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Main and Tail Rotor Theory

He Wharekura-tiniKaihautu 0 Aotearoa

THE OPE NP0l.YTE(HN|(OF NEW ZEALAND

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CONTENTS

Basic Rotors 1

The Main Rotor 1

Tilting the Tip-path Plane 2

Coning and Flapping 5

Forces of the Rotor Head 11

Dissymmetry of Lift 13

Gyroscopic Effect 21

Coriolis Effect 23

Hooke's Joint Effect 25

Drag Effect 27

The Tail Rotor 30

Principle of Operation 31

Forces of the Tail Rotor 32

Dissymmetry of Lift 33

Drift 36

10/91

Copyright

This rn'a'Yerial is for the sole use of enrolled students and may not bereproduced without the written authority of the Principal, TOPNZ.

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HELICOPTERS ASSIGNMENT 3

BASIC ROTORS

The main rotor of a helicopter converts the power suppliedto it from the engine into a lifting force. When tilted forwards,backwards, or to either side, the lifting force propels thehelicopter. The mechanism within the rotor head that tilts thelifting force is controlled by the pilot through the collectivepitch lever and the cyclic pitch~control column. By tiltingthe lifting force, the pilot controls the helicopter about thelateral and longitudinal axes.

The tail rotor is the helicopter's rudder. It consists ofa rotor mounted vertically and at 90° to the centre line of thehelicopter. It is driven by the engine through the same powertrain used to drive the main rotor and is arranged to turnwhenever the main rotor turns. The tail rotor provides an opposingforce to the torque reaction of the main rotor and controls thehelicopter about the vertical axis, especially when hovering. Itis controlled through the tail rotor (rudder) pedals.

In this assignment, we will show you how the lifting force ofa main rotor is tilted and resolved into lift and thrust. We willconsider the tail rotor and discuss the aerodynamic and mechanicalforces acting on the helicopter. You will find the terms used in theTable of Definitions in the Basic Helicopter assignment.

THE MAIN ROTOR

As with an aircraft propeller, the thrust generated by ahelicopter rotor acts at right angles to the tip-path plane.Opposing this force and exactly equalling it, when hovering, isthe weight of the helicopter. In this condition, iii; is equal

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(b) Forward flight. Tip path Plane lilted forward.

LIFT

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(c) Total reaction resolved into lift and thrust forfor-ward flight.

FIG. l .Ti1ting the tip-path plane toobtain thrust

to weight and, because thehelicopter is not moving, £532and thrust are zero. To obtainhorizontal movement of thehelicopter, the tip-path planeis tilted and the total reactionresolves into lift and thrust,with the lift supporting theweight and the thrust beingequal to the drag for straightand level flight. Figure lshows these forces acting on ahelicopter in hover and inforward flight.

When lift and weight areunbalanced, the helicopter willclimb or descend. When thrustand drag are unbalanced, thehelicopter will accelerate orslow down. For example, ina climbing, accelerating flight,the thrust exceeds the drag andthe lift exceeds the weight.

Tilting the Tip-path Plane

The tip-path plane can be tilted in several ways:

l. By tilting the complete rotor head, gearbox, andengine assembly;

2. By changing the centre of gravity of the helicopterby, for example, moving the cabin assembly;

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3. By tilting a gimbal or centrally pivoted rotorhead;

4. By using aerodynamic forces to lift and depressrotor blades hinged to a rotor head that isrigidly mounted on its drive shaft; or

5. By using aerodynamic forces to lift and depressrotor blades rigidly fixed to the rigidly mountedrotor head, thus bending the blades near theirroot ends.

In practice, the last three methods are used, and the rotorsthat use these methods are

1. The semi—rigid rotor,

2. The articulated rotor, and

3. The rigid rotor or hingeless rotor.

Thehingeless and articulated rotor heads tilt the tip~path planeby simply increasing the angle of attack of the retreating blade anddecreasing that of the advancing blade. The retreating blade thengenerates more lift and the advancing blade, less lift. As aresult, the retreating blade flaps up and the advancing bladeflaps down, as shown in Fig. 2 (a) and(b).

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(a) An articulated rotor withthe tip-path plane tilted

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(b) A hingeless rotor with thetip-path plane tilted

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(c) A semi-rigid rotor with thetip-path plane tilted

FIG. 2 Types of rotor

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The tilting is controlledby the cyclic-pitch control columnusually called the cyclic, andcan be effected in any direction.The cyclic column is movedforward to tilt the tip-pathplane forward, which moves thehelicopter forward. It ismoved to the right to tilt thetip-path plane to the rightmoving the helicopter to theright. The same principleapplies to left and aft movementsof the cyclic column and, ofcourse, for any intermediateposition.

The tip~path plane of thesemi-rigid rotor is tilted inthe same way, with the risingof the retreating blade beingequalled by the dropping ofthe advancing blade. Becauseboth blades are mounted on arigid, centrally pivoted yoke,the complete rotor head tiltsor seesaws in the directionchosen. Figure 2 (c) showsa tilted tip-path plane fora semi—rigid rotor.

For vertical flight, theangle of attack of all the bladesis increased or decreasedsimultaneously. This iscontrolled by the collective-

pitch control column, usually called the collective. Thepilot raises the collective forlowers it to go down.

the helicopter to go up and

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The control inputs to the rotor head from the cyclic and thecollective pitch controls are superimposed upon each othermechanically so that, for example, a climbing, turning, forwardflight path is possible.

I SUMMARY

The main rotor converts engine power into a force thatcan both lift and propel the helicopter.

The total reaction of a rotor is at right angles tothe tip-path plane.

Flight in any direction is obtained by tilting thetip-path plane.

In flight, the total rotor reaction is resolved intolift and thrust.

I Three types of rotor are generally used:‘\

p l. The semi—rigid rotor,

2. The articulated rotor, and

3. The rigid or hingeless rotor.

The tail rotor counteracts the torque of the main rotorand gives directional control during hovering.

