Introduction to Helicopters Aerodynamics

8/11/2019 Introduction to Helicopters Aerodynamics

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INTRODUCTION

The wings of the airplane create a lift force

when they move through the air. As we known,

during ight, there are four forces acting on the

helicopter and those are LIFT , DA! ,

T"#$T ,and %&I!"T. In order to make thewings to move through the air , of course, the

helicopter itself has to move. A helicopter works

'y having its wings move through the air while

the 'ody stays still. The helicopter(s wings are

called )ain otor *lades. The shape and the

angle of the 'lades move through the air will

determine how much Lift force is created. After

the helicopter lifted o+ the ground, the pilot can



tilt the 'lades, causing the helicopter to tip

forward or 'ackward or sideward.

HISTORICAL

BACKGROUND

The helicopter is argua'ly one of the earliest

ideas for achieving ight. ver two thousand

years ago, the -hinese constructed what are



known as -hinese Tops. These simple toys

consisted of a propeller attached to a stick thatwould 'e spun rapidly through ones hands to

spin the propeller and achieve lift.

Chinese top Leonardo da Vinci's

"Helicopter"

Later, in the /th -entury, famed inventor and

artist Leonardo da 0inci designed one of the

most pleasing concepts for a helicopter, 'ut such

a craft was never actually constructed.

In &ngland in 123, $ir !eorge -ayley

constructed the 4rst powered models of



helicopters that were driven 'y elastic devices

which attained an altitude of 25ft. In 678,fellow &nglishman %. ". 9hillips constructed a

model helicopter that weighed 85 pounds :2 kg;

and was driven 'y steam. In 616, &nrico

Forlanini, an Italian civil engineer, also

constructed a steam driven model helicopter that

only weighed <./kg.

Sir George Cayley's helicopter

The 4rst manned helicopter to rise vertically

completely unrestrained was constructed 'y 9aul

-ornu, a French mechanic, in 251. -ornu(s



helicopter had two propellers that were rotated at

25 rpm 'y a 6 k% engine. -ornu was mostpro'a'ly the 4rst helicopter e=perimenter who

was concerned with control. %hile cornu>s

helicopter was historically signi4cant, its

performance and control was rather marginal and

it was never a practical machine.

Cornu's helicopter

The ne=t inuential development in the 4eld of

helicopters was 'rought a'out 'y a man who

never actually 'uilt a helicopter himself. In

28<, ?uan de la -ierva successfully ew his



-.7 autogiro, an aircraft that has two propellers,

a powered one to provide thrust, and an unpowered rotor to provide lift. -ierva(s autogiro

was noteworthy 'ecause it was the 4rst to use

an @articulated@ rotor that allowed its 'lades to

ap up and down in response to aerodynamic

forces on the 'lades during forward ight.The

4rst recognied helicopter record was set in

cto'er 2<5 'y Italian -orradino D(Ascanio

when he ew his helicopter over a distance of

one half mile at an altitude of /2 ft :6 m; for

6 minutes and 7/ seconds. D(Ascanio(s

helicopter had two contra rotating coa=ial rotors

:two rotors on the same shaft; that were



controlled 'y aps on 'ooms trailing each 'lade

near its tip.

D'Ascanio's helicopter

?ust 'efore and during %orld %ar II, !ermany

made several large, signi4cant steps in helicopter

development. The FAB3 helicopter, designed 'y

"einrich Focke, 4rst ew in ?une 2<3, and was

later used in pu'licity stunts 'y the Cais. The

FLB868 helicopter, designed 'y Anton Flettner,

'ecame operational with the !erman Cavy, and



over 555 of them were produced. This

helicopter utilied twinBintermeshing rotors, hada forward speed of 7/ kmh, and could operate

at an altitude of <,23/ m with a payload of <35

kg.

Sikorsky's VS-300

The 4rst American helicopter was the 0$B<55,

designed 'y Igor $ikorsky of the 0oughtB

$ikorsky -ompany. The 0$B<55 was the 4rst

helicopter to use a tail rotor to counteract the

torEue produced 'y the main rotor, and it was

this innovation that solved the last maor hurdle



in making helicopters practical ying vehicles.

This design is now the most common in today(shelicopters.

NOMENCLATURE AND

TECHNICAL TERM

Bernoulli's principle: This principle states that as the air

velocity increases, the pressure decreasesG and as the

velocity decreases, the pressure increases.

Airfoil: is technically de4ned as any surface, such as an

airplane aileron, elevator, rudder, wing, main rotor 'lades,

or tail rotor 'lades designed to o'tain reaction from the air

through which it moves.



Anle of A!!"c#: is the acute angle measured 'etween the

chord of an airfoil and the relative wind.

Anle of Inci$ence: is the acute angle 'etween the wing(s

chord line and the longitudinal a=is of the airplane.

Bl"$es : The 'lades of the helicopter are airfoils with a

very high aspect ratio : length to chord ;. The angle of

incidence is adusted 'y means of the control from pilots.

The main rotor of the helicopter may have two, three, four,

4ve or si= 'lades, depending upon the design. The mainrotor 'lades are hinged to the rotor head in such a manner

that they have limited movement up and down and also

they can change the pitch :angle of incidence;. The

controls for the main rotor are called -ollective and -yclic

-ontrols.



The !"il ro!or is small 'lades may have two or four 'lades

and mounted on the tail of the helicopter, it rotates in the

vertical plane. The tail rotor is controlled 'y the rudder

pedals. Its pitch can 'e changed as reEuired to turn the

helicopter in the direction desired.

Bl"$e Roo!: The inner end of the 'lades where the rotors

connect to the 'lade gripos.

Bl"$e Grips: Large attaching points where the rotor 'lade

connects to the hu'.

Ro!or Hu%: $it on top of the mast, and connects the rotor



'lades to the control tu'es.

M"in Ro!or M"s!: otating shaft from the transmission

which connects the main rotor 'lades to helicopter fuselage.

&i!c C"ne Horn: to converts control tu'e movement to

'lade pitch. -ontrol tu'e is a pushBpull tu'es that change

the pitch of the rotor 'lades through the pitch changing

horn.

S("s &l"!e Asse)%l*: The swash plate assem'ly consists

of two primary elements through which the rotor mast

passes. ne element is a disc, linked to the cyclic pitch

control. This disc is capa'le of tilting in any direction 'ut

does not rotate as the rotor rotates. This nonBrotating disc,

often referred to as the $tationary $tar is attached 'y a

'earing surface to a second disc, often referred to as

the otating $tar which turns with rotor and linked to the

rotor 'lade pitch horns.



Tr"ns)ission: The transmission system transmits engine

power to the main rotor, tail rotor, generator and other

accessories. The engine is operated at a relative high speed

while the main rotor turns at a much lower speed. This

speed reduction is accomplished through reduction gears in

the Transmission $ystem

Lif!: is produced 'y a lower pressure created on the upper

surface of an airplane(s wings compared to the pressure on

the wing(s lower surfaces, causing the wing to 'e LIFT&D

upward. The special shape of the airplane wing :airfoil; is

designed so that air owing over it will have to travel agreater distance and faster resulting in a lower pressure

area thus lifting the wing upward. Lift is that force which

opposes the force of gravity :or weight;.



Lift depends upon :; shape of the airfoil :8; the angle of

attack :<; the area of the surface e=posed to the airstream

:7; the sEuare of the air speed :/; the air density.

Rel"!i+e ,in$: is the direction of the airow with respect

to an airfoil or to the rotor 'lades.

&i!c Anle : The rotor 'lade pitch angle is the acute

angle 'etween the 'lade chord line and the rotor plane of

rotation. This pitch angle can 'e varied 'y the pilot throughthe use of cockpit controls :collective and cyclic pitch

control;.

S#i$s: are used mainly 'ecause they weigh less than

wheels. n larger, more powerful helicopters, wheels are

used 'ecause the utility and convenience can 'e more



important than the savings in weight. In order to move a

skidBeEuipped helicopter on the ground, one has to attach a

set of groundBhandling wheels, ack up the helicopter, and

roll it :into the hangar for maintenance;. If your helicopter

already has the wheels as a permanent feature, it is more

convenient to move around when the engine is shut down

or the pilot has wandered o+.

GENERAL Lift is o'tained 'y means of one or more power driven

horiontal propellers which called )ain otor. %hen the

main rotor of helicopter turns it produces lift and reaction

torEue. eaction torEue tends to make helicopter spin. n

most helicopters, a small rotor nears the tail which

called tail rotorcompensates for this torEue. n twin rotor

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helicopter the rotors rotate in opposite directions, their

reactions cancel each other.

M"in Ro!or:

The lifting force is produced 'y the main rotor . As they

spin in the air and produced the lift. &ach 'lade produces

an eEual share of the lifting force. The weight of a

helicopter is divided evenly 'etween the rotor 'lades on themain rotor system. If a helicopter weight 7555 l's and it

has two 'lades, then each 'lade must 'e a'le to support

8555 l's. In addition to the static weight of helicopter

,each 'lade must 'e accept dynamic load as well .

T"il Ro!or:

The tail rotor is very important. If you spin a rotor with an

engine, the rotor will rotate, 'ut the engine and helicopter

'ody will tend to rotate in opposite direction to the rotor.

This is called TorEue reaction. Cewton(s third law of



motion states, Hto every action there is an eEual and

opposite reaction. The tail rotor is used to compensate for

this torEue and hold the helicopter straight. n twinBrotors

helicopter, the rotors spin in opposite directions, so their

reactions cancel each other.

