Main Rotor Thrust in Vertical Climb and Vertical Descent

Main Rotor Thrust in Vertical Climb and Vertical Descent Подпись: T = fyFVf.

Main rotor thrust in vertical climb. It was established above that the thrust of the ideal main rotor in the hovering regime is defined by the formulas

The first formula is of a general nature and is applicable for all axial – flow regime cases. The second is applicable only for determining the thrust in the hovering regime.

During vertical climb, the magnitude of the air mass flowrate m^ through the swept area changes. This is seen from the schematic of main rotor motion during vertical climb (Figure 23a). The rotor travels upward with the velocity V. We can say that an undisturbed flow caused by this motion approaches the rotor (principle of reversibility of motion). In the plane of rotor rotation, the flow velocity V^ will be

If the air mass flowrate is defined as m^ = pFV^, then the thrust is

Main Rotor Thrust in Vertical Climb and Vertical Descent

Figure 23. Operation of main rotor in vertical climb.

defined as T = m„V, or T = pFV, V, , and since the equality V, = 2V. is also S dw 1 dw dw x

valid for vertical climb, the thrust will be

T = ^FV1V^-2oFViVl.

Comparing the main rotor thrust T = 2pFV^2 in the hovering regime, and

the thrust T = 2pFVjV^ in the vertical climb regime, we can say that the

thrust in the climbing regime is higher than that in the hovering regime, since

V, > V.. But this conclusion would be valid only if the induced velocity V. lx x

did not change with change of the rotor motion velocity. In actuality, the induced velocity decreases with increase of the translational velocity, which leads to reduction of the main rotor thrust.

This means that the main rotor must develop more thrust during vertical climb than the weight of the helicopter. The dependence of the main rotor thrust on speed can also be explained from the viewpoint of blade element theory. In helicopter hovering, the blade element angle of attack depends on the pitch and the induced flow velocity (Figure 15b).

With increase of the climb velocity, the angle of attack of the main
rotor blade element decreases, and therefore the main rotor thrust coefficient

Main Rotor Thrust in Vertical Climb and Vertical Descent

Figure 24. Operation of main rotor in vertical descent.

decreases, which in turn leads to reduction of the main rotor thrust, since T = CTF (0)#)2 (Figure 23b) .

Main rotor thrust in vertical descent. During vertical descent (Figure 24a), the undisturbed flow approaches the main rotor from below with the velocity V ; therefore, the flow velocity in the plane of rotation of

the main rotor is V, = V. – V, i. e., it will be less than during hovering.

1 і у

Main rotor thrust in vertical descent is defined by the same formula as for vertical climb T ~Cj. F-%jrU* or T = 2pFV V

The main rotor blade element angle of attack is increased during vertical /32 descent by the amount Act as a result of the vertical descent velocity, which leads to increase of the coefficient and of the main rotor thrust (Figure 24b). Two flows are encountered below the rotor: the induced flow,

accelerated by the rotor, and the undisturbed flow created by descent of the

helicopter. Meeting of these two flows leads to the onset of instability of

the vortices, buffeting of the main rotor, and deterioration of control.

In what season of the year can a helicopter climb to the highest altitude and lift the greatest load?

Answer 1» The air density is higher in winter than in summer. With increase of the air density the induced power required for hovering de­creases while the engine power increases. Consequently, in the winter the

excess power AN = N.. – N is greater, which leads to increase of the avaxl req ° ’

static ceiling and lifting capability of the helicopter.

Answer 2. The air density is higher in winter than in summer. Increase

of the air density leads to increase of the power required = m^^F (wR)^.

This means that the excess power AN = N.. – N decreases, and this leads to

avaxl req ’

reduction of the static ceiling and lifting capability of the helicopter.

Answer 3. The air density is higher in winter than in summer. With increase of the flight weight it is necessary to increase the main rotor thrust force, but this involves increase of the reactive moment, which will be the larger, the higher the air density. The conclusion is that in the winter the helicopter must develop more power than in the summer, i. e., the helicopter lifting capability and static ceiling decrease in the winter.

Azimuthal variation of the blade element autorotation conditions in helicopter gliding

Answer 1. During helicopter gliding in the main rotor autorotative regime, the flow conditions about the blade element change continuously. Therefore, the autorotation conditions will also change. The resultant velo­city (=к+ V sin ф) will increase continuously for the advancing blade. This leads to increase of the elementary force AR and to acceleration of the auto­rotation. The resultant velocity of each blade element of the retreating blade decreases and reaches the minimum (W = u – V) at the ф = 270° azimuth. Therefore, the force AR also decreases, and the autorotation will be decelera­ted. Each blade element becomes alternately "driving", then "driven". Most of the elements of the advancing blade will be "driving"; most of those of the retreating blade will be "driven".

Подпись: Да = arctgAnswer 2. During helicopter gliding, the autorotation conditions of each element depend on the blade azimuth. With change of the azimuth there is a change of the element resultant velocity (W=u+V sin ip). At the 90° azimuth this velocity reaches its maximal value, therefore, the angle of attack incre­ment is minimal (Да = arc tg V ^ sin 0/ior + V ^ cos 0) . The force vector AR tilts aft, and the autorotation will be decelerated.

At the 270° azimuth the element resultant velocity is minimal (Да = arc tg

V, sin 0/u – V, cos 0). The forward tilt of the force vector AR will be gl gl

maximal, and the autorotation will be accelerated. The conclusion is that during gliding the retreating blade creates a driving torque and "drives" the advancing blade, which develops a retarding torque.

Answer 3. The blade element characteristics during helicopter gliding are determined by two factors: azimuthal variation of the resultant flow

velocity over the blade element, and the presence of flapping motions and vertical flapping velocity.

At the 90° azimuth the resultant velocity is maximal; the vertical flapping velocity is also maximal and directed upward. The angle


Подпись: Да = arctggl sin 0 – fl

u + V, cos 0

is minimal; therefore, the force vector AR is tilted aft, and the autorotation will be decelerated.

At the 270° azimuth the resultant flow velocity is minimal, and the vertical flapping velocity is maximal, but directed downward. • The angle [4]

is maximal; therefore, the force vector AR is directed forward, and the blade element autorotation will be accelerated.

The conclusion is that the retreating blade develops a driving torque while the advancing blade develops a retarding torque, but the rotor autoro­tation will be steady-state.


§ 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.