A turbosail is a rotor-type marine propulsion device that creates thrust from wind energy thanks to a physical phenomenon known as the Magnus effect.

A turbosail operates based on a physical process that occurs when a fluid or gas flows around a rotating cylindrical or round body, known as the Magnus effect. The phenomenon got its name from the name of the Prussian scientist Heinrich Magnus, who described it in 1853.

Let's imagine a ball or cylinder that rotates in a flow of gas or liquid washing them. In this case, the cylindrical body must rotate along its longitudinal axis. During this process, a force arises whose vector is perpendicular to the direction of flow. Why is this happening? On the side of the body where the direction of rotation and the flow vector coincide, the speed of the air or liquid medium increases, and the pressure, in accordance with Bernoulli's law, decreases. On the opposite side of the body, where the rotation and flow vectors are multidirectional, the speed of the medium decreases, as if slowed down, and the pressure increases. The pressure difference arising on opposite sides of a rotating body generates transverse force. In aerodynamics, it is known as the lifting force that keeps heavier-than-air craft in flight. In the case of rotor sails, this is a force with a vector perpendicular to the direction of the wind acting on a rotor-sail mounted vertically on the deck and rotating along the longitudinal axis.

Flettner rotating sails

The described physical phenomenon was used by the German engineer Anton Flettner when creating a new type of marine engine. Its rotor sail looked like rotating cylindrical wind power towers. In 1922, the inventor received a patent for his device, and in 1924, the first rotary ship in history, the converted schooner Bukau, left the stocks.
The Bukau turbosails were driven by electric motors. On the side where the rotor surface rotated towards the wind, in accordance with the Magnus effect, an area of ​​increased pressure was created, and on the opposite side - a decreased one. As a result, a thrust arose, which moved the ship, subject to the presence of a side wind. Flettner placed flat plates on top of the rotor-cylinders for better orientation of the air flow around the cylinder. This made it possible to double the driving force. A spinning hollow metal cylinder-rotor that uses the Magnus effect to create lateral thrust was subsequently named after its creator.

In testing, Flettner's turbosails performed excellently. Unlike a conventional sailboat, a strong side wind only improved the performance of the experimental vessel. Two cylindrical rotors made it possible to better balance the ship. At the same time, by changing the direction of rotation of the rotors, it was possible to change the movement of the vessel forward or backward. Of course, the most advantageous wind direction for creating thrust was strictly perpendicular to the longitudinal axis of the vessel.

Turbosail from Cousteau

Sailboats were built in the 20th century, and are still being built in the 21st. Modern sails are made of lighter and stronger synthetic materials, and the sailing rig is quickly folded by electric motors, freeing people from physical work.

However, the idea of ​​a fundamentally new system that uses wind energy to create ship thrust was in the air. It was picked up by the French explorer and inventor Jacques-Yves Cousteau. As an oceanographer, he was very impressed by the use of wind as a thrust - a free, renewable and absolutely environmentally friendly source of energy. In the early 1980s, he began work on creating such propulsors for modern ships. He took Flettner's turbosails as a basis, but significantly modernized the system, making it more complex, but at the same time increasing its efficiency.

What is the difference between a Cousteau turbosail and a Flettner propulsion system? Cousteau's design is a vertically mounted hollow metal tube that has an aerodynamic profile and operates on the same principle as an airplane wing. In cross section, the pipe has a drop-shaped or egg-shaped shape. On its sides there are air intake grilles through which air is pumped through a system of pumps. And then the Magnus effect comes into play. Air turbulence creates a pressure difference inside and outside the sail. A vacuum is created on one side of the pipe, and a seal is created on the other. As a result, a lateral force arises, which causes the ship to move. Essentially, a turbosail is a vertically mounted aerodynamic wing: on one side the air flows slower than on the other, creating a pressure difference and lateral thrust. A similar principle is used to create lift on an airplane. The turbosail is equipped with automatic sensors and is mounted on a rotating platform, which is controlled by a computer. The smart machine positions the rotor taking into account the wind and sets the air pressure in the system.

Cousteau first tested a prototype of his turbosail in 1981 on the catamaran Moulin à Vent while sailing across the Atlantic Ocean. During the trip, the catamaran was accompanied by a larger expedition ship for safety. The experimental turbosail provided thrust, but less than traditional sails and motors. In addition, by the end of the trip, due to metal fatigue, the welding seams burst under the pressure of the wind, and the structure fell into the water. However, the idea itself was confirmed, and Cousteau and his colleagues focused on developing a larger rotary vessel, the Halsion. It was launched in 1985. The turbosails on it are an addition to the aggregation of two diesel engines and several propellers and allow saving fuel consumption by a third. Even 20 years after the death of its creator, Alsion is still on the move and remains the flagship of the Cousteau flotilla.

Turbosail versus canvas wings

Even in comparison with the best modern sails, a turbosail-rotor provides 4 times the thrust coefficient. Unlike a sailboat, a strong side wind is not only not dangerous for a rotary ship, but is most beneficial for its progress. It moves well even with a headwind at an angle of 250. At the same time, a ship with traditional sails “loves” a tailwind most of all.

Conclusions and prospects

Now exact analogues of Flettner's sails are installed as auxiliary propulsors on the German cargo ship E-Ship-1. And their improved model is used on the yacht Alsion, owned by the Jacques-Yves Cousteau Foundation.
Thus, there are currently two types of propulsion systems for the Turbosail system. A conventional rotor sail, invented by Flettner at the beginning of the 20th century, and its modernized version by Jacques-Yves Cousteau. In the first model, the net force arises from the outside of the rotating cylinders; in the second, more complex version, electric pumps create a difference in air pressure inside a hollow pipe.