The tail rotor in normally linked to the main rotor via a

system of driveshaft>s and gear'o=es , that means if you

turn the main rotor , the tail rotor is also turn. )ost

helicopter have a ratio of <J to 3J. That is, if main rotorturn one rotation, the tail rotor will turn < revolutions :for

<J;or 3 revolutions :for 3J;.



Diss*))e!r* of Lif!:

All rotor systems are su'ect to Dissymmetry of Lift inforward ight. At a hover, the lift is eEual across the entire

rotor disk. As the helicopter gain air speed, the advancing

'lade develops greater lift 'ecause of the increased airspeed

and the retreating 'lade will produce less lift, this will

cause the helicopter to roll.



Bl"$e -l"ppin:

Dissymmetry of lift is compensated 'y *lade apping.

*ecause of the increased airspeed and lift on the advancing

'lade will cause the 'lade to ap up and decreasing the

angle of attack. The decreased lift on the retreating 'lade

will cause the 'lade to ap down and increasing the angle

of attack. The com'ination of decreased angle of attack on

the advancing 'lade and increased angle of attack on the

retreating 'lade through 'lade apping action tends to

eEualie the lift over the two halves of the rotor disc.



Te Collec!i+e Con!rol: %hen pilot raises the collective

control or pull collective control up, the collective control

will raises the entire swash plate assem'ly as a unit. This

has e+ect to the 'lades 'y changing the pitch of all 'lades

simultaneously .This causes to increase angle of attack and

give more lift.

Te C*clic Con!rol: The cyclic control will push one side

of the swash plate assem'ly up or down. This has the

e+ect to the rotor head system 'ecause the cyclic control or

cyclic stick controls the angle of the main rotor 'y anglingthe rotor head to which all the 'lades are attached .This

cause the helicopter to move left or right, forward or

'ackward.



An!i !or.ue &e$"ls:



The Thrust produced 'y the au=iliary :tail; rotor is

governed 'y the position of anti torEue pedals. These are

not rudder pedals, although they are in the same place as

rudder pedals on an airplane. They are linked to a pitch

change mechanism in the tail rotor gear 'o= to permit the

pilot to increase the pitch of the tail rotor 'lades. The

primary purpose of the tail rotor and its controls is to

counteract the torEue e+ect of the main rotor.



-li!

Direc!ion Con!rol

-unc!ion of Con!rols

There are three maor controls in the helicopter that thepilot must use during ight. They are J / 0 1 Collec!i+e

pi!c con!rol2 / 3 1 An!i Tor.ue &e$"ls or T"il Ro!or

Con!rol2 / 4 1 C*clic S!ic# Con!rol2



Collec!i+e Con!rol:

The collective pitch lever or stick is located 'y the left side

of the pilot(s seat and is operated with the left hand. The

collective is used to increase main rotor pitch at all points

of the rotor 'lade rotation. It increases or decreases total

rotor thrust. The collective lever is connected to the swash

plate 'y a series of 'ush pull tu'es. aising the collective



lever increases the pitch on the main rotor 'lade, lowering

the collective lever decreases the main rotor 'lade pitch.

The amount of movement of the lever determines the

amount of 'lade pitch change. As the angle of attack

increase, drag increases and otor 9) and &ngine 9)

tend to decrease. As the angle of attack decreases, drag

decreases and the 9) tend to increase. $ince it is

essential that the 9) remain constant, there must 'e some

means of making a proportionate change in power to

compensate for the change in drag. This coordination of

power change with 'lade pitch angle change is controlled

through a collective pitch leverB throttle control cam

linkage which automatically increases power when the

collective pitch lever is raised and decreases power when

the lever is lowered.



Collec!i+e Le+er is connected to the rotor system via push

pull tu'es. It also has droop com pensation devics which

sense change in the collective pitch lever and increases or

decreases fuel to the engine automatically somewhat in

anticipated of a change in power reEuired. This helps tominimie the 9) uctuations during collective pitch

change.

Enine Con!rol /E)erenc*1 is the throttle twist grip.

During emergency condition, 'etween ight and ight idle

positions. This is useful during any event which would

cause engine or rotor 9) to go too high or while landing

after a tail rotor failure.

I$le Rele"se *utton, when the throttle is rolled from @ o+ @

to @ idle @ the idle release 'utton snaps into a detent which



prevents the throttle from 'eing rolled 'ack to @ o+ @

S!"r!er Bu!!on 9ushing this 'utton will cause the starter

generator to act as a starter motor : $tarter !enerator is a

component that function in either mode as a starter or

generator ; , turning over the engine.

L"n$in Li! $witch has a three position which are Ho+,

Hforward and @'oth. In forward, only the forward light is

activated. In 'oth, the forward and downward lights are

activated.

&o(er Tri) $witch ,'y holding it in @ increase @ or @

decrease @ the pilot can set the 9) that the pilot attempt

to maintain.

An!i5Tor.ue &e$"ls or T"il Ro!or Con!rolJ

In accordance with Cewton(s law of action and reaction, the

helicopter fuselage tends to rotate in the direction opposite

to the rotor 'lades . This e+ect is called torEue. TorEue

must 'e counteracted and controlled to make ight is

possi'le. -ompensation for torEue in a single main rotor

helicopter is accomplished 'y means of a varia'le pitch

antitorEue rotor :tail rotor; located on the end of the tail

'oom e=tension at the rear of fuselage.



He"$in Con!rol :

In addition to counteracted torEue, the tail rotor and its

control linkage also permit control of the helicopter heading

during ight. Application of more control than is necessary

to counteract torEue will cause the nose of helicopter to

turn in the direction of pedal movement.

In forward ight, the pedals are not used to control the

heading of the helicopter :e=cept during portions of

crosswind takeo+ and approach;. They are used to

compensate for torEue to put the helicopter in longitudinal

trim so that coordinated ight can 'e maintained.

The thrust of the tail rotor is depend upon the pitch angle



of the tail rotor 'lades. The tail rotor may have a positive

pitch angle or it may have a negative pitch angle which to

push the tail to the right or pull the tail to the left.

%ith the right pedal pressed or moved forward of the

neutral position will cause the tail rotor 'lades to change

the pitch angle and the nose of helicopter will yaw to the

right. %ith the left pedal pressed or moved forward of the

neutral position will cause the tail rotor 'lades to change

the pitch angle opposite to the right pedal and the nose ofhelicopter will yaw to the left.

C*clic Con!rolJ



As mention earlier , the total lift force is always

perpendicular to the tipBpath plane of the main rotor. %hen

the tip path plane is tilt away from the horiontal, the lift

Bthrust force is divide into two components of forces that

are, the horiontal acting force, thrust and the upward

acting force, lift.

The purpose of the cyclic pitch control is to tilt the tip

path plane in the direction that horiontal movement is

desired. The thrust component of force then pulls the

helicopter in the direction of rotor tilt. The cyclic controlchanges the direction of this force, thus controlling the

attitude and air speed of helicopter.



The rotor disc tilts in the same direction of the cyclic stick

was moved. If the cyclic stick is moved forward, the rotor

disc tilts forwardJ if the cyclic is moved aft, the rotor disc

tilt aft, and so on. The rotor disc will always tilt in the

same direction that the cyclic stick is moved.



The r"$io s(i!c is used for pilot to transmit radio 'y

clicking the switch.The !ri) s(i!c, pilot use this switch to neutralie stick

force. 9ilot can use the trim switch to put the stick to the

right, left, forward or 'ackward. This runs electric motor

which will tension the spring which will tend to hold the

stick. The cyclic will stay where it is even the pilot were

let it go . This also releases tension from pilot.

The c"ro rele"se s(i!c is the option switchG some

manufacturer may have other function switch.



AEROFOIL THEORYAND PROPELLOR

ACTION

AERO-OIL THEOR6:An aerofoil is a streamlined 'ody,

which is designed to produce lift or thrust when passed

through air. Airplane wings, propeller 'lades and helicopter

main and tail rotor 'lades are all aerofoil.



Aerooil eatures

-hord is the distance or imaginary line 'etween the leading

and trailing edge of an airfoil. The amount of curve or

departure of the airfoil surface from the chord line is

known as cam'er. #pper cham'er refers to the upper

surfaceG lower cam'er refers to the lower surface. If the

surface is at, the cam'er is ero. The cam'er is positive if

the surface is conve=. The cam'er is negative if the surface

is concave. The upper surface of an airfoil always has

positive cam'er, 'ut the lower surface may have positive,

negative, or ero cam'er.



BERNOULLIS &RINCI&LE: *ernoulli, an eighteenth

century physicist, discovered that air moving over a surface

decreases air pressure on the surface. As air speed

increases, surface air pressure decreases accordingly. This is

directly related to the ight of an aircraft. As an airfoil

starts moving through the air, it divides the mass of air

molecules at its leading edge. The distance across the

curved top surface is greater than that across the relatively

at 'ottom surface. Air molecules that pass over the top

must therefore move faster than those passing under the

'ottom in order to meet at the same time along the trailing

edge. The faster airow across the top surface creates a

lowBpressure area a'ove the airfoil. Air pressure 'elow the

airfoil is greater than the pressure a'ove it and tends to

push the airfoil up into the area of lower pressure. As long

as air passes over the airfoil, this condition will e=ist. It is

the di+erence in pressure that causes lift. %hen air



movement is fast enough over a wing or rotor 'lade, the

lift produced matches the weight of the airfoil and its

attached parts. This lift is a'le to support the entire aircraft.

As airspeed across the wing or rotor increases further, the

lift e=ceeds the weight of the aircraft and the aircraft rises.

