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1. Definition

An Ornithopter, or ornitotero like Leonardo da Vinci termed them, is an aircraft heavier than air, which flies like a bird by flapping its wings. The special feature lies in the wings that do not only generate lift but also thrust.

Ornithopters are mostly built the size of birds or flying models and then are also called flapping wing model.

The basic operating principle of a flapping wing has already been discovered by
literature Otto Lilienthal (1889). To help understanding an effective way of flying of big ornithopters his functional description is still trend-setting to the present day. But many details are still not understood.

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. But powerful drives make very beautiful flights already possible.

Here, too, only a version of the flapping flight theory in a shortened form follows.

2. Operating principle of the flapping wing

optimal lift distributions for ornithopters
Diagram 1
Optimized lift distributions for a gently inclined climb flight with limited wingspan
optimal lift distributions for flapping wings
Diagram 2
Optimized lift distributions for a gently inclined climb flight with unlimited wingspan

On a stretched flapping wing lift is generated similar to an inflexible airfoil flown against from the front.

But during the wing upstroke the air flow hits the wing rather from above and in the downstroke rather from bottom. These modifications are small in the area of the wing root and gets bigger towards the wing tip.

With permanent changing twisting the flapping wing must adapt to these alternating incoming flow directions. Here, however, the lift distribution along the wing span must not be kept constant in the interest of generating thrust (Please look at the diagrams).

During the wing downstroke the lift distribution is bigger altogether than when gliding and more displaced towards the wing tip. It is easy to imagine that thrust is generated along the whole wing span during stroke motion. This works similar to a propeller blade with a very large pitch - only that the propeller torque force that has to be overcome is here called lift and is also used like that.

forces at a location of a flapping wing in the downstroke and upstroke
Vector diagram
of forces and velocities

At the wing upstroke circumstances are reversed. Overall, the lift distribution is smaller and more shifted towards the wing root. With the stroke motion in the direction of the lift force the flapping wing now acts as a wind turbine blade. If the lift force is big enough it presses the wing upward even without a mechanical drive. Thereby, the wing operates with the operating drag or working drag, of a wind turbine against the flight direction (please takes a look at the vector diagram).

forces in the upstroke by Otto Lilienthal
Forces at the stork wing in the upstroke

At the same time, the outboard wing areas are flown against rather from above. There indeed is generated negative lift but similar to a propeller also thrust (Please look at the vector diagram).

Whether in the upstroke the wind turbine or the propeller function dominates depends on the wing twisting and on the shape of the lift distribution (for more details, please see following chapter).

comparison of a flapping wing with propeller and wind turbine
of aerodynamic machines

The adjacent picture clarifies that the comparison does not apply in all respects to a propeller or to a wind turbine. The velocity proportions at the flapping wing are completely different. But the rotating machines are not designed for simultaneous lift generation. Furthermore, at the flapping wing the lift force at mid-span of the wing is never zero - as like at the rotating machines.

A flapping wing is an aerodynamic machine with two working cycles, the upstroke and the downstroke. In unaccelerated horizontal flight of a flying wing ornithopter the degree of efficiency of this machine is equal to zero. It only moves itself but emits no power.

But if you add a fuselage and a tail unit to the flying wing ornithopter, the flapping wing must apply power to overcome the parasitic drag. Now the flapping wing renders output. Now, paradoxically - with an otherwise unchanged flight attitude - the efficiency factor becomes bigger than before (bigger than zero). For example the efficiency factor of the flapping wing increases with the size of the tail unit while keeping the balance of forces. So the parameter efficiency factor is relatively inapplicable for evaluating flapping wings (please take a look at the comparison of the transport performance).

The total thrust gets bigger the more the lift distributions of the up- and downstroke are different from each other - especially at the outboard wing area where the most working will be performed. If the difference equals zero working drag and thrust have the same size and cancel out each other (Please look at literature A. Lippisch 1938 and the vector diagram). The total thrust equals zero, then. At an existing lift difference the thrust is also increased with increasing flapping frequency and flapping amplitude.

The size of lift is also specified by the angle of incidence at the wing root. With the above-mentioned lift distributions the angle of incidence during the flapping motion of the wing is always kept constant. The pictured differences of lift at the wing root results only from different induced downwind angles (Please look at the diagram Downwash distributions).

