Category HELICOPTER AERODYNAMICS

Forces Resisting Rotation of the Main Rotor

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

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

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

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

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

Forces Resisting Rotation of the Main Rotor

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

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

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

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

rotation ДО..

x

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

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

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

b

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

Mr = Qbr<A

where

 

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

 

к

 

Forces Resisting Rotation of the Main Rotor

Figure 17. Main rotor rotational resistance forces.

 

Forces Resisting Rotation of the Main Rotor

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

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

Thrust and Power Required for Hovering

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

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

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

 

Thrust and Power Required for Hovering

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

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

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

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

«Т = – p = 9 – 4 = 5°.

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

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

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

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

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

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

(21)

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

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

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

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

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

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

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

tor

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

x pr

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

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

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

by the respective formulas:

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

V’^ — 0.52 У Cr.

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

Vu = 0.52 у 0.0066 = 0.043.

We substitute this value into (22) and find in

tor

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

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

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

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

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

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

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

(23)

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

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

N = pr 100x*

where V is the inverse of the blade element efficiency.

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

Подпись: C.X

V

 

Thrust and Power Required for Hovering

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

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

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

Thrust and Power Required for Hovering

Thrust and Power Required for Hovering— 136 hp ;

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

Thrust and Power Required for Hovering

Figure 55. Hovering at low height.

 

Thrust and Power Required for Hovering

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

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

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

Подпись: P
Thrust and Power Required for Hovering

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

where P is atmospheric pressure.

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

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

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

Safety Height

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

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

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

Eb = GH,

where G is the helicopter weight;

H is the helicopter flight altitude.

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

GV,

0.2GH = gl, 2g

Подпись: /133

Подпись: H = Safety Height

Hence, we find the safe helicopter hover height

Safety Height Подпись: + 10.
Safety Height

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

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

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

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

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

Подпись: safПодпись:Safety HeightH

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

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

Safety Height
Safety Height
Подпись: + 10.

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

Blade Thrust and Its

Подпись:Azimuthal Variation

Подпись:During rotation of the main rotor in the forward flight regime, there is continuous variation of the blade position relative to the flight velocity vector or the velocity vector of the undisturbed flow approaching the main rotor. This situation in­fluences the nature of the flow over the blade and the forces which arise, the reason for many phenomena which special concept is introduced to

The azimuth, or the angle of the azimuthal position of the blade, is the angle between a reference line and the blade longitudinal axis at a given moment of time (Figure 29).

It is customary to take as the reference line the blade longitudinal axis when the blade is positioned directly aft of the main rotor hub.

The azimuth is reckoned from 0 to 360° in the direction of rotation of the main rotor and is represented by the letter p. The blade traveling from /44 from the 0° azimuth to the 180° azimuth is called the advancing blade. The blade travelling from the 180° azimuth to the 360° azimuth is called the retreating blade. The concepts of "advancing" and "retreating" blades are associated with the variation of the direction of the undisturbed stream approaching the blade.

In the case of the advancing blade, the undisturbed flow created by helicopter flight is directed at some angle to the blade leading edge, while

in the case of the retreating blade, this flow is directed at the trailing edge, increases the vibration of the main rotor and the variation of the blade thrust as a function of azimuth, and reduces the main rotor thrust in the forward flight regime. The main rotor blade has a section of the lifting surface removed in the root region in order to reduce these undesirable phenomena (Figure 30). Increase of the cutout reduces the influence of reverse flow, but increases the root losses and, consequently, the magnitude of the thrust in the forward flight regime. An optimal size of the root cutouts is established for each main rotor.

Подпись:The thrust of an individual blade can be found from the same formula used to obtain wing lift

rb = S5b^TF2’

where C is the blade thrust coefficient;

Tb

S, is the blade planform area; b

W is the resultant blade tip velocity.

The blade thrust coefficient depends on its shape and incidence angle;

consequently, for a fixed pitch ф the quantities C and S are constants.

b

Then for constant air density the blade thrust will vary similarly to the variation of the resultant velocity over the blade.

