An experimental investigation of model rotors operating in vertical

NINETEENTH EUROPEAN ROTORCRAF'l' FORUM

AN EXPERIMENTAL INVESTIGATION OF MODEL ROTORS

OPERATING IN VERTICAL DESCENT

by

Hong Xin and Zheng Gao IMtitute of Helicopter Technolotl'Y

Nanjins University of Aeronautics & Astronautia~

Nanjing 210016, P.R.China

September 14-16, 1993

CERNOBBIO (Como)

ITALY

ASSOCIAZIONE INDUSTRIE AER~AZIALI

AN EXPERIMENTAL INVESTIGATION OF MODEL ROTORS

OPERATING IN VERTICAL DESCENT

Hong

Xin

and Zheng Gao

Institute of Helicopter Technology

Nanjing University of Aeronautics

& Astronautics

Nanjing 210016,

P.R.China

SUMMARY

The helicopter behavior in the vortex-ring state hae been of great concern. To get a better base for further understanding, a seriee of model

teeta

were conducted on a newly-built

eet apparatus - the Whirling Beam. The model rotor is a centrally-articulated one with

two

bladee. In vertical deecent, the thrust, torqi.MI, and pitch and roll moments of the model rotor

were measured as the rate of descent increasing from 0 ot 1.2v.,. Variant collective pitch anglee heve been settled. Either twisted Hl.5' and -9.22' ) and untwisted bladee were tWed. Further more, scaled model fUIIeiarge of Bell-206 helicopter was made and located

below

the model rotor in some

teeta.

The reeults obtained show that, in the vortex-ring state, the rotor thrust and torque fluctuate obviously. Existence of periodicltiee in the fluctuations hae also been observed. The disc loading, blade twiet, and the fuaelage have some effects on the aerodynamic characteristics of the model rotor in the vortex-ring state.

NOTATION

V linear velocity of model rotor, positive for deecent

v equivalent induced-velocity of the model rotor, positive down through the disc

T rotor thruet

Q

rotor shaft torque

e

o. 7 colleCtive pitch angle at 70"/o radius

l\1c

.

longitudinal rotor disc tilt angle

fl.,.

lateral rotor disc tilt angle

Q angular speed of model rotor

(i) angular speed of the beam

R radiua of the model rotor !'t. fluctuation amplitude

Subscripts & SupersCripts

mean value

h hover value

INTRODUCTION

Vertical or near-vertical deecent of helicopter I!Ubjects the rotor to operation at the up-i!tream oppoeite to its Induced

now.

All the deecent velocity is increased from hovering, the helicopter paasee through the normal operation state into a Ieee stable and unsafe region

known as the vortex-ring state. The aerodynamic characteristics of a helicopter rotor operating

in thevortex-ring state hae been of great concern in rotorcraft engineering. Although a number of investigations have been publiabed on this subject, there still remain many qUIII!tiona to be answered. The existing theories fall to give either a aatisfaotory explanation of the behaviour

of the helicopter or an accurate prediction of the boundary of the vortex-ring state. The purpose of the uperiment described herein la to

meaeure

the unsteady

aerodynamic

characteriatice of a model rotor operating in vertical deiiCIIDt in order to get a better base for further

unclel'lltandin.

For vortex-ring uperiments, the wind tunnel la not always satiefactory. First, the wall interference can not be properly modified. Second, mo&t of the available wind tunnels usually have very poor characteristca in low speed range required for vortex-ring state teete. A .200-meter-long track was used at University of Tokyo, on which a carriage loaded with the rotor eystem could move in still air. It did not have the shortcomings of the wind tunnel, but the duration of the teet was limited by the length of the track.

The uperlment deecribed herein was conducted on a newly-built apparatus called the Whirling Beam (Fig.1). It has a 6-meter-long beam that rotates around a central pillar. The· model rotor can be installed at variant location along the beam and move together with it in still air, modeling the turning flight of a helicopter rotor or an airplane propeller. When the model rotor la located at the far end and so has a rather large rotating radius, its motion can be CODIIidered as straight forward flight. Level, elope, or vertical flight

condition can be modeled by adjusting the orientation of the axis of the model rotor (Fig.2).

The effects of circular motion on the measurements la little and· ignorable when rOtating speed of the beam la low. The linear velocity of the model rotor can be changed by changing the rotating speed of the

beam.

