Category HELICOPTER AERODYNAMICS

Drawbacks of Main Rotor with Rigid Blade Retention

The main rotors of the early helicopters (TsAGIl-EA, for example) had blades which were rigidly attached to the hub. The blade incidence angle was changed by means of axial hinges. In their arrangement such rotors are similar to airplane variable pitch propellers. But the very first flights disclosed major deficiencies characteristic of these rotors.

The thrust is created by all the blade elements, but the highest elemental forces will be those on the elements located at 3R/4 (see Figure 15d). The resultant of the elemental forces is applied at the blade center of pressure, which is located at the element with relative radius r = 0.7. This distribu­tion of the elemental thrust forces and this positioning of the resultant leads to the creation of a large bending moment at the blade root (Figure 34a). The approximate magnitude of the blade root bending moment at the blade

attachment to the hub is determined from the formula M, , = T, 0.7R.

Dend b

Thus, if the rotor has four blades and the helicopter flight weight is 6000 kgf, the thrust of a single blade will be = 6000:4 = 1500 kgf. For main rotor diameter D = 20 m, М^еп^ = 1500 x 0.7 x 10 = 10,5000 kgf’m. This moment will be still larger for a heavy helicopter. The large bending moment creates a large load on the blade root. Moreover, the blade is subjected to a centrifugal force which reaches a magnitude of several tens of tons ; con­sequently the root portion of the blade operates under conditions of large loads. In order to avoid blade failure, the area of its root section must be increased, and this leads to increase of the structural weight and reduction of the helicopter’s useful load.

Since the blade thrust varies azimuthally, its bending moment also varies (Figure 34b). The variable bending causes fatigue stresses in the material of the structural elements, which can lead to rapid blade failure. The up and down bending vibrations of the blade tips reach high frequencies (up to 3-4 cycles per second), creating heavy vibration of the helicopter.

The blade thrust does not vary azimuthally in the vertical flight regime, and this means that the main rotor thrust vector, equal to the sum of the blade thrust forces T = T^k, lies along the hub axis (Figure 34c).

In the forward flight regime the blade thrust depends on the azimuth. /49

The thrust is maximal at the 90° azimuth and minimal at the 270° azimuth (Figure 34d). As a result of this variation, half the main rotor disk (advancing blades) has a higher thrust than the other half, formed by the retreating blades.

In this case the main rotor thrust vector T does not pass through the center of the hub, but rather at the distance a from the hub axis. The thrust moment ftL, = Та is created relative to the hub axis.

Drawbacks of Main Rotor with Rigid Blade Retention

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Figure 34. Blade bending moment and main rotor thrust overturning moment.

 

Drawbacks of Main Rotor with Rigid Blade Retention

Since the hub axis is in the helicopter plane of symmetry, the main rotor thrust moment causes the entire helicopter to tend to overturn. This is termed the overturning moment. Thus the main rotor with rigid blade restraint has three major drawbacks:

presence of the overturning thrust moment in the forward flight regime; presence of large thrust bending moment at the blade root; variation of the blade thrust moment azimuthally.

All these drawbacks can be eliminated if the blades are attached to the hub by means of horizontal hinges.

Effect of flight altitude and air temperature on helicopter flight characteristics

Answer 1. Increase of the flight altitude involves reduction of the air density. This leads to reduction of the thrust developed by the main rotor. Since the horizontal flight condition is the equality G = Y, with increase of the altitude the induced velocity must be increased; therefore, the induced power NL = GV^ will increase. The power required curve is shifted upward for low flight speeds.

Подпись: /102At high flight speeds, the induced power increases only slightly, while the power required for motion decreases with increase of the altitude ; there­fore, at high speeds the power required curve is shifted downard. As a result of this change of the power required and available, the minimal and maximal horizontal flight speeds increase up to the engine critical altitude. Above the critical altitude the maximal flight speed will decrease. Increase of the air temperature is equivalent to increase of the altitude.

Answer 2. With increase of the altitude the power required for helicopter horizontal flight increases. The power developed by the engine decreases. The power required curves are shifted upward and the power available curves are shifted downward. As a result of this displacement of the curves, the maximal speed decreases and the minimal increases; the speed range and the excess power decrease. Increase of the air temperature leads to reduction of the power required and available.

