How Ornithopters Fly

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The principle of flight of ornithopters

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 (1889) by literature Otto Lilienthal . To help understanding an effective way of flying of big ornithopters his functional description is still trend-setting to the present day. Especially literature Alexander Lippisch (papers 1925 - 1939) and literature Erich von Holst (papers 1940 - 1943), as well as the research work of many biologists have advanced the theory of the flapping flight further. But many details are still not understood.

There have always been quite different variants 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 strong simplified way. Furthermore, the known drive mechanism and especially wing designs leave a lot to be desired. In every respect ornithopters are still standing at the beginning of their development. But powerful drives make very beautiful flights already possible.

Also here follows only a variant of the flapping flight theory in short version.


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 which is flown 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. However, the lift distribution along the span must not be kept constant, otherwise there is no thrust (please see adjacent 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
forces at upstroke by Otto Lilienthal
Forces at wing upstroke
by literature Otto Lilienthal

On 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).

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
Comparison of aero-
dynamic 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 operating cycles, the upstroke and the downstroke. In unaccelerated level 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. The flapping wing delivers power. Now in seemingly absurd way, at otherwise same flight status, efficiency is higher than before (bigger than zero). So, if the equilibrium of forces is maintained, the efficiency increases with the size of the tail unit. So the parameter efficiency factor is relatively inapplicable for evaluating flapping wings (please take a look at the Comparison of the transport performance).

The flapping wing as an aerodynamic machine with two operating cycles constantly generates positive lift. In the direction of flight, however, it works with its thrust forward (downstroke) or backward (upstroke). Nevertheless, it is also possible at upstroke to use the entire drive energy for generation of thrust forward, with the three possibilities mentioned below. Of course, there are the usual losses due to the profile drag and the induced drag. However, this is always the case for the generation of lift. The advantage of the flapping wing working in the opposite direction during upstroke and downstroke, is the uniform generation of lift. In spite of changing directions of acceleration, flight velocity should be kept constant. Thereby are definitely advantageous a high flapping frequency and a large model mass.

The total thrust at the flapping wing gets bigger, the more the lift distributions of upstroke and downstroke differ in size and/or in the distribution along the span. This is especially true in the outer wing area, where most of the work is done. If the difference equals zero, operating drag and thrust have the same size and cancel out each other. The total thrust then is equal to zero (please look at literature A. Lippisch 1938). If there is a difference in lift, the thrust also increases with increasing flapping frequency and stroke amplitude.

For a steady flight all forces - more precisely the force momentums (product from force and duration of action) - affecting the ornithopter during a complete wing stroke 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.


2.1. Rotation of the flapping wing

The course of the lift along the span is modified by the twisting of the flapping wing. But also, a rotation of the wing at the wing root around its longitudinal axis changes the lift. The rotation of the wing only influences the size of its lift in the calculation model, but not its distribution along the span (see adjacent figure). The wing twisting will be adjusted automatically. This would be different with the rotation of a rigid wing.

lift with a rotation of the flapping wing during wing upstroke
Changes of lift with a rotation of the flapping wing during wing upstroke in the computer model

In the calculation model the rotation of the wing root is indicated starting from the glide position. It is only indirectly determined by the selection of the lift size. For this purpose, the circulation factor kΓ is used (the circulation factor k-Gamma describes the size of the lift in relation to that of the gliding flight). In the adjacent figure the lift with rotation of the wing root during upstroke by about +6 degrees, amounts to almost 80 % of the gliding flight.

When rotating the wing the required twisting becomes smaller, at least in wing upstroke (please see calculated examples in Flapping wings with and without wing rotation, in German, PDF 0.7 MB). However, the rotation is limited by the maximum permissible lift coefficient of the airfoil at the wing root. The rotation and thus the lift, can be further increased by greater camber of the airfoil and/or wing depth in this area. Birds in particular use a very large camber of the airfoil.