Coning and Flapping

when the helicopter is hovering in still air, the airflowcomes from directly above and goes straight down through the rotorThe lift force generated by the turning rotor acts verticallyupward and is equal to the weight (mass) of the helicopter actingvertically downward. In this condition, the main forces actingon the rotor assembly are

1. The lift force from each blade, and

2. The centrifugal force of each blade.

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The lift force acts to lift each blade tip upwards, and thecentrifugal force acts to keep each blade horizontal. The twoforces resolve into a single force, that results in a small upwardmovement of the blade tip. The angle formed between the bladeand a plane at right angles to the rotor shaft is called theconing angle. See Fig. 3.

The articulated rotor has each blade mounted on a horizontalor flapping hinge, which permits its blade to freely move up anddown or flap.

The rigid rotor permits the blade tip to move up andcbwn bythe bending of the blade and the bending of the rotor head justinboard of the blade attachment.

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Coning angle

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FIG. 3 Coning angle

Neither the articulated nor the rigid rotor system can giveflight other than hovering unless a coning angle is generated.The coning angle must be displaced about the main rotor shaftby the flapping of the blades to give the tilted tip-path planenecessary for horizontal movement. See Fig. 2 (a) and (b).

Because the semi-rigid rotor has its tip-path plane tilted bythe complete rotor-head assembly tilting about its central pivotpoint, both blades flap together but in opposite directions.As one blade flaps up, the other blade simultaneously flaps downby an equal amount. See Fig. 2 (c). Thus, the semi-rigid rotordoes not need to make a coning angle, and the lift force bendsthe stiff, heavily built blades evenly but slightly along theirspan. However, the yoke of the semi-rigid rotor does have a smallbuilt-in coning angle of between 2° and 6°. This is done for

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a reason that we shall discuss later in this assignment underCoriolis Effect.

In fact, the coning angle hardly varies during all stages offlight because the rotor and engine rev/min are held in a narrowoperating range. During flight, fuel is burned off and so thehelicopter becomes lighter. Also during flight, loads may bewinched aboard or released from a cargo hook. Any increases/decreasesin load make only a small difference to the coning angle and so-only small changes in blade—pitch angle are made to correct forthem.

The following simplified example shows the change in coningangle caused by an increase in the weight of a helicopter with afour-bladed articulated rotor head. The figures used are notexact.

Helicopter AUW = 8000 lbf

Weight of each blade = llO lbf

Radius of blade at its

C of G location = 13 ft

Rotor rev/min = 210

Lift generated by each blade # gggg

= 2000 lbf

2Centrifugal force = aléloz ><<1TXn2n2n0*x 210) >< 113 lbf

= 21 477 lbf

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FIG. 4 Generating a coning angle

2000tans = are6 = tan 0.093l2

Coning angle or 9 = 5° 19‘

The helicopter is now loaded to ll 000 lb max. AUW.

Lift generatedby each blade = iiggg

= 2750 lb

Centrifugal force = 21477 lb

2750tan“ " nan"9 = tan 0.1280

Coning angle or G = 7° 18‘

A weight increase of 3000 lb has increased the coningangle by about 2°.

During flight, the rotor and engine rev/min can be consideredas constant, with the power being changed by alteration to theengine induction manifold pressure or fuel flow and, at thesame time, collectively altering the main rotor blade angles.

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The power is changed because the inertia of the rotor head andblades assembly makes an increase or decrease in rotor rev/minimpossible to get in a reasonable time, but a quick responseto a change in power may be obtained by changing the blade pitch-angles with a change in engine fuel flow.

We cannot overemphasise the importance of keeping the rev/minin the correct range. If the recommended rev/min are exceeded,damage to the engine, transmission, rotor head, and blades willresult, the severity of the damage depending upon the amount andduration of the overspeed.

If the rev/min fall below those recommended, the collectivepitch must be decreased or the engine power increased and therev/min allowed to increase to their normal value. However,if no more engine power is available, the helicopter will have todescend with the reduced collective pitch. If the collectivepitch is increased to maintain altitude, the increase in bladeangle above normal will produce more drag for the lift generated,the rev/min will decay (slow down) further, and the helicopter willdescend rapidly. When this occurs with a fully articulated rotor,the coning angle increases due to the reduced centrifugal forceuntil a position is reached where it takes a long time to bringthe blades down again by reducing collective pitch. A veryheavylandingp is then unavoidable.

Early helicopters with articulated rotors could get theirblades pointing almost vertically upwards. This condition, knownas candling, resulted in a crash landing. Modern articulatedrotor heads have inbuilt or adjustable upper coning stops toprevent excessive coning of the blades. These stops are set atan angle well outside the normal coning angle of the bladesbut small enough to allow a reasonably rapid increase in rev/minwhen collective pitch is reduced.

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SUMMARY

In flight, the engine and rotor rev/min are kept in anarrow operating range .

The coning angle is caused by the balance of lift andcentrifugal forces.

The tip-path plane is tilted to give forward flightby flapping the blades up at the rear and down at thefront of the helicopter.

3 In a semi-rigid rotor, as one blade flaps up, the‘ other blade flaps down by an equal amount.

1 A very low rotor rev/min will produce a large coningangle, which could endanger flight.

PRACTICE EXERCISE A

State whether each of the following statements is trueor false:

l. The main rotor is controlled by the pilot throughthe collective and cyclic pitch control columns.

2. The main purpose of the tail rotor is to controlthe helicopter about the vertical axis when inlevel flight.

3. The total reaction of the main rotor is resolvedinto lift and drag when the tip-path plane istilted.

4. When the tip-path plane is tilted to the right,the helicopter moves to the right.

5. During hovering, the lift of the main rotor mustslightly exceed the weight of the helicopter.

6. In tilting the tip~path plane of a semi-rigidrotor, the complete rotor head assembly is tilted.

7. The total reaction of a rotor is at right anglesto the tip-path plane.

8. The coning angle is the angle formed between theblades and the relative airflow.

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9. The horizontal or flapping hinges of an articulatedrotor permit the blades to freely flap up and down.

10. A rigid rotor has its blades rigidly attached tothe rotor head, which is itself rigidly attachedto the rotor drive shaft.

