How Ornithopters Fly is only in German)
How does an ornithopter create thrust and lift - despite of alternating flapping directions? The answer can be found in the handbook based on well-known results of research. Apart from the aerodynamics of up- and downstroke, the dynamics of the flapping wing is also taken into consideration. The correlations are described with equations and diagrams. Your own calculations are made possible, which may be helpful for developing specific ornithopter models. Furthermore, you will find useful tips for ornithopter models in practice.
The relatively simple equations for changing circulation distributions make it possible to vary the lift distribution and to determine the appropriate wing twisting.
The ornithopter subject also extends to the field of bionics. It is an attempt to develop better ornithopters by understanding the biological design principles of birds.
You can download the handbook (in German) and photos.
The handbook was translated in French by Jean-Louis Solignac. With his knowledge as an aerodynamics expert and with his experience he has contributed a lot to the improvement of the handbook.
Jean-Louis Solignac, Maître de
Recherche, acted as deputy head of the department
Aerodynamics in the directorate of aerodynamics of the national French
research institute O.N.E.R.A. (Office National d'Études et de Recherches
Aérospatiales). You can find his translation of the handbook here on the
The photos of the handbook
2. Calculation of flapping wings
under the precondition of quasi-stationary conditions
The equations presented in the handbook are used in several calculating tools. Thereby underlies the following method of calculation.
First, the flapping wing is theoretically devided into stripes with a very small span. Then, for each of these wing sections the aerodynamic forces are calculated under stationary or constant oncoming airflow conditions. Their sum results from a numerical integration over the whole wing span.
This way, you get the total forces of lift and propulsion of the flapping wing at a fixed moment of time of the flapping cycle. The corresponding wing twisting, the profile- and induced drag can be determined in the course of this calculating scheme, too.
This process is repeated in equal time segments of the wing stroke motion. Thereby, the changed factors as for instance the distribution of circulation, conditions of oncoming airflow or the dihedral of the wing form the basis. At the same time, stationary conditions are postulated. It is therefore presumed that the airflow does not change during the time span of calculating. Furthermore, unsteady airflow behaviour is not considered.
That way - thus by stringing together different steady conditions - time force progression under quasi-steady conditions results.
The force of a whole stroke motion can be obtained by numeric integration of the force progression over the considered time span. Thereby, up- and downstroke of the wing are advisably considered separately. Finally, the summary of up- and downstroke forces leads to the total forces of a whole flapping cycle.
- Frequency of wing beats
and the weight of birds
by Heinrich Hertel
But according to Erich von Holst this quasi-steady method> only leads to useful results during a fast forward flight with relatively low flapping frequencies (large birds). Otherwise, the influences of unsteady airstream behavious become too strong. Later publications verify these constraints. As an example also the following analysis by M. Neef.
3. Result of the latest research
Dr.-Ing. Matthias F. Neef has examined in his dissertation
of the flapping flight by numeric flow design engineering
the unsteady flow at a moved wing. Thereby, he reached a similar
vorticity system as aforesaid. However, his picture with a sinusoidal
flapping motion-sequence is more specified and more detailed.
The dissertation includes a general view about flapping flight and more exciting pictures (Please look at external link 1. and 2.).
4. The tip vortex of the flapping wing
isolines of circulation of a flapping wing shown
above also can be visualized as single vortex filaments.
Vortex filaments runing parallel and with a similar direction of circulation, twist themselves to a single vortex in their shared center at the wake of the wing.
This way, the majority of the vortex filaments combined build up the wing tip vortex. During the flapping cycle its starting point is moving back and forth along the trailing edge of the wing - especially in the upstroke. Therefore, the vortex trail behind the flapping wing in plan view shows lateral contractions in regular intervals.
Also in birds, which are flying in cruise flight (
with lift) the lateral movement of the starting point of the vortex
along the trailing edge of the wing has already been observed (please look
at external link 3, Fig. 1). This continuous-vortex gait
is contrary to the vortex-ring gait when birds are
with thrust (please look at the discribing of the flight modes).
- Helical wingtip vortices or
slipstreams(blast of air) of a bird in continuous-vortex gait during cruise flight
When we imagine the wing tip vortex in the adjacent picture in three-dimensions be aware a surprising view.
The starting point of the vortex of one wing side not only moves back and forth along the trailing edge of the wing. It also follows the flapping motion. Seen in flight direction these both movements together resulted in an approximately circular path line. If now also include the forward motion of the flapping wing one sees the helical shape of the wing tip vortex spreading backwards.
Also the tip vortices of a propeller are arranged in a helical shape
(Please look at external link 4).
They wrapped the propeller slip stream and are an essential part of it.
In opposite to the propeller at the flapping wing simply the windings
of the tip vortices are pulled more apart. Hence, in the three-dimensional
view of this vortex picture will be visible a
each side of the flapping wing.
An according vortex structure is desirable also at ornithopters in cruise flight. Therefore also in the upstroke, a large lift must exist - maybe larger than indicated here - and the transition between the lift distributions of up- and downstroke must be smooth. In the movie recording of a flying swan for example, you see that the increase and decrease of the angle of incidence moves like a wave from the wing root to wing tip.
In order to generate large thrust at an ornithopter, the cross-section of the slipstream is to make as large as possible. Shifting of the spanwise distribution of lift is a dominant factor here. At downstroke the lift should be shifted as far as possible towards to the wing tip and at upstroke towards to the wing root. Furthermore the stroke angle of the wing should be chosen relatively large without, however, losing sight of thereby decreasing lift.
In case of very great demand of thrust, the shifting of the spanwise distribution
of lift in upstroke can be supported by a strong downward bending and/or backward
bending of the hand wing. At the same time birds are using the shortening
of the arm wing. For more information, please see the article
of wing tip vortices on flapping wings (version
4.0, PDF 0.5 MB).
V-shaped staggered flight formations result in a measurable energy conservation for each single individual. This is particularly the result of aerodynamic influences. With the aid of the ornithopter theory conclusions can be drawn about the mode of functioning concerning the energy savings.
In connection with its lift the leading bird necessarily generates a wing tip vortex at both wing tips. For it this implies a loss of energy. It is relatively big for birds with high wing loadings and short, tapered wing shapes. But the following bird can try to tap the energy content of one of both wing tip vortices to make its own flight work easier.
Well known is the hypothesis (Please look at external link 5) that the following bird uses a field of uplift of its leading bird. It is generated by the tip vortex spreading backwards at the outer edge of the flight formation. This up wind enables the following bird to increase its own thrust without performing additional flight energy. But it is more effective to use the angular momentum of the incoming vortex to reduce the wing tip vortex of its own wing (adjacent picture and external link 6).
The problem for the following bird is the optimal adjustment of all distances
in the three-dimensional space behind the leading bird. It must try to adjust
the distances to the flapping wings of its leading bird in a way that the
proper part of the leading bird's vortex passes it in a suitable moment and
at the optimal position. It can surely feel the best flight position, but
thereby it must also make compromises. Anyway, in the theory of formation
flight of birds many questions remain open. For more information, please see
the handbook, annexe E, (lock
above) and the article
Arrangements of wing tip vortices on flapping wings (version
4.0, PDF 0.5 MB).
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