Category HELICOPTER AERODYNAMICS

Purpose and Principle of the Main Rotor – Tilt Control System

The main rotor tilt control is designed to control the collective and

cyclic pitch. This system is used to control the main rotor thrust force in magnitude and direction. Therefore, the tilt control is the most important unit of the helicopter control system. There are three types of main rotor tilt controls: ring, "spider," and crank types. The latter type of tilt

control is used only on two-rotor helicopters with side-by-side positioning of the rotors.

The

ring type tilt control can be used on

all helicopters. It includes

(Figure

105):

(1)

movable ring (plate);

(2)

fixed ring;

(3)

slider;

(4)

universal hinge or cardan;

(5)

scissors or bellcrank;

(6)

vertical control rods.

The movable ring of the tilt control rotates relative to the fixed ring. It is driven from the main rotor hub by means of a scissors. On the

Подпись: /169movable ring there are levers which are connected with the blade pitch control horns by means of vertical links. The fixed ring is connected with the slider by means of a universal, which consists of a ring and two mutually perpendicu­lar shafts. The universal permits the tilt control rings to deflect in any direction. If the plane of the rings is perpendicular to the main rotor shaft axis, when the movable ring rotates the vertical links will not have any vertical displacement and the blade pitch will not change. Consequently, in this case the rotor will not have any cyclic pitch change.

If the plane of the rings is tilted forward, the vertical links will be at the lowest position at the 180° azimuth and the blades will have the mini­mal pitch at this azimuth. At the 360° azimuth the links occupy the highest

Purpose and Principle of the Main Rotor - Tilt Control System

Figure 105. Ring-type tilt control: 1 – slider; 2 – lateral

control lever; 3 – fixed ring; 4 – movable ring (plate);

5 – lever on movable ring; 6 – vertical link; 7 – blade pitch change horn; 8 – axial hinge; 9 – vertical hinge;

10 – horizontal hinge; 11 – scissors; 12 – universal ring;

13 – universal longitudinal axis; 14 – longitudinal control lever; 15 – cyclic pitch lever; 16 – collective-throttle lever.

position and the blade pitch will be maximal. From 0 to 180° azimuth the links move downward and the blade pitch decreases. From 180 to 360° azimuth the links move upward and the pitch increases. Cyclic pitch change is accom­plished in this way. We mentioned previously that as a result of cyclic pitch change the cone-of-revolution axis is tilted in the direction of minimal pitch. This means that, in order to tilt the cone axis in any direction, the plane of rotation of the movable ring of the tilt control must be tilted in

24-9

this same direction. The tilting is accomplished with the aid of two levers on the fixed tilt control ring. The control system levers are connected with the cyclic pitch stick, located in the cockpit. When the stick is moved forward, the motion is transmitted to the longitudinal control lever on the fixed ring of the tilt control, and the fixed ring rotates around the trans­verse axis of the universal so that its leading edge descends.

This means that the pitch is minimal at the 180° azimuth, and the cone-of – revolution axis is tilted forward. When the cyclic pitch stick is moved aft, the leading edge of the tilt control ring rises and the pitch is minimal at the 0° azimuth and the cone-of-revolution axis tilts aft. The conclusion is that when the stick is deflected the cone axis tilts in the same direction. When the stick is moved to the right or left the motions are transmitted from the stick to the lateral control lever, and the tilt control ring is rotated about the longitudinal axis of the universal. In this case our previous conclusion still holds: when the stick is deflected the main rotor

cone-of-revolution axis deflects in the same direction. Control of the cyclic pitch and direction of the thrust force vector is accomplished from the cockpit with the aid of the cyclic pitch stick.

On the tilt control slider, there is a lever which is connected by the control system with the collective-throttle lever located in the cockpit.

Подпись:When the collective-throttle lever is moved up, the tilt control slider rises. All the vertical links move upward together and rotate all the blades to a higher incidence angle. In this way the collective pitch is increased. When the collective-throttle lever is moved down, the tilt control slider lowers and the main rotor collective pitch decreases. The tilt control slider is connected by the control linkage with the stabilizer rotation lever. There­fore, change of the collective pitch is associated with change of the stabil­izer incidence angle. On some helicopters the main rotor collective pitch control is coupled with the tail rotor pitch control.

