Forces Resisting Rotation of the Main Rotor

The forces resisting rotation are called the aerodynamic forces operating in the plane of rotation of the hub and directed against the rotation.

At each blade element, its own element of force arises to resist rotation.

In a similar way to the drag force of a wing, the elements of the forces re – .

sisting rotation consist of the forces of profile and induced drag.

Profile rotational resistance AQ^ is an aerodynamic force that arises because of the difference of air pressure in the forward and aft parts of the blade, and also due to the friction of the air in the boundary layer. In general, the profile drag depends on the number of revolutions of the main

Forces Resisting Rotation of the Main Rotor

Figure 16. Relationship between the thrust coefficient and the pitch of the main rotor.

deflected elementary thrust force ЛТ is
rotor, the condition of the blade sur­face and the form of the profile. It is changed very little by changes in the pitch of the rotor (Figure 17a).

Induced resistance arises owing to the induced cross flow on the blade of the main rotor. The induced cross flow deflects the vector of elementary thrust force by an angle 6 backwards relative to the axis of the hub (Figure 17b). If the vector of the projected on the rotation plane of the

hub, we obtain the vector of an elementary induced force that resists

rotation ДО..


The induced rotational resistance depends, principally, on the pitch of the main rotor (with an increase in pitch, it increases). Profile and induced drag, just like the thrust force, depend on air density.

The reactive moment of the main rotor. The elementary rotational resis­tance forces arise on each element of the blade. Combining the elementary /21

forces of one blade, we obtain their resultant Q = ZAQ (Figure 17c).


Since the forces resisting rotation are directed opposite the rotor rotation, their geometric sum (resultant) is zero and does not lead to trans­lational motion of the main rotor. But the forces resisting rotation create a torque about the hub axis, termed reactive, and sometimes termed the rotational resistance torque (see Figure 17c)

Mr = Qbr<A



is the radius of the blade center of pressure; is the number of blades.




Forces Resisting Rotation of the Main Rotor

Figure 17. Main rotor rotational resistance forces.


Forces Resisting Rotation of the Main Rotor

The reactive torque depends on those same factors which determine the magnitude of the forces resisting rotation, i. e., rotor pitch, rotor rpm, blade surface condition and shape, and air density.

The reactive torque is directed opposite the rotor rotation, consequently this torque is a retarding torque; it tends to stop the rotor and reduces its angular velocity of rotation.

Thrust and Power Required for Hovering

The thrust required for helicopter hovering is found from the Formula T = G. If we take into account the rotor slipstream flowing over the fuselage, the thrust increases by 1-2% in comparison with the weight. But how can we obtain main rotor thrust equal to the weight of the helicopter? Let us turn /77 to the Formula T = Cj-F(«>/?)’ . The main rotor thrust depends on the thrust coefficient G^, air density p, and rotor angular velocity or rpm.

Knowing the main rotor rpm and the air density in the standard atmosphere, we can calculate the thrust. The thrust coefficient C^, can be found from the formulas

Figure 54. Blade element lift со – r = 0.7; efficient versus angle of attack (Mi-1).


Thrust and Power Required for Hovering

a7 is the solidity ratio at the radius r = 0.7;

a-j is the angle of attack of the blade element located at the relative radius r = 0.7.

Figure 54 shows the blade profile lift coefficient as a function of angle of attack for various M.

We find Су from the figure and then compute both and main rotor thrust at full rpm at the altitude H = 0 for maximal pitch. With account for blade twist ф7=9° , the induced downwash angle g for the given blade element equals about 4° (see Figure 15b). Then the blade element angle of attack is

«Т = – p = 9 – 4 = 5°.

From the same figure we find C,, —0.42 . Knowing that the solidity a for the Mi-1 main rotor is constant along the radius and equal to 0.05, we find

Г — СУ°- — 0.42-0.05 л “t— 3 2 — ‘ 32 — 0.0066.