(Answers on page39)

Forces of the Rotor Head

To achieve flight, the tip-path plane is tilted in the desireddirection, and the total reaction from the rotor head and bladesassembly becomes resolved into lift to support the weight andthrust to propel the helicopter. As the helicopter moves, theairflow direction into the rotor head changes from directlyabove to ahead and above. At the same time, the airflow from therotor changes from straight down, forming a ground cushion, to aftand down.

These changes in the airflow through the rotor disc, and thefact that the tip-path plane has been tilted, create extra forcesand effects above those experienced when hovering.

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Dissymmetry of Lift

The area within the tip~path plane of the main rotor is calledthe disc area or, more generally, the rotor disc. when thehelicopter is hovering in still air, lift is generated by therotor blades equally at all positions around the rotor disc.As the helicopter moves, or as a wind is felt, the velocity of theairflow over the rotor blades changes, with a higher velocityin one half of the rotor disc and a lower velocity in the otherhalf. As a result of the different air velocities, differentlift forces will be generated from one side of the rotor disc tothe other. Unless this unequal distribution of lift is counteracted,the helicopter would roll over in the direction of the side withthe least lift. The unequal distribution of lift, called thedissgngetrg of 1ift,was a considerable problem to the designersof early helicopters and autogiros.

Figure 6 (a) shows typical velocities at different positionson a rotor blade when the helicopter is hovering in still air.Because the air is still and the helicopter is hovering, therotor blade velocity is also the velocity of the air over theblade. The blade will thus experience the same air velocitiesat all positions in the rotor disc.

Figure 6 (b) shows the same helicopter in forward flightwith an IAS of 100 kt. With this IAS, the air velocity feltby the tip of the blade when it is advancing and at 90° to theline of flight is the tip velocity pigs the 100 kt TAS, givinga total of 500 kt. This increase in air velocity of 100 kt isfelt along the span of the advancing blade. when the blade isretreating and at 90° to the line of flight, the air velocityfelt at the tip is the tip velocity minus the lU0—kt IAS, givinga total of 300 kt. This decrease in air velocity of 100 kt isfelt along the span of the retreating blade. For any given angleof attack, the lift generated increases as the velocity of theairflow over the airfoil increases. In fact, the lift increasesas the square of the air velocity. That is

If an air velocity of A m/s gives l unit of lift, then an airvelocity of ZXA m/s gives 4 units of lift, and an air velocityof 3XA m/s gives 9 units of lift.

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Bearing this in mind, a study of Fig. 6 (b) will show thatmore lift will be generated in the advancing half than in theretreating half of the rotor disc unless some correction is used

We have seen that the articulated rotor and the rigid rotorsystems have blades that either flap or bend in the verticalplane. In forward flight, the increased lift on the advancingblade due to forward motion of the helicopter will cause theblade to flap or bend up. This upward movement will decreasethe angle of attack because the relative wind will change froma horizontal direction to more of a downward direction while theblade is moving upward. See Fig. 7.

AIRFLOWFROM ABOVE

its ,dAIRFLOW mom AHEAD

APParen1 angle of attackSpace diagram of two velocities

—-- MRFLOW FROM ABOVE

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True angle of attack

FIG. 7 Change in angle of attack due to flapping

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The decreased lift on the retreating blade will cause theblade to flap or bend downward. This downward movement willincrease the angle of attack because the relative wind willchange from a horizontal direction to an upward direction while theblade is moving down, as shown in Fig. 7.

The combination of decreased angle of attack on the advancingblade and increased angle of attack on the retreating bladethrough blade flapping tends to equalise the lift over the twohalves of the rotor disc. The position of the cyclic pitch—controlcolumn in forward flight also causes a decrease in the angleof attack on the advancing blade and an increase in the angle ofattack of the retreating blade. This movement of the controlcolumn gives the major correction for dissymmetry of lift, withthe correction for blade flap being a minor but necessary contribution

The semi-rigid rotor behaves as a seesaw. As one blade flapsup, the other blade flaps down and, as already explained, thechange in angle of attack of each blade tends to equalise thelift over the rotor disc. Again, however, the major correctionfor dissymetry of lift is supplied by the forward movement of thecontrol column.

Another method that can be used on the articulated and rigidrotor systems to decrease the angle of attack and the consequentlift of an advancing blade flapping up and to increase the angleof attack and the lift of a retreating blade flapping down isto slightly offset the pitch—change horn on the blade in relationto the flapping hinge. Figure 8 shows this offset in a greatlyexaggerated form. The pitch~change control rod that conveysthe input from the pilot to the rotor blade is attached toface A on the control horn and the blade can rotate on the bladespindle.

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FIG. 8 Offset pitch~change horn

In Fig. 8 (a), when the advancing blade flaps up because ofthe increased airflow, there will be no mechanical change in theangle of attack of the blade because the centre lines of theflapping hinge and the contro1—rod attachment to the control horncoincide. However, in Fig. 8 (b), when the advancing blade flapsup, the angle of attack of the blade is mechanically decreasedbecause the centre line of the control rod attachment to thecontrol horn is outboard of the centre line of the flapping hingeAs the blade flaps up, it also rotates on its blade spindle, withthe leading edge going down. The reverse occurs when a bladeretreats and starts to flap down.

In flight, the blades are allowed to flap as they wish.No damping devices or mechanicalrestraintsare used to inhibit orprevent flapping other than the limits of movement imposed by thedesign of the rotor head and,in some helicopters, an upper coningstop.

For practical design and construction reasons, the flappinghinges are offset. That is, they do not lie in the geometriccentre of the rotor head. This offset of the flapping hingeshas a useful dynamic effect in the control of the helicopter.

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In Fig. 9, the strings represent the rotor blades, the arrowsshow the centrifugal force, and the weight represents the fuselageof the helicopter. In Fig. 9 (a), the tip-path plane is tilted,but because the blades are hinged in the centre of the rotor, thefuselage hangs straight down and will be slow to adapt itsattitude to the tilt of the rotor. If its centre of gravity wasanywhere but in the same lateral plane as the lift vector of therotor, the helicopter would be unmanageable. In Fig. 9 Cb), thefuselage quickly follows the tilt of the tip-path plane, andthe position of the centre of gravity is now not so critical. Theresult is a helicopter that is sensitive to the control of thepilot and has a useful working range of permissible centre—of-gravity movement.

