He Wharekura-tini Kaihautu 0 Aotearoa
THE OPE N P0l.YTE(HN|( OF NEW ZEALAND
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Main and Tail Rotor Theory 555—3—3
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 be reproduced without the written authority of the Principal, TOPNZ.
555/3/3
AIRCRAFT Er IHEERING $-
CI)
HELICOPTERS
ASSIGNMENT 3
2
s BASIC ROTORS
The main rotor of a helicopter converts the power supplied to it from the engine into a lifting force. When tilted forwards, backwards, or to either side, the lifting force propels the helicopter. The mechanism within the rotor head that tilts the lifting force is controlled by the pilot through the collective pitch lever and the cyclic pitch~control column.
By tilting
the lifting force, the pilot controls the helicopter about the lateral and longitudinal axes. The tail rotor is the helicopter's rudder. It consists of a rotor mounted vertically and at 90° to the centre line of the helicopter.
It is driven by the engine through the same power
train used to drive the main rotor and is arranged to turn whenever the main rotor turns. The tail rotor provides an opposing force to the torque reaction of the main rotor and controls the helicopter about the vertical axis, especially when hovering. is
It
controlled through the tail rotor (rudder) pedals.
In this assignment, we will show you how the lifting force of a main rotor is tilted and resolved into lift and thrust. We will consider the tail rotor and discuss the aerodynamic and mechanical forces acting on the helicopter.
You will find the terms used in the
Table of Definitions in the Basic Helicopter assignment. THE MAIN ROTOR
WW
As with an aircraft propeller, the thrust generated by a helicopter rotor acts at right angles to the tip-path plane. Opposing this force and exactly equalling it, when hovering, is the weight of the helicopter. In this condition, iii; is equal
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to weight and, because the helicopter is not moving, £532
Lift TOTAL fl
T°ta|
REACTION
ltladkm
and thrust are zero.
To obtain
horizontal movement of the
helicopter, the tip-path plane is tilted and the total reaction resolves into lift and thrust, with the lift supporting the weight and the thrust being equal to the drag for straight
(El) Hovering Qrillair); Tip path Plane horizontal.
rout
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:( lift J Ifnrr|1rIM‘I'\f
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Div-cc! ion of mot] In
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and level flight.
shows these forces acting on a helicopter in hover and in forward flight.
L
When lift and weight are
wucur
unbalanced, the helicopter will climb or descend. When thrust and drag are unbalanced, the
(b) Forward flight. Tip path Plane lilted forward.
LIFT
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Figure l
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helicopter will accelerate or slow down.
DRAG
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For example, in
a climbing, accelerating flight,
L
the thrust exceeds the drag and the lift exceeds the weight. (c) Total reaction resolved into lift and thrust for for-ward flight.
FIG. l .Ti1ting the tip-path plane to obtain thrust
Tilting the Tip-path Plane
The tip-path plane can be tilted in several ways:
l.
By tilting the complete rotor head, gearbox, and engine assembly;
2.
By changing the centre of gravity of the helicopter by, for example, moving the cabin assembly; 555/3/3
_ 3 _ 3.
By tilting a gimbal or centrally pivoted rotor head;
4.
By using aerodynamic forces to lift and depress rotor blades hinged to a rotor head that is rigidly mounted on its drive shaft; or
5.
By using aerodynamic forces to lift and depress rotor blades rigidly fixed to the rigidly mounted rotor head, thus bending the blades near their root ends.
In practice, the last three methods are used, and the rotors that 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 plane by simply increasing the angle of attack of the retreating blade and decreasing that of the advancing blade.
The retreating blade then
generates more lift and the advancing blade, less lift.
As a
result, the retreating blade flaps up and the advancing blade flaps down, as shown in Fig. 2 (a) and(b).
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_ u _
The tilting is controlled by the cyclic-pitch control column usually called the cyclic, and can be effected in any direction. The cyclic column is moved forward to tilt the tip-path plane forward, which moves the helicopter forward. It is moved to the right to tilt the (a)
An articulated rotor with
tip-path plane to the right
the tip-path plane tilted
moving the helicopter to the right.
The same principle
applies to left and aft movements ___ ~
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of the cyclic column and, of course, for any intermediate position. The tip~path plane of the semi-rigid rotor is tilted in the same way, with the rising
(b)
A hingeless rotor with the
of the retreating blade being
tip-path plane tilted
equalled by the dropping of the advancing blade. Because both blades are mounted on a
___===r-—
rigid, centrally pivoted yoke, the complete rotor head tilts or seesaws in the direction chosen. Figure 2 (c) shows a tilted tip-path plane for a semi—rigid rotor.
(c)
A semi-rigid rotor with the
tip-path plane tilted FIG. 2
Types of rotor
For vertical flight, the angle of attack of all the blades is increased or decreased simultaneously. This is
controlled by the collectivepitch control column, usually called the collective. The pilot raises the collective for the helicopter to go up and lowers it to go down.
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_ 5 _ The control inputs to the rotor head from the cyclic and the collective pitch controls are superimposed upon each other mechanically so that, for example, a climbing, turning, forward flight path is possible.
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SUMMARY The main rotor converts engine power into a force that
can both lift and propel the helicopter. The total reaction of a rotor is at right angles to the tip-path plane.
Flight in any direction is obtained by tilting the tip-path plane.
In flight, the total rotor reaction is resolved into lift and thrust. I
Three types of rotor are generally used:
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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 rotor and gives directional control during hovering.
Coning and Flapping when the helicopter is hovering in still air, the airflow comes from directly above and goes straight down through the rotor The lift force generated by the turning rotor acts vertically upward and is equal to the weight (mass) of the helicopter acting vertically downward.
