Average air resistance force formula. How to find air resistance forces

due to deceleration in front of the body, the flow velocity decreases, and the pressure increases. The degree of its increase depends on the shape of the front of the body. The pressure in front of the flat plate is greater than in front of the teardrop body. Behind the body, due to rarefaction, the pressure decreases, while a flat plate has a greater value than a drop-shaped body.

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

With a symmetrical flow around the body, the resistance

pressure and friction resistance are directed in the direction opposite to the movement of the body, and together make up the drag force. Experiments have established that the aerodynamic force depends on the flow rate, air mass density, shape and size of the body, its position in the flow and the state of the surface. With an increase in the speed of the oncoming flow, its kinetic energy, which is proportional to the square of the speed, increases. Therefore, when flowing around a flat plate directed perpendicular to the current, with increasing speed, the pressure in the front part

ty it increases, because most of kinetic energy flow during deceleration is converted into potential energy of pressure. At the same time, behind the plate, the pressure decreases even more, since due to the increase in the inertia of the jet, the length of the low-pressure region increases. Thus, with an increase in the flow velocity, due to an increase in the pressure difference in front of the body and behind it, the aerodynamic drag force increases in proportion to the square of the speed.

Previously, it was found that the density of air characterizes its inertia: the greater the density, the greater the inertia. For the movement of the body in a more inert, and therefore denser air, it is required to apply more efforts to shift the air particles, which means that the air will also greater strength affect the body. Therefore, 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 aerodynamic force is proportional to the cross-sectional area of ​​​​the body perpendicular to the direction of action of this force. For most bodies, such a section is the largest cross section, called the midsection, and for the wing, its area in plan.

The shape of the body affects the nature of the aerodynamic spectrum (the speed of the jets flowing around a given body), and, consequently, the pressure difference, which determines the magnitude of the aerodynamic force. When the position of the body in the air flow changes, its flow spectrum changes, which entails a change in the magnitude and direction of the aerodynamic forces.

Bodies with a less rough surface experience lower friction forces, since on most of the surface their boundary layer has a laminar flow, in which the friction resistance is less than in a turbulent one.

Thus, if the influence of shape and position
body in the flow, the degree of processing of its surface should be taken into account
correction factor, which is called aero
dynamic coefficient, it can be concluded that
that the aerodynamic force is directly proportional to its
its coefficient, velocity head and area of ​​mi-
dividing the body (at the wing -its area),

If we denote the total aerodynamic force of air resistance by the letter R, its aerodynamic coefficient - speed head - q, and the area of ​​\u200b\u200bthe wing, then the formula for air resistance can be written as follows:

attacks as the velocity head is equal to

look like:

the formula will be

The above formula for the air resistance force is considered to be the main one, since it is possible to determine the value of any aerodynamic force by similar to it form-share, replacing only the designation of the force and its coefficient.

Total aerodynamic force and its component

Since the curvature of the wing from above is greater than from below, then when it meets the air flow, according to the law of constancy of the second air flow rate, the local velocity of the flow around the wing at the top is greater than at the bottom, and at the edge of attacks it sharply decreases and at some points drops to zero. According to Bernoulli's law, an area of ​​increased pressure appears in front of the wing and under it; above the wing and behind it there is an area of ​​low pressure. In addition, due to the viscosity of the air. there is a force, friction in the boundary layer. The pattern of pressure distribution along the wing profile depends on the position of the wing in the air flow, which is characterized by the concept of "angle of attack".

The angle of attack of the wing (α) is the angle enclosed between the direction of the wing chord and the oncoming air flow or the direction of the flight velocity vector, (Fig. 11).

