§ 19. Characteristics of Main Rotor Operation in Forward Flight

We recall that the term forward flight refers to operation of the main rotor in an undisturbed stream which approaches the rotor nonparallel to the hub axis (see Figure 12c). While in the axial flow case, the rotor imparts to the air mass traveling along the axis additional momentum in the same direction, in the case of forward flight the rotor also imparts to a definite air mass some additional momentum, only this time not in the direction of the undisturbed approaching stream, rather in the direction along the rotor axis, downward. This leads to the appearance of the so-called downwash (Figure 27a).

The downwash magnitude is connected directly with the magnitude of the thrust which the main rotor develops in the forward flight regime.

In accordance with wing and propeller vortex theory, developed by Zhukovskiy in the 1905-1921 period, the wing lift and the main rotor thrust in the forward flight regime can be determined using the same formulas.

We imagine a stream of circular cross section, flowing past a wing (Figure 27b). The stream approaches the wing with the velocity V. As a result of the formation of the induced vortices, the wing imparts to the air /40 mass per second mg the vertical velocity u, termed the induced velocity.

Vortex theory shows and experimental aerodynamics confirms that there is a gradual increase of the induced velocity behind the wing.


Figure 27. Operation of main rotor in forward flight regime.


At a distance equal to about 0.5Z (wing half-span) the induced velocity

reaches the value 2u (Figure 27c). Thus, the air acquires from the wing

additional momentum equal to m 2u.


The energy conservation law states that the momentum increase equals the impulse of the force. The impulse of the force per second will be simply the wing lift. Consequently,

Y — tns2a. (із)


Let us find the magnitude of the air mass flowrate mg. The stream section area F^, normal to the vector V^, equals the area of a circle of diameter equal to the wingspan l.

The velocity vector Yx=s]/ ц (V is the undisturbed flow velocity, and u is the induced velocity). Then

Substituting this value of the mass flowrate into (13), we obtain

Подпись: (15)Y=2?FnV1u.

Thus, the wing lift depends on the air density, wingspan, flight speed, and the induced velocity with which the wing deflects the stream downward.

From (15) we find the magnitude of the induced velocity /41


U~ 2PFnVx ‘

Since the stream induced downwash angle is small, we can assume that

The downwash formed by the main rotor (see Figure 27a) is similar to the downwash due to a wing with span Ъ = D.

The air approaches the rotor with the velocity V and is deflected downward as a result of the induced inflow velocity V^. The resultant rotor velocity will be equal to the vector sum of the velocities of the undisturbed stream and the induced velocity

Vi^V + Vf.

The angle є between the vectors V and is the induced downwash.

Continuing the comparison with the airplane wing, we can say that the air mass flowrate ftls — pFiiV і passes through the area F normal to the resultant velocity vector Vl:. Since the rotor is taken to be a wing with span Ї = D, then


i. MAIN ROTOR OPERATION IN FORWARD FLIGHTe., the area perpendicular to the vector Vi,. will be equal to the area swept by the main rotor = F.

In the forward flight regime the downwash velocity is also equal to twice the inflow velocity. On this basis and using ideal rotor momentum theory, we find the thrust in the forward flight regime using (4)

T = m V, = m 2V.. s dw s x

Using (14), we can write

If F„ = F, then N

T = tyFViV,.

If we account for tip and root losses, this formula can be written in the form

T= 2xpFVxVt.

Consequently, main rotor thrust in the forward flight regime depends on air density, rotor pitch, and flight velocity.

Effect of Helicopter Weight and Flight. Altitude on Performance

With increase of the helicopter weight there is an increase of the power

* ^ ^

required for horizontal flight, since TV/ — —. Figure 63b shows curves of the power required for the Mi-1 helicopter for flight weights of 2200 kgf and 2300 kgf. In comparing these curves we can say that with increase of the flight weight:

the maximal horizontal flight speed decreases;

the minimal speed when using rated power increases;

the economical and optimal speeds increase, although only slightly;

the horizontal flight speed range decreases;

the excess power decreases;

hovering of the helicopter outside the air cushion influence zone is impossible even when using takeoff power.


