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Fundamentals of rotor aerodynamics. Helicopter lift force design coursework characteristic formula

The calculation of the screw can be conditionally divided into three successive stages.

The purpose of the first stage of the calculation is to determine the expected radius, thrust and efficiency of the propeller.

The initial data of the first stage are:

It is advisable to carry out the calculation using international system SI units.

If the screw speed is given in revolutions per minute, then using the formula

It must be converted to radians per second.

The calculated propeller speed V is selected depending on the purpose of the ALS and the value

Where K is the calculated maximum lift-to-drag ratio of an ultralight aircraft; m - takeoff weight.

When E
With values of E from 1000 to 1500, it is advisable to take the cruising flight speed V cr as the calculated propeller speed V o.

And for values of E more than 1500, the calculated speed can be taken as the speed calculated by the formula

When choosing V o, one should take into account the fact that, for a given engine power, a decrease in the calculated speed V leads to a decrease in the maximum flight speed, and its increase leads to a deterioration in the take-off characteristics of the aircraft.

Based on the condition of preventing transonic flows, the speed of the end of the blade u . should not exceed 230 ... 250 m / s and only in individual cases when it is not supposed to install a gearbox, and the screw cannot remove the full power of the engine, up to 260 m / s is allowed.

The initial value of the desired efficiency above 0.8 for high-speed and above 0.75 for low-speed ALS is inappropriate to choose, since in practice this is not feasible. The step of its decrease can initially be taken equal to 0.05 and then reduced as it approaches the actual value of the efficiency.

Based on the initial data, the following are sequentially determined:

If the required radius R turns out to be greater than the boundary R GR, then this means that the originally specified efficiency cannot be obtained. Need to decrease by the selected amount and repeat the cycle, starting with the definition of a new value? .

The cycle is repeated until the condition RR GR is fulfilled. If this condition is met, then a check is made whether the peripheral speed of the end of the blade u K does not exceed the permissible value u K.GR.

If u K u K.GR, then a new value is set by a value less than the previous one, and the cycle repeats.

After determining the values of the radius R, thrust P and propeller efficiency, you can proceed to the second stage of the calculation.

The second stage of the calculation of the propeller

The purpose of the second stage of the calculation is to determine the thrust, power consumption and geometric dimensions propeller.

The initial data for the second stage of the calculation are:

For calculations, the propeller blade (Fig. 6. 7)

Figure 6.7 Force effect of the flow on the elements of the propeller blade

It is divided into a finite number of sections with dimensions bR.. It is assumed that in each selected section there is no blade twist, and the velocities and angles of the flow along the radius do not change. With a decrease in R, that is, with an increase in the number of sections under consideration, the error caused by the accepted assumption decreases. Practice shows that if for each section we take the speeds and angles inherent in its central section, then the error becomes insignificant when the blade is divided into 10 sections with R = 0.1r. In this case, we can assume that the first three sections counted from the propeller axis thrust is not given, while consuming 4 ... 5% of engine power. Thus, it is advisable to carry out the calculation for seven sections from =0.3 to =1.0.

Additionally set:

Initially, it is advisable to set the maximum relative blade width for wooden propellers to be 0.08.

The law of change in the width of the blade and the relative thickness can be set in the form of a formula, table or drawing of the propeller (Fig. 6. 1).

Figure 6.1 Fixed Pitch Propeller

The angles of attack of the selected sections are set by the designer, taking into account the inverse lift-to-drag ratio. The values of the coefficients Su and K=1/ are taken from the graphs in fig. 6.4 and 6.5, taking into account the selected profile and the values of and .

Fig. 6.4 Dependence of lift force coefficient and inverse lift-to-drag ratio on angle of attack and relative thickness for airfoil VS-2

Figure 6.5 Dependence of the lift coefficient and inverse lift-to-drag ratio on the angle of attack and relative thickness for the RAF-6 airfoil

The first step of the second stage of the calculation is to determine the flow velocity V in the plane of the propeller. This speed is determined by the formula

Obtained from the joint solution of the equations of thrust and air flow passing through the area swept by the propeller.

Estimated values of thrust P, radius R and area S ohm are taken from the first stage of the calculation.