The pressure distribution along the profile is also shown as a vector diagram. To build it, draw a wing profile, mark points on it, in which

pressure was measured, and from these points the values ​​of excess pressures are plotted by vectors. Zeros at this point, the pressure is low, then the arrow of the vector is directed from the profile, if the pressure is high, then to the profile. The ends of the vectors are connected by a common line. On fig. 12 shows the pattern of pressure distribution along the wing profile at low and high angles of attack. It can be seen from it that the greatest rarefaction is obtained on the upper surface of the wing in the place of maximum narrowing of the jets. With an angle of attack equal to zero, the greatest rarefaction will be in the place of the greatest thickness of the profile. Under the wing there is also a narrowing of the streams, as a result of which there will also be a rarefaction zone, but smaller than above the wing. In front of the toe of the wing is an area of ​​high pressure.

With an increase in the angle of attack, the rarefaction zone shifts to the edge of attack and increases significantly. This happens because the place of the greatest narrowing of the streams moves to the edge of attack. Under the wing, air particles, meeting the lower surface of the wing, slow down, as a result of which the pressure rises.

Each overpressure vector shown in the diagram represents a force acting on a unit of wing surface, that is, each arrow indicates, on a certain scale, the amount of overpressure, or the difference between the local pressure and the pressure in the undisturbed flow:

Summing up all the vectors, you can get the aerodynamic force without taking into account the forces of friction. This force, taking into account the air friction force in the boundary layer, will be the total aerodynamic force of the wing. Thus, the total aerodynamic force (R) arises due to 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 air friction in the boundary layer.

The point of application of the total aerodynamic force is located on the wing chord and is called the center of pressure (CP). Since the total aerodynamic force acts in the direction of lower pressure, it will be directed upwards and deflected back.

According to the basic law of resistance

Rice. 13. Decomposition of the total aerodynamic force of the wing into components

air, the total aerodynamic force is expressed by the formula:

The total aerodynamic force is considered as geometric sum two components: one of them, Y, perpendicular to the undisturbed flow, is called the lifting force, and the other, Q, directed opposite to the movement of the wing, is called the drag force.

Each of these forces can be considered as an algebraic sum of two terms: the pressure force and the friction force. For the lifting force, it is practically possible to neglect the second term and consider that it is only a pressure force. The resistance must be considered as the sum of pressure resistance and friction resistance (Fig. 13).

The angle enclosed between the vectors of the lifting force and the total aerodynamic force is called the Quality angle (Θk).

Wing lift

The lifting force (Y) is created due to the difference in the average pressures below and above the wing.

When flowing around an asymmetric profile, the flow velocity 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 Bernoulli's law, the pressure from above is less than from below.

If the wing profile is symmetrical and the angle of attack is zero, then the flow is symmetrical, the pressure above and below the wing is the same, and no lift occurs (Fig. 14). A wing with a symmetrical profile creates lift only at a non-zero angle of attack.

From this it follows that the magnitude of the lift force is equal to the product of the difference in excess pressures under the wing (Rizb.lower) and above it ( Risb. top) on the wing area:

C Y- lift coefficient, which is determined empirically when blowing the wing in a wind tunnel. Its value depends: 1 - on the shape of the wing, which takes the main part in creating lift; 2 - from the angle of attack (orientation of the wing relative to the flow); 3 - on the degree of processing of the wing (absence of roughness, integrity of the material, etc.).

If, according to the data of blowing the wing of an asymmetric profile in a wind tunnel at different angles of attack, a graph is plotted, then it will look as follows (Fig. 15).

It shows that:

1. For some negative value angle of attack, the lift coefficient is zero. This is the zero lift angle and is denoted by α0.

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

Rice. fourteen. Wing subsonic flow: a- flow spectrum (boundary layer not shown); b- pressure distribution (pressure pattern)

Rice. fifteen. dependency graph
coefficient bridge
lifting force and coefficient
front windshield
corner resistance
attacks.

Rice, 16. Stall at supercritical angles of attack: at point A the pressure is greater than at point B, and at point C the pressure is greater than at points A and B

the lift coefficient increases proportionally (in a straight line), after a certain value of the angle of attack, the increase in the lift coefficient decreases, which is explained by the formation of vortices on the upper surface.

