Skalistovskaya secondary school I–III levels

Elective physics course in 10th grade Research project on the topic

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

Bakhchisarai.

Scientific supervisor:

physics teacher Dzhemilev Remzi Nedimovich

Work performed by: Erofeev Sergey

10th grade student

(Skalistovskaya secondary school

school I - III levels

Bakhchisaray District Council

Autonomous Republic of Crimea)

Updating the topic.

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 arise 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 take on the shape of a forward sweep.

The object of our research is the branch of physics aerodynamics - this is a branch of aeromechanics in which the laws of motion of air and other gases and their force interaction with moving solid bodies are studied.

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

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

Aerodynamics is an experimental science. There are no formulas yet that allow us to absolutely accurately describe the process of interaction of a solid body with an incoming 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 wings with the same cross section, but different shapes: rectangular, swept and backward swept when air flows around them.

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

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

History of the study.

Do we feel the air around us? If we don’t move, we practically don’t feel it. When, for example, we are racing in a car with the windows open, the wind hitting our face resembles a springy stream of liquid. This means that air has elasticity and density and can create pressure. Our distant ancestor knew nothing about experiments proving the existence of atmospheric pressure, but he intuitively understood that if he waved his arms very hard, he would be able to push off from the air, like a bird. The dream of flight has accompanied man for as long as he can remember. The famous legend of Icarus speaks about this. Many inventors have tried to take off. IN different countries and in different times There were numerous attempts to conquer the air elements. The great Italian artist Leonardo da Vinci sketched the project aircraft, working only on human muscular strength. However, nature did not allow man to fly like a bird. But she rewarded him with intelligence, which helped him invent a heavier-than-air apparatus 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 a plane in the air? The answer is obvious - wings. What holds up the wings? The plane rushes forward, accelerates, and lift occurs. At sufficient speed, it will lift our aircraft off the ground and hold the plane during flight.

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

Nikolai Egorovich Zhukovsky (1847 -1921) - Russian scientist, founder of modern aerodynamics. At the beginning of the century he built a wind tunnel and developed the theory of an airplane wing. In 1890, Zhukovsky published his first work in the field of aviation, “On the Theory of Flying.”

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 flights with high speeds, which served theoretical basis modern high-speed aviation.

“A person 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

Basics of aerodynamics. Basic concepts.

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

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

movement of gas relative to a stationary body.

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

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

Wing area S – this is the area limited by the contours of the wing. The area of ​​a 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. By decomposing this force into vertical Fy and horizontal Fx components (Fig. 1), we obtain the lift force of the wing and its drag force, respectively.

Description of the experiment.

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

The wing models are made of foam plastic measuring 140 ͯ 50 mm. The wings of modern aircraft can be rectangular, swept, or forward-swept in shape.

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

Wind tunnel;

Meter;

A fixed platform on which the above devices are fixed.

Conducting an experiment.

The model works as follows:

For the experiment, the wing model is attached to the lever and installed at a distance of 20-25 cm from the wind tunnel. Direct the air flow onto the wing model and watch it rise up. Changing the shape of the wing. We bring the lever into balance again so that the model takes its original position, and determine the magnitude of the lifting force at the same air flow speed.

If you install the plate along the flow (zero angle of attack), then the flow will be symmetrical. In this case, the air flow is not deflected by the plate and the lift force Y is zero. Resistance X is minimal, but not zero. It will be created by the friction forces 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, lift grows much faster than 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

Wing lift Rу = = 0.438 N

Drag Rх = = 0.101 N

К = Fu/Fх =0.438/0.101 = 4.34

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

• As the angle of attack increases, it becomes increasingly difficult for airflow to flow around the plate. Although the lift continues to increase, it is slower than before. But the drag is growing faster and faster, gradually outpacing the growth of lift. As a result, the total aerodynamic force R begins to deflect backwards. The picture changes dramatically.

Air streams are unable to smoothly flow around the upper surface of the plate. A powerful vortex forms behind the plate. Lift drops sharply and drag increases. This phenomenon in aerodynamics is called FLOW START. A “torn off” wing ceases to be a wing. It stops flying and starts falling.

