Aircraft lift coefficient. Aircraft lift. See what "Lift force" is in other dictionaries
DEPARTMENT OF EDUCATION OF THE ICHALKOVSK MUNICIPAL DISTRICT
Contest in physics
"PHYSICS AROUND US"
PHYSICAL EXPERIMENT
LIFTING FORCE OF AIRCRAFT WING
Yamanov Victor
MOU "Tarkhanovskaya secondary school", p. Tarkhanovo, grade 9
Leader:
Averkin Ivan Andreevich,
physics and mathematics teacher
MOU "Tarkhanovskaya secondary school"
Ichalkovsky municipal district Republic of Mordovia
2011
Introduction ................................................. ...........................Aircraft wing lift.
Physics experiment
Aircraft wing aerodynamics
Conclusion
Literature. .................................................
Introduction
Why can birds fly despite being heavier than air? What forces lift a huge passenger plane, which can fly faster, higher and farther than any bird, because its wings are motionless? Why can a glider without a motor float in the air? All these and many other questions are answered by aerodynamics - the science that studies the laws of the interaction of air with bodies moving in it.
In the development of aerodynamics in our country, Professor Nikolai Yegorovich Zhukovsky (1847 -1921), "the father of Russian aviation", played an outstanding role. Zhukovsky's merit lies in the fact that he was the first to explain the formation of wing lift and formulate a theorem for calculating this force. He also solved another problem of the theory of flight - he explained the thrust force of the propeller.
Zhukovsky not only discovered the laws underlying the theory of flight, but also paved the way for the rapid development of aviation in our country. He connected theoretical aerodynamics with the practice of aviation, gave engineers the opportunity to use the achievements of theoretical scientists. Under the scientific leadership of Zhukovsky, the Aerohydrodynamic Institute (now TsAGI), which became the largest center of aviation science, and the Air Force Academy (now the Prof. N. Ye. Zhukovsky Air Force Academy), which train highly qualified engineering personnel for aviation, were organized.
The main device used to study the laws of motion of bodies in air is a wind tunnel. The simplest wind tunnel is a profiled channel. A powerful fan is installed at one end of the pipe, driven by an electric motor. When the fan starts to work, an air flow is generated in the pipe channel. In modern wind tunnels, it is possible to obtain various air flow rates up to supersonic. In their channels, you can place not only models, but also real airplanes for research.
The most important laws of aerodynamics are the law of conservation of mass (the equation of continuity) and the law of conservation of energy (the Bernoulli equation).
Let's consider the nature of the lifting force. Experiments carried out in aerodynamic laboratories made it possible to establish that when an air stream runs on a body, air particles flow around the body. The picture of the air flowing around the body is easy to observe if the body is placed in a wind tunnel in a tinted air flow, in addition, it can be photographed. The resulting image is called the flow spectrum.
A simplified diagram of the spectrum of the flow around a flat plate set at an angle of 90 ° to the flow direction is shown in the figure.
Why and how lift occurs
The simplest flying machines are kites, which have been flying for thousands of years both for fun and for scientific research... The inventor of the radio, A.S. Popov, used a kite to raise the wire (antenna) to increase the radio transmission range.
The kite is a flat plate located at an angle α to the direction of the air flow. This angle is called the angle of attack. When this plate interacts with the flow, a lifting force F n , which is the vertical component of the force R acting on the plate from the flow side.
The mechanism of occurrence of the force R is twofold. On the one hand, this is the reaction force that occurs when the air flow is reflected and is equal to the change in its impulse per unit time
On the other hand, when flowing around the plate, vortices are formed behind it, which lower, as follows from the Bernoulli equation, the pressure above the plate.
The horizontal component of the force R is the force of pressure resistanceF from ... The graph of the dependence of lift and drag force on the angle of attack is shown in the figure, from which it can be seen that the maximum lift is achieved at an angle of attack equal to 45 °.
Aircraft wing lift
Bernoulli's equation calculates the lift of an airplane wing when flying in the air. If the air flow velocity over the wing v 1 will be greater than the flow rate under the wingv 2 , then, according to the Bernoulli equation, a pressure drop occurs:
where p 2 - pressure under the wing, p 1 -pressure over the wing. The lifting force can be calculated using the formula
where S - wing surface area,v 1 - air flow speed over the wing,v 2 - the speed of the air flow under the wing.
