Technical and scientific myths. Why planes fly

In today's world, many people are interested in science and technology and try at least in General terms, to understand how things work that surround them. Thanks to this desire for education there is a scientific and educational literature and websites.

And since reading and understanding the ranks of of formulas most people difficult, it is presented in such issues of the theory inevitably undergo considerable simplification in an attempt to convey to the reader the "essence" of ideas using simple and clear explanation that is easy to comprehend and remember.

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Unfortunately, some of these "simple explanations" are fundamentally wrong, but be so "obvious" that without the particular doubt, begin to wander from one edition to another and often become the dominant view, despite its falsity.

As one of the examples try to answer a simple question: "where does the lift force in the wing of the plane?"

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If Your explanation included "different length upper and lower surfaces of the wing", "a different speed of air flow on the upper and lower edges of the wing" and "Bernoulli principle," then I have to tell You that You likely were the victim of a popular myth, which is taught even in the school curriculum.

Let's first recall what it is

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An explanation of wing lift within the framework of the myth as follows:

1. The wing has an asymmetrical profile top and bottom

2. A continuous stream of air the wing is divided into two parts, one of which passes over the wing and the other under it

3. We consider laminar flow in which the flow of air tightly to the surface of the wing

4. Since the profile is asymmetric, in order to get back together with the wing at one point the "upper" thread is necessary to do a bigger way than the "lower", so the air above the wing has to move with greater speed than under it

5. According to the law of Bernoulli the static pressure in the flow decreases with increasing flow rate, so the flow over the wing static pressure will be lower

6.The pressure difference in the flow under the wing and above it is the lifting force

A demonstration of this idea is quite simple flexible and lightweight sheet of paper. Take a sheet, holds it to his mouth, and when the wind blows over it to create a model in which the flow of air over the sheet of paper is moving faster than below it. And voila — with the first or second attempt, a sheet of paper defying gravity is definitely coming under the influence of the lift force upwards. The theorem is proved!

... or is it not?..

There is a story (I really don't know how true is it) that one of the first people who offered a similar theory was none other than albert Einstein. According to the story in 1916 he wrote the relevant article and based on it proposed its version of a "perfect wing," which, in his opinion, maximize the difference of velocities over the wing and under it, and in profile looked like this:

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In the wind tunnel blew a full scale model of the wing with this profile, but alas — its aerodynamic qualities proved to be extremely bad. In contrast — a paradox! — many wings has a symmetrical profile in which the path of air over the wing and under it had to be fundamentally the same.

In the reasoning of Einstein clearly something was wrong. And probably the most obvious manifestation of this abnormality was that some pilots as trick began to fly their planes upside down.

The first planes that tried to roll over in flight, had problems with fuel and oil that did not flow where it is needed, and flowed where it's not necessary, but once in the 30-ies of the last century of aerobatic enthusiasts were created fuel and oil system capable of operating for a long time inverted, flying upside down became a common sight at air shows.

In 1933, for example, one American and even flew upside down from San Diego to Los Angeles. Somehow magically inverted the wing continues to generate lift force, directed upwards.

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Look at this picture showing a plane similar to the one on which the record was set flying in the inverted position. Note regular profile of the wing (Boeing-106B airfoil) which, according to the reasonings above, must create a lifting force from the bottom surface to the top.

So, our simple model of the lift force of the wing there are some difficulties, which could roughly be reduced to two simple observations:

1. The lift of the wing depends on its orientation relative to the oncoming airflow — angle of attack

2. The symmetric profiles (including banal flat sheet of plywood) also create lift

What is the cause of the error? It turns out that in the beginning of the article, the reasoning is completely wrong (and generally speaking, just taken from the ceiling) item number 4. Visualization of the airflow around the wing in a wind tunnel shows that the flow front is divided into two parts wing, not closed back over the edge of the wing.

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Simply put, the air "knows" that he needs to move with a particular velocity around the wing to perform some condition which to us seems obvious. Although the flow speed above the wing is higher than below it, this is not the reason for the formation of lifting force as a consequence of the fact that above the wing there is a region of low pressure, and under the wing — area of increased.