The first turbosail is capable of propelling the vessel only in crosswinds. It is for this reason that Flettner’s turbosails have not become widespread in global shipbuilding. Design feature Turbosails from Cousteau allow you to obtain driving force regardless of wind direction. A vessel equipped with such propulsors can even sail against the wind, which is an undeniable advantage over both conventional sails and rotor sails. But, even despite these advantages, the Cousteau system was also not put into production.

This is not to say that attempts are not being made these days to bring Flettner's idea to life. There are a number of amateur projects. In 2010, the third ship in history, after the Bukau and Alsion, was built with rotor sails - a 130-meter German Ro-Lo class truck. The vessel's propulsion system consists of two pairs of rotating rotors and a couple of diesel engines in case of calm and to create additional traction. Rotor sails play the role of auxiliary engines: for a ship with a displacement of 10.5 thousand tons, four wind power towers on deck are not enough. However, these devices can save up to 40% of fuel on each flight.
But the Cousteau system was unfairly consigned to oblivion, although the economic feasibility of the project was proven. Today, Alsion is the only full-fledged ship with this type of propulsion. It seems unclear why the system is not used for commercial purposes, in particular on cargo ships, since it allows saving up to 30% of diesel fuel, i.e. money.

P. MANTASHYAN.

We continue to publish the journal version of P. N. Mantashyan’s article “Vortexes: from the molecule to the Galaxy” (see “Science and Life No.”). We will talk about tornadoes and tornadoes - natural formations of enormous destructive power, the mechanism of their occurrence is still not entirely clear.

Science and life // Illustrations

Science and life // Illustrations

A drawing from a book by American physicist Benjamin Franklin, explaining the mechanism of tornadoes.

The Spirit rover discovered that tornadoes occur in the thin atmosphere of Mars and photographed them. Photo from NASA website.

Giant tornadoes and tornadoes that occur on the plains of the southern United States and China are a formidable and very dangerous phenomenon.

Science and life // Illustrations

A tornado can reach a kilometer in height, resting its apex on a thundercloud.

A tornado at sea lifts and draws in tens of tons of water along with marine life and can break and sink a small ship. In the era of sailing ships, they tried to destroy a tornado by shooting at it from cannons.

The picture clearly shows that the tornado is rotating, twisting air, dust and rainwater into a spiral.

The city of Kansas City, turned into ruins by a powerful tornado.

Forces acting on a typhoon in the trade wind flow.

Ampere's law.

Coriolis forces on a turntable.

Magnus effect on the table and in the air.

Vortex air movement is observed not only in typhoons. There are vortices larger than a typhoon - these are cyclones and anticyclones, the largest air vortices on the planet. Their sizes significantly exceed the size of typhoons and can reach more than a thousand kilometers in diameter. In a sense, these are antipodean vortices: they have almost everything the other way around. Cyclones of the Northern and Southern Hemispheres rotate in the same direction as the typhoons of these hemispheres, and anticyclones rotate in the opposite direction. A cyclone brings with it inclement weather accompanied by precipitation, while an anticyclone, on the contrary, brings clear, sunny weather. The formation scheme of a cyclone is quite simple - it all starts with the interaction of cold and warm atmospheric fronts. In this case, part of the warm atmospheric front penetrates inside the cold one in the form of a kind of atmospheric “tongue”, as a result of which warm air, lighter, begins to rise, and at the same time two processes occur. Firstly, water vapor molecules, under the influence of the Earth’s magnetic field, begin to rotate and involve all the rising air in the rotational movement, forming a giant air whirlpool (see “Science and Life” No.). Secondly, the warm air above cools, and the water vapor in it condenses into clouds, which fall as precipitation in the form of rain, hail or snow. Such a cyclone can ruin the weather for a period of several days to two to three weeks. Its “life activity” is supported by the arrival of new portions of moist warm air and its interaction with the cold air front.

Anticyclones are associated with the descent of air masses, which at the same time heat up adiabatically, that is, without heat exchange with the environment, their relative humidity drops, which leads to the evaporation of existing clouds. At the same time, due to the interaction of water molecules with the Earth’s magnetic field, anticyclonic rotation of the air occurs: in the Northern Hemisphere - clockwise, in the Southern Hemisphere - counterclockwise. Anticyclones bring with them stable weather for a period of several days to two to three weeks.

Apparently, the formation mechanisms of cyclones, anticyclones and typhoons are identical, and the specific energy intensity (energy per unit mass) of typhoons is much greater than that of cyclones and anticyclones, only due to more high temperature air masses heated by solar radiation.

TOrnadoes

Of all the vortices that form in nature, the most mysterious are tornadoes; in fact, they are part of a thundercloud. At first, in the first stage of a tornado, rotation is visible only in the lower part of the thundercloud. Then part of this cloud hangs down in the form of a giant funnel, which becomes increasingly longer and finally reaches the surface of the earth or water. A giant trunk appears, hanging from a cloud, which consists of an internal cavity and walls. The height of a tornado ranges from hundreds of meters to a kilometer and is usually equal to the distance from the bottom of the cloud to the surface of the earth. A characteristic feature of the internal cavity is the reduced pressure of the air in it. This feature of a tornado leads to the fact that the cavity of the tornado serves as a kind of pump, which can draw in a huge amount of water from the sea or lake, along with animals and plants, transport them over considerable distances and throw them down along with the rain. A tornado is capable of carrying quite large loads - cars, carts, small ships, small buildings, and sometimes even with people in them. A tornado has gigantic destructive power. When it comes into contact with buildings, bridges, power lines and other infrastructure, it causes enormous destruction.