If as a result of the calculation it turns out that the power consumed by the screw differs from the available power by no more than 5 ... 10%, then the second stage of the calculation can be considered completed.

If the power consumed by the propeller differs from the available power by 10 ... 20%, then it is necessary to increase or decrease the width of the blade, given that the power consumption and thrust of the propeller change approximately in proportion to the chord of the blade. The diameter, relative thicknesses and installation angles of the sections remain unchanged.

In some cases, it may turn out that the power consumed by the propeller and its thrust differ by more than 20% from those expected from the results of the first stage of the calculation. In this case, according to the ratio of consumed and available capacities

Using the graph (Fig. 6. 10), the values of the coefficients k R and k P are determined. These coefficients show how many times it is necessary to change the estimated radius and thrust of the propeller, which are the initial ones for the second stage of the calculation. After that, the second stage of the calculation is repeated.

Figure 6.10 Dependence of correction factors on the ratio of consumed and available capacities

At the end of the second stage of the calculation, the geometric dimensions of the screw required for manufacturing (R, r, b, c and ) in units convenient for its manufacture are summarized in a table.

The third stage of the calculation of the propeller

The purpose of the third stage is to test the propeller for strength. This stage of the calculation is reduced to determining the loads acting in various sections of the blades and comparing them with the permissible ones, taking into account the geometry and material from which the blades are made.

To determine the loads, the blade is divided into separate elements, as in the second stage of the calculation, starting from the section =0.3 with a step of 0.1 to =1.

Each selected element of the blade with a mass m at a radius r (Fig. 6. 11) is subject to an inertial force

Figure 6.11 Force effect of aerodynamic forces on the propeller blade element

And the elementary aerodynamic force F. Under the influence of these forces, from all elementary sections, the blade stretches and bends. As a result, tensile-compressive stresses arise in the material of the blade. The most loaded (Fig. 6. 12)

Figure 6.12 Stress distribution in the section of the propeller blade

The fibers of the rear side of the blade turn out to be, since in these fibers the stresses from inertial forces and the bending moment add up. To ensure a given strength, it is necessary that the actual stresses in these areas, which are the most distant from the axis of the blade section, be less than those allowed for the selected material.

The values of the radii r required for calculations, on which the sections of the blade under consideration, chords b, relative thicknesses and forces F are located, are taken from the tables of the second stage of the calculation. Then for each section are sequentially determined:

The fill factor k 3 depends on the profile used for the screw. For the most common screw profiles, it is: Clark-Y-k 3 =0.73; BC-2-k 3 =0.7 and RAF-6-k 3 = 0.74.

After calculating the values of P in on each individual section, they are summed from the free end of the blade to the considered section. By dividing the total force acting in each section under consideration by the area of this section, one can obtain tensile stresses from inertial forces.

Blade bending stresses under the influence of aerodynamic forces F are determined as for a cantilever beam with an unevenly distributed load.

As noted earlier, the maximum stresses will be in the back fibers of the blade and are defined as the sum of stresses from inertial and aerodynamic forces. The magnitude of these stresses should not exceed 60 ... 70% of the tensile strength of the blade material.

If the strength of the blade is ensured, then the calculation of the propeller can be considered complete.

If the strength of the blade is not ensured, then it is necessary either to choose another, more durable material, or, by increasing the relative width of the blade, repeat all three stages of the calculation.

If the relative width of the blade exceeds 0.075 for propellers made of hard wood and 0.09 for propellers made of soft wood, then there is no need to perform the third stage of the calculation, since the necessary strength will certainly be provided.

based on materials: P.I. Chumak, V.F Krivokrysenko "Calculation and design of ALS"

Introduction

Helicopter design is a complex process that develops over time, divided into interrelated design stages and stages. The created aircraft must meet technical requirements and comply with the technical and economic characteristics specified in the terms of reference for the design. The terms of reference contain the initial description of the helicopter and its performance characteristics, providing high economic efficiency and competitiveness of the designed machine, namely: carrying capacity, flight speed, range, static and dynamic ceiling, resource, durability and cost.