In the generally used theory of the cruise flight of birds the rotation of the wing is not considered. Also with the older lift distributions shown above the angle of incidence at the wing root is kept constant during the wing flapping motion (see above-mentioned diagram 1 und diagram 2). The pictured differences of lift at the wing root results only from different induced downwind angles (please look at the diagram Downwash distributions from the site Handbook).

To equalize the total lift literature E. v. Holst (1943) suggests in addition to wing twisting a rotation of the wing root. The angle of attack near the wing root should be increased during upstroke and reduced during downstroke. Based on present knowledge, however, turning is not allowed at up- and downstroke, also like at my flapping wing models EV1 to EV5, but, only during upstroke.

Lift and propulsion along the wing

Lift and propulsion during downstroke along the flapping wing
lift and propulsion during upstroke along the flapping wing

during downstroke
The propulsion is mainly generated by the hand wing, but, about 40 % also by the arm wing.

during upstroke
When rotating the wing root (here about +6 degrees) the negative thrust remains relatively small, despite almost the same lift as in gliding flight (here approximately 80 %).
The stroke torque of the hand wing around its wrist is very small here. With this lift distribution, the course in the area of the hand wing is even roughly maintained when it is bended downward.

In large birds in cruise flight the rotation is sometimes good to observe, especially near the lower final stroke position (see animations of a swan and a stork and the article Lift during wing upstroke, version 10.1, PDF 1.0 MB). The thereby resulting large lift generates so to speak, a large momentum of lift as reserve capacity. Then, the wing does not need to generate so much lift during the following fast upward motion. In this way the wind turbine function and the resulting negative thrust of the upstroke become smaller. Nevertheless, the sum of the momentum of lift will be large over the entire duration of the upstroke.

An increase in lift near the wing root can probably be achieved by birds by other means than wing rotation. It is conceivable a mechanical coupling of the motions when angle the upper arm during wing upstroke. This could automatically increase the angle of attack and/or the airfoil camber in the area of the elbow (please see 3D-form of the bird wing by K. Herzog). Even just one activity of the tension muscle of the anterior pelvis (propatagium) would be suitable for this. Especially with not so high demands on the variation of lift or with long wings, thereby could be dispensed with the rotation of the wing root. Unfortunately, K. Herzog has nothing reported about such functions of the biological wing.

So, during upstroke one have the following possibilities to increase the lift in the arm wing, without the negative thrust becoming too great.

  1. In the close range of the lower final stroke position, i.e. during low stroke speed, starting already at the end of the downstroke, increase the angle of attack by rotating the wing.
  2. In the same period as above, increase the angle of attack in the area of the elbow, e.g. by angling the upper arm.
  3. In the same period as above, together with the bending downward of the hand wing, increase the angle of attack of the arm wing near the wrist.
  4. During the fast upstroke motion, shift as much lift as possible to the span centre by twisting and rotating the wing.
  5. In the upper final stroke position, maintain the large angle of attack of the arm wing in the area of the elbow until the arm wing is stretched.
  6. In the upper final stroke position, maintain the large angle of attack of the arm wing near the wrist, until the hand wing has finished its upstroke and the upstroke of the whole flapping wing ends.

For ornithopters, all this is difficult to achieve (example for 3. and 6. please see on site Articulated flapping wing, chapter 7. Wrist ... ).

If one uses the lift increases in the two final stroke positions, which are also possible without wing rotation, the lift does not have to be very large during the fast upstroke motion. A rotation of the wings with the aim of increasing the lift is not absolutely necessary. This may be a strategy to generate enough lift during upstroke even without wing rotation.

When a seagull is flying with a strong headwind, its whole body swing up and down, something like at the gull in a gusty wind (animation, 0.5 MB). During its motion downward, in this way the inflow at the wing root is more from below. This creates thrust, please note thrust at the wing root. Besides, this increases the lift there. However, this was not yet investigated in closer detail.