To equalize the smaller lift at the wing tip during the upstroke, at least partly the lift should be increased at the wing root at the same time. Here, no researches are known about the angle of incidence at the wing root of birds. To balance the total lift during the flapping motion, literature E. v. Holst (1943) suggests a turning of the wing root synchronic to the wing twisting. There the angle of incidence should get larger in the upstroke and smaller in the downstroke. But this is not to be seen on birds in cruising flight or only in a minor way (take here a look at the animation of a seagull and a stork).

Another way to generate a constant total lift force shows a swan. It increases considerably the angle of attack at the wing root in the lower wing position. But then it reduced the angle once again during the upstroke.

Also, it may be birds increases the angle of attack and/or the airfoil camber in the area of the elbow in the upstroke. Also by this way will be supported the shifting of the lift in the direction to the wing root and the lift force in the upstroke gets larger und the total lift more constant, respectively.

For a steady flight, all forces - more precisely, force impulses - affecting the ornithopter during a complete wing beat cycle must be in balance. The propeller effect must not only balance the wind turbine effect but also all remaining drags of the wing and the aircraft. At the same time, the positive part of the lift must outbalance the negative to an extent, that it can carry the weight of the aircraft.

3. Flapping wing properties during flight

3.1 Gently inclined climb flight

At the wing upstroke the aerodynamic forces along the wing can be adjusted by suitable wing twisting so that the torsional moments round the wing hinge balanced themself (Please look at the following diagram 3). Here, the wing area close to the fuselage acting as a wind turbine directly powers the outboard wing area acting as a propeller. This is the 1st possibility to use the wind turbine energy.

There is no energy consumption or transfer at this upstroke configuration. The wing can virtually be flapped up by the drive without effort. Propeller and wind turbine effects cancel out each other. The overall effect of the upstroke in the thrust direction is thus equal to zero.

lift distribution of a flapping wing in the upstroke with balanced torque
Diagram 3
A special lift distribution at the upstroke when the stroke momentum of the inner and outer wing section balanced each other exactly. Thus, the wing can be moved upwards without an external force.

Due to the lever action of the wing at this upstroke setting the positive lift close to the fuselage must be bigger than the negative lift at the wing tip. In total, there still remains some positive upstroke lift (literature Otto Lilienthal 1889). The wing downstroke with its generally strong generation of lift and thrust can ensure the balance of the remaining forces during the whole flapping cycle.

Would one do without lift in favour of thrust generation in the upstroke the following should be considered. To generate the complete lift impetus only in the downstroke - in virtually half of the available time - the lift force and consequently the wing area, too, would have to be almost doubled. This and the corresponding lift fluctuations are only appropriate in exceptions.

As to be seen in the diagram 1 shown lift distributions the average lift of both working cycles are different in size. At least at low flapping frequency, this will result in an obvious pendulous motion of the fuselage. But due to thereby generated variations of the angle of incidence it deadens itself quite effectively. These variations are not included in the diagrams.

Naturally, other settings are possible in the area close to the preceding lift distribution. They are well suited for gently inclined climb flights with a moderate flapping frequency. My EV-ornithopters have been built for this way of flying.

3.2 Cruising flight * cruise flight

Starting from the previously described flight scenario for the horizontal cruising flight it is more advantageous to increase the total lift during the upstroke and shift it a little more towards the wing tip. There, only a little bit of negative lift is generated - if any at all (Please look at the force vectors of the following picture). But by this way, the wind turbine effect and its working drag are increased.

forces at the wing of a stork in the upstroke and downstroke
Forces at the wing of a stork
during up- and downstroke
by literature Otto Lilienthal

That this should be beneficial is amazing at first. The wind turbine effect now can no longer be used for generating thrust in the area of the wing tip. Would it not be better simply to increase the flapping frequency?

According to a proposal by Otto Lilienthal the wind turbine or the wing upstroke energy may also be used again in a 2nd possibility. At first, the working drag slows down the flying ornithopter. Thereby detracted kinetic energy of the model can be accumulated in a spring. This spring must be positioned in a fashion that it is tensioned at the upstroke. It relaxes in the downstroke, supports thereby the flapping motion, generates thrust and transfers wing upstroke energy back to the kinetic energy of the model.