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FIG. 9 Dynamic effect of offset flapping hinges

The offset distance of the flapping hinges determines thesize of this dynamic effect. The blades in a rigid rotor are,in effect, stiff continuous flapping hinges, and the overalleffect is similar to widely offset flapping hinges.

The semi-rigid rotor also uses a dynamic effect to give amanageable and sensitive response to the pilot’s controls. Thiseffect is obtained by having the rotor assembly underslung on

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its pivot. That is, the centre of gravity of the rotor assemblylies below its central pivot axis.

Figure l0 Ca) shows a semi-rigid rotor helicopter hovering,with the lift vector acting vertically upward and the weightvector acting vertically downward and in the same plane. Figure l0Cb) shows the tip-path plane tilted for forward flight, with thelift vector moved aft because of the tilt of the assembly. As aresult of this movement, a couple is formed by the lift and weightvectors, which lowers the nose of the helicopter. The underslungmounting of the semi-rigid rotor assembly has another importantservice to perform, which we shall discuss later on in thisassignment under Coriolis Effect.

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SUMMARY

Dissymmetry of lift is caused by horizontal flight orby wind during hover.

Y Dissymmetry of lift is the difference in lift that occursbetween the advancing blade half and the retreating bladehalf of the rotor disc area.

\

5 Unless corrected, dissymetry of lift will roll the‘ helicopter to the side opposite to the advancing blade.

Dissymmetry of lift is corrected by

l. An aerodynamic reduction in the angle of attackT as the advancing blade flaps up and an increase

l as the retreating blade flaps down;

2. The blade's angle of attack being reduced as itadvances and increased as it retreats by theposition of the cyclic control column; and some-

] times by

3. Mechanically reducing the angle of attack of the\ advancing blade and increasing it on the retreating1 blade by offsetting the blade control horn with‘ respect to the flapping hinge.

PRACTICE EXERCISE B

l. Show, with the aid of a sketch, why the adyancingblade of a helicopter in horizontal flight tendsto develop more lift than the retreating bladeunless corrected.

2. Make a freehand sketch of an airfoil section meetingan airflw, and show the chord line and angle ofattack of the airfoil.

3. With the aid of a sketch, show that, when a rotorblade flaps up, its angle of attack is aero-dynamically reduced.

(Answers on page39)

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Gyroscopic Effect

The turning main rotor assembly behaves as a large gyroscopein that it tilts at right angles to the direction of a push thatit receives. This behaviour in a gyroscope is called precession—— in a helicopter if is called ggrgscopic effect or phase lag.

Figure ll shows how a gyroscope tilts or precesses in areaction to an applied force or push. -

(Q) 11,, grm,c,,p¢_ (5) The ‘rg':eJegr?;;:>l;!;£::°I:Pi41Y~F" (C) 5ubpose"t£|;’::'Inr;-is split into (d) Attend to two of these segments.

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I(M) This is the key diagram. Study it care- (H) All the other segment: must (0) T-h='=l'¢re the whole wheel trlu. (P) Thu: when a gyroscope is given a pushfH"Y- The axle is rigidly connected In the fin in we mm, wan il "'15 1" Pith! angle: to the directwn ufsegments and must therefore tilt when the the push.

segments move diagonally.

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FIG. ll How a gyroscope tilts

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Figure 12 shows the gyroscopef““~\ rotor without its gimbals, and

fii?T lying in a horizontal plane suchr/,/IF as a main rotor assembly. If

._M/‘\\\\'i§ we apply a push to the rotor 'A'/ at A,it will move in the direction

marked tilt at B. Compare thisLl ‘PUSH movement with that shown in

Fig. ll and you will find thatit is the same. You can thussee that the tilting of the

orotor occurs 90 later in the direction of rotation from, and in

FIG. 12 Tilting of a rotor

the same sense as, the applied force.

We have seen earlier that, for horizontal flight, the tip~path plane is tilted forward by the retreating blade being madeto flap up and the advancing blade being allowed to flap down, andthat a blade is made to flap up or down by its angle of attack,and thus the lift-force generated being increased or decreased.Because of the gyroscopic effect of the turning rotor, the changein angle of attack must be made 90° before it is to take effect.Thus, the desired change for forward flight is made at 90° to thecentre line on the left—hand side of the helicopter —— see Fig. 13.

LOW NTCH APPLIED

HIGH FLAP RESULT

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- FIG. 13 Where the angle of attack is changed

This applies to a rotor which is turning in the conventionaldirection, which is counterclockwise when viewed from above.

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This 90° lead in the control can be seen very easily on aBell helicopter if you position the blades in a fore~and—aftdirection and then move the cyclic control column backwa dr s andforwards, watching the blades at the same time. No movementtakes place at all when this is done, but when the control columnis moved laterally, the blades increase and decrease their pitchas the control is moved. The same effect can be seen, less easily,in a fully articulated rotor if you position the control horn push-pull rod of one blade directly over a control rod into the swash-latp e and then move the cyclic control column.

Coriolis Effect

As a blade of a fully articulated or rigid rotor flaps up, thecentre of mass of the blade moves in towards the centre of therotor disc, and as the blade flaps down, it moves outward.See Fig. lu.

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FIG. 14 Blade centre of mass movement

Remember that, because of coning, a blade of these two typesf .0 rotor will not flap down below a plane passing through thetro or hub and perpendicular to the axis of rotation.

The product of mass and velocity yields momentum. Thatis

Mass X Velocity = Momentum

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_ gu _

Thus, when a rotor is turning, each blade has a certainamount of momentum.

The law of Conservation of Momentum states that "the momentum

of a body does not change unless an unbalanced external forceacts on it". As a blade flaps up, its centre of mass moves towardsthe axis of rotation, and so the length of its path around theaxis becomes shorter. For the blade to retain the same momentum,which it must, its angular velocity must therefore increase. Thereverse holds true as a blade flaps down.