The terms of reference are specified at the stage of pre-project research, during which a patent search, analysis of existing technical solutions, research and development work are carried out. The main task of pre-design research is the search and experimental verification of new principles of functioning of the designed object and its elements.

At the stage of preliminary design, an aerodynamic scheme is selected, the appearance of the helicopter is formed, and the calculation of the main parameters is performed to ensure the achievement of the specified flight performance. These parameters include: helicopter mass, power propulsion system, dimensions of the main and tail rotors, mass of fuel, mass of instrumentation and special equipment. The calculation results are used in the development layout diagram helicopter and compiling a balance sheet to determine the position of the center of mass.

The design of individual units and components of the helicopter, taking into account the selected technical solutions, is carried out at the stage of developing a technical project. At the same time, the parameters of the designed units must satisfy the values corresponding to the draft design. Some of the parameters can be refined in order to optimize the design. During technical design, aerodynamic strength and kinematic calculations of units are performed, as well as the choice of structural materials and structural schemes.

At the stage of the detailed design, the execution of working and assembly drawings of the helicopter, specifications, picking lists and other technical documentation in accordance with accepted standards

This paper presents a methodology for calculating the parameters of a helicopter at the stage of preliminary design, which is used to complete a course project in the discipline "Helicopter Design".

1. Calculation of the takeoff weight of a helicopter of the first approximation

- payload mass, kg; - mass of the crew, kg. -range of flight

kg.

2. Calculation of parameters rotor helicopter

2.1Radius R, m, the main rotor of a single-rotor helicopter is calculated by the formula:

, - helicopter takeoff weight, kg;

g- free fall acceleration equal to 9.81 m/s 2 ;

p- specific load on the area swept by the main rotor,

p =3,14.

Specific load value p for the area swept by the screw is selected according to the recommendations presented in the work /1/: where p = 280

We accept the radius of the main rotor equal to R = 7.9

Angular velocity w, s -1 , rotation of the main rotor is limited by the circumferential speed w R the ends of the blades, which depends on the takeoff weight

helicopter and made w R = 232 m/s.

with -1 .

rpm

2.2 Relative air densities on static and dynamic ceilings

2.3 Calculation of the economic speed near the ground and on the dynamic ceiling

The relative area is determined

equivalent harmful plate: , where S uh = 2.5

The value of the economic speed near the ground is calculated V h, km/h:

where I

km/h.

The value of the economic speed on the dynamic ceiling is calculated V din, km/h:

where I\u003d 1.09 ... 1.10 - induction coefficient.

km/h.

2.4 The relative values of the maximum and economic speeds of horizontal flight on the dynamic ceiling are calculated:

where Vmax=250 km/h and V din\u003d 182.298 km / h - flight speed;

w R=232 m/s - peripheral speed of the blades.

2.5 Calculation of the permissible ratios of the thrust coefficient to the filling of the main rotor for the maximum speed near the ground and for the economic speed on the dynamic ceiling:

pripri

2.6 Main rotor thrust coefficients near the ground and at the dynamic ceiling:

2.7 Calculation of the filling of the main rotor:

Rotor filling s calculated for cases of flight at maximum and economic speeds:

;

As an estimated filling value s rotor, the largest value is taken from s Vmax and s V din .

Introduction

Helicopter design is a complex process that develops over time, divided into interrelated design stages and stages. The created aircraft must meet the technical requirements and comply with the technical and economic characteristics specified in the design specification. The terms of reference contain the initial description of the helicopter and its performance characteristics, which ensure high economic efficiency and competitiveness of the designed machine, namely: carrying capacity, flight speed, range, static and dynamic ceiling, resource, durability and cost.

At the stage of preliminary design, an aerodynamic scheme is selected, the appearance of the helicopter is formed, and the calculation of the main parameters is performed to ensure the achievement of the specified flight performance. These parameters include: the mass of the helicopter, the power of the propulsion system, the dimensions of the main and tail rotors, the mass of fuel, the mass of instrumentation and special equipment. The results of the calculations are used in the development of the layout scheme of the helicopter and the preparation of the balance sheet to determine the position of the center of mass.