In our experience, even at a wing deflection angle α = 600 or more, the wing stalls; it does not fly, g ≈9.8 N/kg

Wing lift Ry = = 0.113 N

Drag Rх = = 0.196 N

Aerodynamic quality wing K = 0.113/0.196 = 0.58

Swept wing.

Wing mass m ≈ 0.01 kg;

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

Wing area S= 0.028 m2

Wing lift Rу = = 0.287 N

Drag R x = = 0.104 N

Aerodynamic quality of the wing

К = Fu/Fх = 0.287/0.104 = 2.76

Forward swept wing.

Wing mass m ≈ 0.01 kg;

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

Wing area S= 0.00265 m2

Wing lift Rу = = 0.380 N

Drag Rх = =0.102 N

Aerodynamic quality of the wing

К = Fu/Fх = 0.171/0.119 = 3.73

Analysis of the experiment

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 turned out to be a rectangular wing and a forward-swept wing. The main advantage of a straight wing is its high lift coefficient K = 4.34. For a swept wing, the lift coefficient is equal to K = 2.76 and, accordingly, the forward-swept 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 forward-swept wing.

We repeated our experience with greater strength air flow: at the same time, the aerodynamic qualities of the straight wing and the forward-swept wing decreased quite sharply to K = 2.76 and K = 1.48, but the aerodynamic quality of the swept wing changed slightly K = 2.25.

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

In this work, we studied the dependence of the lifting force of a wing only on its planform. In real flight, the lifting force of a wing 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 adhered to:

• the air flow was kept constant;
• The wing axis and the wind tunnel axis 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. Tutorial for students of pedagogical institutes. State educational and pedagogical publishing house of the Ministry of Education of the RSFSR. Moscow 1960
• Physics. I'm exploring the world. Children's encyclopedia. Moscow. AST. 2000
• V.B. Baydakov, A.S. Klumov. Aerodynamics and flight dynamics of aircraft. Moscow. "Mechanical Engineering", 1979
• Great Soviet Encyclopedia. 13. Third edition. Moscow. “Soviet Encyclopedia”, 1978.

Questions for review: What experiments were performed to show the role of surface tension forces in respiration? Why does the constant synthesis of surfactants help us breathe, and what happens when it stops? Why should scuba divers breathe compressed air underwater? Why, when descending to great depths, divers cannot use compressed air, but must prepare special breathing mixtures? What is decompression sickness and how to avoid it?

Resistance force to air flow The resistance force is proportional to the number of air molecules that the wing stops, their mass and speed F resistance cross-section (frontal) section of the wing in the direction of movement where is the air density, V is the speed of the aircraft, and S is the area of ​​its wing angle of attack

Drag force change in air momentum Lifting force of air flow mV0mV0 mV1mV1 Lifting force is proportional to the number of air molecules that the wing turns, their mass and speed where is the air density, V is the speed of the aircraft, and S is the area of ​​its wing

Dependence of the speed of an aircraft on its mass. At constant engine power, the greater the mass of the aircraft, the slower it flies. At constant speed and aerodynamic qualities, i.e. C under / C resist = const, load capacity is proportional to the wing area

Is there a connection between attendance and academic performance? attendance, % test results How to quantify whether a change in two quantities is closely related?

Attendance, % test results How to quantify whether a change in two quantities is closely related? Is there a relationship between attendance and academic performance?

We calculate the correlation (connection) coefficient, CORR, between academic performance and attendance attendance, % test results average attendance AB VG average academic performance CORR(10 “B”) = 0

Age: 14 years

Place of study: MBOU LAP No. 135

City, region: Samara, 63

Head: Natalya Yurievna Samsonova, physics teacher

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

Introduction__________________________________________________________ 2

Goals and objectives _________________________________________________________3-4

Main part ________________________________________________________5-12

Lifting force of an airplane wing_____________________________________________5-8

History of aircraft development ________________________________________________9-10

Factors influencing the lift of an aircraft wing_________________________________10

Factors influencing flight range________________________________________________10

Factors affecting flight time________________________________________________10

Observations and experiments_______________________________________________________________10-12

Methodology_________________________________________________________________12

Conclusion _____________________________________________________________13

References________________________________________________ 14

Introduction

People have long dreamed of flying. I would like to make wings like birds, insects, bats. How many living creatures are floating in the air, but a person cannot!

