Gait change of ornithopters
- 1. Basic Gaits
- 2. Start with transition to flying with lift
- 3. Transition to flying with thrust
- 4. Conclusion
- 5. Related Links
The differences between the distinguished gaits are especially in the sign of the normal force during the wing upstroke. Between these basic flight principles for flapping wings, there are various intermediate stages or mixtures. Based on the results of bird flight research, an attempt is made here to describe the attendant circumstances when using the gaits.
Large birds especially use the Continuous-vortex gait (
with lift). In this case the normal force changes its sign in
the outer wing area during upstroke. The bird then flies partly in the Ladder-vortex
Flying with thrust).
A change in the gait of an ornithopter - for example, between hover flight and cruise flight- is about comparable to the transition between the flight of a helicopter and that of a motor glider. Only tiltrotor aircrafts (e.g tiltrotor V-22 Osprey) can approximately cope with this task.
Even Erich von Holst has detected in the analysis of his systematic measurements that during flapping flight the conditions to promote the lift have adverse effects to the thrust and vice versa.
In the following specification, a medium aircraft configuration is assumed. But in flapping flight everything interdepends. Therefore, the size specifications of the described parameters are always relative and similar solutions in the close-up range are absolutely possible.
2. Start with transition to flying with lift
When flying purely with thrust, the weight force of the aircraft will only be balanced by the upward directed thrust force. Let's assume the aircraft has already taken off from the ground and the stroke plane of the wing has approximated the perpendicular of the flight path line to less than 60°. Flapping frequency and wing twisting are still very high. A horizontal movement of the aircraft has started. But first, it is still balanced like a helicopter on its slipstream (blast of air).
Forces short-time after take-off from the ground
A flapping wing generates, particularly during strong thrust generation, the oncoming flow to its stroke plane partly by itself. This works like the oncoming flow to the rotation plane of a propeller at the start of an airplane.
Size and direction of the resulting total inflow in the several flight situations resulted from the flying speed and the slipstream generated by the flapping wing itself. Both speeds are set for the respective gait (estimated). The direction of the drag vector is assumed here in the direction of the total inflow. Its magnitude is determined (total drag of wing and fuselage) in relation to the weight force. Together with the inclination of the wing stroke plane, all other forces arise (see adjacent vector diagram).
Together with the horizontal flying movement, the possibility to replace parts of the thrust by a lift perpendicular to it is now offered to an ornithopter - in contrast to the helicopter. Particularly the wing area close to the fuselage with its' small normal force inclination is suited for this. Therefore, the upward thrust generation can be discharged and can be directed more forward by a further turning of the stroke plane. This in turn will lead to an increase of the flight velocity, from which lift and thrust generation can benefit at the same time.
If the aircraft is streamlined shaped the moment comes when the directly generated lift is sufficient to carry the aircraft alone. The whole thrust can then be directed straight forward and can substantially be decreased together with the wing twisting. The aircraft is now flying completely with the lift which is very energy-saving.
Total forces when flying with lift in cruising flight.
Here the lift is about tenfold the strength of the thrust.
With this flapping wing design the gliding qualities are good.
But in practice, the transition to flying with lift is not as easy as it appears at first. At first, lift and thrust must have achieved relatively high values at the same time in spite of a small flight velocity. However, changing the way of flying is possible for birds with the aid of reserves of lift coefficient at the corresponding problem areas of the flapping wing.
Reserves of lift coefficient can primarily be obtained by dint of great wing depth and by spreading of feathers (extension of area). Also fore flaps, slots in the wing and flaps are very effective. Changeable and strong chambered airfoils which have a well-rounded leading edge heighten and increase the operating range of the airfoil. And with wing sweeps the lift can be displaced from stall periled ranges.
During cruising flight reserves can be used for variation of thrust (climb flight), aircraft payload and flight velocity. In fast cruising flight they are more of a hindrance. Normally, they increase the drag. When changing the ways of flying all reserves are fully utilised.
2.1 When generating lift mainly in the wing area close to the fuselage
When flying with thrust during up- and downstroke, the normal forces in the outboard wing area are intensely directed forward due to the high flapping frequency. Therefore, this wing section can hardly contribute anything to the total lift. But if the aircraft is able to generate the whole lift almost solely in the area close to the fuselage by means of large wing depth and large camber of airfoil, the approach to flying with lift takes place without attracting relatively any attention.
But for the last complete forward thrust alignment the need for thrust becomes clearly smaller again (please look at chapter 3.). Then the change in the ways of flying becomes visible in a sudden reduction of flapping frequency, wing twisting and drive power.
