Wave drive flying saucer

MasterOgon

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It was found that the asymmetric vibrations of the object in homogeneous - liquid and gaseous media lead to the formation of a wave medium in which two oppositely directed waves of different forces, made alternately, exist simultaneously by inertia and create a pressure difference leading to uneven the release of thermal energy from the environment in the form of a vortex, pushing the object. Such an experiment is easy to repeat at home. It is necessary to lower the palm into the water and make a quick movement in one direction and slow in the other. During the reverse movement, the resistance of the water will be greater due to the energy released from the water. A series of experiments was performed in which a vibromotor that simulates the vibrations of an atom during movement was set on a float, discoid and sickle-shaped wing. Fluctuations with the help of an engine set the float in motion, and the lift of the wing in the oncoming flow increased significantly due to the formation of acoustic waves. In the near future, this principle can be used to create reusable spacecraft having high maneuverability when entering the atmosphere and capable of making a controlled landing anywhere in the world through the use of an electric motor. Video experiments

Flying saucer is a reusable air / underwater / spacecraft. The motor used on it is a movable discoid sail, driven by high-frequency electromagnetic inertial propulsion drive. With the help of the wing, the inertial propulsion drive perceives the resistance of the environment and the apparatus comes in forward motion. Thus, the flying saucer uses the principle of movement of birds, fish and other species of creatures moving in a homogeneous environment. This principle is possible in virtually any environment capable of providing resistance in which waves can be created and reflected. This allows you to effectively use the resistance of the environment due to its inertness.
For example, an airplane for the most part simply overcomes air resistance, leaving behind it an air whirlwind that lasts some time by inertia. The vortex contains energy that is not used at all. A bird creating a whirlwind with a wing wave receives back some of the energy spent on it in the form of wind, which pushes it. Thus, the bird is more efficient than the aircraft. But it is technically difficult to create a powerful and fast apparatus in the form of a bird or fish. Such designs have a large number of moving parts that do not withstand the load on friction and vibration, if you install a powerful engine on them. Unlike the ornithopter wing, the wing of the flying saucer will be able to vibrate with high frequency and low amplitude, like the membrane of an acoustic speaker. This can be achieved through the use in the design of the electromagnetic drive of the wing. The suspension of the wing on a magnetic cushion will allow you to realize greater power and frequency of oscillation with a low mechanical load.
The work of the wing in the air or water can be described as follows. The wing makes a fast ascending impulse, as a result of which a shock wave is formed above it, and the flying saucer begins to be drawn into the region of reduced pressure formed behind it. An annular vortex is formed under the wing, which follows it by inertia. Then the wing begins to make a reverse movement downward at low speed, and the flying saucer pushes off from the whirlwind, which catches up with it, carrying it upwards.

2.JPG


In space, a flying saucer can receive acceleration with the help of a wing in the form of a photon mirror and sail. The presence of an electron gun on board will allow the use of the wing and as a mirror of an electric sailing antenna. But unlike conventional ships that use the power of the solar wind to move in space, you can speed up flying not only by determining the pressure of the particles, but also by pushing them away.
Inertial propulsion drive works much more efficiently when there is constant resistance on one side and there is no resistance in the direction of motion. Despite the fact that the solar wind has a very low density, and in it the work of the wing will not be as effective as air or water, the pressure on it of light from only one side will allow the inertia to repel in the direction of the wind and at an angle. Thanks to this, the flying saucer will be able to accelerate and maneuver more effectively than ordinary space sailing ships. It is assumed that it is possible to generate electromagnetic waves in the direction of motion and to perceive their pressure using a sail, which corresponds to the model of motion of the apparatus in a liquid and gaseous medium.

The theory of motion of a flying saucer in a liquid and gaseous medium.

Imagine that the atoms or molecules of a liquid or gas that are as close as possible to each other as a result of compression. The only possible position in which they can be equidistant is triangles, which are combined into hexagons. This corresponds to the crystal structure of water.



3.jpg


Atom 1 gets a boost. Suppose that atoms move along the path of least resistance, as the arrows indicate. If these are billiard balls, then each time the impulse 1 will be divided by 3 and will lose power. But if these are atoms or molecules that oscillate, then each time during a collision, the pulse energy will increase, because the vibrating object itself creates a repulsion impulse.
Due to the repulsion of atoms, a chain reaction will occur, which will first lead to the formation of multiple vortices, the prerequisites for which are in the figure, turning into large vortices. The plate converts the force of the vortex into motion. Thus, the driving force of the saucer is air resistance.
Therefore, the energy that drives the flying saucer is taken from the environment .

Birdplane. Antigravity aircraft

Birdplane is an aircraft, which is a simplified version of a flying saucer. It uses the principle of bird movement. On the picture painted what it looks like on the example of bird flight and jellyfish movement. In reality, it has a more complex wavelike view. I simplified it to asymmetric vibrations. Based on this, the aerodynamics of bird flight, and the motion of the jellyfish are as follows: first, a vortex is generated from the environment, having a greater density and mass than the environment, and then it is thrown backwards as jet fuel. Experiment video


4.jpg
5.jpg


The lifting force of the wing in accordance with new ideas about the whirlwind.

Based on the theory of movement of a flying saucer and experiments conducted to confirm it, as well as the pattern of wing flow observed in a viscous fluid, it can be argued that the lifting force is formed as a result of the forces of intermolecular repulsion and attraction (short-range and long-range) and is equal to them. That is, the lifting force is equal to the thermal energy released from the air.

The figure shows the motion of the boundary layer in a viscous fluid. Viscosity increases the thickness of the layer and allows you to consider the process in detail. First, it must be borne in mind that the flow process is not constant, but rhythmic. The forces of attraction and repulsion prevail alternately, gradually reaching minima and maxima, which we observe as turbulence. This rhythm leads to flutter.

When the wing crashes into the air, squeezing it in front of itself, the distance between the molecules decreases, and they repel each other due to their thermal energy. Molecular repulsion forms rarefied air. Further, attraction begins to act between the molecules, and they tend to attract each other. Due to the fact that during the impact on the leading edge, molecule received an impulse leading to the release of repulsive and attractive forces, their speed gets bigger.

Therefore, they bend around the trailing edge and move under the wing against flight, reaching the leading edge, where, slowing down, they are cut off by molecules repelling from it. Due to this collision, a stream of smoke blowing the wing in the wind tunnel to the last tends to go over the upper part of the wing, even if it is moved strongly down. Thus, the shape of the wing leads to the fact that air from the upper surface flows under the lower one and creates an increased pressure there. An aerodynamic profile convex on both sides allows this force to act in the direction of flight. Molecules continue to be repelled and attracted like a spring, and after being left behind the wing like turbulence.

%D1%82_2.jpg
 
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It was found that the asymmetric vibrations of the object in homogeneous - liquid and gaseous media lead to the formation of a wave medium in which two oppositely directed waves of different forces,

Yes, you are correct. Waves in a medium that is contained can and often do strike and even push at the envelope at different times. Unfortunatly, it has been found that over time, the waves always seem to cancel each other out. So it provides no real net thrust to an object in free space.
We wish it did.
For interests sake, there was a claim in the early 1960's by a Mr. Dean that some mechanism could produce such thrust. He even had a model that did push along a tabletop with no evident reaction mass. Mr. Dean wanted a big chunk of money to reveal his system though. He didn't get it, and he died. As Mr Dean was quite old, that wasn't a surprise. Buhis invention was then taken apart and reassembled. After reassembly, it no longer worked. Devices that did something like that however were produced, They work by having a mass on a wheel like assembly that produce an off center up and down motion. The box then jumps in short hops and so moves forward. There are still some folks who argue that Deans original box worked differently. There was no up and down vibration noted in that device.
There are other "Space Drives" out there as well.
There was a great deal of interest couple of years ago regarding the "Impossible Drive" which was invented in Great Britain. This uses microwaves in an isolated bell shaped cavity, and has been found by NASA, several univeristies and the Chinese to produce small amounts of thrust. It was "Debunked" by a German team two years or so ago. The Germans found that their balance showed the thrust, but showed it b.oth along the axis and perpendicular to it.
That was interpreted as meaning that the devices were producing thrust by reacting with the measuring devices. This was broadly accepted, and the devices dismissed in the Scientific Press.
Personally, I after reading the German groups paper thought they didn't prove that the Impossible Drove didn't work, but rather proved they had a defective force balance.
There are also a couple of devices based on relativity and it's effects on gravity. Those show very small amounts of thrust when measured with force balance devices.
To date, no one has actually sent such a device into orbit and turned it on to see if there is any detectable thrust in actual space.
There is a reason for that.
The thrust produced is measured in Micro-Newtons or even Pico-Newtons per kilowatt of applied power. In other words, it's very low. Some of the devices in question are somewhat massive as well.
So it's simply better all around to use things like ion engines, which while producing a quite low thrust, are still thousands or millions of times more efficient at the cost of a few kilograms of fuel.
Maybe someday we will have a working Space Drive, but for now, we are no closer than Leonardo da Vinci was to powered flight.
 

MasterOgon

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Thanks for the short and informative story. I can add to this that a similar engine was launched into space by students on the Russian satellite Yubileiny. This did not work. All of these engines are similar to mine, but they do not provide for interaction with the environment. Such an engine can give traction only when it has a fulcrum. For example a solar sail. Using such an engine in combination with an aerodynamic surface, I investigated this possibility. And he came to the conclusion that even in air and water, such a movement is different from what science says. Therefore, I return to the old idea that ether is gas, and if you very quickly flap a wing in space, then you can get movement like a jellyfish.
 