This law is well demonstrated by the exhibition ice skater.When the skater pirouettes with her arms outstretched, her rateof spin is not very great, but as she lowers her arms, the rateincreases markedly.

When the blade flaps up and increases its angular velocity,it is said to £551, and as it flaps down and decreases its angularvelocity, it is said to £52. The rigid rotor handles the leadand lag forces by allowing the blade to bend at or near itsattachment to the rotor head. The blade on an articulated rotormoves because it is mounted on a vertical hinge. See Fig. 15.This hinge is sometimes called a @532 or lead-lag hinge.

--- I 6 EDir¢ch.°~ .... -- LE \

W‘-:4. ___. _ ‘I

ca ___.-- ;

'.

_ 1_ ::'

/‘ .7. _’1 _________ __

,. , '=, ‘ _ _ _ - A . _ _ _ __ I:-5/__ I ; ' ' ' ' ' . ~' " .__ If

“--- I . = "--\ :““' 1 I _ ". \.- 3. . :' /Vcrhcal hmge .' I

‘"-~~~.':.AGG”VG / : I '

FIG. l5 Leading and lagging

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-25..

The blade is not free to lead and lag without restraint, whichwould cause mechanical damage to the rotor head and would alsocreate an unbalanced rotor. It is attached to a damping device,which is adjusted to give a specified rate of movement under agiven load.

The semi-rigid rotor is underslung and has a small presetconing angle. These two features greatly reduce the corioliseffect. As a blade flaps up, the centre of gravity of the rotorassembly moves out from the axis of rotation in the direction ofthat blade. See Fig. 16 (b). As the blades flap, they willtend to increase their velocity to maintain their momentum but,because the C of G of the head has moved away from the axis ofrotation, it will generate some added momentum of its own to thesystem. This added momentum partly cancels that needed by theblades. The source of the momentum does not matter, just solong as the total momentum of the system stays the same. Thus,the blade flapping up will have little tendency to increase itsvelocity to conserve momentum, and the blade flapping down willhave little tendency to decrease its velocity. The smalllead-lag forces that are generated by the remaining corioliseffect are absorbed in blade bending and by massive blade dragbraces that locate the blades in their grips.

Ho0ke's Joint Effect

Horizontal flight is obtained by tilting the tip~path plane.When the tip-path plane is tilted, its plane of rotation differsfrom that of the rotor drive shaft. This difference gives riseto Hooke's joint effect, wherein the driven member of a universaljoint accelerates and decelerates twice in each revolution of thedriving member. Figure l6 shows the effect on a four—bladedarticulated rotor. During hover, the tip-path plane is parallelto the rotor drive-shaft plane, and the blades space themselvesat 90° to each other. Because the blades are not flapping, thereis no coriolis effect, and so the blades will not move abouttheir vertical hinges. In horizontal flight with the tip~pathplane tilted(for the rotor shaft plane of rotation to maintaina constant velocity),the two athwartships blades must move on

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_ 25 _

their vertical hinges to positions A and B. The blades thusaccelerate and decelerate twice in each revolution of the rotorshaft.

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wéat .~ at<i“" -a

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\.,_ _ / ,_

‘—-_._—~"" ‘---...-x._.._....----

._. ......................................................................... .._.,;__

.- -‘ - /-'\ _

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(a) Hovering gb) Horizontal flight

FIG. 16 Hooke‘s joint effect

The articulated rotor caters for this effect by allowing theblades to move on their vertical hinges, the rigid rotor bybending the blades at or near their attachments to the rotor head,and the semi-rigid rotor by bending its stiff and heavy blades.

_ 555/3/3

_ 27 _

I Figure l7 shows a constant-Wmwwfii velocity universal joint where

'_:>§.:,‘ .;;|‘

1HL”““J%§a torque is transferred at constantfir

\ _ _ v 3. 1-’4 “'.g.-.-.- 1.

fi a/..q_ :3 V » g '55‘

1|.-4mll-=w|-I-||f"" "'““w“' '1 nfflrm T . .—— - -—i;+fi% ’ steel balls between the driving

speed by the use of free-moving

Q I l 1 n iv

/

"‘=1|li\'1 2‘-.:\\“1_i,1’ ' » _HE “wmi \ ”m and driven members. Each memberin "K -_ /' ,5” has two fingers or arms, in

the sides of which are specially”‘Zé,_

gawn“v 1agave".-A/J’

*hjfffiY;§&§:,»;§/pix,€~;€“‘’. §?Q‘E

shaped grooves. A steel ball formsthe driving connection in the

FIG. l7 Cqnstant—velocity universal two curved channels formed whenjoint the joint is assembled. The

shape of these channels is such that, irrespective of the angle atwhich the joint operates, the balls always lie in a plane that makesequal angles with both driving and driven members of the joint.This feature is common to all makes of constant~velocity universaljoints.

Rotor heads have been designed and built to behave as aconstant-velocity joint but, so far, this type of rotor head hasnot been used in production-run helicopters.

Drag Effect

As a turning blade advances and then retreats, the velocityof the airflow over the blade varies as does the drag generated.This changing value in drag causes the blade to move about itsvertical hinge or, in the case of the rigid and semi»rigid rotors,for the blade itself to bend.

The five main effects discussed, that is

l. Dissymmetry of lift,

2. j Gyroscopic effect,

3. Coriolis effect,

4. Hooke's joint effect, and

5. Drag effect,

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all take place together when the helicopter is in horizontalflight. However, for hovering in still air, only gyroscopic

_28..

and drag effects occur.

SUMMARY

In an articulated rotor

l. Dissymmetry of lift is corrected by the bladeflapping up and down about the horizontal (flapping)hinge;

2. Gyroscopic effect is allowed for by the angle ofattack of the blade being changed approximately90° before the result of the pitch change isdesired; and

3. Coriolis, Hooke‘s joint, and drag effects areabsorbed by each blade being mounted on a vertical(drag) hinge, with its variations in velocitywith respect to the rotor head being controlledby a blade damper.

