Induced velocity model in steep descent and vortex-ring state prediction

Induced velocity model in steep descent

and vortex-ring state prediction

Jérémy JIMENEZ

André DESOPPER,Armin TAGHIZAD and LaurentBINET

LaboratoireONERA-École deL'Air

BaseAérienne 701

13661 SalonAir -France

Steepaproacheswill playanimportantrolein thenearfuture helicoptermissionsinparticularfornoise

reduction, however,in steep descent thehelicopter ightenvelopeis limitedby theregion knowned as

vortex-ring state. Entering this area, while ying close to the ground, can be extremely dangerous.

Indeed,thevortex-ringstatewasimplicatedin32helicopteraccidentsbetween1982and1997[1].

The objectiveof this work is to predict thevortexring statelimitsand to model helicopterbehaviour

during steepapproach.

Becauseoftheimportanceofinducedvelocityinhelicopterightsimulationcode,anempiricalVimmodel

is developed. Firstmomentum theory isextented toall ightcongurations. Then thecomputed Vim

is adjustedto experimental dataavailable,multiplyingbyacoecientthat takesinto accountdierent

lossesthat occurindescentight.

An analytical criterionpredictingthevortexring statelimitsisproposed. Thiscriterion isfounded on

Wolkovitchtheory[2]whichisimprovedin ordertotakeinto accountthewakeskewangle. Inaddition,

thiscriterionisapplied usingthedevelopedVimmodelinsteadof momentumtheory.

Finally,thevortexringstateismodeled,breakingdownintotwoaspects. Inonehand,theow

uctua-tionsthatoccurin vortexringstatearemodeledusingthepreviouscriteriontoestimatetheirintensity.

On the other hand,ight tests performedat CEV haveexhibited particular Vzresponses to collective

inputs including power settling. Eurocopter ightmechanicscode HOST improved with the proposed

Vimmodelreproducedwellthese characteristicphenomenaof thecomplexvortexringstate.

Notations

cmeanchordoftherotorblade,m

DT0collectivepitchangle,deg

Fzrotorthrust, N

Nznormalloadfactor

Pn

o

hoverrequiredpower,kW

P w requiredpower,kW Rrotorradius,m Vi o

hoverinducedvelocity,m:s 1

Vimmeaninducedvelocity,m:s 1 Vhhorizontalvelocity,m:s 1 Vsslipstreamvelocity,m:s 1 V tv

tipvorticesvelocity,m:s 1

Vxinplanevelocitycomponent,m:s 1

Vznormalvelocitycomponent,m:s 1



 normalizedaxial ow



normalizedinplaneow



 normalizedinducedow

 wakeskewangle,deg

airdensity,kg:m 3

rollattitude,deg

 pitchattitude, deg

azimuth,deg

0,1c,1srotorapping angle,deg

rotationalvelocityoftherotor,rad:s 1

Steep descent is an important ight phase as

wellforcivil helicoptersforwhich newsteep

ap-proachprocedures will beused notablyfornoise

reduction as for military ones requiring the

ca-pability ofapproachingand landing shortor

en-rering a conned area for any rescue operation.

However, in steep descent the ight envelope is

limited by the region of vortex ring state. The

turbulent circulating air existing in this

partic-ular state can cause serious handling diculties

that frequently leads to temporary loss of

heli-copter control. Entering this area, while ying

closetotheground,canbeextremelydangerous.

Indeed,thevortex-ringstatewasimplicatedin32

helicopteraccidentsbetween1982and1997[1].

Onechallenge,inthenearfuture,wouldbethe

improvementof rotorcraftshandling qualitiesat

highglideslopeapproaches,viaappropriates

con-trol laws associated to carefree handling means

(activeside-sticks,HUD).Thedesignandthe

de-velopmentofthiskindofsystemsrequireagood

knowledgeof helicopterightsmechanicsin this

specicightconguration.

Because oftheimportance ofinducedvelocity

in helicopteright simulation, rst anempirical

Vimmodelisdeveloped. Thenacriterion

predict-ing the vortex ringstate limits is proposed. An

inducedvelocityuctuationsmodelhasalsobeen

developed. Finally,themeanfeaturesofthe

vor-tex state (parameters uctuations and

particu-larVzresponses)arereproducedwithEurocopter

ight mecanics code HOST (Helicopter Overall

SimulationTool). Thisresultsarecomparedwith

ighttestdataperformedwiththeinstrumented

DAUPHIN 6075 in service in the French Flight

TestCentre(CEV).