Coming from a region of normal pressure, in the sparse region, the air is accelerated by the pressure difference, and once in the area with high pressure is inhibited. An important example of such a "non-bernolakovo" behavior, demonstrate the airfoil: when approaching the wing to the ground its lifting force increases (the pressure drawn in the ground), whereas in the framework of the "bernoullis" arguments, the wing on a couple of the earth form a sort of narrowing tunnel that in the framework of naive reasoning would be to disperse the air and to pull through this wing to the ground just as it is done in a similar sense in discussion of the "mutual attraction passing on parallel courses the steamers."

And in the case of the ekranoplan, the situation is in many respects even worse, as one of the "walls" of the tunnel moving at high speed towards the wing, further "purging" the air and contributing to further reduction in lifting force. However, the actual practice of "ground effect" shows the opposite trend, demonstrating the danger of reasoning about the lifting force is built on a naive attempt to guess the velocity field of the airflow around the wing.

Oddly enough, much more close to the truth explanation gives another incorrect theory of lift forces rejected in the nineteenth century. Sir Isaac Newton assumed that the interaction of the object with impinging air flow can be modeled by assuming that the incoming flow is composed of tiny particles hitting the object and Bouncing off it.

An oblique arrangement of the object relative to the incoming flow, the particles will be preferentially reflected by the object down and to the law of conservation of momentum whenever the deviation of the particle flow down the object is to get the momentum up. The perfect wing in such models would be flat kite is inclined to the oncoming flow:

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The lifting force in this model arises due to the fact that the wing directs some air flow down, this redirect requires a certain force to the air flow, and lift force is the force of counteraction from the air flow on the wing. And while the initial "shock" of the model is generally speaking incorrect, in such a generalized formulation of this explanation is really true.

Any wing works due to the fact that deflects part of the air flow down and this, in particular, explains why the lift of the wing is proportional to the density of the air flow and to the square of its speed. This gives us the first approximation to the correct answer: the wing creates lift because the flow lines of the air after passing the wing on average are pointing down. And the more we turn the flow down (for example by increasing the angle of attack), the lift force is greater.

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A bit unexpected result, right? However, it still does not bring us closer to understanding why the air after the passage of the wing is moving down. The fact that the Newtonian impact model is wrong, it has been shown experimentally by experiments, which showed that the real flow resistance is lower than that predicted by the Newtonian model, and the generated lifting force — is higher.

The reason for this discrepancy is that in Newton's model of air particles does not interact with each other, while the real streamlines can't cross each other, as shown in the figure above. "Bouncing" under the wing down conventional "air particles" collide with others and begin to "push" them from the wing before they'd collide and the particles of the air current caught above the wing to "push" the particles of air are located below in the empty space behind the wing:

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In other words, the interaction "batted" and "incoming" flow under the wing creates a high pressure region (red), and shadow, pushing the wing in the flow, forms an area of low pressure (blue). The first area deflects the flow under the wing down before this thread comes in contact with its surface, and the second causes the flow over the wing to bend down, although it with the wing not in contact at all.

The cumulative pressure of these regions along the contour of the wing actually forms eventually lifting force. An interesting point is that inevitably emerge in front of the wing area of high pressure in a properly designed wing is in contact with its surface only the small area at the front edge of the wing, whereas the area of high pressure under the wing and low pressure above it in contact with the wing at a significantly large area.

In the result, the lift of the wing is formed by two areas around the upper and lower surfaces of the wing can be much greater than the force of air resistance, which provides exposure to the high pressure region located in front of the front edge of the wing.

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Since the presence of areas of different pressure curves the streamlines of air, it is often convenient to identify these areas on this curve. For example, if the streamlines above the wing "bent down", in this region there is a pressure gradient directed from top to bottom. And if at a sufficiently large distance over the wing the pressure is atmospheric, then as you get closer to the wing top-down pressure should fall directly above the wing it will be below atmospheric.

