Aircraft wing lift presentation. An airplane wing is designed to create lift. Observations and experiments

Skalistovskaya secondary school I-III stage

Elective physics course in grade 10 Research project on the topic

"Study of the dependence of the aerodynamic qualities of the wing on its shape".

Bakhchisarai.

Scientific adviser:

physics teacher Dzhemilev Remzi Nedimovich

Work completed: Erofeev Sergey

10th grade student

(Skalistovskaya general educational

school I - III levels

Bakhchisaray district council

Autonomous Republic of Crimea)

Topic update.

One of the main problems in the design of new aircraft is the choice of the optimal wing shape and its parameters (geometric, aerodynamic, strength, etc.). Aircraft designers had to deal with various unexpected effects that occur at high speeds. Hence the sometimes unusual shapes of the wings of modern aircraft. The wings "bend" back, giving them the appearance of an arrow; or vice versa, the wings become swept back.

The object of our study is the section of aerodynamics physics - this is the section of aeromechanics, which studies the laws of motion of air and other gases and their force interaction with moving solid bodies.

The subject of the study is to determine the magnitude of the wing lift at a certain

airflow velocity relative to the wing. One of the main reasons affecting the shape of the wing is the completely different behavior of the air at high speeds.

Aerodynamics is an experimental science. So far, there are no formulas that allow one to absolutely accurately describe the process of interaction of a solid body with an oncoming air flow. However, it was noticed that bodies having the same shape (with different linear dimensions) interact with the air flow in the same way. Therefore, in the lesson we will conduct research on the aerodynamic parameters of three types of wing with the same cross section, but of different shapes: rectangular, swept and reverse swept when air flows around them.

The observations and experiments that we will make will help us better understand some of the new aspects of the physical phenomena that are observed during the flight of an aircraft.

The relevance of our topic lies in the popularization of aviation, aviation technology.

Research history.

Can we feel the air around us? If we do not move, then we practically do not feel it. When, for example, we rush in a car with open windows, the wind beating in the face resembles a springy jet of liquid. This means that air has elasticity and density and can create pressure. Our distant ancestor did not know anything about experiments proving the existence of atmospheric pressure, but he intuitively understood that if you wave your arms very strongly, you will be able to push off from the air, like a bird. The dream of flying has accompanied man for as long as he can remember. This is evidenced by the famous legend of Icarus. Many inventors have tried to take off. In different countries and at different times there were numerous attempts to conquer the air element. The great Italian artist Leonardo da Vinci sketched out a project for an aircraft powered only by human muscle power. However, nature did not allow man to fly like a bird. But she rewarded him with intelligence, which helped to invent an apparatus heavier than air, capable of lifting off the ground and lifting not only itself, but also a person with loads.

How did he manage to create such a machine? What keeps the plane in the air? The answer is obvious - wings. What keeps the wings? The plane rushes forward, accelerates, a lifting force arises. With sufficient speed, it will lift our aircraft off the ground and hold the aircraft during the flight.

The first theoretical studies and important results were carried out at the turn of the 19th-20th centuries by Russian scientists N. E. Zhukovsky and S. A. Chaplygin.

Nikolai Egorovich Zhukovsky (1847 -1921) - Russian scientist, founder of modern aerodynamics. He built a wind tunnel at the beginning of the century, developed the theory of an airplane wing. In 1890, Zhukovsky published his first work in the field of aviation, To the Theory of Flight.

Sergei Alekseevich Chaplygin (1869 - 1942) Soviet scientist in the field of theoretical mechanics, one of the founders of modern hydroaerodynamics. In his work “On Gas Jets”, he gave a theory of high-speed flights, which served as the theoretical basis for modern high-speed aviation.

“A man does not have wings and, in relation to the weight of his body to the weight of his muscles, he is 72 times weaker than a bird .... But I think that he will fly, relying not on the strength of his muscles, but on the strength of his mind.

NOT. Zhukovsky

Fundamentals of aerodynamics. Basic concepts.

A wind tunnel is an installation that creates an air flow for the experimental study of the flow of air around bodies.

Experiments in a wind tunnel are carried out on the basis of the principle of reversibility of motion - the motion of a body in air can be replaced

the motion of a gas relative to a stationary body.

The wing of an aircraft is the most important part of an aircraft, the source of lift that makes it possible to fly an aircraft. Different aircraft have different wings, which differ in size, shape, position relative to the fuselage.

The wing span is the distance between the ends of the wing in a straight line.

Wing area S- is the area bounded by the contours of the wing. The area of ​​the swept wing is calculated as the area of ​​two trapezoids.

S = 2 · · = bav · ɭ [m2] (1)

The total aerodynamic force is the force R with which the oncoming

air flow acts on a solid body. Expanding this force into vertical Fy and horizontal Fx components (Fig. 1), we obtain the lift force of the wing and the force of its drag, respectively.

Description of the experiment.

To increase the clarity of demonstrations and quantitative analysis of ongoing experiments, we will use a measuring device - to determine the numerical value of the wing lift. The measuring device consists of a metal frame on which an arrow with an unequal lever is fixed. By directing the air flow on the wing model, the balance of the lever occurs, the arrow moves along the scale indicating the angle of deviation of the wing from the horizontal.

Wing models are made of 140 ͯ 50 mm foam. The wings of modern aircraft can be rectangular, swept, reverse-swept in shape.

The model for measuring the magnitude of the wing lift includes the following main blocks (Fig. 4.):

wind tunnel;

Measuring device;

A fixed platform on which the above devices are fixed.

Conducting an experiment.

The model works like this:

For the experiment, the wing model is attached to the lever and set at a distance of 20-25 cm from the wind tunnel. Direct the air flow to the model wing and watch how it rises. Change the shape of the wing. We again bring the lever into balance so that the model takes its original position, and determine the amount of lift, at the same airflow speed.