When this coupling is used on helicopters with right-hand rotation of the main rotor, increases of the collective thrust leads to increase of the pitch and of the tail rotor thrust force, and control of the helicopter is made easier. With increase of the main rotor collective pitch, there is an increase of its reactive moment, which causes the helicopter to turn to the left. This rotation is compensated by increase of the tail rotor thrust.

We have examined a very simple tilt control scheme of the ring type.

The real tilt control has two essential characteristics which must be mentioned. The first characteristic is that the hinges of all the levers on the tilt control movable and fixed rings are located in the same plane, which passes through the point of intersection of the universal axes. This arrangement of the hinges makes possible independence of the action of the longitudinal and lateral control of the helicopter. The second characteristic amounts to the following.

In the functional schematic (Figure 106) the longitudinal and lateral control levers are located on the fixed ring opposite the universal axes.

In the real tilt control these levers are located at some angle relative to the universal axes, which is called the control lead angle (x) • In the absence of lead the cone axis will not deflect in the direction of cyclic control stick deflection, rather at some angle ahead in the direction of rotor rotation. This lag in the deflection of the cone-of—revolution axis is associated with the inertia of the blades.

At the 180° azimuth the pitch is minimal, but the blade flapping angle will not be minimal, since the blades will continue to flap down by inertia.

This means that the cone-of—revolution axis tilts in the direction of the 210° azimuth rather than in the direction of the 180° azimuth, i. e., the deflection of the cone-of-revolution axis will not coincide with the stick deflection, and this makes control of the helicopter more difficult. There­fore, the tilt control ring is deflected with a lead angle x = 25 – 30°, which then leads to coincidence of the deflection of the stick and the main rotor cone-of-revolution axis.

Figure 106. Main rotor control lead:

Purpose and Principle of the Main Rotor - Tilt Control System1 – main rotor shaft; 2 – slider;

3 – universal ring; 4 – universal lateral axis; 5 – tilt control fixed ring; 6 – bearing balls; 7 – tilt control movable ring; 8 – longitudinal control lever; 9 – universal longitudinal axis; 10 – lateral control lever;

X-l ~ longitudinal control lead angle;

^2 ~ lateral control lead angle.

Damping of Oscillatory Blade Motions

If we combine all the forces acting on the blade in the hub rotation plane, we obtain their resultant R. In the case of equilibrium relative to the vertical hinge, the resultant R, shifted to the hinge axis, lies along the blade axis and its moment will be zero. We resolve the force R into two components (Figure 47b): R^ and Q^. The force R^ is radial, and its moment about the hub axis is zero. The force creates the moment Q^a, which

twists the rotor shaft. Both the magnitude and moment of the force will change with variation of the lag angle. Consequently, the oscillatory motions of the blades about the vertical hinges are the source of torsional vibrations of the shaft, while variation of the force R^ leads to bending vibrations of the shaft. Various types of dampers are used to eliminate the oscillatory motions (free oscillations) of the blades relative to the vertical hinges.

The dampers may be of two types: friction and hydraulic.

The friction dampers consist of a set of steel and cermet (friction) disks (Figure 48). Half of the steel disks are attached to the intermediate link of the hub, the other half is attached to the body of the axial hinge.

The friction disks, designed to increase the friction force, are located between the steel disks.

The disks are compressed from above by a spring, which is tightened by a bolt which screws into the finger of the vertical hinge. As the blade rotates about the vertical hinge, friction forces develop between the disks.

Damping of Oscillatory Blade Motions

Figure 48. Friction damper for blade vertical hinge.

 

Damping of Oscillatory Blade Motions

Figure 49. Hydraulic damper for blade vertical hinge.

 

helicopters the damping moment varies

The moment of these forces about the vertical hinge axis will be the damping moment. The magnitude of the damping moment can be regulated by tightening the bolt. On modern from 80 to 120 kgf’m.

The magnitude of the damping moment must be monitored during operations, and care must be taken that it is the same for all the main rotor dampers. /67

With a damper installed, the blade rotates relative to the vertical hinge if the torque exceeds the damping moment. This means that the root portion of the blade experiences a load which does not exceed the magnitude of the damping moment, i. e., the blade root is relieved of a large bending moment. At the same time, the blade will not have free oscillations about the vertical hinge, which means that there will be no reason for the onset of severe vibrations.