1 Induced velocity model

Allexistinginducedvelocitymodelsusedinight

mechanicscodesare foundedon amean

compo-nent, generally computed by simple momentum

orvortextheory. Because these theoriesare not

valid in descent ight, many models were

elab-orated for such conditions. Most of them only

holds in verticaldescent, asaresult ofthe

axis-symmetrical ow that simplies the problem in

that case. Thedierences betweenthe methods

used showthat theproblem remainsstill

misun-derstood. Despitemany models are available in

verticaldescent,untilnow,nophysicalmodel

ex-ists in the general case of descent with forward

ight. An empirical approach is elaborated in

ordertocomputeViminallightconditions,

in-cluding descentin forwardight.

Both momentum and simple vortex theory

pro-videthefollowingequation:

F z =2:::R 2 :V t :V i (1) with V t = q V x 2 +(V i +V z ) 2

, the wake

trans-port velocity.

Equation(1)maybenondimensionalizedby

di-viding both sides by the hoverinduced velocity

Vi o ,toyield: 1= 2 [ 2 +(+) 2 ] (2) 1.2 Momentum improvement in vertical descent

Figure1showsthesolutionofequation 2in

ver-tical descent ( = 0) and compares them with

experimental data from [3]. The momentum

in-duced velocity followsand minimizes the

exper-imental data for -1.5< < 0 and for  < 2.

Between = 1:5 and = 2 the

experimen-tal values link the upper and lower branches of

momentumtheory.

−3.5

0

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

0.5

1

1.5

2

2.5

3

3.5

Vz/Vio

Vi/Vio

Momentum Theory

Extended momentum theory

Corrected model

1

2

Figure1: Normalizedinducedvelocityinvertical

descent

Thisregionwheresolutionsof(2)areerroneous

corresponds to a surrounding area of the ideal

autorotationforwhich= . Inthissituation,

thenormalizedinducedvelocitytendstowards

in-nityin orderthat therightsideofequation (2)

keep a constant value. The nite experimental

valuesofmeansthatatermisdecientin

equa-tion(2). Physically,thistermcouldrepresentthe

lated using an interpolatingmethod inspired by

theworksof Baskinandal[5].

Let 

1 and

2

bethe criticalnormalizedrates

ofdescentsurroundingtheidealautorotationand

 

1 and 

2

be the corresponding normalized

in-duced velocities computed by equation (2). The

expression ofthederivativeis noteasyto be

ob-tainedbecauseiscomputednumericallyby

solv-ing equation(2) but noexpression givingasa

function of et  isavailable. Nevertheless,

Pe-ters andChen[6]haveshownthat:

@ @ = 1 1   3 1 q 1   2 + 2

givingrespectivevaluesof( @ @ ) 1 and ( @ @ ) 2 in  1 and  2

. So, four conditions allowto interpolate

thenormalizedinducedvelocitybetweenpoint1

and2(gure1)witha3 rd

orderpolynomial

func-tion. For  < 

2

, only the lower solution of

equation(2)isconsidered.

Normalizedinducedvelocitycalculatedinthat

way in vertical descent is represented in gure

1. Thecalculatedvaluesfollowandminimizethe

experimentalones overtheallrangeofdescent.

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Vz/Vio

Pn/Pno

Momentum Theory

Extended momentum theory

Corrected model

Figure 2: Normalized requiredpower in vertical

descent

The extended momentum theory provides a

lowerboundfortheinducedvelocity. Theresults

obtained with this method in term of required

power(gure2)showsthattheextended

momen-tum theory represent the optimum performance

oftherotorbecausethecalculatedrequiredpower

minimized the experimental one(2). Heyson[7]

and Drees[4]assumesthat thisidealizedpicture

ofrotorperformancecomesfromtheomissionof

viscouslossesandalllossescausedby

nonunifor-mity of momentum transfert. Figures 1 and 2

show also the results obtained by the previous

Vi

takesthesedierentlossesintoaccount.