Cot all of the air met 'y an airfoil is used in lift. $ome of

it creates resistance, or drag, that hinders forward motion.

Lift and drag increase and decrease together. The airfoil>s

angle of attack into the air, the speed of airow, the air

density, and the shape of the airfoil or wing therefore a+ect

them.

!ernoullis principle

#he a$ount o lit that an aerooil de%elop depends on

& Area (si)e or surace area o the air oil*

+ Shape (shape or design o airoil sections*

3 Speed (Velocity o the air passing o%er the aerooil*



, Angle o attack (angle at hich air strikes the aerooil*

. Air density (a$ount o air in a gi%en space*

&RO&ELLORS:The production of thrust in helicopters is

'ased on the propeller action. The rotation of propeller

causes the air to accelerate from one side to the other side

of it, which results in the development of thrust in the

opposite direction of the ow. A propeller does the

conversion of torEue into a=ial thrust 'y changing the

momentum of the uid in which it is su'merged. %hen a

propeller su'merged in an undistur'ed uid rotates, it

e=erts a force on the uid and pushes the uid 'ackwards.

The reaction to this force on the uid provides a forward

thrust, which is used for propulsion. Although the complete

design of a propeller cannot 'e done according to the

momentum theory, yet the application of this theory leads

to some useful results s indicated 'y simple analysis of

pro'lem 'elow.



/ropeller

Let # 'e the upstream velocity and u 'e the downstream

velocity. Let A 'e the propeller disc area and K the mass

ow rate of air. *y *ernoulli>s principle we get the

velocity through the propeller eEual to average of upstream

and far down stream velocities. Therefore the induced

velocity u through the propeller eEuals,

22u

U uU

uU −=−

+=

( )U U u −

+

=

×=

2

uUA

velocityPropulsiveThrustPower opulsivePr

ρ

−

+=

22

uUAInputPower

22 U u ρ

U

u

21

1

InputPower

Power PropulsiveEfficiencyPropulsive

+=

=



If 9 is the power supplied and T the thrust developed then

from momentum theory we have

ρ A

T

T

P

2

1=

This formula is applied for hovering condition of the

helicopter where torEue T eEuals weight to 'e supported.

The actual ow through the propeller di+ers considera'ly

from the model depicted a'ove since the propeller works in

an Hin4nite sea of air HG there is no wellBde4ned 'oundary

'etween the uid at rest and uid motionG therefore the

actual thrust will di+er considera'ly from the values in the

a'ove e=pressions.

CON-IGURATION O-

HELICO&TERS



SINGLE ROTOR HELICO&TER:The most popular

helicopter arrangement is that of single rotor using a tail

rotor. The single rotor helicopter is relatively lightweight

and is fairly simple in design with one rotor one main

transmission and one set of controls.

The disadvantage of single rotor machine are its limited

lifting and speed capa'ilities and a severe safety haard

during ground operation with the tail rotor position several

feet 'ehind the pilot and out of line of his vision.

Single rotor helicopter

TANDEM ROTOR HELICO&TER:This helicopter uses two

synchronied rotor rotating in opposite direction. The

opposite rotation of the rotors causes one rotor to cancel

the torEue of the other.



&ach rotor is fully articulated and has three 'lades. It is

capa'le of lifting large loads. A disadvantage of the tandem

type is that it is not ecient in forward ight 'ecause one

rotor is working in the wake of the other.

#ande$ rotor helicopter

SIDE5B65SIDE HELICO&TER:It has two main rotors

mounted on pylons or wings positioned out from the sides

of the fuselage. The side 'y side has rotors turning in

opposite direction, which eliminates the need for a tail

rotor.The advantages are its e=cellent sta'ility and

disadvantage is having high drag and structural weight 'oth

resulting from structure necessary to support the main rotor.



$ide 'y side helicopter

COA7IAL HELICO&TER: In this fuselage torEue is

eliminated 'y two counter rotating rigid main rotors

mounted one a'ove the other on common shaft

Coaial helicopter

TILT ROTOR AIRCRA-T:The tilt rotor has the a'ility to

com'ine the vertical take o+ low speed capa'ilities of the

helicopter with highBspeed performance of a tur'oprop

airplane.



G6ROSCO&IC

&RECESSION

The term gyroscopic precession descri'es an inherent

Euality of rotating 'odies in which an applied force is

manifested 255 in the direction of rotation from the point

where the force is applied. $ince the rotor of a helicopter

has a relatively large diameter and turns at several hundred

revolutions per minute precession is a prime factor in

controlling the rotor operation.

The cyclic pitch control causes variation in the pitch of the

rotor 'lades as they rotate a'out the circle of the tip path

plane. The purpose of this pitch change is in part to cause

the rotor disc to tilt in the direction in which it is desired

to make the helicopter move. %hen only the aerodynamic

e+ects of 'lades are considered it would seem that when

the pitch of the 'lades is high the lift would 'e high and



the 'lade would rise. Thus if the 'lades had high pitch as

they passed through one side of the rotor disc the side of

the disc having low pitch should rise and the side having

low pitch should fall. This would 'e true e=cept for

gyroscopic precession.

!yroscopic precession is caused 'y a com'ination of a

spinning force and an applied acceleration force

perpendicular to the spinning force. Thus if force is applied

perpendicular to the plane of rotation the precession will

cause the force to take e+ect 255 from the applied force in

the direction of rotation.As a result of the fore going

principle, if a pilot wants the main rotor of a helicopter to

tilt in a particular direction, the applied force must 'e at a

angular displacement 255 ahead of the desired direction of

tilt. The reEuired force is applied aerodynamically 'y

changing the pitch of the rotor 'lades through the cyclic

pitch control. %hen the cyclic control is pushed forward

the 'lade at left increases its pitch as the 'lade on right



decreases pitch. This applies an up force to the left hand

side of the rotor disc, 'ut the up movement is therefore at

rear of the rotor plane and the rotor tilts forward. This

applies a forward thrust and causes the helicopter to move

forward.

8IBRATION

Any type of machine vi'rates. "owever greater than

normal vi'ration usually means that there is a malfunction.

)alfunctions can 'e caused 'y worn 'earings, outBofB

'alance conditions, or loose hardware. If allowed to

continue unchecked, vi'rations can cause material failure or

machine destruction. Aircraft BB particularly helicopters BB

have a high vi'ration level due to their many moving parts.

Designers have 'een forced to use many di+erent

dampening and counteracting methods to keep vi'rations at

accepta'le levels. $ome e=amples are



. Driving secondary parts at di+erent speeds to reduce

harmonic vi'rationsG this method removes much of the

vi'ration 'uild up.

8. )ounting highBlevel vi'ration parts such as drive

shafting on shockBa'sor'ent mounts.

<. Installing vi'ration a'sor'ers in highBlevel vi'ration

areas of the airframe.

LATERAL: Lateral vi'rations are evident in sideBtoBside

swinging rhythms. An outBofB'alance rotor 'lade causes this

type of vi'ration. Lateral vi'rations in helicopter rotor

systems are Euite common.

8ERTICAL:0ertical vi'rations are evident in upBandBdown

movement that produces a thumping e+ect. An outBofBtrack

rotor 'lade causes this type vi'ration.



HIGH5-RE9UENC6

"ighBfreEuency vi'rations are evident in 'uing and a

num'ing e+ect on the feet and 4ngers of crewmem'ers.

"ighBfreEuency vi'rations are caused 'y an outBofB'alance

condition or a highBspeed, moving part that has 'een torEue

incorrectly. The 'alancing of highBspeed parts is very

important. Any 'uildBup of dirt, grease, or uid on or

inside such a part :drive shafting for e=ample; causes a

highBfreEuency vi'ration. This type vi'ration is more

dangerous than a lateral or vertical one 'ecause it causes

crystalliation of metal, which weakens it. This vi'ration

must 'e corrected 'efore the eEuipment can 'e operated.

GROUND

RESONANCE



!round resonance is the most dangerous and destructive of

the vi'rations discussed here. !round resonance can destroy

a helicopter in a matter of seconds. It is present in

helicopters with articulated rotor heads. !round resonance

occurs while the helicopter is on the ground with rotors

turning it will not happen in ight. !round resonance

results when un'alanced forces in the rotor system cause

the helicopter to rock on the landing gear at or near its

natural freEuency. -orrecting this pro'lem is dicult

'ecause the natural freEuency of the helicopter changes as

lift is applied to the rotors. %ith all parts working properly,

the design of the helicopter landing gear, shock struts, and

rotor 'lade lag dampeners will prevent the resonance

'uilding up to dangerous levels. Improper adustment of the

landing gear shock struts, incorrect tire pressure, and

defective rotor 'lade lag dampeners may cause ground

resonance. The Euickest way to remove ground resonance is

to hover the helicopter clear of the ground.



C6CLIC

CONTROL

The tip path plane, or T99, is the plane connecting the

rotor 'lade tips as they rotate. %hile hovering, the thrust

vector of a helicopter is oriented upward, perpendicular to

the tip path plane. In order for the helicopter to travel

forward, this thrust vector needs to 'e rotated slightly in

the forward direction. To rotate the thrust vector, it is in

turn necessary to rotate the T99 'y the same amount.

#ip path planes and thrust %ectors or ho%ering and orard 1ight



$ince tilting the rotor hu' or rotor shaft is impractical, an

alternative means of rotating the T99 is needed. )ost

modern helicopters use a system of swash plates. $een in

the following diagram, the swash plate system is composed

of upper and lower swash plates.