The emergence of a lifting force when there is a difference in the velocities of the air flow around the body can be demonstrated by the following experiment.
Let us fix the wing model in an aerodynamic balance and blow the air using a wind tunnel or vacuum cleaner. To find the lift, you can measure the static air pressure with a micromanometer.above the wing p 1 and under the wing p 2. Calculated by the formulaF n = =(p 2 - p 1 ) Sthe lift value is the same as on the scale of the aerodynamic scale.
Physics experiment
Instruments and equipment for the experiment:
Household fan
Micromanometer
Wing layout
Tripod
Paper
Calculations
P 1 \u003d -2 mm water. Art.
Р 2 \u003d 1 mm of water. Art.
∆Р \u003d Р 2 - Р 1 \u003d 1- (-2) \u003d 3 mm water. Art.
∆Р \u003d ρ gh \u003d 1000 ∙ 10 ∙ 3 10 -3 \u003d 30 Pa
F n \u003d P 2 ∙ S - Р 1 ∙ S = S ∙ ∆Р \u003d 18 ∙ 26 ∙ 10 -4 ∙ 30 \u003d 468 ∙ 30 ∙ 10 -4 ≈
≈ 1.4 N
P \u003d F T \u003d 0.5 N.
Aircraft wing aerodynamics
When air flows around an aircraft wingthe upper and lower parts of the air flow, due to the asymmetry of the wing shape, go through different paths and meet at the rearwing edges at different speeds.
This leads to the emergencevortex, which rotates counterclockwise.
The vortex has a certain angular momentum. But since in a closed system the angular momentum must remain unchanged, air circulation occurs around the wing, directed to the hour hand.
Designating the speed of the air flow relative to the wingcut and, and the speed of the circulation flow throughand, we transform expression for the lift of an aircraft wing:
where v 1 = u + v, u 2 = u- v... Then
This formula was first obtained by Nikolai Yegorovich Zhukovsky in 1905
N.E. Zhukovsky established the wing cross-sectional profile with the maximum lift and minimum drag force. He also created the vortex theory of the aircraft propeller, found the optimal shape of the propeller blade and calculated the thrust force of the propeller.
The cross-section of a wing by a plane parallel to the plane of its symmetry is called a "profile". A typical wing profile looks like this:
The maximum distance between the extreme points of the profile - b, is called the profile chord. The highest profile height - c, is called the profile thickness.
The lift of the wing arises not only from the angle of attack, but also due to the fact that transverse section the wing is most often an asymmetrical profile with a more convex upper part.
The wing of an airplane or glider, while moving, cuts the air. One part of the jets of the oncoming air flow will go under the wing, the other - above it.
At the wing, the upper part is more convex than the lower one, therefore, the upper streams will have to travel a longer distance than the lower ones. However, the amount of air entering and flowing from the wing is the same. This means that the upper streams, in order to keep up with the lower ones, must move faster.
The flow lines of elementary air streams are indicated by thin lines. The profile to the flow lines is at an angle of attack a - this is the angle between the profile chord and unperturbed flow lines. Where the flow lines approach each other, the flow velocity increases and the absolute pressure decreases. Conversely, where they become less frequent, the flow rate decreases and the pressure increases. Hence, it turns out that at different points of the profile, the air presses on the wing with different forces.
According to Bernoulli's equation, if the air flow velocity under the wing is less than above the wing, then the pressure under the wing, on the contrary, will be greater than above it. This pressure difference creates the aerodynamic force R,
The figure shows a schematic representation of the spectrum of the flow past a plate placed at an acute angle to the flow. Under the plate, the pressure rises, and above it, as a result of the separation of the jets, a rarefaction of air is obtained, i.e., the pressure decreases. Due to the resulting pressure difference, aerodynamic force arises. It is directed in the direction of lower pressure, i.e. back and up. The deflection of the aerodynamic force from the vertical depends on the angle at which the plate is placed to the stream. This angle is called the angle of attack (it is usually denoted by the Greek letter a - alpha).
Conclusion
The property of a flat plate to create a lifting force if air (or water) runs on it at an acute angle has been known for a long time. An example of this is kite and the steering wheel of a ship, the time of the invention of which is lost in the centuries.
The higher the incoming flow velocity, the greater both the lift and drag forces. These forces also depend on the shape of the wing profile, and on the angle at which the flow enters the wing (angle of attack), as well as on the density of the incident flow: the higher the density, the greater these forces. The wing profile is chosen so that it gives the greatest possible lift with the lowest possible drag.
