Calculation of aircraft lift. Where does lift come from? About lift

Everyone knows that a wing creates lift only when it moves relative to the air. Those. The nature of the air flow around the upper and lower surfaces of the wing directly creates lift. How does this happen?

Consider the wing profile in the air flow:

Here, the flow lines of elementary streams of air are indicated by thin lines. The profile to the flow lines is under angle of attack ? is the angle between the profile chord and the undisturbed flow lines. The perimeter of the upper part of the wing is larger than the lower one. Because of this, based on continuity considerations, the flow velocity at the top of the edge is greater than at the bottom. Then it turns out that the pressure above the wing is less than below it. The phenomenon of decreasing pressure with increasing flow velocity has long been studied and described by Daniel Bernoulli in 1738. Based on the result of his work, namely Bernoulli’s equation, this fact becomes quite obvious:

Where p-- gas pressure at a point; ? -- gas density; v-- gas flow speed; g-- acceleration of gravity; h-- height relative to the origin; ? -- adiabatic constant.

It turns out that at different points in the profile the air presses on the wing with different forces. The difference between the local pressure at the surface of the profile and the air pressure in the undisturbed flow can be represented in the form of arrows perpendicular to the contour of the profile, so that the direction and length of the arrows are proportional to this difference. Then the pressure distribution picture along the profile will look like this:

Here you can clearly see that on the lower generatrix of the profile there is excess pressure - air backpressure. On the top, on the contrary, there is a vacuum. Moreover, it is greater where the flow velocity is higher. What is noteworthy here is that the magnitude of the vacuum on the upper surface is several times greater than the pressure on the lower surface. The vector sum of all these arrows creates aerodynamic force R, with which the air acts on the moving wing:

Decomposing this force into vertical Y and horizontal X components, we obtain lift wing and the force of its drag. From the pressure distribution picture it is clear that a large proportion of the lift force is formed not from the support on the lower generatrix of the profile, but from the vacuum on the upper one.

The point of application of force R depends on the nature of the pressure distribution over the surface of the profile. As the angle of attack changes, the pressure distribution will also change. Along with it, the vector sum of all forces in absolute magnitude, direction and point of application will also change. By the way, the latter is called center of pressure. Closely related to it is the concept focus profile. For symmetrical profiles these points coincide. For asymmetrical ones, the position of the center of pressure on the chord changes when the angle of attack changes, which makes calculations very difficult. To simplify them, the concept of focus was introduced. At the same time, the resultant of the aerodynamic forces was divided not into two components, but into three - the wing moment was added to the lift and drag forces. This seemingly illogical technique made it possible, by placing the point of application of the lifting force at the focus of the profile, to fix its position and make it independent of the angle of attack. The technique is convenient, but we must not forget about the wing that appears at this moment.

The vacuum at the top of the profile can not only be measured with instruments, but under certain conditions can also be seen with one’s own eyes. As is known, with a sharp expansion of air, the moisture contained in it can instantly condense into water droplets. Anyone who has been to an air show could see how, during sharp maneuvering of the aircraft, streams of white veil break off from the upper surface of the wing. This is water vapor, condensed during discharge into small droplets of water, which very quickly evaporate again and become invisible.

Eh! I wish I could take off!..

I have a cool ginger cat at home. He is “moderately well-fed,” as befits a cozy domestic cat, and although he runs around like an electric broom, he has a not-quite-feline property: he is afraid of heights. For this reason, alas, he cannot be a flying cat, but sometimes he apparently wants to rise into the air, if only to jump onto the sideboard. However, excess weight, unfortunately, does not contribute to this, so sometimes you have to help the poor animal, that is, lift it with your hands and put it where its soul is so eager.

Well, what, you ask, do a cat and an airplane have in common? Yes, in general, nothing, except for one very important thing. They both have a weight that pulls them towards the ground. And in order to climb some onto the sideboard, and some higher, you need strength that will overcome this weight. For my seven-kilogram cat, this is the strength of my hands, but for a multi-ton “iron bird” this is known to everyone. Where does it come from? Everything, in general, is quite simple :-)…

Let's start with a “simple beginning” :-). The main role in this matter is played by the wing of the aircraft (namely, a wing consisting of two consoles, and not wings, in continuation of my other one). For simplicity, let's consider the classic aerodynamic one.

Aerodynamic lift

The air flowing around an airplane wing is divided into two flows: above the wing and below it. The lower stream flows on as if nothing had happened, and the upper stream narrows. After all, the wing profile is convex on top! And now, in order for the same amount of air to pass through the upper flow and in the same time as in the lower flow, it needs to move faster, because the flow itself has become narrower. Next, Bernoulli’s law comes into force: the higher the flow speed, the lower the pressure in it and, accordingly, vice versa. This law is very simply illustrated. If you take a not too narrow horizontal hose (sleeve) made of thin transparent rubber and pour water into it under slight pressure. What will you see? Nothing special, the water will just quickly pour out through the other end. But if at this other end there is a half-closed tap, then you will immediately see that water is pouring out, but slowly and the walls of the sleeve have swelled, that is, the flow rate has decreased and the pressure has increased.

So... When moving in the air flow above the wing, the pressure is less than below it. Because of this difference, . It pushes the wing of the plane and, accordingly, the plane itself upward. The higher the speed, the greater the lift. And if it is equal to the weight, then the plane flies horizontally. Well, the speed depends on the operation of the aircraft engine. By the way, the pressure drop over the top of the wing can be seen with your own eyes.

Condensation of water vapor over the upper surface of the wing as a result of a sharp drop in pressure

In a sharply maneuvering aircraft (usually this happens at an air show), something like streams of a white veil appear above the upper surface of the wing. This is due to the rapid drop in pressure and condenses the water vapor in the air.

By the way, I can’t help but recall another simple, but very accurately illustrating the theory of this issue, school experience. If you take a small narrow sheet of paper by its short side and, bringing it to your mouth, blow horizontally over the sheet, then the sagging sheet will immediately rise quickly. The same lifting force is to blame for this. We blow over a leaf - the flow accelerates, which means the pressure in it drops, but under the leaf it remains the same. It lifts the leaf to a horizontal position. A process fundamentally similar to the work of a profile.

Well, that seems to be all? Can I fly? Despite the completely logical explanation given above (in my opinion :-)), I would say that it is unlikely :-). It must be understood that the described case is still of a private nature. After all, the profile can be symmetrical, then there will not be such a distribution of pressure and vacuum above and below it.

In addition, such a profile can also be located at an angle to the flow (which most often happens). And this very angle, which is called the angle of attack, will play a large role in the formation of the lifting force of the wing, which itself will be of a different nature. About this in. And this will be a “simple continuation” :-).

In fact, of course, the complete theory of this issue is much more complicated and Bernoulli’s law, explained in detail, cannot be done here. This is already the field of physics and aerodynamics, because in our considered case the case itself is . In the near future we will touch a little on this area with its terms and concepts, but a deeper study requires, so to speak, communication with the fundamental sciences.

Postscript after a year.

20.11.12 My website-writing hobbies are now almost a year old. And so, it was necessary to introduce some clarification into this, one of my very first articles. It seems that the people who read it are limited to this. This approach is incorrect, because after it you must definitely read the next article in the same section, written almost immediately after the first. The article “with a cat” 🙂 is a simplified version, and I mentioned this (here the angle of attack is zero), this is something like an introduction to aerodynamics (also, by the way, as simplified as possible :-)), which is why the presentation style is so free :-). However, for a correct understanding of the issue, it cannot exist without the second one.

Due to my inexperience at the time, I said this somewhat indistinctly, and, most importantly, I did not put a link to the “simple continuation”... I’m putting it now. I apologize to readers who are not too knowledgeable (experienced ones already know everything without me :-))... I will be glad to see you on my website :-)...

Photos are clickable.

