§ 1. Purpose and types of propellers
The purpose of the propeller is to convert the torque transmitted from the engine into aerodynamic force. The formation of aerodynamic force is explained by the third law of mechanics. The air screw, as it rotates, captures and throws off a certain mass of air. This mass, resisting to be thrown away, pushes the propeller together with the aircraft in the direction opposite to the direction of the throw.
The reason for the creation of the aerodynamic force of the propeller is the reaction of the air mass thrown by the propeller.
Aircraft propellers are used to create the thrust required for the forward motion of the aircraft.
The main rotor of the helicopter is used to create liftrequired to keep the helicopter in the air, and the thrust force required for the forward motion of the helicopter. As mentioned, one of the advantages of a helicopter is its ability to move in any direction. The direction of movement of the helicopter depends on where the thrust force of the main rotor is inclined - forward, backward or sideways (Fig. 1.32).
The main rotor provides control and stability of the helicopter in all modes. Thus, the main rotor simultaneously serves as a wing, a pulling rotor and the main controls.
Helicopter tail rotor is used to balance the reactive torque and direction control of the helicopter.

§ 2. The main parameters characterizing the rotor
The main parameters characterizing the main rotor of a helicopter are:
Number of blades. Modern helicopters use three-, four- and five-bladed propellers. An increase in the number of blades degrades the rotor performance due to the harmful mutual influence of the blades. A decrease in the number of blades (less than three) leads to a pulsating nature of the thrust generated by the propeller and increased vibrations of the helicopter in flight. Main rotor diameter D - diameter of the circle described by the ends of the blades during rotation. The radius of this circle is designated by the letter R and is called the radius of the main rotor. The distance from the axis of rotation of the main rotor to the section under consideration is denoted by the letter r (Fig. 1.33).

Calculations show that at the same power supplied to the propeller, its thrust increases with increasing diameter. For example, doubling the diameter increases the thrust by 1.59 times, increasing the diameter by five times increases the thrust by 2.92 times.
However, an increase in the diameter is associated with an increase in the weight of the propeller, with a great difficulty in ensuring the strength of the blades, with the complication of the technology for manufacturing blades, an increase in the length of the tail boom, etc.
Therefore, when developing a helicopter, a certain optimal diameter is chosen.

The area swept by the main rotor F0M is the area of \u200b\u200bthe circle described by the ends of the rotor blades during rotation.
The concept of swept area is introduced because this area can be considered as a certain bearing surface, similar to an airplane wing due to the viscosity and inertness of air, which, when flowing through the area swept by the propeller, forms one common jet. Modern helicopters have F0M \u003d 100 -: - 1000 m2.
The load on the swept area p is the ratio of the helicopter's weight G to the area swept by the propeller when it rotates:
FomR \u003d G / Fom (kg / m2).
An increase in p leads to a decrease in the maximum flight altitude and to an increase in the rate of descent in the rotor self-rotation mode.
For modern helicopters P \u003d 12 -: - 45kg / m2, or 118 -: - 440n / m2

Fill factor Q is a value that shows what part of the swept area is the area of \u200b\u200ball rotor blades.

Blade shape in plan (fig. 1.34). The main rotor blade can be rectangular, trapezoidal or mixed in plan. The narrowing of the trapezoidal blade is no more than 2-3.
The narrowing of the blade is the ratio of the chord at the butt to the terminal chord.
The blade profile is the shape of its cross-section. For the rotor blades, profiles are used similar to those of aircraft wings. Usually these are asymmetric profiles with a relative thickness c \u003d
7 - \u003d - 14% '. The shape of the profile along the length can be variable (aerodynamic twist of the blade). When choosing, the shape of the profile strives to ensure that it has the highest aerodynamic quality.

The angle of attack of the blade section a is the angle between the chord of the profile and the direction of the incoming air flow in the given section. The value of the angle of attack determines the values \u200b\u200bof the coefficients of aerodynamic forces.

Installation angle Ф called the angle between the chord of the profile and the plane of rotation of the main rotor. The angle of installation of helicopter propellers is measured at a distance of 0.7 of the propeller radius.This convention was introduced due to the geometrical twist of the blades, as a result of which all sections of the blades have different (decreasing towards the end) installation angles. The need for geometric twist is explained as follows. First, due to the peripheral speed increasing towards the blade tip, there is an uneven distribution of the inductive velocities, and, consequently, of the aerodynamic forces along the blade length. To ensure a more uniform distribution of the load, the angle of installation to the blade tip is reduced. Secondly, in translational flight, due to an increase in the angle of attack in a certain position of the blades, a flow stall occurs from the ends of the blades, the presence of a geometric twist pushes the end stall towards high flight speeds. This issue will be discussed in more detail below.
The pitch of the main rotor blade changes when it is rotated in the axial hinge, i.e. around the longitudinal axis.
Structurally, the main rotor is made so that all its blades in the axial hinge can simultaneously rotate at the same angle or at different angles.
The angle of attack of the main rotor. It was said above that the area swept by the rotor can be considered as a bearing surface, per unit area of \u200b\u200bwhich a certain load falls.
Let us introduce the concept - the angle of attack of the main rotor A, by which we mean the angle between the plane of rotation of the main rotor and the direction of the incoming air flow (direction of flight). If the flow runs onto the plane of rotation of the rotor from below (Fig. 1.36), the angle of attack is considered positive, if from above it is negative.
Since the helicopter moves in the air in any direction, the angle of attack of the main rotor can vary by ± 180 °. With a vertical decline A \u003d + 90 °, with a vertical rise A \u003d -90 °.

The angle of the azimuth position of the blade. During a helicopter flight, the rotational motion of the rotor blades is added to the translational motion of the entire helicopter as a whole. For this reason, the operating conditions of the blades are more dependent on their position relative to the direction of flight. To assess the features of the operation of the blades, depending on their position, the concept of the azimuthal position of the blade is introduced.
The angle of the azimuthal position of the blade is the angle between the direction of flight and the longitudinal axis of the blade (Fig. 1.37).

It is customary to consider f \u003d 0 if the longitudinal axis of the blade coincides with the direction of the incoming air flow. It should be noted (since the helicopter can move forward, backward or sideways) that in all cases the azimuth angle should be read from the direction of the blade, which coincides with the direction of the incoming air flow. It is customary to count in the direction of rotation of the rotor. Obviously, the value of the angle of the azimuthal position of the blade in one revolution changes from 0 to 360 ° (from 0 to 2n).
The number of revolutions of the main rotor. Due to the fact that the main rotor of helicopters are propellers of large diameters, their number of revolutions is small - 100-600 rpm.
Calculations show that in order to have a propeller with the greatest possible thrust (for a given power), it is necessary to increase its diameter and decrease the speed. So, for example, in order to increase thrust by three times, the revolutions must be reduced fifteen times (while the diameter of the propeller will increase by about five times).
For a specific propeller, the thrust increases with increasing speed, but this requires an increase in the input power.
The number of revolutions of the main rotor is limited by a wave crisis arising primarily at the ends of the blades moving towards the incoming flow (near the azimuth r |) \u003d 90 °).
In order to avoid large losses to overcome the wave drag, the number of rotations of the main rotor of modern helicopters is chosen such that the ends of the blades have subsonic flow velocities. In modern helicopters, the peripheral speeds of the blade tips reach 200-250 m / s.
§ 3. The thrust of an ideal main rotor with axial flow
An ideal propeller is a propeller that does not take into account frictional losses and twisting of the jet behind the propeller. The mode of axial flow is a mode in which the air flow is directed along the axis of rotation of the propeller. In this case, the angle of attack of the main rotor is 90 °. In the axial flow mode, the main rotor operates during hovering, vertical ascent and vertical descent of the helicopter.
The main rotor sucks in air at a speed U1 and throws it off at a speed U2. The speeds U1 and U2 are called inductive speeds (Figure 1.38).

If the flow velocity around the propeller is equal to V, then in front of the propeller it becomes equal to V + U1, and behind the propeller V + U2.
The air mass, having passed the swept area, receives acceleration j under the action of the force F created by the propeller. On the basis of the third law of mechanics, with the same magnitude, but oppositely directed force T, air acts on the rotor. Force T is the thrust of the screw. Based on the second law of mechanics, T \u003d mj. The mass of air passing through the swept area can be determined by multiplying the volume by the mass density. N. Ye. Zhukovsky proved theoretically and experimentally confirmed that the inductive throwing speed is twice the inductive suction speed. In other words, the inductive speed at the propeller disk is equal to half of the total speed increment obtained by the air passing through the propeller.

