# Category HELICOPTER AERODYNAMICS

## Characteristics of Operation of Coaxial System of Two Main Rotors

In the coaxial twin-rotor helicopter, the main rotors are positioned on a single axis — one above and the other below. Such a helicopter has certain operational characteristics. The area swept by the two main rotors is equal to the area swept by a single rotor

where Fc is the area swept by the system of coaxial rotors;

F^ is the area swept by a single rotor.

In this case, we have assumed that the diameters of the upper and lower /34

rotors are the same.

Let us examine the system of air jets passing through the areas swept by the upper and lower rotors (Figure 26). Increase of the distance between the hubs of the upper and lower rotors degrades the operating conditions of the lower rotor and complicates the construction of the entire system, while re­duction of this distance leads to the danger of collision of the rotor blades and increases helicopter vibration. This distance is h = 0.08D = 0.8m in the Ka-15 and Ka-18 helicopters. At this distance, the lower rotor has no effect on the operation of the upper rotor. The jet from the upper rotor con­tracts, and in the plane of rotation of the lower rotor its radius is 0.7R,

where R is the rotor radius. In this case, the lower rotor blade tips

operate under the same conditions as those of the upper rotor and draw additional air in from the side.

On this basis, we shall estimate the effective area of the entire system through which the air flows, just as for an isolated rotor in the hovering regime.

From the area swept by the upper rotor, we must subtract the root loss area (of radius 0.25R). Under conditions similar to those in the hovering regime, only the tips of the lower rotor blades operate. The area swept by these tips is

F ігтеЯ* _ тгО.72/?3.

1 V

Consequently, the effective area of both rotors through which the stream flows, as in the case of hovering of an isolated rotor, is found from the formula

Fc = *R2 _ *0.2S2/?2 + кГГ – – *0.7=i42 == 7гД* (1 _10.06 +

. +1 -0.49) = 1.45г,. ‘ ,

That portion of the lower rotor which operates in the jet of the upper rotor has lower efficiency. The angles of attack of the lower rotor blade elements are reduced as a result of the induced velocity of the upper rotor (see Figure 23b), which leads to reduction of the thrust. To reduce this effect, the incidence angles of the lower rotor blades are made 2-3° larger than for the upper rotor, but this does not eliminate entirely the harmful influence of the upper rotor on the lower. In the presence of this influence, the efficiency of the central portion of the lower rotor, which is in the jet from the upper rotor is reduced by a factor of two, in comparison with the efficiency of the tip area outside the jet from the upper rotor.

The swept area of the lower rotor, operating in the jet from the upper /35 rotor, is found from the formula

F± = kPFOJ2 – */?20.252 = = ^20.43-0.43Л.

Since its efficiency is less than that of the upper rotor by a factor of two, the additional effective area of the lower rotor is

F = 0.43^0.5 = 0.22Fi.

e. 1 • –

The effective area of the entire

system isFe ^=lA5Fi–Q.22Fi = l.67Fi •

This formula shows that the thrust of

two coaxial rotors under the same conditions is greater than the thrust of an isolated main rotor of the same diameter by a factor of 1.67.

If the thrusts of the coaxial system and the isolated rotor are the same, then less power is required to create the thrust of the coaxial rotor system, which follows from ideal rotor momentum theory.

The power required to turn the ideal rotor is entirely converted into kinetic energy of the jet, i. e., N = TV^.

If we use Tc, Vc> F^, respectively, to denote the thrust, induced velocity, and effective area of the coaxial system of two rotors, and T^, V^, F^ to denote the thrust, induced velocity, and swept area of the isolated

rotor, then we have T = Tn.

5 cl

Consequently,

We know that

Fc = 1.67/7!.

Then

Hence, we find

T„ 2pFtVf V

Vc~ 2p 1.677?! = 1.67 ’

or

0.78V!.

In order to obtain thrust on a system of coaxial rotors equal to the thrust of an isolated rotor of the same diameter, the induced velocity of the coaxial system must be less than the induced velocity of the isolated rotor.