The teete can last for any long time at a certain condition.

Obviously, this ie valusble for qusntitative measurements. The Whirling Beam proved to be very

useful and powerful formodel rotor experiments even in very low speed.

1 APPARATUS AND MODELS

1.1 The Whirling Beam

The echeme ie ehown In Fig.1. The bight of the central pillar ie 5.1i meters, the range of the available radial location of the model rotor along the beam la from 2.4 through 6

meters, and 5-m radius was used in thla uperiment. The beam ie driven, through a tran!!!1!iasion box and a chain eet with transmitting ratio of 1215:1 totally, by a 4-kw a.i:. motor controled with a frequency inverter. The rate of the beam ranges from 0 tc

ao

rpm. 1.2 Model Rotors and Fuselage

The model rotor eelected for this experiment was a centrally articulated one with two composite blades, driven by a liOO--w a.c.motor at 1400 rpm. The diameter of the

rotOr

ie 1100-mm.

Three sets of bladee were used In the teeta. The physical charactarietice of the blades

are

llated in the following table:

Blade No. I No. 2 No. S

Airfoi I NACA 0012 NACA 23012 OA 212

Slade Twist \degl

o.o

-5.5 -9.22

Chord (mm) 60 73 . I.:' ₇₃

Weight (g) ISO 240 240

Each blade rotates around its

26%

chord axis tc eet the pitch angle In advance. No cyclic pitch mechanism. ie employed. The rotor - b l y la ehown In Fig.8.

For examing the effecm of the fuaelage on the aerodynamic characteri8tics of the rotor in vertical descent, a ecaled model fueelqe of Bell-206 helicopter was made and

located under ite model rotor in the tellte.

2 INSTRUMENTATION

The thrust, torque, and pitch and roll momenta of the model rotor are me8BIJl'ed through a fltrain-gage-balanoe

IIY8tem

located between the motor and the hub of the rotor (Fig.3). The

torque pickup, whiCh conallsU! of e. tomlon tube and four etre.in gags, hu a maximum capacity of · 0.8 kg-DL The thrust-momente pickup COIIIIiJq of four leaf springs and 24 etre.in gage~~.

Each leaf epring hae e. maximum capacity of 7.6 kg. The outpute of these two piclrupe (for the torque outpute, through the alipper ring J. shown in Fig.3 at first) are amplified by a

mini-amplifier in8talled near the model rotor. The amplified aignale are deliwred to the control room

through the slipper ring II shown in Fig.l, and are filtered by a low-pass filter before they

are sampled by a 386/33 computer with a high~ A{D board.

The ratee of rewlutlon of the

rotor

and the beam are measured with puJa.. A

ama1I

plate attachee on eaCh motor shaft, it interrupte a magnetic circuit while rotatinl, 80

creating the pulse signals.

n-e

two re.tee of revolution are displayed on a rpm meter and

sampled by the computer.

Blade . Bet ., . , \ ' ·No.1 ... .No.2 . 'No.3

Collecti1'8 6 and 10 10 10

Pitch (deg)

Fuaelage without with and with and

without without

At eaCh condition, the model rotor

was

teated in hover, vertical climb, and vertical deecent. The rate of rewlution of the beam was increased from 0 to 8 rpm in climb, and f'l'om 0 to 12 rpm in descent. Correapondingly, the linear~ of the model

rotor was

varied from -4.2 to 6.8. m{., · At eaCh teet point, 1:he rotor wu Btarted and accelerated to ·1400 rpm .after the beam was adjusted to rotate ltably at, a certain speecl. then, sampllilg

was

done at the rate of 1.0 Hs , during 6 JllllCODde and four groupe of data

were

l'IIICOided. . They we~e the rotor torque, . ' •

thruat, and pitch and roll momente reapectivel:y. The rpm of the beam

wu--ded

llimultanilouely. Sampling was also debe before and after the rotor's l'lmniDIJ when the beam kept rotating stably, 80 as to 11et the fore and aft E1'0illl of the 11181l11lrelD81te at that velocity.

,>; ·,

i .~ ' . ~ ' ..

