Main Rotor Coning Axis Tilt

With variation of the flapping angles the plane of rotation and the coning axis deflect backward and to the side in the direction of the advancing blade through the angle т (Figure 38a). As a result of the tilt of the coning axis backward by the angle a^, there is an increase of the blade flap­ping angle to 8 = + a^ at the 180° azimuth and a reduction to 8 = a^ – a^

at the 0° azimuth (Figure 38b). Tilting of the cone axis to the side by the angle b^ leads to change of the flapping angles: at the azimuth 90° 8 = ад – b^; at the azimuth 270° 8 = a. Q + b^ (Figure 38c).

Main Rotor Coning Axis Tilt

Figure 38. Blade flapping motions and tilt of main rotor cone axis. 1 – cone for p = 0; 2 – cone for у > 0.

Tilting of the cone axis backward by the angle a^ leads to deflection /55

through the same angle of the thrust vector and the formation of the longitud­inal thrust component H (Figure 39a). This force is the projection of the main rotor thrust on the hub rotation plane. Since it is directed aft, it is a drag force and is analogous to the induced drag of an airplane wing. The

Main Rotor Coning Axis Tilt

Figure 39. Main rotor thrust force components.

larger the flapping motions, the larger the backward tilt of the cone axis and the larger the longitudinal force H resisting helicopter forward motion. Consequently, the flapping motions in the forward flight regime must be restricted.

If the deflected thrust T is projected on the hub axis, we obtain the force required for helicopter flight

Ty =.T cos au

In view of the smallness of the angle a^(2 – 3°) we can take a^ « 1. /56

Then T и T.


The sideward tilt of the cone axis (Figure 39b) leads to the appearance of the side force Sg, which is the projection of the main rotor thrust on the hub rotation plane

S = T sin b.• s 1

Since this force is directed to the left, this direction is unfavorable for single-rotor helicopters. Therefore, the blade flapping motions must be restricted in order to alter the sideward tilt of the cone angle from the

left to the right. Moreover, restriction of the flapping motions is also necessary to reduce main rotor vibrations.


§ 54. General Characteristics of the Descent Regime /10{

Rectilinear flight at constant velocity along an inclined trajectory is termed the helicopter descent regime with operating engine. A characteristic of this regime is the possibility of controlling the vertical rate of descent and the speed along the trajectory by varying the power supplied to the main rotor.

In this regime the following forces act on the helicopter: weight,

main rotor thrust, parasite drag, and tail rotor thrust (Figure 70).

The helicopter motion takes place along a trajectory which is inclined to the horizon at the angle 0, termed the descent angle.

We resolve the weight force G and the main rotor thrust force T into components perpendicular and parallel to the flight trajectory. We obtain the weight force components G^ = G cos 0 and G^ = G sin 0. The main rotor thrust components will be the lift force Y perpendicular to the flight trajectory, and the force P parallel to this trajectory. The force P may be directed


either opposite the helicopter motion direction or in the direction of this motion.

The direction of the force P^ depends on the position of the cone axis and the main rotor plane of rotation. If the cone axis is perpendicular to


Figure 70. Forces acting on helicopter in descent.

the trajectory, then P = 0. If the cone axis is inclined aft relative to the perpendicular, then P^ will be directed opposite the helicopter motion and will retard this motion. If the cone axis is tilted forward, the force P^ will be directed along the motion and together with the component G2 will be a propulsive force. The cone axis direction is connected with the position of the rotor plane of rotation and, consequently, with the main rotor angle of attack. Most frequently, the main rotor angle of attack is close to zero or has a small negative value. During flight with a large descent angle, the angle of attack is positive and the force Px is directed opposite the motion.

Steady state descending flight is possible under the following conditions

The first condition assures rectilinear flight and constant descent angle. Consequently, by varying the lift force Y we can alter the helicopter descent angle. When the lift force is increased, the descent angle decreases, and vice versa. The second condition assures constant helicopter speed. Let us compare these conditions with those for climb along an inclined trajectory.