Since the ideal rotor power required is proportional to 1Л, less power is required to obtain the same thrust for the coaxial system than for the /36

isolated rotor. This is the advantage of the coaxial system. The number

0. 78 ‘v is called the aerodynamic advantage coefficient, and is denoted by Using this coefficient, we express the power required for the coaxial system in terms of the power required of an isolated ideal rotor

This implies that for the same power the coaxial rotor system provides 13-15% more thrust than the isolated main rotor. Therefore, the helicopter with coaxial rotors has smaller dimensions than the single-rotor helicopter.

However, to date only light helicopters have been built using this scheme because of structural complexity and other problems.

Twin-rotor helicopters of other arrangements, for example, with the rotors placed longitudinally and with intermeshing rotors, also have an aerodynamic advantage in the axial flow regime. The aerodynamic advantage coefficient of these systems approaches closer to 0.8, the less the distance between the main rotor hub axes.

## Thrust and Power Required. for Horizontal Flight

In horizontal flight the thrust force vector is tilted forward from the vertical and to the side in the direction of the retreating blade.

mation of the side force S = T,

s t. r

and the result of the forward tilt of the thrust force vector is the forma­tion of the propulsive force P = T sin у which pulls the helicopter forward,

overcoming the parasite drag. We recall that helicopter parasite drag is the resistance of all the nonlifting parts (other than the main rotor).

The projection of the thrust force on the vertical yields the lift force Y = T cos y. Therefore, to generate the lift and propulsive forces it is necessary to have the thrust force T^, which can be found from the force diagram (see Figure 59).

(26)

The thrust required for horizontal helicopter flight depends on its weight and parasite drag, which can be found from the formula

par

The parasite drag coefficient depends basically on the shape and attitude

of the fuselage, and also on the condition of its surface. The parasite drag

2

is proportional to the flight velocity squared, i. e., X ^ = f (V ).

With increase of the horizontal flight velocity the thrust required increases.

In horizontal flight there is a change not only of the magnitude of the thrust required, but also of its direction, i. e., the angle у of deflection of the thrust force vector from the vertical. Increase of the angle у is necessary in order to increase the propulsive force P while leaving the lift force Y unchanged.

Tilt of the thrust force vector and increase of the angle are accomplished in three ways:

1) by deflecting the main rotor cone of revolution axis forward;

2) by tilting the helicopter forward;

3) by establishing the main rotor shaft at some angle g relative to the perpendicular to the fuselage structural axis (the line running along the fuselage), Figure 60.

Tilting the cone axis forward through the angle Г| is accomplished by deflecting the helicopter control stick forward. The main rotor cone axis tilts in the same direction in which the stick is deflected.

Tilting the entire helicopter through the angle 0^ (pitch angle) is accomplished by deflecting the control stick forward. The main rotor shaft

installation angle relative to the helicopter structural axis always remains the same.

Thus, the thrust force vector forward tilt angle will be equal to

the sum of the angles Л» 3. The larger the angle y, the larger the propulsive force P, and the higher the helicopter speed.

The work which must be supplied to the main rotor shaft per unit time is called the power required for

helicopter horizontal flight. The power required is made up of three parts: [1] [2] [3]

Using (26a), we find the power required for motion of the Mi-1 helicopter (G = 2200 kgf, H = 0).

(continued)

 37-20 75

 И hp; 37 hp; 79 hp; 153 hp-

 V = 20 m/sec; N mot V = 30 m/sec; N mot V = 40 m/sec; N mot V = 50 m/sec; N mot

 83-30 75

 147-40 75

 230-50 75

These values make it possible to plot a graph of the variation with

flight speed of the power required for motion of the helicopter (Figure 61a).

2

Since N and the parasite drag X = f (V ), the motion power required mot _ par

N = f (v) and increases more sharply with increase of the flight speed, mot

The average induced velocity for the main rotor of the Mi-1 helicopter decreases with increase of the horizontal flight speed (Figure 61b).

Using this figure and the Formula (27), we calculate the induced power,

i. e., the power expended in creating the helicopter lift force

Nt = -2-^- = 245 hP; m/sec: « -22(^,–5- = 147 hp;

– , дг 2:;00-!>,6 oc

m/sec; N і ——- ycj — OO hp1

From these results we can plot the induced power as a function of flight speed (Figure 61c) .