4 REDUCI'ION OF DATA · "'

4.1 Typical Sampled Data

Four typical groupe of samlped data of rotor thrult and torque are shown in Fig.4. The

presence of BeVere fluctuations of thrust and torque are obviowl in Fig.4b and 4d. It il also

4.2 Mean Values

For each test point, each group of the sampled data were alone averaged over the

sampllns duration, and the coueepondent mean values of the fore and aft 1l8l'OEIII were compared

with each other to examine the zero drift of the system during the time of each test run. It was found that they shew good repeatability. The average value of each pair of the fore and aft zeroee was Wled as the mean zeroee and was mbatracted from the coneepondlng mean value sampled when the rotor was running, 80 as to obtain the mean value of rotor torque or thrust or pitch or roll moment at that velocity.

It should be DOted that the effecta. of the centrifupl force due to the rotation of the beam on the measuremenia would be eliminated by mbatrac:ting the average Z81'0flll meallUred when

the beam is rotating. However, a rotor disc tilt exista when both of the beam and the rotor are rotating . due to a Coriolie moment acting. on the centrally articulated blade~. All a reeult,meallUred thrusta (T..,) are slightly It&~ than the real values (T.,), The difference can be calculated as

longitudial tilt angle

lateral tilt angle · · ( v ia blade Lock number)

The real thruet lhould be

T~·---coa

ll1o

coa jl,.

This correction Is included in the program of data reduction, and the reeulte shew that the tilt angle of rotor disk was small (Fig.6) becauee the beam rate

was

very low. ·

The mean values for each valocity were reduced to dimensionlt&l quantities with reference to the correepoutling mean values meallUred in hover, and are preeented as functions of the dimenaionlt&l velocity (V /v.,.). ·.'

4.3 Fluctuations

For each velocity, the mean square deviations of each group of the 8111llpled data were

calculated.

' ' 1 "

The fore and aft zeroes were plotted as the functionB of the dlmenstonlt&l velocity(V jQ R) · (Fig.6 ahows a typical craph). It Ia found that the mean IICJU8I'8 ckmations of each croup of the · zeroea,which

were

cauaed by tha mechanlcal viberation and the electrical interferenca in the ay8tem, are very small compared with the correeponding mean valuaJ (normally<l%) and increase ·· with the velocity linearly • For each teet point, the mean square cleviatiODJ of each group of the zeroea

were

mbatracted from .the mean square deviation of the correeponding group of data sampled when the rotor waa running, 80 ae to obtain the net deviations of each group which rep1amtted the fluctuations of rotor torque, thrust, pitch and roll momenta respectively. The

net deviations were reduced to percentages of the corresponding mean valuee, and are preaented as functions of the dimenaionlt&l velocity (V /v.,.). The frequencies of the fluctuations were

also analyzed through FFT, and two typical power lqleCtra of rotor thrust and torque are ahown in Flg.7a and 7b.

fi RmruLTS AND DISCUSSION.

The mean values of rotor torque, thrust, and pitch and roll moments are shown in Fig.Sa and 8b as functions of dimenslonle&~ velocity (V /v-.J. The curves of torque and thrust reflect

the transition p!'OCeOOing from the ll01'11l8l-propeller et:ate through the vortex-ring et:ate toward the windmlll-brake et:ate. The increase in torque indicates the beginning of the vortex-ring et:ate (V /v,.-o.4), and the l<B! in thrust indicates the mart turbulent region in vortex-ring et:ate

(0.6<V /v-.<0.8) . .()n the other hand, the mean pitch and roll momente almoet keep the same values ae the velocity varies, except a slight variation due to the tilt of the

rotor

dieo.

The fluctuationa are demonstrated in

Fia.Sc

and 8d. It Is - that the fluctuationa

rises remarkabaly as the rotor falls into the vortex-ring et:ate, peak& at three-quarters of the hover indU()Q(\ velocity. Then, with further increasing of the deeoent velocity, the

fluctuationa IJO down as the rotor moves into the witvlmill brake et:ate. According to the power spectra (Fig. 7), the period of the thrust fluctuation is 0.3.0.6 second, whereas the period of

the torque fluctuation is about 3. 7 seconds

5.2 The Effecte of Disk Leading (Fig.9)

It is - from Fig.9 that, for a given dimenai.onle&~ rate of deeoent, the torque fluctuation of the rotor with lower disk loading is larger than that of the rotor with higher

dieo loading, whereas the thrust fluctuation appearee to be independent of the disc loading.

