The fossils of pterosaurs clearly indicate that these creatures had a pair of wings - each of which was, in expanded form, a leathery membrane stretched between the skeletal "whip" of the leading edge of the wing and the body. Judging by the abundance of these fossils, pterosaurs were not a mistake of Nature: they used their wings for their intended purpose, and they knew how not only to plan, but also mastered the technique of flight with active thrust.
It would seem that pterosaurs could create active thrust on the same principle as used by bats and birds. Namely: during the flapping movements of their wings, jet thrust arises due to the air being thrown back by the flexible rear sections of the wings, which passively bend upward when the wings flap down, and vice versa. However, there is a weight limit on the creature using this flapping flight. To hold more and more weight in the air, it takes - at the same flight speed - an ever larger wing area, and with an increase in this area, resistance forces to flapping movements increase, to overcome which more and more powerful muscles are required, i.e., again, everything more weight … It turns out a vicious circle. Today, the largest flying birds are condors, reaching a weight of only 15 kg (while they drag rams 40 kg each). But pterosaurs significantly outnumbered the condors in wing size and weight! “The flying lizards belonged … giants - for example, the pteranodon found in 1975 during excavations in the Big Bend National Park in Texas (USA): its wingspan reached 15.5 m. This is one of the most amazing creatures that ever lived on Earth. Its wings are four times (or more) longer than those of the albatross, condor, and other modern aviator animals. Under such wings was, like a small motor, suspended in comparison with their torso. Some scientists believe that the pteranodon could not even flap its wings! "5 m. This is one of the most amazing creatures that have ever lived on Earth. Its wings are four times (or more) longer than those of the albatross, condor, and other modern aviator animals. Under such wings was, like a small motor, suspended in comparison with their torso. Some scientists believe that the pteranodon could not even flap its wings! "5 m. This is one of the most amazing creatures that have ever lived on Earth. Its wings are four times (or more) longer than those of the albatross, condor, and other modern aviator animals. Under such wings was, like a small motor, suspended in comparison with their torso. Some scientists believe that the pteranodon could not even flap its wings!"
Indeed, the pteranodon was physically unable to flap its wings like a bird. After all, he had no analogues of either the bird's pectoral muscles, or the bird's keel bone, to which the tendons of these muscles are attached. That is, he simply had nothing to flap his wings like a bird. But could he not have set the wings in motion in a different way?
The researcher of pterosaurs K. Gumerov draws attention to the disproportion in their anatomy: a rather powerful neck and a large head. If a pterosaur stretched its neck forward - as is done in flight, for example, geese - then its centering would be far ahead of the first third of its wing, so the pterosaur would fall into a dive. To ensure the centering of horizontal flight, the pterosaur would have to bend its neck back-up in a swan-like manner so that its head would be approximately above the first third of its wing. K. Gumerov believes that the flapping of the wings was made due to the pendulum movements of a heavy head on a mighty neck. But how did the above-mentioned vicious circle break?
However, we see a theoretical possibility of some gain in the work of flapping wings during horizontal flight, if they were set in motion through the vibrations of a heavy head by the muscles of the bent neck. If the masses are comparable, firstly, the head plus the neck, and, secondly, the body plus the wings, the neck muscles would “chatter” not only the head, but also the body: when, in relation to the center of mass, the head would move upward, the body would move down and vice versa. Thus, the bases of the wings would be imparted an oscillatory movement up and down - which would be the source of their movements, i.e. the method of "excitation of oscillations of the plate through the bump of the fixed end" would work. At the same time, the movements of the wing would not be, in the strict sense, swings, because here the base and the end of the wing would move in antiphase - and, therefore,somewhere in the middle of the wing length there would be a nodal line with zero vibration amplitude.
