The principle of flight of ornithopters
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
flapping wing model.
The basic operating principle of a flapping wing has already been discovered (1889) by 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 Alexander Lippisch (papers 1925 - 1939) and 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.
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
- Diagram 1
- Optimized lift distributions for a gently inclined climb flight with limited wingspan
- 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.
- Vector diagram of forces and velocities
- Forces at the stork wing on upstroke
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 aero-
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
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 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. But 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,
E. v. Holst (1943) suggests a turning of the
wing root additional to the wing twisting. There the angle of incidence should
get larger especially on upstroke. This is sometimes good to be seen in birds
in cruising flight (take here a look at the animations of a swan
and a stork and the article
Lift during wing upstroke, version 8, 2015, PDF 0.9 MB).
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 the force impulses (product from force and duration of action) - 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.
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 ( 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
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.
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?
- Forces at the wing of a stork
during up- and downstroke
by 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 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,
particularly 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.
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.
- 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.
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
- 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 ( 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).
- 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
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 center of the lift distribution is represented by a wing section which is shiftable along the wing semi-span.
- Basic 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 much lift also during the upstroke and still enables the generation of a thrust.
Because birds are aerodynamically efficient shaped it requires for them 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).
The physics of bird's flight, which is commonly used today, is based on an other idea. In it, in particular, the arm wing is intended to generate lift during the up and downstroke. The simultaneous produced thrust during the downstroke is compensated by the back-thrust during upstroke.
- Lift and thrust generation during a flapping period according to descriptions of the bird's flight with strong fluctuating lift.
- Supposedly approximate course of the lift distributions along the span according to the vague descriptions of the cruising flight of birds.
In the hand wing, otherwise, a lot of thrust is been generated during the downstroke. During the upstroke, the hand wing is then guided upwards without any significant force, thus only with the remaining profile drag. In this way, during a whole flapping period the lift of the bird is mainly generated in the arm wing and the thrust in the hand wing.
The large lift in the hand wing, which is necessary for generation of the large thrust during downstroke, is neglected in such a discription. Sometimes, however, it is also said that during the downstroke the most lift arises (see the adjacent diagrams). From the rotation of the wing root during cruising flight of large birds is nothing reported.
Also in descriptions of bird flight the wing downstroke is often compared to a propeller. A corresponding analogy to the wing upstroke with its known additional drag, however, is not considered (wind turbine and its utilization). Also Otto Lilienthal and E. v. Holst mention this context only casually.
- Staggering of the primaries
of a stork during gliding
Both theories of the physics of bird's flight, that is, this with the shift of
roughly constant lift to Erich von Holst and this with strong fluctuating lift,
do not extend so far apart in principle. Both theories work with the displacement
of lift. In both cases the wing moves upwards without any drive, only by the force
of lift. Jeremy Rayner has studied such gaits of birds, even those with constant
circulation (see article
Vertebrate flapping flight mechanics and aerodynamics,
and the Evolution of flight in bats in
Nachtigall W. 1986, BIONA-report 5).
- Roughly approach to a constant lift during a flapping period, using the example of a rectangular flapping wing
For ornithopters, it is easier to realize the method with strong fluctuating lift, as described in the chapter 2. Operating principle of the flapping wing for ornithopters and similar in the commonly used physics of bird's flight. In this case you need no rotation of the wing root. However, you have to forgo the advantages of an at least almost constant lift (please see the article "Lift during wing upstroke, version 8", 2015, PDF 0.9 MB).
A further clarification of the various theories of the flight of birds is possible, in particular, by measurements on technical flapping wings with various twisting adjustments in a wind tunnel.
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.