If the plate is installed along the flow (the angle of attack is zero), then the flow will be symmetrical. In this case, the air flow is not deflected by the plate and the lifting force Y is zero. The resistance X is minimal, but not zero. It will be created by the forces of friction of air molecules on the surface of the plate. The total aerodynamic force R is minimal and coincides with the drag force X.

As the angle of attack gradually increases and the flow slope increases, the lift force increases. Obviously, resistance is also growing. It should be noted here that at low angles of attack, the lift force grows much faster than the drag.

Rectangular wing.

• Wing mass m ≈ 0.01 kg;
• wing deflection angle α = 130, g ≈ 9.8 N/kg.

Wing area S= 0.1 0.027 = 0.0027 m2

Lifting force of the wing Ru = = 0.438 N

Frontal resistance Rх = = 0.101 N

K \u003d Fu / Fx \u003d 0.438 / 0.101 \u003d 4.34

The greater the aerodynamic quality of the wing, the more perfect it is.

• As the angle of attack increases, it becomes more difficult for the airflow to flow around the plate. The lifting force, although it continues to increase, but more slowly than before. But the resistance grows faster and faster, gradually overtaking the growth of lift. As a result, the total aerodynamic force R begins to deviate backwards. The picture is changing dramatically.

The air streams are not able to smoothly flow around the upper surface of the plate. A powerful vortex is formed behind the plate. Lift drops sharply and drag increases. This phenomenon in aerodynamics is called STALL. A "plucked" wing ceases to be a wing. It stops flying and starts falling.

In our experiment, already at the wing deflection angle α = 600 and more, the wing is stalled; it does not fly, g ≈ 9.8 N/kg

Wing lift Ry = = 0.113 N

Frontal resistance Rх = = 0.196 N

Aerodynamic quality of the wing K = 0.113/0.196 = 0.58

Arrow wing.

Wing mass m ≈ 0.01 kg;

wing deflection angle α = 200, g ≈ 9.8 N/kg

Wing area S= 0.028 m2

Lifting force of the wing Ru = = 0.287 N

Frontal resistance R x \u003d \u003d 0.104 N

Aerodynamic quality of the wing

K \u003d Fu / Fx \u003d 0.287 / 0.104 \u003d 2.76

Wing with reverse sweep.

Wing mass m ≈ 0.01 kg;

wing deflection angle α = 150, g ≈ 9.8 N/kg

Wing area S= 0.00265 m2

Lift force of the wing Ru = = 0.380 N

Frontal resistance Rx \u003d \u003d 0.102 N

Aerodynamic quality of the wing

K \u003d Fu / Fx \u003d 0.171 / 0.119 \u003d 3.73

Experiment Analysis

When analyzing the experiment and the results obtained, we proceeded from the thesis that the greater the aerodynamic quality of the wing, the better it is.

In the first case of our experiment, the best wings were a rectangular wing and a swept back wing. The main advantage of a straight wing is its high lift coefficient K = 4.34. For a swept wing, the lift coefficient is K = 2.76 and, accordingly, the reverse sweep wing has a lift coefficient equal to K = 3.73. Therefore, it turned out that the best wing turned out to be a rectangular wing and a swept back wing.

They repeated their experience with a greater force of the air flow: in this case, the aerodynamic qualities of the straight wing and the reverse swept wing decreased K = 2.76 and K = 1.48 quite sharply, but the aerodynamic quality of the swept wing changed slightly K = 2.25.

Analyzing the results obtained for the swept wing, we noticed that with an increase in the speed of the air flow, the drag of the wing increases rather slowly, while maintaining the lift coefficient almost unchanged.

In this paper, we studied the dependence of the wing lift force only on its planform. In real flight, the lift force of a wing also depends on its area, profile, as well as on the angle of attack, speed and flow density, and on a number of other factors.

For the experiment to be clean, the following conditions must be met.

• the air flow was kept constant;
• the axis of the wing and the axis of the wind tunnel coincided.
• the distance from the end of the pipe to the wing attachment point was always the same;

• P.S. Kudryavtsev. AND I. Confederates. History of physics and technology. Textbook for students of pedagogical institutes. State Educational and Pedagogical Publishing House of the Ministry of Education of the RSFSR. Moscow 1960
• Physics. I know the world. Children's encyclopedia. Moscow. AST. 2000
• V.B. Baidakov, A.S. Klumov. Aerodynamics and flight dynamics of aircraft. Moscow. "Engineering", 1979
• Great Soviet Encyclopedia. 13. Third edition. Moscow. "Soviet Encyclopedia", 1978

Age: 14 years old

Place of study: MBOU LAP №135

City, region: Samara, 63

Head: Samsonova Natalya Yurievna, teacher of physics

Historical research work "Paper airplane - children's fun and scientific research"

Introduction____________________________________________________ 2

Targets and goals _________________________________________________________3-4

Main part ________________________________________________________5-12

The lifting force of the aircraft wing _____________________________________________ 5-8

The history of the development of aircraft ________________________________________________9-10

Factors influencing the lift force of an aircraft wing ________________________ 10

Factors influencing the flight range ______________________________________ 10

Factors affecting the flight time ___________________________________________10

Observations and experiments _____________________________________________________________ 10-12

Methodology________________________________________________________________________________12

Conclusion _____________________________________________________________13

Bibliography_______________________________________________ 14

Introduction

People have long dreamed of flying. Make wings like birds, insects, bats. How many different living creatures are carried in the air, but a person cannot!

Bold inventors tried to make wings for people. But no one could fly on such wings. The man did not have enough strength to lift himself into the air. In the best case, the inventors managed to land safely on the ground, gliding on their wings from a mountain or a high tower. This did not require force.