For a semi-rigid rotor

1. Dissymmetry of lift is corrected by the bladesflapping up and down about the rotor-head pivotpoint;

2. Gyroscopic effect is allowed for as in thearticulated rotor;

3. Coriolis effect is absorbed by the rotor assemblybeing underslung on the rotor drive shaft; and

4. Hooke‘s joint and drag effects are absorbed byblade bending.

In a rigid rotor

l. Gyroscopic effect is allowed for as in thearticulated rotor, and

2. All other effects are absorbed by the bladesbending at or very near their attachment to therotor head.

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_ 29 _

PRACTICE EXERCISE C

State whether each of the following statements is trueor false:

l. Dissymmetry of lift is experienced when hoveringin still air.

2. The rotor disc is the area within the tip~path plane.

3. A retreating blade experiences a greater air velocitythan does an advancing blade.

4. A horizontal hinge is often called a flapping hinge.

5. As a blade flaps up, its angle of attack decreases.

6. An offset pitch—change horn has no effect on aflapping blade.

7. No allowance for the gyroscopic effect of therotating rotor is needed in its control.

8. Phase lag is another name for gyroscopic effect.

9. Because of gyroscopic effect, the angle of attackof a blade is changed at about 90° of rotorrotation before the desired effect of the changeis to take place.

10. Coriolis effect is apparent only during hoveringin still air.

ll. An underslung semi-rigid rotor with between.2° to 6° ofpreconing will experience little coriolis effect.

l2. The movement of rotor blades in the vertical planeis called flagging.

13. Rotor blade movement on the vertical hinge iscalled flapping.

14. Coriolis, Hooke‘s joint, and drag effects causea blade to move about the vertical hinge.

15. The vertical hinge is often called the draghinge.

16. The rate of blade flap is controlled by a rotorblade damper.

8 l7. A cyclic pitch change alters the pitch anglesof all the blades by the same amount at thesame time.

18. A rigid rotor uses blade bending instead ofvertical and horizontal hinges.

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_ 30 _

19. A semi-rigid rotor seesaws spanwise about a centralpoint.

20. An articulated rotor blade is free to flap abouta horizontal hinge but is damped in its draggingabout a vertical hinge.

(Answers on page 41)

The Tail Rotor

A tail rotor is used to counteract the torque P€acTiOn frcma single main rotor and, to a much lesser extent, to providedirectional control in flight. Helicopters with twin main rotorscounteract their torque reaction by counter—rotating the rotors.Thus, they obtain directional control by mixing the cyclicinputs to each rotor head and so don't need a tail rotor.

The tail rotor is mounted vertically, or nearly so, on one sideof the fuselage, with its centre line at right angles to thedirection of normal forward flight. See Fig. 18. It is driventhrough shafting and gearboxes from the main rotor and isconnected mechanically with the main rotor so that, when the mainrotor turns, so must the tail rotor. This mechanical connectionbetween the two rotors means that, in autorotation, the pilothas normal behaviour from the tail rotor. Ideally, in levelflight, the tail rotor uses little or no power, nearly all powerbeing available at the main rotor for lifting and propelling thehelicopter. The tail rotor uses most power during a climbingturn in the direction of rotation of the main rotor. This isa climbing, left-hand turn if the main rotor turns in theconventional direction of counter-clockwise when looked at fromabove, with a maximum AUW the power used by the tail rotor

in such a turn can exceed 10% of the total power available fromthe engine.

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nu

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l________l

FIG 18 Position of the tail rotor

We determine the direction of rotation by viewing the tailrotor from the side that it is mounted on the helicopter. Atail rotor may have between two and six blades and will turnmuch faster than the main rotor, but usually slower than theengine rev/min. (The rev/min ratio between tail rotor and enginediffers from one type of helicopter to another.)

Principle of Operation

The tail rotor, which is a type of reversible pitch propeller,is controlled by the pilot through conventional rudder pedals.Movement of the rudder pedals increases or decreases the pitchof all the blades by the same amount and in the same_direction,thereby increasing or decreasing the thrust generated and thelateral force felt by the tail of the helicopter. The bladescan be moved from a positive-pitch angle through 0° to anegative-pitch angle so that a thrust to the right or left may beobtained. See Fig. l9.

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._ 32 _

FORWARD(1-innnnnu

‘\f'—Tai| - rofor gearbox

,—""_°-: "“' -'_'jIi-'*"'::—T'—i1> 1;»—<>°AIR FLOW \_ +.

FIG. 19 Positive and negative angles of atail rotor blade

Forces of a Tail Rotor

The tail rotor is a rotating airfoil sited in an airflow. Aswith the main rotor, the airflow causes dissymmetry of lift to befelt across the disc of the tail rotor. In correcting fordissymmetry of lift, the effects of drag, Hooke's joint, andcoriolis are introduced and absorbed by the relatively stiffblades and heavily built hub assembly. The presence of gyroscopiceffect or phase lag does not matter because the pitch of thetail~rotor blades is always changed collectively. As with thearticulated and semi-rigid main rotors, dissymmetry of lift iscatered for by blade flapping or by the assembly seesawing in avertical plane, and by the geometry of the pitch—change mechanismto the blades.

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_ 33 _

Dissymmetry of Lift

From Fig. 18, you will see that the velocity of the airflowover the top tail—rotor blade is

Blade velocity plus airflow velocity.

Over the lower blade, it is

Blade velocity minus airflow velocity.

Thus, if both blades have the same angle of attack, thenmuch more thrust will be produced by the top half of the discthan by the lower half. This uneven distribution of the thrustwill cause vibration and will unevenly load the tail rotor andthe tail—rotor gearbox assembly. This problem is overcome bythe blades flapping in much the same way as the main rotorblades flap. As the top blade flaps outwards away from thehelicopter, its angle of attack becomes less, and less thrust isproduced. At the same time, the lower blade flaps inwards, itsangle of attack is increased, and more thrust is produced. Thenet‘ result of the flapping action is an even distribution ofthrust over the disc area.