At the detailed design stage, working and assembly drawings of the helicopter, specifications, packing lists and other technical documentation are prepared in accordance with accepted standards

This paper presents a methodology for calculating the parameters of a helicopter at the stage of preliminary design, which is used to complete a course project in the discipline "Helicopter Design".

1. Calculation of the takeoff weight of a helicopter of the first approximation

where is the payload mass, kg;

Crew weight, kg.

Range of flight

kg.

2. Calculation of the parameters of the main rotor of a helicopter

2.1 Radius R, m, single-rotor helicopter main rotorcalculated by the formula:

where is the takeoff weight of the helicopter, kg;

g- free fall acceleration equal to 9.81 m/s 2 ;

p - specific load on the area swept by the main rotor,

 =3,14.

Specific load valuepfor the area swept by the screw is selected according to the recommendations presented in the work /1/: wherep= 280

We accept the radius of the main rotor equal toR= 7.9

Angular velocity , With -1 , rotation of the main rotor is limited by the peripheral speed Rthe ends of the blades, which depends on the takeoff weight of the helicopter and amounted to R= 232 m/s.

With -1 .

rpm

2.2 Relative air densities on static and dynamic ceilings

2.3 Calculation of the economic speed near the ground and on the dynamic ceiling

The relative area of the equivalent harmful plate is determined:

WhereS uh = 2.5

The value of the economic speed near the ground is calculated V h , km/h:

whereI = 1,09…1,10 - coefficient of induction.

km/h.

The value of the economic speed on the dynamic ceiling is calculated V din , km/h:

whereI = 1,09…1,10 - coefficient of induction.

km/h.

2.4 The relative values of the maximum and economic on the dynamic ceiling are calculated horizontal flight speeds:

whereV max =250 km/h andV din \u003d 182.298 km / h - flight speed;

 R=232 m/s - peripheral speed of the blades.

2.5 Calculation of the permissible ratios of the thrust coefficient to the filling of the main rotor for the maximum speed near the ground and for the economic speed on the dynamic ceiling:

2.6 Main rotor thrust coefficients near the ground and at the dynamic ceiling:

2.7 Calculation of the filling of the main rotor:

Rotor filling  calculated for cases of flight at maximum and economic speeds:

;

As an estimated filling value  rotor, the largest value is taken from  Vmax and  V din :

Accept

chord length b and elongation  rotor blades will be equal to:

, where z l - number of rotor blades ( z l =3)

2.8 Relative increase in main rotor thrustto compensate for the aerodynamic drag of the fuselage and horizontal tail:

where S f - area of the horizontal projection of the fuselage;

S th - the area of the horizontal plumage.

S f =10 m 2 ;

S th =1.5 m 2 .

3. Calculation of the power of the helicopter propulsion system.

3.1 Calculation of power when hovering on a static ceiling:

Specific power required to drive the main rotor in hover mode on a statistical ceiling is calculated by the formula:

where N H st - required power, W;

m 0 - takeoff weight, kg;

g - free fall acceleration, m/s 2 ;

p - specific load on the area swept by the main rotor, N/m 2 ;

 st - relative air density at the height of the static ceiling;

 0 - relative efficiency main rotor in hover mode (  0 =0.75);

The relative increase in main rotor thrust to balance the aerodynamic drag of the fuselage and horizontal tail:

3.2 Calculation of specific power in level flight at maximum speed

Specific power required to drive the main rotor in level flight at maximum speed is calculated by the formula:

where is the peripheral speed of the ends of the blades;

- relative equivalent harmful plate;

I uh - induction coefficient, determined depending on the flight speed according to the following formulas:

, at km/h,

, at km/h.