In this condition, the main forces acting
on the rotor assembly are 1.
The lift force from each blade, and
2.
The centrifugal force of each blade.
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_ 5 _ The lift force acts to lift each blade tip upwards, and the centrifugal force acts to keep each blade horizontal. The two forces resolve into a single force, that results in a small upward movement of the blade tip. The angle formed between the blade and a plane at right angles to the rotor shaft is called the coning angle.
See Fig.
3.
The articulated rotor has each blade mounted on a horizontal or flapping hinge, which permits its blade to freely move up and down or flap.
The rigid rotor permits the blade tip to move up andcbwn by the bending of the blade and the bending of the rotor head just inboard of the blade attachment. Z/B
kg
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Coning angle
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Hovering in sffll air’ Comng angk dbphced. FIG. 3
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Coning angle
Neither the articulated nor the rigid rotor system can give flight other than hovering unless a coning angle is generated. The coning angle must be displaced about the main rotor shaft by the flapping of the blades to give the tilted tip-path plane necessary for horizontal movement. See Fig. 2 (a) and (b). Because the semi-rigid rotor has its tip-path plane tilted by the complete rotor-head assembly tilting about its central pivot point, both blades flap together but in opposite directions. As one blade flaps up, the other blade simultaneously flaps down by an equal amount. See Fig. 2 (c). Thus, the semi-rigid rotor does not need to make a coning angle, and the lift force bends the stiff, heavily built blades evenly but slightly along their span.
However, the yoke of the semi-rigid rotor does have a small
built-in coning angle of between 2° and 6°.
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This is done for
_ 7 _
a reason that we shall discuss later in this assignment under Coriolis Effect.
In fact, the coning angle hardly varies during all stages of flight because the rotor and engine rev/min are held in a narrow operating range.
During flight, fuel is burned off and so the
helicopter becomes lighter.
Also during flight, loads may be
winched aboard or released from a cargo hook.
Any increases/decreases
in load make only a small difference to the coning angle and soonly small changes in blade—pitch angle are made to correct for them. The following simplified example shows the change in coning angle caused by an increase in the weight of a helicopter with a four-bladed articulated rotor head.
The figures used are not
exact.
Helicopter AUW
=
8000 lbf
Weight of each blade
=
llO lbf
C of G location
=
13 ft
Rotor rev/min
=
210
Lift generated by each blade
#
gggg
=
2000 lbf
=
aléloz ><<1TXn2n2n0*x 210)
=
21 477 lbf
Radius of blade at its
2 Centrifugal force
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>< 113 lbf
.
_ 8 _
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FIG. 4
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Generating a coning angle 2000
tans = are 6
=
tan 0.093l2
Coning angle or 9
=
5° 19‘
The helicopter is now loaded to ll 000 lb max. AUW.
Lift generated by each blade
Centrifugal force
=
iiggg
=
2750 lb
=
21477 lb 2750
tan“ " nan" 9
=
tan 0.1280
Coning angle or G
=
7° 18‘
A weight increase of 3000 lb has increased the coning angle by about 2°.
During flight, the rotor and engine rev/min can be considered as constant, with the power being changed by alteration to the engine induction manifold pressure or fuel flow and, at the same time, collectively altering the main rotor blade angles.
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i Q _
The power is changed because the inertia of the rotor head and blades assembly makes an increase or decrease in rotor rev/min impossible to get in a reasonable time, but a quick response to a change in power may be obtained by changing the blade pitchangles with a change in engine fuel flow. We cannot overemphasise the importance of keeping the rev/min in the correct range. If the recommended rev/min are exceeded, damage to the engine, transmission, rotor head, and blades will result, the severity of the damage depending upon the amount and duration of the overspeed. If the rev/min fall below those recommended, the collective pitch must be decreased or the engine power increased and the rev/min allowed to increase to their normal value.
However,
if no more engine power is available, the helicopter will have to descend with the reduced collective pitch. If the collective pitch is increased to maintain altitude, the increase in blade angle above normal will produce more drag for the lift generated, the rev/min will decay (slow down) further, and the helicopter will descend rapidly.
When this occurs with a fully articulated rotor,
the coning angle increases due to the reduced centrifugal force until a position is reached where it takes a long time to bring the blades down again by reducing collective pitch.
A very
heavylandingp is then unavoidable. Early helicopters with articulated rotors could get their blades pointing almost vertically upwards.
This condition, known
as candling,
Modern articulated
resulted in a crash landing.
rotor heads have inbuilt or adjustable upper coning stops to prevent excessive coning of the blades.
These stops are set at
an angle well outside the normal coning angle of the blades but small enough to allow a reasonably rapid increase in rev/min when collective pitch is reduced.
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_ 19 _
SUMMARY In flight, the engine and rotor rev/min are kept in a
narrow operating range . The coning angle is caused by the balance of lift and centrifugal forces. The tip-path plane is tilted to give forward flight by flapping the blades up at the rear and down at the front of the helicopter. 3 ‘ 1
In a semi-rigid rotor, as one blade flaps up, the other blade flaps down by an equal amount. A very low rotor rev/min will produce a large coning
angle, which could endanger flight.
PRACTICE EXERCISE A
State whether each of the following statements is true or false:
l.
The main rotor is controlled by the pilot through the collective and cyclic pitch control columns.
2.
The main purpose of the tail rotor is to control the helicopter about the vertical axis when in level flight.
3.
The total reaction of the main rotor is resolved into lift and drag when the tip-path plane is tilted.
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 must slightly exceed the weight of the helicopter.
6.
In tilting the tip~path plane of a semi-rigid rotor, the complete rotor head assembly is tilted.