Every time I see an airplane - a silver bird soaring into the sky - I admire the power with which it easily overcomes the earth's gravity and plows the heavenly ocean and ask myself questions:

• How should an aircraft wing be constructed to support a large load?
• What should be the optimal shape of a wing that cuts through the air?
• What characteristics of the wind help an airplane in its flight?
• What speed can an aircraft reach?

Man has always dreamed of rising into the sky “like a bird” and since ancient times he has tried to make his dream come true. In the 20th century, aviation began to develop so rapidly that mankind could not save many of the originals of this complex technology. But many samples have been preserved in museums in the form of reduced models, giving an almost complete picture of real machines.

I chose this topic because it helps in life not only to develop logical technical thinking, but also to join the practical skills of working with paper, materials science, technology for designing and constructing aircraft. And the most important thing is the creation of your own aircraft.

We put forward hypothesis - it can be assumed that the flight characteristics of the aircraft depend on its shape.

We used the following research methods:

• Study of scientific literature;
• Obtaining information on the Internet;
• Direct observation, experimentation;
• Creation of experimental pilot models of aircraft;

Goal and tasks

Objective: Design aircraft with the following characteristics: maximum range and flight duration.

Tasks:

Analyze information obtained from primary sources;

To study the elements of the ancient oriental art of aerogami;

To get acquainted with the basics of aerodynamics, the technology of designing aircraft from paper;

Test the constructed models;

Develop skills for the correct, effective launch of models;

As the basis of my research, I took one of the areas of Japanese origami art - aerogami(from Japanese “gami” - paper and Latin “aero” - air).

Aerodynamics (from the Greek words aer - air and dinamis - force) is the science of forces arising from the movement of bodies in the air. Air, due to its physical properties, resists the movement of solid bodies in it. At the same time, interaction forces arise between bodies and air, which are studied by aerodynamics.

Aerodynamics is the theoretical basis of modern aviation. Any aircraft flies, obeying the laws of aerodynamics. Therefore, for an aircraft designer, knowledge of the basic laws of aerodynamics is not only useful, but simply necessary. While studying the laws of aerodynamics, I made a series of observations and experiments: "Selecting the shape of an aircraft", "Principles of creating a wing", "Blow", etc.

Design.

Folding a paper airplane is not as easy as it seems. Actions must be confident and precise, folds - perfectly straight and in the right places. Simple designs are forgiving, while in complex designs a couple of imperfect angles can lead the assembly process to a dead end. In addition, there are cases where the fold needs to be intentionally not very precise.

For example, if one of the last steps requires folding a thick sandwich structure in half, the fold will not work unless you make a correction for thickness at the very beginning of the fold. Such things are not described in diagrams, they come with experience. And the symmetry and precise weight distribution of the model determine how well it will fly.

The key point in "paper aviation" is the location of the center of gravity. Creating various designs, I propose to make the nose of the aircraft heavier by placing more paper in it, to form full-fledged wings, stabilizers, and a keel. Then the paper airplane can be controlled like a real one.

For example, through experimentation, I found that the speed and flight path can be adjusted by bending the back of the wings like real flaps, slightly turning the paper keel. Such control is the basis of "paper aerobatics".

Aircraft designs vary significantly depending on the purpose of their construction. For example, aircraft for long-distance flights resemble a dart in shape - they are just as narrow, long, rigid, with a pronounced shift in the center of gravity towards the nose. Planes for the longest flights are not rigid, but they have a large wingspan and are well balanced. Balancing is extremely important for street launched aircraft. They must maintain the correct position, despite the destabilizing fluctuations in the air. Indoor-launched aircraft benefit from a nose-down center of gravity. Such models fly faster and more stable, they are easier to launch.

Tests

In order to achieve high results at the start, it is necessary to master the correct throwing technique.

• To send the plane to the maximum distance, you need to throw it forward and up at an angle of 45 degrees as much as possible.
• In time-of-flight competitions, you should throw the plane to the maximum height so that it glides down longer.

Launching in the open air, in addition to additional problems (wind), creates additional advantages. Using updrafts of air, you can make the plane fly incredibly far and long. A strong updraft can be found, for example, near a large multi-storey building: hitting a wall, the wind changes direction to vertical. A friendlier airbag can be found on a sunny day in a car park. Dark asphalt gets very hot, and the hot air above it rises smoothly.

Main part.

1.1 Aircraft wing lift.

What moving streams do not get up to - they even push ships together. Is it possible to use their power to lift bodies up? Motorists know that at high speed the front of the car can take off from the road, as if to take off. They even put anti-wings to prevent this from happening. Where does lift force come from?

Here we can not do without such a thing as a wing. The simplest wing is, perhaps, a kite (Fig. 216). How does he fly? Recall that we pull the kite by the rope, creating a wind running on its plane, or wing. Let's denote the plane of the wing AB, the tension of the rope Q, the own weight of the kite P, the resultant of these forces R, 1

The AB wind running on the plane of the kite, reflecting from it, creates a lifting force R, which, so that the kite does not fall, should be equal to R, and preferably more, so that the kite rises up. Do you feel that everything is not so simple when it comes to flying? Even more difficult than with a kite, the situation is with the lifting force of an aircraft wing.

The section of the aircraft wing is shown in Fig. 217 a. Practice has shown that in order to carry out the lift, the wing of an aircraft must be located so that there is a certain angle a - the angle of attack, between its bottom line and the direction of flight. This angle is changed by the action of the elevator.

During horizontal flight, the angle a does not exceed 1-1.5 °, while landing - about 15 °. It turns out that in the presence of such an angle of attack, the speed of the airflow flowing around the wing from above will be greater than the speed ^/^ of the flow flowing around the lower surface of the wing. On fig. 217 and this difference in velocities is marked by different density of the streamline.