Figure 20 shows schematically a two—bladed tail rotor withboth the blades mounted on a yoke freely pivoted in the centreabout a trunnion. Each blade can turn on a feathering (spanwise)axis and is connected to the pitch-change mechanism by a push-pullrod. The trunnion is mounted so that its axis lies at an angleto the centre line of the yoke, which gives an angled hinge calleda delta three hinge, This hinge reduces the angle of attack ofthe advancing blade and increases that of the retreating bladeas the tail rotor flaps. The angle of attack is further alteredby the pitchmchange linkage, because each push-pull rod isattached to the leading-edge side of a blade, the angle ofattack of an outward-flapping blade is reduced. As the bladeflaps inward, its angle of attack is increased. The result oftail~rotor flapping is that for level flight in calm air, theassembly assumes a less than vertical angle. Note angle 6 in Fig.2O

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_ 34 _

~-..4--——-~1-?‘d\-5-Han of +=-:1 v-¢,»b__

____,//

Fuih-Pu" Nd

./ I

Fa|F@jrg|{@7/3

"'§ -iv — Fnfch-changeV Yakg Yo “Gfl$

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kg

.. Trunnion J

"W \\ _ 1Tall-rotor drive. shaftan '

""—'— Trunnion,- Pdch-change head /

> "Fail-rota: ‘~‘ A dnv: shaft 1\/6‘ I

Roiaiiu of blade "_' ‘ 'ab rfn :11 axis ‘---_--4’ "L ' PushpunrodBU Q1 C-T

r—'“'\"" \ * :1 o

r5+0

P=-+-.+.-.,.. .r-1.,“ r=""' ‘ i

; Lin --vi FLAP -------—->- Ouk

FIG. 20 Tail--rotor flapping

You can see the change in the angle of attack of the bladesdue to tail~rotor flapping on the delta three hinge very easilyif you balance a 30—cm rule on a pencil with the rule inclined(offset) at a small angle to the pencil. See Fig. 21. Seesaw

555/3/8

_ 35 _

the rule on the pencil. Asthe 30 cm end of the rule liftsup, the numbers between 15 and 30incline down, and the opposite

' happens with the other end of' e the rule. Increase the angle

of the rule relative to theLead'n5edge Tra'ragedge

pencil and see the effect.Position the pencil almost

‘QQR lengthwise under the rule andsee the effect.

The delta-hinge-mountedtail rotor can have only twoblades. If more are needed\

because more thrust is necessaryngedge

ag:~ 1- or because a large~diameter

L¢.;d';gTra tail rotor cannot be used, adifferent type of tail rotor

FIG; 21 Delta—three-—hinge effect is called for. One common

type of tail rotor that can have as few as two and as many assix blades has a central hub rigidly fixed to the tail—rotorgearbox output shaft, with each blade attached to the hub by aflapping hinge. Each blade can be turned about its featheringaxis and is connected to the pitch—change head by a push»pullrod. The geometry of the pitch~change head and the attachmentof the push—pull rod to the blade is arranged so that, as theblade flaps outward, its angle of attack is reduced and viceversa.

Figure 22 shows schematically this angle change and thetip-path plane of this tail rotor during level flight in calmair.

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'- as -

IFt‘? Our

I

ROTATION I-4-—-—-——- 4

7

F -

“-~_a_

Blade

C)

PLKE}H_“'"““

HI‘..__,___-- Biade spindle

Hingfi

ePikh - change. hand

l ., 7 \

WW\

_QTPQTHp/.

\\l I

/fL?‘

.\'1-4';';;;n

otor with flapping hinget FIG. 22 Tail r

Drift

' ' sed to counteractThe force or thrust from the tail rotor 15 uthe torque reaction of the main rotor. A couple is a pair ofequal and opposite parallel forces that tend to produce rotation,that is, a torque. The force produced by the tail rotor actsperpendicularly to an arm. That is, the tail rotor produces

' e is balanced by the moment, which‘ l

The main rotor torqumall translationa

a moment.

stops its rotational effect but results in a s' ter sideways.force that drifts the helicop

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- 37 _

/ Dlrechon of rotationof mam rater

. , F AF 1 RESULTANT

Q I Reaction for ue O ‘ \ - fie t::1*;=..::a.*:..\

, \

! B:i:ru:|r\g momenl produced by Tall-ruler 1

Q _2_+_ ,E Ta}? rotor fare: I

- FIG. 23 Tail~rotor drift

Drift is counteracted by tilting the main rotor to one sideThe tilt can be achieved by the design of the mount supportingthe main transmission or by the cyclic controls being rigged sothat neutral on the cyclic control column results in the tipapath plane of the main rotor being tilted. A combination ofboth methods is often used.

The main rotor control system is often designed to give aprogressively increasing tilt of the tip-path plane as thecollective is raised. Thus, as power is increased by raisingthe collective and as more tail—rotor thrust is applied by thepilot, the resulting increase in drift is automatically opposed.

SUMMARY

The tail rotor counteracts the torque of the main rotor.

The tail rotor's blade angles are changed collectively.That is, all blades have their pitch angle changed bythe same amount and in the same direction at thesame time.

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_33_

The tail rotor, like the main rotor, experiencesdissymmetry of lift, which is corrected by bladeflapping.

Whenever the main rotor turns, so does the tailrotor. They are mechanically connected.

The tail rotor is controlled by the pilot throughthe tail rotor (rudder) pedals.

PRACTICE EXERCISE D

State whether each of the following statements is true orfalse.

l. The tail rotor supplies a small propulsive force forthe helicopter.

2. A two~bladed tail—rotor assembly may be mounted onan angled or delta three hinge.

3. Dissymmetry of lift is corrected by blade flapping.

4. During autorotation, the tail rotor stops turning.

5. Tail rotor blades can be moved either side of 0°pitch angle.

6. In level cruise flight, the tail rotor does littlework.

7. Tail—rotor blade angles are changed independentlyof each other, that is,cyclically.

8. The tail rotor is connected mechanically to themain rotor.

9. The main rotor turns at the same rev/min as thetail rotor.

10. The tail rotor supplies a force to counteract thetorque reaction of the main rotor, especiallyduring hovering.

(Answers on page 42)

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_ 39 i

ANSWERS TO PRACTICE EXERCISES

EXERCISE A

Statements 1, H, 6, 7, 9, and 10 are true.

