT. Experimental verification of the theory of oscillating airfoils. report 673, NACA; 1939.
Giesing, 1969, Vorticity and Kutta condition for unsteady multienergy flows, Trans ASME: J Appl Mech, 36, 608, 10.1115/1.3564724
Maskell EC. On the Kutta–Joukowski condition in two-dimensional unsteady flow. TM ARC-33967, Royal Aircraft Establishment, Farnborough, England; 1972.
Poling, 1986, The response of airfoils to periodic disturbances—the unsteady Kutta condition, AIAA J, 24, 193, 10.2514/3.9244
Poling, 1987, The trailing edge of a pitching airfoil at high reduced frequencies, Trans ASME: J Fluids Eng, 109, 410, 10.1115/1.3242681
Tavares TS. Aerodynamics of maneuvering slender wings with leading-edge separation. PhD thesis, Massachussetts Institute of Technology; September 1990.
Lee NKW. Evolution and structure of leading edge vortices over slender wings. PhD thesis, Massachussetts Institute of Technology; 1991.
Lam, C-MG. Nonlinear wake evolution of Joukowski aerofoils in severe maneuver. Master's thesis, Massachusetts Institute of Technology; 1989.
Dickinson MH. Private communication. California Institute of Technology, Pasadena, CA; 2003.