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".

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

where is the payload mass, kg;

Crew weight, kg.

Range of flight

Calculation of the parameters of the main rotor of a helicopter

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

where is the takeoff weight of the helicopter, kg;

g - free fall acceleration equal to 9.81 m/s2;

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

The value of the specific load p on the area swept by the propeller is selected according to the recommendations presented in the work /1/: where p=280

We take the rotor radius equal to R=7.9

The angular velocity, s-1, of rotation of the main rotor is limited by the circumferential velocity R of the ends of the blades, which depends on the take-off mass of the helicopter and amounted to R=232 m/s.

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:

Where Se=2.5

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

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

where I \u003d 1.09 ... 1.10 is the induction coefficient.

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 Vdyn=182.298 km/h - flight speed;

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

A helicopter is a rotary-wing machine in which the propeller creates lift and thrust. The main rotor is used to maintain and move the helicopter in the air. When rotating in a horizontal plane, the main rotor creates thrust (T) directed upwards, acts as a lifting force (Y). When the main rotor thrust is greater than the weight of the helicopter (G), the helicopter will lift off the ground without a takeoff run and begin a vertical climb. If the weight of the helicopter and the thrust of the main rotor are equal, the helicopter will hang motionless in the air. For vertical descent, it is enough to make the main rotor thrust somewhat less than the weight of the helicopter. The translational motion of the helicopter (P) is provided by tilting the plane of rotation of the main rotor using the rotor control system. The inclination of the plane of rotation of the propeller causes a corresponding inclination of the total aerodynamic force, while its vertical component will keep the helicopter in the air, and the horizontal component will cause the helicopter to translate in the corresponding direction.

Fig 1. Scheme of the distribution of forces

Helicopter design

The fuselage is the main part of the helicopter structure, which serves to connect all its parts into one whole, as well as to accommodate the crew, passengers, cargo, and equipment. It has a tail and end boom to accommodate the tail rotor outside the rotation zone. rotor, and wing (on some helicopters, the wing is installed in order to increase the maximum flight speed due to the partial unloading of the main rotor (MI-24)). Power plant (engines)is a source of mechanical energy for driving the main and tail propellers into rotation. It includes engines and systems that ensure their operation (fuel, oil, cooling system, engine start system, etc.). The main rotor (HB) is used to maintain and move the helicopter in the air, and consists of blades and a main rotor hub. The tail rotor serves to balance the reactive moment that occurs during the rotation of the main rotor, and for directional control of the helicopter. The tail rotor thrust force creates a moment relative to the center of gravity of the helicopter, balancing the reactive moment of the main rotor. To turn the helicopter, it is enough to change the value of the tail rotor thrust. The tail rotor also consists of blades and bushings. The main rotor is controlled by a special device called a swashplate. The tail rotor is controlled by pedals. Take-off and landing devices serve as a support for the helicopter when parked and ensure the movement of the helicopter on the ground, takeoff and landing. To mitigate shocks and shocks, they are equipped with shock absorbers. Take-off and landing devices can be made in the form of a wheeled landing gear, floats and skis

Fig.2 The main parts of the helicopter:

1 - fuselage; 2 - aircraft engines; 3 — rotor (carrier system); 4 - transmission; 5 — tail rotor; 6 - end beam; 7 - stabilizer; 8 — tail boom; 9 - chassis

The principle of creating lift force by the propeller and the propeller control system

In vertical flightThe 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 and the speed of the outgoing jet:

where πD 2/4 - surface area swept by the main rotor;V—flight speed in m/s; ρ — air density;u-outgoing jet velocity m/sec.

In fact, the thrust force of the screw is equal to the reaction force when the air flow is accelerated

In order for the helicopter to move forward, a skew of the plane of rotation of the rotor is needed, and the change in the plane of rotation is achieved not by tilting the main rotor hub (although the visual effect can be just that), but by changing the position of the blade in different parts of the quadrants of the circumscribed circle.

The main rotor blades, describing a full circle around the axis during its rotation, are flowed around by the oncoming air flow in different ways. A full circle is 360º. Then we take the rear position of the blade as 0º and then every 90º full turn. So the blade in the range from 0º to 180º is the advancing blade, and from 180º to 360º is the receding one. The principle of such a name, I think, is clear. The advancing blade moves towards the incoming air flow, and the total speed of its movement relative to this flow increases because the flow itself, in turn, moves towards it. After all, the helicopter flies forward. Accordingly, the lifting force also increases.

Fig. 3 Change in free stream speeds during rotation of the propeller for the MI-1 helicopter (average flight speeds).

The retreating blade has the opposite picture. The speed with which this blade, as it were, “runs away” from it is subtracted from the speed of the oncoming flow. As a result, we have less lifting force. It turns out a serious difference in forces on the right and left sides of the screw, and hence the obvious overturning moment. In this state of affairs, the helicopter, when trying to move forward, will tend to roll over. Such things took place during the first experience of creating rotorcraft.

