What is the power of air resistance. How the power of air resistance from the form of the subject and its mass depends

Reservoirs 20.09.2019

Reservoirs

due to braking in front of the body, the flow rate decreases, and the pressure increases. The degree of its increase depends on the form of the front of the body. In front of the flat plate, the pressure is greater than in front of the drop-shaped body. Behind the body, due to the vacuum, the pressure decreases, with a flat plate of a large value compared to a drop-shaped body.

Thus, in front of the body and the difference in pressures is formed, as a result of which an aerodynamic force is created, called pressure resistance. In addition, due to friction of air in the border layer, an aerodynamic force arises, which is called friction resistance.

With symmetric body streaming resistance

pressure and friction resistance are directed to the side opposite to the movement of the body, and together make up force windshoe resistance. The experiments found that the aerodynamic force depends on the flow rate, the mass density of the air, the shape and sizes of the body, the position of it in the stream and state of the surface. With an increase in the raid flow rate, its kinetic energy, which is proportional to the quad speed, increases. Therefore, when flowing around a flat plate, directed perpendicular to the current, with an increase in the speed of pressure in the front hour

it increases it because most of The kinetic energy flow during braking passes into potential pressure energy. At the same time, the pressure is further reduced by the plate, since due to an increase in the inertness of the jet increases the length of the reduced pressure region. Thus, with an increase in the flow rate due to an increase in the pressure difference in front of the body and the aerodynamic power of resistance increases in proportion to the square of the velocity.

Earlier it was found that the air density characterizes the inertness of it: the greater the density, the greater the inertness. For the movement of the body in a more inert, and therefore, in more dense air it is required to make more efforts to shift the air particles, which means that the air will be with greater power Influence the body. Consequently, the higher the air density, the greater the aerodynamic force acting on the moving body.

In accordance with the laws of mechanics, the magnitude of the aero-dynamic force is proportional to the area of \u200b\u200bthe body cross section perpendicular to the direction of the action of this force. For most bodies, such a cross section is the largest cross section, called Middle, and for the wing - its area in the plan.

The form of the body affects the nature of the aerodynamic spectrum (the rate of pips flowing on this body), and consequently, to the pressure difference, which determines the magnitude of the aerodynamic force. When the position of the body is changed in the air flow, its spectrum of flow changes, which entails a change in the magnitude and direction of aerodynamic forces.

The bodies having a less rough surface are experiencing smaller friction forces, since most of the surface their border layer has a laminar flow in which friction resistance is less than in turbulent.

Thus, if the effect of form and position
bodies in the stream, degree of processing of its surface take into account
correction coefficient called aero
dynamic coefficient, then we can conclude,
that the aerodynamic force is directly proportional to
he is a coefficient, high-speed pressure and square
sharing the body (at the wing Square),

If you designate the full-aerodynamic force of air resistance to the letter R,the aerodynamic coefficient of its high-speed pressure - q,and the area of \u200b\u200bthe wing is the formula of the resistance of the air can be recorded by the following oblivion:

attacks like high-speed head is equal

view:

formula will

The above formula of the resistance force of the air is shaved the main, since for a similar form-share, you can determine the value of any aerodynamic strength, replacing only the designation of the force and its coefficient.

Full aerodynamic force and its component

Since the curvature of the wing from above is greater than the SNA, then when it is encountered with an air flow according to the law of constancy of the second air flow, the local speed of the wing streaming above is greater than at the bottom, and the attack ribs it decreases sharply and falls at some points to zero. According to the law of Bernoulli before the wing and under it there is an area increased pressure; Above the wing and behind it occurs a region of reduced pressure. In addition, due to the viscosity of the air. There is a force, friction in the border layer. Car-tying of pressure distribution on the profile of the wing depends on the position of the wing in the airflow, for whose characteristics use the concept of an "angle of attack".

The angle, the attacks of the wing (α) is called an angle concluded between the direction of the chord of the wing and the incident air flow or the direction of the flight velocity vector (Fig. 11).