Brave inventors tried to make wings for people. But no one managed to fly on such wings. The man did not have enough strength to lift himself into the air. At best, the inventors managed to land safely on the ground, gliding from a mountain or high tower on their wings. 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 gravity and plows the heavenly ocean and ask myself questions:

• How should an airplane wing be designed to support a heavy load?
• What should be the optimal shape of a wing cutting through the air?
• What characteristics of the wind help an airplane fly?
• What speed can a plane reach?

Man has always dreamed of rising into the sky “like a bird” and since ancient times he has been trying to make his dream come true. In the 20th century, aviation began to develop so quickly that humanity was unable to preserve many of the originals of this complex technology. But many examples have been preserved in museums in the form of scaled-down models, giving an almost complete picture of the real machines.

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

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

We used the following research methods:

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

Goal and objectives

Purpose of the work: Design aircraft with the following characteristics: maximum range and flight duration.

Tasks:

Analyze information obtained from primary sources;

Study the elements of the ancient oriental art of aerogami;

Get acquainted with the basics of aerodynamics, technology for constructing aircraft from paper;

Conduct tests of designed models;

Develop skills for correctly, effectively launching models;

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

Aerodynamics (from the Greek words aer - air and dinamis - force) is the science of the forces that arise when bodies move in the air. Air, thanks 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 also simply necessary. While studying the laws of aerodynamics, I carried out a series of observations and experiments: “Choosing the shape of an aircraft”, “Principles of creating a wing”, “Blowing”, etc.

Construction.

Folding a paper airplane is not as easy as it seems. Actions must be confident and precise, bends must be perfectly straight and in the right places. Simple designs mistakes are forgiven, but in complex ones a couple of imperfect angles can lead the assembly process to a dead end. In addition, there are cases when the bend must be deliberately not performed very accurately.

For example, if one of the last steps requires folding a thick multi-layer structure in half, the fold will not work unless adjustments are made for the thickness at the very beginning of folding. Such things are not described in diagrams, they come with experience. And how well it will fly depends on the symmetry and precise weight distribution of the model.

The key point in “paper aviation” is the location of the center of gravity. When creating various designs, I propose to make the nose of the plane 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 out that the speed and flight path can be adjusted by bending the back of the wings like real flaps, slightly turning the paper fin. Such control is the basis of “paper aerobatics”.

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

Tests

In order to achieve high results when starting up, you need to master correct technique throw.

• To send the plane as far as possible, you need to throw it forward and up at an angle of 45 degrees as hard as possible.
• In time-of-flight competitions, you must throw the plane at maximum height so that it takes longer to glide down.

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

Main part.

1.1 Lifting force of an airplane wing.

Moving streams do all sorts of things - they even push ships together. Is it possible to use their strength to lift bodies upward? Motorists know that at high speed the front of the car can come off the road, as if flying up. They even install anti-wings to prevent this from happening. Where does the lifting force come from?

Here we cannot do without such a thing as a wing. The simplest wing is, perhaps, a kite (Fig. 216). How does he fly? Let us remember that we pull the kite by the rope, creating wind flowing onto its plane, or wing. Let us denote the plane of the wing AB, the tension of the rope Q, the dead weight of the kite P, the resultant of these forces R, 1

The wind running onto the plane of the kite AB, reflected from it, creates a lifting force R, which, in order for the kite not to fall, must be equal to R, or better more so that the kite rises to the top. Do you feel that everything is not so simple when it comes to flying? Even more complicated than with a kite is the lifting force of an airplane wing.

The cross section of an aircraft wing is shown in Fig. 217 a. Practice has shown that in order to lift, the aircraft wing must be positioned 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°, when landing - about 15°. It turns out that in the presence of such an angle of attack, the speed of the air flow flowing around the wing from above will be greater than the speed ^/^ of the flow flowing around the lower surface of the wing. In Fig. 217 and this difference in speed 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 plane (b) arise?

But, as we already know, in the place of the flow where the speed is greater, the pressure is less, and vice versa. Therefore, when an airplane moves in the air, there will be a reduced pressure above the upper surface of the wing, and an increased pressure above the lower surface. 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 weight of the body P. If this force more weight plane, the latter will rise up. The second component Q is the drag; it is overcome by the propeller thrust.