The inductive suction speed is determined empirically and is equal to 8-15 m / s.
From the obtained thrust formula it follows that the rotor thrust depends on the mass density of the air, the swept area and the inductive suction speed.
With an increase in the flight altitude or an increase in the ambient air temperature, the mass density P and, consequently, the thrust force decrease. With increasing speed and pitch of the propeller, the inductive speed U1 (propeller thrust) increases.
The area swept by the main rotor Fоv is a design parameter and is constant for a specific rotor.
The thrust of the main rotor can be obtained in another way - as the sum of the aerodynamic forces created by the individual blades, since the flow around the blades is similar to the flow around the wing. The difference, however, is that the blade performs not translational, but rotational motion, in connection with which all its sections (elements) move with different speeds... Therefore, the aerodynamic force generated by the blade must be calculated as the sum of the aerodynamic forces acting
on the blade element (Fig. 1.39).

The lift force of the blade element ΔY and the drag of the element ΔX, respectively, differ in magnitude from the thrust force of the element ΔT and the resistance to rotation of the element ΔQ.
This is explained by the fact that the lifting force is directed perpendicularly to the flow oncoming the section, the drag is directed along the flow, the thrust force is perpendicular to the plane of rotation of the element, and the force of resistance to rotation is placed in the plane of rotation.
§ 4. The thrust of the main rotor with oblique flow
The oblique flow regime is understood as a regime in which the air flow is directed under some arbitrary angle attack to the plane of rotation of the main rotor (not equal to 90 °). This mode is carried out during the horizontal flight of the helicopter, as well as during the ascent and descent along an inclined trajectory.

To simplify the issue under study, let us first consider the case of a lateral flow around the main rotor, i.e., such a case in which the flow is parallel to the plane of rotation of the main rotor and the angle of attack of the rotor is zero. In this case, the speed of the incoming flow V is added with the suction speed u and gives the resulting speed V1 (Fig. 1.41). Obviously, V\u003e u1.

It can be seen from the formula that at the same rejection speed U2, the propeller thrust with lateral flow is greater than with axial flow. Physically, this is explained by an increase in the second mass of air flowing through the area swept by the propeller.
Considering the more general case of oblique flow, when the air approaches the plane swept by the propeller at some arbitrary angle of attack of the main rotor A, we get a similar picture. It is only necessary to keep in mind that in each specific case, the resulting speed of the air flowing to the plane of the rotor should be equal to the geometric sum of the incoming flow speed and the suction speed.
§ 5. Changing the thrust of the main rotor
with oblique flow depending on the azimuthal position of the blades
With oblique flow around the main rotor, the speed of the flow around the blades is the sum of the rotational speed and the forward speed of the incoming air flow. For simplicity of reasoning, let us consider the flow around the blade end section. Note that the component of the incident flow velocity directed along the blade does not participate in the creation of the lift force. The peripheral speed of the end section is wR. Let the incoming flow velocity be equal to V. Let us expand this velocity into the direction along the blade and perpendicular to it (Fig. 1.42).

At an azimuth of 90 ° it becomes + V and at an azimuth of 270 ° it becomes -V. Thus, in one revolution of the blade, the velocity of its flow around it reaches a maximum at an azimuth of 90 ° and a minimum at an azimuth of 270 °.
From the formula we see that the thrust force of the blade is a variable value and depends on the azimuth. It acquires its maximum value at an azimuth of 90 °, when the value of the peripheral speed is added to the flight speed, the minimum value is at an azimuth of 270 °, when the flight speed is subtracted from the peripheral speed.
the magnitude of the thrust force of a two-bladed propeller depends on the azimuth and is a variable value. The variable component of the thrust force of the two-blade propeller causes increased vibration of the helicopter, and therefore the use of two-bladed rotors is limited. To calculate the thrust force of a three-blade propeller, it is necessary to add the thrust of three blades spaced 120 ° apart in azimuth. Elementary mathematical calculations show that for propellers with three or more blades, the variable component disappears and the total thrust becomes a constant value, independent of azimuth.
It is very important to note that the total thrust force of the main rotor with the blades rigidly fixed to the hub during oblique blowing does not coincide with the axis of rotation, but is shifted towards the blades moving against the air flow. This is due to the fact that the lifting force of the blades moving against the flow is greater than that of the blades moving in the direction of the flow, and as a result of geometric addition, the resultant of the lifting forces is shifted towards the blades moving towards the flow. The displaced thrust force of the main rotor creates an overturning (heeling) moment relative to the center of gravity of the helicopter (Fig. 1.43). The main rotor with rigidly fixed blades would inevitably overturn the helicopter when trying to create any significant forward speed.
In addition to the heeling moment that tends to overturn the helicopter relative to the longitudinal axis, with oblique blowing of the main rotor, a longitudinal moment also arises, which turns the plane of rotation of the main rotor relative to the transverse axis to increase the angle of attack. The occurrence of this moment is explained by the fact that the conditions of the flow around the blades near the 180 ° azimuth are better than in the 360 \u200b\u200b° azimuth. As a result, the point of application of the propeller thrust force is displaced forward from the axis of rotation, which leads to the formation of a cobranding moment. The value of the longitudinal moment of the elastic blade additionally increases due to the upward bending of the blades under the action of lifting forces due to the fact that the counter flow acts on the blade located in the azimuth region of 180 ° from below, while in Fig. 1.43.

Occurrence of overturning moment at a propeller with rigidly fixed blades
the blade, located in the azimuth region of 0 °, is from above (Fig. 1.44). Elimination of the harmful influence of overturning and longitudinal moments is carried out by the articulated suspension

blades.
§ 6. Resistance of the main rotor with oblique flow
The plane swept away by the rotor is considered as the bearing surface. This surface creates lift and drag through the incident air flow. The main rotor drag, by analogy with a wing, consists of a profile and an inductive one.
In the case of axial flow, the profile drag of the blades in all azimuths is the same and their resultant is zero.

The physical meaning of the appearance of the profile resistance at oblique
the flow around can be represented as follows.
For one revolution, the blade resistance changes periodically,
reaching its maximum at an azimuth of 90 ° and a minimum at an azimuth of 270 °. The difference between the resistances of the "advancing" and "retreating" blades gives a force directed in the direction opposite to the movement of the helicopter. This force is the profile resistance of the main rotor X pr (Fig. 1.45). The main rotor inductive resistance can be explained by the same
the reasons, as in the flow around the wing, i.e., the formation of vortices, which consume the energy of the flow. The main rotor frontal resistance is the sum of the profile and inductive X nv \u003d X pr + X in
The value of the main rotor drag depends on the shape of the blade profile, the angle of their installation, the number of revolutions, the flight speed and the angle of attack of the main rotor.
The main rotor frontal resistance must be taken into account when flying in the rotor mode.

§ 7. Backflow zone
When the blade moves in azimuths Ф \u003d 180 -: - 360 ° sections of the blades, located near the butt, flow around not from the edge of attack, but from the edge of the flow. Indeed, in azimuth

270 °, such a flow will be for all sections of the blade located from the axis of rotation to the point on the blade at which v \u003d wr, i.e. to the point where the peripheral speed is equal to the flight speed (Fig. 1.46). Due to the opposite direction of these speeds, the total speed
the flow around this point is zero (Wr \u003d 0).
Given different values \u200b\u200bof φ, it is easy to obtain from the latter
expressions for the backflow zone. It is easy to make sure that this zone is a circle with a diameter of d \u003d V / w located on the disk swept by the rotor (Fig. 1.46).
The presence of a backflow zone is a negative phenomenon. The portion of the blade passing through this zone creates a downward force, which reduces the thrust of the main rotor and leads to an increase

vibrations of the blades and the entire helicopter. With an increase in flight speed, the return flow zone increases.
The magnitude of the return flow zone can be estimated by the coefficient of the characteristic of the operating mode of the main rotor m.
the coefficient of the characteristic of the operating mode of the rotor is understood as the ratio of the speed of translational motion to
blade end section speed.
The coefficient shows how much of the blade located in
azimuth 270 °, located in the return flow zone. For example,
if m \u003d 0.25, then d \u003d 0.25 R. This means that the fourth part of the blade works in the opposite
flow, and the diameter of the return flow zone is 25% of the radius of the main rotor.
§ 8 Loss of energy by the main rotor. Relative efficiency of the screw
When deriving the formula for the thrust of an ideal propeller (§ 3 of this chapter), we neglected all types of losses. When a real propeller operates in operating modes, about 30% of the power required for its rotation is spent on overcoming the profile resistance of the blades. The amount of profile losses depends on the profile shape and surface condition.
Analyzing the operation of an ideal screw, we assumed that the inductive speed at all points of the swept area is the same. But this is not the case. The inductive velocity is higher near the blade than in the spaces between the blades. In addition, the inductive speed changes along the blade, increasing with an increase in the radius of the section, due to an increase in the circumferential speed of the section (Fig. 1.47). Thus, the field of inductive velocities created by the rotor is non-uniform.