Pressure distribution by profile is depicted and the form of vector diagram. To build it, the wing profile is drawn, there are points on it, in which

the pressure was measured, and the values \u200b\u200bare laid from these points vectors. excessive pressure. Naly at this point pressure is low, the vector arrow is directed from the profile, if the pressure is increased, then to the profile. The ends of the vectors are connected by a common line. In fig. 12 shows the pattern of pressure distribution on the profile of the wing at small and large corners of the attack. It can be seen that the greatest vacuum is obtained on the top surface of the wing in the place of the maximum narrowing of the pip. At the angle of attack, equal to zero, the greatest vacuum will be in the place of the largest thickness of the profile. Under the wing there is also a narrowing of the pelves, as a result of which there will be a vacuum zone, but less than above the wing. In front of the wing toe - an area of \u200b\u200bincreased pressure.

With an increase in the angle of attack, the vacuum zone is shifted to the edge of the attack and increases significantly. This is because the place of the greatest narrowing of the pip is moved to the edge of the attack. Under the wing of the air particles, encountered the lower surface of the wing, is slowed down, resulting in pressure rises.

Each excess pressure vector shown in the diagram is the force acting on the unit surface of the wing, that is, each arrow denotes the amount of overpressure, or the difference between local pressure and pressure in the unperturbed stream:

Having summed up all vectors, you can get aerodynamic power without taking into account the friction forces. This force, taking into account the friction force in the border layer, will be the complete aerodynamic force of the wing. Thus, full aerodynamic force (R)there is a reason for the difference in pressure in front of the wing and behind it, under the wing and above it, as well as as a result of friction of air in the border layer.

The point of application of complete aerodynamic force is located on the chord of the wing and is called the pressure center (CD). Since complete aerodynamic force acts towards a smaller pressure, it will be directed up and rejected backwards.

In accordance with the basic law of resistance

Fig. 13.The decomposition of the full aerodynamic force of the wing to the components

air full aerodynamic force is expressed by the formula:

Complete aerodynamic force is taken to consider as a geometric sum of two components: one of them, perpendicular to the unperturbed flow, is called lifting force, and the other, q, directed oppositely by the movement of the wing, is called the windshield force.

Each of these forces can be viewed as an algebraic amount of two terms: pressure and friction force. For lifting force, it is practically possible to neglect the second term and assume that it is only powerful power. Resistance should be considered as the sum of the resistance of pressure and friction resistance (Fig. 13).

The angle concluded between the lifting force vectors and complete aerodynamic force is called an angle of quality (θk).

Wing Lift

The lifting force (y) is created due to the difference in medium pressures from below and on top of the wing.

When streamling an asymmetric profile, the flow rate above the wing is greater than under the wing, due to the greater curvature of the upper surface of the wing and, in accordance with the law of Bernoulli, the pressure from above turns out to be less than below.

If the wing profile is symmetrical and the angle of the attack is zero, the flow around is symmetrical, the pressure above the wing and the same and the lifting force does not occur (Fig. 14). The symmetric profile wing creates lifting force only with an attack corner differ from zero.

It follows that the magnitude of the lifting force is equal to the product of the difference in excess pressure under the wing (rhizb.nizhn) and above it (Rizb. Upper) on the area of \u200b\u200bthe wing:

With Y.-Ceficient of the lifting force, which is determined by experimental by purging the wing in the aerodynamic tube. Its value depends: 1 - from the shape of the wing, which takes the main part in the creation of lifting force; 2 - from the angle of attack (orientation of the wing relative to the stream); 3 - on the degree of wing treatment (absence of roughness, material integrity, etc.).

If, according to the purge of the wing of the asymmetric profile in the aerodynamic tube at different angles of attacks to build a chart, it will look like this (Fig. 15).

It can be seen that:

1. At a certain negative value of the angle of attack, the lift coefficient is zero. This is the angle of the ayki zero lifting force and is indicated by α0.

2. With an increase in the angle of attack to a certain value

Fig. fourteen.Wing flowing by a subsonic stream: but- spectrum of flow (the boundary layer is not shown); b.- Pressure Distribution (Pressure Pattern)

Fig. fifteen.Chart dependent
The coefficient's bridges
lifting force and coefficient
Lob's Fireplace
Contacts from the corner
Attacks.