3.3 Calculation of specific power in flight at a dynamic ceiling with economic speed

The specific power to drive the main rotor on a dynamic ceiling is:

where  din - relative air density on the dynamic ceiling,

V din - economic speed of the helicopter on the dynamic ceiling,

3.4 Calculation of specific power in flight near the ground at economic speed in the event of one engine failure during takeoff

Specific power required to continue takeoff at economic speed in case of failure of one engine is calculated by the formula:

where is the economic speed near the ground,

3.5 Calculation of specific reduced powers for various flight cases

3.5.1 The specific reduced power when hovering on a static ceiling is:

where is the specific throttle characteristic, which depends on the height of the static ceiling H st and is calculated by the formula:

 0 - power utilization factor of the propulsion system in the hover mode, the value of which depends on the takeoff weight of the helicopterm 0 :

at m 0 < 10 тонн

at 10 25 tons

at m 0 > 25 tons

3.5.2 The specific reduced power in level flight at maximum speed is:

where - power utilization factor at maximum flight speed,

- Throttle characteristics of engines, depending on the flight speed V max :

;

3.5.3 Specific reduced power in flight at dynamic ceiling with economic speed V din is equal to:

and - engine throttling levels depending on the height of the dynamic ceiling H and flight speed V din according to the following throttle characteristics:

;

3.5.4 The specific reduced power in flight near the ground with an economic speed in case of failure of one engine on takeoff is equal to:

where is the power utilization factor at the economic flight speed,

- the degree of engine throttling in emergency mode,

n = 2 - the number of helicopter engines.

3.5.5 Calculation of the required power of the propulsion system

To calculate the required power of the propulsion system, the maximum value of the specific reduced power is selected:

Required power N helicopter propulsion system will be equal to:

where m 01 - helicopter takeoff weight,

g = 9.81 m 2 /s - free fall acceleration.

3.6 Choice of engines

Accept two turboshaft enginesVK-2500(TV3-117VMA-SB3) total power of each N =1,405∙10 6 Tue

EngineVK-2500(TV3-117VMA-SB3) designed for installation on new generation helicopters, as well as for replacing engines on existing helicopters to improve their flight performance. It was created on the basis of a serial certified engine TV3-117VMA and is produced at the Federal State Unitary Enterprise “Plant named after V.Ya. Klimov".

4. Calculation of the mass of fuel

To calculate the mass of fuel that provides a given flight range, it is necessary to determine the cruising speedV kr . The calculation of cruising speed is carried out by the method of successive approximations in the following sequence:

a) the value of the cruising speed of the first approximation is taken:

km/h;

b) the induction coefficient is calculated I uh :

at km/h

c) the specific power required to drive the main rotor in flight in cruising mode is determined:

where is the maximum value of the specific reduced power of the propulsion system,

- coefficient of power change depending on flight speed V kr 1 , calculated by the formula:

d) The cruising speed of the second approximation is calculated:

e) The relative deviation of the speeds of the first and second approximation is determined:

When the cruising speed of the first approximation is refined V kr 1 , it is taken equal to the calculated speed of the second approximation . Then the calculation is repeated from point b) and ends under the condition .

Specific fuel consumption is calculated by the formula:

where is the coefficient of change in the specific fuel consumption depending on the mode of operation of the engines,

- coefficient of change in specific fuel consumption depending on flight speed,

- specific fuel consumption in takeoff mode.

In the case of flight in cruise mode, the following is accepted:

;

at kW;

at kW.

kg/Wh,

The mass of fuel spent on the flight m T will be equal to:

where is the specific power consumed at cruising speed,

- cruising speed,

L - range of flight.

kg.

5. Determination of the mass of components and assemblies of the helicopter.

5.1 The mass of the main rotor blades is determined by the formula:

where R - rotor radius,

 - filling of the main rotor,

kg,

5.2 The mass of the main rotor hub is calculated by the formula:

where k Tue - weight coefficient of bushings of modern designs,

k l - coefficient of influence of the number of blades on the bushing mass.

You can take into account:

kg/kN,

therefore, as a result of the transformations, we get:

To determine the mass of the main rotor hub, it is necessary to calculate the centrifugal force acting on the bladesN CB (in kN):

kN,

kg.

5.3 Mass of the booster control system, which includes the swashplate, hydraulic boosters, the main rotor hydraulic control system is calculated by the formula:

where b - blade chord,

k boo - weight coefficient of the booster control system, which can be taken equal to 13.2 kg/m 3 .

kg.

5.4 Weight of the manual control system:

where k RU - weight coefficient of the manual control system, taken for single-rotor helicopters equal to 25 kg/m.

kg.

