Forward Flight Lecture1

8/3/2019 Forward Flight Lecture1

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ROTORCRAFT AEROMECHANICS 4

The aerodynamic environment of a helicopter bladein forward flight. (Dr E Gillies, Lecture 1)

The `Sausage plot'

The aerodynamics of a rotor in forward flight are complicated. A useful non-dimensional speed which can be used to describe the aerodynamic phenomenaoccurring in forward flight is the advance ratio

¢ ¡

U £

R(A1.1)

which is the ratio of flight speed U to tip speed Ω R. The maximum speed of most

helicopters tends to be in the region of ¤¥ 0.4 . For the Lynx helicopter, the tip

speed is approximately 210m/s, so ¤¥

0.4 translates to a forward speed of 84m/s

or 163kts. The advance ratio has components in the x direction (tangential to the rotordisc) and in the z direction (down through the disc).

x

¡ cos ¨ (A1.2)

z

¡ sin ¨

where is the forward tilt of the rotor disc.

The tangential velocity at the rotor blade varies along the blade span and around the

rotor azimuth ( 0

o at the rear of the disc, and most helicopters have an

anti-clockwise rotor rotation when viewed from above). If r denotes the non-dimensional spanwise position on the blade, then this tangential velocity is

U T

R r

xsin (A1.3)

The velocity of the airflow down through the rotor disc is U P , and this depends on

the flapping velocity, the disc tilt and the inflow to the rotor.The following figure shows the tangential velocities over a rotor in forward flight atan advance ratio of 0.2.

UT

UP

ROTOR AEROFOIL

VELOCITY FROM ROTATION & FORWARD SPEED

VELOCITY FROM DISC TILT, INFLOW AND FLAPPING




Velocities are greater on the advancing side than the retreating side. As a result, if theif the blades do not flap & pitch as they rotate around the azimuth then more lift isgenerated on the advancing side of the rotor than the retreating side. The rotor is then

unstable in forward flight and the helicopter rolls to the left. The local lift contours foran untrimmed rotor at an advance ratio of 0.2 are shown below.

Local blade lift contours − untrimmed rotor

U

Local blade velocity contours

U

reverse

flow




To trim the rotor the blades flap & their pitch angle is changed via the swashplate,pitch links and feather hinge.

This cyclic pitch is of the form

!" !

0 %

A1cos &

%

B1sin & (A1.4) or

PITCH = COLLECTIVE + LATERAL CYCLIC + LONGITUDINAL CYCLIC

At the moment, consider a rotor which is trimmed approximately, with forwards disctilt caused by longitudinal cyclic pitch. Here we have

'( '

0 1 B1 sin2

(A1.5)

The rolling moment coefficient of a rotor in forward flight is derived from blade-

element-theory (see Newman ) as

C M R

"3 a

2

2

3

!

0 5%

B1

41 7

3

25

2 (A1.6)

Lift curve slope a is empirically given a value of 5.7/radian for rotor blades. For zerorolling moment if forward flight (A1.6) gives a first estimate of the cyclic pitch anglesneeded to trim the rotor. Maximum blade pitch in (A1.5) occurs at 270 degrees

azimuth. For high forward speed (say 8

¡

0.4 ) the maximum pitch can be set

close to the blade section stall angle to exploit the maximum performance of the bladesection.If a typical static stall angle for a blade is 14 degrees, then

14"

!

07 B

1 (A1.7)

Substituting (A1.7) into (A1.6) results in a collective angle @

0 A

7.72o

and a

longitudinal cyclic pitch of B1 B

6.48o

. Putting these approximate values into a

rotor in forward flight balances the natural tendency of the rotor to roll and results in

the lift contours shown below.




In actual flight the rotor blades flap up and down in addition to the cyclic pitch. Atypical longitudinal trim calculation process for a Lynx helicopter is described next.For a given all up weight (AUW) and fuselage drag at a given airspeed the resultantmain rotor thrust vector is fixed in space. This allows calculation of the disc tilt andfuselage tilt angles for moment equilibrium in forward flight. The fuselage drag isavailable from wind tunnel tests at a reference test speed (usually 100ft/s or

30.48m/s). For the Lynx this is D100

(

1112.06N . This is scaled to the correct

speed by the relation

DF

(

D100

U 2

U 100

2

( 1112.06U 2

30.482 (A1.8)

An iteration is performed between the rotor thrust and inflow values to give C T and