In the forward flight regime the blade thrust reaches its maximal value at the 90° azimuth, since in this case the resultant velocity over the blade is maximal. Conversely, at ф = 270° the blade thrust is minimal, since the resultant velocity is least at this azimuth (see Figure 31c).

How can the maximal flight speed of the helicopter be increased?

In order to avoid blade tip stall at the 270° azimuth with increase of the forward speed, it is necessary to reduce the main rotor pitch. But this leads to reduction of the thrust and creation of a deficiency of the lift force (-AY) and of the propulsive force (-ДР) (Figure 65). In order to avoid these phenomena, use is made of an auxiliary wing, which creates the additional lift force ДУ.

The additional propulsive force AP necessary to increase the speed is /98 created either by increasing the engine thrust or by the thrust of additional propellers. Helicopters with an additional wing and additional propellers are called compound helicopters. In these helicopters there is an unloading of the main rotors such that they can operate with lower incidence angles, and blade stall occurs at higher speeds. Helicopters of this type include the

Mi-6 and Kamov’s prop-wing design with side-by-side rotors. The speed of the compound helicopters reaches 400-450 km/hr. However, they also have draw­backs : increased structural weight

Подпись: Figure 65. Techniques for unloading main rotor. and increased parasite drag as a result of the slipstream from the main rotor flowing over the wing.

This situation is particularly charac­teristic for the vertical flight regimes with low horizontal velocities.

Helicopter Static Stability

General analysis of static stability. Static stability is the capability of the helicopter to restore disturbed equilibrium by itself after removal of the factors causing this disturbance. Static stability is attitude stabil­ity. The helicopter will be stable if after equilibrium is disrupted stabili­zing moments develop on the helicopter, i. e., moments directed to restore the previous attitude. Static stability is amplified as a result of damping moments. A damping moment is one which is directed opposite the oscillatory motion of the helicopter about some axis. The difference between the stabili­zing and damping moments is that the former arises as a result of equilibrium disruption and acts after the termination of this disruption. The damping moment acts only in the process of equilibrium disruption and is directed opposite the deviation.

If during and after equilibrium disruption, moments appear on the helicopter which deflect it still further from the previous attitude, such moments are termed destabilizing. The helicopter on which destabilizing moments arise is termed statically unstable. The helicopter on which no moments arise during and after the equilibrium disruption process has indiffer­ent equilibrium and is termed statically neutral.

The factors which disturb equilibrium are:

(1) unsettled state of the air ("turbulence");

(2) random deflection of the control levers;

(3) failure of some part of the helicopter;

(4) change of the eg location.

Characteristic of helicopter equilibrium is the intimate interconnection of the individual equilibrium modes with one another. For example, if longitudinal equilibrium is disrupted, i. e., if the helicopter rotates about the transverse axis, the main rotor angle of attack changes. This involves a change of the thrust force and the reactive moment of the main rotor. The change of the reactive moment disrupts the directional equilibrium. Disrup­tion of directional equilibrium leads to change of the tail rotor thrust force /160 and change of the moment of this force relative to the longitudinal axis, which means disruption of the helicopter transverse equilibrium. The intimate interconnection among the equilibrium modes requires constant action from the pilot, directed toward restoring the disrupted equilibrium, i. e., helicopter control becomes more complicated. Does the helicopter have static stability?

In order to answer this question we must examine the static stability of the main rotor, the static stability of the fuselage, and the effect of the stabil­izer and tail rotor on the static stability.

Main rotor static stability with respect to velocity. When the helicopter equilibrium is disrupted, two motion parameters of the main rotor change: the flight velocity and the angle of attack. Let us assume that the helicopter is performing horizontal flight at the velocity V (Figure 98a). For some reason the flight velocity is increased by AV. As a result there is an increase of the flapping motions of the blades, the main rotor cone axis is deflected aft from the previous position, which is shown dashed in the figure, by the angle є. The tilt of the coning axis leads to the appearance of the force P, directed opposite the flight direction. Under the influence of this force the main rotor velocity will decrease.