Tornadoes have a maximum specific energy intensity, which is proportional to the square of the speed of the vortex air flows. According to meteorological classification, when the wind speed in a closed vortex does not exceed 17 m/s, it is called a tropical depression, but if the wind speed does not exceed 33 m/s, then it is a tropical storm, and if the wind speed is 34 m/s and above , then this is already a typhoon. In powerful typhoons, wind speeds can exceed 60 m/s. In a tornado, according to various authors, the air speed can reach from 100 to 200 m/s (some authors point to supersonic air speed in a tornado - over 340 m/s). Direct measurements of the speed of air flows in tornadoes are practically impossible at the current level of technological development. All devices designed to record the parameters of a tornado are mercilessly broken by them at the first contact. The speed of flows in tornadoes is judged by indirect signs, mainly by the destruction they produce or by the weight of the loads they carry. Besides, distinguishing feature classic tornado - the presence of a developed thundercloud, a kind of electric battery that increases the specific energy intensity of the tornado. To understand the mechanism of the emergence and development of a tornado, let us first consider the structure of a thundercloud.

STORM CLOUD

In a typical thundercloud, the top is positively charged and the base is negatively charged. That is, a giant electrical capacitor many kilometers in size floats in the air, supported by rising currents. The presence of such a capacitor leads to the fact that on the surface of the earth or water over which the cloud is located, its electrical trace appears - an induced electric charge that has a sign opposite to the sign of the charge of the base of the cloud, that is, the earth's surface will be positively charged.

By the way, the experiment on creating an induced electric charge can be carried out at home. Place small pieces of paper on the surface of the table, comb dry hair with a plastic comb and bring the comb closer to the sprinkled pieces of paper. All of them, looking up from the table, will rush to the comb and stick to it. The result of this simple experiment can be explained very simply. The comb received an electric charge as a result of friction with the hair, and on the piece of paper it induces a charge of the opposite sign, which attracts the pieces of paper to the comb in full accordance with Coulomb's law.

Near the base of a developed thundercloud, there is a powerful upward flow of air saturated with moisture. In addition to dipole water molecules, which begin to rotate in the Earth’s magnetic field, transmitting momentum to neutral air molecules, drawing them into rotation, there are positive ions and free electrons in the upward flow. They can be formed as a result of the influence of solar radiation on molecules, the natural radioactive background of the area and, in the case of a thundercloud, due to the energy of the electric field between the base of the thundercloud and the ground (remember the induced electric charge!). By the way, due to the induced positive charge on the surface of the earth, the number of positive ions in the flow of rising air significantly exceeds the number of negative ions. All these charged particles, under the influence of the rising air flow, rush to the base of the thundercloud. However, the vertical velocities of positive and negative particles in an electric field are different. The field strength can be estimated by the potential difference between the base of the cloud and the surface of the earth - according to researchers’ measurements, it is several tens of millions of volts, which, with a height of the base of the thundercloud of one to two kilometers, gives an electric field strength of tens of thousands of volts per meter. This field will accelerate positive ions and retard negative ions and electrons. Therefore, per unit time, more positive charges will pass through the cross section of the upward flow than negative ones. In other words, an electric current will arise between the earth's surface and the base of the cloud, although it would be more correct to talk about a huge number of elementary currents connecting the earth's surface with the base of the cloud. All these currents are parallel and flow in the same direction.

It is clear that, according to Ampere’s law, they will interact with each other, namely, attract. From the course of physics it is known that the force of mutual attraction per unit length of two conductors with electric currents flowing in the same direction is directly proportional to the product of the forces of these currents and inversely proportional to the distance between the conductors.

The attraction between two electrical conductors is due to Lorentz forces. The electrons moving inside each conductor are influenced by the magnetic field created by the electric current in the adjacent conductor. They are acted upon by the Lorentz force, directed along a straight line connecting the centers of the conductors. But for the force of mutual attraction to arise, the presence of conductors is completely unnecessary - the currents themselves are sufficient. For example, two particles at rest that have the same electric charge repel each other according to Coulomb’s law, but the same particles moving in the same direction are attracted until the forces of attraction and repulsion balance each other. It is easy to see that the distance between particles in the equilibrium position depends only on their speed.

Due to the mutual attraction of electric currents, charged particles rush to the center of the thundercloud, interacting with electrically neutral molecules along the way and also moving them to the center of the thundercloud. The cross-sectional area of ​​the ascending flow will decrease by several times, and since the flow rotates, according to the law of conservation of angular momentum, its angular velocity will increase. The same thing will happen to the upward flow as to a figure skater who, spinning on the ice with her arms outstretched, presses them to her body, causing her rotation speed to sharply increase (a textbook example from physics textbooks that we can watch on TV!). Such a sharp increase in the speed of air rotation in a tornado with a simultaneous decrease in its diameter will lead to a corresponding increase in the linear wind speed, which, as mentioned above, can even exceed the speed of sound.

It is the presence of a thundercloud, the electric field of which separates charged particles by sign, that leads to the fact that the speeds of air flows in a tornado exceed the speeds of air flows in a typhoon. Figuratively speaking, a thundercloud serves as a kind of “electric lens”, in the focus of which the energy of an upward flow of moist air is concentrated, which leads to the formation of a tornado.

SMALL VORTEXES

There are also vortices, the formation mechanism of which is in no way connected with the rotation of a dipole water molecule in a magnetic field. The most common among them are dust devils. They are formed in desert, steppe and mountainous areas. In size they are inferior to classic tornadoes, their height is about 100-150 meters, and their diameter is several meters. For the formation of dust devils, a necessary condition is a desert, well-heated plain. Once formed, such a vortex exists for quite a short time, 10-20 minutes, all this time moving under the influence of the wind. Despite the fact that desert air contains virtually no moisture, its rotational motion is ensured by the interaction of elementary charges with the Earth's magnetic field. Over a plain, strongly heated by the sun, a powerful upward flow of air arises, some of the molecules of which, under the influence of solar radiation and especially its ultraviolet part, are ionized. Solar radiation photons knock out electrons from the outer electron shells of air atoms, forming pairs of positive ions and free electrons. Due to the fact that electrons and positive ions have significantly different masses with equal charges, their contribution to the creation of angular momentum of the vortex is different and the direction of rotation of the dust vortex is determined by the direction of rotation of the positive ions. Such a rotating column of dry air, as it moves, lifts dust, sand and small pebbles from the surface of the desert, which in themselves do not play any role in the mechanism of dust swirl formation, but serve as a kind of indicator of air rotation.