The friction dampers can be used on light and intermediate helicopters (Mi-1, Mi-4). They are not used on heavy helicopters because of the small magnitude of the damping moment and the frequent damper regulation required. The hydraulic dampers are being used more and more at the present time.

The hydraulic damper consists of a cylinder and a rod and piston (Figure 49). The cylinder is attached to the body of the vertical hinge, while the rod is attached to the finger of the horizontal hinge. In the piston there are calibrated orifices with relief valves.

As the blade rotates relative to the vertical hinge, the rod and piston

displace relative to the cylinder. The cylinder cavities are filled with a

liquid. As the piston moves in the cylinder, the liquid opens the relief

valves and flows from one cavity into the other through orifices in the piston.

The resistance force P is developed. The moment of this force about the

vertical hinge axis M = Pa will be the damping moment. This moment is easily

9

regulated by selecting the piston area, diameter of the orifices in the piston, and lever arm a (from the damper axis to the vertical hinge axis).

Hydraulic dampers have the following drawbacks:

low damping moments for low rates of blade rotation relative to the vertical hinge;

marked increase of the damping moments during rapid rotation;

dependence of the damping moments on temperature because of variation of the liquid viscosity;

marked variation of the damping moments if air gets into the cylinder chamber.

The hydraulic dampers are sometimes supplemented with spring dampers to eliminate the first problem.

The second problem is eliminated by proper choice of the relief valves. /68

The third problem is alleviated by selection of a liquid whose viscosity depends very little on temperature.

To prevent air entry into the damper, a small supply reservoir is installed on the root portion of the blade, and the damper cavities are replenished with the working fluid from this.

HELICOPTER FLIGHT IN MAIN ROTOR AUTOROTATIVE REGIME

§ 57. Vertical Descent

Подпись:So far we have examined helicopter flight with the engine operating. In powered flight the thrust force developed by the main rotor performs the functions of lifting and propelling forces. But how is flight continued in case of engine failure?

In case of engine failure the helicopter can continue flight only in a descent (vertically downward or along an inclined trajectory). In this sort of flight the propelling force will be the weight force or its component parallel to the flight trajectory. The main rotor will turn, but the turning moment is supplied to the rotor by the aerodynamic forces acting on the rotor blades rather than from the engine. We shall first examine helicopter flight in the autorotative regime along a vertical trajectory (Figure 72).

During steady state vertical descent in the main rotor autorotative regime, the helicopter is acted on by the weight force G, main rotor thrust force T, drag force X of the nonlifting parts of the helicopter, and the tail rotor thrust force T. The helicopter travels vertically downward with the velocity The undisturbed flow approaches the helicopter from below at

this same speed. As this flow passes through the area swept by the main rotor, it is subjected to the action of the blades. The blades of the rotating rotor tend to deflect the approaching stream downward. However, since the

vertical flow velocity V^eg is greater than the induced velocity which the

main rotor blades create, the flow is only retarded rather than deflected

downward. As a result of this retardation, the flow velocity above the

rotor is less than the vertical descent velocity and is equal to the difference

= V^es – V^. Consequently, the mass of air flowing per unit time through

the area swept by the rotor acquires a negative momentum increment mV., which

Ь І

in accordance with the law of momentum conservation will be equal to the main

rotor thrust per unit time, i. e., T = mV., but m = V. Fp, then

ь і ь des

T = FV, pV.. (39)

des і

Thus, the main rotor thrust in the autorotative regime will be larger, the /116 larger the vertical rate of descent and the larger the flow retardation induced velocity.

We shall clarify the conditions for steady state descent in the autoro­tative regime on the basis of the diagram of the forces acting on the helicop­ter. These conditions are expressed by the equalities:

G = T + X;

T = S ;
t. r s

M =0, eg

The first condition ensures a constant rate of descent of the helicopter.

The force X is the drag of all the nonlifting parts of the helicopter and acts in the direction of the thrust force; consequently, it retards the down­ward motion of the helicopter, and therefore, in this case, it cannot be termed the parasite drag force. The larger the force X, the lower the vertical rate of descent. But the drag force of the nonlifting parts is comparatively small and has no significant effect on the vertical rate of descent. Therefore, it can be neglected. Then the first condition is expressed by the approximate equality

For this condition to be satisfied, it is necessary that the helicopter descend at a definite vertical velocity. Formula (39) shows that the thrust force equal to the helicopter weight can be obtained with a lower vertical velocity if the induced velocity is increased by increasing the main rotor pitch. But the main rotor pitch in the autorotative regime cannot be increased arbitrarily. Its magnitude must be strictly defined.

