Thewingbeatofflapping flightconsists of adownstrokewith the wings increasingly twistedtowards the tips with the leading edge downin a motion down-forward, and anupstrokewith the wingtwisted the other way and moving up-backward. In downstroke a wing acts like a sail of a sailing boat in beatingat an angle against the wind, and generates both lift and forwarddrive, whichisused to overcome drag (from the body). Inpassiveupstroke thewingis lifted by the wind without generating drive and lift, while active upstroke can generate drive at the price of negative lift.
Flapping flight by da Vinci. Gliding stork and flapping seagull by Lilienthal.
Leonardo da Vinci
The first scientific study on of bird flight was made by
Leonardo da Vinci in his Codex on the Flight of Birds connecting lift and drag of the flow of air around a wing to the generation ofstreamwise vortices(which he observed in the flow of water around an obstacle), thus anticipating the new mathematical theory by
ornithopter, a heavier than air deviceflying on flapping wings, but found thathuman muscle power was insufficient to get a winged human off ground.Da Vinci expresses a strong belief in sciencebased on mathematics:
The bird is an instrument functioning according to mathematical laws, and man has the power to reproduce an instrument like this with all its movements.
In the 1890s the German engineer
Otto Lilienthalmade careful studies of the gliding flight of birds,and designed wings allowing him to make 2000 successfulheavier-than-air glidingflights starting from a little artificial hill, before in 1896he broke his neck falling to the ground after having stalled at 15 meters altitude.
From all the foregoing results it appears obvious that in order to discover the principles which facilitate flight, and to eventually enable man to fly, we musttake the bird for our model. A specially suitable species of birds to act as our modelis the sea-gull.How does the gull fly? At the very first glance we notice that the slender, slightly curved wings execute a peculiar motion, in so far as only the wing-tips move appreciably up and down, whilst the broader arm-portions near the body take little part in this movement, a condition of things which is illustrated in Fig. 76.May we not assume that the comparatively motionless parts of the wings enable the gull to sail along, whilst the tips, consisting of easily rotating feathers, serve to compensate for the loss of forward velocit? It is unmistakable that the wide Portion of the wing close to the body, which does little work and has little movement, is intended for sustaining, whilst the narrower tips, with their much greater amplitude of movement, have to furnish the tractive power necessary to compensate for the resistance of the bird’s body and for any possible restraining component.This being conceded, we are forced to consider the flying apparatus of the bird as a most ingenious and perfect mechanism, which has its fulcrum in the shoulder joint, which moves up and down, and by virtue of its articulation permits of increased lift or fall as well as of rotation of the light tips.The arm portion of the wing is heavy, containing bones, muscles , and tendons, and therefore opposes considerable inertia to any rapid movement. But it is well fitted for supporting, because being close to the body, the air pressure upon it acts on a short lever arm, and the bending strain is therefore less severe on the wing. The tip is very light, consisting of feathers only, and can be lifted and depressed in rapid succession. If the air pressure produced by it increased in proportion to the greater amplitude of movement, it would require a large amount of work; and would also unduly strain the wings; we therefore conclude that the real function of the wing-tips is not so much the generation of a great lifting effect, but rather the production of a smaller, but tractive effect directed forward.In fact, actual observation leaves no doubt on this point. It is only necessary to watch the gull during sunshine, and from the light effects we tan distinctly perceive the changing inclination of the wing-tips, as shown in Figs. 77 and 78, which refer to the upstroke and downstroke of the wings respectively . The gull , flying away from us, presents at the upstroke, Fig. 77, the upper side of its wings strongly illuminated by the sun, whilst during the downstroke (Fig. 78) we have tlie shaded camber presented to us from the back. The tip evidently ascends with the leading edge raised, and descends with the leading edge depressed, both phases resulting in a tractive effect.
The description of the wingbeat by da Vinci and Lilienthal is essentially the same as that given above
(which is natural since the birds fly the same way now as then):
More precisely, state-of-the-art according to How Ornithopters Fly presents the following key facts:
downstroke requiring muscle power, gives positive lift and forward thrust from propeller action of the twisted wing large twist gives large thrust but requires quick downstroke to give positive lift upstroke with large twist gives positive lift and negative thrust by turbin action, with liftreplacing muscle power quick upstroke with small twist can give forward thrust and negative lift with propeller action twist/motion of the part of the wing close to the body is relatively small and gives consistent lift through thecomplete wingbeat cycle, while the twisted wing gives forward thrust at least in the downstroke.