$\backslash mathbf(Y)+\backslash mathbf(P)\; =\; \backslash oint\backslash limits\_(\backslash partial\backslash Omega)p\backslash mathbf(n)\; \backslash ;\; d\backslash partial\backslash Omega$

• Y is the lifting force
• P- this is traction,
• $\backslash partial\backslash Omega$- profile border,
• p- pressure value,
• n- normal to profile

Lift coefficient

$Y\; =\; C\_y\; \backslash frac(\backslash rho\; V^2)(2)\; S$

$Y$- lifting force (N) $C\_y$- lift coefficient = 0.5...1.5 $\backslash rho$- air density at flight altitude (kg/m³) $V$- free flow speed (m/s) $S$- characteristic area (m²)

This Coefficient, the value of which according to Smeaton’s calculations was 1.005, was used for more than 100 years, and only the experiments of the Wright Brothers, during which they discovered that the lift force acting on gliders was weaker than calculated, made it possible to refine the “Smeaton Coefficient” to a value of 1.0033.

When calculating using this formula, it is important not to confuse the weight and mass density of air. Weight density under standard atmospheric conditions (at ground level at a temperature of +15 ° C) is equal to $\backslash rho$=1.225 kg/m3. But in aerodynamic calculations, the mass density of air is often used, which is equal to 0.125 kg*s 2 /m 4. In this case, the lifting force Y is obtained not in newtons (N), but in kilograms (kg). Books on aerodynamics do not always clarify what density and dimension of lift we are talking about, so in controversial situations you need to check the formulas, reducing the units of measurement.

Myths and misconceptions

The popular myth's explanation of wing lift is as follows:

1. The wing has an asymmetrical profile at the bottom and top
2. A continuous flow of air is divided by the wing into two parts, one of which passes above the wing and the other below it.
3. We consider a laminar flow in which the air flow is tightly adjacent to the surface of the wing
4. Since the profile is asymmetrical, in order to converge behind the wing at one point again, the “upper” flow needs to travel a longer distance than the “lower” one, so the air above the wing has to move at a higher speed than below it
5. According to Bernoulli's law, the static pressure in the flow decreases with increasing flow speed, so in the flow above the wing the static pressure will be lower
6. The difference in pressure in the flow under the wing and above it constitutes the lift force

But we have all probably seen airplanes flying upside down in an inverted position at air shows. They don't fall, and the inverted wing still creates lift.

What is the reason for the error? It turns out that in the above reasoning, point No. 4 is completely incorrect (and generally speaking, simply taken out of thin air). Visualization of air flow around a wing in a wind tunnel shows that the flow front, divided into two parts by the wing, does not close back behind the wing edge at all.

Simply put, the air “does not know” that it needs to move at a certain speed around the wing in order to fulfill some condition that seems obvious to us. And although the flow speed above the wing is indeed higher than below it, this is not the cause of the formation of lift, but a consequence of the fact that there is an area of ​​​​low pressure above the wing, and an area of ​​increased pressure below the wing. When air enters a rarefied area from an area of ​​normal pressure, it is accelerated by the pressure difference, and when it enters an area with increased pressure, it is decelerated. An important particular example of such “non-Bernoullevian” behavior is clearly demonstrated by ekranoplanes: as the wing approaches the ground, its lifting force increases (the area of ​​​​high pressure is pressed by the ground), while within the framework of “Bernoullevian” reasoning, the wing paired with the ground forms something like a narrowing tunnel that within the framework of naive reasoning, it would have to accelerate the air and thereby attract the wing to the ground, just as is done in similar reasoning about “the mutual attraction of steamships passing on parallel courses.” Moreover, in the case of an ekranoplan, the situation is in many ways even worse, since one of the “walls” of this tunnel moves at high speed towards the wing, thereby further “accelerating” the air and contributing to an even greater reduction in lift. However, the real practice of the “screen effect” demonstrates the exact opposite trend, clearly demonstrating the danger of the logic of reasoning about lift based on naive attempts to guess the field of air flow velocities around the wing.

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Excerpt characterizing lifting force

“Another fine for Gallicism,” said the Russian writer who was in the living room. – “The pleasure of being not in Russian.
“You don’t do anyone any favors,” Julie continued to the militiaman, not paying attention to the writer’s remark. “I’m to blame for the caustique,” ​​she said, “and I’m crying, but for the pleasure of telling you the truth I’m ready to pay more; I’m not responsible for Gallicisms,” she turned to the writer: “I have neither the money nor the time, like Prince Golitsyn, to take a teacher and study in Russian.” “Here he is,” said Julie. “Quand on... [When.] No, no,” she turned to the militia, “you won’t catch me.” “When they talk about the sun, they see its rays,” said the hostess, smiling kindly at Pierre. “We were only talking about you,” Julie said with the freedom of lies characteristic of secular women. “We said that your regiment will probably be better than Mamonov’s.”
“Oh, don’t tell me about my regiment,” answered Pierre, kissing his hostess’s hand and sitting down next to her. - I'm so tired of him!
– Surely you will command it yourself? – said Julie, slyly and mockingly exchanging glances with the militiaman.
The militiaman in the presence of Pierre was no longer so caustique, and his face expressed bewilderment at what Julie’s smile meant. Despite his absent-mindedness and good nature, Pierre’s personality immediately stopped all attempts at ridicule in his presence.
“No,” Pierre answered laughing, looking around his large, fat body. “It’s too easy for the French to hit me, and I’m afraid I won’t be able to get on the horse...
Among the people being sorted out for the subject of conversation, Julie's company ended up with the Rostovs.
“They say their affairs are very bad,” said Julie. - And he is so stupid - the count himself. The Razumovskys wanted to buy his house and his property near Moscow, and all this drags on. He is treasured.
“No, it seems that the sale will take place one of these days,” someone said. – Although now it’s crazy to buy anything in Moscow.
- From what? – said Julie. – Do you really think that there is a danger for Moscow?
- Why are you going?
- I? That's strange. I’m going because... well, because everyone is going, and then I’m not Joan of Arc or an Amazon.
- Well, yes, yes, give me some more rags.
“If he manages to get things done, he can pay off all his debts,” the militiaman continued about Rostov.
- A good old man, but very pauvre sire [bad]. And why do they live here for so long? They had long wanted to go to the village. Does Natalie seem to be well now? – Julie asked Pierre, smiling slyly.
“They are expecting a younger son,” said Pierre. “He joined Obolensky’s Cossacks and went to Bila Tserkva. A regiment is being formed there. And now they transferred him to my regiment and are waiting for him every day. The Count has long wanted to go, but the Countess will never agree to leave Moscow until her son arrives.
“I saw them the other day at the Arkharovs’. Natalie looked prettier and cheerful again. She sang one romance. How easy it is for some people!
-What's going on? – Pierre asked displeasedly. Julie smiled.
“You know, Count, that knights like you only exist in the novels of Madame Suza.”
- Which knight? From what? – Pierre asked, blushing.
- Well, come on, dear Count, c "est la fable de tout Moscou. Je vous admire, ma parole d" honneur. [all of Moscow knows this. Really, I'm surprised at you.]
- Fine! Fine! - said the militiaman.
- OK then. You can't tell me how boring it is!
“Qu"est ce qui est la fable de tout Moscou? [What does all of Moscow know?] - Pierre said angrily, getting up.
- Come on, Count. You know!
“I don’t know anything,” said Pierre.
– I know that you were friends with Natalie, and that’s why... No, I’m always friendlier with Vera. Cette chere Vera! [This sweet Vera!]
“Non, madame,” Pierre continued in a dissatisfied tone. “I didn’t take on the role of Rostova’s knight at all, and I haven’t been with them for almost a month.” But I don't understand cruelty...
“Qui s"excuse - s"accuse, [Whoever apologizes, blames himself.] - Julie said, smiling and waving the lint, and so that she had the last word, she immediately changed the conversation. “What, I found out today: poor Marie Volkonskaya arrived in Moscow yesterday. Did you hear she lost her father?
- Really! Where is she? “I would very much like to see her,” said Pierre.
– I spent the evening with her yesterday. Today or tomorrow morning she is going to the Moscow region with her nephew.
- Well, how is she? - said Pierre.
- Nothing, I’m sad. But do you know who saved her? This is a whole novel. Nicholas Rostov. They surrounded her, wanted to kill her, wounded her people. He rushed in and saved her...
“Another novel,” said the militiaman. “This general elopement was decidedly done so that all the old brides would get married.” Catiche is one, Princess Bolkonskaya is another.
“You know that I really think that she is un petit peu amoureuse du jeune homme.” [a little bit in love with a young man.]
- Fine! Fine! Fine!
– But how can you say this in Russian?..