The reduction of the induced power with increase of the flight speed is explained by the fact that the rotor interacts with a larger mass of air ; therefore, less downwash is required to create a lift force equal to the /92

ч N, hp c) pr’ F

11:

cO

ад

ад із

V. m/sec

О 7.0 ад и

‘Л m/sec ‘•< m/sec

Figure 61. Power components versus flight speed.

helicopter weight. The power expended in overcoming profile drag increases with increase of the flight speed (Figure 61d). The increase of the profile power is explained by the increase of the air friction forces in the blade boundary layer with increase of the flow velocity over the blades. In the forward flight regime the flow relative velocity increases for the advancing blades (V7 = U + KsirHi-‘ > while it decreases for the retreating blades

— V Sini^), but since X = f (W^) the drag of the advancing blade increases more rapidly than the drag of the retreating blade decreases. After calculating the component parts of the power required, we find the power required for horizontal flight of the Mi-1 helicopter

V = 10 m/sec; = 4 + 147+ 140 = 291 hp;

V = 30 m/sec; Nh = 37 + 62 + 160 = 259 hp;

V = 50 m/sec; Nh = 153 + 42 + 180 = 375 hp.

Using these values, we plot the power required for horizontal flight as a function of the flight speed for the Mi-1 helicopter(H = 0; G = 2200 kgf)

(Figure 62). We see from this figure that with increase of the velocity from zero to 80 km/hr the power required for horizontal flight decreases. The speed for which the power required for horizontal flight is minimal is called the helicopter’s economical speed.

## HELICOPTER TAKEOFF AND LANDING. Takeoff

Helicopter takeoff is an unsteady accelerated flight mode. During take­off the velocity varies from V = 0 to the velocity at which steady-state climb is established. This climbing speed is usually equal to the economical horizontal flight speed. Depending on takeoff weight, airfield altitude above sea level, and presence of obstacles, the takeoff may be performed helicopter-style, airplane-style, and helicopter-style with or without utilization of the "air cushion."

Sometimes the helicopter travels over the ground prior to or during takeoff, i. e., taxiing is performed. Helicopter taxiing differs significantly from airplane taxiing.

Helicopter taxiing characteristics. Taxiing is accomplished by means of the propulsive force P, which balances the wheel friction force F (Figure 87a). The reactive moment of the main rotor is balanced by the thrust moment of the tail rotor. The basic differences in helicopter taxiing are:

(1) Presence of a large lift force, which is a component of the main rotor thrust and reduces the wheel pressure force on the ground, i. e., reduces the support reaction. As a result, wheel friction on the ground is reduced, and the possibility of helicopter overturning is increased;

(2) Presence of side forces: tail rotor thrust and the side component

of the main rotor thrust (Figure 87b). These forces develop large overturning moments about the wheel support points, which balance one another. But if there is a change of one of the side forces the overturning moment is un­balanced and can cause the helicopter to overturn (Figure 87c);

(3)

A large nose-down moment develops as a result of the propulsive force P, which creates high loads on the landing gear wheels (wheel).

t. r

‘ t. rt? ,

/ї •?

Therefore, helicopter taxiing must be performed more carefully than airplane taxiing. The taxiing speed must not exceed 10 – 15 km/hr. The surface of the area over which taxiing is performed must be smooth. Taxiing in a strong crosswind is not permitted, since this can lead to overturning of the helicopter.

Helicopter-style takeoff is the primary takeoff mode (Figure 88). In this takeoff a vertical liftoff is made and check hovering is performed at a height of 1.5 -2m (operation of the main rotor, engine, and equipment is checked). Then the helicopter is transitioned into climb along an inclined trajectory with simultaneous increase of the speed. In this process "sinking"

 з

 г

Figure 88. Helicopter-type takeoff.

of the helicopter is possible, i. e., a reduction of the altitude, and sometimes the wheels may even come in contact with the ground. This phenomenon is caused by tilting the main rotor coning axis forward to develop the propulsive force P, the result being a decrease of the vertical component of the main rotor thrust. Therefore, along with tilting of the main rotor coning axis forward, there must be an increase of the thrust force by increasing the rotor pitch.