7.
The total reaction of a rotor is at right angles
to the tip-path plane. 8.
The coning angle is the angle formed between the
blades and the relative airflow.
-
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-11..
9.
10.
The horizontal or flapping hinges of an articulated rotor permit the blades to freely flap up and down. A rigid rotor has its blades rigidly attached to the rotor head, which is itself rigidly attached to the rotor drive shaft.
(Answers on page39)
Forces of the Rotor Head To achieve flight, the tip-path plane is tilted in the desired direction, and the total reaction from the rotor head and blades assembly becomes resolved into lift to support the weight and thrust to propel the helicopter. As the helicopter moves, the airflow direction into the rotor head changes from directly above to ahead and above.
At the same time, the airflow from the
rotor changes from straight down, forming a ground cushion, to aft and down. These changes in the airflow through the rotor disc, and the fact that the tip-path plane has been tilted, create extra forces and effects above those experienced when hovering.
555/3/3
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In §eve| flight
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In level flight
FIG. 5
Airflow through the rotor
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_ 13 _
Dissymmetry of Lift The area within the tip~path plane of the main rotor is called the disc area or, more generally, the rotor disc. when the Q
helicopter is hovering in still air, lift is generated by the rotor blades equally at all positions around the rotor disc.
Q
As the helicopter moves, or as a wind is felt, the velocity of the airflow over the rotor blades changes, with a higher velocity in one half of the rotor disc and a lower velocity in the other half.
As a result of the different air velocities, different
lift forces will be generated from one side of the rotor disc to the other.
Unless this unequal distribution of lift is counteracted,
the helicopter would roll over in the direction of the side with the least lift.
The unequal distribution of lift, called the
dissgngetrg of 1ift,was a considerable problem to the designers of early helicopters and autogiros. Figure 6 (a) shows typical velocities at different positions on a rotor blade when the helicopter is hovering in still air. Because the air is still and the helicopter is hovering, the rotor blade velocity is also the velocity of the air over the blade. The blade will thus experience the same air velocities at all positions in the rotor disc. Figure 6 (b) shows the same helicopter in forward flight with an IAS of 100 kt.
With this IAS, the air velocity felt
by the tip of the blade when it is advancing and at 90° to the line of flight is the tip velocity pigs the 100 kt TAS, giving a total of 500 kt. This increase in air velocity of 100 kt is felt along the span of the advancing blade. when the blade is retreating and at 90° to the line of flight, the air velocity felt at the tip is the tip velocity minus the lU0—kt IAS, giving £2
a total of 300 kt. This decrease in air velocity of 100 kt is felt along the span of the retreating blade. For any given angle of attack, the lift generated increases as the velocity of the
5
airflow over the airfoil increases. In fact, the lift increases as the square of the air velocity. That is If an air velocity of A m/s gives l unit of lift, then an air velocity of ZXA m/s gives 4 units of lift, and an air velocity
of 3XA m/s gives 9 units of lift.
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FORWARD
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(b) FIG. 6
Forward flight of 100 kt Rotor—blade velocities in hovér and in forward flight
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_ 15 _
Bearing this in mind, a study of Fig. 6 (b) will show that more lift will be generated in the advancing half than in the retreating half of the rotor disc unless some correction is used an
We have seen that the articulated rotor and the rigid rotor systems have blades that either flap or bend in the vertical
4%
plane.
In forward flight, the increased lift on the advancing
blade due to forward motion of the helicopter will cause the blade to flap or bend up. This upward movement will decrease the angle of attack because the relative wind will change from a horizontal direction to more of a downward direction while the blade is moving upward.
See Fig.
7.
AIRFLOW FROM ABOVE
its ,d
AIRFLOW mom AHEAD
APParen1 angle of attack
Space
diagram of two velocities
—-- MRFLOW FROM ABOVE
V
R55!-1:.rAN r —-_L>_AlRFLOw AIRFLOW FROM AHEAD
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—-__ __ _ __ __
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True angle of attack
6:
x
FIG. 7
Change in angle of attack due to flapping
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_ 15 _
The decreased lift on the retreating blade will cause the blade to flap or bend downward. This downward movement will increase the angle of attack because the relative wind will change from a horizontal direction to an upward direction while the blade is moving down,
as
shown in Fig.
7.
The combination of decreased angle of attack on the advancing blade and increased angle of attack on the retreating blade through blade flapping tends to equalise the lift over the two halves of the rotor disc. The position of the cyclic pitch—control column in forward flight also causes a decrease in the angle of attack on the advancing blade and an increase in the angle of attack of the retreating blade.
This movement of the control
column gives the major correction for dissymmetry of lift, with the correction for blade flap being a minor but necessary contribution The semi-rigid rotor behaves as a seesaw. As one blade flaps up, the other blade flaps down and, as already explained, the change in angle of attack of each blade tends to equalise the lift over the rotor disc.
Again, however, the major correction
for dissymetry of lift is supplied by the forward movement of the control column. Another method that can be used on the articulated and rigid rotor systems to decrease the angle of attack and the consequent lift of an advancing blade flapping up and to increase the angle of attack and the lift of a retreating blade flapping down is to slightly offset the pitch—change horn on the blade in relation to the flapping hinge. exaggerated form.
Figure 8 shows this offset in a greatly
The pitch~change control rod that conveys
the input from the pilot to the rotor blade is attached to face A on the control horn and the blade can rotate on the blade spindle.
555/3/3
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(a) Normai FIG. 8
horn
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(5) Offs“ Offset pitch~change horn
In Fig. 8 (a), when the advancing blade flaps up because of the increased airflow, there will be no mechanical change in the angle of attack of the blade because the centre lines of the flapping hinge and the contro1—rod attachment to the control horn coincide.