Cyclic control and sash plates

The lower swash plate remains stationary relative to the

helicopter. The upper swash plate rotates with the rotor,

while remaining parallel to the lower swash plate. *y

utiliing what is called cyclic control, the swash plates can

'e angled so as to vary the 9itch of the 'lades depending

on their aimuth angle. As the swash plates are tilted in the



proper direction, there is an increased lift on the aft portion

of the rotor, causing the 'lades to ap up, which in turn

causes the T99 to rotate forwards. As the T99 rotates

forwards, the thrust vector does as well, imparting a

forward acceleration to the helicopter.

MOMENTUM

THEOR6

The 4rst analytical theory to consider for a helicopter in

forward :no a=ial; ight is the momentum theory. The

analysis for vertical :a=ial; ight is very similar to that of a

simple propeller, and will not 'e discussed here. ne

nota'le result of that analysis, however, is the induced

velocity of the rotor in hover.

%here w is the disc loading, given 'y



In the terms of 'asic momentum theory, the thrust of a

rotor in no a=ial ight is very dicult to derive. In the

conte=t of this discussion, a relationship for the thrust that

was proposed 'y !lauert in 286 will 'e used. A simple

diagram of an actuator disk in no a=ial ow is depicted

'elow.

Actuator disk in no aial 1o

The thrust of the actuator disk can 'e given 'y



Far downstream from the disk, the downwash vf is dou'led.

Also, the term 'ecomes the mass ow through the

stream tu'e that is de4ned 'y the actuator disk. $ome

validity for these relationships can 'e inferred 'y

comparing them to the formula for the lift of a wing

having 8 span with a uniform downwash. The lift of such

a wing is e=pressed 'y an eEuation similar to that shown

a'ove. After assuming that this eEuation is valid,

determining the thrust reEuires that the induced velocity in

forward ight 'e determined.

These two eEuations allow the determination of thrust and

induced velocity of a helicopter in forward ight.

STRENGTH AND

DESIGN

REQUIREMENTS



The helicopter structure must 'e strong enough to with

stand all the loads e=pected to 'e e=perienced in service

life. This comprises large loads, which are e=perienced

rarely, and repetitive small to medium loads which are

e=perienced in a normal ight. %here as large loads are

important in designing the nonBrotating parts of helicopter

like the fuselage, the tail 'oom, the landing gear etc. The

repetitive loads are important in designing the rotating parts

such as the main rotor, the tail rotor, the shafts, the main

rotor gear'o=, the tail rotor gear'o= etc.

ROTOR STRUCTURE: The rotor 'lade structure must

possess sucient strength to with stand not only the

aerodynamic loads generated on the 'lade surface 'ut also

the inertial loads arising from the centrifugal, the coriolis,

the gyroscopic and the vi'ratory e+ects produced 'y the

'lade movement .the 'lade must also possess sucient

sti+ness and rigidity to prevent e=cessive deformation and



to assure that the 'lades will maintain the desired

aerodynamic characteristics.

8IBRATION: The vi'ration, its causes and reduction are as

discussed previously.

SER8ICE LI-E:%hile considering the e=pected service life

of the helicopter or its components all types of e=pected

loads must 'e considered. Three 'asic factors, which

govern the service life, are

. -orrosion

8. -reep and

<. Fatigue

STRUCTURAL MATERIALS:$ome of the important

factors, which govern the selection of material for airframe

and the primary load selection of material for airframe andthe primary load 'earing mem'ers of the helicopter, are

. A high strength to weight ratio

8. $ti+ness

<. $peci4c gravity



7. esistance to impact loads

/. Temperature e+ects

3. -orrosion resistance

1. Fatigue strength

6. ate of crack propagation

Te Ro!or

Mec"nis)



The Autogiro(s 'lades had evolved into long slender units

with a good airfoil shape B true rotating wings, as opposed

to the primitive, fanBshaped @airscrew@ rotors found on

many early helicopters. The lengthy 'lades of the Autogiro

turned through a greater circle than the stu''y shortBspan

rotors then 'eing tried for helicopters, thus providing that

much more disc area to support the weight of the aircraft.

An aeronautical engineer would descri'e this advantage as

a @lower disc loading@ :less weight for each sEuare foot of

disc area;, and eventually helicopter e=perimenters followed

this lead.

Another 'asic improvement, stemming from -ierva(s work

and perhaps even more important than the shape of the

'lades, was the system for hinging each 'lade to the hu'.

This arrangement permitted each 'lade to ap and to adust

to the uneEual lift forces created on opposite sides of therotor disc as the aircraft sped into forward ight.



Te "iro( p"!!erns cre"!e$ %* !e for("r$ i! of "n "irpl"ne "n Au!oiro; "n$ "

elicop!er "re co)p"re$ ere2 ,i! !e Au!oiro; !e ro!or )"s! is incline$ !o !e re"r

"n$ !e "iro( in!o !e ro!or is fro) !e fron! "n$ %elo(2 In !e elicop!er; !e ro!or

is incline$ for("r$ "n$ !e o( en!ers fro) "%o+e

There were other important 'ene4ts gained from e=perience

with the Autogiro. The use of autorotation itself to turn an

unpowered rotor pointed the way to a means of making a

safe powerBo+ landing in a helicopter. The lateBmodel

directBcontrol and umpBtakeBo+ giros of the 2<5(s went

even furtherJ improved systems of control to the rotor head,

methods for making pitch changes to the 'lades,

mechanical drive systemsBall were developed, and

freEuently 'y trial and error. Cot that current methods are

so very di+erent. It is pro'a'ly more true of helicopter



design than any other phase of aerospace engineering that

the personal element still enters into the eEuation. The

creative process of designing a successful helicopter B

particularly the rotor system M to this day has something

in common with the freeBforBall e=perimentation of the

aeronautical pioneers.

Although designers have created an impressive num'er of

rotor systems, it is possi'le to narrow the 4eld down to

three 'asic typesJ "r!icul"!e$, se)i5rii$, and rii$ rotors.

There are rotor systems that seem to fall outside this

threefold classi4cation, 'ut for the most part these are only

variations or com'inations of the three types. In this

connection, it should 'e appreciated that the term @rotor@ or

@rotor system@ refers to a single unit only, composed of

ust one hu' and the 'lades attached to it. A helicopter

may have more than one main rotorG multiple arrangementsof two, three, four or even more rotors have 'een found on

various aircraft at di+erent times in history, 'ut each rotor

is considered a separate system. For the purposes of the

e=planations that follow :which deal primarily with the

various types of rotor hu's and the workings of cyclic



pitch control; we will 'e concerned primarily with the most

widely used type, the $ikorsky con4guration, which has

ust one main rotor, in com'ination with a small tail rotor.

The most important part of the system is the hu' at the

center. "ere are concentrated all the forces generated 'y

the movement of the 'lades through the airG aerodynamic,

centrifugal, and inertia factors are involved that create very

great loads which simultaneously pull the 'lades upward

and outward. The hu' is designed, for the most part, to

accommodate and control these forces automatically, and

the working of its mechanism is the very essence of the

helicopter(s mechanical nature. In dealing with the three

'asic types of rotor systems we will descri'e how some of

these forces a+ect the rotor hu'.

The "r!icul"!e$ ro!or system is the oldestG it appeared on

the Autogiros of the 285(s and was incorporated in the

4rst worka'le helicopters of the 2<5(s. :The Autogiro

ancestry of the articulated rotor prompted an earlier name,

the @-ierva rotor.@; Today it is perhaps still the most

widely used type, in one form or another.



In " elicop!er (i! "n "r!icul"!e$ ro!or s*s!e); !ere "re !ree #in$s of

)o+e)en! for !e ro!or %l"$e "s i! !urns "roun$ !e )"s!: up "n$ $o(n

/"ppin1; %"c# "n$ for! in !e ori<on!"l pl"ne /le"$ "n$ lu1; "n$c"nes in !e pi!c "nle

In this system, e=clusive of the rotation of the 'lades a'out

the mast, each individual 'lade is attached so that it can

move in three di+erent ways a'out the hu'. ne movement

is common to almost all helicopters and types of rotor

systemsJ the turning of the 'lades along their spanBwise

a=is, owing to the action of the pilot(s controls, in order to

change the pitch angle. The other two kinds of motion,

however, are not under the pilot(s immediate control. These

are movements the 'lades make in response to the powerful

natural forces acting on the rotor, for which the articulated

hu' provides the necessary mechanisms M speci4cally,

hinges M which permit freedom of movement so the

'lades can @articulate,@ or ap up and down and move 'ack



and forth slightly in the horiontal plane. The pivot which

permits the upBandBdown movement is usually called the

@apping@ hinge, while the foreBandBaft pivot, mounted

vertically, which allows the 'lade to move 'ack and forth

slightly in the horiontal plane, is called the @drag@ hinge.

-l"ppin ines in !e ro!or u% elp !o "$=us! !e une.u"l lif! forces in



!e ri! "n$ lef! "l+es of !e ro!ors circle "s !e elicop!er )o+es

!rou !e "ir in for("r$ i!2 Te ines per)i! !e %l"$es !o rise "n$

f"ll "s !e* !urn; !us +"r*in !e "nle of "!!"c# so "s !o e.u"li<e !e lif!

forces

The apping hinge provides the 'lades with apping

freedom, which permits each 'lade to rise and fall, as it

turns, so the tip rides higher or lower in its circular path.