The takeoff is considered terminated when the helicopter reaches a height of 20 – 25 meters or is above the surrounding obstacles. At this time the acceleration, i. e., the increase of the velocity along the trajectory to the optimal climbing speed, which corresponds to the minimum level flight power, is also terminated. But this type of takeoff cannot he performed if:

the helicopter is overloaded (insufficient engine for hovering outside the "air cushion" influence zone);

the air temperature is high (reduced engine power);

the takeoff is made from a high-altitude airfield (low air density at the given altitude so that insufficient engine power is available). Under

these conditions an airplane-type takeoff is made.

Airplane-type takeoff. During the airplane-type takeoff the helicopter accelerates on the ground, then lifts off and transitions into a climb along an inclined trajectory (Figure 89). In this takeoff use is made of the pri­mary advantage of main rotor operation in the forward flight: increase of

the thrust developed by the rotor with increase of the velocity of the air stream approaching the main rotor (see Figure 68).

 Figure 89. Airplane-type takeoff.

As a result of the thrust increase there is an increase of the lift force. /143 When it becomes somewhat greater than the weight force, the helicopter lifts from the ground and transitions into a climb along an inclined trajectory with further increase of the flight speed. We see from the power required and available curves for horizontal flight (see Figure 63a) that the power required for horizontal flight decreases markedly for even a small speed increase. If takeoff is impossible at V = 0 because of insufficient power, at a speed of 40 – 50 km/hr considerable excess power is developed, which then makes it possible for the helicopter to transition to the climb regime with simultaneous increase of the flight speed.

An airfield or at least a small smooth area is required for the airplane – type takeoff. The ground run during takeoff with flight weight exceeding by

10 – 15% the normal takeoff weight for helicopter-type takeoff is 50 – 100 meters. In this case the liftoff speed is 50 – 70 km/hr (with acceleration during the ground run 2.2 m/sec ) and the ground run time is 7 – 10 seconds.

The ground run is performed on all wheels of the landing gear. Some helicopters (the Mi-6, for example) perform the last part of the ground run on the nosewheel. When using this ground run technique the acceleration is increased as a result of the inclination of the fuselage longitudinal axis and the resulting increase of the propulsive force P. The helicopter takeoff is considered complete when a safe height (25 m) and a velocity along the trajectory close to the economical speed for horizontal flight have been reached.

Helicopter-type takeoff utilizing the air cushion. Vibrations may arise during airplane-type takeoff ground run on an uneven surface. Then the take­off is made using the air cushion (Figure 90). In this takeoff the helicopter lifts off vertically, utilizing the increased main rotor thrust in the air cushion influence zone (the distance from the main rotor plane of revolution to the ground does not exceed R).

After liftoff and hovering in the air cushion zone, the helicopter is transitioned into forward flight i. e., flight at low height with increase of the speed. During the transition maneuver the influence of the air cushion diminishes with increase of the speed, but the forward flight effectiveness increases; therefore, the main rotor thrust force increases, which makes it possible to transition the helicopter into a climb along an inclined trajec­tory. In order to perform such a takeoff it is necessary to have a sufficiently smooth area, i. e., there must not be any large ditches or dropoffs, where the influence of the air cushion disappears.

In certain cases none of the techniques examined above are applicable because of obstacles surrounding the area. Then takeoff is made without

utilization of the air cushion, i. e., liftoff and check hovering are performed and then a vertical climb is initiated. At a height of 5 – 10 meters above the surrounding obstacles the helicopter is transitioned into climb along an inclined trajectory with simultaneous acceleration to the economical velocity. Vertical takeoff is rarely used, since it requires high power and is performed in the danger zone. If sufficient power is not available, yet takeoff must be made, the helicopter weight should be reduced.

## PRINCIPLES OF HELICOPTER FLIGHT

§ 1. Brief IWstory of Helicopter Development

і

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

 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:

 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.