Подпись: Figure 72. Vertical descent in autorotative regime. HELICOPTER FLIGHT IN MAIN ROTOR AUTOROTATIVE REGIME

It has been established by experimental aerodynamics that the main rotor thrust in the autorotative regime is approximately equal to the total aero­dynamic force R of a flat plate having an area equal to the area swept by the main rotor at an angle of attack of 90° (Figure 73).

Using (40) and (41), we find the helicopter vertical rate of descent

V 20

des / crf? ■

Подпись: the formulaПодпись:Since G/F = P (specific loading per unit area swept by the rotor) , takes the form

2 P С#?


HELICOPTER FLIGHT IN MAIN ROTOR AUTOROTATIVE REGIME

V des •

Figure 73. Thrust in autorotative regime.

 

We see from this formula that the helicopter vertical rate of descent depends on the specific loading on the area swept by the rotor (on the heli­copter weight), and on the air density, and therefore on the flight altitude. The vertical rate of descent increases with increase of the specific loading (helicopter weight). This relation can be expressed by the formula

where V. is the vertical velocity for helicopter weight G„;

des2 2

V, is the vertical velocity for helicopter weight G.

des^ 1

HELICOPTER FLIGHT IN MAIN ROTOR AUTOROTATIVE REGIME

With increase of the flight altitude, the air density decreases, which means that the vertical rate of descent increases and can be expressed by the equality

Подпись: where HELICOPTER FLIGHT IN MAIN ROTOR AUTOROTATIVE REGIME Подпись: is the vertical velocity at the altitude H; is the vertical velocity at sea level; is the relative air density.

Formula (42) can be simplified if we consider G = 1.2; and p„ ~ kg/sec^/m^.

it u

Подпись: V. = des Подпись: 2 P С/г? Подпись: :3.6 VP. Подпись: (44)

Substituting these values into (42) , we obtain

Подпись: /118We find the vertical rate of descent of the Mi-1 helicopter in the autorotative regime if

Then ^ез =3.6 13.6 = 13.3 m/sec. This answer shows that a high vertical rate of descent is obtained even for a low specific loading. There are heli­copters for which the specific loading on the main rotor reaches values as 2

high as 25 kgf/m. For such helicopters, the vertical descent velocity is 18 m/sec or 65 km/hr.

Thus, during vertical descent in the main rotor autorotative regime the heli­copter travels with a high velocity, and landing is dangerous. The conditions for steady state flight in the autorotative regime differ fundamentally from the flight conditions with the engine operating. The difference is that there is no main rotor reactive moment in the autorotative regime. The blade aero­dynamic forces do not retard rotor rotation; rather they create the turning moment. Therefore, the helicopter, in contrast with the case of flight with
the engine operating, will turn about the vertical axis in the direction of rotation of the main rotor. To eliminate this turning, the tail rotor must create a thrust directed oppositely to its thrust during flight with the engine operating. The main rotor side thrust force Sg will also be reversed in comparison with the side force during flight with the engine operating.

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

V V

Подпись: Да = arctggl sin 0 – fl

u + V, cos 0
gl

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.

Conditions for Blade Equilibrium Relative. to the Horizontal Hinge

Let us examine the blade thrust moment relative to the horizontal hinge.

If this moment is not transmitted to the hub but simply rotates the blade, then a question arises immediately: how is the blade thrust transmitted

through the hinge to the hub? In order to answer this question we examine

Conditions for Blade Equilibrium Relative. to the Horizontal Hinge

the conditions for blade equilibrium relative to the horizontal hinge.

In addition to the thrust force, in the plane perpendicular to the hub /51

rotation plane there act the weight force G^ and the centrifugal force N (Figure 35b).

Each of these forces develops a moment relative to the horizontal hinge.

The blade thrust moment rotates the blade upward. The flapping angle 3 is formed between the blade longitudinal axis and the hub rotation plane. When the blade tip is above the hub rotation plane, the blade flapping angle is considered positive.