5.5 The mass of the main gearbox depends on the torque on the main rotor shaft and is calculated by the formula:

where k ed - weighting factor, the average value of which is 0.0748 kg / (Nm) 0,8 .

The maximum torque on the main rotor shaft is determined through the reduced power of the propulsion systemN and screw speed  :

where  0 - power utilization factor of the propulsion system, the value of which is taken depending on the takeoff weight of the helicopterm 0 :

at m 0 < 10 тонн

at 10 25 tons

at m 0 > 25 tons

N∙m,

Mass of the main gearbox:

kg.

5.6 To determine the mass of the tail rotor drive units, its thrust is calculated T rv :

where M nv - torque on the rotor shaft,

L rv - the distance between the axes of the main and tail screws.

The distance between the axes of the main and tail screws is equal to the sum of their radii and clearance  between the ends of their blades:

where  - gap taken equal to 0.15 ... 0.2 m,

is the radius of the tail rotor, which, depending on the takeoff weight of the helicopter, is:

at t,

at t.

Power N rv , spent on the rotation of the tail rotor, is calculated by the formula:

where  0 - relative efficiency of the tail rotor, which can be taken equal to 0.6 ... 0.65.

Torque M rv transmitted by the steering shaft is equal to:

N∙m,

where is the frequency of rotation of the steering shaft,

With -1 ,

Torque transmitted by the transmission shaft, N∙m, at a speed of rotation n v = 3000 rpm equals:

N∙m,

Weight m v transmission shaft:

where k v - weighting factor for the transmission shaft, which is equal to 0.0318 kg / (Nm) 0,67 . kg

The value of centrifugal force N cbr acting on the tail rotor blades and perceived by the hub hinges,

Tail rotor hub weight m tuesday calculated using the same formula as for the main rotor:

where N CB - centrifugal force acting on the blade,

k Tue - weight factor for the bushing, taken equal to 0.0527 kg/kN 1,35

k z - weighting factor depending on the number of blades and calculated by the formula: kg,

The mass of the electrical equipment of the helicopter is calculated by the formula:

where L rv - the distance between the axes of the main and tail screws,

z l - the number of rotor blades,

R - rotor radius,

 l - relative elongation of the main rotor blades,

k etc and k email - weight coefficients for electrical wires and other electrical equipment, the values of which are equal to:

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Calculate the thrust of the main rotor. If we consider the surface (area F), swept by the screw during its rotation, as an impenetrable plane, then we will see that pressure pi acts on this plane from above, and pressure p2 from below, and p-2 is greater than px.

It is known from the second law of mechanics that a mass receives acceleration only when some force acts on it. Moreover, this force is equal to the product of mass and acceleration and is directed in the direction of acceleration (in our case, down).

What is this power? On the one hand, it is obvious that this force is the result of the action of the screw on the air. On the other hand, is it? force according to the third law of mechanics must correspond to the equal in magnitude and opposite in direction of the effect of air on the screw. The latter is nothing but the thrust force of the propeller.

However, if we look at a dynamometer that measures the actual propeller thrust, we find that our calculation is somewhat inaccurate. In reality, the thrust will be less, since we considered the operation of the propeller to be ideal and did not take into account the energy losses due to friction and swirling of the air stream behind the propeller.

In fact, air particles approach the screw having not only an inductive speed in the axial direction, perpendicular to the plane of rotation, but also a twisting speed. Therefore, when calculating the inductive suction and ejection velocities u2, the swirl of air during rotation of the main rotor is also taken into account.

In the thrust formula, the lift coefficient su is similar to the thrust coefficient; the flight speed corresponds to the circumferential speed of the ends of the propeller blades, having a radius r and angular velocity, the wing area 5 corresponds to the area of the disk swept by the propeller, lg2. The coefficient is determined from the blowdown curve of a given propeller at various angles of attack.

The value of the dimensionless thrust coefficient for a specific, already created propeller operating in a given mode can be calculated by dividing the propeller thrust T, expressed in kilograms, by the product of other propeller parameters, which also has the dimension of thrust force kg.

We have established that if the lift force of an aircraft is created by throwing air down the wing, then the lift force of a helicopter is created by throwing air down the main rotor.