In small birds and ornithopters, because of the high flapping frequency transient flow conditions prevail at the wing. Thereby the lift increases even without wing rotation in the lower final stroke position (please see diagram of lift distributions during a stroke period under non-steady flow conditions from the site Handbook).

For further information about the Rotation of the flapping wing see the following chapter 4. How birds fly.

Very thorough observations of the bird flight and interesting ideas of the wing upstroke and the wing rotation also shows Brendan Body`s homepage, external link 1.

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 turning moments round the wing hinge balanced themselves (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 consumption or transfer of energy 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 torque of the inner and outer wing section balanced exactly each other. Thus, the wing can be moved upwards without an external force.

Due to the leverage of the wing at this upstroke setting the positive lift close to the fuselage must be bigger than the negative lift near the wing tip. In total there still remains some positive lift at upstroke (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 stroke cycle.

As can be seen from the underlying lift distributions in diagram 1 above, the average lift of the two operating 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.

Would one do without lift in favour of thrust generation in the upstroke, the following should be considered. To generate the complete momentum of lift only in the downstroke - so, about in 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.

The only way to reduce negative thrust despite strong lift generation during the upstroke motion, is the concentration of lift in the mid-span. One can support this by bending the hand wing downwards. Thereby, the angle of attack of the hand wing near the wrist should increase significantly during the bending motion (see image of a wrist with pivot angle). This achieves the following:

  • The lift in the arm wing area is, so to speak, held together. Negative lift may be present towards the wing tip.
  • At the same time, the bended hand wing with the effect of an end plate or winglet reduces the induced drag.
  • By the temporal sequence of the stroke motions of the arm and hand wing can be reduced problems with mass moments of inertia, especially in the range of the upper stroke end position.

To enable in birds strong lift during upstroke at inboard section of the wing, it is equipped with large airfoil camber. Only rarely is increased the wing depth at the wing root.

Of course, other settings are also possible in the close range of the lift distributions in diagram 1. They are well suited for gently inclined climb flights with a moderate stroke frequency. My EV-ornithopters have been built for this way of flying.


3.2 Cruise flight

In cruise flight, the lift is greater at upstroke and smaller at downstroke than in gently inclined climb flight. This not only reduces the positive thrust at downstroke, but also increases the negative thrust at upstroke. However, these variations are not great. This is offset by a reduction in the drag of the wing and the induced drag during downstroke. The flapping frequency in cruise flight is a little bit lower than in gently inclined climb flight. If the overall settings are balanced, the average drive power decreases.

The now increased wind turbine effect during upstroke can no longer be fully used to generate thrust in the outer wing area. The wing section with propeller effect is simply too small.

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

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 operating 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 removes the tension in the downstroke and supports thereby the flapping motion. The thereby generated thrust transfers the 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 effected in this way.

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 free movable wing. Therefore, a guidance (e.g. speed controller) or limitation of the upstroke speed is necessary. The energy emitted during wing upstroke is normally relatively small. This is especially true when the lift is concentrated in the middle of the wing span.

Swan in cruise flight

animated gifs of swan pictures
Close to the water surface a Mute Swan during cruise flight.
Slower and augmented (0.4 MB)
  • The downstroke twisting is negligibly low.

  • In order to generate sufficient lift during upstroke, the swan increases the angle of attack by turning the wing root. This already starts before the end of the downstroke. The rotation reaches its maximum shortly after leaving the lower stroke end position and ends before reaching the upper stroke end position (for more details please look at Lift during wing upstroke, version 10.1, PDF 1.0 MB).
    Such a variation in angle of attack near the wing root is a feature in the flight technique of many large bird species. However, it is not always so distinct as here, short after the start of this swan.
  • During upstroke, the strong turning of wing decreases. This may give the wrong impression from the viewing direction, that the wing twisting changes the direction during the upstroke.

  • The leading inner wing section waits at the top until the outer wing section has arrived at the top.