Fig, 16.Flood breaking on the core corners of the attack: at the point and the pressure is greater than at the point B, and at the point in the pressure is greater than at points A and B

the coefficient of lift increases in proportion to (in a straight line), after a certain value of the attack angle, the growth of the lifting coefficient decreases, which is explained by the formation of twists on the upper surface.

3. With a certain value of the angle of attack, the lift coefficient reaches the maximum value. This angle is called critical and denotes α kr. Then, with a further increase in the angle of attack, the lift coefficient decreases, which is due to the intensive breakdown of the flow from the wing caused by the movement of the boundary layer against the movement of the main stream (Fig. 16).

The range of operating angles of the attack is the corners from α 0 to α kr. At the corners of attacks close to critical, the wing does not have sufficient resistance and poorly controlled.

To determine power resistance air Create the conditions under which the body will begin under the action of gravity move evenly and straight. Calculate the value of gravity, it will be equal to the power of air resistance. If the body moves in the air, gaining speed, the strength of its resistance is under Newton's laws, also the power of air resistance can be found from the conservation law. mechanical energy and special aerodynamic formulas.

You will need

rangefinder, scales, speedometer or radar, ruler, stopwatch.

Instruction

Determination of air resistance is uniformly falling body. Measure the body weight using weights. After throwing it from some height, achieve it to move evenly. Multiply body weight in kilograms to accelerate free fall, (9.81 m / c²), the result will be the power of gravity acting on the body. And since it moves evenly and straightly, the strength of gravity will be equal to the power of air resistance.
Determination of air resistance to the body, recruiting the velocity of body weight using weights. After the body began to move, use the speedometer or radar, measure its instantaneous initial speed. At the end of the plot, measure its instantaneous final speed. Speed \u200b\u200bmeasured in meters per second. If the instruments measure it in kilometers per hour, submit a value by 3.6. In parallel with the help of the stopwatch, determine the time for which this change occurred. Related from the end speed is the initial and dividing the result for a while, find the acceleration with which the body moves. Then find the power that causes the body to change the speed. If the body falls, then this is the power of gravity, if the body moves horizontally - the motor thrust force. From this force, take the work of the body mass on its acceleration (FC \u003d F + M A). This will be the power of air resistance. It is important that when moving the body does not concern the earth, for example, moving on an air cushion or falling down.
Determination of air resistance to the body falling with height of the body and reset it from a height, which is known in advance. When contacting the surface of the Earth, fix the body speed using a speedometer or radar. After that, find the product of the acceleration of the free fall of 9.81 m / s² to the height with which the body fell, take the speed from this value raised to the square. The resulting result multiplies the body weight and divide the height with which it fell (Fc \u003d M (9.81 H-V²) / H). This will be the power of air resistance.

One of the manifestations of the power of mutual gravity is the power of gravity, i.e. The power of attraction to the ground. If only gravity is valid on the body, it makes free fall. Consequently, the free fall is a drop in bodies in an airless space under the action of attraction to the ground, starting from the state of rest.

For the first time this phenomenon studied Galilee, but due to lack of air pumps He could not have experience in airless space, so Galilee made experiments in the air. By discarding all the secondary phenomena, when moving tel in the air, Galiley opened the laws of free falling tel. (1590)

1st law. Free drop is a straightforward uniformly asked movement.
2nd law. Accelerating the free fall in this place of the Earth for all bodies equally; The average value is 9.8 m / s.

The dependences between the kinematic characteristics of the free fall are obtained from the formulas for an equilibrium movement, if in these formulas it is possible a \u003d g. At V0 \u003d 0 V \u003d GT, H \u003d GT2 \\ 2, V \u003d √2GH.

Practically air always has resistance to the movement of the falling body, and for this body, the air resistance is the greater, the greater the speed of the fall. Therefore, as the flow rate increases, the air resistance increases, the acceleration of the body decreases and, when the air resistance becomes equal to the strength of gravity, the acceleration of the free incident body will be zero. In the future, the movement of the body will be uniform movement.