These variations of the helicopter flight characteristics should always be taken into account, particularly in those cases when a large fuel supply is carried. If the flight performance is based on takeoff weight, the values obtained will be too low. Therefore, if a large fuel supply is carried, the flight performance is based on the average flight weight with consideration for the fuel consumption





G = G av to






G is the average flight weight;


G is the takeoff flight weight;

(Jfuel is the fuel weight (tanks completely full).


Effect of flight altitude. The helicopter flight characteristics depend on the flight altitude and also on the air temperature and humidity. The air density decreases with increase of the altitude; therefore, the parasite drag decreases, as does the power required for motion




Since the power required for motion has a large value at speeds above the economical speed, a change of flight altitude will have an effect on this speed

In studying the hovering regime, it was established that the thrust developed by the main rotor depends on the flight altitude, i. e., this thrust decreases with increase of the altitude, and this means that the lift force will decrease. But since the horizontal flight conditions specify that Y = G, it is necessary to increase the induced velocity V_^. Consequently, the induced power N. = GV. will increase in proportion to 1/Д, i. e., yV. = //, . The

і і *il *0 La

profile power changes very little with increase of the altitude.

Thus, with increase of the altitude the power required for motion decreases, while that required for creating the lift force increases. These conclusions are illustrated by the plot of power required for different altitudes (Figure 63c). This figure shows also how the power available varies with altitude.

For the supercharged engine the effective power increases up to the critical altitude and then decreases. As a result of this variation of the power available and the variation discussed above of the motion power and the induced power, we can say that with increase of the altitude up to the critical altitude:

1. For speeds lower than optimal, the power required for horizontal flight increases owing to the increase of the induced component of this power.

2. For speeds above optimal, the power required for horizontal flight decreases as a result of decrease of the motion power.

3. The magnitude of the optimal speed changes very little with change of the flight altitude.


4. The maximal and minimal horizontal flight speeds increase.

5. The excess power increases up to the engine critical altitude and then decreases.

Consequently, if flight must be accomplished at high speed, this should /96 be done at high altitude.

Increase of the air temperature is equivalent to increase of the altitude, since the air density decreases as its temperature increases. Increase of the air humidity leads to reduction of engine power and of the maximal horizontal flight speed.

All these conclusions are valid if we ignore the factors which restrict the maximal horizontal flight speed.

HELICOPTER BALANCE, STABILITY, AND CONTROL. Helicopter Center of Gravity and Balance

Подпись: /149The helicopter center of gravity is the point of application of its weight force vector. The center of gravity is the nominal point about which the helicopter rotates. The three principal axes of rotation (body coordinate system) passing through the helicopter center of gravity are used to charac­terize the rotational motions (Figure 94a). The 0 – x^ longitudinal axis lies in the plane of symmetry and runs along the fuselage parallel to the main rotor hub rotation plane. The 0 – z^ transverse axis passes through the center of gravity perpendicular to the plane of symmetry and is directed to the right. The 0 – y^ vertical axis passes through the center of gravity, lies in the plane of symmetry perpendicular to the longitudinal axis, and is directed upward.

Подпись: /150If the external force acting on the helicopter passes through the heli­copter center of gravity, its moment will be zero and the helicopter will not have any rotational motion. If the external force passes outside the center of gravity, it creates a moment relative to some axis, under the influence of which the helicopter will rotate.

Of the cargo is attached rigidly to the helicopter the center of gravity does not move regardless of the attitude the helicopter assumes in the air.

If the cargo moves, the center of gravity will also move. Therefore, we need

to know precisely where the helicopter center of gravity is located. The center of gravity location is determined by balancing the helicopter. The helicopter balance point is the distance x from the main rotor huh axis to the center of gravity, expressed in millimeters, and the distance у from the center of gravity to the hub rotation plane (Figure 94b).

Подпись: /•; І Hr * » The distance x is the horizontal eg location and the distance у is the vertical eg location.

If the center of gravity is located ahead of the hub axis the eg is termed forward and denoted by +x.

If the center of gravity is located behind the hub axis it is termed aft and denoted by – x. Every helicopter has strictly defined eg travel limits. The forward eg limit is considerably greater than the aft limit.

For example, for the Mi-1 the

forward eg limit is +x. . = 150 mm,


Подпись: Figure 94. Helicopter balance: a - helicopter eg definition; b - helicopter balance: x^ -the aft limit is – x,. = -53 mm.