The thrust moment rotates the blade in the direction of increasing flap­ping angle (blade flaps upward). The weight moment = G^b rotates the blade downward, reducing the flapping angle. The centrifugal force moment rotates the blade to bring it closer to the hub rotation plane. If the flapping angle is positive, the centrifugal force moment = Nc rotates the blade downward and coincides in direction with the blade weight force moment. If the flapping angle is negative (Figure 35c), the centrifugal force moment rotates the blade upward and coincides in direction with the thrust force moment. Thus the centrifugal force moment tends to reduce the deflection of the blade from the hub rotation plane.

The centrifugal force always acts in the plane of rotation, is directed outward from the axis, and is applied to the blade center of gravity. It is defined by the formula

Conditions for Blade Equilibrium Relative. to the Horizontal Hingegr у Б

The blade centrifugal force of the Mi-4 helicopter at maximal main rotor rpm exceeds 20,000 kgf. Therefore, even with a small arm, c the moment of this force will be very large.

After seeing what moments act on the blade about the horizontal hinge, we can define the equilibrium condition

This condition can he written as follows for positive and negative flap­ping angles:

for g > 0

MT – MQ + MN or Ta – Gb + N – ; <17>

. b

for g < 0

MQ = MT -f – iAft.

Equilibrium in the case of negative flapping angles is possible, hut only in the course of a very limited time. Therefore in the following we shall con­sider (17) to be the equilibrium condition.

If this condition is violated, the blade will rotate until equilibrium is restored at a new flapping angle. With change of the flapping angle, there will be a change of the centrifugal force arm and therefore of its moment. /52

Thus the blade will flap upward if the thrust force moment is greater than the sum of the moments of the centrifugal force and the weight force, i. e., for. But with increase of the flapping angle, the moment = Nc will increase and equilibrium will again be established. The same process will take place upon reduction of the flapping angle, but in the reverse direction.

The flapping angle has a comparatively small value — 7 – 10°.

The primary reason for violation of blade equilibrium relative to the horizontal hinge is the variation of the blade thrust and its moment.

The horizontal hinges have snubbers (stops) to limit the blade upward and downward rotation. The lower stop is the blade droop limiter, i. e., the blade rests on this stop if the rotor is not turning, which prevents the blade coming into contact with other parts of the helicopter. The stop has a centrifugal regulator which allows the blade to deflect to negative flapping angles in flight.

The upper stop limits the upward rotation of the blade (flapping angle 25 – 30°). The blade does not reach the limiters in flight, since the centrifugal force moment does not permit the blade to deflect very far from the hub rotation plane.

CLIMB ALONG INCLINED TRAJECTORY

§ 50. General Characteristics of the Climb Regime /10^

Along an Inclined Trajectory

Climb along an inclined trajectory is rectilinear flight of the helicopter with constant velocity and constant angle relative to the horizontal plane.

In this flight regime the helicopter is subject to the weight force, main rotor and tail rotor thrust forces, and the parasite drag force (Figure 67). To determine the flight conditions the helicopter weight force /10- can be broken down into components: G^ perpendicular to the flight path, and

G^ parallel to the flight path and directed opposite the motion.

The main rotor thrust force can also be resolved into the components Y (lift force), P (propulsive force), Sg (side force). The conditions for steady climb are expressed by the equalities

— (rectilinear flight and constant climb angle);

— (constant velocity);

— (absence of lateral displacment of the helicopter);

— (absence of helicopter rotation about its center of

gravity).

 

Y = G

 

P

 

G„ + X 2 par

T„ = S t. r s

EM = 0 eg

 

CLIMB ALONG INCLINED TRAJECTORY

Figure 67. Forces acting on helicopter in climb.

 

§ 51. Thrust and Power Required for Climb

The thrust required for climb can be found by using the diagram of the forces acting on the helicopter (Figure 67),

CLIMB ALONG INCLINED TRAJECTORY(31)

where

Gi = G cos 0.; Gz — Gsin9.


Comparing (31) with (26) , we can say that the helicopter parasite drag in climb is practically equal to the parasite drag in horizontal flight at the

*j

same speed. For example, for the Mi-1 in climb (V ^ = 85 km/hr; 0^9°) the

CLIMB ALONG INCLINED TRAJECTORY

slight increase is explained by the fact that during climb the air flow approaches the fuselage at a large negative angle, which leads to increase of the parasite drag force coefficient from 0.009 to 0.0097. The lift force is less during climb than in horizontal flight. The propulsive force during climb will be greater than the propulsive force in horizontal flight by the

 

magnitude G sin 0. Consequently, in (31) the first term of the radicand is smaller than in (26), while the second term is larger than the second term of (26). Therefore, the thrust required for climb along an inclined trajectory is practically the same as the thrust required for horizontal flight at the same speed.