Also during the subsequent flying with lift the lift during up- and downstroke is generated to an extremely high degree in the area close to the fuselage in this case (duck, pigeon). The wing twisting is decreased, so that in the upstroke the normal force in the hand area points downward. This is beneficial for thrust generation but not for lift (please look at the principle/vector diagram). The flapping frequency remains relatively high. Thereby the normal force in the hand wing area is extensively directed forward and particularly effects thrust. Moreover, the normal force in the outer wing area is generally not that major due to the pointed shape. Therefore, during a whole flapping cycle the total lift in the hand area is marginal.
Because of the smaller normal force in the area of the wingtip, the flapping frequency for a sufficient thrust generation needs to be higher than in the option described in the following chapter, but not necessarily the drive power.
Here the total forces with an extensive task sharing of arm and hand wing and flying with lift. Thereby, the arm wing particularly generates lift and the hand wing particularly thrust.
Among small birds this way of flying should be widely-used. But what the
small birds in this connexion are is not specified.
The gliding angle is only so-so with this wing design.
With such a lift arrangement, the average torque at the stroke axis is relatively small in relation to the wing span and the wing shape is pointed. Indeed, the distribution of the normal forces along the wingspan resembles the principle/diagram 4, however with a significantly stronger shifting of the upstroke lift to the wing root. For maintaining the average lift an increase of the angle of attack at the wing root is necessary in this case - either only in the upstroke or during powered flight overall. The latter is easy affected by a marginal erection of the whole aircraft. But the reserves of the operating range of the lift coefficient at the wing root must be dimensioned big enough.
With its large wing chord and chamber of airfoil at the wing root, the big angle of attack of the fuselage and with a wing twisting being too small, surely the EV1 flew this way.
2.2 When generating lift along the whole wing span
If the directly generated lift to carry the aircraft is only sufficient in case the whole wing is available for its generation, it must only perform a relatively slow flapping motion for flying with lift. But then the thrust is not sufficient to increase the horizontal velocity when launching.
To take this hurdle, at first, one must try to achieve a high horizontal velocity with a lot of thrust. With strong wing twisting and intense wing beating, an increase of the flight velocity is possibly. A bit of lift can surely be thereby generated (please look at Fig. 2, take-off).
If then an adequate flight velocity is close at hand, the wings must practically
change abruptly to a low flapping frequency and a small wing twisting. Now they
generate in fact the full lift but significantly less thrust (please look at Fig. 3, cruising flight). But this must now be
only sufficient for flying
with lift. This transition is also visible to the naked eye in the flight image
or motion sequence (Fig. 5). In birds one speaks at this point of a
Scheme of the wing path line of a bird leaking out with marked upstroke forces and a gait change for flying with lift, by Konrad Lorenz (1933, 1965). But the term
gait change first was introduced by Jeremy Rayner (1986, please
look at related link 1.).
With big lift coefficient reserves along the whole wing and a good glide angle, flying with lift succeeds almost instantly after a hearty jump from a standing position - primarily with headwind.
During the subsequent flight with lift the downstroke torque at the flapping axis is relatively big due to the lift generation also in the outboard wing sections (stork, buzzard). At the same time, no high flapping frequency is needed for thrust generation due to the high normal force in the outboard wing area. Therefore, the drive power does not need to be bigger than for the way of flying described in the previous chapter.
For this lift arrangement with limited wingspan, the average torque at the stroke axis will normally be high in relation to the wing span and the wing contour will be almost rectangular shaped (please look at principle/diagram 1 and models EV4 to EV8).
Only for very large aspect ratio (gull), lift distributions with unlimited wingspan with a relatively small torque in relation to the wing span and the pointed wing contour are applied (please look at principle/diagram 2).
But also in this case, due to the large wing length the lift and thereby the thrust generation can be activated in the outboard areas, too. Thereby, the absolute value of the torque is high and a high flapping frequency is not necessary.
2.3 With low Reynolds number
If the total weight of the aircraft is very low it is inevitably flown with an accordingly low Reynolds number. The aircraft drag then has about the same dimension as the weight force. A gliding flight with a useable glide angle can hardly be achieved with this configuration (e.g. sparrow).
Under these conditions lift generation becomes a secondary task. But obviously the possibility exists that the wing downstroke alone is sufficient for lift and thrust generation. For this, small birds use very different wing shapes during up- and downstroke. For example, some of them almost fold up their wings during the upstroke completely (for the corresponding vortex image, please look at Ring-vortex gait). With all these applied sophistications it helps in many ways but technically they are likely hard to copy.
Flying with low Reynolds number (with low flight speed and small dimensions and therefore with a relatively large drag and power requirement). In this configuration angle of glide is bad.