Ether was the presumed medium for electric or magnetic waves to move through. Experiments found it not to exist. The basis there was that if the medium existed, it had to have some preferred reference frame, in other words,it had to be something. But waves moved exactly the same in all directions, in fact, moving objects saw things exactly the same. So the Ether had to be both moving as fast as a satellite did and also not moving at all relative to the ground at the same time and in the same place.
So Ether wasn't a real thing then.
Einstein explained the problem. The result was relativity. Oh, there were several papers that explained everything. Those papers are why Einstein is considered a genius.
It turns out that the electromagnetic field is in fact the medium that electromagnetic fields move through. It creates itself, using the power of the wave. This wave then propagates at the speed of light because that is the only speed it can move at. The magnetic field in it's collapse phase gives rise to an electric field, which grows, then as the magnetic field drops to zero, begins to collapse and in the process generates a magnetic field. In Physics, this is described by Maxwell's Equations. The combined magnetic field and electric field which give rise to each other is together called a Photon, and is the basic 'particle' of light.
At very small scales, all particles are composed of waves and all waves are particles. It's confusing, but that is at the heart of quantum mechanics.
Oh, and just to make things even more confusing, light beams coming from different direction don't interfere with each other. Water waves do interfere with each other. Why not?
There's a good PHd thesis in there somewhere.
 

MasterOgon

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Ether near the Earth is not required to move relative to this. The effect of the attached mass in aerohydrodynamics. The ether near the Earth moves with it. Einstein's relativity can be taken as the relative density of matter. Einstein, like Newton, was recognized as a genius only thanks to those <<Edited by moderator>> in power. Putting an end to the study of matter with his mathematical formalism, he led science in the dark. My experiment with a boat shows that this is not moving in the direction that modern science should move in. But for the sake of current theories, science does not recognize this fact
 
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I see
Ether near the Earth is not required to move relative to this. ...But for the sake of current theories, science does not recognize this fact
I see the Moderator didn't like some of what you put in. For your information, Newton was in no way Jewish. No, he was stanuch Church of England, and at a time when some English institutions discriminated against Jews. Einstein was jewish, vaguely, but his supporters included everyone from Italian Enrico Fermi to German Werner Heisenberg to American Robert Oppenheimer. Religion had nothing to do with it. It was all down to the mathematics.

Science is not bound to current theories. The accepted theories of any given time are frequently overturned or modified by newer ones. That's how Science progresses. Newton went against many of the prevailing theories of his day. His arguments wit Leibniz were the stuff of legend.
Einstein didn't invalidate Newton, and certainly not Maxwell. He did however modify them slightly. Those modifications are accepted because they are constantly being tested and proven correct. There have been a couple of those just this year. It happens quite often really.
To replace anything accepted by 'Mainstream Science' you will need some well documented measurements of an experiment and it has to be something that other people can do without you being involved and get the same result, and it has to be a result that isn't predicted by Einsteins work, or that produces something that Einsteins theories as presently understood denies can happen.
So far I have seen nothing like that from you.
Good luck. If you are right, I hope you succeed. You do need better data however.
 
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MasterOgon

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I proposed a simple experiment that can be repeated. It is believed that a symmetrical body that performs asymmetric oscillations in water (fast in one direction and slow in the other) will move in the direction of slow oscillations, because in this direction the resistance will be less. But in fact, the opposite is happening.
Move your palm in the water. Quickly one way, and slowly the other. During slow motion you will feel more resistance due to the fact that water moves by inertia.
 

MasterOgon

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As for the etheric wind. The experiment to detect it was based on the archaic assumption that the Earth in the ether flies like a stone in the air. In fact, the Earth moves in the ether due to its vibration. The motion of a vibrating body in gas forms an annular vortex in the form of a torus around this. There is such a vortex around the Earth. This is a magnetic field. The direction of motion of matter in this field corresponds to the direction in which the Earth moves along the disk of the galaxy. This magnetic field is the etheric wind. However, there is no difference what to call it, but the analogy with gas is obvious. We must admit that quantum theories also have a large share of truth. We cannot consider the movement of a body in ether as the movement of a body in gas. It is correct to assume that a moving body is the movement of a vortex in an ethereal medium. The body moves in the ether like a tornado of a very complex structure. The planets and stars are not balls in water, but cavitation bubbles in the etheric vortex of the galaxy. The cavitation bubble has a toroidal vortex structure. A vortex is a quasicrystal. Therefore, we perceive it as a solid body. The collapse of large cavitation bubbles creates supernova explosions. Small bubbles, planets, turn into asteroid belts. The solar system is an expanding part of the etheric funnel that runs along the arm of the galaxy to its center. The sun and planets are disturbances caused by the turbulence of this. Truth is in the middle as always.
 

Catastrophe

"Science begets knowledge, opinion ignorance.
"As for the etheric wind. The experiment to detect it was based on the archaic assumption that the Earth in the ether flies like a stone in the air. In fact, the Earth moves in the ether due to its vibration"

Have these experiments been published in any reputable medium?
 
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"As for the etheric wind. The experiment to detect it was based on the archaic assumption that the Earth in the ether flies like a stone in the air. In fact, the Earth moves in the ether due to its vibration"

Have these experiments been published in any reputable medium?

Why do they have to be published in a "reputable medium"? And what makes a medium reputable?

Anybody can do science through trial and error and discovery. You don't need an institution/college to learn that.

And now a good scientist would try to disprove these theories. And if they can't be disproven then that is science.
 
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It was found that the asymmetric vibrations of the object in homogeneous - liquid and gaseous media lead to the formation of a wave medium in which two oppositely directed waves of different forces, made alternately, exist simultaneously by inertia and create a pressure difference leading to uneven the release of thermal energy from the environment in the form of a vortex, pushing the object. Such an experiment is easy to repeat at home. It is necessary to lower the palm into the water and make a quick movement in one direction and slow in the other. During the reverse movement, the resistance of the water will be greater due to the energy released from the water. A series of experiments was performed in which a vibromotor that simulates the vibrations of an atom during movement was set on a float, discoid and sickle-shaped wing. Fluctuations with the help of an engine set the float in motion, and the lift of the wing in the oncoming flow increased significantly due to the formation of acoustic waves. In the near future, this principle can be used to create reusable spacecraft having high maneuverability when entering the atmosphere and capable of making a controlled landing anywhere in the world through the use of an electric motor. Video experiments

Flying saucer is a reusable air / underwater / spacecraft. The motor used on it is a movable discoid sail, driven by high-frequency electromagnetic inertial propulsion drive. With the help of the wing, the inertial propulsion drive perceives the resistance of the environment and the apparatus comes in forward motion. Thus, the flying saucer uses the principle of movement of birds, fish and other species of creatures moving in a homogeneous environment. This principle is possible in virtually any environment capable of providing resistance in which waves can be created and reflected. This allows you to effectively use the resistance of the environment due to its inertness.
For example, an airplane for the most part simply overcomes air resistance, leaving behind it an air whirlwind that lasts some time by inertia. The vortex contains energy that is not used at all. A bird creating a whirlwind with a wing wave receives back some of the energy spent on it in the form of wind, which pushes it. Thus, the bird is more efficient than the aircraft. But it is technically difficult to create a powerful and fast apparatus in the form of a bird or fish. Such designs have a large number of moving parts that do not withstand the load on friction and vibration, if you install a powerful engine on them. Unlike the ornithopter wing, the wing of the flying saucer will be able to vibrate with high frequency and low amplitude, like the membrane of an acoustic speaker. This can be achieved through the use in the design of the electromagnetic drive of the wing. The suspension of the wing on a magnetic cushion will allow you to realize greater power and frequency of oscillation with a low mechanical load.
The work of the wing in the air or water can be described as follows. The wing makes a fast ascending impulse, as a result of which a shock wave is formed above it, and the flying saucer begins to be drawn into the region of reduced pressure formed behind it. An annular vortex is formed under the wing, which follows it by inertia. Then the wing begins to make a reverse movement downward at low speed, and the flying saucer pushes off from the whirlwind, which catches up with it, carrying it upwards.

2.JPG


In space, a flying saucer can receive acceleration with the help of a wing in the form of a photon mirror and sail. The presence of an electron gun on board will allow the use of the wing and as a mirror of an electric sailing antenna. But unlike conventional ships that use the power of the solar wind to move in space, you can speed up flying not only by determining the pressure of the particles, but also by pushing them away.
Inertial propulsion drive works much more efficiently when there is constant resistance on one side and there is no resistance in the direction of motion. Despite the fact that the solar wind has a very low density, and in it the work of the wing will not be as effective as air or water, the pressure on it of light from only one side will allow the inertia to repel in the direction of the wind and at an angle. Thanks to this, the flying saucer will be able to accelerate and maneuver more effectively than ordinary space sailing ships. It is assumed that it is possible to generate electromagnetic waves in the direction of motion and to perceive their pressure using a sail, which corresponds to the model of motion of the apparatus in a liquid and gaseous medium.

The theory of motion of a flying saucer in a liquid and gaseous medium.

Imagine that the atoms or molecules of a liquid or gas that are as close as possible to each other as a result of compression. The only possible position in which they can be equidistant is triangles, which are combined into hexagons. This corresponds to the crystal structure of water.