Подпись: 2We then find the thrust at maximal engine rpm, knowing that F = 162 m and ш = 26;

This force equals the maximal flight weight for which the Mi-1 can make a vertical takeoff.

We can also determine the coefficient C^, from (19), but with less

Hovering can be performed at different altitudes relative to sea level /78 and at different air temperatures; therefore, we shall examine the dependence of main rotor thrust on the air density.


This formula shows that the thrust ‘developed by the rotor will diminish with increase of altitude and temperature. In order to accomplish hovering during

takeoff from a high-altitude airfield or at high air temperatures, it is necessary to increase the thrust to the magnitude of the weight force by increasing rotor pitch and rpm. But (20) and (21) indicate that helicopter takeoff weight decreases for takeoff from a high-altitude airfield or with increased air temperature. Therefore, the helicopter has lower takeoff weight in the summer than in the winter.

The power required for helicopter hovering must be supplied to the main

rotor shaft in order to overcome the retarding action of the reactive moment.

Подпись: M r Thrust and Power Required for Hovering Подпись: mtorF 2 <“E) E-

It is known that N = M. But at constant rpm req rco *

Therefore, the required main rotor torque and power at constant rpm at con­stant altitude depend on the torque coefficient m. It was shown in


Chapter 3 that in = ni + m, i. e., this torque coefficient is made tor tor. tor M

x pr

up from the induced drag coefficient and the profile drag coefficient. The induced drag coefficient depends on the induced velocity.

The coefficient m. and the relative induced velocity V. are defined tor J і

Thrust and Power Required for Hovering Подпись: 1.080^ Подпись: V. і wR’ Подпись: (22)
Thrust and Power Required for Hovering

by the respective formulas:

where V is the relative induced velocity of the element with r = 0.7

V’^ — 0.52 У Cr.

Knowing the value of for the Mi-1 rotor, we can find the relative induced velocity

Vu = 0.52 у 0.0066 = 0.043.

We substitute this value into (22) and find in


mtor= l. OSC^-f = 1.08-0.0066-0.043+ ^«0.00043.

Thrust and Power Required for Hovering Подпись: 0.00043 • 162 X

From (11) and (10) we find the power required for hovering the Mi-1 helicopter at maximal engine rpm.

Подпись: N e Подпись: 374 0.78 Подпись: 480 hp
Thrust and Power Required for Hovering

Knowing the power utilization coefficient (£ = 0.78) , we find the power which must be developed by the engine in hovering

This power is somewhat less than that developed by the AI-26C engine at takeoff power at sea level (575 hp).

The power required to overcome blade induced drag (in creating the induced velocity) can be found from the formula


Consequently, this power depends on helicopter weight and air density.

The power required to overcome profile drag can be found from the formula

N = pr 100x*

where V is the inverse of the blade element efficiency.

The ratio of the profile drag coefficient to the lift coefficient is termed the reciprocal efficiency of the blade element

Подпись: C.X



Thrust and Power Required for Hovering

The blade element reciprocal efficiency varies in the range 0.02-0.04. We see from (24) that the profile power depends on the main rotor rpm. Moreover, if the blade surface roughness is increased, the profile drag coefficient increases and the reciprocal aerodynamic efficiency of the blade element increases. This circumstance must be considered in the wintertime, when the blade may be covered with frost, which leads to a large increase of the profile power.

The profile drag coefficient is highest for blades with fabric covering, lower for blades with plywood covering, and still lower for metal blades. Therefore, main rotors with metal blades are most widely used at the present time. They have recently been installed on the Mi-1 and Mi-4 helicopters and on all the new helicopters.

We can use (23) and (24) to find the induced and profile powers for the Mi-1 helicopter (G = 2200 kgf; = 7.5 m/sec, x=0.9;o)=26;v= 0.03)

Thrust and Power Required for Hovering

Thrust and Power Required for Hovering— 136 hp ;

N = N. + N = 245 + 136 = 381 hp. req і pr

Thrust and Power Required for Hovering

Figure 55. Hovering at low height.