However, in Fig. 8 (b), when the advancing blade flaps
up, the angle of attack of the blade is mechanically decreased because the centre line of the control rod attachment to the control horn is outboard of the centre line of the flapping hinge As the blade flaps up, it also rotates on its blade spindle, with the leading edge going down.
The reverse occurs when a blade
retreats and starts to flap down. In flight, the blades are allowed to flap as they wish. No damping devices or mechanicalrestraintsare used to inhibit or prevent flapping other than the limits of movement imposed by the design of the rotor head and,in some helicopters, an upper coning stop. For practical design and construction reasons, the flapping hinges are offset.
That is, they do not lie in the geometric
centre of the rotor head.
This offset of the flapping hinges
has a useful dynamic effect in the control of the helicopter.
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_ 13 _ In Fig. 9, the strings represent the rotor blades, the arrows show the centrifugal force, and the weight represents the fuselage of the helicopter. In Fig. 9 (a), the tip-path plane is tilted, but because the blades are hinged in the centre of the rotor, the fuselage hangs straight down and will be slow to adapt its attitude to the tilt of the rotor.
If its centre of gravity was
anywhere but in the same lateral plane as the lift vector of the rotor, the helicopter would be unmanageable. In Fig. 9 Cb), the fuselage quickly follows the tilt of the tip-path plane, and the position of the centre of gravity is now not so critical. The result is a helicopter that is sensitive to the control of the pilot and has a useful working range of permissible centre—ofgravity movement. Offset of hi--51.;
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(a) NOT OFFSET FIG. 9
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Dynamic effect of offset flapping hinges
The offset distance of the flapping hinges determines the size of this dynamic effect. The blades in a rigid rotor are, in effect, stiff continuous flapping hinges, and the overall effect is similar to widely offset flapping hinges. The semi-rigid rotor also uses a dynamic effect to give a manageable and sensitive response to the pilot’s controls. This effect is obtained by having the rotor assembly underslung on
555/3/3
.-...]_Q..
its pivot.
That is, the centre of gravity of the rotor assembly
lies below its central pivot axis. Figure l0 Ca) shows a semi-rigid rotor helicopter hovering, with the lift vector acting vertically upward and the weight vector acting vertically downward and in the same plane.
Figure l0
Cb) shows the tip-path plane tilted for forward flight, with the lift vector moved aft because of the tilt of the assembly. As a result of this movement, a couple is formed by the lift and weight vectors, which lowers the nose of the helicopter.
The underslung
mounting of the semi-rigid rotor assembly has another important service to perform, which we shall discuss later on in this assignment under Coriolis Effect. LIFT
_
Rnior Pivol Pom?
C. cf G. cf" rofar assembly
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(a)
Hovering
Tofal reaciion
Rotor pivu+
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(b)
Rotor tilted for forward flight
FIG. 10 -
Semi-rigid rotor helicopter 555/3/3
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_ 29 _
SUMMARY Dissymmetry of lift is caused by horizontal flight or by wind during hover. Y \
5 ‘
Dissymmetry of lift is the difference in lift that occurs between the advancing blade half and the retreating blade half of the rotor disc area.
Unless corrected, dissymetry of lift will roll the helicopter to the side opposite to the advancing blade. Dissymmetry of lift is corrected by
l. T
An aerodynamic reduction in the angle of attack as the advancing blade flaps up and an increase as the retreating blade flaps down;
l 2.
The blade's angle of attack being reduced as it advances and increased as it retreats by the position of the cyclic control column; and sometimes by
3.
Mechanically reducing the angle of attack of the
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advancing blade and increasing it on the retreating
1 ‘
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 adyancing blade of a helicopter in horizontal flight tends to develop more lift than the retreating blade
unless corrected. 2.
Make a freehand sketch of an airfoil section meeting
an airflw, and show the chord line and angle of attack of the airfoil. 3.
With the aid of a sketch, show that, when a rotor blade flaps up, its angle of attack is aerodynamically reduced.
(Answers on page39)
555/3/3
_ 21 _
Gyroscopic Effect The turning main rotor assembly behaves as a large gyroscope in that it tilts at right angles to the direction of a push that it 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 a reaction to an applied force or push.
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t s (Q) 11,, grm,c,,p¢_
(2) Forget all the others.
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(5) The ‘rg':eJegr?;;:>l;!;£::°I:Pi41Y~F"
13!! (C) 5ubpose"t£|;’::'Inr;-is split into
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(d) Attend to two of these segments.
11
fhei, 5|-mp: 5”, not man"
‘-;~t> (gen tgwtlrrxovgggeztgd tltggnulilguéoaie
2 /ct_j):{, (i) Now suppose we apply a torque to the axle an the horizontal plane,
lg’
"lhis imparts a mation in the horizontal (lg) 7,4,", the ngmenls mm M" both dlrecnnn to the segments, one to the right _ 0 ;,,,|z,,nm/ and G "mm, momm and the other to the left.
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%%é%g;€%%%:%?%?%E (M) This is the key diagram. Study it carefH"Y- The axle is rigidly connected In the segments and must therefore tilt when the segments move diagonally.
éégggfiéégé (H) All the other segment: must fin in we mm, wan
FIG. ll
C::(§@§§;§§%§:::D €EiEi!!;g%i§i§§ifir (0) T-h='=l'¢re the whole wheel trlu.
How a gyroscope tilts 555/3/3
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(P) Thu: when a gyroscope is given a push il "'15 1" Pith! angle: to the directwn uf the push.