Rice. 217. How do the lifting force of the wing (a) and the forces acting on the aircraft (b) arise

But, as we already know, in that place of the flow, where the speed is greater, the pressure is less, and vice versa. Therefore, when the aircraft moves in the air, there will be a reduced pressure above the upper surface of the wing, and an increased pressure above the lower one. This pressure difference causes an upward force R to act on the wing.

The vertical component of this force - the force F is a lifting force directed against the body weight P. If this force is greater than the weight of the aircraft, the latter will rise up. The second component Q is the frontal resistance, it is overcome by the thrust of the propeller.

On fig. 217, b shows the forces acting on the aircraft during horizontal uniform flight: F, - lifting force, P - aircraft weight, F., - drag and F - propeller thrust.

A great contribution to the development of the theory of the wing, and indeed of the aerodynamic theory in general, was made by the Russian scientist, Professor N. E. Zhukovsky (1847-1921). Even before human flights, Zhukovsky said interesting words: “Man does not have wings, and in relation to the weight of his body to the weight of muscles, he is 72 times (!) Weaker than a bird. But I think that he will fly, relying not on the strength of his muscles, but on the strength of his mind.

Rice. 218. The shape of the wings in terms of M< 1 и М > 1

Aviation has long crossed the sound barrier, which is measured by the so-called Mach number - M. At subsonic speed M< 1, при звуковой М = 1, при сверхзвуковой М >1. And the shape of the wing has changed - it has become thinner and sharper. The shape of the wings has also changed. Subsonic wings are rectangular, trapezoidal or elliptical. Transonic and supersonic wings are swept, deltoid (like the Greek letter "delta") or triangular (Fig. 218). The fact is that when an aircraft moves at near- and supersonic speeds, so-called shock waves arise, associated with the elasticity of air and the speed of sound propagation in it. To reduce this harmful phenomenon, wings of a sharper shape are used. The pattern of air flow around subsonic and supersonic wings is shown in Fig. 219, where you can see the difference in their interaction with air.

And supersonic aircraft equipped with such wings are shown in Fig. 220.

Rice. 219. Pattern of air flow around subsonic and supersonic wings

Rice. 220. Supersonic bomber (a) and fighters (b)

Aircraft with a speed of M > 6 are called hypersonic. Their wings are built in such a way that the shock waves from the flow around the fuselage and the wing seem to cancel each other out. That is why the shape of the wings of such aircraft is intricate, the so-called W-shaped, or M-shaped (Fig. 221).

Rice. 221. Hypersonic aircraft

Rice. 222. Aircraft evolution

History of aircraft development

Briefly about the history of human flight and the evolution of aircraft (Fig. 222).

In 1882, the Russian officer A.F. Mozhaisky built an airplane with a steam engine, which, due to its heavy weight, could not take off. A few years later, the German engineer Lilienthal made a series of gliding flights on a balancing glider he built, which was controlled by moving the center of gravity of the pilot's body. During one of these flights, the glider lost stability, and Lilienthal died. In 1901, American mechanics, the Wright brothers, built a glider from bamboo and linen and made several successful flights on it. The glider was launched from a gentle hillside using a primitive catapult, consisting of a small log tower and a rope with a load. In the summer, the brothers learned to fly, and the rest of the time they worked in their bicycle workshop, saving up money to continue the experiments. In the winter of 1902-1903, they made a gasoline internal combustion engine, installed it on their glider, and on December 17, 1903, made their first flights, the longest of which, although it lasted only 59 seconds, nevertheless showed that the aircraft was able to take off and stay in air.

Having improved the aircraft and achieved some flying skills, the Wright brothers in 1906 made public their invention. From that moment began the rapid development of aviation in many countries of the world. After 3 years, the French engineer Blériot flew a plane of his design across the English Channel, proving the ability of this machine to fly over the sea. Less than 20 years later, a single-seat plane flew from America to Europe across the Atlantic Ocean, and 10 years later, in the summer of 1937, three Soviet pilots - V.P. Chkalov, G.F. Baidukov and A.V. Belyakov - on the plane of A. N. Tupolev ANT-25 flew from Moscow to America through the North Pole. A few days later, M. M. Gromov, A. B. Yumashev and S. A. Danilin, flying the same route, set a world record for straight flight distance, covering 10,300 km without landing.

Along with the range, the carrying capacity, altitude and speed of aircraft grew. The first super-heavy aircraft "Ilya Muromets" was built in Russia. This four-engine giant was so superior to all the machines of that time that for a long time abroad they could not believe in the existence of such an aircraft. In 1913, Ilya Muromets broke world records for range, altitude and payload.

If the speed of the Wright brothers' plane was about 50 km / h, then modern planes fly several times faster than sound. And rockets fly even faster. For example, the launch vehicle that launched the first artificial Earth satellite into orbit had М>28.

1.2 Factors affecting the lift force of an aircraft wing.

1)air speed

2) wing shape

3) medium density

1.3 Factors affecting flight range.

1) aircraft weight

2) wing shape

1.4 Factors affecting the flight time.

1) high-altitude jet stream;

2) tailwind, headwind, side wind;

3) wing shape

1.5 Observations and experiments.

Observations

The choice of the form of the aircraft.

Experience #1

Conclusion:

The streamlined shape helps keep the aircraft in the air. As it slides forward, it creates lift. The plane will rise until the force with which I launched its air is exhausted. And a simple sheet of paper has too much support surface, which is not conducive to proper flight.

Wing principles.

Equipment:

• Paper;
• Two books.

Experience No. 2

Sudden gust of wind:

Experience No. 3

Equipment:

• Paper;
• Two books.

Experience No. 4

A whiff.