Adjacent air streams move at different speeds, due to which, due to the influence of air viscosity, there are losses due to uneven flow or inductive losses, amounting to about 6% of the required power. One of the ways to reduce these losses is the geometric twist of the blades.
The main rotor not only throws off the air mass, thereby creating thrust, but also twists the jet. Losses for swirling of the jet are about 0.2% of the power supplied to the propeller.
Due to the difference in pressure below and above the plane of rotation of the rotor, air flows from bottom to top along the circumference of the rotor disk. For this reason, a certain narrow ring located around the circumference of the plane swept by the rotor does not participate in the creation of thrust (Fig. 1.48). The butt parts of the blades, where the attachment points are located, also do not participate in the creation of the traction force. In total, the end and butt losses are about 3% of the required power.
Due to the presence of the listed losses, the power required to rotate a real propeller, creating a thrust equal to that of an ideal propeller, is greater.
How successful this or that real propeller is in terms of ensuring a minimum loss can be judged

by the relative efficiency of the main rotor g | 0, which is the ratio of the power required to expel air and obtain a given thrust to the power actually expended to rotate a real propeller that creates the same thrust.

§ 9. Hinged suspension of the rotor blades
In § 2 of this chapter it was indicated that the main rotor has axial hinges, which serve to change the pitch of the propeller in flight. The change in pitch is achieved by turning the blades around the axial hinges within? \u003d 0-15 °. In addition to axial hinges, the screws have horizontal and vertical hinges.
The horizontal joint (GS) allows the blades to deflect in the vertical plane. Thanks to
With this hinge, the blade has the ability to swing up when moving against the flow, and when moving in the direction of the flow - down. Thus, the horizontal hinge allows the blades to swing.
The angle between the axis of the blade and the plane of the rotor hub is called the swing angle?. Con-
structurally, the deflection of the blade relative to the horizontal hinge is limited by stops (upward by
25-30 °, down by 4-8 °). Despite the presence of flapping movements in flight, the blade does not touch the stops, since the range of the flapping angles is less than the angle between the stops. The contact of the stop blade occurs only with a strong drop in speed, and, accordingly, with an unacceptable decrease in the centrifugal force of the blade.
When the helicopter is parked, when the main rotor does not rotate or rotates at low revs, the ends of the blades bend downward due to their weight, and if the blade rests against the lower stop, a blow to the tail boom or fuselage is possible. Therefore, in addition to the lower stop, there is also a special overhang limiter, which at low speeds does not allow the blade to go down excessively and hit the helicopter.
With an increase in revolutions, when the aerodynamic forces bend the ends of the blades upward, the overhang limiter is turned off, after which the blade can swing up to the lower stop.
VERTICAL SHARN AND R (VSH) provides a deflection of the blade relative to the sleeve in the plane
rotation of the screw. It will be shown below that when the main rotor rotates, the blade can move away from the neutral (radial) position backward or forward by a certain angle. This angle is called the lag (lead) angle and is denoted by the letter?. This angle is limited by stops. The blade can be turned back by? \u003d 10 -: - 18 ° and forward by? \u003d 6 -: - 8 ° *.
The presence of horizontal and vertical hinges makes a significant change in the work of the carrier
screw.

* In technical descriptions, the value of the lag (advance) angle is given not relative to the radial position of the blade, but relative to the perpendicular to the horizontal hinge.
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First, it is necessary to note the formation of the so-called cone (tulip) due to the fact that, under the action of lifting forces, the blades deflect relative to the horizontal hinges and rise above the plane of rotation of the sleeve. Secondly, due to the flapping movements, the lifting forces of the blades are leveled in different azimuths, which makes it possible to eliminate the overturning and pitching of the helicopter during forward flight. Finally, the butt sections of the blades are relieved from the large bending moments that occur when the blades are rigidly embedded.
§ 10. Horizontal hinge (GSH)
Consider the equilibrium of the blade relative to the horizontal hinge, i.e., the forces acting on the blade
mouth in a plane perpendicular to the plane of rotation (Fig. 1.49).

In this plane, the following forces act on the blade: (Gl - weight; Yl - lifting force; Fц. Б -
centrifugal force.
The lifting force is 10-15 times the weight of the blade. The largest is the central thrust force, which exceeds the weight of the blade by a factor of 100-150. In the equilibrium position, the sum of the moments of all forces acting on the blade relative to the GS should be equal to zero. In other words, the resultant of these forces must pass through the GS axis.
When rotating, the blade describes a surface close to a cone, and therefore the angle of the swing is called the angle of taper.

With axial flow, constant pitch and revolutions, the angle value
the taper is quite definite. If, for example, increase

blade pitch, then under the influence of the increased moment from the lifting force, the blade will begin to deviate towards an increase in the swing angle.
With an increase in the angle of swing, the moment
centrifugal force, preventing the deflection of the blade, and when equilibrium is re-established, the blade will rotate with great value angle of swing.
With oblique flow in azimuths of 0-180 °, the blade moves towards the flow, and in azimuths of 180-360 ° - in the direction of the flow. A blade moving against the flow receives an increase in lift and swings up, since the moment of lift is greater than the moment of centrifugal force (the moment of force of the weight is neglected due to small values).
For a blade moving in the direction of flow, the lifting force decreases, and under the action of the moment
centrifugal force it swings down. Thus, in one revolution, the blade makes a swing upward and
swing down.
The flow velocity is highest at an azimuth of 90 °, therefore, the increase in lift is greatest here.
The smallest lift will be at the 270 ° azimuth, where the flow velocity is minimal and the effect of the backflow zone is strongest. However, due to the presence of the GS and the flapping movements of the blades, the increase and decrease in the lifting forces in the indicated azimuths are relatively small. This is explained by a change in the angles of attack of the flapping blades. Indeed, with an upward swing of the blade, the angle of attack decreases, and with a downward swing, it increases (Fig. 1.50). For this reason, the magnitude of the lift forces along the azimuths is leveled, which practically eliminates the heeling and longitudinal moments acting on the helicopter.

As a result, it must be said that the purpose of the horizontal hinges is reduced to equalizing the lifting forces of the blades in all azimuths and to unloading the butt sections from bending moments. The horizontal hinges are structurally spaced from the axis of rotation of the screw by a certain distance Lrw (Fig. 1.51). With axial flow, the axis of the cone of revolution and the axis of the sleeve coincide. Therefore, the centrifugal forces of the blades Ftsb, conditionally applied to the GSh, are mutually balanced. In oblique flow, the axis of the cone and the axis of the sleeve do not coincide, and the centrifugal forces lie in different (parallel) planes. These forces on a certain shoulder with create a moment M g w \u003d FcbS, which improves the controllability of the helicopter. In addition, the specified moment in case of accidental deflection of the helicopter relative to the longitudinal or transverse axis has a damping effect, that is, it is directed in the direction opposite to the deflection, which improves the stability of the helicopter.

§ 11. Blockage of the cone of rotation with oblique blowing
In the previous paragraph, it was indicated that due to the presence of horizontal hinges, the blades swing upwards at azimuths 0-180 °, and downward at azimuths 180-360 °. In fact, the picture of the flapping movements of the blades looks somewhat more complicated. Due to the fact that the blades have mass, an increase in the angle

the swing by inertia continues not to the azimuth of 180 °, but somewhat farther, the decrease is not to 360 °, and also not too long. the flow enters the blade from below, and near the azimuth 360 ° - from above, which also further contributes to the continuation of the increase in the swing angle near the azimuth of 180 ° and to the decrease in the swing angle near the azimuth of 360 °.
Figure 1.52, a shows the experimental curve of the dependence of the waveform on the azimuth obtained on the B-1 setup. For the tested model of a main rotor with rigid blades at an oblique blowing speed of 20 m / s, the maximum swing angle was found in the azimuth of 196 °, and the minimum - in the azimuth of 22 °. This means that the axis of the cone of rotation is tilted back and to the left. The phenomenon of deviation of the axis of the rotor cone of rotation during oblique flow is called the collapse of the cone of rotation (Fig. 1.53).

