How to determine the work of the force of air resistance. Drag (aerodynamics)

1. The movement of the vehicle is associated with the movement of air particles, which consumes part of the engine power. These costs are made up of the following:

2. Frontal resistance, which appears due to the difference in pressure in front and behind a moving car (55-60% of air resistance).

3. Resistance created by projecting parts - rear view mirror, etc. (12-18%).

4. Resistance arising from the passage of air through the radiator and engine compartment.

5. Resistance due to friction of nearby surfaces on air layers (up to 10%).

6. Resistance caused by the pressure difference between the top and bottom of the car (5-8%).

To simplify the calculations of air resistance, we replace the resistance distributed over the entire surface of the car with the force of air resistance applied at one point, called sail center car.

It has been established by experience that the force of air resistance depends on the following factors:

On the speed of the car, and this dependence is quadratic;

From the frontal area of the car F;

From the coefficient of streamlining K in, which is numerically equal to the force of air resistance created by one square meter frontal area of the vehicle when moving it at a speed of 1 m/s.

Then the air resistance force .

When determining F use empirical formulas that determine the approximate area of resistance. For trucks F usually: F=H×B(the product of height and width), similarly for buses. Accepted for cars F=0.8H×B. There are other formulas that take into account the track of the car, the probability of changing the height of the vehicle, etc. K in ×F called streamlining factor and denote W.

To determine the streamlining coefficient, special devices are used or the coastdown method, which consists in determining the change in the path of a free-rolling car when moving with different initial speed. When driving a car in air flow air resistance force R in can be decomposed into components along the axes of the ATS. At the same time, the formulas for determining the projections of forces differ only in coefficients that take into account the distribution of force along the axes. The streamlining coefficient can be determined from the expression:

where C X is a coefficient determined empirically and taking into account the distribution of the air resistance force along the "x" axis. This coefficient is obtained by blowing in a wind tunnel, ;

r - air density, according to GOST r \u003d 1.225 kg / m 3 at zero.

We get .

The product is a velocity head equal to kinetic energy cubic meter of air moving at the speed of the car relative to the air.

Coefficient K in has dimension .

Between K in and C X there is a dependency: K in \u003d 0.61С X.

The trailer on the vehicle increases the drag force by an average of 25%.

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

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.
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.
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.

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

where With X - size free airflow coefficient, depending on the shape of the body; ρ in - air density ρ in \u003d 1.202 ... 1.225 kg / m 3; BUT- midsection area (transverse projection area) of the car, m 2; V– vehicle speed, m/s.

Found in the literature air resistance coefficient k in :

F in = k in BUTV 2 , where k in = with X ρ in /2 , - air resistance coefficient, Ns 2 /m 4.

…and streamlining factorq in : q in = k in · BUT.

If instead With X substitute With z, then we get the aerodynamic lift force.

Midsection area for cars:

A=0.9 B max · H,

where AT max - the largest track of the car, m; H– vehicle height, m.

The force is applied at the metacenter, creating moments.

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

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

FROM X some cars

VAZ 2101…07			Opel Astra Sedan
VAZ 2108…15


			Land Rover Free Lander
VAZ 2102…04
VAZ 2121…214
			truck
			trailer truck

Lift resistance force

F P = G a sin α.

In road practice, the magnitude of the slope is usually estimated by the magnitude of the rise of the roadbed, related to the magnitude of the horizontal projection of the road, i.e. the tangent of the angle, and denote i, expressing the resulting value as a percentage. With a relatively small slope, it is permissible to use not sinα., and the value i in relative terms. For large values of the slope, the replacement sinα by the value of the tangent ( i/100) is not allowed.

Overclocking resistance force

When the car accelerates, the progressively moving mass of the car accelerates and the rotating masses accelerate, increasing the resistance to acceleration. This increase can be taken into account in the calculations, if we assume that the masses of the car move forward, but use some equivalent mass m uh, a little bigger m a (in classical mechanics this is expressed by the Koenig equation)

We use the method of N.E. Zhukovsky, equating the kinetic energy of a translationally moving equivalent mass to the sum of energies:

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

Since ω to = V a / r k , ω d = V a · i kp · i o / r k , r k = r k 0 ,

then we get
.

Moment of inertiaJcar transmission units, kg m 2

Automobile	Flywheel with crankshaft J d	driven wheels (2 wheels with brake drums), J k1	Drive wheels (2 wheels with brake drums and axle shafts) J k2

Let's replace: m uh = m a · δ,

If the vehicle is not fully loaded:
.

If the car is coasting: δ = 1 + δ 2

Vehicle acceleration resistance force (inertia): F and = m uh · a a = δ · m a · a a .

As a first approximation, we can take: δ = 1,04+0,04 i kp 2

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 of the flow during braking 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 force of air resistance is 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 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.

Instruction

Find the force of resistance to motion, which acts on a uniformly rectilinear moving body. To do this, using a dynamometer or in another way, measure the force that must be applied to the body so that it moves evenly and in a straight line. According to Newton's third law, it will be numerically equal to the force of resistance to the movement of the body.

Determine the force of resistance to the movement of a body that moves along a horizontal surface. In this case, the friction force is directly proportional to the reaction force of the support, which, in turn, is equal to the force of gravity acting on the body. Therefore, the force of resistance to movement in this case or the friction force Ftr is equal to the product of the body mass m, which is measured by weights in kilograms, and the acceleration free fall g≈9.8 m/s² and proportionality factor μ, Ftr=μ∙m∙g. The number μ is called the coefficient of friction and depends on the surfaces that come into contact during movement. For example, for the friction of steel on wood, this coefficient is 0.5.

Calculate the force of resistance to the movement of a body moving along. In addition to the coefficient of friction μ, body mass m and free fall acceleration g, it depends on the angle of inclination of the plane to the horizon α. To find the force of resistance to movement in this case, you need to find the product of the coefficient of friction, body mass, free fall acceleration and the cosine of the angle at which the plane to the horizon is Ftr=μ∙m∙g∙сos(α).

When a body moves in the air at low speeds, the force of resistance to movement Fс is directly proportional to the speed of the body v, Fc=α∙v. The coefficient α depends on the properties of the body and the viscosity of the medium and is calculated separately. When moving at high speeds, for example, when a body falls from a considerable height or a car moves, the resistance force is directly proportional to the square of the speed Fc=β∙v². Coefficient β is additionally calculated for high speeds.

Sources:

1 General formula for air resistance force In the figure

For determining strength resistance air create conditions under which the body will begin to move uniformly and rectilinearly under the influence of gravity. Calculate the value of gravity, it will be equal to the force of air resistance. If a body moves in the air, picking up speed, its resistance force is found using Newton's laws, and the air resistance force can also be found from the law of conservation of mechanical energy and special aerodynamic formulas.

You will need

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

Instruction

Before measurement resistance used resistor, be sure to unsolder it from the old board or block. Otherwise, it may be shunted by other parts of the circuit, and you will get incorrect readings from it. resistance.

How to determine the work of the force of air resistance. Drag (aerodynamics)

Lift resistance force

Overclocking resistance force