Air vortices, a rather rare natural phenomenon, are also described in the literature. They appear during the hottest time of the day on the banks of rivers or lakes. The lifetime of such vortices is short; they appear unexpectedly and disappear just as suddenly. Apparently, both water molecules and ions formed in warm and humid air due to solar radiation contribute to their creation.

Much more dangerous are water vortices, the formation mechanism of which is similar. The description has been preserved: “In July 1949 in Washington state, on a warm sunny day under a cloudless sky, a high column of water spray appeared on the surface of the lake. It existed for only a few minutes, but had significant lifting power. Approaching the river bank, he lifted a rather heavy motor boat about four meters long, carried it several tens of meters and, hitting the ground, broke it into pieces. Water vortices are most common where the surface of the water is strongly heated by the sun - in tropical and subtropical zones."

Swirling air flows can occur during large fires. Such cases are described in the literature; we present one of them. “Back in 1840, forests were cleared for fields in the United States. A huge amount of brushwood, branches and trees were dumped in a large clearing. They were set on fire. After some time, the flames of individual fires pulled together, forming a column of fire, wide at the bottom, pointed at the top, 50 - 60 meters high. Even higher, the fire gave way to smoke that went high into the sky. The fire and smoke whirlwind rotated with amazing speed. The majestic and terrifying sight was accompanied by a loud noise, reminiscent of thunder. The force of the whirlwind was so great that it lifted large trees into the air and threw them aside.”

Let's consider the process of formation of a fire tornado. When wood burns, heat is released, which is partially converted into kinetic energy of the ascending flow of heated air. However, during combustion another process occurs - ionization of air and combustion products.

fuel. And although in general heated air and fuel combustion products are electrically neutral, positively charged ions and free electrons are formed in the flame. The movement of ionized air in the Earth's magnetic field will inevitably lead to the formation of a fire tornado.

I would like to note that vortex air movement occurs not only during large fires. In his book “Tornadoes” D.V. Nalivkin asks the questions: “We have already talked more than once about the mysteries associated with small-dimensional vortices, tried to understand why all the vortices rotate? Other questions also arise. Why, when straw burns, the heated air does not rise in a straight line, but in a spiral and begins to swirl. Hot air behaves the same way in the desert. Why doesn't it just go up without any dust? The same thing happens with water spray and splashes when hot air rushes over the surface of the water.”

There are vortices that arise during volcanic eruptions; for example, they were observed over Vesuvius. In the literature, they are called ash vortices - ash clouds erupted by a volcano participate in the vortex movement. The mechanism for the formation of such vortices is in general terms similar to the mechanism for the formation of fire tornadoes.

Let's now see what forces act on typhoons in the turbulent atmosphere of our Earth.

CORIOLIS FORCE

A body moving in a rotating reference frame, for example, on the surface of a rotating disk or ball, is subject to an inertial force called the Coriolis force. This force is determined by the vector product (numbering of formulas begins in the first part of the article)

F K =2M[ VΩ], (20)

Where M- body mass; V is the body velocity vector; Ω - vector of angular velocity of rotation of the reference system, in the case globe- the angular velocity of the Earth's rotation, and [VΩ] - their vector product, which in scalar form looks like this:

F l = 2M | V | | Ω | sin α, where α is the angle between the vectors.

The speed of a body moving on the surface of the globe can be decomposed into two components. One of them lies in a plane tangent to the ball at the point where the body is located, in other words, the horizontal component of the velocity: the second, vertical component is perpendicular to this plane. The Coriolis force acting on a body is proportional to the sine of the geographic latitude of its location. A body moving along a meridian in any direction in the Northern Hemisphere is subject to the Coriolis force directed to the right in its motion. It is this force that causes the right banks of the rivers of the Northern Hemisphere to wash away, regardless of whether they flow north or south. In the Southern Hemisphere, the same force is directed to the left in movement and rivers flowing in the meridional direction wash away the left banks. In geography, this phenomenon is called Beer's law. When the river bed does not coincide with the meridional direction, the Coriolis force will be less by the cosine of the angle between the direction of the river flow and the meridian.

Almost all studies devoted to the formation of typhoons, tornadoes, cyclones and all kinds of vortices, as well as their further movement, indicate that it is the Coriolis force that serves as the root cause of their occurrence and that it sets the trajectory of their movement along the surface of the Earth. However, if the Coriolis force were involved in the creation of tornadoes, typhoons and cyclones, then in the Northern Hemisphere they would have a right rotation, clockwise, and in the Southern Hemisphere, a left rotation, that is, counterclockwise. But typhoons, tornadoes and cyclones in the Northern Hemisphere rotate to the left, counterclockwise, and in the Southern Hemisphere - to the right, clockwise. This absolutely does not correspond to the direction of influence of the Coriolis force, moreover, it is directly opposite to it. As already mentioned, the magnitude of the Coriolis force is proportional to the sine of geographic latitude and, therefore, is maximum at the poles and absent at the equator. Consequently, if it contributed to the creation of vortices of different scales, then they would most often appear in polar latitudes, which completely contradicts the available data.

Thus, the above analysis convincingly proves that the Coriolis force has nothing to do with the process of formation of typhoons, tornadoes, cyclones and all kinds of vortices, the formation mechanisms of which were discussed in previous chapters.