Now we can explain how an airplane flies. Airplane propeller driven by an engine or jet reaction jet engine, imparts such a speed to the aircraft that the lift of the wing reaches or even exceeds the weight of the aircraft. Then the plane takes off. In a uniform straight flight, the sum of all the forces acting on the plane is zero, as it should be according to Newton's first law. In fig. 1 shows the forces acting on an airplane during horizontal flight at a constant speed. The engine thrust force f is equal in magnitude and opposite in direction to the air drag force F2 for the entire aircraft, and the force 
Figure: 1. Forces acting on an aircraft during horizontal uniform flight
gravity P is equal in magnitude and opposite in direction to the lifting force F1.
Aircraft designed to fly at different speeds have different wing sizes. Slowly flying transport aircraft should have a large wing area, since at low speed the lift per unit wing area is small. High-speed airplanes also get sufficient lift from small wings. Since the lift of the wing decreases with decreasing air density, to fly at high altitude, the aircraft must move at a higher speed than near the ground. 
Figure: 2. Hydrofoil
Lift also arises when the wing is moving in the water. This makes it possible to build hydrofoil vessels. The hull of such vessels comes out of the water while in motion. This reduces the resistance of the water to the movement of the boat and allows high speed to be achieved. Since the density of water is many times greater than the density of air, it is possible to obtain a sufficient lift of the hydrofoil with a relatively small area and moderate speed.
The purpose of an airplane propeller is to give the airplane a high speed at which the wing creates a lift that balances the weight of the airplane. For this purpose, the aircraft propeller is fixed on the horizontal axis. There is a type aircraft heavier than air, for which wings are not needed. These are helicopters.
Fig 3. Diagram of the helicopter
In helicopters, the propeller axis is vertical and the propeller creates upward thrust, which balances the weight of the helicopter, replacing the wing lift. The helicopter rotor generates vertical thrust whether the helicopter is moving or not. Therefore, when the propellers are operating, the helicopter can hang motionless in the air or rise vertically. To move the helicopter horizontally, it is necessary to create a thrust directed horizontally. To do this, you do not need to install a special propeller with a horizontal axis, but just slightly change the inclination of the vertical propeller blades, which is done using a special mechanism in the propeller hub.http://rjstech.com/aerodinamika-i-modelirovanie/osnovy-aerodinamiki/
Experience shows that when an ideal fluid flows around asymmetric bodies, and even arbitrarily oriented towards the flow, a force will act on these bodies Fdirected at some angle to the flow (see Fig. 4.18). The component of this force parallel to the flow is the drag force. Another component directed across the flow is called lift. As prime example Let us consider the appearance of a lift when air flows around an aircraft wing. A typical picture of a continuous air flow around an airplane wing profile at a small angle of attack is shown in Fig. 4.24a. Already from the mere fact that the flow after flowing has acquired a downward momentum component, it follows that the wing acquires the same upward momentum. For a laminar flow around a wing, based on the structure of streamlines, it is possible to qualitatively analyze the distribution of pressure forces obtained using the Bernoulli equation (Fig. 4.24b). The sum of these forces has the resultant Fdirected at a slight angle to the vertical. Thus, a lifting force is created that is significantly superior to the drag force.
From the pressure force diagram, it can be seen that the lift is created not so much by an increase in pressure under the wing as by a drop in pressure above the wing. This force is proportional to the dynamic pressure, the wing area S and is calculated by the formula
Where C y is the coefficient of lift, depending on the angle of attack. If the air flowed around the wing without separation, then the coefficient C y would increase proportionally. However, experiments show that at angles of attack (depending on the shape of the wing), the lift reaches a maximum, and then begins to fall (Fig. 4.25).
The angle of attack at which the coefficient C y is maximum is called landing or critical, and the corresponding coefficient is also called landing. Ordinary wings. In fig. 4.26 presents photographs of flows at angles of attack and. It is clearly seen that flow stall and vortex formation leads to an increase in pressure above the wing and a decrease in lift.
The coefficient determines the landing speed of the aircraft vp, determined from the equality of the lift (4.46) to the weight of the aircraft. To reduce the landing speed, it is necessary to prevent stalling with increasing angle of attack. In modern aviation, this is achieved by using landing devices on the wings - wing flaps (1) and flaps (2), which are mechanically extended from the wing (3) when the aircraft lands (Fig. 4.27).