In Fig. 217, b shows the forces acting on the aircraft during horizontal uniform flight: F, - lift force, P - weight of the aircraft, F, - drag and F - propeller thrust force.

A great contribution to the development of the theory of the wing, and indeed aerodynamic theory in general, was made by the Russian scientist, Professor N. E. Zhukovsky (1847-1921). Even before human flight, Zhukovsky said interesting words: “Man has no 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 he will fly relying not on the strength of his muscles, but on the strength of his mind.”

Rice. 218. Shape of wings in plan at 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 changed - it became thinner and sharper. The shape of the wings in plan also changed. Subsonic wings have a rectangular, trapezoidal or elliptical shape. Transonic and supersonic wings are made swept, delta-shaped (like the Greek letter “delta”) or triangular (Fig. 218). The fact is that when the aircraft moves from near and supersonic speed so-called shock waves arise, associated with the elasticity of the air and the speed of sound propagation in it. To reduce this harmful phenomenon, wings of a sharper shape are used. The picture of air flow around subsonic and supersonic wings is shown in Fig. 219, where the difference in their interaction with air is visible.

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

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

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

Aircraft with speed M > 6 are called hypersonic. Their wings are built in such a way that the shock waves from the flow around the fuselage and 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. Evolution of aircraft

History of aircraft development

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

In 1882, Russian officer A.F. Mozhaisky built an airplane with a steam engine, which could not take off due to its heavy weight. 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 canvas 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 money to continue their experiments. In the winter of 1902-1903, they manufactured a gasoline internal combustion engine, installed it on their glider, and on December 17, 1903, made the first flights, the longest of which, although it lasted only 59 seconds, still showed that the aircraft was capable of taking off and staying in air.

Having improved the aircraft and achieved some flying skill, the Wright brothers unveiled their invention in 1906. From that moment on, the rapid development of aviation began in many countries around the world. Three years later, the French engineer Bleriot flew an airplane 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 A.N. Tupolev’s ANT-25 plane they flew from Moscow to America via 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 increased. The first super-heavy aircraft “Ilya Muromets” was built in Russia. This four-engine giant was so superior to all machines of that time that for a long time abroad they could not believe in the existence of such an aircraft. In 1913, the 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 aircraft fly several times faster than sound. And rockets fly even faster. For example, the launch vehicle that launched the first artificial satellite Earth, had M>28.

1.2Factors influencing the lift of an aircraft wing.

1)air speed

2) wing shape

3) density of the medium

1.3 Factors affecting flight range.

1) weight of the aircraft

2) wing shape

1.4 Factors affecting flight time.

1) high-altitude jet stream;

2) tailwind, headwind, sidewind;

3)wing shape

1.5 Observations and experiments.

Observations

Choosing the shape of the aircraft.

Experience No. 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 runs out. A simple sheet of paper has too large a supporting surface, which does not contribute to proper flight.

Principles of wing creation.

Equipment:

• Sheet of paper;
• Two books.

Experience No. 2

Sudden gust of wind:

Experience No. 3

Equipment:

• Sheet of paper;
• Two books.

Experience No. 4

Blow.

Equipment:

• Two strips of paper

Conclusion:

Air glides faster over the top, curved part of the wing, where the leading edge is higher 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 upward. The force supporting the wing is caused by the pressure difference. It's called lift. The airflow on the wing can be diverted downwards using flaps or ailerons. They allow the aircraft to take off, make turns and fly at low altitude even at low speeds.

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 airplane models. I have launched aircraft of the same mass with the same force several times. After running all the models, I wrote down the results of the runs and the arithmetic average in the table. Based on the arithmetic average, 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

Point system:

Based on the table, I found the most best option paper airplanes: model No. 4. Model No. 2 is good for range competitions, and Model No. 3 has increased flight duration.

During the experiments, I was unable to accurately measure the flight range and flight time of each aircraft, and launch the aircraft with the same power, but I was able to approximately measure the flight time and range of each aircraft.