C

zD D

C

z EF i . The flapping angles (disc tilt), inflow and rotor thrust are input to

H

80

I

H

6

P

x

IQ R

2

0

I

H

80

I

H

6

P

x

H

3

P

x0

I

H

80

1

3

0

I

P

x

2

0

T

0

A1

B1

a0

U

H

6

P

zD

I

H

8b1 V

1 IQ R

2a1

I

H

8a1

I 1 IQ R

2b1

C T

a `

V

P

zD

2

(A1.9)

Local blade lift contours − roll trimmed rotor

U




and this may be used to calculate the collective and cyclic angles, together with therotor coning angle required for longitudinal trim. A lateral trim analysis is also

necessary due to the amount of cyclic pitch necessary to trim out the effects of tailrotor thrust. In the above, a (=7.10 for the Lynx blades) is the Lock number, which

is a ratio of aerodynamic to flapping inertia; andb

c

2(=1.193 for the Lynx hub) is

the non-dimensional flapping frequency, which is dependent on the rotor hub stiffnessand design. A sample longitudinal trim calculation for the Lynx helicopter in the

speed range 0 ef e

0.35 is shown below:

With forward speed the fuselage rotates forwards and longitudinal cyclic pitch

increases to overcome increasing drag. Of note is the fact that the collective pitchdecreases from its hover value to a minimum at around 30m/s- this is evidence that arotor in forward flight benefits from `translational lift', which is greater than the liftgenerated in the hover. Eventually however, the increased downflow through the rotorcaused by the forwards disc tilt causes the collective to rise at higher speeds. Thefollowing anecdote describes the phenomenon of translational lift:

... " I slowly raised the collective to pull the Huey into a hover. No go. I pulled in full power

but the Huey just sat there shuddering. [In] an overloaded condition like this [a helicopter]

can be made light on the skids with [full] collective and then urged forwards with the cyclic

so that it slides across the ground on its skids. If it can slide along [fast] enough, it will take

off like an airplane, even though it can't hover " R Mason, 1 st (Air) Cavalry Vietnam 1965,writing in Chickenhawk'

0 10 20 30 40 50 60 70 80−10

−5

0

5

10

15

20

25

30

Forward speed (m/s)

A n g l e ( d e g r e e s )

COLLECTIVE

PITCH

FUSELAGE TILT

LONG.

CYCLIC

LAT.

CYCLIC




The longitudinal trim equations are strongly coupled to the lateral trim equations. Inlateral trim the procedure is essentially the same, but the tail rotor thrust is alsoimportant.

These changes in flapping, collective and cyclic angles mean that the rotor bladesthemselves experience rapid changes in angle of attack as they rotate about theazimuth. To determine the aerodynamic environment experienced by a rotor blade inforward flight, a `sausage plot' is used (sometimes called a `figure of eight' diagram).This is a plot of blade incidence versus Mach number.

Blade pitch isi

p i 0 r

A1cos s

r

B1sin s

Flap angle is tu

a0

w

a1cos x

w

b1sin x (A1.10)

From before the tangential velocity at the rotor is

U T y R r

sin

and, taking into account the flapping of the blades into the expression for theperpendicular airflow we have

U P

i

cos

r

.

(A1.11)

The inflow angle of air to the blade is

tan

U P

U T

(A1.12)

And the blade angle of attack is therefore calculated as

.

The blade Mach number is M

y

M t

r sin

Plotting out the locus of M , results in a `sausage plot'. A typical high speed

plot for the Lynx helicopter is shown below:




Note that the blade experiences a very severe aerodynamic environment in forwardflight. The advancing blade Mach number towards the tip is very high and in thetransonic regime. The retreating blade incidence is close to, or above, the static

aerofoil section stall angle. This environment leads to conflicting requirements for

aerofoil design.

1) The very high Mach numbers on the advancing side require very thin uncamberedsections to prevent drag divergence from shockwaves forming on the blades.

2) The high lift required on the retreating side necessitates high blade angles of attack. The appropriate aerofoil shape for this task is a thick cambered section.

This is a very significant conflicting design requirement. Other parts of helicopterdesign also reveal conflicting requirements (e.g. twist is desireable for good hoverperformance, but undesireable in forward flight).

Moreover, blade flexibilty is a serious design issue. Blades are relatively flexible intorsion and the aerofoil section must therefore be designed to have a very low pitchingmoment.

The challenge is to design a blade which has good performance in both of these highMach and high incidence regimes. These design requirements, and aerofoils whichmeet them, are discussed in the next two lectures.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.80

2

4

6

8

10

12

14

16

Mach number

I n

c i d e n c e

( d e g r e e s )

µ = 0.3

r = 0.9

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Forward Flight Lecture1