Real movement of tel in earthly atmosphere It occurs through a ballistic trajectory, significantly different from parabolic due to air resistance. For example, if we release a bullet from a rifle with a speed of 830 m / s at an angle α \u003d 45O to the horizon and fix the actual trajectory of the tracing bullet and the place of its fall, then the range of flight will be approximately 3.5 km. And if calculated by the formula, it will be 68, 9 km. The difference is huge!

Air resistance depends on four factors: 1) the size of the moving item. The big object will obviously get more resistance than small. 2) Form of a moving body. A flat plate of a certain area will have a much greater resistance to the wind than the streamlined body (a drop shape) having the same cross section area for the same wind, really 25 times more! The round item is somewhere in the middle. (This is the reason why the hulls of all cars, airplanes and paragliders have, if possible, a rounded or drop-shaped form: it reduces air resistance and allows you to move faster with smaller engine to the engine, which means that at lower fuel costs). 3) air density. We already know that one cubic meter Weighs about 1.3 kg at sea level, and, the higher you rise, the air becomes the dense. This difference can play some practical role when takeoff only very much with a high height. 4) speed. Each of the three currently discussed factors gives a proportional contribution to air resistance: if you increase one of them twice, resistance is also doubled; If you reduce any of them twice, the resistance drops half.

The resistance of the air is half the air density multiplied by the resistance coefficient multiplied by the cross-sectional area and multiplied by the Speed \u200b\u200bSquare.

We introduce the following characters: D - air resistance; p - air density; A - cross-sectional area; CD - resistance coefficient; υ - air speed.

Now we have: d \u003d 1/2 x p x Cd x a x υ 2

When the body falls in real conditions, the acceleration of the body will not equal to the acceleration of the free fall. In this case, 2 Newton's law will take the form Ma \u003d Mg - FSPR -farh

Farh. \u003d ρqv, since the air density is small, can be neglected, then Ma \u003d Mg - ηυ

Let us analyze this expression. It is known that the power of resistance is valid on the body. It is almost obvious that this force depends on the speed of the movement and size of the body, for example, the cross-sectional area S, and this dependence of the type "the larger υ and s, the greater F". You can still clarify the type of this dependence, based on the considerations of dimensions (units of measurement). Indeed, the force is measured in Newton ([F] \u003d H), and H \u003d kg · m / s2. It can be seen that the second in the square enters the denominator. From here it is immediately clear that the force should be proportional to the square of the body velocity ([υ2] \u003d m2 / C2) and the density ([ρ] \u003d kg / m3) - of course, the environment in which the body is moving. So,

And in order to emphasize that this force is directed against the velocity vector.

We have already learned a lot, but that's not all. Surely the resistance force (aerodynamic force) depends on the body shape - it is not by chance that the aircraft are made "well-streaming". To take into account this alleged dependence, it is possible to introduce a dimensionless multiplier to the above relation, which will not violate the equality of dimensions in both parts of this ratio, but will turn it into equality:

Imagine a ball moving in the air, for example, a crushing, horizontally flowing at the initial speed - if there were no air resistance, then at a distance x during the crusher would shift the vertically down. But due to the action of the resistance force (directed against the velocity vector), the time of the crushing time to the vertical plane X will be greater than T0. Consequently, the strength of gravity will act longer on the crusher, so it drops below y0.

And in general, the crusher will move on another curve that is no longer a parabola (it is called a ballistic trajectory).

If there is an atmosphere of falling bodies, in addition to the strength of gravity, have an impact of viscous friction forces on air. In a rough approximation at low speeds, viscous friction can be considered proportional speed of movement. In this case, the equation of body movement (the second law of Newton) has the form Ma \u003d Mg - η υ

The strength of viscous friction, acting on the spherical form moving with small velocities, is approximately proportional to the area of \u200b\u200btheir cross section, i.e. Square radius tel: F \u003d -η υ \u003d - const R2 υ

The mass of the spherical body of a constant density is proportional to its volume, i.e. Cuba radius M \u003d ρ V \u003d ρ 4 / 3π R3

The equation is written, taking into account the direction of the OY axis down, where η is an air resistance-cell. This value depends on the state of the environment and body parameters (body weight, sizes and shapes). For the body of a spherical shape, according to the Stokes formula η \u003d 6 (m (r where m is the mass of the body, R is the radius of the body, (is the air viscosity coefficient.