Change of Main Rotor Collective and Cyclic Pitch

Simultaneous rotation of all the blades relative to the axial hinges in the same direction and through the same angle is termed collective pitch change. Increase of the collective pitch leads to increase of the main rotor thrust force. Sequential change of the blade pitch in azimuth is termed cyclic

pitch change. During cyclic pitch change, the pitch of each blade increases over a 180° azimuth range and decreases in the other half of the circle (Figure 104a).

Change of Main Rotor Collective and Cyclic Pitch

Figure 104. Main rotor cyclic pitch variation.

When the pitch is changed, the blade thrust changes and its moment about the horizontal hinge changes, which leads to flapping motions and tilt of the cone-of-revolution axis and deflection of the thrust force vector.

If the thrust force vector needs to be deflected in the direction of the 210° azimuth, the blade pitch must be minimal at this aximuth and maximal at the opposite azimuth — 30°. Then the pitch decreases from the 30° azimuth to the 210° azimuth and increases from the 210° azimuth to the 30° azimuth.

A similar pitch change is observed for each blade. Change of the collective and cyclic pitch is accomplished with the aid of a special system — the main rotor tilt control.

Oscillatory Blade Motions

The vertical hinges have stops to limit the oscillatory motions of the blade. However, the blade does not reach the stop in flight, since equilibrium is established under the influence of the moments of the forces acting on the blade in the main rotor hub rotation plane (Figure 47a).

The condition for equilibrium relative to the vertical hinge in general form is expressed by the equality

ХЛ.Н – °-

For a positive lag angle, this equality can be written as

Oscillatory Blade Motions

Figure 47. Blade equilibrium about vertical hinge.

MN = MQ±MP.

The lag angle is the angle £ between the radial line and the longitudinal /65 axis of the blade. The radial line is the line passing through the main rotor axis and the vertical hinge axis.

The lag angle will be positive when the blade rotates aft relative to the radial line, opposite the main rotor rotation. In the last equality, the blade centrifugal force moment = Nc will be larger, the larger the centrifugal force and the larger the lag angle. With increase of the lag angle there is an increase of the centrifugal force arm c and its moment relative to the vertical hinge.

For a positive lag angle, the moment rotates the blade ahead in the direction of rotation of the main rotor about the vertical hinge.

If the lag angle is negative, the centrifugal force moment rotates the blade aft, opposite the direction of rotation of the main rotor. Therefore, the centrifugal force moment rotates the blade toward the radial line: it

acts as a sort of regulator of the oscillatory motions. Under the influence of this moment, the positive lag angles £ do not exceed 3-5° (with the main rotor driven by the engine). Negative blade lag angles are developed when the main rotor operates in the autorotation regime. In this case, the lag angles reach 8-12°.

The moment = Qa of the rotational drag force always opposes rotation of the rotor. Since the force varies with azimuth, its moment will also vary.

The Coriolis force moment M^, = F^b varies as a function of azimuth, both in magnitude and direction. At azimuth angles close to 90° the Coriolis force reduces the lag angle, while at azimuths close to 270° the lag is increased.

Now (18) can be written in expanded form

Nc = Q^a + Fcb = 0.

This will then be the condition for equilibrium of the blade relative to the vertical hinge.

The moments and vary continuously in azimuth, and their variation is one of the reasons for the oscillatory motions of the blade relative to the vertical hinge in the forward flight regime.

Another reason for the oscillatory motions is the action of the centrifu­gal force and its moment relative to the vertical hinge. Its action can be compared with the action of the weight force on a freely suspended body.

If a freely suspended body is deflected, oscillations similar to those of a pendulum develop.

Since the centrifugal force is several times stronger than the weight force, it creates significant "pendulous" oscillations, which combine with the oscillations from the variable moments of the rotational drag force and the Coriolis force to amplify or attenuate the amplitudes of the blade /66

oscillations about the vertical hinge.

Helicopter vertical rate of descent and what it depends on

Answer 1. The vertical rate of descent is the altitude which the heli­copter loses per second, i. e., V^es = V^eg ^ sin 0. It depends on the

velocity along the trajectory and the descent angle. The flight velocity along the trajectory depends on the main rotor thrust force component +P^, directed parallel to the flight trajectory. The descent angle depends on the lift force Y, i. e., on the magnitude of the main rotor pitch.