1.2.1 Descentin forward ight

The same method is applied to the descent in

forwardightwithinterpolationlimits

1 and

2

andacoecientk

Vi

adjusted to thenormalized

forward speed . Beyond a critical value 

crit

thenormalized induced velocity is computed by

equation 2 again for any value of  (gure 3).

As themodel is extrapolated when6=0,more

experimental dataare needed to updatevertical

measurementsandtoextendthemtoforward

de-scent.

−2.5

0

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

Vz/Vio

Vi/Vio

Vx/Vio=0

Vx/Vio=0.5

Vx/Vio=1

Figure3: Normalizedinducedvelocityinforward

ight

Themodelhasbeenimplementedinthe

Euro-copterightmecanicscodeHOST.Thelast

chap-terwill showthat thecorrected modelimproved

greatlythecode, reproducingthe meanfeatures

ofvortexringstate.

2 Vortex ring state prediction

Even if all helicopter world actors know the

vortex-ring state, the phenomenon remains still

misunderstoodand thehelicopterightenvelope

indescentremainsnotcorrectlyestimated.

Pre-viousexperimentalstudiesofthevortexringstate

presentdierentaspectsofthephenomenon:

 Circulatory ow shown by visualisation,

bothinwind tunnel[8]andighttest[9],

 Unsteadyowexhibitedbywindtunnel

mea-surements[10]involvingightinstabilities,

 Ct reduction at constant collective pitch

All these dierent aspects are connected.

In-deed,thecirculatoryowprovidesaninduced

ve-locityaugmentationandowuctuations.

More-over,theCtreductionisdue toVi increasethat

decreaseslocalanglesofattack.

Fromthepilotpointofview,thatcanbe

char-acterized by turbulence and sudden increase of

therateofdescent.

It is proposed,rst to determinethe limitsof

the region of roughness, then to generate ow

uctuationsandnallytoanalyzephenomena

im-plying thespecicVzevolutionindescentight.

2.1 Wolkovitch criterion [2]

TheowmodelconsideredbyWolkovitchconsists

ofaslipstreamwithuniformowat anysection,

surroundedbyaprotectivetubeofvorticitywhich

separate the slipstream from the relative wind.

This tube ismadeupby thetipvorticesleaving

the rotorand it is postulated that the unsteady

vortex ringow is associated with a breakdown

in thisprotectivesheath ofvorticity. Wolkovitch

assumesthatthevelocityofthevortexcoresisthe

mean between velocities inside and outside the

tube (gure 4). Moreover,the vortex ring state

issupposedtooccurwhentherelativevelocityof

the tip vortices falls to zero. This leads to the

criterionfortheupperlimit:

 =   2

Vi+Vz

Vi+Vz

Vz

Rotor disk

Inner

Slipstream

Vz+Vi/2

Tip Vortices

Figure4: Wolkovitchowmodel

For the lower limit, Wolkovitch used a

coef-cient k

W

that take into account the distance

above the rotorwhere the"pile-up" of vorticity

occurs. Thelowerlimitisthendenedby:

 = k W : 2 ; 1k W 2

Therecommendedvalueofk

W is1:4.

Figure5representsthelimitobtainedwiththis

criterion (k

W

=1:4) where theinduced velocity

iscomputedbymomentumtheory.

Thelimitsobtainedareclosetothe

experimen-tal ones at low advance ratio. Nevertheless, the

0

0.5

1

1.5

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

Vx/Vio

Vz/Vio

Wolkovitch upper limit

Wolkovitch lower limit

ONERA criterion

Brotherhood limits

∆

Fz=15% (Yaggy)

∆

Fz=30% (Yaggy)

Azuma limits

Max Fz fluctuations (Azuma)

Washizu limits

Max Vi fluctuations (Washizu)

CEV limits

ε

=0.2

=0.1

ε

70°

30°

Figure5: Vortexringstatelimits

criterionpredictsvortexringstateevenforhigh

advanceratios. Thisisconsistentwithneither

ex-periencenorthephysicalmechanismsthatcauses

thevortexringstate.

2.2 Improved Wolkovitch model

As was mentioned by Peters and Chen [6], the

deciencyof theprevioustheorycomesfrom the

factthatthewakeskewangleisnotconsideredin

thewakegeometry. Inordertotakeintoaccount

theskew angle theowmodel shownin gure

6isused.

Vz

V

Vx

s

V

V

s

Vx

Vi+Vz

χ

Tip Vortex

Figure6: Flowmodelin forwarddescent

Thetip vorticesvelocities !