The first condition is the same for descent and climb. The second condi­tions differ fundamentally from one another: in climb, the propulsive force

is the main rotor thrust component P, while in descent this force will be the weight force component G^. The thrust force component P^ may be either a part of the propulsive force or a part of the retarding force, depending on the position of the main rotor cone axis. The third and fourth descent conditions are analogous to the same conditions for the other flight regimes.


Подпись:Подпись: /178§ 79. General Analysis of Vibrations

Periodic reciprocating motions of the elements of an elastic system can be termed vibrations or oscillations. The problem of helicopter vibrations remained unresolved for a long time ; therefore, large-scale helicopter flying was not possible. Experimental flights performed prior to the middle 1940’s frequently terminated in accidents as a result of severe vibrations.

Several hundred different vibrations of individual parts and of the entire helicopter as a unit can he counted on a helicopter.

Parameters of oscillatory motions. We consider an elastic plate with one end clamped and a small weight on the other end (Figure 109a). If the end with the weight is deflected and then released, oscillations of the plate develop. This will be the simplest example of vibrations (Figure 109b). The oscillatory motions are characterized by three basic parameters: period,

frequency, and amplitude. The period is the time for a complete oscillation (T).

Frequency is the number of periods per unit time

/ if

Amplitude is the largest deviation of an oscillating point from the neutral position

Подпись: Figure 109. Parameters of vibrational motion. (y).

Подпись: subdivided into forced, natural, and self-

Oscillatory motion modes. With regard to nature of onset, oscillatory motions can be excited.

Forced vibrations are those which are caused by periodic external forces. Such forces are exciting. Forced vibrations take place with a frequency equal to that of the exciting forces. Damping forces or forces which attenuate the vibrations arise during all vibrations. The damping forces may be either internal or external. The internal damping forces arise as a result of elasticity of the material itself from which the structure is fabricated. External damping forces arise as a result of resistance of the medium in which the vibrations take place. The larger the damping forces, the faster the vibrations decay.

Natural vibrations are those which continue after termination of the action of the disturbing forces. The basic characteristic of natural vibrations is that each structure has a very definite vibration frequency, which is independent of the exciting force and is determined by the mass and stiffness of the structure.

The larger the mass of the structure, the lower the natural vibration frequency. The greater the structure stiffness, the higher the natural vibration frequency.

With regard to nature of the amplitude variation, vibrations can be divided into damped and increasing. If the amplitude decreases, in the course of time, the vibrations will be damped. Natural vibrations are always

damped. If the amplitude increases with time, the vibrations will be increasing. Increasing vibrations develop at resonance.

Resonance is coincidence of the frequency of the exciting forces with /179

the frequency of the natural vibrations of the structure. Vibrations of helicopter parts are most often forced vibrations.


§ 1. Brief IWstory of Helicopter Development


The idea of creating a flying apparatus with an aerial screw, which ]_3

created a lifting force, was suggested for the first time in 1475 by Leonardo de Vinci. This idea was too premature owing to the impossibility of technical realization of the project and opposition by religious opinions. The idea was buried in the archives. A sketch and description of this flying apparatus was displayed in the Milan library and published at the end of the 19^ century.

In 1754, M. V. Lomonosov substantiated the possibility of creating a heavier than air flying apparatus and built a model of a dual rotor helicopter with the rotors arranged coaxially.

In the 19^ century many Russian scientists and engineers developed projects for flying machines with main rotors. In 1869, electrical engineer A. N. Lodygin proposed a projected helicopter powered by an electric motor.

In 1870 the well known scientist M. A. Rykachev was engaged in the develop­ment of propellers.

Metallurgist-scientist D. K. Chernov devised a helicopter scheme with longitudinal, transverse, and coaxially arranged rotors.

Numbers in the margin indicate pagination in the original foreign text.

