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Introduction |
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Criticism of the
conventional aerodynamics |
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Criticism of conventional planes |
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Possibilities of optimal
planes |
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Introduction |
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The
classical aerodynamics is based on the Euler's equations on the
incompressible ideal liquid's movement and the Bernoulli’s law on the
connection of the pressure in a liquid with its flood's speed.
The
classical aerodynamics deal with the speed smaller than the speed of
sound. Caused by its imperfection the planes are based on forced
regimes.
The conventional aerodynamics is based on the classical one and on its
developments taking into account the air's viscosity, its
compressibility and its heating with the description of the border layer
by transition to the Navie-Stocks equations. The conventional
aerodynamics deals with the speeds equal or bigger than the speed of
sound. Caused by its imperfection the planes are based on the forced
regimes and are oriented mainly to the military purposes. As a rule the
civil aviation planes represent the old models of military planes or
imitate them with the corresponding minuses.
Attempts at the optimization of civil aviation planes have been
undertaken but in vain, since the math apparatus of aerodynamics is so
complex and aimed at the forced regimes, that with its aid it is
impossible to solve the optimization problems. It must be also taken
into account, that the prominent specialists on aerodynamics have been
brought up on forced regimes, which limit their possibilities on
optimization.
The aerodynamic tubes and computers will not help to solve this problem
either, since they can not produce independent results, i.e. they can
not produce a new quality, and may only develop the quality, which you
put into them.
As a result we have such separate and limited measures as the wing's
flaps, changeable wing's geometry, propellers with many blades, the
"Concord" (the worst of all planes) and the attempts to build new planes
on its basis.
To obtain the principally new results in aviation it is necessary to
distract from the math apparatus of aerodynamics and to penetrate into
the essence of the investigated phenomena from the general positions of
Mechanics of Continuous Media, to develop its hypotheses, to replace the
forced regime by the optimal (compromised) interaction of a rigid body
with the air from positions of the Theory of the Thin Elastic Elements
of Structures, to take into account the decreasing density of the
atmosphere along its altitude to increase the speed of a plane in
accordance with this decrement of density to keep the minimal negative
air resistance.
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Criticism of the
conventional aerodynamics |
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1.
Its limited theoretical basis.
One of
the main aerodynamics' hypothesis is the media's
continuity (N.F.Krasnov. Aerodinamika. V. 1. M. 1976. p. 8), i.e. a
possibility of continuous transition from one point of the media to
another. This hypothesis ensures the use of Mathematical Analysis and
hence of Theoretical Mechanics and of the Theory of Complex Variables.
However, in liquids and especially in gasses it is also necessary to
take into account the media's discreteness, i.e. to consider a media as
a great number of separate material points.
An artificial introduction of the imaginary unit and on its basis of the
complex variables allows to reduce the volume of math calculations and
to present the result in a more compact form. For this benefits they
have to pay by a bigger abstraction from the reality and by limited
possibilities of aerodynamics. This is expressed in the fact, that "the
conditions of differentiation in the Theory of Complex Variables turn to
be more tough or limited, than for the real variables" and "there
disappears the usual geometrical display of functions with the aid of a
curve on a plane, and instead there appears the notion about a function
as a reflection of a plane's great number (M.A.Lavrentjev i B.V.Shabat.
Metodi Teorii Functii Kompleksnogo Peremennogo. M. 1958. p. 10), i.e.
one has to disengage oneself from the physical reality.
Thus, there is being strengthened the notion of a great number of
elements and weakened the notion of orientation, i.e. there is being
strengthened the quantity side of a phenomenon and weakened the quality
one. It leads to the increment of consumption of a theory and to the
decrement of its supplement, i.e. of its development.
The artificial hypothesis of a reversed movement leads to the changes of
mechanical properties of the air, to the necessity to change its
temperature, to a limited space. That is why the aerodynamic tubes are
good for the comparatively simple problems only. These tubes can check
the air compression only from the speed of 400km/h, whereas this
compression takes place from the very beginning of the flight.
2. The "Effect of Magnus" is a phenomenon, which generates a lifting
force by the air
flood's streamlining a cylinder, that rotates in a corresponding
direction (S.E.Haikin. Fisicheskie Osnovi Mehaniki. M. 1971. p. 563).
For the math description of this phenomenon the picture of streamlining
of a rotating cylinder is presented as an interaction of the air flood
with the circulation around the immovable cylinder. With the aid of the
conform reflection this artificial picture is reflected on the outer
space of the wing's profile. As a result they get the prominent formula
of Zhukovski for the lifting force of a wing. Such a formal definition
of the lifting force reflects the real picture in the first
approximation: on account of the angle of attack the pressure under the
wing is bigger than in the flood and the pressure above the wing is
smaller than in the flood. The difference of pressures under and above
the wing defines the lifting force.
3. However, the Zhukovski formula has an irremovable contradiction,
which blocks the
development of the theory. The artificially introduced circulation
around the wing's profile is substantiated by the presence of a
whirlwind or a vortex at the rear end of the profile. They say, that the
circulation around a profile and the vortex at its rear end have to
balance each other, that is the sum of the moments of the quantity of
movement must be equal to zero (the quantity of movement is a product of
mass and speed). Hence, if there appears a vortex at the profile's rear
end, there must appear a circulation around the profile in the opposite
direction to the direction of the vortex and with the equal values of
their moments. This strained interpretation is caused by the artificial
introduction of a circulation around the wing's profile. In reality
there is no circulation around a profile and the vortex appears as a
result of the compressed air bursting from under the wing and of the
decompressed air above the wing sucking it in, thus creating a rotation
for the generation of a vortex.