A 3rd possibility for using the wind turbine force lies in the acceleration of the wing mass in upstroke direction. If the wings are then slowed down at the upper final wing position by a spring and accelerated in downstroke direction, retransfer of the upstroke energy is also affected in this way. Thereby, the acceleration of the wing must not be limited to the initial stage of the upstroke.

In the upstroke, a mechanical drive of the flapping wing is not necessary in these cases. The wing even releases energy to the above-mentioned springs. Anyway, the wind turbine motion must act against any force otherwise no lift can be developed on a freely movable wing.

The wing upstroke energy output normally is relatively small.
It will be adjusted bigger the more flow-favorable the aircraft is built

A good way to decrease the wind turbine effect in spite of strong lift generation is the pulling or the dragging of the outboard wing section during the upstroke of the inboard wing section. Thereby the outboard section of the wing becomes a winglet to the inboard section of the wing.

  • - This mainly has a bisecting effect on the effective wind turbine span.
  • - At the same time, it reduces with its winglet effect the induced drag
    of the inboard wing section.
  • - Furthermore, it reduces problems of wing inertia especially in the area
    of the upper final wing position.

To enable at the upstroke strong lift at the inboard wing section it will be equipped with large airfoil camber.

animated gifs of swan pictures
Delayed and heightened (0.4 MB)
Swan in cruising flight

Close to the water surface a Mute Swan during cruising flight. The picture series has been presented to me by
literature A. Piskorsch privately.

  • The downstroke twisting is negligibly low.

  • Thus sufficient lift can also be generated during upstroke here the angle of attack is increased near the wing root. This already starts before the end of downstroke, reaches the maximum near the lower stroke end position and ends approximately at the middle of the wing upstroke. The changing of the angle of attack near the wing root is a characteristic of the flapping flight of birds. It increases the shifting of lift distribution along the semi-span, but is not always as pronounced as in this flight situation (after starting obviously the full cruising speed is not yet reached here).

  • Due to the extended shifting of the lift distribution toward the wing root also increases the area of the slipstream (blast of air) or the thrust. More details about this you can find in the Handbook, annexe E (in German) and in the article Arrangements of wing tip vortices on flapping wings (version 4.0, chapter 2, PDF 0.5 MB).

  • In the upstroke increase and decrease of the angle of incidence move like a wave from the wing root to wing tip. Therefore wing twisting changes the direction in the upstroke.

  • Due to the pressure difference on the upper and lower side of inboard wing section the turnable outboard wing section intends to stroke up. But it is probably prevented by the negative lift at the wing tip section.

  • The leading inboard wing section stoped at the upper position until the outboard wing section reached the top of its stroke.

  • After the outboard wing section was pulled up hanging on its hinge, also its turning in the upper stroke position occurs only with the lift.

If in total lift results in the upstroke, the flapping wing permanently acts indeed as an aerodynamic two-stroke machine in lift direction, but as seen in flight direction alternatingly reversed. Nevertheless, via wind turbine energy utilisation the whole drive energy will be used for thrust generation - of course with the usual losses of the profile drag and of the induced drag. But these also always accrue for the lift generation.

In spite of changing acceleration direction, flight velocity should be kept constant. Thereby are definitely advantageous a high stroke frequency and a large model mass.

During such cruising flight configurations of the upstroke, its lift increase more than during the gently inclined flight. Apart from thrust generation also lift generation during downstroke can be released. Therefore, its lift distribution will be shifted rather towards the wing root and concurrently be adjusted smaller.

lift distributions for a cruising flight
Diagram 4
Distributions of lift for a cruising flight with unlimited wingspan. Also the distribution of the upstroke is optimized in relation to the induced drag.

Altogether, in cruising flight the lift distributions of both of the work cycles have been approximated to those of gliding. One approximates them the more flow-favourable the aircraft is built. Less thrust is then necessary. Furthermore, the induced drag of the downstroke decreases noticeably this way.

Perhaps it might be enough to shift the lift only a little along the span, without changing its size - in the upstroke towards the wing root, in the downstroke towards the wing tip. However, a twisting of the wing root is necessary for that.

animated gifs of a super 8 film
At an easy rate and heightened
Seagull in cruising flight

(From a 16 mm movie by
literature A. Piskorsch)

During the whole downstroke and at the beginning of the upstroke the angle of attack is increased in the center of the semi-span.