An outstanding role in the development of the theory of flow around bodies, which played an extremely important role for the development of aviation, belongs to N.E. Zhukovsky. He showed that the lift of a wing is associated with vortices: there is a vortex near the wing, which he called attached. The basic idea of \u200b\u200bcalculating the lift is as follows. If there were no viscous forces in the air, then the flow pattern around the wing would be the same as in Fig. 4.28 (a). Lift, however, will be zero as the flow behind the wing has not changed direction. Real air flow around the wing, shown in Fig. 4.28 (c) can be considered as a superposition of inviscid flow (a) and vortex motion of air around the aircraft wing clockwise (b).
The magnitude of the lift is directly related to the presence of the circulation of the velocity Г (4.24) along the contour that encloses the aircraft wing. This contour should be outside the boundary layer (b), the thickness of which for an aircraft moving at a subsonic speed is several centimeters. From the law of conservation of angular momentum it follows that vortices should form behind the wing with counterclockwise air movement in them. In fig. 4.29 presents photographs of the vortex street formed when flowing around a reduced model of an airplane wing.
This chain of vortices appears because when one vortex is detached from the wing, the circulation around the wing Г is constantly decreasing due to viscosity. The flow tends to return to configuration (a) in Fig. 4.28, in which air particles "strive" to go around the "bottom-up" trailing edge of the wing. And this, in turn, will lead to the formation of a new vortex and the appearance of the circulation of Г around the wing. During the flight of the aircraft, the vortices periodically detach from the wing and are carried away by the air flow. Thus, the viscosity contributes to the formation of the flow around the wing corresponding to the situation (c). The calculation of the lifting force can be carried out on the basis of the resulting pressure forces, based on the theory of the flow of an ideal fluid. The pressure distribution near the boundary layer is related to the flow rate by the formula:
The force acting on a wing surface element of length L is
And it depends on the difference in pressure from below and above the wing element (Fig. 4.30). This pressure difference can be expressed using (4.47) in terms of velocities:
The velocities v n v v are taken at symmetric points relative to the chord of the wing with length b (the greatest distance between the leading and trailing edge of the wing), the length element in formula (4.48) is the chord length element, since the force dF is directed perpendicular to the chord. Substituting (4.49) into (4.47) in the approximation that v n + v in 2v and performing integration, we find the total force:
This formula was obtained by N.E. Zhukovsky and bears his name. The circulation Г, which determines the lift, is proportional to the angle of attack and for a flat wing
For the profile wing shown in Fig. (4.30) lift exists at zero angle of attack (\u003d 0) and disappears when the angle of attack reaches a certain negative value.
Note that with an increase in the angle of attack, the drag also increases. The ratio of useful lift to harmful drag determines the "wing quality". For light sports aircraft and fighters, this quality is in the range of 12-15, and for heavy cargo and passenger aircraft it reaches values \u200b\u200bof 17-25. The aerodynamic quality increases with improved streamlining (decreasing C x) and increasing the ratio of the wingspan L to the length of its chord b. From the diagram of pressure forces it follows that the resultant of these forces is displaced towards the leading edge of the wing. This must be taken into account when determining the moments of forces acting on the wing, which determine the stability of the aircraft. The experiment with a thin disk in a stream of air is very instructive. If the jet from the fan is directed to the disk, which can freely rotate around the vertical axis (Fig. 4.31), then the disk will take a stable position when its plane becomes perpendicular to the air flow. If the disk accidentally rotates, and the edge K 1 of the disk is closer to the fan than the edge K 2, then a lifting force will arise, the point of application of which will be located between the edge K 1 and the axis of rotation of the disk. A moment of this force will turn the disc back to its original stable position. Note that the position at which the plane of the disk is directed downstream is also an equilibrium position, but this equilibrium is unstable.
The creation of a general theory of the effect of a plane flow of an ideal fluid on an airfoil placed in it is the merit of the great Russian scientist N. Ye. Zhukovsky, who published his famous theorem on the lift of a wing in 1906 in the classic memoir "On attached vortices". N. Ye. Zhukovsky was the first to establish the vortex nature of the forces acting from the side of the flow on the wing, and pointed out the existence of a simple proportionality between this force and the intensity of the vortex "attached" to the streamlined body.