When Pierre returned home, he was given two Rastopchin posters that had been brought that day.
The first said that the rumor that Count Rostopchin was prohibited from leaving Moscow was unfair and that, on the contrary, Count Rostopchin was glad that ladies and merchant wives were leaving Moscow. “Less fear, less news,” the poster said, “but I answer with my life that there will be no villain in Moscow.” These words clearly showed Pierre for the first time that the French would be in Moscow. The second poster said that our main apartment was in Vyazma, that Count Wittschstein defeated the French, but that since many residents want to arm themselves, there are weapons prepared for them in the arsenal: sabers, pistols, guns, which residents can get at a cheap price. The tone of the posters was no longer as playful as in Chigirin’s previous conversations. Pierre thought about these posters. Obviously, that terrible thundercloud, which he called upon with all the strength of his soul and which at the same time aroused involuntary horror in him - obviously this cloud was approaching.

In every aviation design bureau there is a story about the statement of the chief designer. Only the author of the statement changes. And it sounds like this: “I’ve been working on airplanes all my life, but I still don’t understand how this piece of iron flies!” Indeed, Newton’s first law has not yet been canceled, and the plane is clearly heavier than air. You need to figure out what force prevents a multi-ton car from falling to the ground.

Ways to travel by air

There are three ways to travel:

1. Aerostatic, when lifting off the ground is carried out using a body whose specific gravity is lower than the density of atmospheric air. These are balloons, airships, probes and other similar structures.
2. Jet, which is the brute force of the jet stream from burned fuel, allowing it to overcome the force of gravity.
3. And finally, an aerodynamic method of creating lift, when the Earth's atmosphere is used as a supporting substance for heavier-than-air vehicles. Planes, helicopters, gyroplanes, gliders and, by the way, birds move using this particular method.

Aerodynamic forces

When moving through the air, an airplane is affected by four main multidirectional forces. Conventionally, the vectors of these forces are directed forward, backward, down and up. That is, almost a swan, crayfish and pike. The force pushing the plane forward is generated by the engine, backward is the natural force of air resistance, and down is the force of gravity. Well, what prevents the plane from falling is the lifting force generated by the air flow due to the flow around the wing.

Standard atmosphere

The state of the air, its temperature and pressure can vary significantly in different parts of the earth's surface. Accordingly, all the characteristics of aircraft when flying in one place or another will differ. Therefore, for convenience and to bring all characteristics and calculations to a single denominator, we agreed to define the so-called standard atmosphere with the following basic parameters: pressure 760 mm Hg above sea level, air density 1.188 kg per cubic meter, speed of sound 340.17 meters per second, temperature +15 ℃. With increasing altitude above sea level, these parameters change. There are special tables that reveal the parameter values ​​for different heights. All aerodynamic calculations, as well as determination of the flight performance characteristics of aircraft, are carried out using these indicators.

The simplest principle of creating lift

If you place a flat object in the oncoming air flow, for example, by sticking the palm of your hand out of the window of a moving car, you can feel this force, as they say, “on your fingers.” When you turn your palm at a small angle relative to the air flow, you immediately feel that in addition to air resistance, another force has appeared, pulling up or down depending on the direction of the rotation angle. The angle between the plane of the body (in this case, the palm) and the direction of the air flow is called the angle of attack. By controlling the angle of attack, you can also control the lift. You can easily notice that as the angle of attack increases, the force pushing the palm upward will increase, but up to a certain point. And when an angle close to 70-90 degrees is reached, it will disappear altogether.

Airplane wing

The main load-bearing surface that creates lift is the aircraft wing. The wing profile usually has a curved teardrop shape, as shown in the figure.

When air flows around a wing, the speed of the air passing along the top of the wing exceeds the speed of the bottom flow. In this case, the static air pressure at the top becomes lower than under the wing. The pressure difference pushes the wing up, creating lift. Therefore, to ensure a pressure difference, all wing profiles are made asymmetrical. For a wing with a symmetrical profile at zero angle of attack, the lift force in horizontal flight is zero. With such a wing, the only way to create it is to change the angle of attack. There is another component of the lifting force - inductive. It is formed due to the bevel of the air flow downwards by the curved lower surface of the wing, which naturally leads to the appearance of a reverse force directed upward and acting on the wing.

Calculation

The formula for calculating the lift force of an airplane wing is as follows:

• Cy is the lift coefficient.
• S - wing area.
• V is the speed of the free flow.
• P - air density.

If everything is clear with air density, wing area and speed, then the lift coefficient is a value obtained experimentally and is not a constant. It varies depending on the wing profile, its aspect ratio, angle of attack and other values. As you can see, the dependencies are mostly linear, with the exception of speed.

This mysterious coefficient

The lift coefficient of a wing is an ambiguous value. Complex multi-stage calculations are still verified experimentally. This is usually done in a wind tunnel. For each wing profile and for each angle of attack its value will be different. And since the wing itself does not fly, but is part of the aircraft, such tests are carried out on corresponding reduced copies of aircraft models. Less commonly, wings are tested separately. Based on the results of numerous measurements of each specific wing, it is possible to construct the dependence of the coefficient on the angle of attack, as well as various graphs reflecting the dependence of the lift on the speed and profile of a particular wing, as well as on the installed wing mechanization. A sample graph is shown below.

In essence, this coefficient characterizes the ability of the wing to convert the pressure of incoming air into lift. Its usual value is from 0 to 2. The record is 6. Man is still very far from natural perfection. For example, this coefficient for an eagle, when it rises from the ground with a caught gopher, reaches a value of 14. From the above graph it is obvious that an increase in the angle of attack causes an increase in lift up to certain angle values. After which the effect is lost and even goes in the opposite direction.

Flow stall

As they say, everything is good in moderation. Each wing has its own limit in terms of angle of attack. The so-called supercritical angle of attack leads to a breakdown of the flow on the upper surface of the wing, depriving it of lift. The stall occurs unevenly over the entire area of ​​the wing and is accompanied by corresponding, extremely unpleasant phenomena such as shaking and loss of controllability. Oddly enough, this phenomenon depends little on speed, although it also influences, but the main reason for the occurrence of stall is intensive maneuvering, accompanied by supercritical angles of attack. It was because of this that the only crash of the Il-86 plane occurred, when the pilot, wanting to “show off” on an empty plane without passengers, sharply began to gain altitude, which ended tragically.

Resistance

Hand in hand with lift comes the drag force that prevents the aircraft from moving forward. It consists of three elements. This is the frictional force that arises due to the action of air on the aircraft, the force that arises due to the difference in pressure in the areas in front of the wing and behind the wing, and the inductive component discussed above, since the vector of its action is directed not only upward, contributing to an increase in lift, but also back, being an ally of the resistance. In addition, one of the components of inductive drag is the force that arises due to the flow of air through the ends of the wing, causing vortex flows that increase the bevel of the direction of air movement. The formula for aerodynamic drag is absolutely identical to the formula for lift, with the exception of the coefficient Su. It changes to the coefficient Cx and is also determined experimentally. Its value rarely exceeds one tenth of a unit.

Aerodynamic quality

The ratio of lift to drag force is called aerodynamic quality. One feature needs to be taken into account here. Since the formulas for the lift and drag forces, with the exception of the coefficients, are the same, it can be assumed that the aerodynamic quality of the aircraft is determined by the ratio of the coefficients Su and Cx. The graph of this relationship for certain angles of attack is called the wing polar. An example of such a graph is shown below.

Modern airplanes have a lift-to-drag ratio in the region of 17-21, and gliders - up to 50. This means that on airplanes the lift force of the wing at optimal conditions is 17-21 times greater than the drag force. Compared to the Wright brothers' plane, with a rating of 6.5, progress in design is obvious, but it is still a long way from an eagle with an unfortunate gopher in its paws.