V

tv

is supposed to

beagainthemeanbetweenthevelocitiesoutside

andinside theslipstreambut owingtothe wake

skewangle : ! V tv = 1 2 :( ! V+ ! V s )=  V tvx V tvz  =  Vx Vi 2 +Vz 

Normalizingbythehoverinducedvelocity:

! V tv =      2 + 

UnlikeWolkovitch,asingleconditionisusedto

occurswhenthetipvorticesstandinthevicinity

oftherotor. Inotherwords,therotorisinvortex

ringstatewhentheinitialvelocityoftipvortices

is not large enough to carry them far from the

rotordisk. This wouldleadto the following

cri-terion: j ! V tv j= q V 2 tvx +V 2 tvz <"

This criterion gives good results near vertical

descentbutdoesn'tmatchverywellwith

experi-mental datafrom [8] and[11] when6=0. That

is due to the fact that the normalizedaxial and

inplane owsdon'tplayasymetric roleasgure

7shows.

d

2

1

d

Tip Vortex

Figure 7: Physical dierence between axial and

inplane ow

Let'sconsider

①

and

②

astwovortexrings leav-ingtherotoratthesamevelocity,moving

respec-tively in the axial and inplane direction. After

atime t,thevorticeshavebothcoveredthe

dis-tancedbutgure7showsthattipvortex

②

isstill incontactwithrotorwhilevortex

①

nolonger in-teract withtherotordisk. Asaresult,therotor

issupposed tobein vortexringstatewhen:

 V tv x " x V tv z " z (" z <" x ) Putting " x =k:" z

=k:"with k>1,the

crite-rionbecome 1 : s (   k ) 2 +(   2 +) 2 " (3)

In the previous criteria ([2] and [6]), induced

velocity was calculated with momentum theory

whichisnotvalidindescent. Hereiscomputed

withtheinducedvelocitymodeldescribedabove

whichisadaptedto descentight.

Value of coecient k = 4 is chosento match

withexperimentaldomainsfrom[8]and[11]. The

value of " traduces the intensity of the vortex

ring state uctuations. Figure 5 represents the

limits obtained with " = 0:2 and " = 0:1, that

correspondsrespectivelyto lightand severe

uc-tuations levels. Flight test havebeen performed

1

Newmanetal[12]havealsoconsideredsuchcoecient

in the French Flight Test Centre (CEV) to get

thevortex ringstate limits in ight. First data

obtainedarerepresentedongure5alsowith

ex-perimental datareportedby[12].

Dimensionallimits: Thephysicallimitis

ob-tainedbymultiplyingthenormalizeddomain by

Vi o = q Fz 2:::R 2

. Consequently,the vortex ring

statedimensional domaindependson:

F

z

approximately equivalent to the helicopter

mass,

R expressingtherotordimensions,

 expressingightconditions.

Figure 8compares thelimits obtainedfor the

DAUPHIN attwodierentmasses.

0

5

10

15

20

25

30

35

−18

−16

−14

−12

−10

−8

−6

−4

Vz (m/s)

Vx (km/h)

M=3t

M=4t

Figure8: Helicoptermassinuenceonthevortex

ringstatedomain

Axis inuence: Rigorouslycriterion (3) must

be applied in rotor axis. Trim calculations

real-izedwithDauphin365Natz=0m,usingHOST

code,givethelimitrepresentedongure9.

Sim-plemultiplicationofcriterion(3)byVi

o

applied

directlyinhelicopteraxisisalsorepresented.

Be-causeofsmallvaluesofthehelicopterpitchangles

intheseightconditions,gure9showslittle

dif-ferencesbeetweenthetwolimits. Asaresult,the

simplecriterion(3)canbeusedinhelicopteraxis

multiplyingbythehoverinducedvelocity.

2.3 Application of the criterion to

D6075 vortex-ring state ight

Duringenginefailureighttests,DAUPHIN6075

encounteredaccidentallythevortex-ringstate.