%hile the hinge may 'e located very close to the center of

the rotor drive shaft, it is more freEuently designed to 'e a

short distance from this center line. This is termed an

@o+set@ apping hinge, and it o+ers the designer a num'er

of important advantages. The apping motion is the result

of the constantly changing 'alance 'etween lift, centrifugal,

and inertial forcesG this rising and falling of the 'lades is

characteristic of most helicopters and has often 'een

compared to the 'eating of a 'ird(s wing. ne other point

should 'e mentionedG the apping hinge, in company withthe natural e=i'ility found in most 'lades, permits the

'lade to droop considera'ly when the helicopter is at rest

and the rotor is not turning over. During ight the

necessary rigidity is provided 'y the powerful centrifugal

force which results from the rotation of the 'ladesG this



force pulls outward from the tip, sti+ening the 'lade, and is

actually the only factor which keeps it from folding up.

Dr"(in so(s roo! "!!"c)en! of ro!or %l"$e !o "n "r!icul"!e$ u%2

Te "ppin ine per)i!s e"c %l"$e !o rise "n$ f"ll "s i! !urns;

"n$ !e +er!ic"ll* )oun!e$ $r" ine "llo(s le"$5l" )o!ion

The vertically mounted drag hinge as we have already

noted, permits each 'lade to move 'ack and forth slightly

in the horiontal plane independently of the movement of

the other 'lades. The terms @dragging,@ @hunting,@ and@leadBlag@ are also used to descri'e this movement, which

is necessary to relieve the powerful forces that might

otherwise 'end and even 'reak the 'lades. To prevent this

'ackBandBforth hunting from developing into serious

vi'ration, it is restricted 'y hydraulic dampers which slow



down and @damp@ the movementG this action is very similar

to the damping e+ect of an ordinary hydraulic doorBcloser.

The early Autogiros, incidentally, used friction discs to

accomplish the same thing.

The position that the 'lades actually assume while the

helicopter is in ight o'viously is the result of the various

forces acting upon them. Cormally, the 'lades will 'e

lagged 'ack slightly on the drag hinge and tilted up a few

degrees on the apping hingeG this upward tilt is termed the

@coning angle@ and is the result of the lifting force pulling

upward on each 'lade while, simultaneously, centrifugal

force is pulling outward. $ince the centrifugal loading is so

much greater, the 'lades only tilt upward a few degrees,

and their path through the air takes the form of a shallow

cone.

The articulated type of rotor is designed to leave the 'lades

as free as possi'le, to avoid trying to restrict their natural

tendencies to ap up and down or move in the horiontal

plane. ne e+ect is that the 'lades can 'e very slender and

light, since great strength is reEuired only to resist the



tension of the powerful centrifugal force pulling along the

span of the 'lade. An articulated 'lade is designed to have

the inertial, centrifugal, and aerodynamic forces developed

in ight all 'alancing a'out the same point on the 'lade

chordMthis is ordinarily oneBfourth of the way 'ack from

the leading edge, or, as it is called, the @Euarter chord

point.@ *alancing the forces in this manner makes it

possi'le for the pilot to control the 'lades with a minimum

of e+ort and tends to hold down vi'ration as well. These

highly desira'le characteristics are reasons why the

traditional articulated rotor is still so widely used.

The other two types of rotors are the semiBrigid and the

rigid :or @hingeless@;. *oth are primary types currently in

use, and 'oth duplicate the function of the articulated rotor.

Though di+erent mechanisms are involved, the aerodynamic

e+ects are essentially the same.

In the se)i5rii$ ro!or :sometimes called a @rocking hu'@

or @teetering@ rotor;, the 'lades are attached rigidly to the

hu' 'ut the hu' itself is free to tilt in any direction a'out

the top of the mast. Although there is no leadBlag



movement, the 'lades can still ap or, in the true sense,

rock up and down in order to compensate for dissymmetry

of lift when moving forward. $emiBrigid rotors have

appeared on helicopters with two, three, and four 'lades

and provide some simpli4cation, although they cause other

pro'lems. ne important advantage is the fact that there

are no drag hinges, and therefore no drag dampers are

reEuired. *ut there are complications including the

necessity for providing a type of universal oint 'etween

the drive shaft and the rotor hu'.

The rii$ ro!or , which until fairly recently was still in the

e=perimental stage, is used in relatively few helicopters. In

theory the rigid rotor is similar to an ordinary propellerG the

'lades are 4=ed to the hu' without hinges and the hu' in

turn is 4=ed to the shaft. f the various systems, it is

closest to the elemental concept of the airscrew whichtantalied e=perimenters in centuries past. :'viously, there

can 'e no such thing as a completely rigid rotor, since all

'lades inherently e=hi'it some degree of e=i'ilityMfrom

a structural viewpoint it would 'e almost impossi'le to

'uild a truly rigid 'lade.; $ince there are no apping



hinges, or any other provisions for movement at the hu',

other systems have 'een developed to overcome the

uneEual forces on the rotor, including preBconing and

feathering of the 'lades.

&re5conin, as the word suggests, is an arrangement for

presetting the 'lade at a slight upward angle from the hu'

to the tip. This is the same angle that the 'lade would

ordinarily take, due to its coning upward in normal ight.

If the upward tilt for average operating conditions is

determined, and the 'lades mounted on the hu' at this

angle, the 'ending loads can 'e reduced materially. 9reB

coning is thus a fairly simple design approach for dealing

with the stresses on a semiBrigid or rigid rotor.

-e"!erin, on the other hand, involves the incorporation of

an entirely new mechanism in the rotor head. This system

compensates for the lift di+erential 'etween the advancing

and retreating 'lades 'y reducing the angle of attack as the

'lade starts to rise and decreasing it as the 'lade starts to

fallG this, of course, means that the 'lade has to 'e

mounted on the hu', so that it can 'e rotated along its



spanBwise a=is. As part of the system, the hu' mechanism

can 'e designed so the pitch changes are made

automatically 'y the apping :in this case the term

@coning@ is sometimes used, as well; of the 'lades as they

turn. As the 'lade starts to ap, it activates linkage which

changes the 'lade(s angle of attack. This techniEue has

'een incorporated in many modern helicoptersG the

arrangement has 'een called @pitchBcone coupling.@

The semirigid and rigid rotor systems represent attempts to

simplify helicopter design, 'ut the end result more often

than not has usually 'een the need for added complications

such as preBconing or pitchBcone coupling, which tend to

defeat the designer(s original aim. This pattern has 'een

repeated over and over again in the development of new

rotor systems and of other parts of the helicopter, as wellG

the designer succeeds in simplifying one mechanism and4nds that he has to add another device somewhere else in

the system.

The pro'lem of trying to reduce comple=ities that refuse to

'e 'anished has plagued designers since the days of the



4rst helicopters. ne e=perimenter, D. ". Naplan, in

writing of the intricacies of the rotor cyclic control system,

summed up one part of the pule thusJ @In a cyclicB

controlled rotor, every time the designer tries to deny the

'lade a freedom, it demands compensation somewhere else

in the rotor mechanism. The history of the helicopter is

4lled with attempts to reduce complication... invaria'ly this

turns into a game of -hinese checkers as the designer

feverishly moves the complicated pro'lem from one part to

another, never getting rid of it.@

As with the other mechanisms found on a modern

helicopter, the rudiments of the cyclic system can 'e traced

'ack to the Autogiro, on which the 4rst e+ective rotatingB

wing controls were developed. The designers of the 4rst

Autogiros of the early 285(s did not attempt to control the

rotor 'lades directly. Instead, conventional airplaneBtypecontrols were furnishedBrudder, elevators, ailerons mounted

on stu' wingsMand the rotor was controlled 'y the

aerodynamic forces on these surfaces.



$ince the ailerons were outside the propeller slipstream :the

direct 'last of air from the propeller;, at low airspeeds they

were the weakest link in the systemG eventually a method

was devised for o'taining lateral control 'y @rocking@ the

rotor hu' from side to side. This meant that the ailerons

and the stu' wings that supported them could 'e dispensed

with, and the wingless Autogiro appeared.

The rocking head played a part in the development of

cyclic pitch control systems. %hen the system was applied

to some of the early helicopters, it was used for rocking

the head not only from side to side 'ut in all directionsG in

e+ect the hu' was now mounted on a kind of universal

oint. The idea was that 'y tilting the mova'le head :when

the pilot moved his control stick; the a=is of rotation would

'e inclined slightly from the vertical, and thus its lift

would pull slightly in that direction. "owever, there werepro'lems when this system was used with the powerBdriven

rotor of a helicopter, caused 'y the drive shaft as it rotated

the tilted hu'. %hen the hu' was tilted the mass of the

rotor was no longer @on center@ over the shaft, and this



caused serious vi'ration. Also, very great control forces

were needed to move the rotor head.

The answer to this was the cyclic pitch control used on the

maority of helicopters today. It had 'een discovered that

you could get the same e+ect as rocking the hu' 'y

increasing the pitch of the 'lades in cycles as they rotated.

As each 'lade swept through its full <35Bdegree circle, it

changed pitch cyclicallyMthat is, it assumed a high pitch

at one point in the disc and then assumed a low pitch as it

moved around to the opposite position. As the pitch was

increased or decreased, the 'lades rose or fell on their

apping hinges, thus inclining the disc slightly from its

vertical a=is. The e+ect was that the tip path of the 'lades,

as the rotor whirled around, was very much the same as it

would have 'een with a rocking head rotor inclined in that

direction.