Having considered a similar "bending down", but under the wing, we find that if you start with a fairly low point under the wing, then, approaching the wing from the bottom up, we come to the area of the pressure to be above atmospheric. Similarly, a "repulsion" of the streamlines in front of the front edge of the wing corresponds to the existence before the edge of the Plenum. Within this logic we can say that the wing generates lift, curving streamlines of air around the wing.

Because the streamlines of the air "stick" to the surface of the wing (the Coanda effect) and to each other, by changing the wing profile, we are forcing the air to move around it in a curved trajectory and shape because of this, we need the gradient of pressure. For example, to ensure flight upside down is enough to create the desired angle of attack, pointing the nose of the aircraft away from the ground:

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Again a bit of a surprise, right? However, this explanation is closer to the truth than the original version of "the air is accelerated over the wing, because on the wing he needs to go a greater distance than under him." In addition, the terms easier to understand the phenomenon which is called "stall" or "stall of the airplane". Under normal circumstances, increasing the angle of attack of the wing thereby we increase the curvature of the air flow and accordingly the lifting force.

The price for this is the increase in aerodynamic drag as an area of low pressure has gradually shifted from the "above the wing" to "slightly behind the wing" and accordingly begins to slow down the plane. However, after a certain limit, the situation suddenly changes drastically. The blue line in the chart above the coefficient of lift, red drag coefficient, the horizontal axis corresponds to the angle of attack.

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The fact that the "stickiness" of flow to a streamlined surface is limited, and if we try too hard to bend the flow of air, it will "break away" from the surface of the wing. Formed behind the wing area of low pressure begins to "suck" no air flow coming from the leading edge of the wing, and the air from the region behind the wing, and the lifting force generated by the upper part of the wing completely or partially (depending on the gap) will disappear, and the drag will increase.

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For conventional aircraft the stall is an extremely unpleasant situation. Lifting force of the wing decreases with decreasing speed of the aircraft or reduction of air density, and in addition the rotation of the airplane requires a greater lifting force than just horizontal flight. In normal flight all of these factors exactly compensate for the range of angle of attack. The slower the plane flies, the less dense the air (the plane climbed to a higher altitude or getting into the hot weather) and the steeper the turn, the more you have to do this angle.

And if a careless pilot beyond a point, the lift rests on the "ceiling" and becomes insufficient to keep the plane in the air. Adds to the problems and the increased air resistance, which leads to loss of speed and further reduce the lifting force. As a result, the plane begins to fall — "fall down".

Along the way, may have problems with management due to the fact that the lift force is redistributed on the wing and begins to try to "rotate" a plane or the control surfaces are in a region disrupted the flow and fail to generate a sufficient actuation force. And in a sharp turn, for example, a thread can break with only one wing, causing the plane will just start to lose altitude, but also spin — in spin.

The combination of these factors remains a frequent cause of aircraft accidents. On the other hand, some modern combat aircraft are being designed in such a special way to retain control in such a supercritical modes of attack. This allows such fighters if necessary, to brake in the air.

Sometimes it is used for braking in straight flight, but often demand in the bends, because the smaller the speed, the less other things being equal, the turning radius of the aircraft. And Yes, You guessed it — it's the same "maneuverability", which is deservedly proud of the experts designed the aerodynamics of the domestic fighters 4 and 5 generations.

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However, we still have not answered the main question: where, in fact, occur areas of high and low pressure around the wing to the oncoming airflow? After all, both phenomena ("flow sticking to the wing and over the wing the air travels faster"), which may explain the flight, are the result of a certain distribution of pressure around the wing, and not its cause. But why it formed such a picture of the pressures, and not some other?

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Unfortunately, the answer to this question inevitably requires the involvement of mathematics. Let's imagine that our wing is infinitely long and uniform along the entire length, so that the movement of air around him can be modeled in a two-dimensional slice. And let's assume for starters that the role of our wing is infinitely long cylinder in fluid flow.

Because of the infinite cylinder this task can be reduced to the consideration of the flow of circles in the plane flow of an ideal fluid. For such a trivial and idealized case there is an exact analytical solution that predicts, at a fixed cylinder overall impact of the liquid on the cylinder is zero.