3.jpg


Atom 1 gets a boost. Suppose that atoms move along the path of least resistance, as the arrows indicate. If these are billiard balls, then each time the impulse 1 will be divided by 3 and will lose power. But if these are atoms or molecules that oscillate, then each time during a collision, the pulse energy will increase, because the vibrating object itself creates a repulsion impulse.
Due to the repulsion of atoms, a chain reaction will occur, which will first lead to the formation of multiple vortices, the prerequisites for which are in the figure, turning into large vortices. The plate converts the force of the vortex into motion. Thus, the driving force of the saucer is air resistance.
Therefore, the energy that drives the flying saucer is taken from the environment .

Birdplane. Antigravity aircraft

Birdplane is an aircraft, which is a simplified version of a flying saucer. It uses the principle of bird movement. On the picture painted what it looks like on the example of bird flight and jellyfish movement. In reality, it has a more complex wavelike view. I simplified it to asymmetric vibrations. Based on this, the aerodynamics of bird flight, and the motion of the jellyfish are as follows: first, a vortex is generated from the environment, having a greater density and mass than the environment, and then it is thrown backwards as jet fuel. Experiment video


4.jpg
5.jpg


The lifting force of the wing in accordance with new ideas about the whirlwind.

Based on the theory of movement of a flying saucer and experiments conducted to confirm it, as well as the pattern of wing flow observed in a viscous fluid, it can be argued that the lifting force is formed as a result of the forces of intermolecular repulsion and attraction (short-range and long-range) and is equal to them. That is, the lifting force is equal to the thermal energy released from the air.

The figure shows the motion of the boundary layer in a viscous fluid. Viscosity increases the thickness of the layer and allows you to consider the process in detail. First, it must be borne in mind that the flow process is not constant, but rhythmic. The forces of attraction and repulsion prevail alternately, gradually reaching minima and maxima, which we observe as turbulence. This rhythm leads to flutter.

When the wing crashes into the air, squeezing it in front of itself, the distance between the molecules decreases, and they repel each other due to their thermal energy. Molecular repulsion forms rarefied air. Further, attraction begins to act between the molecules, and they tend to attract each other. Due to the fact that during the impact on the leading edge, molecule received an impulse leading to the release of repulsive and attractive forces, their speed gets bigger.

Therefore, they bend around the trailing edge and move under the wing against flight, reaching the leading edge, where, slowing down, they are cut off by molecules repelling from it. Due to this collision, a stream of smoke blowing the wing in the wind tunnel to the last tends to go over the upper part of the wing, even if it is moved strongly down. Thus, the shape of the wing leads to the fact that air from the upper surface flows under the lower one and creates an increased pressure there. An aerodynamic profile convex on both sides allows this force to act in the direction of flight. Molecules continue to be repelled and attracted like a spring, and after being left behind the wing like turbulence.

%D1%82_2.jpg

Magnificent!!
 
Why do they have to be published in a "reputable medium"? And what makes a medium reputable? . . .
To be actual Science, it has to be provided with enough information to repeat the experiment.

For the Ether, experiments were conducted in the late 1800's that conclusively showed that the earth is not moving through a medium of any kind for electromagnetic waves.

Sorry, there is no Ether.

But if you or someone you know has actual experimental evidence that such a thing actually exists, please publish it. Just saying 'It's a theory' is meaningless.

Please provide meaning, not just drivel.
 

MasterOgon

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To be actual Science, it has to be provided with enough information to repeat the experiment.

For the Ether, experiments were conducted in the late 1800's that conclusively showed that the earth is not moving through a medium of any kind for electromagnetic waves.

Sorry, there is no Ether.

But if you or someone you know has actual experimental evidence that such a thing actually exists, please publish it. Just saying 'It's a theory' is meaningless.

Please provide meaning, not just drivel.
The discovered phenomenon refers to aerohydrodynamics, and indicates contradictions in fundamental physics. To confirm this phenomenon, a simple experiment was proposed. Namely, a body that performs asymmetric vibrations (fast in one direction, and slow in the other) in a liquid or gas will move in the direction of fast vibrations. This can be checked by hand dangling in the water or by installing a symmetrical vibration motor on the boat. Such an experiment has been carried out many times in erroneous attempts to create an inertial propulsion.
In accordance with the conclusions drawn from this experiment, drawing an analogy between gas and ether, we can conclude that the ether wind should not exist. There is a circulation of ether around the Earth in the form of a toroidal vortex, caused by the vibration of the Earth, and which is the cause of the movement of the planet. This is a magnetic field.
 
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To be actual Science, it has to be provided with enough information to repeat the experiment.

For the Ether, experiments were conducted in the late 1800's that conclusively showed that the earth is not moving through a medium of any kind for electromagnetic waves.

Sorry, there is no Ether.

But if you or someone you know has actual experimental evidence that such a thing actually exists, please publish it. Just saying 'It's a theory' is meaningless.

Please provide meaning, not just drivel.

Well yea, and it also must be tried to be proved wrong in science. But I am just saying that some things that seem to be reputable are not very reputable. Just because someone claims to be an "expert" because they had so many years in an institution /college don't make it 100 percent that they know what they are talking about. There is also certain agendas in which certain things need to be upheld.

There is the power of the "Status Quo". For example The first publication of Galileo’s telescope observations of the planets in 1610 was followed by years of public controversy and attacks on him. But now there is a new power at hand which are "Gate Keepers" who want to keep the Status Quo and it isn't the Catholic Church anymore.
 
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EXPERIMENTAL RESEARCH OF FLYING FLIGHT, NOT EXPLORED PHENOMENON IN AERODYNAMICS AND THE QUESTION OF FLYING SAUCER EFFICIENCY
http://sci-article.ru/stat.php?i=1601957819

Kandyba Pavel Yurievich

Annotation:
As a result of experiments with the motion of asymmetrically oscillating bodies in a viscous medium, it was found that the generally accepted idea of such a principle of motion is not correct. A description of the experiments and the observed effect is given, as well as its interpretation.

Abstract:
As a result of experiments with the motion of asmmetscillating bodies in a viscous medium, it was found that the generally accepted idea of such a principle of motion is not correct. A description of the experiments and the observed effect is given, as well as its interpretation.

Keywords:
aerodynamics; hydrodynamics; turbulence; vortex; experiment; flapping flight, vibrating flight, flying saucer

UDC 533.664

Introduction

The purpose of this article is to draw attention to a little-studied phenomenon in the field of aerodynamics, a more detailed study of which, in the author's opinion, will give a significant impetus to the development of the aerospace field. Now 4 basic principles of engines are used: screw; reactive; using air currents as a driving force; using light gas. All of these principles have their advantages and disadvantages, and their combination often leads to a decrease in overall performance. New types of engines, the principles of which are based on theoretical research, have not been found, and their searches have created a lot of pseudoscientific ideas. And at the same time in nature there is the most perfect form of flight, which man has not mastered to the end. This is a flapping flight, which, as the reader will be convinced, is a synthesis of the above flight methods.

Relevance

To date, research is underway in different countries of the world with the aim of using the principle of flapping flight for practical purposes. There are some robotic models that have flapping wings, but they are inferior in efficiency to classical aircraft. Their resource is significantly limited by the complexity of the design, which does not allow them to realize high power. Nevertheless, for many years there has been a technical solution to this issue that has remained on paper - vibrating flight.

Goals and objectives

The author carried out experimental work, the purpose of which was to study the method of motion in a homogeneous medium by means of asymmetric oscillations. He created mock-ups of aircraft with vibrating wings, and carried out a series of tests in which their characteristics were investigated. The author found that the results of his experiments did not correspond to the generally accepted scientific theory of the motion of such devices.

Classic description of the principle

To begin with, consider the generally accepted theories of motion in a viscous medium of asymmetrically vibrating bodies. The most famous of them is the explanation of the principle of motion of an inertion propulsion drive in a liquid:

The principle of operation of inertion propulsion drive lies in the fact that their purposeful movement is caused by the difference in the resistance force during the forward and reverse half-cycle of work. With dry friction, the resistance to slow movement exceeds the resistance to fast movement (in one half cycle, when a small force is applied, the static friction force is not overcome and the apparatus remains in place; in the reverse half cycle, the friction force is overcome, the apparatus moves). In liquids, on the contrary, resistance to fast movement prevails over resistance to slow movement. The explanation of the effect in liquids is fundamentally different (since there is no static friction force in liquids and gases) and is based on viscous friction forces.

The description of the principle of movement in air, the same as the movement of an inertioid in a liquid medium, has a vibrating flight:

To get an idea of the mechanism of the appearance of the thrust force, let us first consider the appearance of the thrust force when the plate moves in the same medium with different speeds of forward and reverse strokes.

The thrust force in different modes of forward and reverse motion in the same medium of movement arises due to the following two effects.

1) Nonlinear dependence of the resistance of the medium to the displacement of the propeller on its speed and its derivatives - even for a symmetrically executed propeller (for example, a round plate moving along the normal). Due to the different modes of forward and reverse strokes, the average resistance force will not be zero and can reach a value sufficient for the movement. When the propeller moves in a working stroke at a speed 10 times higher than the idle speed, the efficiency of the propeller, i.e. the ratio of the energy used by the mover to the energy received by the mover can reach a value approaching 90%.
2) The asymmetry of the propulsion unit relative to the plane perpendicular to the direction of motion can lead to the fact that a tractive effort arises even when the speeds of the straight about and reverse moves. This effect - the dependence of the drag on the shape of the body and with its asymmetry on the direction of motion - is well known in aerodynamics.