Thrust and Power Required for Hovering

This result nearly coincides with that obtained using (10) and (11) — 374 hp.

In the hovering regime the thrust required equals the helicopter weight. If low power is required to achieve this condition, the main rotor has high relative efficiency. On the average the magnitude of this coefficient varies in the range 0.6-0.65 if the main rotor blades operate at the optimal angles of attack (5-6°).

Effect of air cushion on_hovering. The so-called air cushion (Figure 55a) develops during helicopter hovering at low height (H < D). The essence of this phenomenon is as follows. The air from the rotor travels downward and its velocity decreases to zero as it encounters the ground. In this case the pressure below the helicopter increases as a result of the velocity head.

Подпись: P
Thrust and Power Required for Hovering

The total pressure at the center of the disk, projected onto on the ground, is

where P is atmospheric pressure.

The thrust force increases as a result of the pressure increase below the /81 rotor. For H = 0.2R the main rotor thrust increases by 50% in comparison with the thrust without the air cushion effect, for H = R the increase is 25%, for H = 2R it is 10%. At the height H = 4R the effect of the air cushion disap­pears completely.

The variation of the thrust increment under the influence of the air cushion is shown in Figure 55b. The air cushion is used in takeoff with an overload or from a high-altitude airfield, when there is a shortage of power.

The air cushion effect has a favorable influence on helicopter stability, since there will be an increase of the thrust for that portion of the main rotor which is closest to the ground when the rotor tilts to one side, and this leads to the development of a righting moment.

Safety Height

The minimal vertical rate of descent at which flight is safest is achieved when gliding at the economical speed. However, if the engine fails while hovering, the helicopter speed V = 0. In order to transition into a glide at a speed close to the economical speed, some altitude must be lost in

order for the helicopter to acquire a definite kinetic energy E =

Подпись: mV2 GV2 _Sl Si 2 2g • Only part rather than all of the helicopter’s potential energy is used in acquiring the velocity (approximately two tenths of the total potential energy). The remaining energy goes to overcome parasite drag and main rotor profile drag, to turn the tail rotor and the accessories. The total potential energy of the helicopter is

Eb = GH,

where G is the helicopter weight;

H is the helicopter flight altitude.

We find the kinetic energy with loss of altitude from the formula


0.2GH = gl, 2g

Подпись: /133

Подпись: H = Safety Height

Hence, we find the safe helicopter hover height

Safety Height Подпись: + 10.
Safety Height

But experience shows that an additional height margin of about ten meters is required for the landing maneuver; therefore, the formula for determining the safe hover height takes the form

Safety Height Подпись: 24.82 4 Подпись: + 10 = 165 m.

Example. The economical flight speed for the Mi-1 helicopter is Vgc = 90 km/hr or 24.8 m/sec. We find the safe hovering height.

If the helicopter has translational velocity in the horizontal direction prior to transition to the main rotor autorotative regime, the safe height is found from the formula 196

For example, the Mi-1 helicopter is flying horizontally at a speed of 70 km/hr or 20 m/sec. In this case, the safe height is defined as

Подпись: safПодпись:Safety HeightH

Therefore, in case of engine failure in horizontal flight or in climb along an inclined trajectory, less altitude is required for transition into the auto­rotative regime than for transition into this regime from hover or when per­forming vertical climb or vertical descent with the engine operating. After determining the safe heights for transition into the autorotation regime for different flight speeds, we can plot the safe flight height diagram (Figure 84).

Подпись: //, MПодпись: 20 60 60 SO WO 120 V, km/hr Figure 84. Helicopter flight danger zone.

Safety Height
Safety Height
Подпись: + 10.

This diagram shows the danger zone, and we see that the safe hover height is up to ten meters or above 200 meters. The safe hover and flight height limitation at low speeds makes the use of helicopters at low altitudes difficult in practice. It is not advisable to fly, the helicopter in the danger zone except in extreme emergencies.


§ 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.