3. At a certain value of the angle of attack, the lift coefficient reaches its maximum value. This angle is called critical and is denoted by α cr. Then, with a further increase in the angle of attack, the lift coefficient decreases, which occurs due to the intense flow separation from the wing caused by the movement of the boundary layer against the movement of the main flow (Fig. 16).

The range of operational angles of attack is angles from α 0 up to α cr. At angles of attack close to critical, the wing does not have sufficient stability and is poorly controlled.

When any object moves on the surface or in the air, forces arise that prevent it. They are called forces of resistance or friction. In this article, we will explain how to find the resistance force and consider the factors that affect it.

Air resistance is used during skydiving. As a result of the resulting friction between the dome and the air, the speed of the skydiver is reduced, which allows parachuting without damage to life.

It is a component of the total aerodynamic force.

The drag force is usually represented as the sum of two components: drag at zero lift and induced drag. Each component is characterized by its own dimensionless drag coefficient and a certain dependence on the speed of movement.

Drag can contribute to both icing aircraft(at low temperatures air), and cause heating of the frontal surfaces of the aircraft at supersonic speeds by impact ionization.

Resistance at zero lift

This drag component does not depend on the magnitude of the created lift force and consists of the profile drag of the wing, the resistance of aircraft structural elements that do not contribute to lift, and wave drag. The latter is significant when moving at near- and supersonic speeds, and is caused by the formation of a shock wave that carries away a significant portion of the motion energy. Wave drag occurs when the aircraft reaches a speed corresponding to the critical Mach number, when part of the flow around the wing of the aircraft acquires supersonic speed. The critical number M is the greater, the greater the sweep angle of the wing, the more pointed the leading edge of the wing and the thinner it is.

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

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

• in the simplest case (ball) - cross-sectional area;
• for wings and empennage - the area of ​​the wing / empennage in plan;
• for propellers and rotors of helicopters - either the area of ​​the blades or the swept area of ​​the propeller;
• for oblong bodies of revolution oriented along flow (fuselage, airship shell) - reduced volumetric area equal to V 2/3, where V is the volume of the body.

The power required to overcome a given drag force component is proportional to Cuba speed.

Inductive reactance

Inductive reactance(English) lift-induced drag) is a consequence of the formation of lift on the wing of finite span. The asymmetric flow around the wing leads to the fact that the air flow escapes from the wing at an angle to the flow on the wing (the so-called flow bevel). Thus, during the movement of the wing, there is a constant acceleration of the mass of incoming air in a direction perpendicular to the direction of flight and directed downward. This acceleration is, firstly, accompanied by the formation of a lifting force, and secondly, it leads to the need to impart kinetic energy to the accelerating flow. The amount of kinetic energy required to communicate the speed to the flow, perpendicular to the direction of flight, will determine the value of the inductive resistance.

The magnitude of the inductive drag is influenced not only by the magnitude of the lift force, but also by its distribution over the span of the wing. The minimum value of the inductive reactance is achieved with an elliptical distribution of the lifting force along the span. When designing a wing, this is achieved by the following methods:

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

Inductive reactance proportional to square lift force Y, and inversely wing area S, its elongation λ, medium density ρ and square speed V:

Thus, inductive drag makes a significant contribution when flying at low speed (and, as a result, at high angles of attack). It also increases as the weight of the aircraft increases.

Total resistance

It is the sum of all types of resistance forces:

Since the resistance at zero lift X 0 is proportional to the square of the speed, and the inductive X i is inversely proportional to the square of the speed, then they contribute differently at different speeds. With increasing speed, X 0 is growing, and X i- falls, and the graph of the dependence of the total resistance X on speed (“required thrust curve”) has a minimum at the point of intersection of the curves X 0 and X i, at which both resistance forces are equal in magnitude. At this speed, the aircraft has the least resistance for a given lift (equal to weight), and therefore the highest aerodynamic quality.

Wikimedia Foundation. 2010 .