Experimental observation of the phenomenon

If the effect caused by the difference in resistances during symmetric oscillations of an asymmetric body does not raise any doubts, then in relation to asymmetrically oscillating symmetric bodies, the experiment shows the exact opposite of the theory - the movement occurs in the direction of a fast jerk, and not a slow one. This is clearly demonstrated by the simplest experiment: we lower a straight palm into the water, make a quick movement in one direction, slow in the other, and in the opposite movement we feel much more resistance than we would expect. The following happens - when we push the water forward, a rarefied medium forms behind the palm, and its subsequent collapse creates pressure. This is explained by the work of the forces of repulsion and attraction of water molecules, Brownian motion, which becomes directional in a catching turbulent vortex.

Thus, the classic example with a barge and a car has the following description: the ship is displaced relative to the center of mass, the resistance of the water pushes it back slightly, and then, after some time, the current caused by the displacement of the ship pushes it towards this displacement. Equally, with asymmetric vibrations of a symmetric body, and with symmetric vibrations of an asymmetric body, the movement of the medium occurs according to the same principle.

Similar phenomena are well known in aerodynamics. With a sharp descent of the helicopter, a subsequent uncontrolled loss of altitude occurs as a result of the formation of an annular vortex caused by the downward movement of the air mass, which, while descending, was pushed by the helicopter. Another example is the "cobra" maneuver, in which the fighter suddenly lifts its nose, which causes an updraft below it, allowing it to sharply slow down and seem to hover in place.

Experiments

1. Hydrodynamic testing of boat models with vibration motors.

To study the phenomenon, a mechanism was made, with a principle similar to the inertion propulsion drive of V.N. Tolchin, with the difference that the acceleration and deceleration of the pendulums was carried out not by a spring, but by magnets. In some cases, for simplicity, only one pendulum was used, and the torque was compensated by the support. First, the engine was installed on a boat with a symmetrical hydrodynamic profile, and during the experiment it was seen that its movement in the water is in the direction of fast jerks. Then the engine was installed on a boat with an asymmetric profile, more streamlined in the front and less streamlined in the rear. In this case, the asymmetry of the oscillations was eliminated. During the experiment, no obvious movement was observed, probably due to the relatively small asymmetry of the profile. Further, the vibrations were made asymmetric so that the boat made quick jerks in the direction in which the streamlining is greater, and this allowed it to move in that direction.

During the experiment, the formation of waves of different lengths, created by the vibrating hull of the boat, was observed - short weak waves propagated in the direction of movement, forward, and long stronger ones behind in the opposite direction (Fig. 1). This allows us to describe this principle of movement as a wave. The formation of these waves by the example of a single jerk is as follows: with a fast jerk, a certain mass of water receives an impulse and begins to move in the direction of the impact according to the principle of an annular vortex, which is observed as a surface wave. In this case, a low pressure zone forms behind the boat, which, when filled, takes the energy of this wave in the process of flowing around, which creates turbulence. Water molecules under the action of their own forces of repulsion and attraction with acceleration rush into the zone of reduced pressure, and something like the collapse of a cavitation bubble or the explosion of a vacuum bomb occurs. The collapse energy pushes the boat from behind, and, reflected from it, forms a backward wave.
Accordingly, with a slow jerk of the boat backward, as a result of these interactions, a weak forward wave is formed.
In some cases, in particular when a boat with a symmetrical profile is moving, performing asymmetric oscillations at a high frequency, at which the wavelength is much less than the length of the boat, it was observed that the movement occurs at intervals of large oscillation frequencies. This is probably due to the accumulation of wave energy. In the immediate vicinity of the boat to the walls of the container with water, the achieved effect decreased. The hull of the boat adhered to the walls, similar to the convergence of nearby ships, which was overcome by direct repulsion of the hull from the walls.



2. Tests of models of vibrating flights in free fall.

To establish that the resulting motion was caused not by the differences in the heights of the surface waves, but by the difference in pressure, experiments were carried out in air. A lightweight asymmetric vibration motor was manufactured, which It was a motor with an eccentric that makes half a turn with acceleration and a half turn with a deceleration, which was carried out by a magnet rigidly attached to the body, acting on the eccentric. The engine was mounted on a disk-shaped wing with a symmetrical airfoil (Fig. 2). Difficulties in detecting the presence of engine thrust were that fixing the result with the help of weights would lead to the fact that the scales would become a fulcrum during repulsion, and, not having time to respond to changes in weight, could show its decrease as an average result even when jumping them an engine without a wing. One of the features of inercioids is that, pushing off straight and nonlinearly, they use everything that prevents their oscillations as a fulcrum. This is probably the reason for the emergence of pseudoscientific prejudices regarding this type of engine.
It was decided to test the model in free fall. But even in this case, the measurement of the falling speed turned out to be impossible for the reason that when the maximum falling speed was reached, this structure turned over or shifted relative to the vertical from the excess pressure and then fell faster. Therefore, the following test method was applied. The maximum height from which the model fell without overturning and displacement was determined (about 1.5 m), and then the model was thrown from the same height with the engine running. When the operating model fell, there was a noticeable displacement from the vertical and subsequent overturning already at a height of about 0.5 m.
The torque generated by the engine has been taken into account. To compensate for this, a similar engine with the opposite torque was not used due to the complexity of synchronization and the increase in weight. A feature of the design of the engine was its self-winding in the direction of rotation as a result of the influence of the accelerating and decelerating magnet on the eccentric. At the same time, the eccentric, approaching the magnet, accelerated, and created a fast impulse with pressure on the axis in the opposite direction, forcing the engine to spin slightly in the opposite direction of rotation, and passing by the magnet, slowed down, creating a slow reverse impulse and attracting the magnet after it, forcing the engine more noticeably scroll in the direction of rotation. This self-winding was not strong, and was largely compensated by the aerodynamic plane. In most cases, the flip direction of the model did not correspond to this torque, and depended primarily on other factors, such as accidental tilt at the beginning of the fall, curvature of the plane, uneven weight distribution and application of force.

Later, an improved engine with a vertical axis of rotation was made, which eliminated the overturning reactive moment, and created a gyroscopic effect to maintain the horizontal position of the model in flight. The design of the engine consisted in the fact that a rotor with magnets rotated over magnets mounted on a movable aerodynamic plane, mounted on springs. The alignment of the magnets forced them, attracting, to raise the plane. As the magnets approached, the rotor would accelerate, and slow down as the magnets moved away. Therefore, the plane moved faster up and slower down. It was not possible to completely eliminate overturning, but when the engine was turned on, the tendency to it decreased, and the tendency to horizontal displacement increased under the same experimental conditions.

To take into account the ground effect, the height of the fall was increased, and in this case, the rollover occurred approximately after passing the same distance of 1 m. Due to the lack of accurate measuring instruments, it was difficult to judge the presence of the ground effect. But, apparently, he had to exert influence, creating additional support for repulsion at a certain distance to the ground. Also, when throwing from a height of 1 m, in which the model did not have time to roll over, it was noticed that at the minimum distance from the ground, the fall sharply accelerates, probably due to a violation of air circulation.

3. Visualization of the air flow.

In order to establish that the air circulates exactly as described earlier, the following experiments were carried out. A tape was attached to the edge of the plate indicating the direction of the air flow. The plate was lifted up perpendicular to the plane, and during the ascent the tape was pulled under the plate into the turbulence zone, and after stopping the plate at the upper lifting point it took a horizontal position on the outside of the plate, parallel to its plane. This suggests that after the plate stops, an ascending air flow continues to exist under it, striking its lower part, and being reflected, distributed to the sides.
Next, a simple installation was assembled with an electromagnetic linear motor and an asymmetric aerodynamic plane in the form of a cone with a low top, making a vertical vibrations perpendicular to its plane. The installation was connected to a frequency generator. A smoke source was located under the plane, closer to its edge. The smoke naturally rose up, partially flowed around the edge of the plane, and rose further. When the installation was switched on to the mode of symmetric oscillations, the following happened: when the plane was raised, the smoke was completely drawn under it, forming a turbulent vortex, and when lowering, it was thrown out to the side horizontally, also in the form of a vortex. It should be noted that this happened only at the optimum vibration frequency, at which the amplitude was maximum. For this setup, the maximum amplitude was about 2 mm at a frequency of 18 Hertz. The diameter of the plane was about 5 cm. With a significant increase in frequency, the movement of smoke became the same as without turning on the engine, but at the same time, the presence of acoustic waves of the same length was visually observed in it both from above and below. Apparently, in order to achieve the maximum effect, it is necessary to take into account the optimal vibration mode.

Next, a single lift of the plate was studied, that is, a symmetrical airfoil completely surrounded by smoke. During the ascent of the plate perpendicular to the plane, a turbulence zone is formed under it in the form of an annular vortex with an upward flow in the center, which repeats the shape of a nuclear fungus (Fig. 3). When the plate stops at the top point, the annular vortex catches up with it and flows around it, continuing to move upward by inertia. In this case, the vortex turns into a thin ring, increasing in diameter, and eventually collapsing in the space above the plate (Fig. 4). The upward flow in the center of the vortex hits the bottom of the plate, and, being reflected to the sides, makes the vortex expand as it flows around the plate (Fig. 4). Since the plate takes energy from the moving air mass, the vortex collapses around the plate. That is, a single upward jerk of the plate perpendicular to the plane creates an air flow pushing the plate after it stops. If the reverse motion of the plate has a lower speed, and the energy of the flow created by it is less, the resulting force will be lifting.