Equipment:

• Two strips of paper

Conclusion:

The air slides faster over the top, curved part of the wing, which has a higher leading edge than the trailing edge (this helps the air slide off the wing). Therefore, the air pressure under the wing is higher, so it pushes the wing up. The force supporting the wing is caused by the pressure difference. It's called lift. The airflow on the wing can be diverted down by means of flaps or ailerons. They allow the aircraft to take off, make turns and fly at low altitude even at low speed.

1.6 Methodology

I decided to conduct an experiment proving the dependence of flight time and range on the shape of the wing. I made 5 paper plane models. I have launched planes of the same mass with the same force several times. After running all the models, I recorded the results of the runs and the arithmetic average result in the table. Based on the arithmetic mean, I found the winners in terms of flight range and time (model No. 2 and model No. 5). The flight time and range are different for all models => the flight range and time depend on the shape of the wing.

Conclusion

Analysis of test results:

To evaluate the models, I decided to use 5

Ball system:

Based on the table, I found the best option for paper planes: model No. 4. Model #2 is good for long range competitions, while Model #3 has a longer flight time.

During the experiments, I did not manage to accurately measure the range and flight time of each aircraft, launch aircraft with the same force, I managed to approximately measure the flight time and range of each aircraft.

Thanks to these experiences and information from the Internet, I was able to compile a table of cross-sectional shapes of aircraft wings and their purpose:

List of used literature

1) Antonov O.K., Paton B.I. Gliders, airplanes. Sciences. Dumka, 1990. - 503 p.

2) The Big Book of Experiments for Schoolchildren / ed. Antonella Meyani. - M.: CJSC "ROSMEN-PRESS", 2007. - 260 p. http://www.ozon.ru/context/detail/id/121580 /

3) Mikortumov E.B., Lebedinsky M.S. aircraft modeling; Digest of articles. Manual for leaders of aircraft modeling circles. - M. Uchpedgiz, 1960. - 144 p.

4) Nikulin A.P. Collection of the best paper models (origami). The art of paper folding. - M.: Terra - Book Club, 2005, 68 p.

5) Svishchev G.P.. Belov A.F. Aviation: an encyclopedia. - M.: "Great Russian Encyclopedia", 194. - 756 p. Sukharevskaya O.N. Origami for the little ones. - M.: Iris Press, 2008. - 140 p.

6) Amazing physics - What N.V. Gulia's textbooks were silent about

By clicking on the "Download archive" button, you will download the file you need for free.
Before downloading this file, remember those good essays, control, term papers, theses, articles and other documents that are unclaimed on your computer. This is your work, it should participate in the development of society and benefit people. Find these works and send them to the knowledge base.
We and all students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

To download an archive with a document, enter a five-digit number in the field below and click the "Download archive" button

Similar Documents

Calculation and construction of the polars of a subsonic passenger aircraft. Determination of the minimum and maximum drag coefficients of the wing and fuselage. Summary of detrimental aircraft drags. Construction of polars and lift coefficient curve.

term paper, added 03/01/2015


Structural and aerodynamic features of the aircraft. Aerodynamic forces of the Tu-154 wing profile. Influence of flight mass on flight characteristics. Aircraft takeoff and descent. Determination of moments from gas-dynamic rudders.

term paper, added 12/01/2013


Air flow around a body. Aircraft wing, geometric characteristics, mean aerodynamic chord, drag, lift-to-drag ratio. Aircraft polar. The center of pressure of the wing and the change in its position depending on the angle of attack.

term paper, added 09/23/2013


Study of aircraft takeoff and landing characteristics: determination of wing dimensions and sweep angles; calculation of the critical Mach number, aerodynamic drag coefficient, lift force. Construction of takeoff and landing polars.

term paper, added 10/24/2012


Calculation of the strength of the wing of a large aspect ratio of a transport aircraft: determination of the geometric parameters and weight data of the wing. Construction of a diagram of transverse forces and moments along the length of the wing. Design and verification calculation of the wing cross section.

term paper, added 06/14/2010


Flight characteristics of the Yak-40 aircraft for the loading case. Geometric characteristics of power elements of the wing. Converting a complex wing into a rectangular wing. Calculation of loading forces and loads. Determination of stresses in wing sections.

term paper, added 04/23/2012


Parameters of an aircraft with a rectangular wing. Determination of bevel angles in the central and end sections of the wing, with a U-shaped model of the vortex system. Calculation of the maximum pressure drop on the wing skin under the action of the total pressure of the oncoming flow.

test, added 03/24/2019

slide 1

Project in physics on the topic: Completed by: Popov Ruslan, student of class 10 "A" of the NOU "Secondary school No. 38 of Russian Railways" Teacher: Valoven S. A. Michurinsk, 2008

slide 2

slide 3

slide 4

The lifting force of the wing (let's denote it F) arises due to the fact that the cross section of the wing is most often an asymmetric profile with a more convex upper part. The wing of an airplane or glider, moving, cuts through the air. One part of the streams of the oncoming air flow will go under the wing, the other - above it. F menu next exit

slide 5

The upper part of the wing is more convex than the lower part, therefore, the upper jets will have to travel a longer distance than the lower ones. However, the amount of air entering the wing and flowing down from it is the same. This means that the upper streams, in order to keep up with the lower ones, must move faster. The pressure under the wing is greater than over the wing. This pressure difference creates the aerodynamic force R, one of the components of which is the lifting force F. menu next exit

slide 6

The lift force of the wing is the greater, the greater the angle of attack, profile curvature, wing area, air density and flight speed, and the lift force depends on the speed squared. The angle of attack must be less than the critical value, with an increase in which the lift drops. menu next exit α

Slide 7

Developing lift, the wing always experiences drag X directed against the movement and, therefore, slows it down. The lifting force is perpendicular to the oncoming flow. The force R is called the total aerodynamic force of the wing. The point of application of the aerodynamic force is called the center of pressure of the wing (CP). menu next exit