At the end of the 19^ century, the development of flying machines engaged the attention of the distinguished Russian scientists D. I. Mendeleyev, К. E. Tsiolkovskiy, N. Ye. Zhukovskiy and S. A. Chaplygin. A period of indepth scientific substantiation of the idea of flight with heavier than air flying machines began.

A close associate of N. Ye. Zhukovskiy, B. N. Yur’yev, in 1911 proposed a well-developed single rotor helicopter project with a propeller for direc­tional control and also a fundamental arrangement for helicopter control, that of automatically warping the main rotor. After the Great October Socialist Revolution, when our country began to develop its own aviation industry, work on the creation of a helicopter was continued.

In 1925, in TSAGI, an experimental group for special constructions was organized under the leadership of B. N. Yur’yev This group was engaged in the development of a helicopter.

In 1930 the first Soviet helicopter was built, the TSAGI 1-EA (Figure 1). LA This helicopter was tested by the engineer responsible for its construction, Aleksey Mikhaylovich Cheremyukhin. Cheremyukhin set a world record altitude of 605 m in this helicopter.



Figure 1. TSAGI 1-EA Helicopter.

In 1948 the single rotor helicopters Mi-1 and Yak-100 were built. As a result of the State trials, the helicopter Mi-1 proved to have the most satis­factory characteristics and it was accepted for mass production.

In 1952 the helicopter Mi-4 was built, which, for that time, had a very large useful load. The same year saw the completion and first flight of the tandem arrangement dual rotor helicopter, the Yak-24, "Flying Wagon" designed by A. S. Yakovlev (Figure 2).


In 1958 the heavy helicopter Mi-6 was constructed which, up to the J_5_

present time, has no equal abroad.

In 1961 the helicopters Mi-2 and Mi-8 (Figure 3), which have gas turbine engines, were built. At the present time they are in mass production and they will gradually replace the Mi-1 and Mi-4 helicopters.

The ability of a helicopter to fly vertically, and the possibility of motion in every direction, makes the helicopter a very maneuverable flying machine, and since it can operate independent of airfields its boundaries of utilization are considerably widened.


Figure 3. Mi-8 single rotor helicopter.

At the present time helicopters are found in more and more wider applica­tion in the national economy. They appear as a basic means of conveyance in locations where it is impossible to utilize ground transport or fixed wing airplanes. Helicopters are utilized in civil construction work and to rescue people and property at times of various natural calamities. Lately helicopters are being widely used in the rural economy. From the examples given, it can be seen that the possibilities of utilizing helicopters as flying machines are far from exhausted.

The Helicopter and its Basic Components

Principles of Flight

A helicopter is a heavier than air flying machine that has a lifting force created by a main rotor according to aerodynamic principles.

The basic components of a helicopter are as follows:

Main rotor. Put in motion by the power plant (engine).

Fuselage. Intended for accomodation of crew, passengers, equipment and cargo.

Landing gear, that is, arrangement intended for movement over the ground J6_ or for parking.

Tail rotor. Provides directional equilibrium and directional control of the helicopter.

Propulsion system which sets in motion the lifting and tail rotors and auxiliary systems.

Transmission transfers the torque from the power plant to the main and tail rotors.

All components of the helicopter are attached to the fuselage or are set in it.

Flight is possible for a flying machine if there is a lifting force counterbalancing its weight. The lifting force of the helicopter originates at the main rotor. By the rotation of the main rotor in the air a thrust force is developed perpendicular to the plane of rotor rotation. If the main rotor rotates in the horizontal plane, then its thrust force T is directed vertically upwards (Figure 4a), that is, vertical flight is possible. The characteristics of the flight depend on the correlation between the thrust force of the main rotor and the weight of the helicopter. If the thrust force equals the weight of the helicopter, then it will remain motionless in the air. If, though, the thrust force is greater than the weight, then the helicopter will pass from being motionless into a vertical climb. If the thrust force is less than the weight, a vertical descent will result.