It is believed that it is the Coriolis force that determines their trajectories, especially since in the Northern Hemisphere typhoons, as meteorological formations, deviate to the right during their movement, and in the Southern Hemisphere - to the left, which corresponds to the direction of action of the Coriolis force in these hemispheres. It would seem that the reason for the deviation of typhoon trajectories has been found - this is the Coriolis force, but let’s not rush to conclusions. As mentioned above, when a typhoon moves along the surface of the Earth, a Coriolis force will act on it, as a single object, equal to:

F к = 2MVΩ sin θ cos α, (21)

where θ is the geographic latitude of the typhoon; α is the angle between the speed vector of the typhoon as a whole and the meridian.

To find out the real reason deviations of typhoon trajectories, let's try to determine the magnitude of the Coriolis force acting on the typhoon and compare it with another, as we will now see, more real force.

THE POWER OF MAGNUS

A typhoon moved by the trade wind will be affected by a force that, to the best of the author’s knowledge, has not yet been considered by any researcher in this context. This is the force of interaction of the typhoon, as a single object, with the air flow that moves this typhoon. If you look at the picture depicting the trajectories of typhoons, it will become clear that they move from east to west under the influence of constantly blowing tropical winds, trade winds, which are formed as a result of the rotation of the globe. At the same time, the trade wind not only carries the typhoon from east to west. The most important thing is that a typhoon located in the trade wind is affected by a force caused by the interaction of the air flows of the typhoon itself with the air flow of the trade wind.

The effect of the emergence of a transverse force acting on a body rotating in a flow of liquid or gas impinging on it was discovered by the German scientist G. Magnus in 1852. It manifests itself in the fact that if a rotating circular cylinder flows around an irrotational (laminar) flow perpendicular to its axis, then in that part of the cylinder where the linear speed of its surface is opposite to the speed of the oncoming flow, an area of ​​​​high pressure appears. And on the opposite side, where the direction of the linear velocity of the surface coincides with the speed of the oncoming flow, there is an area of ​​​​low pressure. The pressure difference on opposite sides of the cylinder gives rise to the Magnus force.

Inventors have attempted to harness Magnus's power. A ship was designed, patented and built, on which, instead of sails, vertical cylinders rotated by engines were installed. The efficiency of such rotating cylindrical “sails” in some cases even exceeded the efficiency of conventional sails. The Magnus effect is also used by football players who know that if, when hitting the ball, they give it a rotational movement, then its flight path will become curvilinear. With such a kick, which is called a “dry sheet”, you can send the ball into the opponent’s goal almost from the corner of the football field, located in line with the goal. Volleyball players, tennis players, and ping-pong players also spin the ball when hit. In all cases, the movement of a curved ball along a complex trajectory creates many problems for the opponent.

However, let's return to the typhoon moved by the trade wind.

Trade winds, stable air currents (which blow constantly for more than ten months a year) in the tropical latitudes of the oceans, cover 11 percent of their area in the Northern Hemisphere, and up to 20 percent in the Southern Hemisphere. The main direction of the trade winds is from east to west, but at an altitude of 1-2 kilometers they are supplemented by meridional winds blowing towards the equator. As a result, in the Northern Hemisphere the trade winds move southwest, and in the Southern Hemisphere

To the northwest. The trade winds became known to Europeans after Columbus's first expedition (1492-1493), when its participants were amazed at the stability of strong northeastern winds that carried caravels from the coast of Spain through the tropical regions of the Atlantic.

The gigantic mass of the typhoon can be considered as a cylinder rotating in the air flow of the trade wind. As already mentioned, in the Southern Hemisphere they rotate clockwise, and in the Northern Hemisphere they rotate counterclockwise. Therefore, due to interaction with the powerful flow of trade winds, typhoons in both the Northern and Southern Hemispheres deviate away from the equator - to the north and south, respectively. This nature of their movement is well confirmed by the observations of meteorologists.

(The ending follows.)

AMPERE'S LAW

In 1920, French physicist Anre Marie Ampere experimentally discovered a new phenomenon - the interaction of two conductors with current. It turned out that two parallel conductors attract or repel depending on the direction of the current in them. Conductors tend to move closer together if currents flow in the same direction (parallel), and move away from each other if currents flow in opposite directions (antiparallel). Ampere was able to correctly explain this phenomenon: the interaction of magnetic fields of currents occurs, which is determined by the “gimlet rule”. If the gimlet is screwed in in the direction of current I, the movement of its handle will indicate the direction of the magnetic field lines H.

Two charged particles flying in parallel also form an electric current. Therefore, their trajectories will converge or diverge depending on the sign of the particle charge and the direction of their movement.

The interaction of conductors must be taken into account when designing high-current electrical coils (solenoids) - parallel currents flowing through their turns create large forces that compress the coil. There are known cases when a lightning rod made of a tube, after a lightning strike, turned into a cylinder: it was compressed by the magnetic fields of a lightning discharge current with a force of hundreds of kiloamperes.

Based on Ampere's law, the standard unit of current in SI - ampere (A) - was established. The state standard “Units of physical quantities” defines:

“An ampere is equal to the current strength which, when passing through two parallel straight conductors of infinite length and negligibly small cross-sectional area, located in a vacuum at a distance of 1 m from each other, would cause an interaction force equal to 2 on a section of the conductor 1 m long . 10 -7 N.”

Details for the curious

MAGNUS AND CORIOLIS FORCES

Let us compare the effect of the Magnus and Coriolis forces on the typhoon, imagining it to a first approximation in the form of a rotating air cylinder flown by the trade wind. Such a cylinder is acted upon by a Magnus force equal to:

F m = DρHV n V m / 2, (22)

where D is the diameter of the typhoon; ρ - trade wind air density; H is its height; V n > - air speed in the trade wind; V t - linear air speed in a typhoon. By simple transformations we get

Fm = R 2 HρωV n, - (23)

where R is the radius of the typhoon; ω is the angular speed of rotation of the typhoon.