  • In the upstroke the variation of the angle of incidence move like a wave from the wing root to wing tip.

The picture series has been presented to me by literature A. Piskorsch privately.

lift distributions for a cruise flight
Diagram 4
Optimum lift distribution for gliding with unlimited wingspan. The lift distribution of upstroke is also optimal in relation to the induced drag.
(maybe used in gulls)
about like diagram 2

Altogether, in cruise flight the lift distri­butions of both of the operating cycles have been approximated to this of gliding (please see adjacent diagram). It can get closer, the more streamlined the aircraft is built. Because then is necessary less thrust. Furthermore, the induced drag of downstroke decreases noticeably in this way.

Perhaps, it might be enough to shift the lift only a little along the span without changing its size. However, for that is nessessary a rotation of the wing root.

Seagull in cruise flight

animated gifs of a super 8 film
Slower and augmented

An increase of the angle of attack near the wing root is not visible during upstroke.

From a 16 mm movie by literature A. Piskorsch

When the cruise flight is perfected, according to literature Konrad Lorenz (1933) it shows in particular the two following characteristics, a very slight, sometimes barely observable bending of the hand wing downwards, and a constant lift. Thereby an up and down swinging of the bird is no longer observable (for more information please see the site Gait change, chapter 4.).


3.3 Strong inclined climb and hovering flight

Similar to a helicopter during flapping flight the weight force can be balanced by a thrust jet directed downward or by a thrust force directed upward. It is the Flying with thrust. Thereby, the wing upstroke practically happens only with the drive. At least in steady flight, the thrust force is always perpendicular to the stroke plane of the wing. Therefore, the thrust force can be aligned with the inclination of the stroke plane of the wing.

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

If the thrust force points exactly in direction of flight, there is either pure flying with thrust (perpendicular climb flight or hovering flight) or pure flying with lift (level flight). At settings between these extremes, the balancing of the weight force resulted by thrust as well as by lift. These mixed configurations are also assigned here to flying with thrust.

At least for large ornithopters, starting from a standing position, hovering on the spot, a strong inclined climb flight, or a very slow level flight, can only be realized by flying with thrust. Cruising flight or the slightly faster level flight, on the other hand, can only be achieved by flying with lift.

In flight praxis, especially the inclination of the stroke plane acts as identification criteria for ways of flying. In level flight it is nearly vertical to the flight direction. If it differs considerably (more than about 10 degrees) it is flying with thrust. In addition, when passive wing twisting is used, a large twist during upstroke is an indication of this flight type - at least at high Reynolds numbers. Also, a relatively high energy consumption in relation to the speed in level flight also indicates flying with thrust.

by A. Pénaud
A. Pénaud (1872)

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

In publications about the bird flight is rarely referred to the different flight techniques. The high-power consumption during slow flight is commonly only ascribed to the thereby increasing induced drag. But already Otto Lilienthal has distinguished clearly between two types of power flight in birds and has known the large amount of work in the slow flight.


4. How birds fly

Also, birds apply the displacement 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 centre of 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
Basic principle of lift and thrust
generation in the flight of birds

At the upper reversal point of the stroke motion 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 normal force Q (or the lift) the thrust S gets larger than the backward directed force R.

With this ingenious trick of nature, it is possible to generate much lift also during the upstroke and nevertheless, seen over an entire operating cycle, a thrust generation is made possible. Since birds are very streamlined shaped, a relatively small displacement of lift is sufficient for them during cruise flight (see for example the position of the centres of pressure in diagram 4, above).

Stork in cruise flight

bird flight animation
Slower and augmented

In contrast to small birds, here the wing feathers are spread out during up- and downstroke.

The nodding motion of the bird's body causes an increase in the angle of attack on the wing root, especially at the beginning of the wing upstroke.