Theoretically, the main rotor cone with oblique blowing tilts back and to the left. This blockage is confirmed by the above experiment. However, the direction of the lateral blockage is significantly influenced by the deformation of the blades and the spacing of the horizontal hinges. The real rotor blade does not have sufficient rigidity and under the influence of forces acting on it
27

strongly deformed - bends and twists. The twist occurs in the direction of decreasing the angles of attack, and therefore the upward swing stops earlier (Ф \u003d 160 °). Accordingly, the downward swing stops earlier (φ \u003d 340 °).
Figure 1.52, b shows the experimental curve of the dependence of the swing angle a on the azimuth, obtained with the V-2 setup. When testing a propeller model with flexible blades, the maximum swing angle was obtained in azimuth φ \u003d 170 °, and the minimum - in azimuth φ \u003d 334 °. Thus, in real helicopters, the cone of rotation falls back and to the right. The value of the angle of obstruction depends on the flight speed, propeller pitch and rpm. With an increase in the pitch of the screw and speed and with a decrease in revolutions behind the shaft, the taper of rotation increases.
Control of modern helicopters is carried out by tilting the cone of rotation towards the movement of the helicopter. For example, to move forward, the pilot deflects the axis of the rotor cone of rotation forward (using the swashplate). The tilt of the cone is accompanied by the tilt of the main rotor thrust in the appropriate direction, which gives the necessary component for the movement of the helicopter (Fig. 1.32). However, as soon as the flight speed begins to increase, due to the oblique flow around the cone falls back and sideways. The effect of the obstruction of the cone is countered by an additional movement of the helicopter control stick.
§ 12. Vertical hinge (HS)
In order to make sure that it is necessary to install, in addition to a horizontal, also a vertical ball-
nira, consider the forces acting on the blade in the plane of rotation.
When the propeller rotates on its blades in the plane of rotation, there are forces of resistance to rotation Q l. In hover mode, these forces will be the same in all azimuths. With an oblique flow around the propeller, the resistance of the blade moving against the flow is greater than that of the blade moving in the direction of the flow. The presence of horizontal hinges and flapping movements of the blades helps to reduce this difference (due to the alignment of the angles of attack), but does not completely eliminate it. Therefore, the force of resistance to rotation is a variable force that loads the roots of the blades.
When the speed changes, inertial forces act on the rotor blades, when the speed increases, they are directed against rotation, and when the speed decreases, in the direction of the rotor rotation. Inertial forces can also arise at constant revolutions of the main rotor hub due to the unevenness of the air flow entering the rotor disk, which leads to a change in aerodynamic forces and an additional tendency of the blades to move relative to the hub. In flight, the inertial forces are relatively small. However, on the ground, at the moment the carrier starts spinning
propeller, the inertial forces reach a large value and with a sharp engagement of the transmission can even lead to breakage of the blades.
In addition, the presence of horizontal hinges, which ensure the swinging motion of the blades, leads to the fact that the center of gravity of the blade periodically approaches and moves away from the axis of rotation of the screw (Fig. 1.54).

Based on the law of conservation of energy, the kinetic energy of a rotating carrier
the propeller must remain constant regardless of the flapping motion of the blade (changes in other types of energy are neglected). The kinetic energy of a rotating screw is determined by the formula:

where m is the mass of the rotating blades;
w -
the angular speed of rotation of the blade,
r is the distance from the axis of rotation to the center of gravity of the blade;

It can be seen from the formula that, at constant kinetic energy, the approach of the center of gravity of the blade to the axis of rotation (swing up) should be accompanied by an increase in the angular velocity of rotation, and the removal of the center of gravity of the blade from the axis of rotation (swing down) should be accompanied by a decrease in the angular speed of rotation. This phenomenon is well known to dancers who increase the speed of rotation of their bodies by bringing their hands sharply to the body (Fig. 1.55). The forces under the influence of which an increase or decrease in the angular velocity of rotation occurs when the moment of inertia of the rotating system changes is called Coriolis.

When the blades are flapping upwards, the Coriolis forces are directed in the direction of rotation of the main rotor, and when they are flapping down, they are directed against.
Coriolis forces arising during flapping movements reach a significant value and load the root parts of the blades with variables
bending moments acting in the plane of rotation of the main rotor.
Thus, the setting of horizontal hinges, which allowed
to eliminate the transfer of bending moments to the rotor hub and unload the butt parts of the blades in the flapping plane, at the same time, it also caused undesirable phenomena associated with the occurrence of Coriolis forces loading the root parts of the blades with a variable moment in the plane of rotation. A variable torque from Coriolis forces is transmitted to the bearings of the main rotor, the rotor hub and the engine shaft, causing alternating loads, which leads to accelerated wear of the main rotor bearings and vibrations
helicopter.
To unload the root parts of the blades from alternating bending moments acting in the plane of rotation, and the bushings from alternating loads that cause helicopter vibrations, vertical hinges are installed, which in the plane of rotation of the propeller provide oscillatory motion of the blades.
In addition to the forces considered, centrifugal force also acts on the blade in the plane of rotation.
In the presence of a vertical hinge and a uniform field of velocities of the incoming air flow in the mode
hovering, the blade lags behind the radial position at a certain angle?. Figure 1.56 shows the value of the lag angle?, Due to the equality of the moments:

Fts.bLts.b \u003d Ql LQ.
During the transition to flight with translational speed, variable inertial and Coriolis forces are added to the aerodynamic forces, and the aerodynamic forces themselves also become variable. Under the action of these forces, the blade makes a complex movement, consisting of a rotational motion, translational (together with the helicopter), flywheel relative to the main shaft and oscillatory relative to the main shaft.
In the presence of a VSC, the blade rotates by

Some angle of lag? (Figure 1.57, a). In this case, the blade is located so that the resultant of the aerodynamic and centrifugal forces N is directed along its axis. Transferring the resultant to the GSh axis and expanding it into forces A and B, we make sure that the GSh bearings are not equally loaded. Indeed, in the presence of one force A as
the front and rear bearings of the GSh would be loaded with the same radial loads. However, the strength
B, unloading the rear bearing, additionally loads the front bearing, causing uneven bearing wear. In addition, the force B, which is axial for the GSH, requires the installation of thrust bearings.
To approximate the operating conditions of GSH bearings to the conditions of symmetric load, a displacement is applied
GSh relative to the sleeve forward in rotation (Fig. 1.57, b). In this case, is there a lag angle?
leads to the fact that the axis of the blade is located approximately perpendicular to the axis of the GS.

Since the vertical hinges allow the blades to perform oscillatory movements in the plane of rotation of the rotor, to prevent the possibility of an increase in the amplitude of these oscillations on the carriers

the propellers of modern helicopters are equipped with special dampers - vibration dampers. There are frictional and hydraulic dampers. The principle of operation of both those and others consists in converting the energy of vibrations into thermal energy, which then dissipates into the surrounding space.
On the ground, before starting the engine and spinning the main rotor, its blades must be placed on the front stops of the VSh. This is done to reduce the angular acceleration (force of inertia) of the blades at the initial moment of spin.
The unequal rotation of the blades relative to the VH causes the center of gravity of the main rotor to shift from the axis of rotation. As a result, when the propeller rotates, an inertial force arises, causing vibration (swinging) of the helicopter.
This phenomenon is especially dangerous when the main rotor is operating on the ground, since the frequency of natural oscillations of a helicopter on an elastic landing gear can be equal to or a multiple of the frequency of the driving force, which leads to oscillations that are commonly called ground resonance.
§ 13. Swing compensation
As you know, the main cause of the propeller rotation cone blockage is the swinging motion of the blades with oblique flow. The greater the maximum upward swing angle, the greater the obstruction of the cone of rotation. The presence of a large blockage of the cone is undesirable, since it requires additional deflection of the command levers to compensate for the blockage when controlling the helicopter in forward flight. Therefore, it is necessary that the equilibrium of the moments relative to the GS should be established at a smaller value of the amplitude of the swinging movements.
In order for the amplitude of swing movements to be within the tolerance, swing compensation is applied. The principle of swing compensation is that the control leash attachment point (A) is not installed on the axis of the horizontal hinge, but is shifted towards the blade (Fig. 1.58).

If point A does not lie on the axis of the horizontal hinge and is motionless, then when swinging up, the angle of installation, and therefore the angle of attack of the blade, decreases, and when swinging down, it increases. Due to the change in the angles of attack during the flapping of the blade, aerodynamic forces arise that prevent an increase in the amplitude of flapping movements.
The compensation efficiency depends to a large extent on tg ≈ 1 (Fig. 1.58), which is called the swing compensation characteristic. The larger tg? 1, the greater the angle changes the angle of the blade during swing. Consequently, with an increase in tg ≈ 1, the efficiency of swing compensation increases.
Is there a lag angle? when installing a vertical hinge, it can increase the amplitude of the swing
movements (Fig. 1.59). When the blade deviates around the VS at an angle? the leading edge (point A) will be farther from the GS than the trailing edge (point B). Therefore, when swinging, the path of point A is greater than the path traversed by point B, as a result of which when swinging upward, the angle of attack of the blade increases, when swinging downward, the angle of attack of the blade decreases.