Подпись:If a helicopter can hover, then it can climb along an inclined trajectory. This conclusion is confirmed by the fact that excess thrust appears in the forward flight regime (Figure 68). Consequently, even with some thrust deficiency for hovering (dashed curve in Figure 68), climb along an inclined trajectory at a speed greater than the minimal horizontal flight speed is possible. This circumstance is utilized in the running helicopter takeoff.

CLIMB ALONG INCLINED TRAJECTORY

The power required for climb is found from the same formula as used to find the power required for horizontal flight

But in this formula the terms may differ from the corresponding terns for the power required for horizontal flight.

During climb N will not differ from the profile power for horizontal flight if the rpm and flight speed are the same.

The induced power in climb is practically equal to the induced power for

»

horizontal flight, since

N. = YV., and Y, = G cos 0 % G. і і cl

But the power required for motion during climb differs considerably from the motion power for horizontal flight

N t = PV = (X + G.) V = X V. + G. V..
mot cl par 2 cl par cl 2 cl

= N „ + AN.

Подпись:mot, h

Climb is possible if there is excess power AN (i. e., the power available exceeds the power required for horizontal flight)

Подпись:

CLIMB ALONG INCLINED TRAJECTORY

N = N, + AN. cl h

Single-rotor Helicopter Control Principles

Helicopter control involves control of the rotation of the helicopter about its principal axes and control of the vertical displacement. On this basis the entire control complex considered as the sum of the pilot’s actions can be divided into longitudinal, lateral, and directional control, and also control of the up-and-down displacement of the helicopter. This division is purely arbitrary, since the pilot’s control actions are unified and are accomplished simultaneously and synchronously. However, this division facilitates study of the control question and corresponds to the construction of the control system, which includes four control loops which are independent of one another and are named the same as the names of the particular control modes.

Lontitudinal control is control of helicopter rotation about the trans­verse axis. It is achieved by the action on the helicopter of the longitudinal

control moments M, which are created with fore-and-aft deflection of the

zcont

cyclic pitch control stick. As a result of the tilt of the cone-of-revolution axis in the direction of the stick deflection, the main rotor thrust vector tilts. If prior to deflection of the stick the helicopter was in equilibrium, i. e., the thrust force moment was zero (Figure 107a), after forward deflection of the stick the cone-of-revolution axis deflects in the same direction. The thrust force vector passes at the distance a from the transverse axis and creates the thrust moment = Та, which will be a diving moment. In addition
to the thrust moment, the horizontal hinge diving moment Mjjj = Nc is created. The sum of these two moments creates the longitudinal control moment. The helicopter will be rotated about the transverse axis in the nose-down direc­tion under the action of this moment. Aft deflection of the stick leads to the formation of a nose-up pitching moment, under the action of which the helicopter nose rises.

Подпись:

Подпись: Figure 107. Control of single-rotor helicopter.
Single-rotor Helicopter Control Principles

If the helicopter has longitudinal static stability, the rotation will continue until the stabilizer longitudinal moment balances the control moment. If the helicopter does not have static stability, it will be necessary to deflect the stick in the opposite direction to stop the rotation. As a result of helicopter rotation there is a change of the inclination of the thrust force vector and its horizontal component P. This leads to a change of the flight velocity. Hence we can conclude that forward deflection of the cyclic pitch stick leads to lowering of the helicopter nose and increase of the flight speed. Aft deflection of the stick leads to the helicopter nose rising and reduction of the flight speed. If the stick is moved aft while the helicopter is hovering, it will start to move backward. Therefore the operation of the cyclic pitch stick is analogous to the operation of the control stick in an airplane.