._ 22 _
Figure 12 shows the gyroscope rotor without its gimbals, and
f““~\ fii?T r/,/IF ‘\\\\'i§._M/ A'/ Ll
lying in a horizontal plane such as a main rotor assembly. If we apply a push to the rotor ' at A,it will move in the direction marked tilt at B. Compare this movement with that shown in
‘PUSH
Fig. ll and you will find that FIG. 12
it is the same.
Tilting of a rotor
You can thus
see that the tilting of the o rotor occurs 90 later in the direction of rotation from, and in 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 made to flap up and the advancing blade being allowed to flap down, and that 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 change in 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 the centre line on the left—hand side of the helicopter —— see Fig. 13. LOW NTCH APPLIED HIGH FLAP RESULT
W-I
F ""_\\,-__ ’
\%f"ilktow rm aesutt
- FIG. 13
‘id
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IGH mcla APPLIED
Where the angle of attack is changed
This applies to a rotor which is turning in the conventional direction, which is counterclockwise when viewed from above.
555/3/3
_ 23 _
This 90° lead Bell helicopter if direction and then forwards, watching
in the control can be seen very easily on a you position the blades in a fore~and—aft move the cyclic control column backwar d s and the blades at the same time. No movement
takes place at all when this is done, but when the control column is moved laterally, the blades increase and decrease their pitch as the control is moved.
The same effect can be seen, less easily,
in a fully articulated rotor if you position the control horn pushpull rod of one blade directly over a control rod into the swashp lat e and then move the cyclic control column.
Coriolis Effect As a blade of a fully articulated or rigid rotor flaps up, the centre of mass of the blade moves in towards the centre of the rotor disc, and as the blade flaps down, it moves outward. See Fig. lu.
Axis of rotaficn
UP
\
‘.
X3
Blade flapping
“ \
X2
\\|
I
\ \
X:
DOWN
_ '
Xwn
W
\KC8ntre of mass
I
FIG. 14
Blade centre of mass movement
Remember that, because of coning, a blade of these two types . 0 rotor will not flap down below a plane passing through the ro t or hub and perpendicular to the axis of rotation. f
The product of mass and velocity yields momentum. Mass X Velocity
=
Momentum
555/3/3
Thatis
_ gu _ Thus, when a rotor is turning, each blade has a certain amount of momentum. The law of Conservation of Momentum states that
"the momentum
of a body does not change unless an unbalanced external force acts on it".
As a blade flaps up, its centre of mass moves towards
the axis of rotation, and so the length of its path around the axis becomes shorter.
For the blade to retain the same momentum,
which it must, its angular velocity must therefore increase. reverse holds true as a blade flaps down.
The
This law is well demonstrated by the exhibition ice skater. When the skater pirouettes with her arms outstretched, her rate of spin is not very great, but as she lowers her arms, the rate increases markedly. When the blade flaps up and increases its angular velocity, it is said to £551, and as it flaps down and decreases its angular velocity, it is said to £52.
The rigid rotor handles the lead
and lag forces by allowing the blade to bend at or near its attachment to the rotor head.
The blade on an articulated rotor
moves because it is mounted on a vertical hinge.
See Fig. 15.
This hinge is sometimes called a @532 or lead-lag hinge.
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FIG. l5
Leading and lagging 555/3/3
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-25..
The blade is not free to lead and lag without restraint, which would cause mechanical damage to the rotor head and would also create an unbalanced rotor. It is attached to a damping device, which is adjusted to give a specified rate of movement under a given load. The semi-rigid rotor is underslung and has a small preset coning angle. effect.
These two features greatly reduce the coriolis
As a blade flaps up, the centre of gravity of the rotor
assembly moves out from the axis of rotation in the direction of that blade.
See Fig. 16 (b).
As the blades flap, they will
tend to increase their velocity to maintain their momentum but, because the C of G of the head has moved away from the axis of rotation, it will generate some added momentum of its own to the system.
This added momentum
partly cancels that needed by the
blades.
The source of the momentum
does not matter, just so
long as the total momentum of the system stays the same. Thus, the blade flapping up will have little tendency to increase its velocity to conserve momentum, and the blade flapping down will have little tendency to decrease its velocity.
The small
lead-lag forces that are generated by the remaining coriolis effect are absorbed in blade bending and by massive blade drag braces 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 differs from that of the rotor drive shaft. to Hooke's
This difference gives rise
joint effect, wherein the driven member of a universal
joint accelerates and decelerates twice in each revolution of the driving member.
Figure l6 shows the effect on a four—bladed
articulated rotor.
During hover, the tip-path plane is parallel
to the rotor drive-shaft at 90° to each other.
plane, and the blades space themselves
Because the blades are not flapping, there
is no coriolis effect, and so the blades will not move about their vertical hinges. In horizontal flight with the tip~path plane tilted(for the rotor shaft plane of rotation to maintain a constant velocity),the two athwartships blades must move on 555/3/3
_ 25 _
their vertical hinges to positions A and B.
The blades thus
accelerate and decelerate twice in each revolution of the rotor shaft.
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(a) Hovering
gb) Horizontal
FIG. 16
flight
Hooke‘s joint effect
The articulated rotor caters for this effect by allowing the blades to move on their vertical hinges, the rigid rotor by bending 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 1HL”““J%§a _ _ v 3. 1-’
velocity universal joint where torque is transferred at constant
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speed by the use of free-moving . . steel balls between the driving
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and driven members.