Thus, the lag angle will contribute to the appearance of additional aerodynamic forces on the blade, tending to increase the amplitude of flapping movements. Therefore, it is especially advisable to use compensation for the flapping of blades with a vertical hinge.

§ 14. Reactive moment of the main rotor
When the main rotor rotates, air resistance forces act on its blades, which create a rotation resistance torque relative to the rotor axis. To overcome this moment, torque is supplied to the main rotor shaft in mechanically driven helicopters from an engine installed in the fuselage. The torque is transmitted through the main gearbox to the main rotor shaft. In accordance with the third law of mechanics (the law of equality of action against reaction), a reactive moment arises, which is transmitted through the attachment points of the main gearbox to the helicopter fuselage and tends to rotate it in the direction opposite to the torque. The torque and reactive moment, regardless of the mode of operation of the screw, are always equal in magnitude and opposite in the direction of Мкр \u003d Мр.
If the motors are mounted on the blades themselves, it is obvious that there is no reactive torque. Reactive
the moment is also absent in the rotor self-rotation mode, i.e., in all cases when the torque
torque is not transmitted to the rotor shaft from the engine installed in the fuselage even.
Earlier it was said that the balancing of the reactive moment on single-rotor helicopters with a mechanical drive is performed by the moment created by the tail rotor thrust relative to the helicopter's center of gravity.
In twin-rotor helicopters, the reactive moments of both rotors are compensated by rotating the propellers in different directions. Moreover, to maintain the equality of oppositely directed reactive moments of both screws, the screws are made exactly the same with exact synchronization of their revolutions.

The power transmitted in May to the carrier is equal
It can be seen from the formula that the lower the rotor speed, the greater the torque, and consequently
solid and reactive.
The number of revolutions of the main rotor of the helicopter is much less than the number of revolutions of the aircraft propeller. Therefore, with the same engine power, the reactive moment of the main rotor of the helicopter is much greater than that of the aircraft propeller.
Torque and reactive moments Vary also depending on the magnitude of the rotor thrust. So, for example, to increase the propeller traction force, it is necessary to increase the total pitch. An increase in the pitch of the screw is accompanied by an increase in the moment of resistance to its rotation. Therefore, with an increase in the pitch of the screw, it is necessary to increase the torque supplied to the screw. If this is not done, then the number of revolutions of the main rotor will decrease, which will lead to a decrease in the thrust of the main rotor.
Therefore, to increase the rotor thrust, it is necessary to increase not only the propeller pitch, but also the torque. For this, a "pitch-gas" lever is installed in the cockpit, which is kinematically connected to the engine and a mechanism that changes the propeller pitch. When the lever is moved, there is a proportional change in the torque and pitch of the screw and, at the same time, a change in the reactive torque. On a single-rotor helicopter, a change in the reactive torque requires a corresponding change in the tail rotor thrust to eliminate the turn.

§ 15. Tail rotor thrust
The magnitude of the traction force of the tail rotor (Fig. 1.60) can be determined from the equality

the power consumed by the propeller will increase, and, consequently, the required thrust created by the tail rotor also increases.
The tail rotor operates under oblique blowing conditions, since in flight the plane of its rotation is not perpendicular to the direction of its incoming flow.
With oblique blowing of a rigid screw, the changing speed of the flow incident on it
blades, will cause periodic
changing the thrust force of each blade and will lead to vibrations.
To equalize the thrust force of the blades in all azimuths and
unloading the blades from action
bending moments, the blades of a real tail rotor are attached to the hub by means of horizontal hinges that allow the blades to swing.
The presence of axial hinges in the design of the screw sleeve ensures the rotation of the blades relative to the
fractional axis, which is required to change the pitch.
On heavy helicopters, the vertical hinges can also be mounted on the tail rotor.
§ 16. Available power of the main rotor
The power plants of modern helicopters use piston or turboprop aircraft engines.
A feature of the piston aircraft engines air cooling in helicopters is
the need for forced blowing of the cooled surfaces of the engine using special fans. Forced blowing of engines in helicopters is associated with insufficient capabilities to use the high-speed pressure for cooling in forward flight and with the lack of pressure in the hover mode. On helicopters with turboprop engines, as a rule, fans are installed to cool the main gearbox, oil coolers, generators and other units. Part of the power of the Noxl motor is consumed to drive the fans.
Part of the engine power is spent on overcoming friction in the transmission connecting the engine to
screws N TP, for the rotation of the Npv tail rotor and for the drive of pumps of the hydraulic system and other units
Na.
Thus, the power transmitted to the rotor is less than the effective power
Ne developed on the motor shaft.
If we subtract costs from the effective power, we obtain the available rotor power Np
Np \u003d Ne.- Noxl. - Ntp - Npv - Nа
For various helicopters, Np is 75-85% Ne.
In other words, the power losses for cooling, transmission, steering gear and drive units are
15-25% of effective engine power.
Effective engine power and available rotor power depend on speed and altitude
flight, however, due to the low flight speeds of the helicopter, the effect of speed on Ne and Np can be neglected.
The nature of the change in the available power from the flight altitude depends on the type of engine and is determined
its altitude characteristic (Fig. 1.61).

It is known that the power of a piston engine without a supercharger, at constant speed with an increase of
the height falls due to a decrease in the weight charge, the air-fuel mixture entering the cylinders. Similarly, the power transmitted to the rotor changes (Fig. 1.61 / a).
The power of a piston engine equipped with a single-speed supercharger increases to the calculated height as it rises to the height due to an increase in the weight charge of the air-fuel mixture due to a decrease in the ambient temperature and an improvement in cylinder blowing. By gradually opening the blower damper, the boost pressure is kept constant up to the design height. At the design height, the air damper opens fully and the engine power reaches its maximum. Above the design height, the effective power, and hence the available power of the main rotor, decreases in the same way as for an engine without a supercharger (Fig. 1.61, b).

For an engine with a two-speed supercharger, the nature of the change in effective and available power versus flight altitude is shown in Fig. 1.61, c.
For a turboprop engine, the nature of the dependence of the available power of the main rotor on the flight altitude is shown in Fig. 1.61, d. The increase in the power of the turboprop engine to a certain height is explained by the adopted control system, which ensures an increase in the temperature of the gases in front of the turbine to a certain height.

0

Design coursework

Light helicopter

1 Development of tactical and technical requirements. 2

2 Calculation of the parameters of the helicopter. 6

2.1 Calculation of the mass of the payload. 6

2.2 Calculation of the parameters of the helicopter main rotor. 6

2.3 Relative air densities on static and dynamic ceilings 8

2.4 Calculation of the economic speed at the ground and at the dynamic ceiling. 8

2.5 Calculation of the relative values \u200b\u200bof the maximum and economic horizontal flight speeds on the dynamic ceiling. ten

2.6 Calculation of the permissible ratios of the coefficient of thrust to the filling of the rotor for the maximum speed at the ground and for the economic speed at the dynamic ceiling. ten

2.7 Calculation of the thrust coefficients of the main rotor at the ground and on the dynamic ceiling 11

2.8 Calculation of the filling of the rotor. 12

2.9 Determination of the relative increase in rotor thrust to compensate for the aerodynamic drag of the fuselage and horizontal tail. 13

3 Calculation of the power of the propulsion system of the helicopter. 13

3.1 Power calculation when hanging from a static ceiling. 13

3.2 Calculation of power density in level flight at maximum speed. 14

3.3 Calculation of specific power in flight on a dynamic ceiling with economic speed. 15

3.4 Calculation of power density in flight near the ground at economic speed in case of failure of one engine during takeoff. 15

3.5 Calculation of specific reduced powers for different cases of flight 16

3.5.1 Calculation of the specific reduced power when hovering on a static ceiling 16

3.5.2 Calculation of the specific reduced power in level flight at maximum speed. 16

3.5.3 Calculation of the specific reduced power in flight at the dynamic ceiling with economic speed .. 17

3.5.4 Calculation of specific reduced power in flight near the ground with economic speed in case of failure of one engine. eighteen

3.5.5 Calculation of the required power of the propulsion system. 19

3.6 Choice of engines. 19

4 Calculation of fuel mass. twenty

4.1 Calculation of the cruising speed of the second approximation. twenty

4.2 Calculation of specific fuel consumption. 22

4.3 Calculation of fuel mass. 23

5 Determination of the mass of components and assemblies of the helicopter. 24

5.1 Calculation of the mass of the rotor blades. 24

5.2 Calculation of the mass of the main rotor hub. 24

5.3 Calculation of the mass of the booster control system. 25

5.4 Calculation of the mass of the manual control system. 25

5.5 Calculation of the mass of the main gearbox. 26

5.6 Calculation of the mass of the tail rotor drive units. 27

5.7 Calculation of the mass and basic dimensions of the tail rotor. thirty

5.8 Calculation of the mass of the propulsion system of the helicopter. 32

5.9 Calculation of the mass of the fuselage and helicopter equipment. 32

5.10 Calculation of the second approximation helicopter take-off mass. 35

6 Description of the layout of the helicopter. 36

References .. 39

1 Development of tactical and technical requirements

The designed object is a light single-rotor helicopter with a maximum take-off weight of 3500 kg. We select 3 prototypes in such a way that their maximum take-off weight is in the range of 2800-4375 kg. The prototypes are light helicopters: Mi-2, Eurocopter EC 145, Ansat.