Подпись: Figure 98. Main rotor speed stability.
If the flight velocity is reduced by AV (Figure 98b), the cone axis is deflected forward, the force Px in the direction of flight develops, and the flight velocity will increase. The conclusion is that the main rotor has static stability with respect to velocity.

Main rotor static stability with respect to angle of attack. The heli­copter is flying horizontally and the main rotor angle of attack is A. Under the influence of a vertical air current, the helicopter drops its nose and the main rotor angle of attack is reduced by AA (Figure 99a). Prior to dis­ruption of equilibrium, the main rotor thrust force vector passed through the helicopter center of gravity and the moment of the thrust force was zero.

Upon disruption of the equilibrium, the thrust force vector T is deflected forward and the moment Mz = T^a develops relative to the helicopter transverse axis; this moment rotates the helicopter and the main rotor in the direction to reduce the angle of attack. Consequently, this moment will be destabili­zing.

If for some reason the main rotor angle of attack is increased (Figure 99b), the thrust force vector tilts aft and a nose-up moment M^ = T^a is created, which causes the angle of attack to increase. A destabilizing thrust moment is created. The conclusion is that the main rotor is unstable with respect to angle of attack.

Helicopter Static Stability

Figure 99. Main rotor angle-of-attack stability.

Helicopter fuselage static stability. The fuselage has the second largest influence, after the main rotor, on the static stability of the helicopter.

The fuselage of the single-rotor helicopter has static instability about all three axes. A small stabilizer is installed at the aft end of the fuselage to improve longitudinal static stability in horizontal flight. In the hover regime and in flight at low velocity the stabilizer has practically no effect on longitudinal static stability. But with increase of the flight velocity and with reduction of the angle of attack, the longitudinal instability present in a hover decreases, and at negative angles of attack the fuselage plus stabilizer has longitudinal static stability. Thus, the fuselage of the Mi-1 has static stability at angles of attack from -10 to -2°. At positive angles of attack, the fuselage has indifferent longitudinal equilibrium.

The helicopter stabilizer is controllable. Stabilizer control is accomplished with the aid of the collective-throttle lever. When this lever is moved upward, main rotor pitch and stabilizer incidence angle are increased. The controllable stabilizer makes it possible to tilt the helicopter fuselage to a negative angle at the maximal slight speed. If the stabilizer angle were constant, a large negative lift force would develop on the stabilizer at a negative angle of attack, and this force would create a large nose-up moment to prevent tilting of the fuselage. When the rotor pitch is decreased the

stabilizer incidence angle becomes negative and a nose-up moment is developed, which aids in transitioning the main rotor into the autorotative regime. The main rotor angle of attack becomes positive, and as a result of the increase /162 of the angle of each blade element the rotor rpm increases.

The tail rotor also affects the fuselage static stability. The fuselage acquires directional stability as a result of the tail rotor. Thus, when directional equilibrium is disrupted, if the helicopter turns to the right for example (with right-hand rotation of the main rotor), the angles of attack of the tail rotor blade elements increase, and the tail rotor thrust force increases by ДТ. The moment of the tail rotor thrust also increases and equilibrium is restored.

If the helicopter turns to the right, the blade element angles of attack will decrease and therefore the thrust will decrease. The tail rotor moment becomes less than the main rotor reactive moment, and this leads to restoration of the equilibrium.

Since the tail rotor is mounted above the helicopter longitudinal axis and creates a transverse thrust moment, this leads to increase of the trans­verse static stability. Therefore, the tail rotor gives the fuselage directional and transverse static stability.

The conclusion is that the helicopter has slight static stability in horizontal flight and indifferent equilibrium in hover and in the other vertical flight regimes.