Flight modes

Different flight modes require different aerodynamic qualities. During cruising horizontal flight, the aircraft speed is quite high, and the lift coefficient, proportional to the square of the speed, is at high values. The main thing here is to minimize resistance. During takeoff and especially landing, the lift coefficient plays a decisive role. The aircraft's speed is low, but it requires a stable position in the air. An ideal solution to this problem would be to create a so-called adaptive wing, which changes its curvature and even area depending on flight conditions in approximately the same way as birds do. While the designers have not succeeded in this, changing the lift coefficient is achieved by using wing mechanization, increasing both the area and the curvature of the profile, which, by increasing drag, significantly increases the lift force. For fighter aircraft, a change in wing sweep was used. The innovation made it possible to reduce drag at high speeds and increase lift at low speeds. However, this design turned out to be unreliable, and recently front-line aircraft have been manufactured with a fixed wing. Another way to increase the lift of an aircraft wing is to additionally blow the wing with flow from the engines. This is implemented on the An-70 and A-400M military transport aircraft, which, thanks to this property, are characterized by shortened takeoff and landing distances.

AERODYNAMIC FORCES

AIR FLOW FLOW OF BODIES

When flowing around a solid body, the air flow is subject to deformation, which leads to changes in speed, pressure, temperature and density in the flow streams. Thus, a region of variable air velocities and pressures is created near the surface of the streamlined body. The presence of pressures of different magnitudes at the surface of a solid body leads to the emergence of aerodynamic forces and moments. The distribution of these forces depends on the nature of the flow around the body, its position in the flow, and the configuration of the body. To study the physical pattern of flow around solid bodies, various methods are used to display the visible pattern of flow around a body. The visible pattern of air flow around bodies is usually called aerodynamic spectrum.

To obtain aerodynamic spectra, instruments such as smoke ducts (Fig. 1), silkworms, optical research measures (for supersonic flows), etc. are used.

Rice. 1 Smoke channel

1 - smoke source; 2 - streams of smoke; 3 - streamlined body; 4 – fan

In a smoke channel, the aerodynamic spectrum is created by streams of smoke released from a special smoker into the air flow flowing around the body.

The essence of the method using silk threads is that in the places of interest, special silk threads are glued to the surface of the streamlined body, which, when blowing over the body, are located along the streams flowing around the body. The position of the silks is used to judge the nature of the flow near the surface of the body.

Let us consider the aerodynamic spectra of some bodies.

Flat plate (Fig. 2), placed in the flow at an angle of 90°, creates a rather sharp change in the direction of movement of the flow flowing around it: deceleration of the flow in front of it, compression of the streams at its edges and the formation directly behind the edge of the rarefaction plate and large vortices that fill the entire area behind the record. A clearly visible co-current stream can be observed behind the plate. In front of the plate, the pressure will be greater than in the undisturbed flow, and behind the plate, due to rarefaction, the pressure will decrease.

Rice. 2 Aerodynamic spectrum of a flat plate and a ball

Symmetrical streamlined (drop-shaped) body has a smoother flow pattern both in the front and tail parts.

In section A - B (the largest cross-sectional value, the aerodynamic spectrum shows the greatest deformation of the jets, their greatest compression. In the tail part, small flow vortices are formed, which create a co-current jet and are carried away by the flow, gradually fading (Fig. 3).

Rice. 3 Aerodynamic spectrum of a streamlined body

Streamlined, asymmetrical body in terms of the nature of the flow it is close to a streamlined symmetric one, and differs in the amount of deformation of the streams in the upper and lower parts of the body (see Fig. 4).

Rice. 4 Aerodynamic spectrum of a streamlined asymmetrical body (wing profile)

The greatest deformation of the streams is observed where the body has the greatest amount of curvature of the body surface (point K). In the area of ​​this point, the streams are compressed, and their cross-section decreases. The lower, less curved surface has little effect on the flow pattern. Here the so-called asymmetrical flow takes place. When an air flow flows around symmetrical (and asymmetrical) streamlined bodies placed at a certain angle a to the velocity vector of the undisturbed flow (Fig. 5), we will also have a picture of an asymmetrical flow around us and obtain an aerodynamic spectrum similar to that obtained when flowing around an asymmetrical streamlined body (see Fig. 4).

Rice. 5 Aerodynamic spectrum of a streamlined body (wing profile) placed in the flow at an angle a

On the upper surface of the body, in the place of greatest compression of the jets, according to the law of continuity of jets, a local increase in flow velocity and, consequently, a decrease in pressure will be observed. On the lower surface, the flow deformation will be less and, therefore, the change in speed and pressure will be less.

It is easy to see that the degree of deformation of the streams in the flow will depend on the configuration of the body and its position in the flow. Knowing the spectrum of flow around a body, it is possible to calculate the value of air pressure for each point and thus judge the magnitude and nature of the action of aerodynamic forces. Since pressure forces of different magnitudes act on different points on the surface of a streamlined body (wing profile), their resulting force will be different from zero. This difference in pressure at different points on the surface of a moving wing is the main factor responsible for the appearance of aerodynamic forces.

The magnitude of surface pressures for various bodies is determined in laboratories by blowing in wind tunnels. The obtained pressure values ​​for each point are plotted on special graphs (Fig. 6)

In addition to pressure forces, friction forces act on the surface of the wing tangentially to it, which are caused by the viscosity of the air and are entirely determined by the processes occurring in the boundary layer.

Summing up the pressure and friction forces distributed over the surface of the wing, we obtain the resultant force, which is called total aerodynamic force .

The point of application of the total aerodynamic force on the chord of the wing profile is called center pressure.

Rice. 6 Pressure distribution along the wing profile

WING AND ITS PURPOSE

An airplane wing is designed to generate the lift needed to keep the airplane in the air.

The greater the lift force and the lesser the drag, the greater the aerodynamic quality of a wing.

The lift and drag of a wing depend on the geometric characteristics of the wing. The geometric characteristics of a wing mainly come down to the characteristics of the wing in plan and the characteristics of the wing profile.

WING GEOMETRICAL CHARACTERISTICS

The geometric characteristics of the wing are reduced mainly to the characteristics of the wing shape in plan and to the characteristics of the wing profile. The wings of modern aircraft can be shaped in plan (Fig. 7): ellipsoidal (a), rectangular (b), trapezoidal (c), arrow-shaped (d) and triangular (e)

The best aerodynamic shape is the elliptical shape, but such a wing is difficult to manufacture and is therefore rarely used. A rectangular wing is less advantageous from an aerodynamic point of view, but is much easier to manufacture. A trapezoidal wing has better aerodynamic characteristics than a rectangular one, but is somewhat more difficult to manufacture.

Swept and triangular wings are aerodynamically inferior to trapezoidal and rectangular ones at subsonic speeds, but at transonic and supersonic speeds they have significant advantages. Therefore, such wings are used only on aircraft flying at transonic and supersonic speeds.

Rice. 7 Wing planforms

Rice. 8 Angle of transverse V wing

Rice. 9 Wing geometric characteristics

The shape of the wing in plan is characterized by its span, area of ​​elongation, tapering, sweep (Fig. 9) and transverse V(Fig. 8)

Wingspan L is the distance between the ends of the wing in a straight line.

Wing area in respect of S cr limited by the contours of the wing.

The area of ​​the trapezoidal and swept wings is calculated as the areas of two trapezoids

(2.1)

Where b 0 - root chord, m;

b to - terminal chord, m;

Average wing chord, m.

Wing extension l called the ratio of wing span to mean chord

If instead b avg substitute its value from equality (2.1), then the wing elongation will be determined by the formula

For modern supersonic and transonic aircraft, the wing aspect ratio does not exceed 2-5. For low-speed aircraft, the aspect ratio can reach 12-15, and for gliders up to 25.

Wing narrowing h called the ratio of the axial chord to the terminal chord

For subsonic aircraft, the wing taper usually does not exceed 3, but for transonic and supersonic aircraft it can vary within wide limits.

Sweep angle c called the angle between the line of the leading edge of the wing and the transverse axis of the aircraft. Sweep can also be measured along the focal line (1/4 chord from the attack edge) or along another line of the wing. For transonic aircraft it reaches 45°, and for supersonic aircraft it reaches 60°.