Table 1.1 shows their tactical and technical characteristics required for the calculation.

Table 1.1- Tactical and technical characteristics of prototypes

Helicopter
Main rotor diameter, m
Fuselage length, m
Empty weight, kg
Flight range, km
Static ceiling, m
Dynamic ceiling, m
Maximum speed, km / h
Cruising speed, km / h
Fuel weight, kg
Power point	2 GTE Klimov GTD-350	2 TVD Turbomeca	Whitney РW-207K
Engine power, kW

Figures 1.1, 1.2 and 1.3 show prototype schematics.

Figure 1.1 - Diagram of the Mi-2 helicopter

Figure 1.2 - Diagram of the Eurocopter EC 145 helicopter

Figure 1.3 - Diagram of the Ansat helicopter

From the tactical and technical characteristics and prototype schemes, we determine the average values \u200b\u200bof the values \u200b\u200band obtain the initial data for the design of the helicopter.

Table 1.2 - Initial data for helicopter design

Maximum takeoff weight, kg
Empty weight, kg
Maximum speed, km / h
Flight range, km
Static ceiling, m
Dynamic ceiling, m
Cruising speed, km / h
Number of rotor blades
Number of tail rotor blades
Fuselage length, m
Load on the area swept away by the rotor, H / m 2

2 Calculation of helicopter parameters

2.1 Calculation of the payload mass

Formula (2.1.1) to determine the mass of the payload:

where m mg is the mass of the payload, kg; m eq is the mass of the crew, kg; L - flight range, km; m 01 - maximum takeoff weight of the helicopter, kg.

Payload weight:

2.2 Calculation of the parameters of the helicopter main rotor

Radius R, m, the main rotor of a single-rotor helicopter is calculated by the formula (2.2.1):

, (2.2.1)

where m 01 - 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 rotor, p \u003d 3.14.

We take the radius of the rotor equal R= 7.2 m.

Determine the value of the peripheral speed wR the ends of the blades from the diagram shown in Figure 3:

Figure 3 - Diagram of the dependence of the end speed of the blade on the flight speed for constant values M 90 and μ

When V max \u003d 258 km / h wR = 220 m / s.

Determine the angular velocity w, s -1, and the main rotor speed according to the formulas (2.2.2) and (2.2.3):

2.3 Relative air densities on static and dynamic ceilings

The relative air densities on static and dynamic ceilings are determined by formulas (2.3.1) and (2.3.2), respectively:

2.4 Calculation of economic speed at the ground and at the dynamic ceiling

The relative area is determined S e of the equivalent harmful plate according to the formula (2.4.1):

where S E is determined from Figure 4.

Figure 4 - Change in the area of \u200b\u200bthe equivalent harmful plate of various transport helicopters

We accept S E \u003d 1.5

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

where I - induction coefficient:

I =1,02+0,0004V max = 1,02+0,0004258=1,1232 ,

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

2.5 Calculation of the relative values \u200b\u200bof the maximum and economic horizontal flight speeds on the dynamic ceiling

The calculation of the relative values \u200b\u200bof the maximum and economic horizontal flight speeds on the dynamic ceiling is carried out according to the formulas (2.5.1) and (2.5.2), respectively:

; (2.5.1)

. (2.5.2)

2.6 Calculation of the permissible ratios of the coefficient of thrust to the filling of the rotor for the maximum speed at the ground and for the economic speed at the dynamic ceiling

Since the formula (2.6.1) for the ratio of the permissible thrust coefficient to the filling of the rotor for the maximum speed at the ground has the form:

Formula (2.6.2) for the ratio of the permissible thrust coefficient to the rotor filling for the economic speed on the dynamic ceiling:

2.7 Calculation of the thrust coefficients of the main rotor at the ground and on the dynamic ceiling

The calculation of the rotor thrust coefficients at the ground and on the dynamic ceiling is carried out according to formulas (2.7.1) and (2.7.2), respectively:

2.8 Calculation of the filling of the main rotor

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

As calculated filling value s the main rotor value is taken from condition (2.8.3):

we accept.

Chord length b and elongation l rotor blades will be equal:

2.9 Determination of the relative increase in rotor thrust to compensate for the aerodynamic drag of the fuselage and horizontal tail

The relative increase in the rotor thrust to compensate for the aerodynamic drag of the fuselage and horizontal tail is taken.

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

3.1 Power calculation when hanging from a static ceiling

The specific power required to drive the main rotor in hovering mode on the statistical ceiling is calculated by the formula (3.1.1)

where N H st is the required power, W;

Throttle characteristic, which depends on the height of the static ceiling and is calculated by the formula (3.1.2)

m 0 - takeoff weight, kg;

g - free fall acceleration, m / s 2;

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

D Art - the relative density of air at the height of the static ceiling;

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

Relative increase in rotor thrust to balance the aerodynamic drag of the fuselage:

3.2 Calculation of power density in level flight at maximum speed

The specific power required to drive the main rotor in level flight at maximum speed is calculated by the formula (3.2.1)

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

Relative equivalent hazardous plate;

Induction coefficient determined by the formula (3.2.2)

3.3 Calculation of power density in flight on a dynamic ceiling with economic speed

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

where is the relative density of air on the dynamic ceiling;

Economic speed of the helicopter on the dynamic ceiling;

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

The specific power required to continue takeoff at an economic speed in case of failure of one engine is calculated by the formula (3.4.1)

where is the economic speed at the ground;

3.5 Calculation of specific reduced powers for different cases of flight

3.5.1 Calculation of the specific reduced power when hovering on a static ceiling

The calculation of the specific reduced power when hovering on a static ceiling is carried out according to the formula (3.5.1.1)

where is the specific throttle characteristic:

x 0 - power utilization factor of the propulsion system in hover mode. Since the mass of the projected helicopter is 3.5 tons,;

3.5.2 Calculation of the specific reduced power in level flight at maximum speed

The calculation of the specific reduced power in level flight at maximum speed is carried out according to the formula (3.5.2.1)

where is the power utilization factor at maximum flight speed,

Throttle characteristics of engines depending on flight speed:

3.5.3 Calculation of the specific reduced power in flight at the dynamic ceiling with economic speed

The calculation of the specific reduced power in flight on a dynamic ceiling with an economic speed is carried out according to the formula (3.5.3.1)

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

and - the degree of throttling of the motors, depending on the height of the dynamic ceiling H and flight speed V din in accordance with the following throttling characteristics:

3.5.4 Calculation of specific reduced power in flight near the ground with economic speed in case of failure of one engine

The calculation of the specific reduced power in flight near the ground with economic speed in case of failure of one engine is carried out according to the formula (3.5.4.1)

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

The degree of engine throttling in emergency operation;

Number of helicopter engines;

The degree of engine throttling when flying near the ground at economic speed:

3.5.5 Calculation of the required power of the propulsion system

To calculate the required power of the propulsion system, the value of the specific reduced power is selected from the condition (3.5.5.1)

Power requirement N the propulsion system of the helicopter will be equal to:

where is the takeoff weight of the helicopter;

g \u003d 9.81 m 2 / s - acceleration of gravity;

3.6 Engine selection

We accept two gas turbine engines GTD-1000T with a total power of 2 × 735.51 kW. The condition is met.

4 Calculation of fuel mass

4.1 Calculation of the cruising speed of the second approach

We take the value of the cruising speed of the first approximation.

Since we calculate the induction coefficient by the formula (4.1.1):

We determine the specific power required to drive the main rotor in flight in cruise mode according to the formula (4.1.2):

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

Power change factor depending on flight speed, calculated by the formula:

We calculate the cruising speed of the second approach:

Determine the relative deviation of the cruising speeds of the first and second approximations:

Since we are refining the cruising speed of the first approximation, it is taken equal to the calculated speed of the second approximation. Then we repeat the calculation by formulas (4.1.1) - (4.1.5):

We accept.