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Now let's look at some tricky transformation of the plane into itself, that of mathematics called conformal mapping. Is possible to find a transformation, which on the one hand preserves the equations of motion of fluid flow, and on the other transformerait round in shape, having a similar wing profile. Then transformed by the same transformation of streamlines of fluid to cylinder be the solution for the fluid flows around our makeshift wing.

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Our original circle in the fluid flow has two points at which the streamlines in contact with the surface of the circle, and therefore the same two points will exist on the surface of the profile after application to cylinder conversion. And depending on the rotation of the flow relative to the original cylinder ("angle of attack") they will be located in different places of the surface formed a "wing". And almost always this will mean that some of the streamlines of fluid around the profile should go around the rear edge of the wing, as shown in the picture above.

It is potentially possible for an ideal fluid. But not for real.

The presence of real liquid or gas even for small friction (viscosity) leads to the fact that a thread like the one shown in the picture immediately violated — upper flow will move the point where the line current is in contact with the surface of the wing for as long as it is not strictly on the trailing edge of the wing (the postulate of the Zhukovsky-Chaplygin, he's aerodynamic condition Kutta). And if you convert the "wing" back to "cylinder", then the shifted line current will be approximately:

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But if the viscosity of the fluid (or gas) is very small, resulting in this way a solution must be appropriate for cylinder. And it turns out that this solution will actually find, if we assume that the cylinder is rotated. That is, the physical limitations associated with overflow of liquid around the trailing edge of the wing lead to the fact that the fluid motion of all the possible solutions will strive to come to one particular decision in which part of the liquid flow rotates around the equivalent of the cylinder, interrupting him in a strictly defined point.

And since the rotating cylinder in a fluid flow creates a lifting force that creates it and the corresponding wing. The component of movement corresponding to that "the speed of rotation of the cylinder" is called the circulation of the flow around the wing, and the theorem Zhukovsky says that the same characteristic can be generalized for arbitrary wings, and allows us to quantitatively calculate the lift of the wing.

Under this theory, the lift of the wing is provided by circulation of air around the wing, which is created and maintained by the moving wing by the above-mentioned friction forces, which excludes the flow of air around the sharp trailing edge.

Amazing result, isn't it?

The described theory is of course highly idealized (infinitely long uniform wing, an ideal homogeneous incompressible flow of gas / fluid without friction around the wing), but gives a fairly accurate approximation to the actual wings and conventional air. Just do not take part in its circulation as an indication that the air is really spinning around the wing.

Circulation is just a number, showing how needs vary according to the speed of the flow on the upper and lower edges of the wing, to the solution of the motion of the fluid flow provided the separation of the streamlines is strictly on the trailing edge of the wing. It is also important to perceive "the principle of a sharp trailing edge" as a necessary condition for the occurrence of the lifting force: a sequence of reasoning is that it sounds like "if sharp wing trailing edge, the lift is generated-so."

Let's try to summarize. The interaction of the air with the wing around the wing creates high and low pressure, which distort the air flow so that it hugs the wing. The sharp trailing edge of the wing leads to the fact that in the perfect flow of all the potential solutions of the equations of motion is only one particular precluding the flow of air around the sharp trailing edge.

 



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This decision depends on the angle of attack of a conventional wing is an area of low pressure over the wing and area of high pressure beneath. The corresponding pressure difference generates the lift of the wing causes the air to move faster over the top edge of the wing and slows down the air under the bottom. Quantitatively, the lift force is convenient to describe numerically using the difference of velocities over the wing and under it in the form of features called "circulation" flow.

In accordance with Newton's third law acting on wing lift force means that the wing deflects downward a portion of the incoming air flow in order that the plane could fly, part of the surrounding air must continuously move downward. Based on this moving downward flow of the air plane and "flying".

The simple explanation of "air that needs to pass through a longer path above the wing than under it" — is wrong.published  

 

 



Source: geektimes.ru/post/279734/