Angle of transverse V wing called the angle between the transverse axis of the aircraft and the lower surface of the wing (Fig. 8). Modern aircraft have a transverse angle V ranges from +5° to -15°.

Wing profile is called the shape of its cross section. Profiles can be (Fig. 10): symmetrical and asymmetrical. Asymmetrical ones, in turn, can be biconvex, plano-convex, concave-convex and S-shaped. Lenticular and wedge-shaped can be used for supersonic aircraft.

Modern aircraft mainly use symmetrical and biconvex asymmetrical profiles.

The main characteristics of the profile are: profile chord, relative thickness, relative curvature (Fig. 11).

Profile chord b called a straight line segment connecting the two most distant points of the profile.

Rice. 10 Wing profile shapes

1 - symmetrical; 2 - not symmetrical; 3 - plano-convex; 4 - biconvex; 5 - S-shaped; 6 - laminated; 7 - lenticular; 8 - diamond-shaped; 9 - D prominent

Rice. eleven Profile geometric characteristics:

b - profile chord; C max - greatest thickness; f max - curvature arrow; x c - coordinate of the greatest thickness

Rice. 12 Wing angles of attack

Rice. 13 Total aerodynamic force and its point of application

R - total aerodynamic force; Y - lift force; Q - drag force; a - attack angle; q - quality angle

Relative profile thickness With is called the ratio of maximum thickness With max to the chord, expressed as a percentage:

(2.5)

Maximum profile thickness position X c expressed as a percentage of the chord length and measured from the toe

(2.6)

For modern aircraft, the relative profile thickness is in the range of 4-16%.

Relative profile curvature f called the maximum curvature ratio f to the chord, expressed as a percentage.

The maximum distance from the profile centerline to the chord determines the curvature of the profile. The middle line of the profile is drawn at an equal distance from the upper and lower contours of the profile.

(2.7)

For symmetrical profiles the relative curvature is zero, but for asymmetrical profiles this value is different from zero and does not exceed 4%.

AVERAGE AERODYNAMIC WING CHORD

Any rotational movement of an aircraft in flight occurs around its center of gravity. Therefore, it is important to be able to quickly determine the position of the CG and know how the balancing will change when its position changes. The position of the center of gravity, as a rule, is oriented relative to the average aerodynamic chord of the wing.

Average aerodynamic chord of the wing (SAH) is called the chord of such a rectangular wing, which has the same area as the given wing, the magnitude of the total aerodynamic force and the position of the center of pressure (CP) at equal angles of attack (Fig. 14).

Rice. 14 Average aerodynamic chords of wings

Magnitude and coordinates SAR for each aircraft are determined during the design process and are indicated in the technical description.

If the magnitude and position SAR of this aircraft are unknown, they can be determined approximately. For a trapezoidal unfurled wing SAR determined by geometric construction. To do this, the aircraft wing is drawn in plan (and to a certain scale). On the continuation of the root chord, a segment equal in size to the terminal chord is deposited (Fig. 15), and on the continuation of the terminal chord (forward), a segment equal to the root chord is deposited. The ends of the segments are connected by a straight line. Then draw the midline of the wing, connecting the straight midpoint of the root and terminal chords. The average aerodynamic chord will pass through the intersection point of these two lines (SAH).

Rice. 15 Geometric definition of the MAR

Knowing the magnitude and position SAR on an airplane and taking it as a baseline, determine the position of the airplane’s center of gravity, the wing’s center of pressure, etc. relative to it.

The aerodynamic force of an airplane is generated by the wing and is applied at the center of pressure. The center of pressure and the center of gravity, as a rule, do not coincide and therefore a moment of force is formed. The magnitude of this moment depends on the magnitude of the force and the distance between the CG and the center of pressure, the position of which is defined as the distance from the beginning SAR, expressed in linear quantities or as a percentage of length SAH.

Rice. 16 Aircraft center of gravity position

Rice. 17 Calculation of alignment when aircraft weight changes

WING DRAG

Drag - this is the resistance to the movement of an airplane wing in the air. It consists of profile, inductive and wave impedances:

X cr = X cr + X ind + X B. (2.8)

Characteristic impedance will not be considered, since it occurs at flight speeds above 450 km/h.

Profile resistance consists of pressure resistance and friction resistance:

X pr = X D + X tr .(2.9)

Pressure resistance - this is the difference in pressure in front of and behind the wing. The greater this difference, the greater the pressure resistance. The pressure difference depends on the shape of the profile, its relative thickness and curvature (Fig. 18, indicated in the figure WITHX- coefficient of profile resistance).

Rice. 18 Graph of profile resistance versus profile thickness

The greater the relative thickness With profile, the more the pressure increases in front of the wing and the more it decreases behind the wing, at its trailing edge. As a result, the pressure difference increases and, as a result, the pressure resistance increases. Air flow around the wings of the Yak-52 and Yak-55 aircraft in the operating range of angles of attack (linear section of the characteristic C y =f( a ) occurs without separation of the boundary layer from the entire surface of the wing profile; as a result, pressure resistance arises due to the difference in pressure between the front and rear parts of the wing. The amount of pressure resistance is small. The appearance of pressure resistance is accompanied by the formation of weak vortices in the accompanying jet formed from the boundary layer.

When an air flow flows around the wing profile at angles of attack close to the critical angle, the pressure resistance increases significantly. In this case, the dimensions of the swirling cocurrent jet and the vortices themselves increase sharply.

Friction resistance arises due to the manifestation of air viscosity in the boundary layer of the flow around the wing profile. The magnitude of the friction forces depends on the structure of the boundary layer and the state of the streamlined surface of the wing (its roughness). In a laminar boundary layer of air, frictional resistance is less than in a turbulent boundary layer. Consequently, the more of the wing surface the laminar boundary layer of air flow flows around, the lower the friction drag.

The amount of friction drag is affected by: aircraft speed; surface roughness; wing shape. The higher the flight speed, the worse quality the wing surface is processed and the thicker the wing profile, the greater the friction resistance.

Rice. 19 Flow around a wing of finite span

To reduce frictional drag when preparing aircraft for flight, it is necessary to maintain the smoothness of the surface of the wing and parts of the aircraft, especially the wing tip. Changing the angles of attack has virtually no effect on the amount of friction resistance.

The relationship between friction resistance and pressure resistance largely depends on the profile thickness (see Fig. 18). The figure shows that with increasing relative thickness of the profile, the proportion attributable to pressure resistance increases. The same can be said by analyzing and comparing the profiles of the Yak-52 and Yak-55 aircraft.

Inductive reactance - this is an increase in drag associated with the formation of the lifting force of the wing. When an undisturbed air flow flows around the wing, a pressure difference arises above and below the wing. As a result, part of the air at the ends of the wings flows from a zone of higher pressure to a zone of lower pressure (Fig. 19).

The air flow flows from the lower surface of the wing to the upper and is superimposed on the air flow flowing onto the upper part of the wing, which leads to the formation of turbulence in the air mass behind the trailing edge, i.e., a vortex rope is formed. The air in the vortex rope rotates. The speed of rotation of the vortex rope is different, in the center it is greatest, and as it moves away from the vortex axis it decreases.

Rice. 20 Downward deflection of airflow caused by a vortex line

Since air has viscosity, the rotating air in the bundle carries with it the surrounding air. The vortex bundles of the left and right half-wings rotate in different directions in such a way that within the wing the movement of air masses is directed from top to bottom.

This movement of air masses imparts additional downward speed to the air flow flowing around the wing. In this case, any part of the air flowing around the wing at a speed V, deflects downward at speed U. The magnitude of this speed is inversely proportional to the distance of the point from the axis of the vortex rope, i.e., ultimately, to the elongation of the wing, to the pressure difference above and below the wing, and to the shape of the wing in plan.