Formation of air resistance force. On fig. 78 and 81 show the air flows generated during the movement of a car and a truck. Force of air resistance Pw consists of several components, the main of which is the drag force. The latter occurs due to the fact that when the car is moving (see Fig. 78), excess pressure is created in front of it +AR air, and behind - reduced -AR(compared to atmospheric pressure). The pressurization of air in front of the car creates resistance to movement forward, and the rarefaction of air behind the car forms a force that tends to move the car back. Therefore than more difference pressures in front and behind the car, the greater the drag force, and the pressure difference, in turn, depends on the size, shape of the car and its speed.

Rice. 78.

Rice. 79.

On fig. 79 shows the values ​​(in conventional units) of the frontal resistance depending on the shape of the body. It can be seen from the figure that with a streamlined front part drag air is reduced by 60%, and when streamlining the rear - only by 15%. This indicates that the air pressure created in front of the car has a greater influence on the formation of the force of frontal air resistance than the rarefaction behind the car. The streamlining of the rear of the car can be judged by the rear window - with a good aerodynamic shape, it will not

it smells dirty, and with poor streamlining, the rear window sucks dust.

In the general balance of air resistance forces, the drag force accounts for approximately 60%. Among other components, it should be noted: the resistance arising from the passage of air through the radiator and the engine compartment; resistance created by protruding surfaces; frictional resistance of air on the surface and other additional resistances. The values ​​of all these components are of the same order.

Total air resistance force Pw is concentrated in the center of windage, which is the center of the largest sectional area of ​​the body in a plane perpendicular to the direction of motion. In general, the center of windage does not coincide with the center of gravity of the car.

The force of frontal air resistance is the product of the cross-sectional area of ​​​​the body and the high-speed pressure of air, taking into account the streamlining of the shape:

where c x - dimensionless frontal coefficient (aerodynamic) resistance, taking into account streamlining; / '- frontal area or area front projection, m 2 ; q\u003d 0.5p B v a 2 - air velocity pressure, N / m 2. As can be seen from the dimension, the velocity head of air is a specific force acting per unit area.

Substituting the expression for velocity head into formula (114), we obtain

where v a - vehicle speed; p in - air density, kg / m 3.

frontal area

where a is the area fill factor; a = 0.78 ... 0.80 for cars and a = 0.75 ... 0.90 - for trucks; H a , V a - highest values respectively the width and height of the vehicle.

The force of the frontal air resistance is also calculated by the formula

where w = 0.5s x p in - air resistance coefficient, having the dimension of air density - kg / m 3 or N s 2 / m 4. At sea level, where the air density p in \u003d 1.225 kg / m 3, w = 0,61 with x, kg / m 3.

physical meaning coefficients kw and with x is that they characterize the properties of the streamlining of the car.

Aerodynamic testing of the car. The aerodynamic characteristics of the car are studied in a wind tunnel, one of which was built at the Russian Research Center for Testing and Fine-tuning Automotive Equipment. Let us consider the method of testing a car in a wind tunnel developed in this center.

On fig. 80 shows the system of coordinate axes and the direction of action of the components of the total aerodynamic force. During testing, the following forces and moments are determined: the force of the frontal aerodynamic drag R x, side force R, lifting force Pv roll moment M x, overturning moment M y, turning moment M v

Rice. 80.

During the tests, the car is installed on a six-component aerodynamic balance and fixed on the platform (see Fig. 80). The vehicle must be filled, completed and loaded in accordance with technical documentation. The air pressure in the tires must comply with the factory operating instructions. The tests are controlled by a computer in accordance with the program for automated type weight tests. In the process of testing, a special fan creates air flows moving at a speed of 10 to 50 m/s with an interval of 5 m/s. Various angles of air flow onto the vehicle relative to the longitudinal axis can be created. The values ​​of forces and moments shown in fig. 80 and 81, registers and processes the computer.

During tests, the velocity (dynamic) air pressure is also measured q. Based on the measurement results, the computer calculates the coefficients of the forces and moments listed above, from which we present the formula for calculating the drag coefficient:

where q- dynamic pressure; F- frontal area.

Other coefficients ( With y, c v c mx, c tu, c mz) are calculated similarly with the substitution of the corresponding value into the numerator.