Such a mode of oscillation of the wings of a pterosaur - with the presence of a nodal line - would allow, in our opinion, somewhat larger wing sizes and flight weight than those of birds. Indeed, the force of resistance to the flapping motion is directly proportional to the wing area and the square of the flapping speed. In the wing of a bird, zero vibration amplitude falls on the connection of the wing to the body, while in the wing of a pterosaur it would fall on the middle of the wing. Therefore, with the same angular span and frequency of wing movements, the average swing speed of a pterosaur's wing would be half that of a bird's wing of the same length. Then, with the same coefficients of dynamic resistance to flaps and the same ratios of wing length to width, the wing of a pterosaur would experience the same resistance to flaps as a bird's wing, being 4 1/4 longer than it.»1.41 times (just something!) In this case, the areas of the wings of a pterosaur and a bird would be treated as squares of their lengths, i.e. a pterosaur's wing would be twice as large. Accordingly, with the same flight speed and the same aerodynamic drag coefficients, the wings of a pterosaur would have twice the lifting force, which would allow it to hold twice as much weight in the air. But, even with these idealized assumptions, the problem of pterosaur flight is obviously far from being solved. In addition, as can be seen in the reproduction of a pterodactyl fossil - Fig. 1, from a publicly available web resource - for a head bump on a backward neck, this neck is too short - given the long length of the cervical vertebrae.
Fig. 1.
So, pterodactyls could not flap their wings either like a bird, or through the swing of the body due to recoil when head banging. What could they do? Did they really possess the technique of active flight, in which they did not flap their wings? Analysis of Fig. 1 allows you to answer this question in the affirmative!
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We looked at a number of reproductions of pterosaur fossils - the above one is the best of them in the sense that there is practically no damage or displacement of bones relative to each other. Therefore, we proceeded from the assumption that this fossil reproduces the anatomically normal position of the skeletal bones in a pterodactyl with folded wings. Here, as in other photographs, one "oddity" is striking, namely, the presence of an "extra" joint in the wing. Indeed, after the single humerus, there is a two-boned forearm, and then … another two-boned segment of almost the same length as the forearm. Moreover, the humerus itself is so unnaturally short and brought into such a position in the shoulder joint that the conclusion suggests itself: it did not go beyond the body, and, therefore, the front part of the wing membrane was attached,starting from the forearm. It was this anatomy that made it possible, in our opinion, to implement a method of creating thrust with outstretched webbed wings, striking in its simplicity and efficiency.
Indeed, let us pay attention to a pair of clavicles connected in the form of the letter V. With the horizontal position of the body, this pair of clavicles departed from the shoulder joints backwards and downwards, and the humerus bones - backwards and upwards. Now imagine that a pterodactyl had muscles between the humerus and their corresponding collarbones. The contraction of these muscles pulled the humerus and collarbone together. At the same time, the clavicles rested against the chest, and, therefore, the humerus bones turned somewhat in their joints so that their ulnar ends dropped down. Thus, contraction of the clavicle-brachial muscles pulled down the root portions of the front edges of the outstretched wings; when these muscles were relaxed, a passive return to the initial position of the humerus and, accordingly, of the leading edges of the wings occurred. There can hardly be any doubtthat the periodic contraction of the clavicle-brachial muscles caused the leading edges of the wings to oscillate - which generated a wave in the membrane traveling to the trailing edge. This wave carried with it a certain amount of air and threw it back - which generated jet thrust.
The following difference in the structure of its wings and the wings of a bat also testifies in favor of just such a flight propulsor of a pterodactyl. The membranous wings of a bat have skeletal stiffening ribs formed by highly elongated finger bones. It is clear that such ribs of rigidity impede the travel of a traveling wave in the membrane - and bats brush the air away like a bird. In a wing devoid of such stiffening ribs, the conditions for the travel of a traveling wave are ideal - with the required webbing tension.
Figure: 2.
By the way, it would be very problematic to provide the necessary tension of the membrane if, in the flight position of the wing, the bones of its leading edge would be stretched almost along a string - as is usually assumed. Based on Figure 1, we are presented with the flight configuration of the skeleton, schematically depicted in Figure 2. Wings were needed for pterodactyls not in order to amaze them with the scope of modern explorers, but in order to fly. And just the arched leading edges of the wings brought forward made it possible, in our opinion, to solve several technical problems at once. First, it was easy to provide, over the entire wing area, the required webbing tension - with the ability to adjust it. Second, a ratio between the length and width of the wing was created, close to the optimal one for generating a traveling wave. Third, the alignment problem was elegantly solved:It was enough for a pterodactyl to raise its neck and move its head back a little, and the projection of the center of mass would be on the first third of the wing. We are dealing with an ingenious technical solution again!