Corner Da, by which the air flow flowing around the wing at a speed is deflected V induced by vertical velocity U, called the flow angle (Fig. 20). Its value depends on the value of the vertical speed induced by the vortex rope and the speed of the oncoming flow V:

(2.10)

Therefore, due to the flow bevel, the true angle of attack aist the wing in each section will differ from the geometric or apparent angle of attack aeach by the amount Da(Fig. 21):

(2.11)

As is known, the lift of a wing Y always perpendicular to the oncoming flow and its direction. Therefore, the wing lift vector deviates by an angle Da and perpendicular to the direction of air flow V.

The lifting force will not be the entire force Y" and its component Y, directed perpendicular to the oncoming flow:

Rice. 21 Formation of inductive reactance

Rice. 22 Dependence of the drag coefficient C x on the angle of attack of the Yak-52 and

Yak-55

Due to the small size Da We consider another component force Y" will be equal

(2.13)

This component is directed along the flow and is called inductive reactance (Fig. 21).

To find the value of inductive reactance, you need to calculate the speed U and flow angle.

Dependence of the flow bevel angle on the wing elongation and lift coefficient WITHat and the shape of the wing in plan is expressed by the formula

Where A- coefficient taking into account the shape of the wing in plan.

For airplane wings the coefficient A equals

(2.15)

Where lef- wing extension without taking into account the area of ​​the fuselage, which occupies part of the wing;

d- a value depending on the shape of the wing in plan.

Let us substitute the values ​​of formulas (2.14), (2.15) into formula (2.13), transforming it, we obtain

(2.16)

Where Cxi- coefficient of inductive reactance.

It is determined by the formula. From the formula it is clear that C x directly proportional to the lift coefficient and inversely proportional to the wing aspect ratio.

At zero lift angle of attack aO the inductive reactance will be zero.

At supercritical angles of attack, the smooth flow around the wing profile is disrupted and, consequently, the formula for determining Cx1 not acceptable for determining its value.

Since the value WITHX is inversely proportional to the wing aspect ratio, so aircraft designed for long-distance flights have a high wing aspect ratio: l=14…15.

WING AERODYNAMIC QUALITY

From an aerodynamic point of view, the most advantageous would be a wing that has the ability to create the greatest possible lift with the lowest possible drag. To assess the aerodynamic perfection of the wing, the concept of aerodynamic quality of the wing is introduced.

The aerodynamic quality of a wing is the ratio of the lift force to the drag force of the wing at a given angle of attack.

Where Y- lifting force, kg;

Q- drag force, kg. Substituting the values ​​into the formula Y and Q , we get

The greater the aerodynamic quality of the wing, the more perfect it is. The amount of quality for modern aircraft can reach 14-15 , and for gliders 45-50. This means that an airplane wing can produce a lift force that exceeds drag by a factor of 14-15 times, and for gliders even in 50 times.

The aerodynamic quality is characterized by the angle (see Fig. 13).

The angle between the vectors of lift and total aerodynamic forces is called the quality angle. The greater the aerodynamic quality, the smaller the quality angle, and vice versa.

The aerodynamic quality of the wing, as can be seen from formula (2.18), depends on the same factors as the coefficients C y And C x, i.e., on the angle of attack, profile shape, wing planform, flight Mach number and surface treatment.

INFLUENCE ON AERODYNAMIC QUALITY OF ANGLE OF ATTACK.

Based on known values ​​of aerodynamic coefficients C y And C x plot a graph for different angles of attack TO = f ( a) (Fig. 23).

The graph shows that with an increase in the angle of attack to a certain value, the aerodynamic quality increases. At a certain angle of attack the quality reaches its maximum value K max. This angle called the most advantageous angle of attack, a naive .

At zero lift angle of attack a O Where WITH at =0 the aerodynamic quality will be zero.

The influence on the aerodynamic quality of the profile shape is associated with the relative thickness and curvature of the profile. In this case, the shape of the profile contours, the shape of the toe and the position of the maximum profile thickness along the chord have a great influence (Fig. 24).

Rice. 23 Graph of the dependence of aerodynamic quality on the angle of attack

Rice. 24 Dependence of aerodynamic quality on the angle of attack and profile thickness

Rice. 25 . Formation of suction force

Rice. 26 Change in the aerodynamic quality of a wing depending on the Mach number

When flowing around profiles with rounded and thickened toes, a suction force is formed at the toe of the profile, which can significantly reduce drag. It reaches its greatest value at angles of attack close to anaive when the suction force can exceed the friction force (Fig. 25).

To get larger values TOMax the optimal thickness and curvature of the profile, contour shapes and wing elongation are selected.

The wing planform also affects the aerodynamic quality of the wing. To obtain the highest quality values, the best wing shape is elliptical with a rounded leading edge. This wing has the least inductive drag. Increasing the wing aspect ratio reduces its induced drag (remember) and therefore increases the aerodynamic efficiency.

As the number increases M flight before the wave crisis appears, the quality will increase slightly (for a given angle of attack), since the manifestation of air compressibility increases C y . With the onset of a wave crisis, the quality decreases sharply because the lift coefficient decreases and C x increases (Fig. 26).

The condition of the wing surface (roughness, waviness, deviation from a given shape) affects the value of the profile drag. Therefore, by improving the condition of the wing surface (or maintaining it in good condition), it is possible to improve the aerodynamic quality of the aircraft.

CONSTRUCTION OF AERODYNAMIC CHARACTERISTICS OF WINGS AND AIRCRAFT

WING POLAR

For various calculations of wing flight characteristics, it is especially important to know the simultaneous change C y And C x in the range of flight angles of attack. For this purpose, a graph of the dependence of the coefficient is plotted C y from C x, called polara.

To construct a polar for a given wing, the wing (or its model) is blown in a wind tunnel at different angles of attack. When blowing, the lift force values ​​are measured for each angle of attack using aerodynamic balances Y and drag forces Q. Having determined the magnitude of the forces Y and Q for a given profile, their aerodynamic coefficients are calculated. From the formula for lift and drag forces we find:

(2.20)

This calculation is made for each angle of attack. The results of measurements and calculations are entered into a table.

To construct a polar, two mutually perpendicular axes are drawn. Values ​​are plotted on the vertical axis C y , and on the horizontal - C x . Scales for C y And C x Usually different ones are taken.

Accepted for C y take a scale 5 times larger than for C x , since within the flight angles of attack the range of change C y several times greater than the range of change C x . Each point of the resulting graph corresponds to a certain angle of attack.

Name "polar" is explained by the fact that this curve can be considered as a polar diagram constructed on the coordinates of the total aerodynamic force coefficient With R And j , Where j - angle of inclination of the total aerodynamic force R to the direction of the oncoming flow velocity (provided that the scale C y and C x take the same).

Rice. 27 The principle of constructing a wing polar

Rice. 28 Wing polarity

If we draw a vector from the origin of coordinates (Fig. 27), combined with the center of pressure of the profile, to any point on the polar, then it will represent the diagonal of a rectangle, the sides of which are respectively equal WITH y And C x . drag and lift coefficient from angles of attack - the so-called wing polarity.

Since the coefficients WITH y And C x are proportional to the aerodynamic forces, then it is easy to verify that the angle between the vectors With r And WITH y , represents the quality angle q. The quality angle q can be directly measured on a polar built on equal scales WITH y And C x, and since polars are built, as a rule, on different scale coefficients WITH y And C x , then the quality angle is determined from the ratio

The polar is constructed for a very specific wing with given geometric dimensions and profile shape (Fig. 28). Based on the wing polarity, a number of characteristic angles of attack can be determined.

Zero lift angle a O is at the intersection of the polar and the axis C x . At this angle of attack the lift coefficient is zero (WITH y = 0).

For the wings of modern aircraft it is usually a O = .

The angle of attack at which C x has the smallest value a C h.min . is found by drawing a tangent to the polar parallel to the axis WITH y . For modern wing profiles, this angle ranges from 0 to 1°.

The most favorable angle of attack anaive . Since at the most favorable angle of attack the aerodynamic quality of the wing is maximum, the angle between the axis WITH y and a tangent drawn from the origin, i.e., the quality angle , at this angle of attack, according to formula (2.19), will be minimal. Therefore, to determine a naive you need to draw a tangent to the polar from the origin. The touch point will correspond a naive . For modern wings a naive lies within 4 - 6°.