Slide 8

F = CF 2/2 S is the formula for calculating lift, where: F is the lift of the wing, CF is the lift coefficient, S is the area of ​​the wing. R = CR 2/2 S is the formula for calculating the aerodynamic force, where: CR is the aerodynamic force coefficient. S is the area of ​​the wing. menu exit

Slide 9

The lifting force of the aircraft, balancing its weight, makes it possible to fly, while drag slows down its movement. Frontal resistance is overcome by the traction force developed by the power plant. An aircraft needs a power plant to develop lift and to move in space. The greater the speed, the greater the lift. On modern aircraft, the wings are made of a swept design so that the wing does not collapse in flight from drag. menu next exit

slide 10

The design of aircraft engines has changed over time. There are three main types of aircraft engines: 1. piston, 2. turboprop, 3. jet. All these engines differ in speed and traction performance. The jet engine is more advanced. Modern combat aircraft with this type of engine exceed the speed of sound by several times. menu next exit

slide 11

(1847 -1921) Great Russian scientist, founder of modern hydro- and aeromechanics, "father of Russian aviation". Zhukovsky was born into the family of a railway engineer. In 1858 he entered the 4th Moscow Men's Classical Gymnasium and graduated from it in 1864. In the same year he entered the Faculty of Physics and Mathematics at Moscow University, graduating in 1868 with a degree in applied mathematics. In 1882, Zhukovsky was awarded the degree of Doctor of Applied Mathematics. menu next exit

slide 12

From the beginning of the 20th century, Zhukovsky's main attention was directed to the development of aerodynamics and aviation issues. In 1904, under his leadership, in the village of Kuchin, near Moscow, the first aerodynamic institute in Europe was built. Huge work was done by Zhukovsky on the training of aviation personnel - aircraft designers and pilots. One of the most striking centers of the emerging domestic aviation science was the aeronautics circle organized by N.E. Zhukovsky at the Moscow Technical School. It was here that the world-famous aviation designers and scientists began their creative path: A.S. Tupolev, V.P. Vetchinkin, B.N. Yuryev, B.S. Stechkin, A.A. Arkhangelsky and many others. menu next exit

slide 13

In 1904, in the Kuchinsky laboratory, Zhukovsky made a remarkable discovery that served as the basis for all further development of modern aerodynamics and its application to the theory of aviation. Zhukovsky did not work, only when he slept. He had never flown in an airplane in his life. In connection with the first successes of aviation, the scientist faced the task of finding out the source of the lift force, the possibility of its increase, and finding a mathematical method for its calculation. On November 15, 1905, Zhukovsky gave a formula for determining the lift force, which is the basis of all aerodynamic calculations of an aircraft. menu next exit 1. Ermakov A. M. “The simplest aircraft models”, 1989 2. Abstracts of the Kirsanov Aviation Technical School of Civil Aviation, 1988 3. TSB, ed. Vvedensky B.A., v.16 4. Internet resources: http://media.aplus.by/page/42/ http://sfw.org.ua/index.php?cstart=502& http:// www.atrava.ru/08d36bff22e97282f9199fb5069b7547/news/22/news-17903 http://www.airwar.ru/other/article/engines.html http://arier.narod.ru/avicos/l-korolev.htm http ://kto-kto.narod.ru/bl-bl-3/katanie.html http://www.library.cpilot.info/memo/beregovoy_gt/index.htm http://vivovoco.ibmh.msk.su /VV/PAPERS/HISTORY/SIMBIRSK/SIMBIRSK.HTM exit menu

* An aircraft wing is designed to generate the lift needed to support the aircraft in the air. The aerodynamic quality of the wing is greater, the greater the lift and the less drag. The lift and drag of the wing depend on the geometric characteristics of the wing. The geometric characteristics of the wing are reduced to the characteristics of the wing in plan and the characteristics

The wings of modern aircraft are elliptical in plan (a), rectangular (b), trapezoidal (c), swept (d) triangular (e)

The angle of the transverse V wing Geometric characteristics of the wing The shape of the wing in plan is characterized by span, area elongation, narrowing, sweep and transverse V Wingspan L is the distance between the ends of the wing in a straight line. The area of ​​the wing in terms of Skr is limited by the contours of the wing.

The area of ​​the trapezoidal and swept wings is calculated as the area of ​​two trapezoids where b 0 is the root chord, m; bk - end chord, m; - the average wing chord, m Wing extension is the ratio of the wing span to the average chord. If instead of bav we substitute its value from equality (2. 1), then the wing extension will be determined by the formula For modern supersonic and transonic aircraft, the wing extension does not exceed 2 - 5. For low-speed aircraft, the aspect ratio can reach 12-15, and for gliders up to 25.

Wing taper is the ratio of the axial chord to the end chord. For subsonic aircraft, the taper of the wing usually does not exceed 3, and for transonic and supersonic aircraft, it can vary widely. The sweep angle is 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 line of foci (passing 1/4 of the chord from the edge of attack) or along another line of the wing. For transonic aircraft, it reaches 45°, and for supersonic aircraft - up to 60°. The transverse angle V of the wing is the angle between the transverse axis of the aircraft and the lower surface of the wing. In modern aircraft, the transverse V angle ranges from +5° to -15°. The profile of a wing is the shape of its cross section. Profiles can be symmetrical or asymmetrical. Asymmetric, in turn, can be biconvex, plano-convex, concave-convex, etc. S-shaped. Lenticular and wedge-shaped can be used for supersonic aircraft. The main characteristics of the profile are: profile chord, relative thickness, relative curvature

Profile chord b is a straight line segment connecting the two most distant points of the profile Forms of wing profiles 1 - symmetrical; 2 - not symmetrical; 3 - plano-convex; 4 - biconvex; 5 - S-shaped; 6 - laminated; 7 - lenticular; 8 - diamond-shaped; 9 prominent