Lateral control refers to control of helicopter rotation about the longitudinal axis. Lateral control is accomplished by deflecting the cyclic pitch stick to the right or left. The main rotor coning axis and the thrust force vector tilt to the same side as the stick (Figure 107b). The deflection of the thrust force vector and the main rotor plane of rotation leads to creation of the lateral control moment as the sum of the moments of the thrust force and the horizontal hinges. The magnitude of the moment will be larger, the higher the main rotor rpm, the larger the stick deflection, and the lower the position of the helicopter center of gravity. Under the in­fluence of the control moment, the helicopter will rotate until the stick is moved in the opposite direction.

Directional control refers to control of helicopter rotation about the vertical axis. The helicopter rotates about the vertical axis under the influence of the directional moment, which is created as a result of the difference of the main rotor reactive moment and the tail rotor thrust moment Mv = M – Mt. Change of the tail rotor thrust force and its moment about the helicopter vertical axis is accomplished by deflecting the directional control pedals. These pedals are coupled by linkage with the pitch change mechanism mounted on the tail rotor gearbox.

If the right pedal is pushed, the tail rotor pitch is increased. As a result of increase of the thrust force by the amount AT, its moment increases. The tail rotor thrust moment becomes greater than the main rotor reactive moment and the helicopter turns to the right. If the left pedal is pushed, the tail rotor pitch is reduced. In view of the decrease of the tail rotor thrust and moment, the latter becomes smaller than the main rotor reactive moment. Under the influence of this moment the helicopter turns to the left.

BASIC CHARACTERISTICS OF THE MAIN ROTOR

§ 4. General Characteristics

The main rotor (MR) is a basic component of a helicopter. It is utilized to create the lift and motive force and to control the helicopter.

The basic parts of the main rotor are the hub and the blades.

The blades create the thrust force that is necessary for flight. The hub connects all the blades and serves to fasten the main rotor to the drive shaft. The drive shaft causes the rotor to rotate.

It is possible to subdivide main rotors into three types depending on the structural arrangement:

Those with rigidly fastened blades;

Those with fully articulated blades;

Those with a semi-rigid (flapping) arrangement.

A main rotor with rigidly fastened blades (Figure 6) has the simplest construction and this is its main advantage. But this rotor has inherent and serious disadvantages, which will be discussed in Chapter IV. Therefore, this type of rotor is not utilized in contemporary helicopters. At present, on some light helicopters, as for example the American helicopters, Hughes UH-6A,

Hiller EH-1100 and others, main rotors with spring fastened blades are used. /J-.Q. These rotors can be considered as a variety of rotor with rigid blades.

BASIC CHARACTERISTICS OF THE MAIN ROTOR

by definite geometric parameters: file shape, blade incidence angle, and the solidity coefficient.

 

The diameter of the rotor is the diameter of the circle swept out by the blade tips. It is designated by the letter D and the radius R. The radius of a blade element is designated r (Figure 8a). The ratio of the radius of a blade element to the radius of the rotor is termed the relative radius

 

BASIC CHARACTERISTICS OF THE MAIN ROTOR

BASIC CHARACTERISTICS OF THE MAIN ROTOR

which gives r = rR

The blade planform shape can be rectangular, trapezoidal or a combination (Figure 8b).

In form, the blade resembles the wing of an airplane. The forward edge of the blade is called the leading edge, and the aft edge is called the trail­ing edge.

Trapezoidal blades have the most uniform distribution of aerodynamic /11

forces along the blade. Rectangular blades are simpler to manufacture, but they have several poor aerodynamic characteristics. The most widely used blades are trapezoidal and rectangular in combination.

Подпись: a)Подпись: ВПодпись:The profile of the blade is the term used for the form of the blade section perpendicular to the longitud­inal axis. The profile of a blade resembles the profile of a wing.

Most often double convex asymmetri­cal sections are used (Figure 8c).

The requirements for a blade profile are:

High aerodynamic efficiency,

BASIC CHARACTERISTICS OF THE MAIN ROTOR

Small shift of center of pres­sure with changes in angle of attack;

The ability to autorotate over a considerable range of angles of attack.

The profile of the blade is characterized by the relative thick­ness о = c/b and the relative camber f = f/Ъ (Figure 9).

BASIC CHARACTERISTICS OF THE MAIN ROTOR-p.__ n j According to the relative thick-

Figure 9. Blade profile parameters. °

ness, the profile is classified as

thin (c < 8%), medium (c = 8 – 12%), or thick (c > 12%). Most blades have

a relative thickness of c > 12%. The use of thick profiles allows an in­crease in the force resistance of an element and the stiffness of the blade.