G.3 The EffecU! of Blade Twist (Fig.10)

Fig.10 shows that, the thrust drop of the rotor with .. uo blade twist is larger than

that of the rotor with -9.22° blade twist within the vortex-rinr et:ate, whereas the thrust and torque fluctuati0118 seems to be almost the same for different blade twists.

G.4 The EffecU! of Fuselage (Fig.ll)

Ae shown in Fig.lla and llb, the presence of the model fuselage gives a similar effect on the mean thrust and torque to the 'ground effect'. No effect on the thruet and torque fluctuation is found.

1. J.M.Drees and W.P.Hendal, Airflow patterns in the neighbourhood of helicopter rotors,

Aircrft Engineerins, Vol.23, 1961.

2. P.F.Yaggy and K.W.Mort, Wind-tunnel ta!ts of two VTOL propellers in deeoent, NASA TN D-1766, Dec.19, 1962.

3. J.Koo and T.Oka, Experiments on a model bellcopter rotor operating in the vortex-ring et:ate, Jonrnal of Aircraft, Vol.3,No.3, May-June 1966.

4. A.Azuma and A.Obata, Induced flow variation of the helicopter rotor operating in the vortex-rinr et:ate, Journal of Aircraft, Vol.6, No.4, July-Aug 1968.

Balancing

Weight

1.4-kw A.C. Motor & Transmission Box Slipper Ring II

Beam

Chain Set

antral Pillar

Fig.1 The Whirling Beam

Level

Flight

v

Slope

Descent

_v

Vertical

Descent

v

Cross Section of Beam

•

•

AmpiHier Mini-· Thrust-Moments

Model Rotor

Beam Slipper Ring I 550-w A.C.Motor

•

Pickup L-.'1'1'"'....1

Fig.2 Orientations of the Rotor Axis and Corresponding Flight Conditions

Hub

Fig.3 Rotor System

0.36 0.36 '0.36

~

0.34 0.32 ; _0.32 0.3L---~---~ o o.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 e 0.3~---~---~ o o.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 e Time (s)

Average Value = 0.3!5!5, Mean Square Deviation

=

0.00302

(a) Thrust in Hover

0.56 0.52 . _; . ; . . ; . ; ; ; ; . ; . ; ; 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Time (s) .

e

Time (s)

Av•rage Value= 0.357, Mtaan Square Deviation= 0.0132

(b) Thrust Jn Descent f'//v"=0.75)

0.43

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

Time (s)

Average Value= 0.541, Mean Square O.Viation = 0.00329 Average Value= 0.478, Mean Square Deviation= 0.0181

(c) Torque In Hover (d) Torque In Descent f'//Vh=0.75)

Fig.4 Typical Sampled Data

(Oaf='

10°, Blade Set No.3, without Fuselage)

4 _ ,- -, _ _, - - -,_ " - -

.

- -

: /3; -'-

- c _,

--2

-4~--~--~--~--~--~--~--~--~--~--~ -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

V/V"

Fig.5 Tilt Angle Of Rotor Disc (Blade Set No.3)

6.---.

.6« H:z 3.014 Hz 4

:L__~~~~~A~~~---~~~~·3~H~z

0 2 4 6 8 10 12 14 16 18 20 22 24 Freque"oy (Hz) 8 -

..

- - ·- -,_

~

2 ~ 0~~~~--~--~--~~~~~~--~~--~--~ -2

-4 ---Fore Zero in Climb "*-Aft Z.ro In Climb

-6-For• Zero In Descent *Aft Zero in Descent

~L_----~---~

-0.0!5-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 0.0!5 0.06 0.07

V/OR

Flg.6 Mean Square Deviation of the Zeroes of Thrust as a Function of the Dimensionless Velocity

( Q,_, -10', Blade Set No.3, w~hout Fuselage)

7.---.

_{0.273 (Hz)}

6 2 1

oL-'-~/\~~--~---~~)(L.3~H~z

0 2 4 6 8 10 12 14 16 18 20 22 24 Frequency (Hz)

(a) Thrust (b) Torque

1.6 +TORQUE 1.4 *THRUST 1.2

.

. ·,

-1 0.8 oel

-. 0.4 -0.8 -o.e -0.4 El% +TORQUE +THRUST {a) . . . .

-..0.2 0 M•an Values 1.6

.

•. . . _. 1.4 . . _{. .} 1.2 1

-

'

-

'.

-

_'

-0.8 . .

.

. . _; .