In the previous section, it was already indicated that the solution to the problem of the flow around any airfoil contains some arbitrariness: one and the same airfoil, with a given in magnitude and direction of the incoming flow velocity, can flow around an infinite number of images. It all depends on the magnitude of the velocity circulation, calculated along a closed loop that encompasses the streamlined airfoil. The magnitude of this circulation, as well as the nature of the appearance of vortices in an ideal fluid, the sum of the intensities of which should be equal to this circulation, represented for a long time unsolvable problem.
The physical reason for the occurrence of circulation is associated with the presence of friction (viscosity) in the fluid. As has been mentioned several times earlier, in a real fluid with internal friction, particles passing in close proximity to the profile surface form a thin boundary layer. In this region, the imperfection of the liquid is sharply manifested, the motion of the liquid will be vortex, and the intensity of the vortices can reach large values, since the particle velocity in the boundary layer changes sharply from zero on the surface of the streamlined body to a value of the order of the velocity at infinity on the outer boundary of the layer. For example, on an aircraft wing, the maximum boundary layer thickness does not exceed a few centimeters, while the difference in velocities on the wing surface and on the outer boundary of the boundary layer reaches 100-200 m per second.
With such significant inhomogeneities of the velocity field, the total intensity of eddies over the entire wing, and, consequently, the circulation of the velocity along a closed loop that encompasses the wing, can reach large values.
The theory of an ideal fluid, which does not take into account the presence of friction, naturally, could not explain the appearance of vortices in a vortex-free flow running on a trill. In order, while remaining within the framework of the theory of an ideal irrotational flow, to determine the magnitude of the impact
flow to a body placed in it, we replace, following Zhukovsky, the contour of the body with a closed streamline and assume that inside it there is a fluid motion with a vortex having the same intensity as the sum of the intensities of the vortices that would actually form in a thin layer on the surface of a body when flowing around it with a real liquid. Such a vortex was called by N. Ye. Zhukovsky attached to the solid body under consideration. The intensity of the "attached vortex", or, which is the same, the circulation of the velocity along the contour surrounding the airfoil, could in principle be calculated only by calculating the motion of a real fluid in the boundary layer or by using some additional assumption about general nature flow around the body. The latter path was followed, as indicated in the previous paragraph, by S. A. Chaplygin, who proposed his remarkable postulate of the finiteness of velocity on the trailing edge of the wing, which made it possible to determine the magnitude of the "superimposed" circulation, or, what is the same, the intensity of the "attached vortex"
These two deep ideas of the great Russian aerodynamics N. Ye. Zhukovsky and S. A. Chaplygin: the added vortex and the postulate of the finite velocity at the trailing edge of the wing - formed the basis of the entire modern wing theory.
We begin with the proof of Zhukovsky's theorem on the lift of a wing in a plane-parallel flow. The vector proof of Zhukovsky's theorem presented below differs only in form from the classical proof of this theorem given by its author. We apply the theorem of the quantities of motion in the Euler form [§ 23, formula (38)] to the volume of fluid enclosed between the surface of the streamlined contour C (Fig. 89) and drawn at a distance from the contour C by a circle with a center at point O and a radius. Ignoring volume forces , we will have, replacing in formula (38) §23,
due to the flat nature of the flow, on
In this equality, as equal to zero, the transfer of the momentum through the solid surface of the C profile is omitted. The first integral represents the main vector of pressure forces from the side of the streamlined body to the fluid. The same value with the opposite sign will determine the desired principal vector of the forces of pressure of the fluid on the body
where is the normal external to the considered volume of liquid. Thus, according to the previous formula, we obtain the expression of the required force in terms of the main pressure vector and the transfer of the momentum related to the contour of the circle remote from the profile
By Bernoulli's theorem
moreover, as we already know, the constant on the right, in the case of irrotational motion, has the same value in the entire flow region, and, consequently, on the circle, so that
We decompose the velocity vector V into two terms by setting
where is the velocity at an infinite distance from the airfoil, the velocity of the disturbance introduced by the airfoil into a uniform plane-parallel flow. With respect to this perturbation velocity decreasing to zero with distance from the streamlined body, we will assume that its modulus V decreases with increasing distance from the origin of coordinates, near which the profile is placed, like y. This assumption corresponds to the presence of a vortex "attached" to the body and the finiteness of the velocity circulation along any closed contour, for example, a circle C, of \u200b\u200blength, the order of the disturbance velocity will be discussed in more detail below.