Assuming as a first approximation that the air density of the trade wind is equal to the air density in the typhoon, we obtain

M t = R 2 Hρ, - (24)

where M t is the mass of the typhoon.

Then (19) can be written as

F m = M t ωV p - (25)

or F m = M t V p V t / R. (26)

Dividing the expression for the Magnus force by expression (17) for the Coriolis force, we obtain

F m /F k = M t V p V t /2RMV p Ω sinθ cosα (27)

or F m /F k = V t /2RΩ sinθ cosα (28)

Taking into account that, according to the international classification, a typhoon is considered to be a tropical cyclone in which the wind speed exceeds 34 m/s, we will take this smallest figure in our calculations. Since the geographic latitude most favorable for the formation of typhoons is 16 o, we will take θ = 16 o and, since immediately after their formation typhoons move almost along latitudinal trajectories, we will take α = 80 o. Let's take the radius of a medium-sized typhoon to be 150 kilometers. Substituting all the data into the formula, we get

F m / F k = 205. (29)

In other words, the Magnus force is two hundred times greater than the Coriolis force! Thus, it is clear that the Coriolis force has nothing to do not only with the process of creating a typhoon, but also with changing its trajectory.

A typhoon in the trade wind will be affected by two forces - the aforementioned Magnus force and the force of the aerodynamic pressure of the trade wind on the typhoon, which can be found from a simple equation

F d = KRHρV 2 p, - (30)

where K is the aerodynamic drag coefficient of the typhoon.

It is easy to see that the movement of the typhoon will be caused by the action of the resultant force, which is the sum of the Magnus forces and aerodynamic pressure, which will act at an angle p to the direction of air movement in the trade wind. The tangent of this angle can be found from the equation

tgβ = F m /F d. (31)

Substituting expressions (26) and (30) into (31), after simple transformations we obtain

tgβ = V t /KV p, (32)

It is clear that the resulting force F p acting on the typhoon will be tangent to its trajectory, and if the direction and speed of the trade wind are known, then it will be possible to calculate this force with sufficient accuracy for a specific typhoon, thus determining its further trajectory, which will minimize the damage caused by it. The trajectory of a typhoon can be predicted using a step-by-step method, with the likely direction of the resulting force being calculated at each point in its trajectory.

In vector form, expression (25) looks like this:

F m = M [ωV p ]. (33)

It is easy to see that the formula describing the Magnus force is structurally identical to the formula for the Lorentz force:

F l = q .

Comparing and analyzing these formulas, we notice that the structural similarity of the formulas is quite deep. Thus, the left sides of both vector products (M& #969; and q V) characterize the parameters of objects (typhoon and elementary particle), and the right sides ( V n and B) - environment (trade wind speed and magnetic field induction).

Physical training

CORIOLIS FORCES ON A PLAYER

In a rotating coordinate system, for example on the surface of the globe, Newton's laws are not satisfied - such a coordinate system is non-inertial. An additional inertial force appears in it, which depends on the linear velocity of the body and the angular velocity of the system. It is perpendicular to the trajectory of the body (and its speed) and is called the Coriolis force, named after the French mechanic Gustav Gaspard Coriolis (1792-1843), who explained and calculated this additional force. The force is directed in such a way that to align with the velocity vector, it must be rotated at a right angle in the direction of rotation of the system.

You can see how the Coriolis force “works” using an electric record player by performing two simple experiments. To carry them out, cut out a circle from thick paper or cardboard and place it on the disk. It will serve as a rotating coordinate system. Let's make a note right away: the player disk rotates clockwise, and the Earth rotates counterclockwise. Therefore, the forces in our model will be directed in the direction opposite to those observed on Earth in our hemisphere.

1. Place two stacks of books next to the player, just above the platter. Place a ruler or straight bar on the books so that one of its edges fits the diameter of the disk. If, with the disk stationary, you draw a line along the bar with a soft pencil, from its center to the edge, then it will naturally be straight. If you now start the player and draw a pencil along the bar, it will draw a curved trajectory going to the left - in full agreement with the law calculated by G. Coriolis.

2. Build a slide from stacks of books and tape to it a thick paper groove oriented along the diameter of the disk. If you roll a small ball down a groove onto a stationary disk, it will roll along the diameter. And on a rotating disk it will move to the left (if, of course, the friction when it rolls is small).

Physical training

THE MAGNUS EFFECT ON THE TABLE AND IN THE AIR

1. Glue together a small cylinder from thick paper. Place a stack of books not far from the edge of the table and connect it to the edge of the table with a plank. When the paper cylinder rolls down the resulting slide, we can expect that it will move along a parabola away from the table. However, instead, the cylinder will sharply bend its trajectory in the other direction and fly under the table!

Its paradoxical behavior is quite understandable if we recall Bernoulli’s law: the internal pressure in a gas or liquid flow becomes lower, the higher the flow speed. It is on the basis of this phenomenon that, for example, a spray gun works: higher atmospheric pressure squeezes liquid into a stream of air with reduced pressure.

It is interesting that human flows also obey Bernoulli’s law to some extent. In the subway, at the entrance to the escalator, where traffic is difficult, people gather in a dense, tightly compressed crowd. And on a fast-moving escalator they stand freely - the “internal pressure” in the flow of passengers drops.

When the cylinder falls and continues to rotate, the speed of its right side is subtracted from the speed of the oncoming air flow, and the speed of the left side is added to it. The relative speed of air flow to the left of the cylinder is greater, and the pressure in it is lower than to the right. The pressure difference causes the cylinder to abruptly change its trajectory and fly under the table.