%hat made this approach particularly attractive was that at

the time of this e=perimentation, many rotatingBwing

aircraft, helicopters and rotorplanes alike, were already

furnished with collective pitch control. This was a system



for changing the pitch on all 'lades to the same degree,

simultaneously, in order to take o+ vertically, and the

'lades were therefore mounted on 'earings so they could

'e moved for pitch control along the spanBwise a=is. All

that was needed was the mechanical system for controlling

the pitch of the 'lades cyclically as well as collectively.

The device in a helicopter control system which

accomplishes this, feeding the cyclic control movements to

the rotor hu', is known 'y the rather interesting name of

@swash plate.@ It is a doughnutBshaped unit that 4ts around

the mast, actually consisting of two platesMan upper one

and a lower oneMwith a 'earing 'etween the two. The

upper plate is connected to the rotor hu' 'y rods and

conseEuently it spins around on the 'earing as the rotor

turns. The lower plate is linked to the pilot(s cyclic control

stick system and does not rotate. "owever this lower plateis mounted on pivotsMeither a spherical 'earing or a

gim'al ringMso that it can 'e tilted in any direction. As

it tilts, the upper plate :which is moving in company with

the hu'; will 'e tilted as well. This results in a constant up

and down movement in the link rods which connect the



upper plate to the hu', accomplishing the cyclic pitch

changes in the 'lades as they sweep around, and thus

transmitting the pilot(s control movements to the rotor.

%hile it is not intended here to delve too deeply into the

design of the cyclic control system, there is another factor

which should 'e considered, since it helps e=plain the

workings of the linkage from the swash plate to the rotor

hu'. This is called the @25Bdegree phase lag@ or time lag.

%hen the pitch of a rotor 'lade is increased, the 'lade does

not immediately rise 'ut has to rotate for appro=imately

another 25 degrees :a Euarter of a revolution; 'efore it

reaches the highest apped positionG thus, there is a lag of

appro=imately 25 degrees, attri'uted to 'lade inertia and

gyroscopic factors, 'etween the point at which the pitch is

increased or decreased and the point where the full e+ect

registers on the 'lade. )ost helicopters have the controllinkage from the swash plate to the hu' o+set 'y

appro=imately 25 degrees to compensate for thisG the pitch

change is fed into the rotor at a point oneBEuarter of a

revolution early in the plane of rotation. For e=ample, when

the pilot pushes the cyclic control stick forward so as to



incline the rotor forward, as each 'lade comes around it

will receive the decrease in pitch at the 25Bdegree point on

the right :advancing; side and the increase in pitch at the

opposite point on the left :retreating; side. *ecause of the

time lag, each 'lade is in its highest apped position

directly over the tail of the helicopter and its lowest apped

position directly over the nose. This, of course, inclines the

rotor disc forward as desired to propel the helicopter into

forward ight.

In connection with the design of cyclic systems, one vital

consideration is that the forces and loads acting on the tip

of the 'lade are hundreds of times greater than the control

forces which can 'e transmitted from the hu' to the 'lade.

The tip is going to go where it pleases, and the hu' must

'e designed either to provide it with mechanical freedom

through the use of hinges or, through structural e=i'ility,to move as it must under its dynamic loads. &ven the soB

called rigid rotor tends to 'ehave like an articulated rotor

'ecause of the 'ending of the 'lades. :A 'lade rigid

enough to resist these forces would 'e too heavy to y.;



There is one important structural rigidity, however, that is

essential to the correct functioning of a cyclic control

system. The 'lade must 'e constructed so that it will not

twist when pitch changes are made at the hu'G it must have

what a designer calls @torsional rigidity.@ If the 'lade failed

to have this sti+ness it would not 'e possi'le to transmit

the pitch changes from the hu' along the span of the 'lade

out to the tip. Cevertheless, as with many of the 'asic

concepts in rotor design, there are e=ceptions to this rule.

ne important e=ample is the torsionally e=i'le 'lade

used on some helicopters. %ith this system a type of pitch

control is used that reEuires a 'lade that is deli'erately

e=i'le in torsion. n these rotors the pitch control is

accomplished 'y actually warping the 'lades through the

leverage o'tained from a small, controlla'le, aerodynamic

surface mounted on the trailing edge of the 'lade, similar

to the trim ta' used on airplane control surfaces.



Groun$ e>ec!

The high power reEuirement needed to hover out of ground

e+ect is reduced when operating in ground e+ect. !round

e+ect is a condition of improved performance encountered

when operating near :within 8 rotor diameter; of the

ground. It is due to the interference of the surface with the

airow pattern of the rotor system, and it is more

pronounced the nearer the ground is approached. Increased

'lade eciency while operating in ground e+ect is due to

two separate and distinct phenomena. First and most

important is the reduction of the velocity of the induced

airow. $ince the ground interrupts the airow under the

helicopter, the entire ow is altered. This reduces

downward velocity of the induced ow. The result is less

induced drag and a more vertical lift vector. The lift

needed to sustain a hover can 'e produced with a reduced



angle of attack and less power 'ecause of the more vertical

lift vectorJ

The second phenomenon is a reduction of the rotor tip

vorte= J



%hen operating in ground e+ect, the downward and

outward airow pattern tends to restrict vorte= generation.

This makes the out'oard portion of the rotor 'lade more



ecient and reduces overall system tur'ulence caused 'y

ingestion and recirculation of the vorte= swirls.

otor eciency is increased 'y ground e+ect up to a

height of a'out one rotor diameter for most helicopters.

This 4gure illustrates the percent increase in rotor thrust

e=perienced at various rotor heightsJ

At a rotor height of oneBhalf rotor diameter, the thrust is

increased a'out 1 percent. At rotor heights a'ove one rotor

diameter, the thrust increase is small and decreases to ero

at a height of a'out 7 rotor diameters.

)a=imum ground e+ect is accomplished when hovering

over smooth paved surfaces. %hile hovering over tall grass,

rough terrain, revetments, or water, ground e+ect may 'e

seriously reduced. This phenomenon is due to the partial



'reakdown and cancellation of ground e+ect and the return

of large vorte= patterns with increased downwash angles.

Two identical airfoils with eEual 'lade pitch angles are

compared in the following 4gureJ

The top airfoil is outBofBgroundBe+ect while the 'ottom

airfoil is inBgroundBe+ect. The airfoil that is inBgroundB

e+ect is more ecient 'ecause it operates at a larger angle

of attack and produces a more vertical lift vector. Its

increased eciency results from a smaller downward



induced wind velocity which increases angle of attack. The

airfoil operating outBofBgroundBe+ect is less ecient

'ecause of increased induced wind velocity which reduces

angle of attack.

If a helicopter hovering outBofBgroundBe+ect descends into a

groundBe+ect hover, 'lade eciency increases 'ecause of

the more favoura'le induced ow. As eciency of the rotor

system increases, the pilot reduces 'lade pitch angle to

remain in the groundBe+ect hover. Less power is reEuired

to maintain however inBgroundBe+ect than for the outBofB

groundBe+ect hover.

LIMITATIONS

There are a num'er of factors that govern the ma=imum

speed of a helicopter J

Dr" In aerodynamics, drag is the force opposing thrust.



Drag is present in helicopters in two main typesJ

"2 &"r"si!e $r" 9arasite drag is the drag forces created 'y

the components that protrude into the airow around the

helicopter. *ecause this drag is opposing thrust it is

reducing the amount of thrust availa'le to make the

helicopter y faster. 9arasite drag includes the landing gear,

antennas, cowlings, doors, etc. The shape of the fuselage

will also produce parasite drag. n later helicopters where

the manufacturer has attempted to raise the speed of the

helicopter, the landing gear is retracta'le to reduce the

amount of parasite drag produced. !enerally, for a given

structure, the amount of parasite drag is proportional to the

speed that the structure is passing through the air and

therefore parasite drag is a limiting factor to airspeed.

%2 &ro?le $r" 9ro4le drag is the drag produced 'y the

action of the rotor 'lades 'eing forced into the oncoming

airow. If a rotor 'lade was cut in half from the front of

the 'lade :leading edge; to the rear of the 'lade :trailing

edge;, the resulting shape when looking at the crossBsection

is considered to 'e the 'lade @pro4le@. For a rotor 'lade to

produce lift, it must have an amount of thickness from the



upper skin to the lower skin, which is called the @cam'er@

of the 'lade. In general terms the greater the cam'er, the

greater the pro4le drag. This is 'ecause the oncoming

airow has to separate further to pass over the surfaces of

the rotor 'lade. The 'lade pro4le for a given helicopter has

'een designed as a compromise 'etween producing

sucient lift for the helicopter to ful4l all of its roles, and

minimising pro4le drag. To alter the amount of lift

produced 'y the rotor system, the angle of attack must 'e

altered. As the angle of attack is increased then the pro4le

drag also increases. This is generally referred to as

@induced drag@, as the drag is induced 'y increasing the

angle of attack.

Re!re"!in Bl"$e S!"ll To understand retreating 'lade stall

it is 4rst necessary to understand a condition known

as@Diss*)e!r* of Lif!@. -onsider a helicopter hovering in

still air and at ero ground speed. The pilot is maintaining

a constant 'lade pitch angle with the collective pitch

control lever and the aircraft is at a constant height from

the ground. The airow velocity over the advancing 'lade

and the retreating 'lade is eEual.

http://www.helis.com/howflies/bladlift.php

http://www.helis.com/howflies/bladlift.php



If the tip of the advancing 'lade is travelling at <55mph

then the tip of the retreating 'lade must also 'e travelling

at <55mph. The velocity of the airow over the 'lade is

progressively reduced as we look closer toward the root

end of the 'lade :toward the rotor hu'; as the distance that

the o'served point has to travel around the circle is

reduced.