4.2 Calculation of specific fuel consumption

We calculate the specific fuel consumption by the formula (4.2.1):

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

The coefficient of change in specific fuel consumption depending on the flight speed, which is determined by the formula (4.2.2):

Specific fuel consumption in takeoff mode,;

Coefficient of change in specific fuel consumption depending on temperature,

Coefficient of change in specific fuel consumption depending on the flight altitude,;

4.3 Calculation of fuel mass

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

, (4.3.1)

where is the specific power consumed at cruising speed;

Cruising speed;

Specific fuel consumption;

L - range of flight;

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

5.1 Calculation of the mass of the rotor blades

The mass of the rotor blades is determined by the formula (5.1.1):

where R - the radius of the rotor;

s - filling the rotor;

5.2 Calculation of the mass of the main rotor hub

The main rotor hub mass is calculated by the formula (5.2.1):

where is the weight coefficient of bushings of modern designs,;

The coefficient of influence of the number of blades on the mass of the sleeve, which is calculated by the formula (5.2.2):

Centrifugal force acting on the blade, which is calculated by the formula (5.2.3):

5.3 Calculating the mass of the booster control system

The booster control system includes a swashplate, hydraulic boosters, and a hydraulic control system for the main rotor. The calculation of the mass of the booster control system is carried out according to the formula (5.3.1):

where b - blade chord;

The weight coefficient of the booster control system, which can be taken equal to 13.2 kg / m 3;

5.4 Calculating the mass of the manual control system

The calculation of the mass of the manual control system is carried out according to the formula (5.4.1):

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

5.5 Calculating the mass of the main gearbox

The mass of the main gearbox depends on the torque on the main rotor shaft and is calculated using the formula (5.5.1):

where is the weight coefficient, the average value of which is 0.0748 kg / (Nm) 0.8.

The maximum torque on the rotor shaft is determined through the reduced power of the propulsion system N and the rotor speed w:

where is the power utilization factor of the propulsion system, the value of which is taken depending on the takeoff weight of the helicopter Since, then;

5.6 Calculation of the mass of the tail rotor drive units

The tail rotor thrust is calculated:

where is the torque on the rotor shaft;

The distance between the axes of the main and tail rotor.

Distance L between the axes of the main and tail rotor is equal to the sum of their radii and clearance d between the ends of their blades:

where is the gap taken equal to 0.15 ... 0.2 m;

Tail rotor radius. Since then

The power spent on the rotation of the tail rotor is calculated by the formula (5.6.3):

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

The torque transmitted by the steering shaft is:

where is the frequency of rotation of the steering shaft, which is found by the formula (5.6.5):

The torque transmitted by the transmission shaft at a speed of rpm is:

Weight m in the transmission shaft:

where is the weight factor for the transmission shaft, which is 0.0318 kg / (Nm) 0.67;

The mass of the intermediate gear is determined by the formula (5.6.9):

where is the weight factor for the intermediate gearbox equal to 0.137 kg / (Nm) 0.8.

Weight of the tail gear that rotates the tail rotor:

where is the weighting factor for the tail gear, the value of which is 0.105 kg / (Nm) 0.8;

5.7 Calculation of the mass and basic dimensions of the tail rotor

The mass and main dimensions of the tail rotor are calculated depending on its thrust.

The tail rotor thrust coefficient is:

The filling of the tail rotor blades is calculated in the same way as for the main rotor:

where is the admissible value of the ratio of the thrust coefficient to the filling of the tail rotor,

The chord length and the relative elongation of the tail rotor blades are calculated by the formulas (5.7.3) and (5.7.4):

where is the number of rotor blades,

The mass of the tail rotor blades is calculated using the empirical formula (5.7.5):

The value of the centrifugal force acting on the tail rotor blades and perceived by the hub joints is calculated by the formula (5.7.6):

The mass of the tail rotor hub is calculated using the same formula as for the main rotor:

where is the centrifugal force acting on the tail rotor blade;

The weight factor for the sleeve, which is 0.0527 kg / kN 1.35;

The weighting factor depending on the number of blades and calculated by the formula (5.7.8):

5.8 Calculation of helicopter propulsion system mass

The specific gravity of the helicopter propulsion system is calculated using the empirical formula (5.8.1):

, (5.8.1)

where N - power of the propulsion system;

The mass of the propulsion system will be equal to:

5.9 Calculation of the mass of the fuselage and helicopter equipment

The mass of the helicopter fuselage is calculated by the formula (5.9.1):

where is the area of \u200b\u200bthe washed fuselage surface:

Table 5.8.1

Takeoff weight of the first approximation;

Coefficient equal to 1.1;

Weight fuel system:

where is the mass of fuel spent on the flight;

The weighting factor for the fuel system is 0.09;

The mass of the helicopter landing gear is:

where is the weighting factor depending on the chassis design. Since the designed helicopter has a retractable landing gear,

The mass of the helicopter electrical equipment is calculated using the formula (5.9.5):

where is the distance between the axes of the main and tail rotor;

The number of rotor blades;

R - the radius of the rotor;

Elongation of the main rotor blades;

and - weighting factors for electrical wires and other electrical equipment,

Weight of other helicopter equipment:

where is the weighting factor, the value of which is 1.

5.10 Calculation of the second approximation helicopter take-off mass

The mass of an empty helicopter is equal to the sum of the masses of the main units:

Takeoff weight of the second approximation helicopter:

We determine the relative deviation of the masses of the first and second approximations:

The relative deviation of the masses of the first and second approximations satisfies the condition. This means that the calculation of the parameters of the helicopter is correct.

6 Description of the layout of the helicopter

The projected helicopter is made according to a single-rotor scheme with a tail rotor, two gas turbine engines and a skid landing gear.

The fuselage is semi-monocoque. The load-bearing structural elements of the fuselage are made of aluminum alloys and have an anti-corrosion coating. The nose part of the fuselage with the cockpit canopy and the nacelle hoods are made of a composite material based on fiberglass. The cockpit has two doors, the glass is equipped with an anti-icing system and wipers. The left and right doors of the cargo-passenger compartment and an additional hatch in the rear of the fuselage ensure the convenience of loading patients and victims on stretchers, as well as bulky cargo. The skid chassis is made of solid bent metal tubes. The springs are covered with fairings. The tail support prevents the tail rotor from touching the landing pad. The main and tail rotor blades are made of composite materials based on fiberglass and can be equipped with an anti-icing system. The four-bladed rotor hub is non-hinged, made of two crossing fiberglass beams, to each of which two blades are attached. Two-blade tail rotor hub with common horizontal joint. Fuel tanks with a total capacity of 850 liters are located in the fuselage floor. Helicopter control system is fly-by-wire without mechanical wiring, with four-fold digital redundancy and double-redundant independent power supply. Modern flight and navigation equipment provides flights in simple and difficult weather conditions, as well as flights under VFR and IFR rules. Control of the parameters of helicopter systems is carried out using the onboard information system control BISK-A. The helicopter is equipped with a warning and alarm system.

The helicopter can be equipped with a water landing system, as well as fire extinguishing and chemical spraying systems.

The power plant is two gas turbine engines GTD-1000T with a total power of 2 × 735.51 kW. The engines are mounted on the fuselage in separate nacelles. Side air intakes are equipped with dust protection devices. The side panels of the nacelles are hinged to form service platforms. The engine shafts extend at an angle to the center gearbox and the accessory compartment. The exhaust nozzles of the engines are angled outward at an angle of 24 ". For protection from sand, filters are installed that prevent by 90% the penetration of particles with a diameter of more than 20 microns into the engine.

The transmission consists of motor gearboxes, intermediate gearboxes, bevel gearboxes, main gearbox, auxiliary power unit shaft and gearbox, steering wheel shaft and bevel gearbox. The transmission system uses titanium alloys.

The electrical system consists of two isolated circuits, one of which is powered by an alternator generating a voltage of 115-120V, and the second circuit is powered by a generator direct current with a voltage of 28V. The generators are driven by the main rotor gearbox.

The control is duplicated, with rigid and cable wiring and hydraulic boosters driven from the main and backup hydraulic systems. The AP-34B four-channel autopilot provides stabilization of the helicopter in flight in terms of roll, heading, pitch and altitude. The main hydraulic system provides power to all hydraulic units, and the redundant one - only hydraulic boosters.

The heating and ventilation system supplies heated or cold air to the cockpits and passengers, the anti-icing system protects the rotor and tail rotor blades, front cockpit windows and engine air intakes from icing.

Communication equipment includes command HF band - "Yurok", intercom SPU-34.