The laws of Coriolis and Magnus are taken into account when launching rockets, precision shooting over long distances, calculating turbines, gyroscopes, etc.

2. Wrap the paper cylinder with paper or textile tape several turns. If you now sharply pull the end of the tape, it will spin the cylinder and at the same time give it forward motion. As a result, under the influence of Magnus’s forces, the cylinder will fly, describing loops in the air.

Strange changes in the trajectory of the ball seem like a miracle to the average person. But for professional football players, basketball players, and billiard players, such tricks are an indicator of skill. And this is where we remember the laws of physics, which throws up such gifts as the Magnus effect. Initially noticed in aerodynamics, today this law of changing the trajectory of a spherical object has found very wide application. Quite recently, a video appeared on the Internet that clearly demonstrated this physical phenomenon using the example of a basketball. The video received more than 9 million views in two days and fueled interest in the Magnus effect and its incredible applications.

Background

It all started with the fact that the Prussian gunners could not understand why the cannonballs from their cannons constantly hit the wrong places. The rotation of the core in flight with its center of gravity not coinciding with the geometric one distorted the flight path. Isaac Newton wrote about the aerodynamic force influencing the flight of a rotating ball, and Prussian commanders turned to the famous German scientist Heinrich Gustav Magnus (1802-1870) for clarification of the curvilinear trajectories of the ball's flight, who in 1853 gave a scientific explanation of this phenomenon.

The scientist suggested that the problem is not in the center of gravity of the object, but in its rotation. He conducted a series of experiments, and although he did not make any mathematical calculations, he was the first to prove the aerodynamic force that changes the flight path of a rotating body.

After Magnus, Ludwig Prandtl (1875-1953) became interested in this force, who measured strength and speed. His most important achievement is the establishment of the possibility of using the resulting force on a rotating rotor (cylinder) to ensure translational motion. But in practice this idea was implemented by another German - engineer Anton Flettner (1885-1961). More on the rotor sails of Flettner and Cousteau a little later.

The explanation is not for physicists

Considering the laws of Newtonian solid state physics, in simple words The process looks like this. A swirling round object picks up speed, the air in front of the object moves in the direction of its rotation and is pulled along and toward the center. On the other side of the object, the air moves in the opposite direction to the direction of rotation. As a result, the flow moves away and the object displaces air on one side, and the air on the other side forms a response force, but in a different direction, which changes the flight path of the object. The process diagram is shown in the figure above; this is the notorious Magnus effect.

Flettner wind ship

Anton Flettner received a German patent for a rotary vessel on September 16, 1922. And already in October 1926, a real sensation in Kiel Bay was caused by an unusual ship with two large pipes on board and an openwork mast. This was the first Buckau rotary vessel to leave the slipways of the Friedrich Krupp shipbuilding company.

Flettner used the Magnus effect and the force generated when flowing around rotating cylinders and directed perpendicular to the direction of flow. From the side where the direction of the vortex flow created by the rotating body coincides with the direction of the air flow, the force and speed of movement increase sharply. It was precisely these rotors that would later be named after him that the young engineer Flettner replaced the sails with.

The rotors of this vessel were driven by electric motors. Where the rotor rotated against the wind, an area of ​​increased pressure was created. On the opposite side - with a decrease. The resulting force moved the ship.

Buckau passed the test with honor. In 1925 he sailed from Danzig to Scotland in weather conditions when sailing ships did not dare go to sea. The voyage was successful, and the ship's crew was reduced to 10 people, compared to 20 on the sailing ship.

Forced oblivion

A bright future was opening up for Flettner rotors. The success of the project was confirmed by the ship of the Hamburg company “Barbara”. It was a cargo liner, the movement of which was provided by three 17-meter rotors, setting a speed of 13 knots in a wind of 4-6 forces.

Despite the apparent success of the project, it was forgotten for a long time. And there are several reasons for this. Flettner himself lost interest in shipping and became interested in aviation during the Great Depression of the 1920s.

Reanimation of ships with rotor installations

A continuation of Flettner's rotary vessel is the turbosail of Jacques-Yves Cousteau. Famous explorer and a fighter for environmentally friendly means of transportation in April 1885 launched the Alcyone ship, equipped with patented turbosails, in which the Magnus effect was used. This ship is still underway today.

Unfortunately, Cousteau's followers were not very interested in rotary installations on ships, and interest in them faded again. They were remembered with the onset of the oil crisis, and in 2010 a third vessel with rotary installations was launched. This is Enercon's heavy 130m E-Ship 1 with four Flettner rotors. Today it transports wind generators from Germany to European countries, can withstand up to 9 tons of cargo and reaches a speed of 17 knots. The crew is only 15 people.

The ship companies Wind Again (Singapore), Wartsila (Finland) and some others became interested in rotary installations. It looks like oil shortages and an alarming warming climate will play a role in the return of wind propulsion to modern ships.

Application in aircraft industry

The use of the Magnus effect in aviation was implemented in various design solutions. The simplest forms used shaft-shaped wings that rotated during flight. Among the founders of this direction was the Austrian inventor Karl Gligorin, who proposed installing a fairing on the rotor that follows the shape of the wing. In Amsterdam, E.B. worked on similar projects. Wolf, Americans John D. Gerst and K. Popper even tested their aircraft with shaft-shaped wings in 1932.

The North American-Rockwell YOU-10A Bronco, converted to rotating shafts in 1964, proved to be functional. It was the project of a professor from Peru, Alberto Alvarez-Calderon. However, the prototype had more disadvantages than advantages.

Despite efforts, the Magnus effect did not take root in aviation. The practical use of rotor-type wings is associated with a number of problems and is not yet economically justified.