Consider for example the fall of balls from miscellaneous material. Take two balls of the same diameter, plastic and iron. We accept for clarity that the density of iron is 10 times more plastic density, so the iron ball will have a mass 10 times more, respectively, its inertness will be 10 times higher, i.e. Under the influence of the same strength, it will accelerate 10 times slower.

In the vacuum on the balls there is only the power of gravity, on the iron 10 times more than plastic, accordingly they will accelerate with the same acceleration (10 times big power Severity compensates for 10 times greater inertness of the iron ball). With the same acceleration, the same distance both balls will be held in the same time, i.e. In other words, fall at the same time.

In the air: the force of the gravity is added the power of aerodynamic resistance and Archimedean force. Both of these forces are directed up, against the action of gravity, and both depend on the size and speed of the movement of the balls (do not depend on their mass) and with equal speeds of movement are equal to both balls.

T.O. The resulting three forces acting on the iron ball will no longer be 10 times higher than the similar resulting wooden, and in more than 10, the inertness of the iron ball remains more inertness of the wooden all in the same 10 times .. accordingly, the acceleration of the iron ball will be greater than plastic, And he will fall before.

It is a component of complete aerodynamic force.

The overhead resistance force is usually represented as the sum of the two components: resistance at zero lifting power and inductive resistance. Each component is characterized by its own self-dimensional resistance coefficient and a certain dependence on the speed of movement.

The windshield can contribute to both icing of aircraft (at low air temperatures) and cause heating the front surfaces of LA with supersonic speeds by shock ionization.

Resistance at zero lifting force

This component of the resistance does not depend on the value of the lifting force being created and consists of the profile resistance of the wing, the resistance of the structural elements of the aircraft, which are not contributing into the lifting force, and wave resistance. The latter is essential when moving with about and supersonic speed, and caused by the formation of a shock wave, carrying a significant proportion of motion energy. Wave resistance occurs when the speed is reached by airplane corresponding to the critical number of Mach, when part of the flow that flows around the wing of the aircraft becomes supersonic speed. The critical number M is greater than the greater the angle of the wing, the more the front edge of the wing is pointed and the thinner.

The strength of the resistance is directed against the speed of the movement, its value is proportional to the characteristic area S, the density of the medium ρ and the square of the velocity V:

C. x.0 - a dimensionless aerodynamic resistance coefficient, it turns out from the criteria of similarity, for example, Reynolds and Frouda numbers in aerodynamics.

The definition of the characteristic area depends on the body shape:

in the simplest case (ball) - cross-sectional area;
for wings and plumage - the area of \u200b\u200bthe wing / plumage in the plan;
for propellers and carrier screws of helicopters - either the area of \u200b\u200bthe blades, or an ovens of the screw area;
for oblong bodies of rotation oriented along The flow (fuselage, the airship envelope) is a given volumen area equal to V 2/3, where V is the volume of the body.

The power required to overcome this component of the windshield strength is proportional to cuba Speed.

Inductive resistance

Inductive resistance (eng. lift-Induced Drag) - This is a consequence of the formation of lifting force on the wing of the final scope. Asymmetric flow around the wing leads to the fact that the flow of the air runs off the wing at an angle to the focus on the wing (T.N. SKO stream). Thus, during the movement of the wing, there is a constant acceleration of the mass of the incident air in the direction perpendicular to the direction of flight, and the directional downwards. This acceleration is first accompanied by the formation of lifting force, and secondly, it leads to the need to inform the accelerating flow kinetic energy. The amount of kinetic energy required to communicate the speed flow perpendicular to the field of flight, and will determine the value of inductive resistance.