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

List of used literature

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

2) Big book of experiments for schoolchildren / ed. Antonella Meyani. - M.: JSC "ROSMEN-PRESS", 2007. - 260 p. http://www.ozon.ru/context/detail/id/121580 /

3) Mikortumov E.B., Lebedinsky M.S. Aircraft modeling; Collection of articles. A manual for leaders of aircraft modeling clubs. - 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: encyclopedia. - M.: “Big 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

Wing lift
Wing lift
Author: Sinegubov Andrey
Group: E3-42
Artistic director: Burtsev Sergey
Alekseevich

Statement of the problem

Environment model

Aerodynamic profile

Control surface

Calculation formulas

Zhukovsky's theorem

Wing lift

List of sources used

*An airplane wing is designed to create 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 the wing are reduced to the characteristics of the wing in plan and characteristics

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

Transverse angle V of a wing Geometric characteristics of a wing The shape of a wing in plan is characterized by its span, aspect ratio, taper, sweep and transverse V. The wing span L is the distance between the ends of the wing in a straight line. The wing area in plan Scr is limited by the contours of the wing.

The area of ​​the trapezoidal and swept wings is calculated as the areas of two trapezoids where b 0 is the root chord, m; bk - end chord, m; - average chord of the wing, m Wing aspect ratio 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 aspect ratio 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.

The taper of the wing is the ratio of the axial chord to the terminal chord. For subsonic aircraft, the taper of the wing usually does not exceed 3, but for transonic and supersonic aircraft it can vary within wide limits. 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 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°. The wing V angle 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. Asymmetrical, 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 segment connecting the two most distant points of the profile. Shapes 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; Smax - greatest thickness; fmax - curvature arrow; x-coordinate of the 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 - lift force; Q - drag force; - angle of attack; q - quality angle Relative profile thickness c is the ratio of the maximum thickness Cmax to the chord, expressed as a percentage:

The relative profile thickness c is the ratio of the maximum thickness Cmax to the chord, expressed as a percentage: The position of the maximum profile thickness Xc is expressed as a percentage of the chord length and is measured from the nose. In modern aircraft, the relative thickness of the profile is within 416%. The relative curvature of the profile f is the ratio of the maximum curvature 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. 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 CHORD OF A WING The average aerodynamic chord of a wing (MAC) is the chord of a rectangular wing that has the same area, the magnitude of the total aerodynamic force and the position of the center of pressure (CP) as the given wing at equal angles of attack.

For a trapezoidal untwisted wing, the MAR is 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 laid, and on the continuation of the terminal chord (forward), a segment equal to the root chord is laid. 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 (MAC) will pass through the intersection point of these two lines.

Knowing the magnitude and position of the MAR on the airplane and taking it as a baseline, determine relative to it the position of the airplane’s center of gravity, the wing’s center of pressure, etc. The aerodynamic force of the airplane 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 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 of the MAR, expressed in linear quantities or as a percentage of the length of the MAR.

WING DRAG Drag is the resistance to the movement of an aircraft wing in the air. It consists of profile, inductive and wave resistance: Xcr = Xpr + Hind + XV. Wave drag will not be considered, since it occurs at flight speeds above 450 km/h. Profile resistance is composed of pressure and friction resistance: Xpr = XD + Xtr. 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 it is indicated by Cx - the coefficient of profile resistance).

The greater the relative thickness of the 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. 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 vortex accompanying jet and the vortices themselves increase sharply. Frictional resistance arises due to the manifestation of air viscosity in the boundary layer of the flowing 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 surface of the wing is processed and the thicker the wing profile, 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 air flow flowing around the wing with a speed V induced by the vertical speed U is deflected is called the flow angle. Its value depends on the value of the vertical velocity induced by the vortex rope and the oncoming flow velocity V

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

Due to the smallness of the value, we assume that it is equal to The other component of the force Y" will be This component is directed along the flow and is called inductive drag (Figure shown above). To find the value of inductive drag, it is necessary to calculate the speed ^ U and the flow bevel angle. Dependence of the flow bevel angle on the wing elongation , the lift coefficient Su and the wing shape in plan view is expressed by the formula where A is the coefficient taking into account the shape of the wing in plan view. For aircraft wings, coefficient A is equal to where eff is the elongation of the wing without taking into account the area of ​​the fuselage that occupies part of the wing; in plan.

where Cxi is the coefficient of inductive reactance. It is determined by the formula From the formula it can be seen that Cx is directly proportional to the lift coefficient and inversely proportional to the wing aspect ratio. At an angle of attack of zero lift, the inductive drag will be zero. At supercritical angles of attack, the smooth flow around the wing profile is disrupted 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 wing aspect ratio, therefore aircraft intended for long-distance flights have a large wing aspect ratio: = 14... 15.