Critical angle of attack aCrete . To determine the critical angle of attack, it is necessary to draw a tangent to the polar parallel to the axis C x . The point of contact will correspond a Crete . For modern aircraft wings a Crete = 16-30°.

Angles of attack with the same aerodynamic quality are found by drawing a secant from the origin to the polar. At the intersection points we find the angles of attack (a 1 And a 2 ) when flying, in which the aerodynamic quality will be the same and necessarily less TO Max .

POLAR AIRCRAFT

One of the main aerodynamic characteristics of an aircraft is the aircraft's polar. It was previously established that the wing lift coefficient WITH y equal to the lift coefficient of the entire aircraft, and the drag coefficient of the aircraft for each angle of attack is greater C x wing by the size C x vr , i.e.

Therefore, the plane's polar can be obtained by adding the quantity C x vr To C x wing on the wing polar for the corresponding angles of attack. The plane's polarity will be shifted to the right of the wing polarity by an amount C x vr (Fig. 29). Typically, an aircraft polar is built using constraint data WITH y =f( a ) And C x =f( a ), obtained experimentally by blowing models in wind tunnels. Angles of attack on the aircraft's polar plane are set by horizontally translating the angles of attack marked on the wing's polar plane.

Determination of the aerodynamic characteristics and characteristic angles of attack along the aircraft polarity is carried out in the same way as was done at the wing polarity.

Zero lift angle of attack a aircraft is practically no different from the angle of attack of a zero-lift wing. Because on coal a 0 the lift force is zero, then at this angle of attack only vertical downward movement of the aircraft is possible, called a vertical dive, or a vertical slide at an angle of 90°.

Rice. 29 Wing and airplane polars

Rice. 30 Airplane polars with flaps extended

Angle of attack at which the drag coefficient has a minimum value () is located parallel to the axis WITH y tangent to the polar. When flying at this angle of attack, there will be the least drag loss. At this angle of attack (or close to it) the flight is performed at maximum speed.

The most favorable angle of attack ( a naive ) corresponds to the highest value of the aerodynamic quality of the aircraft. Graphically, this angle, just like for the wing, is determined by drawing a tangent to the polar from the origin. The graph shows that the inclination of the tangent to the polar of the aircraft is greater than that of the tangent to the polar of the wing. And since

(2.22)

then we can conclude that the maximum quality of the aircraft as a whole is always less than the maximum aerodynamic quality of an individual wing.

From the same graph it is clear that the most favorable angle of attack of the aircraft is 2 - 3° greater than the most favorable angle of attack of the wing.

Rice. 31 Airplane polars for different M numbers

Aircraft critical angle of attack (aCrete) its value does not differ from the value of the same angle for the wing.

In Fig. 29 shows the plane's polars in three versions:

- flaps are retracted;

- flaps are extended to take-off position ( d 3 = 20°);

- flaps are extended to landing position ( d 3 = 45°).

Raising the flaps to the take-off position (d 3 = 15-25°) allows you to increase the maximum lift coefficient Su max with a relatively small increase in the drag coefficient. This makes it possible to reduce the required minimum flight speed, which practically determines the takeoff speed of the aircraft during takeoff. By deploying the flaps (or flaps) to the takeoff position, the takeoff run length is reduced by up to 25%.

When the flaps (or flaps) are extended to the landing position (d 3 = 45 - 60°), the maximum lift coefficient can increase to 80%, which sharply reduces the landing speed and run length. However, the drag increases more rapidly than the lift force, so the aerodynamic quality is significantly reduced. But this circumstance is used as a positive operational factor - the steepness of the trajectory during gliding before landing increases and, consequently, the aircraft becomes less demanding on the quality of approaches to the landing strip.

Previously, we considered the polars of the wing and aircraft for such flight speeds (numbers M), when the influence of compressibility could be neglected. However, when such numbers are reached M, at which compressibility can no longer be neglected ( M> 0.6 - 0.7) the lift and drag coefficients must be determined taking into account a correction for compressibility.

(2.23)

where Su сж is the lift coefficient taking into account compressibility;

Su incompressible flow coefficient of lift force of incompressible flow for the same angle of attack as Su compressed.

Up to the numbers, all polars are practically the same, but at large numbers M they begin to shift to the right and at the same time increase the inclination to the axis C x . Polar shift to the right (by large C x ) due to an increase in the coefficient of profile resistance due to the influence of air compressibility, and with a further increase in the number (M> 0.75 - 0.8) due to the appearance of wave resistance (Fig. 31).

The increase in the inclination of the polars is explained by the increase in the coefficient of inductive drag, since at the same angle of attack in a subsonic flow of compressible gas it will increase proportionally. The aerodynamic quality of the aircraft from the moment the compressibility effect noticeably manifests itself begins to decrease.

WING MECHANIZATION

On modern aircraft, in order to obtain high flight-tactical characteristics, in particular to achieve high flight speeds, both the wing area and its aspect ratio are significantly reduced. And this negatively affects the aerodynamic quality of the aircraft and especially the takeoff and landing characteristics.

To keep an airplane in the air in straight flight at a constant speed, it is necessary that the lifting force be equal to the weight of the airplane - Y = G . But since

(2.24)

From formula (2.24) it follows that to keep the aircraft in the air at the lowest speed (when landing, for example), it is necessary that the lift coefficient WITH y was the largest. However WITH y can be increased by increasing the angle of attack only up to aCrete . An increase in the angle of attack greater than the critical one leads to a disruption of the flow on the upper surface of the wing and to a sharp decrease WITH y , which is unacceptable. Therefore, to ensure equality of lift and weight of the aircraft, it is necessary to increase the flight speed .

Due to these reasons, the landing speeds of modern aircraft are quite high. This greatly complicates takeoff and landing and increases the aircraft's range.

In order to improve takeoff and landing performance and ensure safety during takeoff and especially landing, it is necessary to reduce the landing speed if possible. To do this you need to WITH y was perhaps more. However, wing profiles having a large Su Max , have, as a rule, large values ​​of drag Cxmin , since they have large relative thickness and curvature. And the increase Cx.min , prevents an increase in maximum flight speed. To produce a wing profile that simultaneously satisfies two requirements: obtaining high maximum speeds and low landing speeds - almost impossible.

Therefore, when designing aircraft wing profiles, they strive first to ensure maximum speed, and to reduce landing speed, special devices are used on the wings, called wing mechanization.

By using a mechanized wing, the magnitude of SuMax , which makes it possible to reduce the landing speed and length of the aircraft's run after landing, reduce the speed of the aircraft at the moment of takeoff and shorten the length of the takeoff run. The use of mechanization improves the stability and controllability of the aircraft at high angles of attack. In addition, reducing the speed during takeoff and landing increases the safety of their execution and reduces the cost of constructing runways.

So, wing mechanization serves to improve the takeoff and landing characteristics of the aircraft by increasing the maximum value of the wing lift coefficient SuMax .

The essence of wing mechanization is that, with the help of special devices, the curvature of the profile (in some cases, the wing area) is increased, as a result of which the flow pattern changes. The result is an increase in the maximum value of the lift coefficient.

These devices, as a rule, are controlled in flight: when flying at low angles of attack (at high flight speeds), they are not used, but are used only during takeoff and landing, when an increase in the angle of attack does not provide the required amount of lift.

There are the following types of wing mechanization : flaps, flaps, slats, deflectable socks wings, boundary layer control, jet flaps .

shield is a deflecting surface, which in the retracted position is adjacent to the lower, rear surface of the wing. The shield is one of the simplest and most common means of increasing Su max.

The increase in Su max when the flap is deflected is explained by a change in the shape of the wing profile, which can be conditionally reduced to an increase in the effective angle of attack and the concavity (curvature) of the profile.

When the flap is deflected, a vortex suction zone is formed between the wing and the flap. The reduced pressure in this zone extends partially to the upper surface of the profile at the trailing edge and causes the boundary layer to be suctioned from the surface lying upstream. Due to the suction action of the flap, stalling of the flow at high angles of attack is prevented, the flow velocity over the wing increases, and the pressure decreases. In addition, deflection of the flap increases the pressure under the wing by increasing the effective curvature of the profile and the effective angle of attack a ef .