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Each member
has two fingers or arms,
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in
the sides of which are specially shaped grooves. A steel ball forms the driving connection in the
FIG. l7
Cqnstant—velocity universal
two curved channels formed when
joint the joint is assembled. The shape of these channels is such that, irrespective of the angle at which the joint operates, the balls always lie in a plane that makes equal angles with both driving and driven members of the joint. This feature is common to all makes of constant~velocity universal joints. Rotor heads have been designed and built to behave as a constant-velocity joint but, so far, this type of rotor head has not been used in production-run helicopters.
Drag Effect As a turning blade advances and then retreats, the velocity of the airflow over the blade varies as does the drag generated. This changing value in drag causes the blade to move about its vertical 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. 2.
Dissymmetry of lift, j
Gyroscopic effect,
3.
Coriolis effect,
4.
Hooke's joint effect, and
5.
Drag effect,
555/3/3
_28..
all take place together when the helicopter is in horizontal flight. However, for hovering in still air, only gyroscopic and drag effects occur.
SUMMARY In an articulated rotor l.
Dissymmetry of lift is corrected by the blade flapping up and down about the horizontal (flapping) hinge;
2.
Gyroscopic effect is allowed for by the angle of attack of the blade being changed approximately 90° before the result of the pitch change is desired; and
3.
Coriolis, Hooke‘s joint, and drag effects are absorbed by each blade being mounted on a vertical (drag) hinge, with its variations in velocity with respect to the rotor head being controlled by a blade damper.
For a semi-rigid rotor 1.
2.
Dissymmetry of lift is corrected by the blades flapping up and down about the rotor-head pivot point; Gyroscopic effect is allowed for as in the articulated rotor;
3.
Coriolis effect is absorbed by the rotor assembly being underslung on the rotor drive shaft;
4.
and
Hooke‘s joint and drag effects are absorbed by blade bending.
In a rigid rotor l.
Gyroscopic effect is allowed for as in the articulated rotor, and
2.
All other effects are absorbed by the blades bending at or very near their attachment to the rotor head.
555/3/3
_ 29 _
PRACTICE EXERCISE C State whether each of the following statements is true or false: l.
Dissymmetry of lift is experienced when hovering in still air.
2.
The rotor disc is the area within the tip~path plane.
3.
A retreating blade experiences a greater air velocity than 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 a
flapping blade. 7.
No allowance for the gyroscopic effect of the rotating rotor is needed in its control.
8.
Phase lag is another name for gyroscopic effect.
9.
Because of gyroscopic effect, the angle of attack
of a blade is changed at about 90° of rotor rotation before the desired effect of the change is to take place. 10.
Coriolis effect is apparent only during hovering in still air.
ll.
An underslung semi-rigid rotor with between.2° to 6° of preconing will experience little coriolis effect.
l2.
The movement of rotor blades in the vertical plane is called flagging.
13.
Rotor blade movement on the vertical hinge is called flapping.
8
14.
Coriolis, Hooke‘s joint, and drag effects cause a blade to move about the vertical hinge.
15.
The vertical hinge is often called the drag hinge.
16.
The rate of blade flap is controlled by a rotor blade damper.
l7.
A cyclic pitch change alters the pitch angles of all the blades by the same amount at the same time.
18.
A rigid rotor uses blade bending instead of vertical and horizontal hinges.
555/3/3
_ 30 _
19.
A semi-rigid rotor seesaws spanwise about a central point.
20.
An articulated rotor blade is free to flap about a horizontal hinge but is damped in its dragging about a vertical hinge.
(Answers
on page
41)
The Tail Rotor A tail rotor is used to counteract the torque P€acTiOn frcm a single main rotor and, to a much lesser extent, to provide directional control in flight.
Helicopters with twin main rotors
counteract their torque reaction by counter—rotating the rotors. Thus, they obtain directional control by mixing the cyclic inputs to each rotor head and so don't need a tail rotor. The tail rotor is mounted vertically, or nearly so, on one side of the fuselage, with its centre line at right angles to the direction of normal forward flight.
See Fig. 18.
It is driven
through shafting and gearboxes from the main rotor and is connected mechanically with the main rotor so that, when the main rotor turns, so must the tail rotor. This mechanical connection between the two rotors means that, in autorotation, the pilot has normal behaviour from the tail rotor. Ideally, in level flight, the tail rotor uses little or no power, nearly all power being available at the main rotor for lifting and propelling the helicopter.
The tail rotor uses most power during a climbing
turn in the direction of rotation of the main rotor.
This is
a climbing, left-hand turn if the main rotor turns in the conventional direction of counter-clockwise when looked at from above,
with a maximum AUW the power used by the tail rotor
in such a turn can exceed 10% of the total power available from the engine.
555/3/3
_ 31 i
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FIG
18
Position of the tail rotor
We determine the direction of rotation by viewing the tail rotor from the side that it is mounted on the helicopter. A tail rotor may have between two and six blades and will turn much faster than the main rotor, but usually slower than the engine rev/min.
(The rev/min ratio between tail rotor and engine
differs 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 pitch of all the blades by the same amount and in the same_direction, Q!‘
thereby increasing or decreasing the thrust generated and the lateral force felt by the tail of the helicopter. The blades can be moved from a positive-pitch angle through 0° to a negative-pitch angle so that a thrust to the right or left may be obtained.
See Fig. l9.
S55/3/3
._ 32 _
FORWARD (1-innnnnu
‘\f'—Tai| - rofor gearbox
'::—T'—i1> AIR FLOW FIG. 19
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-'_'jIi-'*"
,—""_°
1;» —<>° \_ +.
Positive and negative angles of a tail rotor blade
Forces of a Tail Rotor The tail rotor is a rotating airfoil sited in an airflow. As with the main rotor, the airflow causes dissymmetry of lift to be felt across the disc of the tail rotor.