Now let's make some elementary estimates of the parameters of the traveling wave wings. Let the ratio of the characteristic wing length l to its characteristic width d be 2.5, let the wing area be S = 0.8 × ld. The oscillation frequency f of the leading edge of the pterodactyl's wings could not exceed several hertz. Let one traveling wave length fit on the characteristic wing width d, then its velocity v of movement along the membrane is v = fd. The static jet thrust developed by a traveling wave wing at rest relative to the air medium is F stat = mv / t, where m is the air mass thrown back in time t, equal to d / v. Considering the so-called. the added mass of the discharged air, we will assume that m "r S (d / 5), where r is the air density, and thus F stat " (1/5) r Sv 2… As we will see below, this static thrust is too low, and flying on it is unrealistic. However, the dynamic thrust F dyn of the wing of a traveling wave does not decrease at all as its speed in the air grows - as in propeller driven vehicles - but, on the contrary, initially increases. This is due to the fact that the incoming air forms ordered vortex tubes in the concavities of the membrane, as shown schematically in Fig. 3.
Figure: 3.
Contrary to the notions of classical aerodynamics - which claims that the formation of vortices, for example, when the flow is detached from the wing, is a harmful effect, since the aerodynamic drag increases and the lift force decreases - the formation of vortex tubes in the concavities of the wing of a traveling wave is a useful effect. An air vortex has a much greater inertness and elasticity than the same mass of non-swirling air, and therefore "repulsion" from vortices is much more effective. At low speeds of a traveling wave wing, the following occurs: the higher the speed, the more powerful vortices are formed, and, accordingly, the greater the dynamic thrust. But, when the flight speed and the traveling wave speed v are equal, the dynamic thrust is obviously equal to zero. Therefore, there is some optimal (cruising) flight speed,at which the dynamic thrust is maximum. We will assume that the cruising speed is Vcr = 0.75v, and that at the cruising speed Fdin = 3Fstat. To estimate the flight weight that the wings of a traveling wave are capable of carrying, we also need an estimate of the relative decrease in free gliding. Indeed, with free planning, the weight of the aircraft is balanced by the lifting force, and the aerodynamic resistance is balanced by the traction force, which is performed by the force of gravity when the aircraft is lowering. For this work of gravity, a simplified expression MgDh = MVDV can be written, where M is the mass of the vehicle, g is the acceleration of gravity, h is the flight altitude, and V is the flight speed. Then the traction force due to the force of gravity with free planning isand that at cruising speed Fdin = 3Fstat. To estimate the flight weight that the wings of a traveling wave are capable of carrying, we also need an estimate of the relative decrease in free gliding. Indeed, with free planning, the weight of the apparatus is balanced by the lifting force, and the aerodynamic resistance is balanced by the traction force, which is performed by the force of gravity when the apparatus is lowering. For this work of gravity, a simplified expression MgDh = MVDV can be written, where M is the mass of the vehicle, g is the acceleration of gravity, h is the flight altitude, and V is the flight speed. Then the traction force due to the force of gravity with free planning isand that at cruising speed Fdin = 3Fstat. To estimate the flight weight that the wings of a traveling wave are capable of carrying, we also need an estimate of the relative decrease in free gliding. Indeed, with free planning, the weight of the apparatus is balanced by the lifting force, and the aerodynamic resistance is balanced by the traction force, which is performed by the force of gravity when the apparatus is lowering. For this work of gravity, a simplified expression MgDh = MVDV can be written, where M is the mass of the vehicle, g is the acceleration of gravity, h is the flight altitude, and V is the flight speed. Then the traction force due to the force of gravity with free planning iswith free planning, the weight of the apparatus is balanced by the lifting force, and the aerodynamic resistance is balanced by the traction force, which is