Due to this, the release of the flaps increases the difference in relative pressures above and below the wing, and therefore the lift coefficient Su .

In Fig. Figure 35 shows the dependence graph WITH y from the angle of attack for a wing with different flap positions: retracted, takeoff d = 15°, landing d = 40°.

When the flap is deflected, the entire curve Su sch = f( a ) moves upward almost equidistant to the curve Su = f ( a ) main profile.

The graph shows that when the flap is deflected to the landing position (d = 40°), the increment Su is 50-60%, and the critical angle of attack decreases by 1-3°.

To increase the efficiency of the flap, it is structurally designed in such a way that when deflected, it simultaneously moves back, towards the trailing edge of the wing. This increases the efficiency of boundary layer suction from the upper surface of the wing and the length of the high-pressure zone under the wing.

When the flap is deflected, simultaneously with an increase in the lift coefficient, the drag coefficient also increases, while the aerodynamic quality of the wing decreases.

Flap . The flap is a deflecting part of the trailing edge of the wing or a surface that extends (with simultaneous deflection down) back from under the wing. By design, flaps are divided into simple (non-slotted), single-slotted and multi-slotted .

Rice. 32 Wing profile with flap moving rearward

Rice. 33 Flaps: a - non-slotted; b - slotted

Non-slotted flap increases lift coefficient WITH y by increasing the curvature of the profile. If there is a specially profiled gap between the flap tip and the wing, the efficiency of the flap increases, since air passing at high speed through the narrowing gap prevents swelling and disruption of the boundary layer. To further increase the efficiency of flaps, double-slot flaps are sometimes used, which increase the lift coefficient WITH y profile up to 80%.

The increase in Su max of a wing when extending flaps or flaps depends on a number of factors: their relative sizes, deflection angle, wing sweep angle. On swept wings, the efficiency of mechanization is usually less than on straight wings. The deflection of flaps, as well as flaps, is accompanied not only by an increase WITH y , but to an even greater extent by the increase WITH x , therefore, the aerodynamic quality decreases when the mechanization is extended.

The critical angle of attack with the flaps extended decreases slightly, which makes it possible to obtain Cmax with less lift of the aircraft nose (Fig. 36).

Rice. 34 Wing profile with shield

Rice. 35 The influence of the release of flaps on the curve Cy=f( a)

Rice. 36 Aircraft polars with flaps retracted and extended

The slat is a small wing located in front of the wing (Fig. 37).

Slats are either fixed or automatic.

Fixed slats on special stands are permanently fixed at some distance from the tip of the wing profile. When flying at low angles of attack, automatic slats are tightly pressed to the wing by the air flow. When flying at high angles of attack, the pressure distribution pattern along the profile changes, as a result of which the slat seems to be sucked out. The slat automatically extends (Fig. 38).

When the slat is extended, a narrowing gap is formed between the wing and the slat. The speed of the air passing through this gap and its kinetic energy increase. The gap between the slat and the wing is profiled in such a way that the air flow, leaving the gap, is directed at high speed along the upper surface of the wing. As a result, the speed of the boundary layer increases, it becomes more stable at high angles of attack, and its separation is pushed back to high angles of attack. In this case, the critical angle of attack of the profile increases significantly (by 10°-15°), and Cy max increases on average by 50% (Fig. 39).

Typically, slats are not installed along the entire span, but only at its ends. This is because, in addition to increasing the lift coefficient, the efficiency of the ailerons increases, and this improves lateral stability and controllability. Installing a slat along the entire span would significantly increase the critical angle of attack of the wing as a whole, and to implement it during landing it would be necessary to make the main landing gear struts very high.

Rice. 37 Slat

Rice. 38 The operating principle of the automatic slat: a - small angles of attack; b – large angles of attack

Fixed slats They are installed, as a rule, on low-speed aircraft, since such slats significantly increase drag, which is an obstacle to achieving high flight speeds.

Deflectable toe (Fig. 40) is used on wings with a thin profile and a sharp leading edge to prevent stall behind the leading edge at high angles of attack.

By changing the angle of inclination of the movable nose, for any angle of attack it is possible to select a position where the flow around the profile will be continuous. This will improve the aerodynamic characteristics of thin wings at high angles of attack. In this case, the aerodynamic quality can increase.

Curving the profile by deflecting the tip increases the wing's Sumax without significantly changing the critical angle of attack.

Rice. 39 Curve Su =f ( a ) for a wing with slats

Rice. 40 Deflectable wing tip

Boundary Layer Control (Fig. 41) is one of the most effective types of wing mechanization and comes down to the fact that the boundary layer is either sucked into the wing or blown away from its upper surface.

To suck out the boundary layer or to blow it away, special fans are used or compressors of aircraft gas turbine engines are used.

The suction of inhibited particles from the boundary layer into the wing reduces the thickness of the layer, increases its speed near the wing surface and promotes continuous flow around the upper surface of the wing at high angles of attack.

Deflation of the boundary layer increases the speed of movement of air particles in the boundary layer, thereby preventing flow stall.

Boundary layer control works well when combined with flaps or flaps.

Rice. 41 Boundary Layer Control

Rice. 42 Jet flap

Jet flap (Fig. 42) represents a stream of gases flowing at high speed at a certain downward angle from a special slot located near the trailing edge of the wing. In this case, the gas jet affects the flow flowing around the wing, like a deflected flap, as a result of which the pressure in front of the jet flap (under the wing) increases, and behind it decreases, causing an increase in the speed of the flow above the wing. In addition, a reactive force is generated R, created by the flowing jet.

The effectiveness of the jet flap depends on the angle of attack of the wing, the angle of exit of the jet and the magnitude of the thrust force R. They are used for thin, swept wings of low aspect ratio. The jet flap allows for increased lift coefficient Su Max 5-10 times .

To create a jet, gases coming out of a turbojet engine are used.

MOVEMENT OF THE CENTER OF PRESSURE OF THE WING AND AIRPLANE

Wing pressure center is called the point of intersection of the resultant aerodynamic forces with the chord of the wing.

The position of the center of pressure is determined by its coordinate X D - the distance from the leading edge of the wing, which can be expressed in fractions of a chord

Direction of force R determined by the angle j , formed with the direction of the undisturbed air flow (Fig. 43, a). From the figure it is clear that

Where TO - aerodynamic quality of the profile.

Rice. 43 The center of pressure of the wing and the change in its position depending on the angle of attack

The position of the center of pressure depends on the profile shape and the angle of attack. In Fig. 43, b shows how the position of the center of pressure changes depending on the angle of attack for the profiles of the Yak 52 and Yak-55 aircraft, curve 1 - for the Yak-55 aircraft, curve 2 - for the Yak-52 aircraft.

From the graph it is clear that the position CD when the angle of attack of the symmetrical profile of the Yak-55 aircraft changes, it remains unchanged and is located approximately 1/4 of the distance from the toe of the chord.

Table 1

Designation of weight (cargo)

Empty plane

Takeoff weight

Pilot in the front cockpit

Pilot in the rear cockpit

Fuel in tanks

Oil in tanks

When the angle of attack changes, the pressure distribution along the wing profile changes, and therefore the center of pressure moves along the chord (for the asymmetrical profile of the Yak-52 aircraft), as shown in Fig. 44. For example, with a negative angle of attack of the Yak 52 aircraft, approximately equal to -1°, the pressure forces in the nose and tail parts of the profile are directed in opposite directions and are equal. This angle of attack is called the zero lift angle of attack.

Rice. 44 Moving the center of pressure of the Yak-52 aircraft wing when changing the angle of attack

At a slightly larger angle of attack, the pressure forces directed upward are greater than the force directed downward, their resultant Y will lie behind the greater force (II), i.e., the center of pressure will be located in the tail part of the profile. With a further increase in the angle of attack, the location of the maximum pressure difference moves closer and closer to the leading edge of the wing, which naturally causes movement CD along the chord to the leading edge of the wing (III, IV).

Most forward position CD at critical angle of attack a cr = 18° (V).