The product ^ is called drag factor or flow factor.

Air resistance coefficient values kw and with x for cars of different types are given below.

Ways to reduce the force of air resistance. To reduce drag, they improve the aerodynamic properties of a car or road train: in cars they change the shape of the body (mostly), and in trucks they use fairings, an awning, and a tilted windshield.

Antenna, mirror appearance, roof rack, extra lights and other protruding parts, or open windows increase air resistance.

The air resistance force of a road train depends not only on the shape of individual links, but also on the interaction air currents flowing around the links (Fig. 81). In the intervals between them, additional turbulences are formed, increasing the total air resistance to the movement of the road train. For main road trains moving along highways with high speed, the energy consumption to overcome air resistance can reach 50% of the power of an automobile engine. To reduce it, deflectors, stabilizers, fairings and other devices are installed on road trains (Fig. 82). According to prof. A.N. Evgrafov, the use of a set of hinged aerodynamic elements reduces the coefficient with x saddle road train by 41%, trailer - by 45%.

Rice. 81.

Rice. 82.

At speeds up to 40 km/h Pw less rolling resistance force on an asphalt road, as a result of which it is not taken into account. Above 100 km/h, air resistance is the main component of traction loss.

How to find the force of air resistance? Please advise, thanks in advance.

1. But YOU don't have a job!! ? If when falling in the air, then according to the formula: Fc=m*g-m*a; m- body mass g=9.8 ms a-acceleration with which the body falls.
2. The resistance force is determined by Newton's formula
   F=B*v^2,
   where B is a certain coefficient, for each body (depends on the shape, material, surface quality - smooth, rough), weather conditions(pressure and humidity), etc. It is applicable only at speeds up to 60-100 m / s - and then with big reservations (again, it depends on the conditions).
   More precisely, it can be determined by the formula
   F=Bn*v^n
   , where Bn is, in principle, the same coefficient B, but it depends on the speed, as does the exponent n (n = 2 (approximately) when the speed of the body in the atmosphere is less than M / 2 and and more than 2..3M, with these parameters Bn practically constant).
   Here M is the Mach number - if simply - equal to speed sound in the air - 315 m/s.
   Well, in general - the most effective method- experiment.

   It would be longer information - I would say more.

3. When an electric vehicle (car) moves at speeds exceeding the speed of a pedestrian, the force of air resistance has a noticeable effect. The following empirical formula is used to calculate the air resistance force:

   Fair = Cx*S*#961;*#957;2/2

   Fair air resistance force, N
   Cx air resistance coefficient (streamline coefficient), N*s2/(m*kg) . Cx is determined experimentally for each body.
   #961; air density (1.29kg/m3 at normal conditions)
   S frontal area of ​​an electric vehicle (car), m2. S is the projection area of ​​the body on a plane perpendicular to the longitudinal axis.
   #957; electric vehicle (car) speed, km/h

   To calculate the acceleration characteristics of an electric vehicle (car), the acceleration resistance force (inertia force) should be taken into account. Moreover, it is necessary to take into account not only the inertia of the electric vehicle itself, but also the influence of the moment of inertia of the rotating masses inside the electric vehicle (rotor, gearbox, cardan, wheels). The following is the formula for calculating the acceleration resistance force:

   Fin. = m*a*#963;vr

   Fin. acceleration resistance force, N
   m mass of the electric vehicle, kg
   a electric vehicle acceleration, m/s2
   #963;VR factor for rotating masses

   Approximately, the coefficient of accounting for rotating masses #963;vr can be calculated by the formula:

   #963;vr=1.05 + 0.05*u2kp

   Where ukp is the gear ratio of the gearbox

   It remains to describe the force of adhesion of the wheels to the road. However, this force is of little use in further calculations, so for now we will leave it for later.

   And now, we already have an idea about the main forces acting on an electric car (car). Knowing this theoretical question will soon lead us to study the next question of calculating the characteristics of an electric vehicle necessary for an informed choice of motor, battery and controller.