The advantages of the flapping wing working in opposite directions during wing up- and downstroke lies especially in the relative even lift generation. The perpendicular motion of the fuselage disappears almost completely in horizontal flight.

Altogether, a very effective steady cruising flight can be achieved with thrust only directed forward and not upward. Thereby, the flapping frequency is obviously lower than during the following way of flying.

3.3 Strong inclined climb and hovering flight

Precedingly, flight situations are described during which lift is directed upward and thrust forward. The all up weight is thereby carried by the wing lift. In short, this can be called Flying with lift.

But similar to a helicopter, during flapping flight the weight force can be balanced by a slipstream directed downward or by a thrust force directed upward. This is Flying with thrust. Thereby, the wing upstroke practically affected only with the drive. At least in steady flight, the thrust force is always perpendicular to the wing-stroke plane and can be adjusted according to their inclination.

total forces at a small bird on approach
Small bird
on approach

If the thrust force points exactly in flight direction, there is either pure flying with thrust (perpendicular climb flight) or pure flying with lift (horizontal flight). In settings between these extremes and during a horizontal motion not too slow, the balance of all up weight is affected both by thrust and by lift directly generated at the wing. These mixed configurations are also assigned to flying with thrust.

The taking off of an ornithopter, hovering on the spot, strong inclined climbing flight and slow horizontal flight are only possible according to the method flying with thrust.

In contrast, moderate fast horizontal flights can be conducted with both ways of flying - with quite a different demand for power, though. Relatively fast horizontal flights or cruising flight can be achieved only by flying with lift.

In flight praxis, especially the inclination of the stroke plane acts as identification criteria for ways of flying. In horizontal flight it is vertical to the flight direction. If it differs considerably (more than about 10 degrees) it is flying with thrust. Furthermore, a big upstroke wing twisting in a passive wing twisting is an indication for this way of flying - at least at high Reynolds numbers. Also, a relatively high power consumption relating to the horizontal velocity points to a flying with thrust.

Furthermore, the legs of birds, at least of the larger ones, are not fully stretched backwards when flying with thrust and their body still is not fully directed in flight direction (literature R. Demoll 1930). But in publications of bird flight research it is only rarely pointed out to these both unequal ways of horizontal flight. The high power consumption during slow flight is commonly only ascribed to the thereby increasing induced drag (for an example please look at external link 1).

by A. Pénaud
A. Pénaud (1872)

Flying with thrust can be carried out in technical model making since the beginnings of aviation. But in horizontal flight of large and weightily ornithopters this way of flying demands considerably more energy than flying only with lift.

Otto Lilienthal had already distinguished clearly between these two ways of powered flying among birds and has pointed out the enormous flight energy during slow flight.

4. How birds fly

Birds also apply the shifting of lift along the wing for propulsion or thrust generation. Erich v. Holst has illustrated it very clearly in the following scheme. In it, the location of the center of the lift distribution is represented by a wing section which is shiftable along the wing semi-span.

lift and thrust forces in the flight of birds
Function principle of lift and thrust
generation in the flight of birds

On the top of the stroke it is shifted towards the wing tip and at the bottom point to the wing root. In this way, seen over a whole flapping period, while maintaining the transverse force Q (or the lift) the thrust S gets larger than the backward directed force R.

This ingenious trick of nature makes it possible to generate lift also during the upstroke and still enables the generation of a thrust.

Because birds are aerodynamically efficient shaped it requires only a relatively small shifting of lift for the cruise flight (see, for example the position of the centers of pressure in diagram 4, above).

Though biological flapping wings serve as archetype, they are much more complex than that of ornithopters.

bird flight animation
At an easy rate and heightened
or the animation in color
Stork in cruising flight

(From a 16 mm movie by
literature A. Piskorsch)

Other than small birds, here, the primary feathers are splayed during up- and downstroke.