Further, a single rise in the smoke of an asymmetric aerodynamic profile in the form of a hemisphere with a large streamlining in the direction of travel was studied. During the rise of the hemisphere, a process is observed, the same as the rise of the plate - an annular vortex with an upward flow resembling a mushroom. And when the hemisphere stops at the top point, the flow hitting it from below is reflected not to the sides, as in the case of the plate, but downward, which is facilitated by the shape of the hemisphere. In many ways, this resembles a jet stream flowing from a rocket nozzle. You can see these processes using the simplest experiments - dangling a mug in a bucket of water or a spoon in soup.

In addition, the movement of air during the operation of the acoustic speaker membrane was studied using smoke. Air access was only to the front side of the membrane, and to the back was limited. For the experiment, an ordinary smartphone with a sound generator and a cigarette as a source of smoke were used. When the speaker was operating in a wide range of ultrasonic frequencies, the ambient air was drawn to the speaker on the sides and fired with a jet stream from its center.

3. Testing of models of vibrating flights in flight after initial acceleration.

To study this effect in free flight after the initial acceleration, several models were created in the form of "flying saucers" with different aerodynamic profiles and types of vibration motors (Fig. 5 and 6). In these experiments, it was not possible to obtain an accurate visual result in view of the multiple extraneous factors affecting the flight and the instability of the apparatus. Eliminating these factors would be possible under laboratory conditions.

In the course of these experiments, it was found that a "flying saucer" with a convex profile at the top, or resembling two rear halves of an aircraft wing laminar profile joined together (Fig. 7), can receive a very significant increase in lift from the wind, provided there is a force that holds in a horizontal position. Thrown like a frisbee, but with little force and a strong twist for stability, during the gusts of wind, it abruptly changed its trajectory, gaining altitude until the rotation stopped maintaining its stability. Thus, it was impossible to judge the efficiency of the engine.

To simplify the experiment and obtain a more visual result, a simple asymmetric vibration motor was installed on the flying wing glider at the center of gravity. During his work, he created fast jerks up and slow down, but the lack of the necessary conditions for the experiment did not allow obtaining an accurate result. Apparently, the operation of the engine led to pitching - the glider periodically gained altitude and slowed down.
For greater clarity of the experiment, a glider was made in the form of a wing in the shape of a crescent (Fig. 8), the center of gravity of which, and, accordingly, vibromotor perpendicular to its plane. The installation was connected to a frequency generator. A smoke source was located under the plane, closer to its edge. The smoke naturally rose up, partially flowed around the edge of the plane, and rose further. When the installation was switched on to the mode of symmetric oscillations, the following happened: when the plane was raised, the smoke was completely drawn under it, forming a turbulent vortex, and when lowering, it was thrown out to the side horizontally, also in the form of a vortex. It should be noted that this happened only at the optimum vibration frequency, at which the amplitude was maximum. For this setup, the maximum amplitude was about 2 mm at a frequency of 18 Hertz. The diameter of the plane was about 5 cm. With a significant increase in frequency, the movement of smoke became the same as without turning on the engine, but at the same time, the presence of acoustic waves of the same length was visually observed in it both from above and below. Apparently, in order to achieve the maximum effect, it is necessary to take into account the optimal vibration mode.

Next, a single lift of the plate was studied, that is, a symmetrical airfoil completely surrounded by smoke. During the ascent of the plate perpendicular to the plane, a turbulence zone is formed under it in the form of an annular vortex with an upward flow in the center, which repeats the shape of a nuclear fungus (Fig. 3). When the plate stops at the top point, the annular vortex catches up with it and flows around it, continuing to move upward by inertia. In this case, the vortex turns into a thin ring, increasing in diameter, and eventually collapsing in the space above the plate (Fig. 4). The upward flow in the center of the vortex hits the bottom of the plate, and, being reflected to the sides, makes the vortex expand as it flows around the plate (Fig. 4). Since the plate takes energy from the moving air mass, the vortex collapses around the plate. That is, a single upward jerk of the plate perpendicular to the plane creates an air flow pushing the plate after it stops. If the reverse motion of the plate has a lower speed, and the energy of the flow created by it is less, the resulting force will be lifting.

Further, a single rise in the smoke of an asymmetric aerodynamic profile in the form of a hemisphere with a large streamlining in the direction of travel was studied. During the rise of the hemisphere, a process is observed, the same as the rise of the plate - an annular vortex with an upward flow resembling a mushroom. And when the hemisphere stops at the top point, the flow hitting it from below is reflected not to the sides, as in the case of the plate, but downward, which is facilitated by the shape of the hemisphere. In many ways, this resembles a jet stream flowing from a rocket nozzle. You can see these processes using the simplest experiments - dangling a mug in a bucket of water or a spoon in soup.

In addition, the movement of air during the operation of the acoustic speaker membrane was studied using smoke. Air access was only to the front side of the membrane, and to the back was limited. For the experiment, an ordinary smartphone with a sound generator and a cigarette as a source of smoke were used. When the speaker was operating in a wide range of ultrasonic frequencies, the ambient air was drawn to the speaker on the sides and fired with a jet stream from its center.

3. Testing of models of vibrating flights in flight after initial acceleration.

To study this effect in free flight after the initial acceleration, several models were created in the form of "flying saucers" with different aerodynamic profiles and types of vibration motors (Fig. 5 and 6). In these experiments, it was not possible to obtain an accurate visual result in view of the multiple extraneous factors affecting the flight and the instability of the apparatus. Eliminating these factors would be possible under laboratory conditions.

In the course of these experiments, it was found that a "flying saucer" with a convex profile at the top, or resembling two rear halves of an aircraft wing laminar profile joined together (Fig. 7), can receive a very significant increase in lift from the wind, provided there is a force that holds in a horizontal position. Thrown like a frisbee, but with little force and a strong twist for stability, during the gusts of wind, it abruptly changed its trajectory, gaining altitude until the rotation stopped maintaining its stability. Thus, it was impossible to judge the efficiency of the engine.

To simplify the experiment and obtain a more visual result, a simple asymmetric vibration motor was installed on the flying wing glider at the center of gravity. During his work, he created fast jerks up and slow down, but the lack of the necessary conditions for the experiment did not allow obtaining an accurate result. Apparently, the operation of the engine led to pitching - the glider periodically gained altitude and slowed down.
For greater clarity of the experiment, a glider was made in the form of a wing in the shape of a crescent (Fig. 8), the center of gravity of which, and, accordingly, engine, atelier, were on the very nose. Thus, the characteristics of the airframe with a small initial acceleration were similar to those of a projectile with plumage. This made it possible to aim it at a small distance with minor differences in launch conditions, since at this distance, about 5 m, it flew almost along a ballistic trajectory. As a result of these modifications, it became possible to visually observe significant changes in the flight path.

The flight trajectory with the engine on was significantly different from the control flight trajectory with the engine off, which greatly exceeded the possible launch errors. The glider covered the first 2-3 meters along the initially specified ballistic trajectory, but, as the air resistance grew, the engine began to perceive it as a support. This allowed him to push off, as if bouncing on a hard surface. As a result, the amplitude of the leading edge oscillations increased, and the engine vibration frequency decreased. A similar dependence of amplitude and frequency on resistance is also valid for the previously described hydrodynamic models and "flying saucers". (The motion of the hydrodynamic model led to a decrease in the clock rate up to the complete sticking of the pendulums opposite the magnet.)

Asymmetric oscillations of the leading edge of the wing of the crescent model led to a sharp lifting of the nose, right up to reaching critical angles of attack and hovering in place, followed by falling down like a stone. If the height of the fall was sufficient, the newly increased resistance allowed the engine to start working, and the model suddenly went out of the dive. This was significantly different from the control flight along the ballistic trajectory, even with an error of several meters.

Experimental results
The direction of motion of asymmetrically oscillating bodies in a viscous medium established in the experiment is directly opposite to the direction described in the sources known to the author. The efficiency of this principle of movement directly depends on the resistance of the medium, and increases in proportion to its growth, and if the optimal modes are observed, energy accumulation is possible. The limiting factor that makes it impossible to "perpetuum mobile" in this case is the engine power, since when the critical resistance is reached, the ability to overcome it disappears.

Model of the possible cause of the formation of an annular vortex and the motion of asymmetrically vibrating bodies towards a fast jerk

Let us consider the proposed model of the occurrence of this phenomenon based on geometric patterns. Imagine a conditional homogeneous viscous medium, liquid or gas, in a state of absolute rest in the form of equidistant particles in this position due to the equilibrium of the forces of attraction and repulsion between them. In a plane section, connecting these particles with conventional lines, we get a lattice consisting of equilateral triangles. This is the only structure in which the points can be equidistant (Fig. 9).

Suppose this lattice has a certain elasticity, which allows it to generate a force similar to the surface tension of water. This is the force of resistance of the given environment. Let's place an object in this environment. Let it be particle number one. Imagine that this object is displaced relative to its center of mass, making a single jerk along the path of least resistance between two particles numbered 2, but the force of its jerk does not exceed the force of the binding particle together. Then it will create some tension in the lattice, which will propagate in the form of a wave, supported by the energy of the forces of repulsion and attraction of particles with a limited speed inherent in this environment. Having transmitted the impulse imparted by object 1 further, the particles return to their original position under the action of their own forces, and, accordingly, will push the object back to its original position. Let us assume this is the resistance force that pushes back the barge with the car mentioned at the beginning.