Geometric characteristics of the profile: b - profile chord; Cmax - maximum thickness; fmax - curvature arrow; x-coordinate of greatest thickness Angles of attack of the wing

The total aerodynamic force and the point of its application R is the total aerodynamic force; Y - lifting force; Q is the drag force; - attack angle; q - quality angle The relative profile thickness c is the ratio of the maximum thickness Сmax to the chord, expressed as a percentage:

The relative airfoil thickness c is the ratio of the maximum thickness Cmax to the chord, expressed as a percentage: The position of the maximum airfoil thickness Xc is expressed as a percentage of the chord length and is measured from the toe. For modern aircraft, the relative airfoil thickness is in the range of 416%. The relative profile curvature f is the ratio of the maximum curvature f to the chord, expressed as a percentage. The maximum distance from the center line of the profile 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. For symmetrical profiles, the relative curvature is equal to zero, while for asymmetric profiles this value is nonzero and does not exceed 4%.

AVERAGE AERODYNAMIC WING CHORD The average aerodynamic wing chord (MAC) is 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

For a trapezoidal untwisted wing, the MAR is determined by geometric construction. To do this, the wing of the aircraft is drawn in plan (and on a certain scale). On the continuation of the root chord, a segment equal in size to the end chord is deposited, and on the continuation of the end 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 middle line of the wing, connecting the straight middle of the root and end chords. The mean aerodynamic chord (MAC) will pass through the intersection point of these two lines.

Knowing the magnitude and position of the MAR on the aircraft and taking it as a baseline, the position of the aircraft's center of gravity, the center of pressure of the wing, etc., is determined relative to it. The aerodynamic force of the aircraft is created by the wing and 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 forces is formed. The value 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 of the MAR, expressed in linear terms or as a percentage of the length of the MAR.

WING Drag Drag is the resistance to the movement of an airplane's wing in the air. It consists of profile, inductive and wave resistance: Xcr=Xpr+Hind+XV. Wave drag will not be considered, as it occurs at flight speeds above 450 km/h. The profile resistance is made up of pressure and friction resistance: Хpr=ХД+Хtr. Pressure drag 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, in the figure Cx is indicated - the coefficient of profile resistance).

The greater the relative thickness c of the airfoil, the more the pressure rises 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, consequently, the pressure resistance increases. When an air flow flows around the wing profile at angles of attack close to critical, the pressure resistance increases significantly. In this case, the dimensions of the swirling wake jet and the vortices themselves increase sharply. Friction resistance arises due to the manifestation of air viscosity in the boundary layer of the flowing wing profile. The magnitude of 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, friction resistance is less than in a turbulent boundary layer. Consequently, the greater part of the wing surface flows around the laminar boundary layer of the air flow, the lower the friction resistance. The value of friction resistance is affected by: aircraft speed; surface roughness; wing shape. The higher the flight speed, the wing surface is processed with worse quality and the wing profile is thicker, the greater the friction resistance.

Inductive drag is an increase in drag associated with the formation of wing lift. When an undisturbed air flow flows around a 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

The angle at which the flow of air flowing around the wing with a speed V induced by a vertical speed U is deflected is called the skew angle of the flow. Its value depends on the value of the vertical velocity induced by the vortex bundle and the oncoming flow velocity V

Therefore, due to the bevel of the flow, the true angle of attack of the east of the wing in each of its sections will differ from the geometric or apparent angle of attack each by an amount. As you know, the lift force of the wing ^ Y is always perpendicular to the oncoming flow, its direction. Therefore, the lift force vector of the wing deviates by an angle and is perpendicular to the direction of the air flow V. The lift force will not be the entire force ^ Y "but its component Y, directed perpendicular to the oncoming flow

In view of the smallness of the value, we consider equal to Another component of the force Y "will be This component is directed along the flow and is called inductive drag (Fig. presented above). To find the value of inductive drag, it is necessary to calculate the speed ^ U and the flow angle. Dependence of the flow angle on the aspect ratio of the wing , the coefficient of lift Su and the shape of the wing in plan is expressed by the formula in terms of.

where Cxi is the coefficient of inductive resistance. It is determined by the formula It can be seen from the formula that Cx is directly proportional to the lift coefficient and inversely proportional to the aspect ratio of the wing. At an angle of attack of zero lift o, the inductive reactance will be zero. At supercritical angles of attack, the smooth flow around the wing profile is disturbed and, therefore, the formula for determining Cx 1 is not acceptable for determining its value. Since the value of Cx is inversely proportional to the aspect ratio of the wing, therefore, aircraft intended for flights over long distances have a large aspect ratio of the wing: = 14 ... 15.

WING aerodynamic quality 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 is the lift force, kg; Q - drag force, kg. Substituting the values ​​of Y and Q into the formula, we get The greater the aerodynamic quality of the wing, the more perfect it is. The value of quality for modern aircraft can reach 14-15, and for gliders 45-50. This means that the wing of an aircraft can create lift that is 14 to 15 times the drag, and for gliders even 50 times.

The lift-to-drag ratio is characterized by the angle The angle between the vectors of lift and total aerodynamic forces is called the lift-to-drag angle. The greater the lift-to-drag ratio, the smaller the lift angle, and vice versa. The aerodynamic quality of the wing, as can be seen from the formula, depends on the same factors as the coefficients Cy and Cx, i.e., on the angle of attack, airfoil shape, wing shape in plan, flight M number and surface treatment. INFLUENCE ON THE ANGLE OF ATTACK QUALITY 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 Kmax. This angle is called the most advantageous angle of attack, naive. equals zero. The effect on the lift-to-drag ratio of the airfoil shape is related to the relative thickness and curvature of the airfoil. In this case, the shape of the profile lines, the shape of the nose and the position of the maximum thickness of the profile along the chord have a great influence. To obtain the highest quality values, the best wing shape is elliptical with a rounded leading edge.