The value of the inductive resistance is influenced not only by the magnitude of the lifting force, but also its distribution by wing wing. The minimum value of inductive resistance is achieved with the elliptic distribution of the lifting force on the scope. When designing the wing, this is achieved by the following methods:

the choice of rational shape of the wing in the plan;
the use of geometric and aerodynamic twist;
installation of auxiliary surfaces - vertical clamps of the wing.

Inductive resistance proportionally square lifting force y and inversely The area of \u200b\u200bthe wing S, its elongation λ, the density of the medium ρ and square Speed \u200b\u200bV:

Thus, inductive resistance makes a significant contribution when flying at low speed (and, as a result, at the large corners of the attack). It also increases with an increase in the weight of the aircraft.

Total resistance

It is the sum of all types of resistance forces:

X. = X. 0 + X. i.

Since resistance with zero lifting force X. 0 proportionally square square, and inductive X. i. - inversely in proportion to the square of speed, then they contribute a different contribution when different speeds. With increasing speed X. 0 grows, and X. i. - falls, and a graph of the dependence of the total resistance X. From speed ("curve required traction") has a minimum at the point of intersection of curves X. 0 I. X. i. In which both resistance forces are equal in size. At this speed, the aircraft has the smallest resistance at a given lifting force (equal weight), which means the highest aerodynamic quality.

Wikimedia Foundation. 2010.

All components of air resistance are difficult to determine analytically. Therefore, in practice, an empirical formula has been used, having a movement speed range characteristic of a real car, the following form:

where from h. - size free air conditioning coefficientdepending on the shape of the body; ρ B - air density ρ B \u003d 1,202 ... 1,225 kg / m 3; BUT - the area of \u200b\u200bthe Middeev section (cross-projection area) of the car, m 2; V. - vehicle speed, m / s.

The literature meets air resistance coefficient k. in :

F. in = k. in BUTV. 2 where k. in \u003d S. h. ρ in /2 , Coefficient of air resistance, NA 2 / m 4.

…and factor of encruptionq. in : q. in = k. in · BUT.

If instead from h. lay down from z. , I get aerodynamic lifting force.

Middeev area of \u200b\u200bthe section for cars:

A \u003d 0.9 · in max · N.,

where IN Max is the largest car river, m; N. - Car height, m.

The force is applied in the meticenter, the moments are created.

The speed of air flow resistance, taking into account the wind:

where β is the angle between the directions of the car and wind movement.

FROM h. Some cars

VAZ 2101 ... 07			Opel Astra Sedan.
VAZ 2108 ... 15


			Land Rover Free Lander
VAZ 2102 ... 04
VAZ 2121 ... 214
			truck
			truck with trailer

Resistance strength rise

F. p = G. but sin. α.

In road practice, the magnitude of the slope is usually assessed by the value of the lifting of the road of the road, assigned to the magnitude of the horizontal projection of the road, i.e. tangent angle, and denote i., expressing the value obtained in percent. With a relatively small magnitude of the slope, permissible in the calculated formulas in determining the resistance force to use sin. α., And the amount i. in relative values. With large values \u200b\u200bof the slope of replacement sin. α value of tangent ( i./100) unacceptable.

The power of resistance overclocking

When the car is accelerated, there is an overclocking of the transmitting mass of the car and the acceleration of rotating masses that increase the resistance of acceleration. This increase can be taken into account in the calculations, if we assume that the mass of the car is moving properly, but to use some equivalent mass m. e, somewhat bigger m. a (in classical mechanics it is expressed by the Kenig equation)

We use the N.E. method. Zhukovsky, equating the kinetic energy of the progressively moving equivalent mass of the amount of energies:

where J. d. - moment of inertia of the engine flywheel and related parts, N · C 2 · m (kg · m 2); ω. d. - engine angular speed, rad / s; J. to -Moment inertia of one wheel.

As ω k \u003d V. but / r. k. , ω d. = V. but · i. kP · i. o. / r. k. , r. k. = r. k. 0 ,

that we get
.

Moment of inertiaJ. Prommissions of cars, kg · m 2

Car	Flywheel with crankshaft J. d.	Slave wheels (2 wheels with brake drums), J. k1.	Drive wheels (2 wheels with brake drums and with semi-axes) J. k2.