Figure10showsthatthehelicopter enters the

0

5

10

15

20

25

30

35

40

45

50

−20

−18

−16

−14

−12

−10

−8

−6

−4

−2

0

Vh (km/h)

Vz (m/s)

Helicopter axis

Rotor axis

Figure 9: Comparison of vortex domains

ex-pressedin rotor andhelicopter axis(m=3500kg,

z=0m)

dropped while the pilot tries to reduce the

de-scentrate(WAa)(betweenpoints1and2). This

maneuverimpliesadecreaseofthecriterionvalue

thatreaches0.2atpoint2and0.1atpoint3,

sig-nifying an augmentation of vortex ringstate

in-tensity,thatleadsinasharplyVzdecrease. Next

thehelicopterleavesvortexringstateareaby

in-creasingitsforwardspeedthat augmentsthe

cri-terion value(0.2at point4). Inthisway,the

pi-lot managestostabilizeand nextto increaseVz.

Thebottomdiagramshowsagoodcorrelation

be-tweentheighttestbeginningofVzdecreaseand

proposedlimit.

3 Helicopter behaviour

pre-diction in vortex ring state

3.1 Flow uctuations

Method: Aswind tunneltestexhibitedahigh

level of ow uctuations during the vortex ring

state,ithasbeendecidedtointroduceVi

uctu-ations in HOST code. Moreover,measurements

ofFzspectrumisavailableinliterature[13]. This

experimentalspectrumobtainedfromamodel

ro-tor is rst sampled and then is adapted to the

Dauphin rotor with the help of the normalized

frequency: !

0 =

:R

c

. However, this spectrum

corresponds to a single ight condition ( = 0,



=0:75)nearmaximumuctuationslevel.

Yet, criterion (3) gives not only the limit of

vortexringbutpermitsabovealltoestimatethe

intensityofuctuations. Indeed,thevalueofthe

leftsideofequation(3)givestheintensityof

uc-tuations. Morelowisthevalueofcriterionmore

importanttheuctuationswill. Accordingly,the

spectrumisinterpolatedovervortexdomainwith

0

5

10

15

20

25

30

35

−20

−15

−10

−5

0

5

10

15

20

25

30

1

2

3

4

tps (s)

Velocities (m/s)

UAa

VAa

WAa

0

5

10

15

20

25

30

35

−100

0

100

200

300

400

500

1

2

3

4

tps (s)

Pw (kW)

TotPw

MrPw,

0

5

10

15

20

25

30

35

0

0.2

0.4

0.6

0.8

1

1.2

1

2

3

4

tps (s)

Vortex criterion

0

5

10

15

20

25

30

−18

−16

−14

−12

−10

−8

−6

−4

t=0s

t=34s

1

2

3

4

Forward Speed (m/s)

Rate of Climb (m/s)

Figure10: Mainightparametersandvortexring

state criterion during D6075 vortex-ring state

ight

criterion (3) supposing that excited frequencies

arethesameonthewhole domain.

AsFzuctuationsis aconsequenceof Vi

uc-tuations, a uctuating term ~

Vi is added to the

induced velocity. In view of the experimental

Fz spectrum form, ~ Vi is chosen to be pseudo-harmonic: ~ Vi= n X i=1 Ai:cos(! i :t+ i )

analyzed and compared with experimental one.

Next, ~

Vimustbeadjusted,throughAiand!

i in

order thatcomputed spectrummatcheswith

ex-perimentalone. Thephase

i

isarandomnumber

takenbetween0and2:.

Figure 11 represents comparison between

thrust uctuations intensity computed with the

model,someexperimentaldata[10]andEuler

nu-mericalsimulation[14]. Inallthecases,a

maxi-mumofuctuationof12-14%ofthemeanthrust

 Fz appearsnear= 1.

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Vz/Vio

∆

Fz/Fz

Experiment

Euler 3D

HOST

Figure 11: Comparison betweenthrustvariation

computed, experimental data andEuler

numeri-cal simulationin verticaldescent

Figure 12 validates the model in term of

fre-quencies, showingin onehand the experimental

spectrum deducted from [13] and on the other

hand the spectrum computed by HOST

simula-tion.

1

2

3

4

5

6

7

0

10

20

30

40

50

60

70

f (Hz)

Fz power spectrum

Deducted from experiments

Calculations

Figure 12: Comparison between experimental

andcalculatedspectrum

Consequences: Figure 13 represents a

simu-lation realized at Vh=10km/h, Vz=-10m/s and

tionsdirectlyactonFzandonthebladeapping

angles. Whereas thefuselage attitudeangles (,

)presentlowerfrequenciesduetodampingthat

acted between the rotor and the fuselage. The

verticalspeedVzand thenormalloadfactor Nz

arealsomodiedbyVi uctuations.