And now suppose that the force of the jerk when the object 1 is displaced relative to the center of mass exceeds the binding force of the particles 2. Then the particles, thanks to the momentum they received, sequentially begin to move along a given trajectory, and simultaneously along the path of least resistance. If they were billiard balls, the momentum would be divided by 2 each time, and, in the end, dissipated. But if we take into account that the particles have their own energy, which makes it possible to transfer the energy of the impulse through waves, we will get a chain reaction, thanks to which the impulse can travel a considerable distance without significant losses. If we lay down a logical path of impulse transmission, and enumerate each stage, we get that already at the expense of 6 this impulse will return to the starting point in two ways, along trajectories resembling an eight, and will be communicated to the object 1 from behind that created it. Thus, object 1, having moved forward relative to the center of mass, will receive a force pushing it from behind.

It should noted that in the formed due to and the displacement of the object 1 is a zone of reduced pressure, the particles from behind will immediately rush behind it, since the repulsive forces of other particles will act on them. From them, the leg of the previously described mushroom is formed. Therefore, the collapse of this cavity when all the particles meet will have a certain excess energy, the manifestation of which can be observed during the explosion of a vacuum bomb.

The resulting trajectory in the form of a figure eight is consistent with the observed phenomenon - the dynamics of an annular vortex in the section. The particles alternately transfer momentum to each other and fall into a closed circle, which explains the long existence of the vortex. It is precisely the harmonious organization of chaotic Brownian motion that is the energy that feeds the vortex.
If we trace the propagation of the pulse further, we will see a pattern due to which the particles form smooth fronts. These are waves caused by a single displacement of object 1. Object 1 itself will move pushed by the particles that form a figure eight or the top of the mushroom, slowing down as their energy dissipates. This is viscous friction, thermal energy, which moves the object that has brought it out of equilibrium in the direction of this impulse. This makes us think about the meaning of the expression "everything comes back" from the standpoint of logic and common sense.

Model compliance with known phenomena

Let's consider this model using the example of the lift force of an airplane wing. It is generally accepted that the movement of a wing through the air is continuous. But we also know that this movement is always associated with vibration, which ultimately leads to flutter and the destruction of the wing. And we also know that turbulence has a rhythm of vortex formation and destruction. By the example of an aircraft overcoming the sound barrier (Fig. 10), or the outflow of a jet stream from a nozzle, one can see that the movement of gases has a rhythmic, wave character. This is due to cyclic rarefaction and collapse of the medium. The resonance of the structure with these cycles is the cause of the vibrations that occur during the movement of the wing.

Having singled out one such cycle from the general rhythm, we can say that the wing with its front part imparts an impulse to the air in the forward upward direction, pushing it over itself. As a result, a region of reduced pressure is formed above the wing, which collapses in the direction of the pulse. Due to the fact that the wing is on the path of the air rushing into the rarefaction above it, it receives an impulse directed forward upward. The laminar profile is faster because the inclination of its rear lower plane allows the impulse to collapse the cavity to push the wing in the direction of flight.

Since the rhythm of these cycles is not taken into account when the wing moves, in other words, the wing does not stop to wait for the energy that overtakes it, a significant part of it remains behind the aircraft, and can affect other aircraft. It has long been known that wedge-flying birds use this energy.

A vortex, similar to an annular vortex in the section, is also present when air flows around the wing (Fig. 11). One part of it is well known in aerodynamics. This is a vortex following at some distance from the trailing edge of the wing. The other counter-rotating part is located directly at the trailing edge of the wing, in a small turbulent zone. This part has a very small diameter, since it is compressed, and at the same time significant energy is concentrated in it, due to which the destruction of the wing at high speed begins from the trailing edge. When a compressed vortex at the trailing edge breaks off the wingtip, it expands in size and forms a turbulence zone behind the aircraft.

Between these two vortices, air moves under the wing from the space above it, as evidenced by the circulation of the boundary layer around the wing. Boundary layer air above the top surface bends around the trailing edge and enters under the wing. Therefore, the mushroom, like an annular vortex, has an asymmetric, curved arc, in which the leg is bent upward. The air injected under the wing moves against the flight in the boundary layer, and is the cause of the counterflow at the leading edge of the wing. Because of this, the stream of smoke in the aerodynamic tube seeks to bypass the wing from above to the last, even when it is displaced to the very bottom.
At critical angles of attack, when the flow stalls, the compressed vortex from the trailing edge moves into the space above the wing and increases in size. Then the flow that builds up pressure under the wing moves behind it and begins to put pressure on the upper part of the wing. In this case, the wing no longer creates lift and only provides frontal resistance to the fall.

The proposed model can also be considered on the example of a bird's flight. The generally accepted opinion is that a bird, with a flap of its wings, spreads its feathers and feels less air resistance, and when lowering its wings, it connects the feathers and, thus, feeling more resistance, is repelled. This statement was based on the principle of known th aircraft with a waving umbrella, built in the early 20th century. The umbrella had flaps that let air in when moving up, and closed when moving down. In accordance with the proposed model, this led to the emergence of a force pressing to the ground, which was somewhat reduced by opening the valves when the umbrella was lifted.

The principle of bird flight in accordance with this model is as follows: bird feathers on the wings have an S-shaped profile and work as vortex generators. By flapping its wings and spreading feathers, the bird not only reduces resistance, but also generates an annular vortex with an upward flow, relying on which it repels, lowering its wings. The flight of insects can be described in a similar way.

The vortex has a quasi-crystalline structure and has the properties of a solid. Thus, it is like a solid object formed from the environment that can be thrown away as a reactive mass before it collapses.

An example of a jet propulsion that is best suited for a flying saucer is the jellyfish. It is generally accepted that a jellyfish, shrinking, throws out a jet stream, and this sets it in motion. This is true, but it requires a certain addition. After the jellyfish has ejected the jet stream, it needs to refill the dome, which requires a certain amount of energy. The jellyfish takes this energy from the environment. When a jet stream is thrown out and the jellyfish begins to move forward, with its frontal resistance it creates a wave, followed by a catching ring vortex behind the jellyfish. When the energy of the jet pulse is exhausted and the jellyfish slows down, the flow in the ring vortex that has caught up with it fills it, straightening the dome. Medusa simply allows the vortex to push and flow around itself, completely repeating its shape (Fig. 12) and without making any special efforts. When the energy of the vortex is depleted, the jellyfish contracts again, starting a new cycle. We will see the same if we put an asymmetric linear motor on a very flexible plate.
A special resemblance of the jellyfish to the tested models of "flying saucers" is that it very often flips over from excessive pressure. Replacing the complex movements of the jellyfish with simple oscillations of the aerodynamic profile, we will lose its energy efficiency, but we will get the absolute simplicity and versatility of the principle of movement using the environment as a jet fuel.

Output

In theory, the method of motion by asymmetric vibrations is suitable for any environment in which vortices and pressure waves can be created.

According to the author, based on modern technologies, it is quite possible to build:

1) An ultralight air sailboat that will be driven by a low-power engine and held in the air like soaring birds.
2) An improved solar sail craft. In view of the fact that an asymmetric vibration motor (inertioid) has the ability to push off straight and nonlinearly, having a minimum resistance to the support, the solar wind pressure will be enough to achieve the effect.
3) A descent spacecraft with increased controllability, which will be able to use the resistance of the environment for maneuvers and soft landing during descent.

The idea of this method as a wave method indicates the probable possibility of using it in space as a vacuum jet engine. It is still too early to talk about a real flying saucer as they are presented. The difficulty lies in the fact that the strength and power characteristics required to create a full-fledged apparatus that surpasses modern jet aircraft in all respects are prohibitive. For example, the body and the moving part of such an aircraft must be 3D printed monolithic from heat-resistant and hard metal. Now such technologies are only at the initial stage of development, but you can start thinking about it today.

Boat
View: https://youtu.be/ECjTOa_mm5k

Plane
View: https://youtu.be/aCAFfisXYa4

Saucer
View: https://youtu.be/lC1fVgYwXJw


Bibliographic list:

1. Wikipedia: Inercioids [Electronic resource] - access mode: https://ru.wikipedia.org/wiki/Инерцо% D0% B8% D0% B4% D1% 8B (date accessed: 09/07/2020)
2. Lozovsky L.A., Lozovsky A.L., Khokhlushkina F.A. The method of movement of the vehicle and the universal device "vibrating flight" for its implementation // RF Patent No. 2147786, 1998.10.08
3. Damn E. Physics for a flying saucer or quantum theory of gravitation, Physical and mathematical model of the fourth method [Electronic resource]. - access mode: http://www.ukraviaforum.com/index.php/topic,13470.0.html (date accessed: 09/06/2020)
4. Sebin AL Transformation of atmospheric heat. Physical basis of technology and indirect confirmation of its performance [Electronic resource]. - access mode: https://lenr.su/forum/index.php?threads/sozdanie-tmp-kljuchevaja-informacija.152/ (date of access: 09/06/2020)
5. Tolchin VN Video demonstration of the inertioid work by the author of the invention [Electronic resource) urs]. - access mode:
View: https://www.youtube.com/watch?v=pcEdpb-rIX4
(date accessed: 09/08/2020)
6. Shipov GI Personal site: experiments [Electronic resource]. - access mode: http://www.shipov.com/science.html (date accessed: 09/07/2020)
7. Sorokodum E. D. Personal site: Vortex-Oscillatory Technologies Ltd. [Electronic resource]. - access mode: http://www.vortexosc.com/index.php (date accessed: 09/08/2020)
8. Author's site: antigravity, engine, experiments with a flying saucer [Electronic resource]. - access mode: http://new-original-style.com.ua/pages/article2/antigravity/engine.htm (date accessed: 09/07/2020)

The review is here http://sci-article.ru/stat.php?i=1601957819
 

MasterOgon

Sci fi space cyberpunk artist
Jan 29, 2020
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Popular science about flying saucers

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In the photo, it is not an alien spaceship at all, and not a secret development of scientists, but just a landing capsule of the Curiosity rover, which in its shape very much resembles a flying saucer. Is it an accident? Of course not. This is a technical decision made after carefully considering the pros and cons of NASA's best minds. A trade-off between falling deceleration and resilience. No matter how NASA jokes about flying saucers, their descent vehicles for Martian missions are exactly what flying saucers trace their ancestry from.
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Another example is the B2 bomber. Some believe that it is built using UFO technology - its profile very much resembles something extraterrestrial. In fact, this form was not taken from the classified materials about UFOs, copied from nature. Millions of years of bird evolution have saved engineers a lot of time.