Downstroke with forward thrust and lift. Upstroke with lift and drag.
The (meager) theoretical understanding is described in How Ornithopters Fly as follows:
Always there have been several different versions of the flapping flight theory. They all exist in parallel and their specifications are widely distributed. Calculating the balance of forces even of a straight and merely slowly flapping wing remained difficult to the present day. In general, it is only possible in a simplified way. Furthermore, the known drives mechanism and especially wing designs leave a lot to be desired.In every respect ornithopters are still standing at the beginning of their design development.
New Theory of Bird Flight
The flight of birds does not seem to be well understood, which is understandable since not even the flight of an airplane is well understood, and there is thus aneed of a mathematical theory giving an understandable explanation.We now present the elements of such a theory:
We display the basic mechanisms generating lift and drag of a wing and drive and lift/heeling of a sail:
Principle of action of a wing:Potential flow (upper left) with zero lift/drag modified by low-pressure counter-rotating rolls of streamwise vorticity from instability mechanism at separation (upper right), switching the pressure on rear wing (lower left) to give both lift and drag (H high, L low pressure).
Computational simulation with sideway of velocity and pressure and topview of streamwise vorticitity at 14 degrees angle of attack.
The flow of air around a wing and a sail function can be seen as perturbations of zero lift/drag potential flow arising from a specific instablility at separation changing the pressure distribution at the trailing edge so as to give both lift and drag.The perturbed real flow shares the property of potential flow of following the boundary and not separating until well afterthe crest of the flow.Potential flow can only separate at apoint of stagnationwith vanishing velocity, because it isincompressible, irrotational and satisfies a slip boundary condition,andstagnation does not occur on the crest where velocity is maximal.Slightly viscous flow has a turbulent boundary layer which acts like a slip/small friction boundary condition, and thus separates only after the crest, while viscous flow always separates at the crest and thereby looses wing/sail action. Gliding flight in heavy syrup is not possibly, only paddling.
The Crucial Lift/Drag Ratio
In both gliding flight and sailing against the wind it is completely essential the the lift/drag ratioL/DwithLthe lift andDthe drag, is sufficiently large: For a symmetric wing like a Naca0012L/D > 10for3 < aoa < 15,where aoa is the angle of attack, but at maximal lift before stall at aoa = 20, L/D drops to 3which is too small to work. On the other hand,for a non-symmetric wing like a sail,L/D> 10 at maximal lift at aoa = 20, which is crucial in beating against the wind because the sail needs aoa = 20.The reason drag is smaller for a sail than a symmetric wing atmaximal lift, is (of course) that the lower part of the symmetric wing is absent for a sail. These crucial facts are displayed in the following graphs of L/D as functions of aoa:
L/D for Naca0012 wing as function of angle of attack. L/D for sail as function of angle of attack.
The wings of a bird can have a more or less non-symmetrical cross-section from that of a thick sailto that of a more symmetric airfoil, depending on flight conditions including bird speed, angle of attack and wing motion.For flapping flight it is essential that
L/D > 6withL/D > 10desirable, since otherwise the available muscle power will not be sufficient. The many unsuccessful attempts of flapping flight by humans show that a veryefficient design is needed, and theL/Dis a good measure of efficiency.
The gliding flight of birds is explained on Why It Is Possible to Fly . To achieve a sufficiently large lift/drag ratio,the boundary layer needs to be turbulent, which requires a sufficiently large Reynolds number. This meansthat small birds and even more so insects, cannot glide well, but larger birds can.
Confusion and Desinformation
The aerodynamics of bird flight, like that ofairplane flight and sailing, is surrounded by much confusion and desinformation including NASA confusion and
Fluid dynamic theory in the form of Kelvin’s circulation theorem requires that changes in wake circulation are directly proportional to force changes on the wing/aerofoil that generated the wake…However, the wakes were never as clean as the idealized cartoon models of the vortex theory of bird flight, and previous paradoxical results were shown to be attributable to the resulting difficulty in accounting for all wake components Because the wing is concavely curved, air traveling over the upper surface has to cover a greater distance and moves faster to catch up with air taking the shorter bottom route from the front to the back of the wing. This fast-moving air creates a low pressure zone along the upper surface of the wing. With low pressure above and higher pressure below, the wing is “sucked” up The Bird Site . In the field of rigid aerofoils, everything already seems to be discovered and measured, whereas in the field of flexible aerofoils (as in paragliding) theories are just starting to be developed. The field of flapping flight remains even more unknown; everything still remains to be discovered because all that has been written is nonsense Truefly – revolution in aeronautics. But for generations of adult human beings, among them, one presumes, the brightest and the best, to receive from their intellectual forbears, and pass to their heirs as the received wisdom, the curious congeries of notions that comprise the momentum theory of lift is a delusion of a higher order, one approaching sublimity. With charity for all, we acknowledge its special power to enthrall the human mind The Wing Is The Thing .