0

4

8

18

20

22

TEMPS S

VIM-RP M/S

0

4

8

2000

3000

4000

TEMPS S

FZA-RP DAN

0

4

8

-10.4

-10

-9.6

-9.2

TEMPS S

VZ M/S

0

4

8

1

2

TEMPS S

B0-RP DEG

0

4

8

1.1

1.2

1.3

1.4

TEMPS S

BC-RP DEG

0

4

8

0.4

0.44

0.48

TEMPS S

BS-RP DEG

0

4

8

0.6

0.8

1

1.2

TEMPS S

NZ G

0

4

8

3.6

4

4.4

TEMPS S

PHI DEG

0

4

8

2

2.4

2.8

3.2

3.6

TEMPS S

TETA DEG

Figure 13: HOST simulationfor Dauphin 365N

(Vh=10km/,Vz=-10m/s), controls xed with Vi

uctuations

Conclusion: Flowuctuationshas been

mod-eledinthecodeHOSTwithanexperimental

spec-trum [13] measuredon asingle point and

inter-polated overthewhole vortexringstate domain

with criterion (3). The excited frequencies are

supposedtobeconstantonthewholevortex

do-main. Moreexperimentaldataareneededto

val-idatethishypothesisandtocorroboratethe

spec-trumform.

3.2 Vz response to collective pitch

in descending ight

Vortexringstatecanbequitedangerousbecause

oftheamazingVzresponsestoDT0implying

sud-denVzfall. Flighttests,performedatthefrench

ighttestcentre(CEV),exhibitsuch

characteris-ticphenomena. ThesimpleVimmodeldescribed

abovepermitstoreproducesqualitativelythisVz

responses.

3.2.1 Vzresponseto DT0 reduction

Suchanexampleisshownongure14. Thepilot

decreasesprogressivelythecollectivepitch. First,

Vzresponses"normally"toDTOinputs: thetwo

rst DTO reductions of about 0:2 Æ

produce a

Vz decrease of about 2.5m/s. The third DTO

reduction rather smallerthan the previous ones

0

10

20

30

40

50

60

70

80

90

6

6.2

6.4

6.6

6.8

7

tps (s)

DTO (deg)

0

10

20

30

40

50

60

70

80

90

−15

−10

−5

0

5

tps (s)

Va (m/s)

Vh (m/s)

Vz (m/s)

Figure14: FlighttestexampleofVzresponse

tocollectivepitch reductions

0

5

10

15

20

25

30

35

40

5.8

6

6.2

6.4

6.6

6.8

tps (s)

DT0 (deg)

Initial model

Proposed model

0

5

10

15

20

25

30

35

40

−20

−15

−10

−5

0

tps (s)

Vz (m/s)

Initial model

_{Proposed model without fluctuations}

Proposed model with fluctuations

Figure15: HOSTcalculationsofVzresponse

tocollectivepitch reductions

The explanation of this phenomenon comes

fromtheevolutionofDT0asfunctionofVz

(g-ure 16). This curve presents a local minimum

nearVz=-6.5m/s(pointA).Betweenhover

con-tition and this local minimum, Vz response is

approximatelya linearfunction of DTO inputs.

Close to point A (on the hover side), any light

DT0reductionwillimplynewtrimcondition

cor-respondingto Vz greater thanthose ofpointB.

It isto notethat segment[AC]representsan

in-stable region.

A HOST simulation reproducing this

phe-nomenonisshownongure15withandwithout

induced velocity uctuations. Simulation with

theinitialVimmodelisalsoindicated. Withthe

initialmodel,nosuddenVzfallisvisible,because

oftheuniformdecreaseofDTOwithdescentrate

increase. With the proposed model a large

in-crease of the descent rate is obtained as in the

ighttests.

−20

−15

−10

−5

0

5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

Vz (m/s)

DT0 (deg)

Proposed model

Initial model

A

B

C

jump

jump

Figure16: DT0versusVzinverticalight(HOST

trimcalculations)

3.2.2 Vz response to DT0 increase:

Power-settling

Power-settlingisanotherimportantphenomenon

occurring during descent ights. This

phe-nomenonstillmisunderstoodcouldbedenedas

aninsensitivityofVzto collectivepitchincrease.