The plane of rotation of the main rotor with respect to the ground can be inclined in any direction (Figure 4b, c). In this case the rotor will fulfill a two-fold function; its vertical component Y will be the lift force and the horizontal component P — the propulsive force. Under the influence of

The Helicopter and its Basic Components

Figure 4. Principle of flight controls of a helicopter, a – vertical flight; b – horizontal flight forwards; c – horizontal flight backwards.

this force the helicopter moves forward in flight. JJ_

If the plane of the main rotor is inclined backwards, the helicopter will move backwards. (Figure 4c). The inclination of the plane of rotation to the right or to the left causes motion of the helicopter in the corresponding direction.

Classification of Helicopters

The basic classification of helicopter types is that of the number of main rotors and their disposition. According to the number of main rotors, it is possible to classify helicopters as single rotor, dual rotor and multi­rotor types.

Single rotor helicopters appear in many varieties. Helicopters of the single rotor scheme have a main rotor, mounted on the main fuselage and a tail rotor mounted on the tail structure (see Figure 3). This arrangement, which

was developed Ъу B. N. Yur’yev in 1911, provides a name for one classification.

The basic merit of single rotor helicopters is the simplicity of con­struction and the control system. The class of single rotor helicopters includes the very light helicopters (flight weight about 500 kgf), and very heavy helicopters (flight weight greater than 40 tons). Some of the deficien­cies of the single rotor helicopter are:

Large fuselage length;

A significant loss of power due to the tail rotor drive train (7 – 10% of the full power of the engine);

A limited range of permissible centering;

A higher level of vibration (the long transmission shafts, extending into the tail structure, are additional sources of spring oscillations).

Dual rotor helicopters appear in several arrangements.

Rotors arranged in tandem; this is the most prevalent arrangement (Figure 5a)

Rotors in a transverse arrangement (Figure 5b);

A cross connected rotor scheme (Figure 5c);

A coaxial rotor arrangement (Figure 5d).

The basic merits of helicopters with a tandem rotor arrangement are:

Wider range of permissible centering;

Large fuselage volume; which allows it to contain large-sized loads;

Increased longitudinal stability;

Large weight coefficient.

Helicopters with a tandem arrangement of rotors can have one or two engines, which are located in the forward or aft parts of the fuselage. These helicopters have the following serious deficiencies:

Classification of Helicopters

Figure 5. Dual rotor helicopters.

A complicated system of transmission and control; /8

Adverse mutual interaction between the main rotors which causes, in addition, a loss of power;

Complicated landing techniques are required in the autorotation regime of main rotors.

The following advantages are attributed to helicopters with a transverse arrangement of rotors:

Convenient utilization of all parts of the fuselage for crew and passengers, since the engines are located outside the fuselage;

Absence of harmful interaction of one rotor with the other;

Higher lateral stability and controllability of the helicopter;

The presence of an auxiliary wing, where the engines and main rotors are located, allows the helicopter to develop a high speed.

Deficiencies of these helicopters are as follows:

A complicated system of control and transmission;

An increase in size and structure weight due to the presence of the auxiliary wing.

Dual rotor helicopters with cross connected rotors have a considerable advantage over helicopters with transverse rotors; they do not have an auxil­iary wing, which reduces the size and structure weight. But, at the same time, with these advantages there is a deficiency, — a complicated transmission /9

and control system.

These helicopters are not produced in the Soviet Union. They are en­countered, on occasion, abroad.

The basic advantage of dual rotor helicopters with coaxial rotors is their small size. Their disadvantages:

Complicated structure;

Deficient directional stability;

Danger of collision of the rotor blades;

Considerable vibration.

In the Soviet Union, there are only light helicopters with this rotor arrangement.

Multi-rotor helicopters are not widely used in view of their complex construction.

In all dual-rotor helicopters, the main rotors rotate in opposite direc­tions. In this way the mutual reactive moments are balanced, and the necessity of having a tail rotor is eliminated. Thus the power loss from the engine is reduced.