Why does the slower moving air generate more pressure against the wing than the faster moving air? In calm air, the molecules are moving randomly in all directions. However, when air begins to move, most (but not all) molecules are moving in the same direction. The faster the air moves, the greater the number of air molecules moving in the same direction. So, air moving a bit slower will have more molecules moving in other directions. In the case of a wing, because air under the wing is moving a bit slower than air over the wing, more air molecules will be striking the bottom of the wing than will be striking the top of the wing Lecture Notes Bird Flight I, Eastern Kentucky University. Flight is relatively easy… Air is being sucked in by viscosity Flight in Birds and Aeroplanes .
How a wing/sail does not work.When the wind flows over one side it fills the sail while the air flowing on the other side is moving faster and cannot push as hard and thus the sail recieves a force that is perpendicular to the direction of the wind.Thewind moving around the “upper,” or downwind, side ofthe sail is forced to take the longer pathThere are all kinds of controversies about sails…Physics of Sailing.It is difficult to explain the generation of lift forlaymenThe wind passes around the sail and because the distance is greater on the leeward side of the sail, the wind must travel fasterQUB Sailing Club.The air being also deflected by the upper side of the wing, by the Coanda effect, is harder to understandsailtheory.The air traveling over the leeward surface of the cambered sail creates the second force. It has to travel a longer way to reach the end of the sail (the leech), and as a consequence goes faster. This is causing a pressure differential in accordance with Bernoulli’s principleUniversity of Hawai.The sails propel the boat by redirecting the wind coming in from the side towards the rear. In accordance with the law ofconservation of momentum, air is redirected backwards, making the boat go forwardSail, Wikipedia.The fact that, after all these years, there is still any question about how sails work suggests that somewhere we’ve started with some wrong assumptions…Sailing World Magazine. Air will follow the curved shape of an airfoil due to Coanda effect. Why is this important? As long as airflow is laminar or in contact with the airfoil surface, it will continue to be turned in the same direction of the airfoil’s shape. This ensures the change in wind direction needed to drive the boat forward  . The fundamental problem as to how a surface such as a sail generates lift is rather difficult to understand for the average non-technical sailor. The fact that it is the viscosity of air which makelift possible is even more difficult to grasp…Although the circulation about the airfoil as generated in theoretical aerodynamics and as simulated by potential flow programs seems like just a mathematical trick, this is not the case…A good introduction to sail theory can be obtained in the work of Arvel Gentryfx sails.Aerodynamics is a difficult subject, and all attempts to simplify it for the average person leads to wrong interpretations. The facts are that lift comes about because air has viscosity, which leads to the starting vortex. This is followed by the formation of a circulation field about the airfoil necessary to meet one of Helmoltz’s theorems of vortex motion. Then the Kutta condition is satisfied at the trailing edge, and bingo — we have lift. These principles, together with knowledge of boundary layer theory, lead to a correct understanding of the interaction between the jib and the mainsail (Arvel Gentry).
Arvel Gentry repeats the classical circulation theory as the explanation of lift, with support froma two-dimensional bath tub experiment supposedly showing the existence of a so-called starting vortex required to balance the claimed circulation around the wing section.In  an attempt is made to apply classical circulation theory to bird flight.
In Why It Is Possible to Fly it is shown that the classical circulation theory is non-physical, and that bothlift and drag of a wing in three-dimensional reality results from a three-dimensional instability mechanism at separation (generating turbulent streamwise vorticity as shown above) without both starting vortex and circulation around the wing. The bath tub experiment thus does not describe the action of a real wing or sail.
In fact, you can neither fly nor sail against the wind in two dimensions (in a bathtub).
Classical theory is split into inviscid circulation theory for lift and viscous boundary layer theory for drag.
The new theory captures both lift and drag and the completely crucial lift/drag ratio, which is beyond classical theory. The new theory explains the miracle of sailing against the wind, and it is a miracle, while classical theory does notexplain anything correctly.