DT0 increase within vortex ring state:

Figure 17 exhibits a ight test illustrating this

phenomenon. The Helicopter enters the vortex

ring state by a deceleration, implying an

aug-mentation of the rate of descent. At t  14:5s

thepilot increases DT0in order to stabilize Vz.

Despitethis DT0increase(+1 0

),Vzcontinueto

fallduring5sstabilizingat Vz 12m=s.

Thisphenomenoncouldbeexplainedwiththe

help of gure16. Supposing that the helicopter

isinaightconditionsomewherebetweenpoints

Aand B.If thecollectivepitch isincreasedat a

valuesmallerthanthoseatpointC,thehelicopter

willgotoatrimconditionsituatedonthestable

partofthecurve,betweenpointsBandC.

Such phenomenon is reproduced qualitatively

with HOST simulation using the proposed Vim

modelasshownongure18. Beginningat

Vz=-6m/s, the rate of descent increases in response

to theDT0decrease, temptingto reach thenew

trimposition (beyondpointCon gure16). At

t=8s,DT0isincreasedtoitsinitialvalue. Instead

of going back to its rst value (Vz=-6m/s), the

rateofdescentgoesto thesecond trimposition,

situatedbetweenBandCongure16. Withthe

initialmodel,thehelicoptercomes backto

Vz=-6m/s.

DT0 increase beyond vortex ring state:

The"jump"phenomenonalsoexistswhenthe

0

2

4

6

8

10

12

14

16

18

20

5

5.5

6

6.5

tps (s)

DT0 (deg)

0

2

4

6

8

10

12

14

16

18

20

0

5

10

15

tps (s)

Vh (m/s)

0

2

4

6

8

10

12

14

16

18

20

−12

−10

−8

−6

−4

tps (s)

Vz (m/s)

Figure 17: Flight test exampleof power

set-tling

0

5

10

15

20

25

30

5.9

6

6.1

6.2

6.3

6.4

6.5

tps (s)

∆

DT0 (deg)

0

5

10

15

20

25

30

−20

−15

−10

−5

tps (s)

Vz (m/s)

Initial model

Proposed model without fluctuations

Proposed model with fluctuations

Figure18: HOSTsimulationofpowersettling

inverticaldescent

ahighrateofdescent. However,thisismore

dif-cult to exhibit in ight. Because of the large

Vz, thepilot hasto increaseDT0rather quickly

anditisdiculttorealizestepinputs. Figure19

showsaightteststartingat Vz 20m=sand

Vh8m=s. ThepilotaugmentsDT0inorderto

decrease the rate ofdescent. Att=50s, Vzonly

reaches  15m=s despite a collective increase

of about +4 Æ

. Beyond t=50s collective pitch is

still slightly increases (' 0:2 Æ

) and Vz increases

sharply(about10m/sin 10s).

Supposing atrim positionat arateofdescent

greaterthantheoneatpointBontheDT0curve

of gure16 (betweenautorotationandpointB).

IfDT0isincreasedatvaluesmallerthanthoseat

point C, the trim position moves upward.

Tak-ing into accountthe slope of thecurvebetween

autorotationandpointC,thedierenceofVz

be-tweenthetwotrimpositionswillbesmall. When

DT0isincreasedatavaluegreaterthanthoseat

point C, the Vz will increase, going to positive

value.

Such phenomenon is reproduced with HOST

calculationsongure20.

25

30

35

40

45

50

55

60

65

2

4

6

8

tps (s)

DT0 (deg)

25

30

35

40

45

50

55

60

65

7

8

9

10

11

12

tps (s)

Vh (m/s)

25

30

35

40

45

50

55

60

65

−20

−15

−10

−5

tps (s)

Vz (m/s)

Figure19: DT0increaseighttest

0

5

10

15

20

25

30

35

40

45

−2

0

2

4

6

8

tps (s)

DT0 (deg)

0

5

10

15

20

25

30

35

40

45

−25

−20

−15

−10

−5

0

5

tps (s)

Vz (m/s)

Proposed model without fluctuations

Proposed model with fluctuations

Figure 20: HOSTsimulationofDT0increase

beyondvortexringstateinverticaldescent

Conclusion: Meanfeaturesofthecomplex

vor-tex ring state including collective pitch

insensi-bility(powersettling) canbereproducedwith a

simpleVim model. Theoretical study aswellas

ighttestsshowthatsegment[AC]representsan

The induced velocity model elaborated

im-provesgreatlyHOSTcodepredictions. Themean

characteristicsof the vortex ring state observed

during experimentalstudiesarewellreproduced.