When the helicopter has forward speed, then, naturally, the volume of air thrown down increases.

Because of this, with the expenditure of the same power, the main rotor of a helicopter with translational speed develops more thrust than the rotor of a hanging helicopter.

And, vice versa, to create the same thrust, less power must be transferred to the propeller of a helicopter having forward speed than to the propeller of a hanging helicopter.

The decrease in the required power with an increase in speed occurs only up to a certain speed value, at which an increase in air resistance to the movement of the helicopter not only absorbs the gain in power, but even requires the latter to be increased.

lifting force and thrust for the translational movement of the helicopter are created using the main rotor. In this it differs from an airplane and a glider, in which the lifting force when moving in the air is created by the bearing surface - the wing, rigidly connected to the fuselage, and the thrust - by a propeller or jet engine(Fig. 6).

In principle, the flight of an airplane and a helicopter can be compared. In both cases, the lifting force is created due to the interaction of two bodies: air and an aircraft (airplane or helicopter).

According to the law of equality of action and reaction, it follows that with what force the aircraft acts on the air (weight or gravity), with the same force the air acts on the aircraft (lift force).

During the flight of an aircraft, the following phenomenon occurs: an oncoming oncoming air flow flows around the wing and bevels down behind the wing. But air is an inseparable, rather viscous medium, and not only the air layer located in the immediate vicinity of the wing surface, but also its neighboring layers participate in this mowing. Thus, when flowing around a wing, a rather significant volume of air is beveled backwards every second, approximately equal to the volume of a cylinder, in which the cross section is a circle with a diameter equal to the wingspan, and the length is the flight speed per second. This is nothing more than a second flow of air involved in creating the lift force of the wing (Fig. 7).

Rice. 7. The volume of air involved in creating the lift force of the aircraft

It is known from theoretical mechanics that the change in momentum per unit time is equal to the acting force:

where R - acting force;

as a result of interaction with the wing of the aircraft. Consequently, the lift force of the wing will be equal to the second increase in the momentum along the vertical in the outgoing jet.

and -vertical slant velocity behind the wing in m/sec. In the same way, the total aerodynamic force of a helicopter's main rotor can be expressed in terms of the air flow per second and the slant velocity (the induced velocity of the outgoing air stream).

The rotating main rotor sweeps away the surface, which can be imagined as a carrier, similar to the wing of an aircraft (Fig. 8). Air flowing through the surface swept by the main rotor, as a result of interaction with the rotating blades, is thrown down with inductive speed and. In the case of horizontal or inclined flight, air flows to the surface swept by the main rotor at a certain angle (oblique blowing). Like an aircraft, the volume of air involved in the creation of the total aerodynamic force of the main rotor can be represented as a cylinder, in which the base area is equal to the surface area swept away by the main rotor, and the length is equal to the flight speed, expressed in m/sec.

When the main rotor is in place or in vertical flight (direct blowing), the direction of the air flow coincides with the axis of the main rotor. In this case, the air cylinder will be located vertically (Fig. 8, b). The total aerodynamic force of the main rotor is expressed as the product of the mass of air flowing through the surface swept away by the main rotor in one second by the inductive speed of the outgoing jet:

inductive velocity of the outgoing jet in m/sec. It is necessary to make a reservation that in the considered cases both for the aircraft wing and for the main rotor of the helicopter for the induced speed and the inductive velocity of the outgoing jet is taken at some distance from the carrier surface. The inductive speed of the air jet that occurs on the bearing surface itself is twice as small.

Such an interpretation of the origin of the lift force of the wing or the total aerodynamic force of the main rotor is not completely accurate and is valid only in the ideal case. It only fundamentally correct and clearly explains the physical meaning of the phenomenon. Here it is appropriate to note one very important circumstance that follows from the analyzed example.

If the total aerodynamic force of the main rotor is expressed as the product of the mass of air flowing through the surface swept by the main rotor and the inductive speed, and the volume of this mass is a cylinder whose base is the surface area swept by the main rotor, and the length is the flight speed, then absolutely it is clear that in order to create thrust of a constant value (for example, equal to the weight of a helicopter) at a higher flight speed, and hence with a larger volume of ejected air, a lower inductive speed and, consequently, lower engine power are required.