Graph of the dependence of the aerodynamic quality on the angle of attack Formation of suction force Dependence of the aerodynamic quality on the angle of attack and airfoil thickness Change in the aerodynamic quality of the wing depending on the M number

WING POLAR For various calculations of the flight characteristics of a wing, it is especially important to know the simultaneous change in Cy and Cx in the range of flight angles of attack. For this purpose, a graph of the dependence of the coefficient Su on Cx is constructed, called the polar. The name “polar” is explained by the fact that this curve can be considered as a polar diagram built on the coordinates of the coefficient of the total aerodynamic force CR and, where is the angle of inclination of the total aerodynamic force R to the direction of the oncoming flow velocity (provided that the scales Su and Cx are taken the same ). The principle of construction of the wing polar Wing polar If from the origin, aligned with the airfoil pressure center, a vector is drawn to any point on the polar, then it will be a diagonal of a rectangle, the sides of which are respectively equal to Сy and Сх. drag and lift coefficient from angles of attack - the so-called wing polar.

The polar is constructed for a well-defined wing with given geometric dimensions and profile shape. A number of characteristic angles of attack can be determined from the wing polar. The zero-lift angle o is located at the intersection of the polar with the Cx axis. At this angle of attack, the lift coefficient is zero (Сy = 0). For the wings of modern aircraft, usually o = Angle of attack at which Cx has the smallest Cx value. min. is found by drawing a tangent to the polar parallel to the Cy axis. For modern wing profiles, this angle is in the range from 0 to 1°. The most advantageous angle of attack is naive. Since at the most favorable angle of attack the aerodynamic quality of the wing is maximum, the angle between the axis Сy and the 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 the naive, it is necessary to draw a tangent to the polar from the origin. The touch point will match the naive. For modern wings, naive lies in the range of 4 - 6 °.

Critical angle of attack crit. To determine the critical angle of attack, it is necessary to draw a tangent to the polar parallel to the Cx axis. The touch point and will correspond to crit. For the wings of modern aircraft, crit = 16 -30°. The angles of attack with the same lift-to-drag ratio are found by drawing a secant from the origin to the polar. At the intersection points, we find the angles of attack (u) during flight, at which the lift-to-drag ratio will be the same and necessarily less than Kmax.

AIRCRAFT POLAR One of the main aerodynamic characteristics of an aircraft is the aircraft polar. The lift coefficient of the wing Cy is equal to the lift coefficient of the entire aircraft, and the drag coefficient of the aircraft for each angle of attack is greater than Cx of the wing by the value of Cxvr. In this case, the aircraft polar will be shifted to the right of the wing polar by Cx temp. The aircraft polar is built using the data of the dependences Сy=f() and Сх=f(), obtained experimentally by blowing models in wind tunnels. The angles of attack on the aircraft's polar are affixed by horizontally transferring the angles of attack marked on the wing's polar. The determination of aerodynamic characteristics and characteristic angles of attack along the aircraft polar is carried out in the same way as it was done on the wing polar.

The zero-lift angle of attack of an aircraft is practically the same as the zero-lift angle of attack of a wing. Since the lift force is zero at the angle, at this angle of attack only vertical downward movement of the aircraft, called a vertical dive, or a vertical slide at an angle of 90 ° is possible.

The angle of attack at which the drag coefficient has a minimum value is found by drawing a tangent to the polar parallel to the Cy axis. When flying at this angle of attack, there will be the least drag losses. At this angle of attack (or close to it), the flight is performed at maximum speed. The most favorable angle of attack (naive) corresponds to the highest value of the aerodynamic quality of the aircraft. Graphically, this angle, as well as for the wing, is determined by drawing a tangent to the polar from the origin. It can be seen from the graph that the slope of the tangent to the aircraft polar is greater than that of the tangent to the wing polar. Conclusion: the maximum quality of the aircraft as a whole is always less than the maximum aerodynamic quality of a single wing.

It can be seen from the graph that the most advantageous angle of attack of the aircraft is greater than the most advantageous angle of attack of the wing by 2 - 3°. The critical angle of attack of an aircraft (crit) does not differ in its value from the value of the same angle for the wing. The extension of the flaps to the takeoff position (= 15 -25°) allows you to increase the maximum lift coefficient Sumax 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. Due to the release of the flaps (or flaps) in the takeoff position, the takeoff run is reduced by up to 25%.

When the flaps (or flaps) are extended to the landing position (= 45 - 60°), the maximum lift coefficient can increase up to 80%, which drastically reduces the landing speed and the length of the run. However, the drag in this case increases more intensively than the lifting force, so the aerodynamic quality is significantly reduced. But this circumstance is used as a positive operational factor - the steepness of the trajectory increases during gliding before landing and, consequently, the aircraft becomes less demanding on the quality of approaches in the alignment of the runway. However, when such M numbers are reached at which compressibility can no longer be neglected (M > 0.6 - 0.7), the lift and drag coefficients must be determined taking into account the correction for compressibility. where Suszh is the lift coefficient taking into account compressibility; Suneszh is the lift coefficient of an incompressible flow for the same angle of attack as Suszh.

Up to the numbers M = 0.6 -0.7, all the polars practically coincide, but at large numbers ^ M they begin to shift to the right and simultaneously increase the slope to the Cx axis. The displacement of the polars to the right (by large Cx) is due to an increase in the profile resistance coefficient 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. An increase in the tilt of the polars is explained by an increase in the coefficient of inductive drag, since at the same angle of attack in a subsonic flow of compressible gas, the lift-to-drag ratio of the aircraft begins to decrease from the moment the effect of compressibility is noticeable.