The static stability of twin-rotor helicopters differs somewhat from that of the single-rotor helicopter. The two-rotor helicopter with tandem arrangement of the rotors has considerably greater longitudinal static stability, while the two-rotor helicopter with side-by-side arrangement has higher transverse stability. This is explained by the variation of the thrust of the lifting rotors when equilibrium is disrupted.

Effect on helicopter static stability of horizontal hinge offset. If the main rotor huh has offset horizontal hinges, the horizontal hinge moments have considerable effect on the longitudinal and transverse static stability of the helicopter. The larger the horizontal hinge offset and the higher the main rotor rpm, the larger the main rotor damping moment and the greater the helicopter static stability. Thus, increase of the static stability is achieved by increasing the horizontal hinge offset. The appearance of the damping moment is explained by the gyroscopic properties of the main rotor.

As is well known, the basic property of the gyroscope is its ability to maintain the attitude of its axis of rotation fixed in space. This property shows up more strongly, the larger the mass and the higher the rpm of the rotating body. What effect does the gyroscopic effect of the main rotor have on the behavior of the helicopter? We shall use an example to investigat this question.

Подпись: /163Let us assume that the longitudinal equilibrium of the helicopter has been disturbed and it has started to rotate about the transverse axis in the nose-

Подпись: Figure 100. moment. down direction (Figure 100). In view of its gyroscopic properties the main rotor will lag behind the helicopter rotation, therefore the main rotor hub axis is deflected from the cone-of – rotation axis. The horizontal hinge moment = Nc will be directed

Подпись: Main rotor dampingopposite the tilt of the helicopter; therefore it will be a damping moment. When equilibrium is disrupted, the helicopter will rotate relative to the stationary cone-of-rotation axis of the main rotor as a result of the gyroscopic effect. And this means that the helicopter center of gravity will also displace together with the helicopter

A

 

relative to the cone-of-rotation axis (shown dashed in Figure 100). The result is the formation of the thrust moment = Та. The damping moment will be equal to the sum of the two moments + Hj, = Nc + Та. The

damping moment will be larger, the. higher the main rotor rpm, the larger the horizontal hinge offset, and the lower the position of the helicopter center of gravity, i. e., the larger the vertical eg displacement. The arm a and the thrust force moment will increase with increase of the distance Y from the hub rotation plane to the center of gravity.

Azimuthal Variation of Rotational Resistance Forces and Reactive Torque

Both the rotational resistance forces and the thrust forces of the blades vary azimuthally as a function of the resultant flow velocity over the blades.

Azimuthal Variation of Rotational Resistance Forces and Reactive Torque

Figure 44. Blade element angle of attack diagram.

 

Azimuthal Variation of Rotational Resistance Forces and Reactive Torque

Figure 45. Blade rotational resis­tance forces at different azimuths.

 

The resistance to rotation of a single blade reaches its maximal value at the 90° azimuth and minimal value at the 270° azimuth.

At the 0° and 180° azimuths the rotational drag in the forward flight regime is equal to the drag in the axial flow regime, if the main rotor pitch and flight altitude remain the same (Figure 45).

As a result of this variation of the resistance to rotation, there will /61 be azimuthal variation of the main rotor reactive torque from the maximal value when the blades are at the 90° and 270° azimuths to the minimal value when they are located at the 0°and 180° azimuths.

The variation of the reactive torque causes vibration (torsional oscil­lations) with a frequency equal to the main rotor rpm or some multiple thereof.

For two blades at opposite azimuth angles the rotational resistance forces are directed oppositely relative to the rotor diameter. At the 0° and 180° azimuths their sum is zero; however, at the 90° and 270° azimuths the sum of these forces is not equal to zero and is directed opposite the helicopter

flight direction, since is larger at the 90° azimuth than at the ф = 270° azimuth. This force is the profile drag of the main rotor.

Effect of Number of Blades on Main Rotor Aerodynamic Characteristics

Single-blade main rotors are not used because of the high degree of /60

unbalance.