On the contrary, to keep the helicopter in the air while “hovering” in place, more power is required than during the flight at a certain forward speed, at which there is a counter flow of air due to the movement of the helicopter.

In other words, with the expenditure of the same power (for example, the rated power of the engine), in the case of an inclined flight at a sufficiently high speed, a greater ceiling can be achieved than with a vertical climb, when the total speed of movement

there are fewer helicopters than in the first case. Therefore, the helicopter has two ceilings: static when climbing in vertical flight, and dynamic, when the altitude is gained in inclined flight, and the dynamic ceiling is always higher than the static one.

There is much in common between the operation of the main rotor of a helicopter and the propeller of an aircraft, but there are also fundamental differences, which will be discussed later.

Comparing their work, it can be seen that the total aerodynamic force, and hence the thrust of the main rotor of the helicopter, which is a component of the force

Rin the direction of the hub axis, always more (5-8 times) for the same engine power and the same weight aircraft due to the fact that the diameter of the main rotor of the helicopter is several times larger than the diameter of the aircraft propeller. In this case, the air ejection speed of the main rotor is less than the ejection speed of the propeller.

The amount of thrust of the main rotor depends to a very large extent on its diameter.

Dand number of revolutions. If the diameter of the propeller is doubled, its thrust will increase by approximately 16 times; if the number of revolutions is doubled, the thrust will increase by approximately 4 times. In addition, the main rotor thrust also depends on the air density ρ, the blade angle φ (main rotor pitch),geometric and aerodynamic characteristics of a given propeller, as well as on the flight mode. The influence of the last four factors is usually expressed in the propeller thrust formulas through the thrust coefficient a t . .

Thus, the thrust of the main rotor of the helicopter will be proportional to:

- thrust coefficient............. a r
It should be noted that the thrust value during flights near the ground is influenced by the so-called “air cushion”, due to which the helicopter can take off the ground and rise several meters at a power consumption less than that required for “hovering” at a height of 10- 15 m. Availability " air cushion”is explained by the fact that the air thrown by the propeller hits the ground and is somewhat compressed, i.e., increases its density. The effect of the “air cushion” is especially strong when the propeller is operating near the ground. Due to air compression, the thrust of the main rotor in this case, with the same power consumption, increases by 30-
40%. However, with distance from the ground, this influence quickly decreases, and at a flight altitude equal to half the diameter of the propeller, the “air cushion” increases thrust by only 15- 20%. The height of the “air cushion” is approximately equal to the diameter of the main rotor. Further, the increase in traction disappears.
For a rough calculation of the thrust of the main rotor in the hover mode, the following formula is used:
coefficient characterizing the aerodynamic quality of the main rotor and the influence of the “air cushion”. Depending on the characteristics of the main rotor, the value of the coefficient a when hovering near the ground, it can have values of 15 - 25.

The main rotor of a helicopter has an extremely important property - the ability to create lift in the mode of self-rotation (autorotation) in the event of an engine stop, which allows the helicopter to perform a safe gliding or parachuting descent and landing.

A rotating main rotor maintains the required number of revolutions when planning or parachuting, if its blades are moved to a small installation angle

(l--5 0) 1 . At the same time, the lifting force is preserved, which ensures the descent with a constant vertical speed (6-10 m/s), s its subsequent decrease during alignment before landing to l--1.5 m/sec.

There is a significant difference in the operation of the main rotor in the case of a motor flight, when the power from the engine is transferred to the propeller, and in the case of flight in the self-rotation mode, when it receives energy to rotate the propeller from the oncoming air stream, there is a significant difference.

In a motor flight, oncoming air runs into the main rotor from above or from above at an angle. When the screw is operating in the self-rotation mode, air runs into the plane of rotation from below or at an angle from below (Fig. 9). The flow bevel behind the rotor in both cases will be directed downward, since the induced velocity, according to the momentum theorem, will be directed directly opposite to the thrust, i.e., approximately down along the axis of the rotor.

Here we are talking about the effective installation angle, in contrast to the constructive one.

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