Also in nature there is a prototype for a particular flying saucer with a disc-shaped wing, which we are used to seeing in the pictures. This is a jellyfish, which, let me say, uses the reactive principle of movement without the consumption of a working medium (the dream of all astronauts), since this working medium is the environment. It would seem - where is the jellyfish to the missiles, it hardly moves? Such a scheme has enormous potential, and I will try to explain in simple words what it is.

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In previous posts, I have already written about my amateur aerodynamic research that led me to this conclusion. I don't like to brag about this at all, but I just have to emphasize it so that what I said next makes sense. I made a small scientific discovery that touched on many very complex topics at once.

My original idea was not a flying saucer at all. I came to this form solely in an attempt to improve the efficiency of my experimental models. At first I wanted to improve the controllability of a solar sail or lander with a device such as an inertial propulsion drive.

Simplified, it is an asymmetrically oscillating pendulum that moves by simply pushing straight or at an angle from anything that resists the oscillations of its support. This is comparable to how to ride on a chair with wheels pulling forward, or how a gyroscope suspended by one end on a string, while rotating, can hover in a horizontal position. Due to the fact that this method of repulsion may seem unnatural, many associate it with the miracle of antigravity, but in fact it is the work of the well-known laws of mechanics, working as a result of nonlinear application of forces. The same thing happens with a sailboat capable of sailing upwind at an angle.

My guess was that since an inertioid can push off using any fulcrum, why not push off the solar wind with a solar sail? After all, the solar wind also exerts pressure and can be a fulcrum. And the same is with the descent vehicle - when it enters the atmosphere and experiences strong air resistance, can this resistance serve as a support from which one can push off in order to control the trajectory?

To test this idea, I built a rigid parachute from a garbage bag and bamboo sticks, and installed on it a lightweight inertioid that I had invented, or, more correctly, an asymmetric vibration motor. Experiencing this structure in free fall and hoping to see a displacement or slow fall when the engine is turned on in an incoming flow. In the process, a number of technical problems were discovered, the solution of which logically led me to the shape of a flying saucer, in which the engine and the battery are located in the central convex part, and a disc-shaped vibrating wing is located around.
This shape was resistant to falling and could even glide well in an arbitrary direction, provided the weight was very low.

The ambiguity of the results of these experiments made the principle to be tested on water. I assembled a small boat with a vibration motor that jerked to one side faster than the other, and found that it was not sailing in the direction of conventional theory.
View: https://youtu.be/ECjTOa_mm5k
 

MasterOgon

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What kind of thrust can a flapping flight develop?
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1911 "Flying car" of the inventor Pitts.


This strange design is interesting in that it is the only theoretically possible aircraft, the principle of which makes it necessary to use the shape of a flying saucer. Many flying saucers have been built and invented, based on various principles, but each time this form was more a kind of fetish, or at best was due to its compactness. But a vibrating flight is essentially just an umbrella waving up and down, and it can also be thought of as an ordinary acoustic speaker.
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Simplified vibroplane diagram.

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Diagram of Lozovsky's vibroplane.

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Project of a multi-domed vibroplane.

This principle is interesting, if only because it underlies the movement of all floating and flying creatures, which often force scientists to puzzle over in an attempt to unravel the reason for their effectiveness. Vibrating is essentially the maximum simplification of the movement of living beings, which is beneficial from the point of view of mechanics. And although it seems simple, its principle of operation has hardly been researched to date. It is not known what kind of thrust a vibratory flight can develop, can it be maneuverable like flies, accelerate in the atmosphere to cosmic speeds and fly into space by inertia, just like a fish jumps out of water, or is it a dead-end way of development?

There are three variations on this concept:

  • The umbrella has an asymmetric shape, such as a cone, and oscillates symmetrically (at the same speed up and down)
  • A symmetrical umbrella or plate that oscillates asymmetrically (up and down at different speeds).
  • Asymmetrical umbrella that oscillates asymmetrically.

Current theory defines thrust as the difference in drag between the upward and downward movement of the umbrella. Due to the asymmetric shape or vibrations, the air resistance in one direction is greater than in the other, and the vibrating flight should move in the direction of lower resistance. In three cases, it should be like this:

  • A symmetrically oscillating cone should move in the direction of its apex, since it is more streamlined when moving in this direction.
  • An asymmetrically vibrating plate should move in the direction of slow jerks, since it experiences less resistance when moving slowly than when moving quickly.

  • An asymmetrically oscillating cone should move in the direction of the top if it makes slow jerks in this direction, for the two reasons given above.
Vibrating flight projects, in which this principle is described and the calculations are given, can be viewed here(rus):
https://patents.google.com/patent/RU2147786C1/ru
http://www.journalpro.ru/articles/vibrolet-alternativa-vertoleta/

But there is reason to believe that the thrust of a vibrating flight cannot be defined as the difference in frontal resistance arising between the up and down movements of the umbrella.
Few experimental studies of the vibrational principle of motion have yielded an ambiguous and sometimes contradictory result, the accuracy of which is in doubt in many cases. The difficulty in carrying out experiments to measure thrust is that when measured with weights, the vibrations of the two-body system, which is essentially a vibrating flight, affect the scales. Thus, a non-existent result is obtained, which is often presented as evidence of inercioids, EM drives, etc. For example, due to fast vibration, the scales may not have time to react and show an average result that can be perceived as a decrease in weight. Really flying vibroplanes have not yet been created, and in the case of tests of such structures in free fall, the result is not accurate because the tested structure does not fall exactly like any umbrella, but tends to roll over. The only way to measure thrust is to use a mechanism that completely and perfectly compensates for vibrations, which is not easy at all. Such a device is described here (rus) https://top-technologies.ru/ru/article/view?id=24651

First of all, it's worth remembering Peet's "Flying car". His umbrella had blinds that opened when moving up and let air in, and closed when moving down. He was just trying to push the air downward with no result.

About a century later, an experiment was carried out in which an oscillator with a conical umbrella was suspended from a balance by means of a damping spring, which simultaneously played the role of an oscilloscope element. The weight of the operating device, the energy consumed by the motor, and the dependence of these parameters on frequency were measured. For calibration, measurements were first taken of a working device without an umbrella. It was necessary to understand how a vibrating device affects the readings of the scales without interacting with air. After that, the umbrella was installed on the oscillator and the same measurements were carried out. It was assumed that with an increase in the oscillation frequency, the weight of the oscillator with the umbrella would decrease, and the energy consumed by the engine to create the lifting force would increase in comparison with the control measurements without the umbrella.
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Diagram of an experimental setup with a oscillating umbrella.

The amount of energy consumed has indeed increased as expected. But judging by the readings of the scales, it turned out that the oscillating umbrella in the shape of a cone creates thrust not in the direction of the top, but vice versa, that is, in the direction of fast jerks despite the shape, which should feel the maximum resistance when moving in this direction. As a result, in this way it was possible to understand that this principle somehow works, but it is not clear how and what kind of traction can be obtained in this way. This experiment is detailed here (rus):
http://ucom.ru/doc/na.2016.06.02.208.pdf
 

MasterOgon

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Free fall tests of the vibrating flight were carried out as follows. It was planned to compare its fall rate in the inoperative and on state. But in reality this turned out to be impossible, since the fall was not stable and the vibrating flight was constantly turning over. It is impossible to understand how it works and how effective it is.
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Experimental model of vibroplane.

In another experiment, a vibro boat with an asymmetric body and an oscillator operating in two modes - symmetrical and asymmetric - was used. In the symmetrical mode, no significant movement was observed, which implies that the shape is not so important. And in the mode of asymmetric oscillations, the movement took place precisely in the direction of a fast jerk and not a slow one, as the initial theory predicted, explaining the principle of vibration movement by a simple difference in frontal resistance. It turned out that the boat, as it were, squeezes through the water and moves in the same way as if it was doing it on a hard surface, experiencing dry friction.
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Hydrodynamic model of vibrating flight in motion.

This is explained as follows - as a result of a fast jerk behind, a turbulent vortex is formed, which, during a slow return movement, continues to move forward by inertia and pushes the boat from behind. This is confirmed by the effect observed with the help of smoke during a single movement of the plate. After stopping the plate, the vortex under it continues to move in the same direction and, catching up, is reflected to the sides, increasing in diameter.
Since the force contained in the vortex is greater than the force of the return movement, the boat moves forward.
A vortex, generally annular, since the rest are its derivatives, really has the properties of a solid and can be considered as a soliton with the properties of a particle-wave, or as a moving mass. That is, he has impulse. And since the vortex, forming behind the boat, moves in the same direction, when the boat stops, the impulse of the vortex created by it is communicated back to it.
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Ring vortex in the turbulent zone during plate movement (left) and after stopping (right)

The easiest way to see the effect is to run back and forth with your palm in the water, or something flat and light in the air. The pressure is quite noticeable. You can observe with the help of smoke. These experiments are described here
https://www.interconf.top/10.11232-2663-4139.17.01.html

From all this it follows that it is still not clear how the vibrating flight actually works, and how you can calculate the thrust it develops. But apparently his movement depends little on the form and he moves in the direction of a fast jerk.