In addition, the aerodynamic efficiency depends less on the angle of attack for thick profiles. This peculiarity of the profile improves the blade properties in the autorotation regime. Generally, the outermost element of the blade has a greater thickness ratio than at the root.

A relative camber of the blade of f = 2 – 3% brings the profile form /12

closer to symmetry, which leads to a decrease in the shift of the center of pressure with changes of angle of attack.

The incidence angle of the blade element is termed the angle ф; it is formed by the angle between the element chord and the plane of rotation of the main rotor hub (Figure 10) . The incidence angle is often called the pitch of the blade element. This is an arbitrary definition. In a more strict definition the pitch of the blade element is the distance H. This distance is obtained from the distance a blade element travels parallel to the chord after one revolution of the main rotor

H = 2ттг tan ф

Owing to the fact that the pitch of a blade element depends only on the incidence angle ф, then in the subsequent discussion we will identify the con­cept "incidence angle" with the concept "blade element pitch". At different elements of the blade the incidence angles will be different.

The pitch of the blade is taken as the incidence angle, or the pitch of the blade element, with a relative radius of r = 0.7. This angle is defined as the incidence angle (pitch) of the main rotor.

Подпись: Figure 10. Incidence angle of the blade. As the blade turns relative to the longitudinal axis, the incidence angle changes. Such turning is possible thanks to the presence of the axial hinge. Consequently, the axial hinge of the main rotor blade is intended for pitch alteration.

The alteration of the pitch of the blade elements over the radius of the main rotor is termed the geometric twist of the blade.

At the root of the blade elements, the incidence angles are the largest, while at the tip they are the smallest (Figure 11). Geometric twist improves the operating conditions of the blade elements, and the angles of attack approach the optimum. This causes an increase of the thrust force of the lift­ing rotor of 5 – 7%. Therefore, geometric twist increases the useful loading of the helicopter at constant engine power.

Owing to geometric twist a more uniform force loading on the blade element is achieved and the speed, at which flow breakdown occurs on the retreating blade, is increased. The majority of blades have a geometric twist which does not exceed 5-7°

Stiffness is understood to mean the ability of the blade to retain its /13 form. With great stiffness, even force loading is not capable of deforming the structure and external shape of the blade. With small stiffness the blade becomes flexible and easily yields to deformation, that is, the blade is strongly bent and twisted. If the flexibility is too great, the optimum

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Подпись:Подпись: іBASIC CHARACTERISTICS OF THE MAIN ROTORПодпись: in.6. 4 – 2 • О –

-г –

twist cannot be maintained on the blade. This leads to inferior aerodynamic characteristics of the main rotor.

In order to obtain great stiffness, it is necessary to increase the size of the load supporting elements, which leads to increased weight of the blade. Unnecessarily high stiffness leads to an increase of vibration of the main rotor.

The greatest stiffness is obtained with blades of metal or of continuous wooden construction, but the latter are very heavy and are utilized only on light helicopters.

BASIC CHARACTERISTICS OF THE MAIN ROTOR

The area swept out by the main rotor is the area of the circle described by the blade tips

This characteristic of the main rotor has approximately the same impor­tance as the wing area of a fixed wing airplane, that is, it is similar to the lifting surface area.

The disk loading, based on the swept area, is defined as the ratio of helicopter weight to area, that is, the area swept out by the main rotor.

Подпись: /> =G_ F •

2

where, P = specific loading, kgf/m ;

G = helicopter weight, kgf;

„ 2 F = swept area, m.

Contemporary helicopters have specific loadings that vary from 12 to 25 kgf. m2 (or 120 – 150 N/m2).

The solidity coefficient is equal to the ratio of the total planfrom area of all the blades to the area swept out by the main rotor.

Подпись: aSBk

F

where, = planform area of one blade, m ;

D

к = number of blades

Contemporary main rotors have perhaps from 2 to 6 blades. Most often there are 3-4 blades on light helicopters and 5-6 blades on heavy heli­copters. The space factor has a value from.04 to.07. This means that 4 – 7% of the area swept out by the rotor is taken up by the blades. The larger the space factor, within the limits indicated, the larger the thrust developed by the rotor. But if the space factor exceeds.07, then the forces of resistance to rotation are increased and the blade efficiency of the main rotor is decreased.