performed by the force of gravity when the apparatus is lowered. For this work of gravity, a simplified expression MgDh = MVDV can be written, where M is the mass of the vehicle, g is the acceleration of gravity, h is the flight altitude, and V is the flight speed. Then the traction force due to the force of gravity with free planning iswith free planning, the weight of the apparatus is balanced by the lifting force, and the aerodynamic resistance is balanced by the traction force, which is performed by the force of gravity when the apparatus is lowered. For this work of gravity, a simplified expression MgDh = MVDV can be written, where M is the mass of the vehicle, g is the acceleration of gravity, h is the flight altitude, V is the flight speed. Then the traction force due to the force of gravity with free planning is
where V vert is the rate of descent; at V vert << V the ratio (V / V vert) is approximately equal to the value of the aerodynamic quality. Let's make estimates for the case of a relative descent of 1:10 with free gliding at cruising speed. At the same time, as follows from the above, the dynamic thrust F din would provide a horizontal flight (without lowering!) Of a pterodactyl with a weight of 10 F din; flight with a climb of 1:10 would be provided for a weight of 9 F din… The resulting estimates are given in the table; the wing dimensions were taken as the initial parameter. As you can see, starting from a wing length of 2.5 m, the ratio between wing size and weight becomes realistic for an active flight of a creature on the wings of a traveling wave.
| Wing length, m | Full wing area, m 2 | Oscillation frequency, Hz | Traveling wave speed, m / s | Cruising flight speed, m / s | Dynamic thrust, kg | Weight, for climb 1:10, kg |
| 2.0 | 2.56 | 2.4 | 1.92 | 1.44 | 0.75 | 6.75 |
| 2.5 | 4.00 | 2.3 | 2.30 | 1.73 | 1.68 | 15.1 |
| 3.0 | 5.76 | 2.2 | 2.64 | 1.98 | 3.21 | 28.9 |
| 3.5 | 7.84 | 2.1 | 2.94 | 2.21 | 5.40 | 48.6 |
| 4.0 | 10.24 | 2.0 | 3.20 | 2.40 | 8.34 | 75.1 |
The obtained figures, it would seem, do not correspond to the technical parameters of ultralight aircraft. Indeed, in the case of dead wings of hang gliders and paragliders, with the same flight weights and the same wing areas, flight speeds are required that are a couple of times higher than those obtained by us. But remember that the wings of a traveling wave work in an orderly swirling air - not only pushing away from it, but also leaning on it. Therefore, the lifting force of the traveling wave wings is correspondingly higher. If this increase in lift is described by a factor equal to three - like the increase in dynamic thrust, see above - then our estimates would be quite reasonable … if not for one more circumstance.
Let's remember: the condor, with its own weight of 15 kg, is capable of carrying an additional load of 40 kg in the air. In principle, a condor could fly with its own weight of 50 kg. But such a flight would require the utmost exertion of forces. A creature that would constantly have to strain would obviously be out of its element. It is not for nothing that the condor, as we can see, has an almost threefold "margin of safety"! So: our estimates are obtained for the technical limiting flight conditions. These modes, theoretically, are possible - but, in practice, pterodactyls needed a "trick" that would allow them to fly not at the limit of their capabilities.
We saw such a "trick" after we noticed that the pterodactyls had neither rudder, nor elevators, nor ailerons! How did they manage their flight? To make a turn, the pterodactyl could release the tension on the membrane on the wing on the side to which it was required to turn. This move would reduce the wing's thrust and lift. The asymmetry of the wing thrust would cause a turn, and to compensate for the asymmetry of the lifting forces of the wings, the pterodactyl could flip its head in the direction opposite to the turn. As for the elevator, at low speeds it would still be ineffective, therefore, pitch control, in our opinion, could be provided only in a small range of deviations of the flight vector from the horizontal plane - centering shifts through head displacements backward or forward. As you can seethe opportunities for aerobatics in the pterodactyl were more than modest. If a gust of wind tilted the pterodactyl that gained altitude, then it would no longer be able to return to its horizontal flight!