Both D6075 ight test and HOST calculations

havedemonstratedthat vortexringstatecanbe

consideredasaninstableregion. TheVimmodel

matcheswellwithexperimentaldataavailablein

verticaldescentbutitisextrapolatedinthecase

of descent with forward velocity. More

experi-mental data are needed to update vertical

mea-surementsandtoextendthemtoforwarddescent.

A vortexringstatepredictedcriterionis

elab-orated. More experimental data are necessary

to obtain more precisely the vortex ring state

domainin ordertovalidatethiscriterion.

Inthenearfuture,ighttestplanedonD6075

willpermit:

 to establishthe vortexring statedomain in

ight,

 toincreaseexperimentaldatainorderto

ad-just theVimmodel.

Induced velocities measurements with probes

located on a boom xed on the D6075 fuselage

arealsoscheduled.

References

[1] VARNESD.J. DUREN R.W. WOOD E.R.

Anonboardwarningsystemtoprevent

haz-ardous "vortex ring state" encounters. In

26 th

European Rotorcraft Forum, pages 88

1, 8815, The Hague, The Netherlands,

September2000.

[2] WOLKOVITCH Julian. Analytical

predic-tionofvortex-ringboundariesforhelicopters

insteepdescents. JournalofAmerican

Heli-copterSociety,Vol.3(No.3):1319,July1972.

[3] CASTLES Walter GRAY Robin.

Empiri-calrelationbetweeninducedvelocity,thrust,

and rate of descent of a helicopter rotor

asdetermined by wind-tunnel tests on four

model rotors. TechnicalNote 2474, NACA,

1951.

[4] MEIJER DREES IR.J. A theory of

air-ow throught rotors and its application to

somehelicopterproblems.Journalofthe

he-licopter society,3(No.2),1949.

DAYEN YE.S. MAYKAPAR G.I. Theory

oftheliftingairscrew.TechnicalTranslation

F-823,NASA,1976.

[6] PETERS DavidA.CHENShyi-Yaung.

Mo-mentum theory, dynamic inow, and the

vortex-ringstate. Journalof American

He-licopter Society, Vol.27(No.3):1824, July

1982.

[7] HEYSON Harry H. A momentum analysis

of helicopters and autogyros in inclined

de-scent,withcommentsonoperational

restric-tions. TechnicalNoteD-7917,NASA,

Octo-ber1975.

[8] MEIJER DREES J. HENDAL W.P. The

eld of ow throughta helicopter rotor

ob-tainedfromwindtunnelsmoketests.T

echni-calReportA.1205,NationalLuchtvaart

Lab-oratorum,TheNetherlands,1953.

[9] BROTHERHOODP. Flowthroughthe

he-licopter rotor in verticaldescent. Technical

Report2735,ARCR&M,1949.

[10] AZUMA A. OBATA A. Induced ow

vari-ation of the helicopter rotor operating in

the vortex ring state. Journal of Aircraft,

Vol.5(No.4), 1968.

[11] WASHIZUK.AZUMAA. K 

OOJ.OKAT.

Experimentsonamodelhelicopterrotor

op-erating in the vortex ring state. Journalof

Aircraft,Vol.3(No.3),1966.

[12] NEWMAN S. BROWN R. PERRY J.

LEWISS.ORCHARDM.MODHAA.

Com-parativenumericalandexperimental

investi-gationsofthevortexringphenomenonin

ro-torcraft.InAmericanhelicoptersociety,57 th

annualforum,May2001.

[13] XIN H. GAO Z. An experimental

investi-gation of model rotorsoperatingin vertical

descent.InProceedingsofthe19 th

European

RotorcraftForum,Cernobbio,Italy,1993.

[14] INOUE O. HATTORI Y. AKIYAMA K.

Calculations of vortex ring states and

au-torotation in helicopterrotorowelds. In

Americaninstituteofaeronauticsand