To prevent this from happening, the designer used one trick. The fact is that the main rotor blades are fixed to the sleeve (this is such a massive assembly mounted on the output shaft), but not rigidly. They are connected to it with the help of special hinges (or devices similar to them). Hinges are of three types: horizontal, vertical and axial.

Now let's see what will happen to the blade, which is hinged to the axis of rotation. So, our blade rotates with constant speed without any external control.

Rice. 4 Forces acting on a blade suspended from a hinged propeller hub.

From From 0º to 90º, the speed of the flow around the blade increases, which means that the lifting force also increases. But! Now the blade is suspended on a horizontal hinge. As a result of excess lift, it, turning in a horizontal hinge, begins to rise upwards (experts say “does a swing”). At the same time, due to an increase in drag (after all, the flow velocity has increased), the blade deviates backward, lagging behind the rotation of the propeller axis. For this, the vertical ball-nir serves just as well.

However, when swinging, it turns out that the air relative to the blade also acquires some downward movement and, thus, the angle of attack relative to the oncoming flow decreases. That is, the growth of excess lift slows down. This deceleration is additionally affected by the absence of a control action. This means that the swashplate link attached to the blade keeps its position unchanged, and the blade, swinging, is forced to turn in its axial hinge, held by the link and, thereby, reducing its installation angle or angle of attack with respect to the oncoming flow. (The picture of what is happening in the figure. Here Y is the lifting force, X is the drag force, Vy is the vertical movement of air, α is the angle of attack.)

Fig.5 The picture of the change in the speed and angle of attack of the oncoming flow during the rotation of the main rotor blade.

To the point The 90º excess lift will continue to increase, but with increasing deceleration due to the above. After 90º, this force will decrease, but due to its presence, the blade will continue to move up, though more slowly. It will reach its maximum swing height already several times over the 180º point. This is because the blade has a certain weight, and inertia forces also act on it.

With further rotation, the blade becomes receding, and all the same processes act on it, but in the opposite direction. The magnitude of the lifting force falls and the centrifugal force, together with the force of the weight, begin to lower it down. However, at the same time, the angles of attack for the oncoming flow increase (now the air is already moving upwards relative to the blade), and the installation angle of the blade increases due to the immobility of the rods. helicopter swash plate . Everything that happens maintains the lift of the retreating blade at the required level. The blade continues to descend and reaches its minimum stroke height somewhere after the 0º point, again due to inertia forces.

Thus, the blades of a helicopter, when the main rotor rotates, seem to “wave” or even say “flutter”. However, you are unlikely to notice this flutter, so to speak, with the naked eye. The rise of the blades up (as well as their deflection back in the vertical hinge) is very small. The fact is that centrifugal force has a very strong stabilizing effect on the blades. The lifting force, for example, is 10 times more than the weight of the blade, and the centrifugal force is 100 times. It is the centrifugal force that turns the seemingly “soft” blade bending in a stationary position into a rigid, durable and perfectly working element of the main rotor of a helicopter helicopter.

However, despite its insignificance, the vertical deviation of the blades is present, and the main rotor describes a cone during rotation, although it is very gentle. The base of this cone is plane of rotation of the screw(See pic1.)

To give the helicopter translational motion, you need to tilt this plane so that the horizontal component of the total aerodynamic force appears, that is, the horizontal thrust of the propeller. In other words, you need to tilt the entire imaginary cone of rotation of the screw. If the helicopter needs to move forward, then the cone must be tilted forward.

Based on the description of the movement of the blade during the rotation of the propeller, this means that the blade in the 180º position should descend, and in the 0º (360º) position it should rise. That is, at the point 180º, the lifting force should decrease, and at the point 0º (360º) it should increase. And this, in turn, can be done by reducing the installation angle of the blade at the point 180º and increasing it at the point 0º (360º). Similar things should happen when the helicopter moves in other directions. Only in this case, of course, similar changes in the position of the blades will occur at other corner points.

It is clear that at intermediate angles of rotation of the propeller between the indicated points, the installation angles of the blade should occupy intermediate positions, that is, the installation angle of the blade changes as it moves in a circle gradually, cyclically. It is called the cyclic installation angle of the blade ( cyclic pitch). I emphasize this name because there is also a common propeller pitch (total pitch angle). It changes simultaneously on all blades by the same amount. This is usually done to increase the overall lift of the main rotor.

Such actions are performed helicopter swashplate . It changes the angle of installation of the main rotor blades (propeller pitch), rotating them in the axial hinges by means of rods attached to them. Usually there are always two control channels: pitch and roll, as well as a channel for changing the total pitch of the main rotor.

Pitch means the angular position of the aircraft relative to its transverse axis (nose up and down), akren, respectively, relative to its longitudinal axis (left-right tilt).