Probably, this is mostly also
the way of flying of ornithopters with membrane flapping wings. Not only
because of low Reynolds number their drag is relatively high and their
payload small. In contrast, the thrust forces of membrane flapping wings
are relatively big.
If the lift during upstroke und downstroke changed its leading sign along the whole span, the vortex image of the flapping wings looks like that of an insect (please look at Ladder-vortex gait).
If required, thrust can also be generated in the upstroke, for example till
initiation of negative lift (zero lift). With a small ratio of forward
peripheral speed, a relatively high flapping frequency or an accordingly
strong wing twisting turning this appears to be possible. Furthermore,
very big stroke angles can be used because of secondary lift generation.
But the total of the directly generated lift becomes too small when
strongly increasing the upstroke thrust and that leads to a forward
flight only with thrust. Thereby the air is being
like a fish the water with a thrust only slightly inclined upward
(For example butterfly). But one can presume that even the large flying
models by Erich von Holst - with wing
spans up to 2.45 meters [96 in] anyhow - were flying according to this
method due to their low Reynolds number.
If flying with lift is possible with a low Reynolds number at all, it
still remains a flying with a high demand for thrust. One could call this
flying against drag. But depending on the level of energy-saving
a change in the way of flying may be hardly recognisable in the flight scene.
But flapping flight calculations or clear statements for low Reynolds
numbers do not exist.
Flying with a low Reynolds number and with high drag, even though it is widespread in nature and ornithopter modelling, can be regarded as a sparsely described special case. Thereby, flying with lift is rather the exception (swallow, swift). In general, the aircraft should have a good glide angle for the latter way of flying R. Demoll).
The constructive transition to a configuration for flying with lift generation mainly at the area close to the fuselage (chapter 2.1) is flowing - but not the transition to the way of flying pictured there.
2.4 Without lift coefficient reserve
If no lift coefficient reserves are available - particularly when flying
with a large Reynolds number - a simultaneous lift generation at the wing
and therefore a change in the way of flying is hardly possible when flying
with thrust. It is then better to start directly to fly with lift. But in
this case, starting only succeeds with a strong headwind, a long runway (swan,
albatross) or from a heightened position. The ornithopter models
EV4 to EV8 are examples for this.
3. Transition to flying with thrust
Also the reversed transition to flying with thrust is not quite easy. As the following considerations show, the way of flying must probably be always changed to a wide degree.
In slow flight lift decreases with the square of flight velocity. To substitute only 10 % of the supporting force in cruising flight by thrust, it must be more than quadrupled here (please compare Fig. 3, cruising flight and the following Fig. 7). Despite reserves of lift coefficient the pictured balance of forces may therefore hardly be possible.
Slow flight with necessary generation of lift along the whole wing. It is very unlikely that lift and thrust can thereby grow that much simultaneously.
First of all, all reserves of lift coefficient are mobilized in slow flight. Furthermore, the flapping frequency is clearly increased. Therefore, at the outer parts of the wing area the normal force and the thrust are strongly increased at least.
But by increasing the velocity of the wing beat the normal force especially at the outer parts of the wing area inclines further in the direction of thrust. This works only at the account of lift generation. Furthermore the lift gets smaller at the area of the wing root due to decreasing oncoming flow. Therefore, the total lift is unsustainable in the pictured size (compare forces - particularly the size of thrust with Fig. 3, cruising flight).
Furthermore, for the new thrust direction the stroke plane must be turned off the perpendicular. In connection with the erection of the fuselage, the parasitic drag of the aircraft increases which boosts the demand for thrust as a result. One part of the increased thrust is already necessary for this.
The pictured balance of forces is unsustainable especially because of insufficient generation of lift. Therefore, flight situation must be skipped. It is simply impossible to generate a large amount of lift and thrust at the same time due to the limited airfoil data.
- Figure 8
Gait change between the ways of flying
Thereby the flight situation in the center will be skipped.
Due to all of these effects, the transition to flying with thrust takes place abruptly or in stages. Then the propulsive force must equalise the weight almost by itself (like for example in the right figure). This abrupt transition was also discovered at the tip vortex of birds by Jeremy Rayner (England, please look at Nachtigall W. 1986, BIONA-report 5) and Tyson Hedrick (USA 2002, please look at related link 1.).
In flapping flight very diverse combinations of forces are applicable. But the aircraft must comply with the respective requirements. That one and the same aircraft handles all combinations of forces is not known, not even of birds with their very variable wings.
Since the wings of ornithopters are only a little modifiable in flight so far one should determine the way of flying before fabrication. A gait change of ornithopters is still rather the exemption.