Category HELICOPTER AERODYNAMICS

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

the 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.

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

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;

4) The 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.

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.

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.

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.

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.

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.

movable 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

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.

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:

1 – 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.

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.

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.

§ 57. Vertical Descent

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.

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? ■

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

2 P С#?

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

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

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

it u

Substituting these values into (42) , we obtain

We 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. 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

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

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.