From a 16 mm movie by literature A. Piskorsch

Lift distributions correspond to the bird flight theory
Supposedly approximate course of the lift distributions along the span according to the vague descriptions of the cruise flight of birds.
lift forces during up- and downstroke in bird`s flight
Normal force during a flapping period according to descriptions of bird's flight with strong fluctuating lift.

The theory of bird's flight which is commonly used today, is based on another idea. Accordingly, at downstroke in the outer wing area is generated much lift and therewith also much thrust. Thus, the outer wing area is guided upwards without significant force generation. In this way additional drag should be avoided to a large extent (please see adjacent diagrams).

The fundamental principle of thrust generation by lift displacement is not mentioned. About a rotation of the wing root during cruise flight of large birds or other measures to increase lift during wing upstroke is nothing reported. Thus, the lift fluctuates considerably seen over a whole flapping period. According to literature Konrad Lorenz (1933), however, the cruise flight only occurs when no up and down motion of bird is observable. You can see this yourself in many videos with travelling birds.

Both bird flight theories, i.e. the common theory with strongly fluctuating lift and that with constant lift, are not so far apart in principle. They simply describe two different gaits of flying with lift (please see scheme by K. Lorenz from the site Gait change). Both methods work with the displacement of lift, in common theory it just doesn't explain it in that way. The energy-saving gait with constant lift is used by birds in particular for cruise flight over long distances, such as in bird migration. Therefore, it is difficult accessible for research. Unfortunate I have not always distinguished between the two ways of flying so far (2019), also not here on this website.

If one compares in this context the calculated examples in the article Flapping wings with and without wing rotation (in German, PDF 0.7 MB) it confirms that equable and uneven lift have preferences. This is also the case there, because the size of the lift during wing upstroke is determined in particular by the choice of lift distribution. The flight mode with strongly fluctuating lift offers advantages for gently inclined climb flight (see example 1, with c_Γ1=0) and the flight mode with relatively constant lift for long-distance flights (see example 10, with c_Γ1=5 or 6). But here, too, the general rule applies, what is good for the lift is detrimental to the thrust and vice versa.

Increased lift distribution during the wing upstroke
Increased lift distribution at upstroke with the aim of a nearly constant lift during a stroke period

For ornithopters it is easier to realize the method with strong fluctuating lift, as described in the commonly used physics of bird's flight. In this case you need no rotation of the wing root. For long-distance flights, however, one should not do without the advantages of an at least almost constant lift (please see also Lift during wing upstroke, version 10.1, PDF 0.9 MB).

foto of a stork during gliding, from behind
Staggering of the primaries
of a stork in gliding

Professor Jeremy Rayner has researched the flight of birds at the University of Leeds (England). Thereby he also already largely described the way of flying with constant circulation or constant lift (see article Vertebrate flapping flight mechanics and aerodynamics and the Evolution of flight in bats in literature Nachtigall W. 1986, BIONA-report 5). He emphasizes the importance of this gait and sees its strong experimental confirmation in the flow visualization experiments with a kestrel in fast flight by G. R. Spedding (, 1984, 1986, 1987). The resulting image of the continuous vortex gait shows a non-planar vortex pair closely following the wings, with variable mutual distance between the two wing tip vortices. According to J. Rayner, the starting point of each tip vortex at the trailing edge of the wing moves bidirectionally between the wrist and the wing tip. Approach vortices are not visible (please look at external link 3).

A further clarification of the different theories of bird's flight is possible, in particular by measurements on technical flapping wings in wind tunnel. Thereby the effects of various twists and rotations on the lift distributions along the span should to be researched. Also, the behaviour of the wing tip vortices and the downward bending of the outer wing-section are interesting.

Motions and forces in flapping flight of a bird Motions and forces in flapping flight of a bird

Motions of a bird wing and the changes in normal force and drag over a stroke cycle at points of the arm- and the hand wing
according to the commonly used theory of bird's flight.

The vertical upward or in direction of flight acting components of the resultant R form lift and thrust. 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.

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.