In correcting for
dissymmetry of lift, the effects of drag, Hooke's joint, and coriolis are introduced and absorbed by the relatively stiff blades and heavily built hub assembly. The presence of gyroscopic effect or phase lag does not matter because the pitch of the tail~rotor blades is always changed collectively.
As with the
articulated and semi-rigid main rotors, dissymmetry of lift is catered for by blade flapping or by the assembly seesawing in a vertical plane, and by the geometry of the pitch—change mechanism to the blades.
555/3/3
_ 33 _ Dissymmetry of Lift From Fig. 18, you will see that the velocity of the airflow over 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, then much more thrust will be produced by the top half of the disc than by the lower half.
This uneven distribution of the thrust
will cause vibration and will unevenly load the tail rotor and the tail—rotor gearbox assembly.
This problem is overcome by
the blades flapping in much the same way as the main rotor blades flap.
As the top blade flaps outwards away from the
helicopter, its angle of attack becomes less, and less thrust is produced. At the same time, the lower blade flaps inwards, its angle of attack is increased, and more thrust is produced. The net‘ result of the flapping action is an even distribution of thrust over the disc area. Figure 20 shows schematically a two—bladed tail rotor with both the blades mounted on a yoke freely pivoted in the centre about a trunnion. Each blade can turn on a feathering (spanwise) axis and is connected to the pitch-change mechanism by a push-pull rod.
The trunnion is mounted so that its axis lies at an angle
to the centre line of the yoke, which gives an angled hinge called a delta three hinge, This hinge reduces the angle of attack of the advancing blade and increases that of the retreating blade as the tail rotor flaps.
The angle of attack is further altered
by the pitchmchange linkage, because each push-pull rod is attached to the leading-edge side of a blade, the angle of attack of an outward-flapping blade is reduced.
As the blade
flaps inward, its angle of attack is increased.
The result of
tail~rotor flapping is that for level flight in calm air, the assembly assumes a less than vertical angle. Note angle 6 in Fig.2O 555/3/3
_ 34 _
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Tall-rotor drive. shaft
an
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Roiaiiu of blade
ab BUrfnQ1:11 C-T axis
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Pushpunrod
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L in --vi FLAP -------—->- Ouk
FIG. 20
Tail--rotor flapping
You can see the change in the angle of attack of the blades due to tail~rotor flapping on the delta three hinge very easily if you balance a 30—cm rule on a pencil with the rule inclined (offset) at a small angle to the pencil.
555/3/8
See Fig. 21.
Seesaw
_ 35 _ the rule on the pencil.
As
the 30 cm end of the rule lifts up, the numbers between 15 and 30 incline down, and the opposite happens with the other end of the rule. Increase the angle
' '
e
Lead' edge n5
Tra' ragedge
of the rule relative to the pencil and see the effect. Position the pencil almost lengthwise under the rule and
‘QQR
see the effect. The delta-hinge-mounted tail rotor can have only two blades.
\
~
edge ng
Tra
FIG; 21
If more are needed
ag:
because more thrust is necessary
1-
or because a large~diameter
L¢.;d';g
tail rotor cannot be used, a different type of tail rotor
Delta—three-—hinge effect
is called for.
One common
type of tail rotor that can have as few as two and as many as six blades has a central hub rigidly fixed to the tail—rotor gearbox output shaft, with each blade attached to the hub by a flapping hinge. Each blade can be turned about its feathering axis and is connected to the pitch—change head by a push»pull rod. The geometry of the pitch~change head and the attachment of the push—pull rod to the blade is arranged so that, as the blade flaps outward, its angle of attack is reduced and vice versa.
Figure 22 shows schematically this angle change and the tip-path plane of this tail rotor during level flight in calm air.
555/3/3
'- as -
I Ft‘? Our I
ROTATION -4-—-—-——-
I 4
7
F
-
Blade “-~_a_
HI‘ ..__,___-- Biade spindle
C)
Hingfi
e l ., 7
H_“'PLKE} "“ Pikh - change. hand \
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FIG. 22
Tail rotor with flapping hinge
Drift The force or thrust from the tail ' rotor 15 ' u sed to counteract the torque reaction of the main rotor. A couple is a pair of equal and opposite parallel forces that tend to produce rotation, that is, a torque. The force produced by the tail rotor acts perpendicularly to an arm.
That is, the tail rotor produces
The main ' rotor torqu e is balanced by the moment, which stops its rotational effect but results in a s mall translationa ‘ l force that drifts the helicop ' ter sideways.
a moment.
555/3/3
- 37 _
/
.
Dlrechon of rotation of mam rater
,
F
A
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RESULTANT
fie
Reaction for ue
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Ta}? rotor fare:
I
- FIG. 23
Tail~rotor drift
Drift is counteracted by tilting the main rotor to one side The tilt can be achieved by the design of the mount supporting the main transmission or by the cyclic controls being rigged so that neutral on the cyclic control column results in the tipa path plane of the main rotor being tilted.
A combination of
both methods is often used. The main rotor control system is often designed to give a progressively increasing tilt of the tip-path plane as the collective is raised.
Thus, as power is increased by raising
the collective and as more tail—rotor thrust is applied by the pilot, 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 by the same amount and in the same direction at the same time.
555/3/3
_33_
The tail rotor, like the main rotor, experiences dissymmetry of lift, which is corrected by blade flapping. Whenever the main rotor turns, so does the tail rotor. They are mechanically connected. The tail rotor is controlled by the pilot through the tail rotor (rudder) pedals.
PRACTICE
EXERCISE D
State whether each of the following statements is true or false.
l.
The tail rotor supplies a small propulsive force for the helicopter.
2.