As a result of the mentioned irremovable contradiction the lifting force
formula is inseparably linked with the vortex. This vortex is a negative
phenomena, but we can not get rid of it using the conventional theory,
since there will disappear the lifting force with the lifting force
formula being invalid.
The way out is to return to the real variables and to investigate the
physical picture of this phenomenon, taking into account the elastic
properties of the air and of the wing in their interaction. It allows to
get a more precise math description, confirmed by the published tests (K.P.Petrov.
Aerodinamika Letatelnikh Apparatov. M.1985. p.p. 18, 103), by
investigation of the birds' wings functioning in gliding and by the work
of the fish's tail, from positions of the author's main and adjacent
specialties. |
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Criticism of conventional
planes |
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The commercial
planes have the low level of safety, economy and speed. With the take
off and landing speed of about 250km/h it is difficult to react
adequately to the small deviations from the calculation scheme, which
may always take place. That is why a flight begins with many precautions
and under a high strain, strongly depends on weather and so on. The
other important feature of low security is unability to glide. It is
caused by the low aerodynamic quality of the wing. That is why there is
the inadequately high speed in the dense layers of the atmosphere,
causing high air resistance, forced engines and high fuel expenditure.
All these minuses are caused mainly by the rigid (unelastic) wings,
which produce too high pressure on the air and meet the corresponding
too high air resistance.
The propellers of planes and the helicopters' rotors have analogical
minuses, defined by the same cause.
The conventional jet engines have low efficiency in the dense layers of
the atmosphere, which brake the jet's free exit or movement and thus
hampers the effectiveness of the jet engine principle.
Fundamental results on the optimization of engines are obtained. The
optimal engines will combine the positive features of the piston and jet
engines. However, the optimal engines may be effective only together
with the elastic wings. |
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Possibilities of optimal
planes |
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The main
thing is to reduce sharply the negative air resistance.
It must be small in comparison with the driving force.
Considering the notion of a mall value as a complex phenomenon we'll
have choose among 0.1, 0.01, 0.001. A compromised approach shows, that
we have to take for a small value 0.01 part of the whole. Thus, it is
necessary to keep the negative air resistance equal to or less than the
0.01 part of the driving force during the whole flight.
Let us find out what will be in this case the value of the take off and
landing speed. If to take into account that the air resistance changes
in proportion to the square of speed, then the 100 times reduction of
air resistance will lead to the 10 times reduction of the take off and
landing speed. The take off and landing speed of conventional passenger
planes is equal to 250-300km/h. Then the take off and landing speed of
the optimal planes will be equal to 25-30km/h. This is the speed of good
gliders and of big birds gliding near the surface of the earth.
Now we have to define the angle of the take off. The best direction for
the use of wings is a horizontal one. The best direction to increase
speed is a vertical one, since the atmosphere's density decreases
sharply with the altitude. We have to keep the main part of the best
direction for the flight and the secondary part of the best direction to
increase the speed. It means, that the best angle for the take off is 30
degrees. It is also good for passengers and is about equal to the take
off angle of conventional planes.
Next we have to define the regime of movement. Up to the altitude of
30km the density of the atmosphere changes according to the hyperbolic
law. Then the density along the slope line of movement will be changed
according to the same law. Putting in the formula of air resistance the
air resistance equal to a constant we'll get after its integration, that
the movement will be with a constant acceleration.
To find out the value of acceleration when moving up the slope of 30
degrees to the horizon we have to take into account that to avoid the
increment of air resistance the speed must be less than the speed of
sound in the dense layers of the atmosphere, i.e. under 30km. On the
other hand, above 30km we can afford a speed bigger, than the speed of
sound. Then, at the altitude of 30 km the speed must be equal to the
speed of sound. So we'll get along the 60km long slope way with the
change of speed from zero to 330m/s=1200km/h the acceleration about 1m
per square second (this is the acceleration of a starting car).
To have the optimal movement above 30km we must take into account, that
the sharp fall of the atmosphere's density allows to reduce sharply the
angle of movement. There also takes place a significant fall of the
gravity force thanks to the centrifugal force, which turns to be
considerable at high speeds of movement. The optimal acceleration will
be equal to 2m per square second as a compromise between 1m, 2m, 3m per
square second. (It is quite bearable for people).
After reaching the middle of the way there may begin gliding down with
the vise versa regime of movement on account of special braking by the
new propellers of special structure with elastic and turning blades.
This operation will allow to restore the main part of energy spent on
the way up. It will be possible also to glide down without braking to a
bigger distance, but there will be no restoration of energy and the
movement down will be much longer. The optimal planes will have the
highest ability to glide, about the aerodynamic quality of the best
gliders, i.e. about 50.
The approximate calculations show, that the
optimal planes will be covering 1,000 km in 35 min and 10,000 km in 90
min, going up half of the way and gliding down the other half with the
special braking.
The optimal planes will be the most effective
transport, since they may have the most streamlined form, since the
resistance against the air is smaller of that against the water and the
earth and the resistance against the air is practically equal to zero
above 30km, since in the air there are more possibilities for
maneuvering, since it will be possible to fly in any weather, to take
off from any place and to land at any place. |
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