The basic moving components of a bird wing in addition to the forward motion are:

  • Flapping motion at the shoulder joint. In cruising flight the axis lies almost parallel to the axis of fuselage. Stroke angle, flapping frequency and time flow are within wide limits.
  • Pulling or dragging of the outboard wing section in the upstroke by the inboard wing section. Depending on the bird species and the flight situation this motion is pronounced very differently.
  • Inclination of the stroke plane. It is determined by the inclination of the stroke axis. Birds have the possibility to lift the stroke axis at the front in comparison to the fuselage and additionally, the axis of the fuselage in comparison to the flight direction.
  • Twisting of the wing. It increases towards the wing tip - mostly in the upstroke in the direction of a positive and in the downstroke in the direction of a negative angle of incidence.
  • Turning of the wing root, especially when flying with thrust and mostly in direction of the wing twisting. Such a thing is rarely visible among big birds in cruising flight.
  • Sweep, especially of the outboard wing section in the upstroke with the backward motion of the wing tip. In general, multiple sweepings are applied within a semi-span at the same time. Especially small birds use them. They fold up the wing in the upstroke partially or completely.

The flapping motion of the wings is absolutely necessary for thrust generation. In general, it is also the wing twisting for aerodynamic reasons. In contrast, the turning and sweeping of the wing as well as the pulling of the outboard wing section serve only to increase efficiency. About their effects there are merely vague perceptions.

Whether birds have other possibilities for wing upstroke energy utilisation beside the aforesaid 1st option, for example using elastic devices like jumping kangaroos, is unknown here.

All preceding motion components are used by the birds combined and beyond

foto of a stork during gliding, from behind
Staggering of the primaries
of a stork during gliding
  • the airfoil will be modified,
  • fore flap effects are used by spreading of the thumb pinion,
  • primaries at the wing tip are used for decreasing the induced drag by expanding and staggering,
  • the airstream is pressed outwards by a wavelike and phase-delayed flapping motion of the inboard and outboard wing section, as well as by additionally bending of the wing tips and so the induced drag is further reduced,
  • Air boundary layers at the leading edge, on the surface and at the trailing edge of the wing are affected ... and a lot of more.

It will remain technically impossible for a long time to reach such a level of sophistication even only approximately.

Also in descriptions of bird flight, the functioning of the wing downstroke is mostly compared to the mode of functioning of a propeller. However, for birds this is said to be valid in the outer wing area only. Furthermore, it is agreed that most of the lift is generated during the wing downstroke. Approximately this perception complies with the above-mentioned theory.

Motions and forces in flapping flight of a bird
Motions of a bird wing and the changes in transverse force and drag
over a flapping cycle at a point of the arm- and the hand wing
Vertically upwards or in flight direction acting components of the resulting force build lift and thrust (Please look at the diagram: Configuration of the forces). In the upper and lower final wing position for a short time these forces have similar sizes to those of gliding flight. Up and down movements of the fuselage due to changing lift has been disregarded.

But this differs during the upstroke of the wing of birds. At least for cruise flight it is described differently and often only vaguely. To avoid the additional drag in the upstroke, lift is mostly required in the wing area near the fuselage only. In contrast, the outer wing area should be pulled up without any noteworthy force generation.

Small birds sometimes avoid the difficulties of the additional drag. They do the upstroke nearly completely without lift. Therefore, they widely fold up the winin the upstrokeoke. Lift in the upstroke is almost always described as small compared to that during the wing downstroke.

Statements about the cause for the well-known additional drag in the upstroke with lift (energy of a wind turbine) are only rarely made. Also literature Otto Lilienthal and
literature E. v. Holst make only casual remarks about this circumstance.

This stated lift distribution for the bird's wing upstroke - that is near the fuselage with lift and in the outer wing area without - is hardly feasible due to the occurring equalisation of the air pressure along the wing span. A lift distribution whose generation ends in the middle of the wing is contrary to the vortex laws (Helmholtz vortex theorem), too. But in the upstroke birds certainly are able to significantly reduce lift generation in the outer wing area. At the same time they can adjust the remaining positive and negative lift forces, that average lift at the outer wing area equals zero, if necessary. This then looks approximately like in the above-mentioned diagrams (for example for the climb flight, diagram 2 or the cruising flight, diagram 4).

Further details of the flapping wing theory and a calculation method that uses quasi-steady aerodynamics and blade element theory, which has already been used for flapping wings by Otto Lilienthal, can be found in the handbook.