The larger the main rotor pitch for the same rpm and the larger the back­ward tilt of the cone axis, the smaller the descent angle, velocity along the trajectory, and helicopter vertical rate of descent.

Answer 2. The vertical rate of descent is the altitude which the heli­copter loses per second sin 0. This rate depends on the velocity

along the trajectory V and the descent angle. The velocity along the

QcS • u

trajectory will be the larger, the larger the propulsive force G^, which is a part of the helicopter weight force (G^ = G sin 0).

This means that the larger the descent angle, the larger the propulsive force G^, the larger the flight velocity V^eg, and the higher the vertical rate of descent.

Answer 3. The vertical rate of descent is the altitude which the heli­

copter loses per second (Vjeg = sin 0). It is larger, the higher ;her

the velocity along the trajectory and the larger the descent angle. The vertical velocity along the trajectory depends on the propulsive force G^ and

Подпись: The larger the descent angle, the larger thethe parasite drag force X. propulsive force G^ = G sin 0.

The larger the angle between the fuselage longitudinal axis and the flight trajectory, the larger the parasite drag force and the lower the velo­city along the trajectory. This means that, by altering the position of the helicopter fuselage relative to the flight trajectory and by altering the descent angle, we can alter the flight velocity along the trajectory and the vertical rate of descent.

Main Rotor Power Available

The power required to turn the main rotor is supplied to the rotor from the engine through the transmission. But the rotor does not receive all the power the engine develops, since part of this power is expended for other purposes and does not reach the rotor. The overall power losses are made up of the losses in:

Turning the tail rotor;

Turning the engine cooling fan;

Overcoming friction in the transmission components;

Driving the accessories;

Overcoming air drag on fuselage and other parts of the helicopter.

Let us examine the magnitudes of these losses, or the energy balance of the helicopter.

On the average, 8% of the engine power is expended in turning the tail

rotor (N ) ;

t. r ’

The fan absorbs 5% (N_ );

tan

The accessories absorb 1% (N );

acc

Helicopter parasite drag absorbs 2% (N.

That portion of the engine power which is supplied to the main rotor is called the power available. It is defined as the difference between the effective engine power and the sum of the losses

N = N – (N + + N + N + N ).

avail e t. r fan trans acc par

Main Rotor Power Available

The ratio of the power available to the effective engine power is termed the Bower utilization coefficient

hence

Navail = N £ .

e

The difference 1 – t, = is called the power loss coefficient.

For single-rotor helicopters, the average power utilization coefficient is 0.75-0.80, and the average power loss coefficient is 0.25-0.20. The power utilization coefficient, and consequently the power available, vary with variation of the helicopter flight speed. The speed dependence of the power /30 available is shown in Figure 22.

The following conclusions can be drawn from this figure:

1) The effective engine power is independent of the flight speed;

2) The overall power loss decreases with speed up to 80-100 km/hr and then increases with further increase of the flight speed;

3) The power available increases with increase of the flight speed to 80-100 km/hr and then decreases;

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4) Подпись: NПодпись: transNПодпись: асеMain Rotor Power AvailableThe maximal power available is obtained at a flight speed from 80 to 100 km/hr for most helicopters.

V

Figure 22. Main rotor power available versus speed.

Why does a helicopter have different vertical flight regimes if T = G in all the regimes?

Answer 1. The equality T = G is approximate. It does not take into

account the effect of the parasite drag force X. With account for this

par

force in hovering, climb, and descent T ~ G + X But the parasite drag

force will be different in the different regimes: it will be greatest in a

vertical climb and least in a vertical descent. Therefore, the thrust is

actually greater than the weight during climb and less during descent; in

hovering T = G + X.

par

Answer 2. All the vertical flight regimes are characterized by absence of vertical acceleration, i. e., constant vertical velocity. According to the law of inertia, the acceleration will be zero if no force acts on the body.

The equality T = G is equivalent to the equality T – G = 0, which means that it is valid for all regimes.

But in the different regimes the rotor performs different work; in

climb the main rotor work N. = T(V. + V ); in hovering N. = TV.; in descent

x і у x 1*

N_^ = T(V_^ – Vjeg) ; therefore, more power is required for climbing than for hovering and descent.