The question is as follows - is it possible to somehow substantiate the motion of an asymmetrically oscillating symmetric body in a viscous medium without relying on the idea of the difference in frontal resistance when moving forward and backward and calculate the thrust that arises in this case?

Perhaps the answer to this question can be given by a smooth solution of the Navier-Stokes equation. This equation describes the movement of water, air, streams of cosmic plasma and is quite accurate, but problems begin where turbulence begins. A smooth solution is one that can describe the flow with absolute accuracy to every smallest vortex. And for such a solution they give not a lot, not a little million dollars, because it is recognized as one of the problems of the millennium. Well, since it is the vortex that sets the vibratory flight in motion, then most likely this decision is necessary for it. It would let you know how much pressure the air is putting on his umbrella. But this requires not much, not a little, a great mathematician.

Perhaps light on this problem can be shed by the use in calculations of a triangular coordinate system, which is used extremely rarely, and for other purposes, for example, in chemistry. Here's the thing. Usually the Navier-Stokes equation is solved in a Cartesian coordinate system, that is, consisting of rectangles.

Modeling flows using the Navier-Stokes equation in a rectangular coordinate system.

The triangular coordinate system is interesting in that it corresponds to the absolute uniformity of an ideal environment for the initial conditions, whereas in a rectangular system all points are not initially equidistant. If vectors are logically laid in it according to the principle of momentum distribution as if it were a game of billiards, then the automatic figures are formed that correspond to the structure of a torus or a toroidal vortex. But it is known that any vortex is a derivative of a toroidal vortex.
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Possible form of the solution of the Navier-Stokes equation in a triangular coordinate system.

Regular hexagons are also obtained, which are present in the vortices at the poles of the giant planets.

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Hexagonal vortex.

If a similar principle of billiards is applied in the Cartesian coordinate system, which is usually used to describe flows, pictures, then we get a broken pattern, more likely similar to the deformation of a metal than to the flow of liquids or gases. Maybe the problem of the Navier-Stokes equation is connected with this? If this is so, then the task becomes extremely difficult, since the solution of the neural network in a triangular coordinate system in a direct form is impossible, and indeed such a system is even difficult to represent in three-dimensional form. Therefore, the question of the thrust of the vibroplane is still open.
 
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It was found that the asymmetric vibrations of the object in homogeneous - liquid and gaseous media lead to the formation of a wave medium in which two oppositely directed waves of different forces, made alternately, exist simultaneously by inertia and create a pressure difference leading to uneven the release of thermal energy from the environment in the form of a vortex, pushing the object. Such an experiment is easy to repeat at home. It is necessary to lower the palm into the water and make a quick movement in one direction and slow in the other. During the reverse movement, the resistance of the water will be greater due to the energy released from the water. A series of experiments was performed in which a vibromotor that simulates the vibrations of an atom during movement was set on a float, discoid and sickle-shaped wing. Fluctuations with the help of an engine set the float in motion, and the lift of the wing in the oncoming flow increased significantly due to the formation of acoustic waves. In the near future, this principle can be used to create reusable spacecraft having high maneuverability when entering the atmosphere and capable of making a controlled landing anywhere in the world through the use of an electric motor. Video experiments

Flying saucer is a reusable air / underwater / spacecraft. The motor used on it is a movable discoid sail, driven by high-frequency electromagnetic inertial propulsion drive. With the help of the wing, the inertial propulsion drive perceives the resistance of the environment and the apparatus comes in forward motion. Thus, the flying saucer uses the principle of movement of birds, fish and other species of creatures moving in a homogeneous environment. This principle is possible in virtually any environment capable of providing resistance in which waves can be created and reflected. This allows you to effectively use the resistance of the environment due to its inertness.
For example, an airplane for the most part simply overcomes air resistance, leaving behind it an air whirlwind that lasts some time by inertia. The vortex contains energy that is not used at all. A bird creating a whirlwind with a wing wave receives back some of the energy spent on it in the form of wind, which pushes it. Thus, the bird is more efficient than the aircraft. But it is technically difficult to create a powerful and fast apparatus in the form of a bird or fish. Such designs have a large number of moving parts that do not withstand the load on friction and vibration, if you install a powerful engine on them. Unlike the ornithopter wing, the wing of the flying saucer will be able to vibrate with high frequency and low amplitude, like the membrane of an acoustic speaker. This can be achieved through the use in the design of the electromagnetic drive of the wing. The suspension of the wing on a magnetic cushion will allow you to realize greater power and frequency of oscillation with a low mechanical load.
The work of the wing in the air or water can be described as follows. The wing makes a fast ascending impulse, as a result of which a shock wave is formed above it, and the flying saucer begins to be drawn into the region of reduced pressure formed behind it. An annular vortex is formed under the wing, which follows it by inertia. Then the wing begins to make a reverse movement downward at low speed, and the flying saucer pushes off from the whirlwind, which catches up with it, carrying it upwards.

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In space, a flying saucer can receive acceleration with the help of a wing in the form of a photon mirror and sail. The presence of an electron gun on board will allow the use of the wing and as a mirror of an electric sailing antenna. But unlike conventional ships that use the power of the solar wind to move in space, you can speed up flying not only by determining the pressure of the particles, but also by pushing them away.
Inertial propulsion drive works much more efficiently when there is constant resistance on one side and there is no resistance in the direction of motion. Despite the fact that the solar wind has a very low density, and in it the work of the wing will not be as effective as air or water, the pressure on it of light from only one side will allow the inertia to repel in the direction of the wind and at an angle. Thanks to this, the flying saucer will be able to accelerate and maneuver more effectively than ordinary space sailing ships. It is assumed that it is possible to generate electromagnetic waves in the direction of motion and to perceive their pressure using a sail, which corresponds to the model of motion of the apparatus in a liquid and gaseous medium.

The theory of motion of a flying saucer in a liquid and gaseous medium.

Imagine that the atoms or molecules of a liquid or gas that are as close as possible to each other as a result of compression. The only possible position in which they can be equidistant is triangles, which are combined into hexagons. This corresponds to the crystal structure of water.



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Atom 1 gets a boost. Suppose that atoms move along the path of least resistance, as the arrows indicate. If these are billiard balls, then each time the impulse 1 will be divided by 3 and will lose power. But if these are atoms or molecules that oscillate, then each time during a collision, the pulse energy will increase, because the vibrating object itself creates a repulsion impulse.
Due to the repulsion of atoms, a chain reaction will occur, which will first lead to the formation of multiple vortices, the prerequisites for which are in the figure, turning into large vortices. The plate converts the force of the vortex into motion. Thus, the driving force of the saucer is air resistance.
Therefore, the energy that drives the flying saucer is taken from the environment .

Birdplane. Antigravity aircraft

Birdplane is an aircraft, which is a simplified version of a flying saucer. It uses the principle of bird movement. On the picture painted what it looks like on the example of bird flight and jellyfish movement. In reality, it has a more complex wavelike view. I simplified it to asymmetric vibrations. Based on this, the aerodynamics of bird flight, and the motion of the jellyfish are as follows: first, a vortex is generated from the environment, having a greater density and mass than the environment, and then it is thrown backwards as jet fuel. Experiment video


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The lifting force of the wing in accordance with new ideas about the whirlwind.

Based on the theory of movement of a flying saucer and experiments conducted to confirm it, as well as the pattern of wing flow observed in a viscous fluid, it can be argued that the lifting force is formed as a result of the forces of intermolecular repulsion and attraction (short-range and long-range) and is equal to them. That is, the lifting force is equal to the thermal energy released from the air.

The figure shows the motion of the boundary layer in a viscous fluid. Viscosity increases the thickness of the layer and allows you to consider the process in detail. First, it must be borne in mind that the flow process is not constant, but rhythmic. The forces of attraction and repulsion prevail alternately, gradually reaching minima and maxima, which we observe as turbulence. This rhythm leads to flutter.

When the wing crashes into the air, squeezing it in front of itself, the distance between the molecules decreases, and they repel each other due to their thermal energy. Molecular repulsion forms rarefied air. Further, attraction begins to act between the molecules, and they tend to attract each other. Due to the fact that during the impact on the leading edge, molecule received an impulse leading to the release of repulsive and attractive forces, their speed gets bigger.

Therefore, they bend around the trailing edge and move under the wing against flight, reaching the leading edge, where, slowing down, they are cut off by molecules repelling from it. Due to this collision, a stream of smoke blowing the wing in the wind tunnel to the last tends to go over the upper part of the wing, even if it is moved strongly down. Thus, the shape of the wing leads to the fact that air from the upper surface flows under the lower one and creates an increased pressure there. An aerodynamic profile convex on both sides allows this force to act in the direction of flight. Molecules continue to be repelled and attracted like a spring, and after being left behind the wing like turbulence.

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Yes, this posting is a wonderful, true, lucid, compelling breakthrough in physics that has not been noticed before. Kudos to the poster/author!!
 

MasterOgon

Sci fi space cyberpunk artist
Jan 29, 2020
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I don't understand why everyone clung to the word ether. This is an ancient word which means that space is not emptiness. Yes, there was an erroneous theory that the Earth, like an airplane, is blown by the ethereal wind, and we see that this is not so. But we also see that space-time is not empty and has gaseous properties. It just cannot be explained by primitive theories.
 

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