Magnus effect and wind turbines

The development of the alternative energy sources industry is especially important in our time. And in this industry, the Magnus effect has been used. Blade wind generators are being replaced by rotor units, which are most effective at frequent and low wind speeds of 2-6 m/s. They are based on an axis around which the cylinders rotate. The first such installation, manufactured by Aerolla, appeared near Minsk (Belarus) in 2015. Its power was 100 kW, the diameter of the turbine rotor was 36 meters. Operates at a design wind speed of 9.5 m/s.

Work in this direction continues at the Novosibirsk Institute of Applied Mechanics SB RAS, and there are already prototypes of wind generators that use the Magnus effect with a power of up to 2 MW.

Not quite a common use

This effect of changing the trajectory of the ball is widely used in sports: topspin shots and “dry sheet” in football, the Hop Up system in airsoft.

The Magnus effect is widely used in aircraft model design today. For example, an airplane made from cardboard, an electric motor and paper fast food cups was designed by the PeterSripol channel.

The Magnus effect is used in the production of kites. For example, a snake in the form of a pinwheel designed by D. Edwards or S. Albertson.

But for “hurricane hunters” this physical phenomenon can become very dangerous. If the bottom between the car and the ground is not well sealed, then through the gap a hurricane wind can create a huge lifting force that can easily lift the car into the air.

Chapter 3 Magnus effect and Lorentz force

Similar to the Zhukovsky-Chaplygin wing, the Magnus force arises due to the difference in pressure of the medium flow on the surface of the rotating cylinder. This effect was discovered by the German scientist H. G. Magnus in 1852. In Fig. Figure 8 shows a diagram of the addition of the velocity vectors of the medium flow and the surface of the rotating cylinder.

Rice. 8. Magnus effect for a rotating cylinder

In the upper part of the cylinder (end view), the direction of movement of the flow of the medium and the surface of the rotating cylinder coincide, and in the lower part of the cylinder, its surface moves towards the flow of the medium. Since the flow in the lower part of the rotating cylinder is slowed down by its surface moving towards the flow, the dynamic pressure of the flow decreases, and the static pressure of the medium on the surface increases, in accordance with Bernoulli’s law on the total pressure of the flow. As a result, the pressure of the medium on the upper part of the rotating cylinder becomes less than on the lower part of the cylinder. A lifting force arises, as with the effect of a wing having a Zhukovsky-Chaplygin profile.

The Magnus effect is well known to football and tennis players, who use it to create a curved flight path for a spinning ball. With a “curve hit,” the ball flies straight but rotates around its axis. In flight, a stream of air flows towards it, which creates the Magnus effect, and the flight path is curved. As a result of such a blow, the ball flies along a curve and hits the wrong place where it is expected...

Let us assume that we have constructed a closed flow of a moving medium (air, water, etc.), in which several rotating cylinders are placed, as shown in Fig. 9. Let us assume that the rotation of each cylinder is provided by an independent electric drive, with adjustable speed and direction of rotation.

Rice. 9. Propulsion based on the Magnus effect

Unlike a design with a wing installed in a flow of a moving medium, this scheme has an important advantage: the magnitude and direction of the axial lift force can be changed by changing the speed and direction of rotation of the cylinders. The speed and direction of the circulating flow can not be changed, which provides significant advantages in the speed and maneuverability of this vehicle. This type of propulsion unit can be installed vertically or horizontally, creating traction force.

An interesting analogy with the Magnus effect arises when considering the electromagnetic phenomenon known as the Lorentz force: a current-carrying conductor in a magnetic field is subjected to a force in the direction shown in Fig. 10. Previously there was no clear explanation for the reason for the appearance of this force. Assuming analogies with the Magnus effect, we can interpret the Lorentz force as a result of the pressure gradient of the ethereal medium. This was first shown in the report in 1996.

Rice. 10. Lorentz force, as a result of the ether pressure gradient

However, in the diagram in Fig. 10, we get a picture inverse to the superposition of vectors, which was shown in Fig. 8. The Magnus force acts on a cylinder rotating in a flow of medium in the direction of coordinated motion of the surface of the cylinder and the medium. In Fig. Figure 10 shows that the Lorentz force acts in the direction of the opposing superposition of vectors. Why?

The fact is that the vectors in Fig. 10 are shown conventionally, according to the accepted designations of the vectors of electric current (flow of positively charged particles) and magnetic field. The direction of movement of real flows of electrons and ether particles (magnetic field vectors) differs from the conventional designations. Fundamentally, the effect is created similarly to the Magnus effect, due to the pressure gradient of the medium due to different relative speeds, but electromagnetic systems use the ethereal medium, not air or water.

It is important to note that an electron or other charged particle that creates a magnetic field when moving is a rotating object. It would be more accurate to consider its linear movement as a helical line, a right or left spiral, depending on the sign of the electric charge of a given particle of matter.

A lot has been written about the structure of the electron, but I would like to recommend to the reader the work of father and son Polyakov. These authors examined in their book “Experimental Gravitonics” the structure of the electron, and showed that it can be represented as a photon of circular polarization closed on itself, that is, as a dynamic process of movement of an electromagnetic wave of circular polarization in a closed toroidal space. Later, we will cover this issue in more detail. Here we only briefly note that, with this consideration, the appearance of a magnetic field when a charged particle moves in the ether has a clear analogy with the disturbance of the physical environment that occurs when a rotating cylinder or ball moves in a given environment.

We can say that the interaction of the external magnetic field across which an electrically charged particle moves with its own magnetic field deflects the particle in the same way as a flow of air deflects a spinning ball, namely, due to the creation of a pressure gradient of the medium on a particle of matter moving in it.

In this case, Lorentz forces and Ampere forces are external forces in relation to the current-carrying conductors on which they act, that is, they can ensure their movement in space.

These interesting analogies between aerodynamics and aetherdynamics provide many constructive ideas.