The principle of flight of ornithopters

1. Definition

An Ornithopter, or ornitotero - like Leonardo da Vinci termed them - is an aircraft heavier than air, that flies like a bird by flapping it's 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 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 much 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

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

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

With permanently changing twisting the flapping wing must adapt to these alternating incoming flow directions. Nevertheless, the lift distribution is modified along the span (please take a look at the diagrams).

At the wing downstroke the lift distribution is bigger altogether than when gliding and more shifted 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.

A flapping wing is an aerodynamic machine with two strokes, the up- 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 parasite drag. Now the flapping wing renders output. Now, paradoxically - inspite of equal 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 paramter efficiency factor is relatively inapplicable for evaluating flapping wings.

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 work of thrust will be performed. If the difference equals zero work drag and thrust have the same size and cancel out each other (please take a look at A. Lippisch 1938 and the vector diagram above). The total thrust equals zero, then. At an existing lift difference the thrust is also increased with increasing flapping frequency.

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 result from different induced down wind angles. 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 synchronal to the wing twisting.

For a steady flight, all forces - more precisely, force impulses - affecting the ornithopter during a complete wingbeat 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 balance themselves (please take a look at the following picture). 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 total thrust effect of the upstroke thereby equals 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 during upstroke the following should be considered. To generate the complete lift impetus only during 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 movement 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 at 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 take a look at the force vectors of the following picture). But by this way, the wind turbine effect and its work 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?

According to a proposal by Otto Lilienthal the wind turbine and the wing upstroke energy, respectively, may also be used again in a 2nd possibility. At first, the work 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 at downstroke, supports thereby the flapping movement, 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 effected in this way. Thereby, the acceleration of the wing must not be limited to the initial stage of the upstroke.

During 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 at a lose mobile 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.

During such cruising flight configurations of the upstroke, it lift gets bigger 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.

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 - at upstroke towards the wing root, at downstroke towards the wing tip. However, a twisting of the wing root is necessary for that.

delayed and heightened (1.0 MB)

Seagull in cruising flight

(from a 16 mm movie by A. Piskorsch)

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

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 movement of the fuselage disappeares 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 thrust stream directed downward and by a thrust force directed upward, respectively. This is flying with thrust. Thereby, the wing upstroke is practically effected 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.

Small bird at 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 effected 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 and cruising flight respectively 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.

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 work during slow flight.

4. How birds fly

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

Stork in cruising flight

(From a 16 mm movie by 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 and dragging, respectively, of the outboard wing section during 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 possiblity 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 during upstroke in the direction of a positive and during 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 during upstroke with the backward motion of the wing tip. In general, multiple sweepings are applied within a half span at the same time. Especially small birds use them. They fold up the wing during upstroke partially or completely.

The flapping motion of the wings is absolutely necessary for thrust generation. In general, 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. There are merely vague perceptions about their effects.

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

• airfoils are 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. This idea approximately complies with the above-mentioned theory.

But this differs at the wing upstroke of birds. At least for cruise flight it is described differently and often only vaguely. To avoid the additional drag during 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. Statements about the cause for the well known additional drag (energy of a wind turbine) are only rarely made, too (only by Otto Lilienthal and E. v. Holst). Small birds sometimes avoid the difficulties of the additional drag. They do the upstroke nearly completely without lift, then. Therefore, they widely fold up the wings during upstroke. Lift during upstroke is almost always described as small compared to that during the wing downstroke.

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 feasable due to the occuring 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. 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 inclined climb flight and the cruising level flight).

Further details of the flapping wing theory and a calculation method according to the stripes method, which has already been used for flapping wings by Otto Lilienthal, can be found in the handbook.