Substituting the indicated velocity expansion into equality (82), we obtain:
According to the previous [Ch. I, formula (68)], the first integral is equal to zero; the fourth integral also disappears, since in the absence of sources - sinks and incompressibility of the liquid, the total flow rate of the liquid through the circuit is equal to zero:
Consider a set of the second and fifth integrals:
which, according to the well-known expansion formula for a triple vector product, can be represented as
or, replacing V with what can be done, since this will add the integral
identically equal to zero, we obtain
Thus, we will have the following expression for the main vector of the flow pressure forces on the profile С:
is directed along the perpendicular to the plane of motion, and its projection onto this perpendicular, which we denote simply by and we will consider the sign included in the definition of the value, will be equal (Fig. 89)
that is, the circulation of velocity along the contour or along any other contour that covers the streamlined profile. Thus, the first term in the expression of the main vector of forces does not depend on the position of the contour, the other two are of order since the integrands represent quantities of the order of -K and the length of the integration contour is From this, when passing to the limit, when the circle moves away to infinity, the sought formula follows
where the vector is defined as the curvilinear integral
taken along any contour enclosing the streamlined profile C, in particular along the profile C. The magnitude of this vector is equal to the velocity circulation along a closed contour enclosing the profile.
From equality (84) we find the value of the main vector of the pressure forces of the flow on the body:
The main vector, as shown by formula (84), lies in the flow plane and is directed perpendicular to the velocity at infinity in the direction determined by the vector product (84). It is usually very difficult to determine in advance in which direction the vector Γ is directed: inward or outward relative to the plane of the drawing. If the direction of the loop bypass is known, in which this direction is conventionally called the direction of positive circulation, or, in short, the "direction of circulation" - then along general rules the "right screw" adopted in our course, it is easy to find the side in which the vector is directed. So, if the direction of circulation coincides with the clockwise rotation, and the flow runs from the left, the vector is directed deep into the drawing, and the force is directed upward; The same can be obtained if the velocity vector is rotated 90 ° in the direction opposite to the circulation.
Thus, we come to the classical formulation of Zhukovsky's theorem, given by the author himself: the force of a crushed non-vortex flow flowing at a speed and flowing around a contour with circulation is expressed by the formula:
we get the direction of this force if we turn the vector through a right angle in the direction opposite to the circulation.
The first conclusion to be drawn from Zhukovsky's theorem is that there is no component of the force directed along the motion of the fluid, or, which is all the same, the direction of motion of the body in relation to the fluid, i.e., the absence of a resistance force. This important fact constitutes the content of the d'Alembert paradox, which was discussed in the historical essay placed in the introductory part of the course. Zhukovsky's theorem confirms the d'Alembert paradox for any plane irrotational motion of an ideal fluid both in the presence of “attached vortices” and in the absence of them. The only force acting on the streamlined airfoil is a force transverse to the movement of the body, which can be called a lifting or supporting force, since it is this force that provides the airplane ascending into the air and supports its wing during horizontal flight.
Using the Zhukovsky theorem and the Zhukovsky-Chaplygin postulate, using formulas (86), (80), or (81), we can obtain an expression for the magnitude of the lift in the form
It turns out to be somewhat overpriced. In fig. 90 shows for comparison the theoretical straight and experimental curves for a symmetric profile with the ratio of the maximum thickness to the chord equal to As can be seen from the figure, in the range of angles of attack - (the area of \u200b\u200bnegative angles is not shown in the figure, but due to the symmetry of the profile it does not differ from the area positive angles), the discrepancy between the theoretical coefficient of lift of the plate and the experimental one for a thin profile is small.
Strictly speaking, it is impossible to apply Zhukovsky and Chaplygin's formulas (86) and (87) to the plate, since the velocity at the front sharp edge of the plate becomes infinity, which breaks the continuity of the flow. It becomes incomprehensible how, in general, a force can arise on the plate, perpendicular to the direction of its movement.
Indeed, in the absence of friction, the pressure forces normal to the surface of the plate should give the main vector directed also along the perpendicular to the plane of the plate, and not to the velocity at infinity, as required by Zhukovsky's theorem. In this case, along with the lifting force, there would be a resistance force. This paradox was explained by Zhukovsky in the second of the previously cited articles. In an actual flow around the plate, its front edge is actually some surface of a very small radius of curvature, on which a significant rarefaction arises, leading to a "sucking" force directed against the flow, destroying the resistance.