'

o.e 0.4 0.2 0.4 0.6 0.8 i 1.2 V(v,

of Torque & Thru.t

4% 2% ._.ROLL-MOMENT *PITCH-MOMENT _.

_.

_. ·' . .• . ' . .

_-

_;

_.

. . .

.

.

_-

_.

.

. .

_-.

.

--·

-

....

~-~

"'

_"''

_.

·~·

...

.

-'

-

-

_'

.

-'

- -

. . .' . . .

•

. . ' . ·, .

.

-

-.

--o.8 -o.e -0.4 ..0.2 0 0.2 0.4 0.6 o.e

V/v,

{b) Mean Values of Ro!l & Pitch Moment•

.,.. ROLL-MOMENT *PITCH-MOMENT . -'

-

-

.-

_'

.

d.

-

_::...;.

-.

_. _. .

_-

.

-' 1 1.2

0%~---~---~--~----~ _{-o.s -o.e -o.4 -0.2}

0 0.2 0.4 0.6 0.8

V/v, 1 1.2

{o) Fluotuationa of Torque & Thrust (d) Fluotuations of Roll & Pitoh Moment•

ftf,

4 Collective Pitch 1 .!5

I •

a.oo deg "' 10.0 deg 1.25. -1 -- ~~

••

...

....

•••

'

-, ·, - . '

-••

•

~-·-:*-'."'

'

••.

"'

. • 't>(

:...,.i.~~-"" ~

tfii • I~ :A:,

••

""'""

0.75L---~---~ ·0.8 -0.6 ·0.4 -0.2 0 0.2 0.4 O.l5 0.8 V/V,

(a) Mean Thrust

1 1.2 1.4

~r~-~"---~--~~--~~~--~~~

8%r Collective Pitch • 6.00 deg 6% I

*

10.0 deg -' -

....

'-

-

-

··,;.

-

.

- -

..

4%•-2% ... '

.

""

..

...

.

.

••

·•

'

.

"'' "'

"'

...

"'

"'

...

..:

'

"'

•1.8-.

...

,...,..--

'

...

'

-o.6 -o.6 -0.4 -0.2 o 0.2 0.4 o.6 o.8 1

V/v, 1.2 1.4 0/0...---,---.--~,..-..,....,...,.,.,..,....,..,...,..-,----,--,---, Collective Pitch 1.5 \ • l5.00 deg "' 10.0 deg 1.25·---1 _{- -}

-··

_-

.... *- -·

' ' ~

_""

....

-

.

.-'

- - -' - . '. -

-.

.:•

••

- - , A

...

-·"'

'-~<*-' '-J( '-

-

- - : - ' .;.,..•• '

--~

...

...

_~

-

....

,....·:-' , ' ' .,

Q.75L---'

-o.8 -o.a -0.4 -0.2 o 0.2 o.4 o.6 0.8 ·1 1.2 1.4

V/v, (b) Mean Torque

~//QQ..~---.~~~--~~~~--~l

8%r Collectiv• Pitoh • 6.00 deg 6% I *- 10.0 deg .

·-·-•

4%. -'

"'

··-'

.

••

'

.

'

.

'

.•

-·

.•

.. - "'-

'

,.{';•-~<'

•.

A -.

...

-

..

'

""

"'*

'·~""

·- ..

.A

"

...

'

""

' 2% .. -0~ ...

* : • ... •

j -0.8 -0.6 -o.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 V/v,

(c) Thrust Fluctuation (d) Torque Fluctuation

Fig.9 Effects of Disc Loading (Blade Set No.1 ,without Fuselage)

..

f;;

I

Blade TWist

f

.

'

- - -

'

- - - ! ! ! ' ! ! ] Ia 1.2~ 1 .... ~.50 deg C8l Q.22 deg .-

..

-- -·---

..

-- -·---

..

- - _,_--

..

....

t81•

.,.

181. 'C8l

....

.

' '

"""'

' ' . :. y . . :

~~

C8l • 181 '1(!J .

~181rzJ

"f((, r,;;_ . .'

riiP : l:!l '~

.,.

_' . . .

.

...

_...

_•...:

.,.

Ia .... 181

....

....

....

0.7~~~---~----~--~~

-o.8 -o.e -o.4 -o.2 o o.2 o.4 o.e o.8

V/V,

(a) Mean Thrust

1 1.2

AT~-···~---.~~--~---.--~--~--~--~--~

8%~ Blade TWist ... ~-~deg 6% I Ia 9.22 d"ll 4% 2%

....