In this condition the amount of lift 'eing generated 'y each

'lade is the same 'ecause the amount of lift produced is a

function of velocity and angle of attack. "owever, if the

helicopter started to move forward then the airow velocity

over the advancing 'lade would 'e increased 'y the

amount of the forward speed as the 'lade is moving in the

opposite direction to the ight. If the helicopter was then

travelling forward at 55mph, then the airow at the

advancing 'lade tip would 'eJ

0elocity induced 'y the

'lades turningJ

<55m

ph

9lus the velocity from

forward ightJ

55m

ph

Total e+ective velocity at 755m



the tipJ ph

At the retreating 'lade the velocity is reduced 'y the

amount of forward speed as the 'lade is travelling in the

same direction as the airow created 'y forward ight. $o

the tip is now e+ectively travelling at 855mph, or half the

speed of the advancing 'lade. From the Formula for Lift, it

is known that the amount of lift produced varies as the

sEuare of velocity. From the e=ample a'ove this means that

the advancing 'lade will produce four times more lift than

the retreating 'lade. If this situation was not corrected, the

helicopter could not y forward in a straight line when

forward ight was attempted. :It would actually pitch noseB

up, 'ut that(s another storyO;

To correct for this the rotor system is allowed to @ap@

where'y one 'lade tip can rise a'ove the other with

reference to the rotor plane of rotation. The e+ect this has

is to reduce lift on the advancing 'lade and increase lift on

the retreating 'lade. The lift across 'oth 'lades is then

eEualised.

Cow that we understand @Dissymetry of Lift@, we can look

at retreating 'lade stall. Pou will recall that the retreating



'lade has a lower airow velocity than the advancing 'lade

in forward ight. If we were to accelerate our helicopter

from the a'ove e=ample to <55mph, then the advancing

'lade would have an airow velocity of 355mph, and the

retreating 'lade would 'e ero. For the 'lade to produce

lift it must have some airow over it, so in this case the

'lade would @stall@. $tall is a condition where there is a

'reakdown of smooth laminar airow over the surfaces of

an aerofoil :rotor 'lade;.

%ith each 'lade entering a stall condition as it passed

down the left side of the helicopter, forward ight could

not 'e maintained at this speed. *efore the 'lade actually

stalled it would produce a series of harsh vi'rations known

as @'u+eting@. %hen a manufacturer produces a new

helicopter, the speed at which this 'u+eting will occur is

esta'lished during ight test trials and a lower 4gure is

su'seEuently pu'lished which is commonly known as 8NE

or 8eloci!* 5 Ne+er Ecee$ . This esta'lishes a safety

margin 'elow the speed where retreating 'lade stall may

occur.



Airo( Re+ers"l Airow eversal will normally occur

'efore retreating 'lade stall. Pou will recall that the airow

velocity is progressively reduced along a 'lade from 'eing

highest at the tip, to lowest at the root end.

If the velocity is <55mph at the tip, it is feasi'le for the

velocity to 'e as low as 55mph at the root. Therefore

when forward speeds as low as 55mph :appro=. 35 Nts;

are encountered, the root end of the 'lade is e+ectively

stalled. %hen higher speeds are attempted, the airow

across the root end of the 'lade can actually reverse and

travel from the trailing edge to the leading edge. This is

'ecause the airow velocity produced 'y the forward speed

is greater than that 'eing produced 'y the rotor 'lades

turning. Airow reversal is counterBproductive to producing

lift and rotor thrust.

To reduce the e+ects of lift variations from the root to the

tip of a 'lade the manufacturer will either twist the 'lade

along its length, or apply a taper to the 'lade. Twist is the

reduction of angle of attack from the root to the tip.

emem'er that lift increases with velocity and angle of

attackQ *ecause the tip is travelling faster than the root, the



angle of attack must 'e reduced toward the tip to maintain

the same amount of lift at the tip and the root ends. Taper

is the gradual reduction of the width of a 'lade from the

leading edge to the trailing edge. A straight line drawn

from the centre of the leading edge to the centre of the

trailing edge is called the @-hord Line@. *y reducing the

chord line from the root to the tip, less surface area is

availa'le for the airow to act on to produce lift.

n higher speed helicopters :%estland Lyn=;, the root end

of the 'lade is a 'lade spar and attachment area only. The

aerofoil shape does not start until several feet out from the

centre of the rotor system. This is done to reduce the

e+ects of airow reversal 'y placing the liftBproducing

surface further out where the rotational velocity is higher.

Air Co)pressi%ili!* Air is a gas and therefore conforms to

the properties of a gas, namely the a'ility to 'e

compressed. %hen studying aerodynamics however, air

must also 'e considered to have some of the properties of a

uid. A uid has far less compressi'ility than a gas.

%hen the airow over a rotor 'lade strikes the leading

edge, it is split into two streams, which then pass a'ove



and 'elow the 'lade. At lower speeds, this splitting action

occurs relatively easily reEuiring little energy. As speeds

increase, the air striking the leading edge tends to 'e

compressed 'efore separating into two streams. Think of

this as slapping your hand onto a water surface. If you

chop your hand into the water, like a karate chop, you can

separate the water fairly easily. If you slap your open hand

onto the water however, it takes considera'ly more force to

su'merge your hand. The airow at the leading edge is

very similar. As the air at the leading edge is progressively

compressed, it reEuires considera'ly more rotor thrust for

the 'lade to separate the airow into two streams.

C*clic Con!rol S!ic# $esin "elicopter designers are

forever trying to 4t more eEuipment into the cockpit of a

helicopter to satisfy market demands. At the same time,

they are trying to minimise the weight of the aircraft so

that it can carry and lift more. %hen designing the pilot

and copilots workstations the designers attempt to place the

controls in a position where the crew can easily and

comforta'ly operate all controls without e=cessive reaching



or stretching. This places limitations on the amount of

movement availa'le at the cyclic control stick.

The designers could feasi'ly arrange the controls such that

very small amounts of stick movement were reEuired for

normal ight, 'ut this would make control in the hover

very dicult as the controls would 'e super sensitive to

small inputs. For this reason, the controls are arranged so

that a reasona'le control movement is availa'le, generally

3B6 inches of stick movement depending on the particular

aircraft model.

A+"il"%le Enine &o(er The engine system in a helicopter

is reEuired to provide power for a range of demands, not

only the rotor system. In the rotor system, thrust is reEuired

to overcome drag. As speed is increased, so does drag. If

more power is availa'le to overcome drag, then potentially

the helicopter can y faster.

It can 'e seen that from these factors that it is very

dicult for helicopter designers to increase the ma=imum

speed of a helicopter as many factors are 'eyond their

control. )uch research and development has occurred in



areas such as reducing drag, 'etter rotor 'lade designs and

increasing availa'le engine power.

The current %orld "elicopter $peed ecord is held 'y the

%estland Lyn= at 81./ Nts :758 kmh; using specially

designed highBspeed rotor 'lades.

USES O-

HELICO&TER

Sikorsky S-64 Skycrane lifting a prefab house

http://en.wikipedia.org/wiki/Sikorsky_S-64


http://en.wikipedia.org/wiki/File:Sikorsky_Skycrane_carrying_house_bw.jpg




Kern County (California) Fire Department Bell !" #ropping $ater on fire

% British &estlan# &%'-64 %pache attack helicopter

''-6" Dolphin #emonstrating hoist rescue capability

% Sikorsky S-6C air ambulance being loa#e# by fire-fighters

*%F &estlan# Sea King for rescue of people

http://en.wikipedia.org/wiki/Bell_204/205


http://en.wikipedia.org/wiki/Westland_WAH-64_Apache



http://en.wikipedia.org/wiki/HH-65_Dolphin



http://en.wikipedia.org/wiki/RAF


http://en.wikipedia.org/wiki/Westland_Sea_King

http://en.wikipedia.org/wiki/File:Sea_King_HAR3_XZ585_at_RIAT_2010_arp.jpg

http://en.wikipedia.org/wiki/File:Traumahawk_Loading_2.JPG

http://en.wikipedia.org/wiki/File:HH-65C_Dolphin.jpg

http://en.wikipedia.org/wiki/File:Westland_apache_wah-64d_longbow_zj206_arp.jpg

http://en.wikipedia.org/wiki/File:Kfd-205-N408KC-050428-26cr.jpg



http://en.wikipedia.org/wiki/HH-65_Dolphin



http://en.wikipedia.org/wiki/Westland_Sea_King



A helicopter used to carry loads connected to long ca'les

or slings is called an aerial crane. Aerial cranes are used to

place heavy eEuipment, like radio transmission towers and

large air conditioning units, on the tops of tall 'uildings, or

when an item must 'e raised up in a remote area, such as

a radio tower raised on the top of a hill or mountain.

"elicopters are used as aerial cranes in the logging industry

to lift trees out of terrain where vehicles cannot travel and

where environmental concerns prohi'it the 'uilding of

roads. These operations are referred to as logline 'ecause

of the long, single sling line used to carry the load.