AERODYNAMIC QUALITY OF A WING 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 obtain. The greater the aerodynamic quality of the wing, the more perfect it is. The quality value for modern aircraft can reach 14 -15, and for gliders 45 -50. This means that an aircraft wing can create a lift force that exceeds drag by 14 -15 times, and for gliders even 50 times.

Aerodynamic quality is characterized by the angle. 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 the formula, depends on the same factors as the coefficients Su and Cx, 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 With an increase in angle of attack to a certain amount aerodynamic quality increases. At a certain angle of attack, the quality reaches the maximum value Kmax. This angle is called the most favorable angle of attack, naive At the angle of attack of zero lift about where Su = 0 the lift-to-drag ratio will be. equals 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 thickness of the profile along the chord have a great influence. To obtain large values ​​of Kmax, the optimal thickness and curvature of the profile, the shape of the contours and the wing elongation are selected. To obtain the highest quality values, the best wing shape is elliptical with a rounded leading edge.

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

WING POLAR For various calculations of wing flight characteristics, 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 Cy on Cx, called a polar, is plotted. The name “polar” is explained by the fact that this curve can be considered as a polar diagram constructed 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 Cy and Cx are taken to be the same ). Principle of constructing a wing polar Wing polar If we draw a vector from the origin, 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 to Сy and Сх. drag and lift coefficient from angles of attack - the so-called wing polarity.

The polar is built for a very specific wing with given geometric dimensions and profile shape. Based on the wing polarity, a number of characteristic angles of attack can be determined. The angle of zero lift o is located at the intersection of the polar with the Cx axis. At this angle of attack, the lift coefficient is zero (Cy = 0). For the wings of modern aircraft, usually o = Angle of attack at which Cx has the smallest value Cx. min. is found by drawing a tangent to the polar parallel to the Cy axis. For modern wing profiles, this angle ranges 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 Cy axis and the tangent drawn from the origin, i.e., the angle of quality, at this angle of attack, according to formula (2.19), will be minimal. Therefore, to determine the naive, you need to draw a tangent to the polar from the origin. The touch point will correspond to naive. For modern wings, naive lies within 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 point of contact will correspond to the crit. For the wings of modern aircraft, crit = 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 will find the angles of attack (i) during flight, at which the aerodynamic quality will be the same and necessarily less than Kmax.

POLAR OF THE AIRCRAFT One of the main aerodynamic characteristics of the aircraft is the polar of the aircraft. 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 amount of Cx. The plane's polarity will be shifted to the right of the wing polarity by the amount Cx time. The plane's polarization is constructed using data from the dependences Сy=f() and Сх=f(), 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.

The angle of attack of a zero-lift aircraft is practically the same as the angle of attack of a zero-lift wing. Since the lift force at the angle is zero, 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°.

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 loss. 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, 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. Conclusion: the maximum quality of the aircraft as a whole is always less than the maximum aerodynamic quality of an individual wing.

The graph shows that the most favorable angle of attack of the aircraft is 2 - 3° greater than the most favorable angle of attack of the wing. The critical angle of attack of an aircraft (crit) is no different in magnitude from the same angle for a wing. Raising the flaps to the take-off 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. 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 (= 45 - 60°), the maximum lift coefficient can increase to 80%, which sharply reduces landing speed and length of run. However, the drag increases more rapidly than the lift, 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. 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 a correction for compressibility. where Suszh is the lift coefficient taking into account compressibility; Suneszh is the lift coefficient of the incompressible flow for the same angle of attack as Suszh.

Up to numbers M = 0.6 -0.7, all polars practically coincide, but at large numbers ^ M they begin to shift to the right and at the same time increase the inclination to the Cx axis. The shift of the polars to the right (by large Cx) is due to an increase in the profile drag 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 drag. The increase in the inclination 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 it will increase proportionally. The aerodynamic quality of the aircraft from the moment the compressibility effect noticeably manifests itself begins to decrease.