Statement 2 is false. The main purpose of the tail rotoris to counteract the torque reaction of the main rotor.

Statement 3 is false. The total reaction of the mainrotor is resolved into lift and thrust.

Statement 5 is false. when the lift exceeds the weight,the helicopter climbs. To hover (neither gain norlose height), lift must exactly equal weight.

Statement 8 is false. The coning angle is the angleformed between the blades and a plane at right angles tothe rotor shaft.

EXERCISE B

1.

1

I./'\.S. 60 knbfs

0/fer,/8

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80 aQ N K.Q

1

1 ADVANCING r|Au=

0 1W; ' '7 ' ' ' an 4&0

‘I Blade Hp velocify whenREYREANNG HALF i‘ hovering in siill a|r:400 knots.

AH

FIG. 24 Difference in blade velocities

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...L[»Q_

If, instead of the helicopter flying forward at 60 kt IAS,we hover in a steady head wind of 60 kt, the ASI will read60 IAS. when the advancing blade is at 90° to the air-craft centre line, the velocity of the air over the bladetip is now the still—air tip velocity plus the airvelocity of 60 kt, and the retreating blade tip experiencesthe still-air tip velocity minus the air velocity of 60 kt.More lift is now generated by the advancing blade and lesslift by the retreating blade. As a result, the helicopterwill tend to roll to the side of the retreating blade.

2.

~ ~ chord fine $74;-‘Aug/e 0!" EH36}:

Relam Iir'_’f|OW ,._ L -_->- —-v'- E " "7 _

FIG. 25 Relative airflow and angle of attack

3. when a rotor blade is turning and flapping up, ithas two velocities. One velocity is in the directionof rotation and the other is upwards and at rightangles to the first. If we hold the blade still andapply to it the air velocities it felt when turningand flapping up, we will have an airflow from aheadand an airflow from above. Figure 26 shows thespace diagram of the two velocities.

Air mofion

‘R ' A lI"Qr\7“L"i' t|°n irigle of aliids

_

Blade motion

FIG. 26 Space diagram of two velocities

555/3/3

-141-

These two velocities are combined to give atriangle of velocities. Its resultant gives usthe new velocity and direction. See Fig.27.

*

/' °"', 7, -;:.:. . _ _ “-A"_f|°w Airflow from ahead “ ‘ ~ ~ _ _ ___mm abut “ * ~ - _ _ _ _ _ 5 New angle. of afiack

FIG. 27 The new angle of attack

The change in direction gives a decrease in theangle of attack of the blade and, it follows, adecrease in the lift generated. The oppositeoccurs as a blade flaps down.

EXERCISE C

Statements 2, H, 5, 8, 9, ll, 12, lH,l5, 18, 19, and 20are true.

Statement l is false. Dissymmetry of lift is caused byan airflow meeting the rotor disc and causing differingair velocities over the advancing and retreating rotorblades. Thus, during hover in still air, there is nodissymmetry of lift.

Statement 3 is false. A retreating blade experiences alesser air velocity than an advancing blade.

Statement 6 is false. An offset pitch change hornchanges the pitch angle of the blade as it flapsup and down. The offset is arranged so that, as theblade flaps up, the pitch angle is reduced.

Statement 7 is false. Because of the gyroscopic effectthe change in angle of attack must be made 90° of rotor"rotation ahead of where the effect is to take place.

Statement 10 is false. Coriolis effect occurs becauseof the flapping up and down of the blades needed totilt the rotor disc for flight other than hover. Duringhover in still air, no tilting of the rotor disc isneeded, and so no Coriolis effect will be felt.

Statement l3 is false. Rotor blade movement on the verticalhinge is called dragging or leading and lagging.

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Statement 16 is false. A rotor blade damper controlsthe lead—lag rate of t

Statement 17 is false. A collective pitch change altersthe pitch angles of all the blades by the same amountat the same time.

EXERCISE D

Statements 2, 3, 5, 6, 8 and 10 are true.

Statement l is false. The propulsive force for thehelicopter is supplied by the main rotor.

Statement H is false. The tail rotor turns at alltimes that the main ro

Statement 7 is false. Tail rotor-blade angles are onlychanged collectively.

Statement 9 is false. The rev/min of the tail rotorare higher than those of the main rotor.

l. In your own words, state the purpose of

(a) A main rotor, and

(b) A tail rotor.

2. Draw two sketches showing a helicopter of 1200 kg AUW,

(a) Hovering in still

_ n2 _

he blade.

tor turns.

TEST PAPER 3

air, and

(b) In straight and level flight.

In each sketch, show the main rotor force resolved intolift and thrust forces and also show the drag and weightforces. Assign values to the lift, drag, and thrustforces.

555/3/3

Fe‘$3

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§ 8-

9

-3

..L1_3 _

Discuss briefly the main differences between semi-rigid,articulated, and hingeless rotors.

With the aid of a diagram, show how dissymmetry of liftmay be felt by a main rotor unless corrected. Whatwould happen to the helicopter if no correction weremade?

Give alternative names for

(a) A vertical hinge, and

(b) A horizontal hinge.

(c) What type of rotor head uses both of thesehinges?

Explain why the angle of attack of a main rotor blade ischanged 90° of rotor~head rotation before the desiredeffect of the change is to take place.

(a) Name the three effects that will cause a main rotorblade to lead and lag about its vertical hinge.

(b) when the helicopter is hovering in still air, do theblades lead and lag? Give reasons for your answer.

with the aid of a diagram, show how dissymmetry of liftcan be felt by a tail rotor unless corrected. Whatwould happen to the tail rotor if no correction were made?

Briefly describe one method used to correct dissymmetry oflift of a tail rotor.

Why is the tail rotor mechanically connected to the mainrotor so that it must turn when the main rotor turns?

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