"elitack is the use of helicopters to com'at wildland

4res.The helicopters are used for aerial 4re4ghting :or

water 'om'ing; and may 'e 4tted with tanks or

carry heli'uckets. "eli'uckets, such as the *am'i 'ucket,

are usually 4lled 'y su'merging the 'ucket into lakes,

rivers, reservoirs, or porta'le tanks. Tanks 4tted onto

helicopters are 4lled from a hose while the helicopter is on

the ground or water is siphoned from lakes or reservoirs

through a hanging snorkel as the helicopter hovers over the

water source. "elitack helicopters are also used to deliver

http://en.wikipedia.org/wiki/Aerial_crane

http://en.wikipedia.org/wiki/Helitack

http://en.wikipedia.org/wiki/Wildland_fire_suppression


http://en.wikipedia.org/wiki/Aerial_firefighting

http://en.wikipedia.org/wiki/Helicopter_bucket

http://en.wikipedia.org/wiki/Aerial_crane

http://en.wikipedia.org/wiki/Helitack



http://en.wikipedia.org/wiki/Aerial_firefighting

http://en.wikipedia.org/wiki/Helicopter_bucket



4re4ghters, who rappel down to inaccessi'le areas, and to

resupply 4re4ghters. -ommon 4re4ghting helicopters

include variants of the *ell 85/ and the &rickson $B

37Aircrane helitanker.

"elicopters are used as air am'ulances for emergency

medical assistance in situations when an am'ulance cannot

easily or Euickly reach the scene. "elicopters are also usedwhen a patient needs to 'e transported 'etween medical

facilities and air transportation is the most practical method

for the safety of the patient. Air am'ulance helicopters are

eEuipped to provide medical treatment to a patient while in

ight. The use of helicopters as an air am'ulance is often

referred to as )&D&0A-, and patients are referred to as

'eing @airlifted@, or @medevaced@.

9olice departments and other law enforcement agencies use

helicopters to pursue suspects. $ince helicopters can

achieve a uniEue aerial view, they are often used in

conunction with police on the ground to report on suspects(

locations and movements. They are often mounted with

lighting and heatBsensing eEuipment for night pursuits.

http://en.wikipedia.org/wiki/Rappel

http://en.wikipedia.org/wiki/Bell_205



http://en.wikipedia.org/wiki/Air_ambulance

http://en.wikipedia.org/wiki/Ambulance

http://en.wikipedia.org/wiki/MEDEVAC

http://en.wikipedia.org/wiki/Police_aircraft


http://en.wikipedia.org/wiki/Thermographic_camera

http://en.wikipedia.org/wiki/Rappel

http://en.wikipedia.org/wiki/Bell_205



http://en.wikipedia.org/wiki/Air_ambulance

http://en.wikipedia.org/wiki/Ambulance

http://en.wikipedia.org/wiki/MEDEVAC



http://en.wikipedia.org/wiki/Thermographic_camera



)ilitary forces use attack helicopters to conduct aerial

attacks on ground targets. $uch helicopters are mounted

with missile launchers and miniguns. Transport

helicopters are used to ferry troops and supplies where the

lack of an airstrip would make transport via 4=edBwing

aircraft impossi'le. The use of transport helicopters to

deliver troops as an attack force on an o'ective is referred

to as Air Assault. #nmanned Aerial $ystems :#A$;

helicopter systems of varying sies are 'eing developed 'y

companies for

military reconnaissance andsurveillance duties. Caval forces

also use helicopters eEuipped with dipping sonar for antiB

su'marine warfare, since they can operate from small ships.

il companies charter helicopters to move workers and

parts Euickly to remote drilling sites located out to sea or

in remote locations. The speed over 'oats makes the high

operating cost of helicopters cost e+ective to ensure that oil

platforms continue to ow. 0arious companies specialie in

this type of operation.

ther uses of helicopters include, 'ut are not limited toJ

http://en.wikipedia.org/wiki/Attack_helicopter

http://en.wikipedia.org/wiki/Missile_launchers

http://en.wikipedia.org/wiki/Minigun

http://en.wikipedia.org/wiki/Military_helicopter


http://en.wikipedia.org/wiki/Airstrip

http://en.wikipedia.org/wiki/Air_Assault

http://en.wikipedia.org/wiki/Unmanned_aerial_vehicle

http://en.wikipedia.org/wiki/Reconnaissance

http://en.wikipedia.org/wiki/Surveillance_aircraft

http://en.wikipedia.org/wiki/Sonar#Anti-submarine_warfare

http://en.wikipedia.org/wiki/Anti-submarine_warfare


http://en.wikipedia.org/wiki/Attack_helicopter

http://en.wikipedia.org/wiki/Missile_launchers

http://en.wikipedia.org/wiki/Minigun



http://en.wikipedia.org/wiki/Airstrip

http://en.wikipedia.org/wiki/Air_Assault

http://en.wikipedia.org/wiki/Unmanned_aerial_vehicle

http://en.wikipedia.org/wiki/Reconnaissance

http://en.wikipedia.org/wiki/Surveillance_aircraft

http://en.wikipedia.org/wiki/Sonar#Anti-submarine_warfare





Aerial photography

)otion picture photography

&lectronic news gathering

eection seismology

$earch and escue

Tourism or recreation

Transport

&A,AN HANS

HELICO&TERS

&"("n H"ns Helicop!ers Li)i!e$ is

a helicopter service company 'ased in India. The

operations are 'ased at 0ile 9arle:%est;. ther

than providing helicopter services to C!- to

http://en.wikipedia.org/wiki/Aerial_photography

http://en.wikipedia.org/wiki/Motion_picture_photography

http://en.wikipedia.org/wiki/Electronic_news_gathering

http://en.wikipedia.org/wiki/Reflection_seismology

http://en.wikipedia.org/wiki/Search_and_Rescue

http://en.wikipedia.org/wiki/Tourism

http://en.wikipedia.org/wiki/Recreation

http://en.wikipedia.org/wiki/Transport

http://en.wikipedia.org/wiki/Helicopter

http://en.wikipedia.org/wiki/India

http://en.wikipedia.org/wiki/Vile_Parle

http://en.wikipedia.org/wiki/Oil_and_Natural_Gas_Corporation

http://en.wikipedia.org/wiki/Aerial_photography

http://en.wikipedia.org/wiki/Motion_picture_photography

http://en.wikipedia.org/wiki/Electronic_news_gathering

http://en.wikipedia.org/wiki/Reflection_seismology

http://en.wikipedia.org/wiki/Search_and_Rescue

http://en.wikipedia.org/wiki/Tourism

http://en.wikipedia.org/wiki/Recreation

http://en.wikipedia.org/wiki/Transport

http://en.wikipedia.org/wiki/Helicopter

http://en.wikipedia.org/wiki/India

http://en.wikipedia.org/wiki/Vile_Parle

http://en.wikipedia.org/wiki/Oil_and_Natural_Gas_Corporation



its o+Bshore locations, this pu'lic

sector company is often engaged for providingservices to various state governments in India,

particularly in CorthBeast India, 0aishno

Devi "elicopter service for devotees.

His!or*

9awan "ans was incorporated on / cto'er

26/ as the "elicopter -orporation of India

:"-L;, the country(s national helicopter company

with the o'ective of providing helicopter

support services to the oil sector for its o+Bshore

e=ploration operations, services in remote areas

and charter services for promotion of tourism. It

is a government owned enterprise with 16./R in

government hands S 8./R with C!-.

C!- has upped its stake to 72R recently, a

http://en.wikipedia.org/wiki/Public_sector


http://en.wikipedia.org/wiki/North-east_India

http://en.wikipedia.org/wiki/Vaishno_Devi


http://en.wikipedia.org/wiki/ONGC



http://en.wikipedia.org/wiki/North-east_India



http://en.wikipedia.org/wiki/ONGC



move that will see the eEuity 'ase of 9""L

'eing enhanced to 87/ crore from the e=isting

< crore.

The corporate oce is located at Coida with

regional oces at Delhi and )um'ai. The

company has a net worth of <1,5/ million and

eEuity capital is ,<1 million. 9awan "ans is

@Approved )aintenance -entre of &urocopter@

and also the 4rst I$ 255 J 8555 certi4ed

aviation company in India.

It o+ers helicopter services for B

+ $hore operations

Inter island transportation

-onnecting inaccessi'le areas

-ustoms and pipeline surveillance

-asualty and rescue work

http://en.wikipedia.org/wiki/Equity_(finance)

http://en.wikipedia.org/wiki/Noida

http://en.wikipedia.org/wiki/Bombay

http://en.wikipedia.org/wiki/ISO_9001

http://en.wikipedia.org/wiki/Equity_(finance)

http://en.wikipedia.org/wiki/Noida

http://en.wikipedia.org/wiki/Bombay

http://en.wikipedia.org/wiki/ISO_9001



-harter services

0I9 transportation

Film shooting and aerial photography

Flower dropping and other

-ustomied services.

CONCLUSION

&ven though the concept of the helicopter is argua'ly

older than that of the airplane, there is still a great

amount of research and advancement yet to occur. As the



political climate of our world continues to change and

military conicts approach the smallBscale ur'an warfare

of recent years, the importance of the helicopter will

continue to grow. It is rather ironic that an idea 4rst

conceived long 'efore the -ommon &ra will 'e key to

winning military conicts in the 8st century.

otary wing research and development is a comple=

interrelated challenge. The advanced tools used are

-omputational uid dynamics :-FD;, Finite element

method :F&);, and -omputational structural dynamics

:-$D; for physical understanding of comple=

aerodynamics and structural phenomena. Integration of

these will ena'le us to design rotorcraft, which will have

superior productivity, enlarged mission capa'ilities and

improved environmental acceptance.



The future of helicopter is 'right with its a'ility to land

in any small clear areaG the helicopter 4nds use in air

ta=i service, police work, Inter city mail, and rescue

work, power line patrolling and other areas. The

development is still to continue.

Documents

Introduction to Helicopters Aerodynamics