Structurally helicopter swashplate made quite difficult, but it is quite possible to explain its structure using the example of a similar unit of a helicopter model. The model machine, of course, is simpler than its older brother, but the principle is absolutely the same.

Rice. 6 Model helicopter swashplate

This is a two-bladed helicopter. The angular position of each blade is controlled through the rods6. These rods are connected to the so-called inner plate2 (made of white metal). It rotates together with the screw and in steady state is parallel to the plane of rotation of the screw. But it can change its angular position (inclination), as it is fixed on the axis of the screw through a ball bearing3. When changing its inclination (angular position), it acts on the rods6, which, in turn, act on the blades, turning them in axial hinges and thereby changing the cyclic pitch of the propeller.

Inner plate at the same time it is the inner race of the bearing, the outer race of which is the outer plate of the screw1. It does not rotate, but can change its inclination (angular position) under the influence of control through the pitch channel4 and through the roll channel5. Changing its inclination under the influence of control, the outer dish changes the inclination of the inner dish and, as a result, the inclination of the plane of rotation of the main rotor. As a result, the helicopter flies in the right direction.

The overall pitch of the screw is changed by moving the inner plate2 along the screw axis using a mechanism7. In this case, the installation angle changes immediately on both blades.

For a better understanding, I put a few more illustrations of the screw hub with a swashplate.

Rice. 7 Screw hub with swashplate (diagram).

Rice. 8 Rotation of the blade in the vertical hinge of the main rotor hub.

Rice. 9 Main rotor hub of MI-8 helicopter

PHYSICS OF THE ROTOR

Great car - helicopter! Remarkable qualities make it indispensable in thousands of cases. Only a helicopter is capable of taking off and landing vertically, hanging motionless in the air, moving sideways and even tail first.

Why such wonderful opportunities? What is the physics of its flight? Let's try to briefly answer these questions.

The propeller of a helicopter creates lift. The propeller blades are the same snouts. Installed at a certain angle to the horizon, they behave like a wing in the flow of incoming air: pressure arises under the lower plane of the blades, and rarefaction occurs above it. The greater this difference, the greater the lifting force. When the lifting force exceeds the weight of the helicopter, it takes off, if the opposite happens, the helicopter descends.

If on an aircraft wing lift occurs only when the aircraft is moving, then on the “wing” of a helicopter it appears even when the helicopter is standing still: the “wing” is moving. This is the main thing.

But then the helicopter gained altitude. Now he needs to fly forward. How to do it? The screw creates thrust only upwards! Let's take a look at this moment in the cockpit. He pushed the control stick away from him. The helicopter banked slightly on its nose and flew forward. Why?

The control stick is connected to an ingenious device - an automatic transfer. This mechanism, extremely convenient for helicopter control, was invented by Academician B. N. Yuryev in his student years. Its device is rather complicated, and the purpose is as follows: to enable the pilot to change the angle of inclination of the blades to the horizon at will.

It is easy to understand that during the horizontal flight of a helicopter, pushing from its blades moves relative to the surrounding air with different speed. That blade, which goes forward, moves towards the air flow, and turning back - along the flow. Therefore, the speed of the blade, and with it the lift force, will be higher when the blade moves forward. The propeller will tend to turn the helicopter on its side.

To prevent this from happening, the nonstruntors connected the blades to the axis movably, on hinges. Then the blade going forward with a larger lifting force began to soar, to wave. But this movement was no longer transmitted to the helicopter, it flew calmly. Thanks to the flapping motion of the blade, its lifting force remained constant throughout the revolution.

However, this did not solve the problem of moving forward. After all, you need to change the direction of the propeller thrust force, make the helicopter move horizontally. This made it possible to make a swashplate. It continuously changes the angle of each propeller blade so that the greatest lift occurs approximately in the rear sector of its rotation. The resultant thrust force of the main rotor tilts, and the helicopter, also tilting, begins to move forward.

Such a reliable and convenient helicopter control apparatus was not immediately created. A device for controlling the direction of flight did not immediately appear either.

Of course, you know that a helicopter does not have a rudder. Yes, he does not need a rotorcraft. It is replaced by a small propeller mounted on the tail. The pilot would have tried to turn it off - the helicopter would have turned itself. Yes, he turned so that he would begin to rotate faster and faster in the direction opposite to the rotation of the main rotor. This is a consequence of the reactive moment that occurs when the rotor rotates. The tail rotor does not allow the tail of the helicopter to turn around under the influence of the reactive moment, it balances it. And if necessary, the pilot will increase or decrease the thrust of the tail rotor. Then the helicopter will turn in the right direction.

Sometimes they completely do without a tail rotor, installing two rotors on helicopters that rotate towards each other. Reactive moments in this case, of course, are destroyed.

This is how an "air all-terrain vehicle" and a tireless worker - a helicopter fly.

I

The lift and thrust for translational motion of the helicopter are generated by 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 this screw, 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 but 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.