Bibliography

1. Designing helicopters / V.S. Krivtsov, L.I. Losev, Ya.S. Karpov. - Textbook. - Kharkiv: Nat. aerospace. un-t "Khark. Aviation Institute ", 2003. - 344s.
2. www.wikipedia.ru
3. www.airwar.ru
4. narod.ru
5. http://www.vertolet-media.ru/helicopters/kvz/ansat/

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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 estimated radius, thrust and efficiency of the propeller.

The initial data of the first stage are:

It is advisable to calculate using international system SI units.

If the rotor speed is set in rpm, then using the formula

It needs to be converted to radians per second.

The design speed of the screw V is selected depending on the purpose of the ALS and the value

Where K is the calculated maximum aerodynamic quality of an ultralight aircraft; m is the takeoff weight.

When E
With values \u200b\u200bof E from 1000 to 1500 for the design speed of the propeller V o it is advisable to take the cruising speed V cr.

And with values \u200b\u200bof E more than 1500 for the design speed, you can take 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 design speed V leads to a decrease in the maximum flight speed, and its increase leads to a deterioration in the take-off characteristics of an ALS.

Based on the condition of avoiding transonic flows, the blade tip velocity u. should not exceed 230 ... 250 m / s and only in certain cases, when the gearbox is not supposed to be installed, and the propeller cannot remove the full power of the engine, up to 260 m / s is allowed.

The initial value of the desired efficiency is higher than 0.8 for high-speed and higher than 0.75 for non-high-speed ALS, it is impractical to choose, since in practice this is impracticable. The step of decreasing it can initially be taken equal to 0.05 and then decreased 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, this means that the initially specified efficiency cannot be obtained. Is it necessary to decrease by the selected value and repeat the cycle, starting with the definition of a new value? ...

The cycle is repeated until the condition RR ГР is fulfilled. If this condition is met, then further checks are 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 an amount less than the previous one, and the cycle is repeated.

After determining the values \u200b\u200bof the radius R, thrust P and the efficiency of the propeller, you can proceed to the second stage of the calculation.

The second stage of calculating the propeller

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

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

For calculations, the propeller blade (Fig. 6.7)

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

It is divided into a finite number of sections with dimensions bR .. In this case, it is assumed that there is no swirl of the blade at each selected section, and the velocities and angles of flow along the radius do not change. With a decrease in R, that is, with an increase in the number of considered sections, 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 split into 10 sections with R \u003d 0.1r. In this case, it can be assumed that the first three sections, counted from the screw axis, they do not give thrust, while consuming 4 ... 5% of engine power. Thus, it is advisable to carry out the calculation for seven sections from \u003d 0.3 to \u003d 1.0.

Additionally set:

Initially, the maximum relative blade width for wooden propellers should be set equal to 0.08.

The law of variation of the blade width and relative thickness can be specified in the form of a formula, table or drawing of the propeller (Fig. 6.1).

Fig 6.1 Fixed Pitch Propeller

The angles of attack of the selected sections are set by the designer, taking into account the inverse aerodynamic quality. The values \u200b\u200bof the coefficients Cy and K \u003d 1 / are taken from the graphs in Fig. 6.4 and 6.5, taking into account the selected profile and the values \u200b\u200bof and.

Fig 6.4 Dependence of the lift coefficient and reverse aerodynamic quality on the angle of attack and relative thickness for the ВС-2 airfoil

Fig 6.5 Dependence of the lift coefficient and reverse aerodynamic quality on the angle of attack and relative thickness for the RAF-6 airfoil

The first step in the second stage of the calculation is to determine the flow velocity V in the plane of the screw. 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.

The assumed values \u200b\u200bof 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 propeller differs from the available one 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 blade width, taking into account that the power consumption and the propeller thrust vary approximately in proportion to the chord of the blade. The diameter, relative thicknesses and angles of installation of the sections remain unchanged.

In some cases, it may turn out that the power consumed by the propeller and its thrust are more than 20% different from those assumed based on 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 \u200b\u200bof the coefficients k R and k P are determined. These coefficients show how many times it is necessary to change the assumed radius and thrust of the screw, 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 power

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

The third stage of calculating the propeller

The purpose of the third stage is to check the strength of the propeller. This stage of the calculation is reduced to determining the loads acting in different 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 with a section \u003d 0.3 with a step of 0.1 to \u003d 1.

Each highlighted element of the blade with mass m at radius r (Fig. 6.11) is acted upon by an inertial force

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

And elementary aerodynamic force F. Under the influence of these forces, from all elementary sections, the blade is stretched and bent. As a result, tensile-compressive stresses arise in the blade material. The most loaded (Fig. 6.12)

Figure 6.12 Distribution of stresses in the section of the propeller blade

It turns out that the fibers of the rear side of the blade, since in these fibers the stresses from inertial forces and bending moment add up. To ensure the specified strength, it is necessary that the actual stresses in these areas farthest from the blade section axis are less than the allowable ones for the selected material.

The values \u200b\u200bof the radii r required for calculations, on which the considered sections of the blade, 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, the following are determined in sequence:

The fill factor k 3 depends on the profile used for the screw. For the most common screw profiles it equals: Clark-Y- k 3 \u003d 0.73; BC-2- k 3 \u003d 0.7 and RAF-6- k 3 \u003d 0.74.

After calculating the values \u200b\u200bof P in, at each separate section, they are summed from the free end of the blade to the section under consideration. By dividing the total force acting in each considered section by the area of \u200b\u200bthis section, we can obtain tensile stresses from inertial forces.

Bending stresses of the blade 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 trailing 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 ultimate 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, increasing the relative blade width, repeat all three stages of the calculation.

If the relative blade width exceeds 0.075 for screws made of hard wood, and 0.09 for screws made of soft wood, then the third stage of the calculation is unnecessary, since the required strength will certainly be ensured.

based on materials: PI Chumak, VF Krivokrysenko "Calculation and design of an ALS"

Introduction

Helicopter design is a complex, evolving process that is divided into interrelated design stages and stages. The aircraft being created must satisfy technical requirements and comply with the technical and economic characteristics specified in the design specification. Technical task contains the initial description of the helicopter and its flight performance characteristics that ensure 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-design studies, during which 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, the aerodynamic scheme is selected, the appearance of the helicopter is formed and the main parameters are calculated to ensure the achievement of the specified flight performance characteristics. These parameters include: the mass of the helicopter, the power of the propulsion system, the dimensions of the main and tail rotor, the mass of the fuel, the mass of instrumental and special equipment. The calculation results are used in the development layout diagram helicopter and drawing up a centering sheet to determine the position of the center of mass.

The design of individual units and assemblies of the helicopter, taking into account the selected technical solutions, is carried out at the stage of developing a technical design. In this case, the parameters of the designed units must satisfy the values \u200b\u200bcorresponding to draft design... Some of the parameters can be refined to optimize the design. During technical design, aerodynamic strength and kinematic calculations of units, selection of structural materials and structural schemes are performed.

At the stage of the working project, the design of working and assembly drawings of the helicopter, specifications, picking lists and other technical documentation is carried out in accordance with the accepted standards.

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

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

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

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

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

, 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 rotor,

p =3,14.

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

m.

We take the radius of the rotor equal R = 7.9

Angular velocity w , s -1, the rotation of the rotor is limited by the value of the peripheral speed w R blade ends, 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 economic speed at the ground and at the dynamic ceiling

The relative area is determined

equivalent harmful plate: where S eh = 2.5

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

,

where I

km / h.

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

,

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

km / h.

2.4 The relative values \u200b\u200bof the maximum and economic at the dynamic ceiling of the horizontal flight speeds are calculated:

, ,

where V max \u003d 250 km / h and V dean \u003d 182.298 km / h - flight speed;

w R \u003d 232 m / s - the peripheral speed of the blades.

2.5 Calculation of the admissible thrust to rotor filling ratio for the maximum speed at the ground and for the economic speed at the dynamic ceiling:

prip

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

, , , .

2.7 Calculation of the rotor filling:

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

; .

As calculated filling value s the rotor is adopted greatest value of s Vmax and s V dean .

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

where is the takeoff weight of the helicopter, kg;

g - acceleration due to gravity, equal to 9.81 m / s2;

p is the specific load on the area swept by the rotor,

The value of the specific load p on the area swept by the screw is selected according to the recommendations presented in the work / 1 /: where p \u003d 280

m.

We take the radius of the rotor equal to R \u003d 7.9

The angular speed w, s-1, of rotation of the main rotor is limited by the value of the peripheral speed wR of the ends of the blades, which depends on the take-off mass of the helicopter and was wR \u003d 232 m / s.

s-1.

rpm

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