A two~bladed tail—rotor assembly may be mounted on
an 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 little work.
7.
Tail—rotor blade angles are changed independently
of each other, that is,cyclically. 8.
The tail rotor is connected mechanically to the main rotor.
9.
The main rotor turns at the same rev/min as the tail rotor.
10.
The tail rotor supplies a force to counteract the
torque reaction of the main rotor, especially during hovering.
(Answers on page 42)
555/3/3
_ 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 rotor is to counteract the torque reaction of the main rotor. Statement 3 is false. The total reaction of the main rotor is resolved into lift and thrust. Statement 5 is false. when the lift exceeds the weight, the helicopter climbs. To hover (neither gain nor lose height), lift must exactly equal weight. Statement 8 is false. The coning angle is the angle formed between the blades and a plane at right angles to the rotor shaft. EXERCISE
B
1. 1
E-4
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D
I./'\.S. 60 knbfs
->
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1 W;
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REYREANNG
0 '7:1.' ' O“. HALF
ADVANCING
r|Au=
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an
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4&0
Blade Hp velocify when
i‘
hovering in siill a|r:400 knots.
AH FIG. 24
Difference in blade velocities
555/3/3
...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 read 60 IAS. when the advancing blade is at 90° to the aircraft centre line, the velocity of the air over the blade tip is now the still—air tip velocity plus the air velocity of 60 kt, and the retreating blade tip experiences the still-air tip velocity minus the air velocity of 60 kt. More lift is now generated by the advancing blade and less lift by the retreating blade. As a result, the helicopter will tend to roll to the side of the retreating blade. 2.
~
~
Relam Iir'_’f|OW
FIG. 25
3.
chord fine
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_
Relative airflow and angle of attack
when a rotor blade is turning and flapping up, it has two velocities. One velocity is in the direction of rotation and the other is upwards and at right angles to the first. If we hold the blade still and apply to it the air velocities it felt when turning and flapping up, we will have an airflow from ahead and an airflow from above. Figure 26 shows the space diagram of the two velocities.
Air mofion
‘R
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A
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irigle of aliids
_
Blade motion
FIG. 26
Space diagram of two velocities 555/3/3
-141-
These two velocities are combined to give a triangle of velocities. Its resultant gives us the new velocity and direction. See Fig.27.
*
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, 7,
-;:.:. .
Airflow from ahead
°"'
_ _ “-
FIG. 27
“ ‘ ~ ~ _ _ ___
“* ~ -___ __ 5
New angle. of afiack
The new angle of attack
The change in direction gives a decrease in the angle of attack of the blade and, it follows, a decrease in the lift generated. The opposite occurs as a blade flaps down. EXERCISE C
Statements 2, H, 5, 8, 9, ll, 12, lH,l5, 18, 19, and 20 are true.
Statement l is false. Dissymmetry of lift is caused by an airflow meeting the rotor disc and causing differing air velocities over the advancing and retreating rotor blades. Thus, during hover in still air, there is no dissymmetry of lift. Statement 3 is false. A retreating blade experiences a lesser air velocity than an advancing blade. Statement 6 is false. An offset pitch change horn changes the pitch angle of the blade as it flaps up and down. The offset is arranged so that, as the blade flaps up, the pitch angle is reduced. Statement 7 is false. Because of the gyroscopic effect the 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 because of the flapping up and down of the blades needed to tilt the rotor disc for flight other than hover. During hover in still air, no tilting of the rotor disc is needed, and so no Coriolis effect will be felt. Statement l3 is false.
Rotor blade movement on the vertical
hinge is called dragging or leading and lagging.
555/3/3
_ n2 _
Statement 16 is false. A rotor blade damper controls the lead—lag rate of t he blade. Statement 17 is false. A collective pitch change alters the pitch angles of all the blades by the same amount at the same time. F e
EXERCISE D
‘$3
ii
Statements 2, 3, 5, 6, 8 and 10 are true. Statement l is false. The propulsive force for the helicopter is supplied by the main rotor. Statement H is false. The tail rotor turns at all times that the main ro tor turns. Statement 7 is false.
Tail rotor-blade angles are only
changed collectively.
Statement 9 is false. The rev/min of the tail rotor are higher than those of the main rotor.
TEST PAPER 3 l.
2.
In your own words, state the purpose of (a)
A main rotor, and
(b)
A tail rotor.
Draw two sketches showing a helicopter of 1200 kg AUW, (a)
Hovering in still air, and
(b)
In straight and level flight.
In each sketch, show the main rotor force resolved into lift and thrust forces and also show the drag and weight forces. Assign values to the lift, drag, and thrust forces.
555/3/3
..L1_3
_
Discuss briefly the main differences between semi-rigid, articulated, and hingeless rotors.
With the aid of a diagram, show how dissymmetry of lift may be felt by a main rotor unless corrected. What would happen to the helicopter if no correction were made?
% % e
Give alternative names for (a)
A vertical hinge, and
(b)
A horizontal hinge.
(c)
What type of rotor head uses both of these hinges?
Explain why the angle of attack of a main rotor blade is changed 90° of rotor~head rotation before the desired effect of the change is to take place.
§
8-
(a)
Name the three effects that will cause a main rotor blade to lead and lag about its vertical hinge.
(b)
when the helicopter is hovering in still air, do the blades lead and lag? Give reasons for your answer.
with the aid of a diagram, show how dissymmetry of lift can be felt by a tail rotor unless corrected. What would happen to the tail rotor if no correction were made?
Briefly describe one method used to correct dissymmetry of lift of a tail rotor. 9
-3
Why is the tail rotor mechanically connected to the main rotor so that it must turn when the main rotor turns?
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