Подпись: limiting forward; x„ - limiting aft.The helicopter eg location must be known prior to every flight. The eg location changes with variation of

helicopter loading. The locations where the heaviest cargo is to be located is indicated in the operating manual for every helicopter. This manual also defines the sequence for finding the eg location, which amounts to the follow­ing. The basic helicopter weight (weight at a definite loading) and the basic eg location must be known. These data are presented in the helicopter specifications. Moreover, the weights and locations of the cargo must be

known. The distance from the main rotor hub axis to the cargo is measured in meters. The total moment about the main rotor hub axis is calculated and the new helicopter weight is determined as the sum of the basic weight and the weights of all the cargo. The new eg location is found from the formula


X – £0′ •

Example of eg calculation of Mi-1 using the data:

(1) basic helicopter weight 1930 kgf;

(2) basic eg location 123 mm;

(3) eg limits +150, -53;

(4) additional cargo on helicopter:

= 85 kgf (at distance – 1.2 m ahead of hub axis);

= 38 kgf (at distance = 1.4 m behind hub axis);

G^ = 105 kgf (at distance = 0.5 m ahead of hub axis);

(5) cargo G^ = 72 kgf removed, was located at distance = 0.6 m aft

of hub axis.

Solution. We find the moments of the basic weight and the weight of each cargo

Consequently, flight cannot be made with this eg location; the helicopter will be uncontrollable. Some of the cargo must be shifted aft.

Let us find how far the cargo G = 105 kgf must be moved aft to locate

° car

the eg at +150 mm.


1. We find the moment required to shift the eg 34 mm

AM = G Ax = 2086-0.034 =70.9 kgf. new


Подпись: § 69. HELICOPTER BALANCE, STABILITY, AND CONTROL. Helicopter Center of Gravity and Balance Подпись: /152

We find the distance which the cargo must be shifted

That state of the helicopter for which it travels in a straight line with constant velocity and does not rotate about its principal axes (about the center of gravity) is called equilibrium.

The equilibrium conditions follow from the definition. According to Newton’s first law, a body moves uniformly and rectilinearly if no external forces act on it. Therefore, it is necessary that the sum of the forces acting on the helicopter be equal to zero

ZF =0. eg

The second equilibrium characteristic (absence of rotation) will hold if the sum of the moments of the forces acting on the helicopter equals zero

EM =0. eg

Moments relative to the о – z transverse axis are termed longitudinal

(M ). Under the action of this moment the helicopter pitches up (nose rises) z

or pitches down (nose descends). The moments about the 0 – x^ longitudinal axis are termed transverse or rolling moments (M^). The moments about the 0 – y^ vertical axis are termed directional (M^). A general remark on the sign of the moments: a positive moment causes clockwise helicopter rotation

if we look along the direction of the axis.

Equilibrium of the helicopter exists in all the steady-state flight regimes. The steady-state flight conditions, which we examined previously, are the equilibrium conditions written in expanded form. It is true that these conditions were written in application to the velocity coordinate system. The velocity or wind coordinate system is a system fixed with the flight velocity vector. In this system the longitudinal axis is denoted by 0 – x and coincides in direction with the velocity vector (see Figure 94a). The angle between the axes 0 – x^ and 0 – x of the body and wind coordinate systems is equal to the main rotor angle of attack A. The angle between the longitudinal axis of the velocity coordinate system and the helicopter plane of symmetry is called the sideslip angle. If the flight velocity vector is in the plane of symmetry, the sideslip angle equals zero. In the absence of sideslip, the transverse axes of the body and velocity coordinate systems

coincide. The angle between the vertical axes 0 – y^ and 0 – у of the body and velocity coordinate system equals the angle of attack of the main rotor.

We take for example the conditions for horizontal helicopter flight

HELICOPTER BALANCE, STABILITY, AND CONTROL. Helicopter Center of Gravity and Balance

We see from these equalities that the sum of the forces acting on the helicopter along the vertical, longitudinal, and transverse axes of the velocity coordinate system equals zero.

Consequently, these three equalities express the first equilibrium

condition EF =0. The fourth horizontal flight condition (EM = 0) eg eg

expresses the second equilibrium characteristic, i. e., the absence of rotation about the center of gravity.


§ 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.