LECTURE 2. AERODYNAMIC FORCES AND THEIR COEFFICIENTS
Forces acting on the plane... In flight, the engine thrust force, total aerodynamic force, and weight force act on the plane (Fig. 1). The thrust is usually directed forward along the longitudinal axis of the aircraft.
Figure: 1. Forces acting on an airplane in flight
The force of weight is applied at the center of gravity and is directed along the Vertical to the center of the Earth. The total aerodynamic force is the result of the interaction forces between the air environment and the aircraft surface. It decomposes into three components of force. The force Y is directed perpendicular to the incoming flow and is called lift. The drag force X is directed parallel to the oncoming flow in the direction opposite to the movement of the aircraft. The lateral aerodynamic force Z is directed perpendicular to the plane containing the force components X and Y.
Force R and its components Y, X, Z are applied at the center of pressure. The position of the center of pressure in flight changes and does not coincide with the center of gravity. Depending on the location of the engines on the aircraft, the thrust P may also not pass through the center of gravity.
The movement of an aircraft in air is usually regarded as the movement of a rigid body, the mass of which is concentrated in its center of gravity.
The profile to the streamlines is under angle of attack α Is the angle between the airfoil chord and unperturbed flow lines Fig. 2. Where the flow lines approach each other, the flow velocity increases and the absolute pressure decreases. Conversely, where they become less frequent, the flow rate decreases and the pressure increases.
Figure: 2. Wing profile in the air stream
At different points of the profile, the air presses on the wing with different strengths. The difference between the local pressure at the profile surface and the air pressure in the undisturbed flow can be represented in the form of arrows perpendicular to the profile contour, so that the direction and length of the arrows are proportional to this difference. Then the picture of the pressure distribution along the profile will look as shown in Figure 3.
Figure: 3. Pattern of pressure distribution along the profile.
There is overpressure on the lower generatrix of the profile - air pressure. At the top, on the contrary, there is rarefaction. Moreover, it is larger where the flow velocity is higher. The vacuum value on the upper surface is several times higher than the back pressure on the lower one.
It can be seen from the pressure distribution pattern that the lion's share of the lifting force is formed not because of the back pressure on the lower generatrix of the profile, but because of the vacuum on the upper one.
The vector sum of all surface forces creates the total aerodynamic force R, with which the air acts on the moving wing. 4:
Figure: 4. The lifting force of the wing and the force of its drag.
Expanding this force into vertical Y and horizontal X components, we get wing lift and the force of its drag.
The pressure distribution along the top of the airfoil has a large pressure drop from the rear half of the airfoil to the front half, that is, the pressure drop is directed towards the streamline flow. Starting from a certain angle of attack, this difference becomes the cause of the reverse air flow along the second half of the upper generatrix of the airfoil. five:
Figure: 5. Formation of vortex flow with return flow lines.
At point B, the boundary layer is separated from the wing surface. A vortex flow with reverse flow lines arises behind the separation point. The flow is stalling.
Figure: 6. The coefficient of lift of a wing with a nose of different curvature.
It is customary to calculate the lift and drag force through the lift force coefficient C y and the drag force coefficient: C x and)
The graphical dependence of the lift coefficient C y and the drag force coefficient C x on the angle of attack is shown in Fig. 7.
Figure: 7. Lift coefficient and drag coefficient of the wing.
Aerodynamic qualityprofile is called the ratio of lift to frontal resistance. The term quality itself comes from the function of the wing - it is designed to create lift, and the fact that this creates a side effect - drag, a harmful phenomenon. Therefore, it is logical to call the relation of benefit to harm quality. Can build dependency With from C x on the graph Fig. eight.
Dependence C y from C x in rectangular coordinates is called polar profile... The length of the segment between the origin and any point on the polar is proportional to the total aerodynamic force Racting on the wing, and the tangent of the angle of inclination of this segment to the horizontal axis is equal to the aerodynamic quality TO.
Polar makes it very easy to evaluate the change in the aerodynamic quality of the wing profile. For convenience, it is customary to plot reference points on the curve, marking the corresponding angle of attack of the wing. The polar is easy to estimate the profile drag, the maximum achievable aerodynamic quality of the profile and its other important parameters.
Polar depends on the number Re... It is convenient to estimate the profile properties by a family of polar, built in one grid of coordinates for different numbers Re... Specific profile polars are obtained in two ways:
By blowing in a wind tunnel;
Theoretical calculations.