The primary advantage of the two-blade main rotors is the simplicity of the construction. But the two-blade rotor has low solidity and consequently poor aerodynamic characteristics (low thrust coefficient C^).

Increase of the solidity with increase of the area of each blade (by increasing its width) leads to increase of the profile drag and reduction of the main rotor efficiency.

Moreover, the blades of any rotor cannot be made perfectly identical.

They always differ from one another in their characteristics; therefore the overall blade thrust varies in the forward flight regime. The main rotor resistance to rotation will also vary, i. e., the load on the rotor shaft will vary, and torsional vibrations of the shaft, main rotor vibrations, and vibrations of the entire helicopter will develop.

These problems can be resolved by increasing the number of blades. The larger the number of blades, the smaller the amplitude of the main rotor thrust variations and the smaller the azimuthal variation of the rotor torque, i. e., the rotor becomes more balanced. However, at the same time rotor fabri­cation and blade balancing and adjustment become more difficult. On this basis, main rotors with 4-5 blades are most frequently encountered.

Thrust required for various flight regimes and its variation in the different regimes

Answer 1. The thrust required for a given regime is the force necessary to provide flight along the given trajectory at the required velocity. For constant velocity the thrust required is practically the same for horizontal flight, climbing flight, and descending flight.

Answer 2. The thrust required for a given flight regime is the force required necessary to balance the airplane weight and create the propulsive force. In a climb the thrust required will be considerably greater, and during descent it will be considerably less than in the horizontal flight regime.

Answer 3. The thrust required for a given regime is the force necessary to overcome the parasite drag. At a constant speed the thrust required will be the same for horizontal flight, inclined climb, and inclined descent.

Power and Torque Required to Rotate Main Rotor

In order for the main rotor to turn, the action of the reactive torque must be overcome, i. e., driving torque must be supplied to the rotor.

The torque Mt ^ which must be supplied to the main rotor is termed the /22

required torque. In magnitude, it equals the reactive torque — in direction, it opposes the latter

= пі F £ (toR)2 R tor tor 2

where in is the torque coefficient, tor

The torque coefficient is a composite quantity, i. e.,

m = m + m

tor tor tor.

pr і

Подпись: where m.Подпись:Подпись: m.Подпись:is the part of the torque coefficient due to profile drag forces. This part depends on the condition of the blade surface, the rotor rpm, and the blade shape; is the part of the torque coefficient due to the induced drag forces and depends primarily on the main rotor pitch (Figure 18).

The formula for the required torque, and also the curve of this torque coefficient versus rotor pitch, makes it possible to conclude that the main rotor required torque will increase with increase of the pitch, rpm, and air density.

We recall that power is work per unit time. The concept of the power required to turn the main rotor can be obtained if we examine the work ex­pended in overcoming the forces resisting the rotation of a single blade, and then the work expended in overcoming the reactive torque of the entire rotor (Figure 19).

The work of a single blade during one revolution of the main rotor is

A,“°b2’V

The main rotor work per second, i. e., the power required, is /23

Power and Torque Required to Rotate Main Rotor

Figure 19. Action of rotational resistance forces.

 

Power and Torque Required to Rotate Main Rotor

Figure 18. Torque coefficient versus main rotor pitch.

 

N = A, kn req b s

where к is the number of blades;

n is the rps.

s

Consequently,

N = Q. 2irr_kn req b Q s

since

Q rnk = and 2Ttn. — «),

Q P J

then

Подпись: (IDN = M o) .
req p

Both the power required and the torque required for the main rotor
change with change of the pitch, rpm, and air density. In order to turn the

J

 

rotor, engine power equal to the power required must be supplied to the rotor shaft. This equality is the condition for constant rpm

N = N sup req

where Ng Is the power supplied to the rotor from the engine.

If the power supplied NgUp > rotor rPm will increase. However,

if N < N the rotor rpm will decrease, sup req r