The question arises: why did the pterodactyls need to gain altitude, if it was mortally dangerous for them? Flight at ultra-low altitude is justified only in huge open spaces with a flat horizontal surface. The conclusion suggests itself: pterodactyls were adapted to flight at extremely low altitude above the sea surface! And then the "focus" that facilitated such a flight was probably the ground effect, due to the use of which ekranoplanes fly - the optimal flight height in this case is about half of the characteristic wing width. That is why pterodactyls did not need ailerons: the thickening of air between the wings and the water surface automatically worked out the roll disturbances, including when turning (see above). Apparently, pterodactyls hunted fish and other inhabitants of the sea,grabbing the victim from the approach with its toothy beaks - “diving” into the water from a meter height was, technically, completely safe. And taking off from the water - at a speed of 2-3 meters per second - should not have been a problem. A pterodactyl could pick up such a takeoff speed by launching a running wave, with a reduced amplitude, along its wings outstretched on the water - while pushing off not from the air, but from the water (compare: a six-meter swordfish, sending a running wave through its body, moves in water at a speed of up to 120 km / h). As a result, a marvelous picture of the creeping flight of a pterodactyl is emerging - ultra-low and ultra-slow, on the wings of a traveling wave, the efficiency of which is increased due to the screen effect. Such a flight, from a technical point of view, is a rare masterpiece!And taking off from the water - at a speed of 2-3 meters per second - should not have been a problem. A pterodactyl could pick up such a takeoff speed by launching a running wave, with a reduced amplitude, along its wings outstretched on the water - while pushing off not from the air, but from the water (compare: a six-meter swordfish, sending a running wave through its body, moves in water at a speed of up to 120 km / h). As a result, a marvelous picture of the creeping flight of a pterodactyl is emerging - ultra-low and ultra-slow, on the wings of a traveling wave, the efficiency of which is increased due to the screen effect. Such a flight, from a technical point of view, is a rare masterpiece!And taking off from the water - at a speed of 2-3 meters per second - should not have been a problem. A pterodactyl could pick up such a takeoff speed by launching a running wave, with a reduced amplitude, along its wings outstretched on the water - while pushing off not from the air, but from the water (compare: a six-meter swordfish, sending a running wave through its body, moves in water at a speed of up to 120 km / h). As a result, a marvelous picture of the creeping flight of a pterodactyl is emerging - ultra-low and ultra-slow, on the wings of a traveling wave, the efficiency of which is increased due to the screen effect. Such a flight, from a technical point of view, is a rare masterpiece!on the wings outstretched on the water - while pushing off not from the air, but from the water (compare: a six-meter swordfish, sending a running wave through its body, moves in the water at a speed of up to 120 km / h). As a result, a marvelous picture of the creeping flight of a pterodactyl is emerging - ultra-low and ultra-slow, on the wings of a traveling wave, the efficiency of which is increased due to the screen effect. Such a flight, from a technical point of view, is a rare masterpiece!on the wings outstretched on the water - while pushing off not from the air, but from the water (compare: a six-meter swordfish, sending a running wave through its body, moves in the water at a speed of up to 120 km / h). As a result, a marvelous picture of the creeping flight of a pterodactyl is emerging - ultra-low and ultra-slow, on the wings of a traveling wave, the efficiency of which is increased due to the screen effect. Such a flight, from a technical point of view, is a rare masterpiece!Such a flight, from a technical point of view, is a rare masterpiece!Such a flight, from a technical point of view, is a rare masterpiece!
And, despite the very narrow flight specialization of the pterodactyl, there is an undeniable advantage: in comparison with bird wings, the wings of a traveling wave are able to hold much more weight in the air, and even with a much smaller ratio of the mass of flight muscles to the total body weight. Let us express the hope that it will be possible to create an aircraft in which flight will be based on the principles described above - and which will be able to carry a significant payload.
The author is very grateful to K. Gumerov for setting the problem, for the addresses of information resources, and for a useful discussion.
Author: A. A. Grishaev, independent researcher