. . .

-~

..

~lip

:18l

.~

:·

...

--.--

...

--

--·,;.

·:-.;,..·

.

-.: . ..,. ~..,. 181a 'f; .,. Ia . ..,. ' • . - rij181 - - 18181la - ,_ ' 181 ... ' 'f1'J' . fi!t Ia

...

18l!

18] ....

...

~-

I

....

...

l:!l l8l

~

-0.8 -o.6 -0.4 -0.2 o 0.2 o.4 o.6

V/v, 0.8 1.2

~~~~B--1.,-d--eTW--Ist~f---·r·_-_-_-r~---.-_T:-_-_-.~~----.~.:r_---_,~---.-_T:-_-_-~~·.~f

... 181 .... ~-~deg t8l Q.22 deg 1.2!5'- .. --

-·-1'

~. ·~a!·

C8JII' -- o-~­ l!!l

.

'

'

rZ"

-~-CI-~-~~~~:

'

...

jQ!l

- - . 0.7~ L....--~---~---~--~---~...1

-0.8 -o.e ·0.4 -o.2 o 0.2 0.4 o.e 0.8

V/Vn (b) Mean Torque 1 1.2

Aa!.-~~----r-~--~~--~~--~--~~

8%~ Slede Twiat ""~-~Odeg 6% I 181 9.22 deg 4% ' 181 ' -

...

-~ t8l ' ' ' ~ - · - .ill' ' .,.

- ·.,;.-.... · ,. . - . d · .,. .

.

181 181

,.

~···· ~·~

- . .,;.

.

w e'\,o;f4... . •

•

~

ar

«

C!l IZI ... • .,. • __ ...JI 2% • I • • • ~

-o.8 -o.6 -o.4 -o.2 o 0.2 o.4 0.6 0.8 1 1.2

V/v,

(c) Thrust Fluctuation (d) Torque Fluctuation

Fig.10 Effects of Blade Twist (6o.r10°,without Fuselage)

T;;

I

*without Fuselage

I'

'

1

' '

---

' '

1

.A. with Fuselage

*

~

*

...

"'"""

1.25

'* ....

...

1

...

. : •

' : '

""""~

*""

-lj(- ,

li,.i:•~

..

~

' * '

***~*-

. -: .

...~

*

...

' --,· .

*·

*'

0.75"C... _ _ _ _ ~-~-~---~--..._J

-o.e -o.e -o.4 -o.2 o 0.2 0.4 o.e 0.8 V/vh

{a) Mean Thrust

1 1.2

AT~.,h~---~~----~--~--~--~--~--~

8%~

*without Fuselage

.& with Fuselage

6% 4% 2%

l'·

_*·

...

...

~ ~

.,. "'*··- ... -.

'*

*

' *' ...;

... *

"')IC

....

~

....

.... * ' •

.

-

...

~- -~

-·-' '

.

...

.... *

~:

*

0%~-~---~---~---~--~--~----_J -o~ 4 6 -o.4 -0.2 0 0.2 0.4 0.6 0.8 V/Vh 1 1.2

~~~

*

without f!selaga 1: · -

~

· · _: · : : - · · : · · · : · · ·:

.ij

A with Fus,elage 1.25

1"'

-~:-

t:

i. -

~-·

*

""

* '

*""

- •-:11E -··

*•

*~

*""'

' - .. ' - - -)!<**** ....

-· ****** ...

...

...

0.75L---~

-0.8 -o.e -0.4 -o.2 o 0.2 o.4 o.e o.8 V/Vh {b) Mean Torque 1 1.2

da,/~~~---~r--~~--~~--~~--~

8%r

*

'Nithout Fuselage A with fuselage 6% 4% 2%

....

...

...

....

0%

*

-o.a -0.6 -o.4 -0.2

'·

*

.. j( \_.•

·*

. -

:-

- . ~ - - ~-

-....

iii,!~*

""'**'1. ...

*

~·

'

o 0.2 o.4 o.e o.a V/vh

.

-· l l .... lli

l!<.~-~-1 1.2

{c) Thrust Fluctuation {d) Torque Fluctuation

Fig.11 Effects of Fuselage

(8o:F

10 , Blade Set No.3)