Variation of autorotation conditions for the different blade elements

Answer 1. The different blade elements have different autorotation conditions. These conditions are determined by the geometric twist of the blade, i. e., by the magnitude of the blade element incidence angle and the magnitude of the angle of attack increment caused by the vertical rate of descent. The incidence angles are larger for the root elements than for the tip elements. Increase of the incidence angles leads to deceleration of the autorotation.

The angle of attack increment (Да = arc tg VjesA°r) depends only on r, which means that its magnitude is larger for the root elements. The larger Да, the more accelerated the autorotation will be. The effect of the angle of attack increment on autorotation is greater than the influence of geometrical twist, therefore, the root elements will have accelerated autorotation while the tip elements will have decelerated autorotation.

Answer 2. The autorotation conditions are different for the different blade elements. The autorotation conditions are determined by the tilt of the force vector AR, and this tilt, in turn, depends on the pitch of the given element. Consequently, the autorotation conditions are determined by the pitch of the given element. As a result of the geometric twist, each element has its own pitch. The pitch for the root elements is larger, and this means that for these elements the force vector AR is tilted aft more, and the auto­rotation is decelerated. The tip elements have lower pitch, therefore, they have accelerated autorotation.

Answer 3. The autorotation conditions of the different blade elements are determined by the geometric twist, circumferential velocity tor of the blade element, and the induced velocity. As a result of geometric twist, the root blade elements have more pitch and higher induced velocity, therefore, they will have a lower vertical flow velocity. As a result of the higher incidence angle and lower vertical velocity, there is a reduction of the angle of attack increment (Да = acr tg V^eg д/шг) » and, therefore, the force vector AR is tilted aft. The conclusion is that the autorotation of the root elements will be decelerated, while that of the tip elements is accelerated.

Purpose of Main Rotor Hub Horizontal Hinges

The horizontal hinge (HH) has its axis in the plane of rotation of the hub, perpendicular to the longitudinal axis of the. blade (Figure 35a). The blade thrust develops a moment which rotates the blade about this hinge. The thrust moment M.^, = Та causes rotation of the blade relative to this hinge, /50

and this means that the moment is not transmitted to the hub (the thrust overturning moment is eliminated) (Figure 35b).

When the horizontal hinge is used, the thrust-force bending moment at the root of the blade becomes zero, thus unloading the root section; the blade bending is reduced and therefore blade fatigue stresses are reduced and blade service life is increased. The vibrations caused by azimuthal variation of the blade thrust-force moment are also reduced. Summarizing, we can say that the horizontal hinges are intended to:

eliminate the main rotor thrust overturning moment in the forward flight regime;

relieve the blade root section of the thrust bending moment;

reduce fatigue stresses in the blade and vibrations caused by azimuthal variation of the blade thrust moment.

In addition, the horizontal hinges simplify control of the main rotor and helicopter, improve helicopter static stability, and reduce the magnitude of the azimuthal blade thrust variation.

Factors limiting maximal helicopter horizontal flight speed and ways to increase this speed

Answer 1. The maximal horizontal flight speed of a helicopter is limited by the engine power available. Flight at speeds higher than the maximal is not possible, since more power is required for such flight than the engine develops. Powerful gas turbine engines are installed on the new helicopters, for example, the Mi-2, Mi-6, and Mi-8, to increase the maximal flight speed.

Answer 2. With increase of the horizontal flight speed, the forward tilt of the main rotor plane of rotation must be increased. This leads to reduction

of the main rotor angle of attack. As a result of the reduction of the angle

of attack, the rotor thrust force decreases. This is then the reason for the maximal speed limitation. To increase the maximal speed we must increase the main rotor rpm, which requires the more powerful gas turbine engines.

Answer 3. The rotor thrust force must be increased in order to increase the flight speed. If the thrust force is increased by increasing the rpm, local compression shocks develop on the blades. If we increase the thrust force by increasing the main rotor pitch, then the angles of attack of the blade elements at the 270° azimuth increase. The speed is limited by the onset

of blade stall at angles of attack above the critical value. To increase the

speed the main rotor must be unloaded by installing an additional wing or thrusting propellers, i. e., compound helicopters such as the Mi-6, Kamov rotor-wing, and so on must be constructed.