A detailed biomechanical pilot model for multi-axis involuntary rotorcraft-pilot couplings

41 EuropeanRotor raftForum

A DETAILED BIOMECHANICAL PILOT MODEL FOR

MULTI-AXIS INVOLUNTARY ROTORCRAFT-PILOT

COUPLINGS PierangeloMasarati

∗

,GiuseppeQuaranta

∗

,AndreaZanoni

∗

∗

Dipartimentodi S ienzeeTe nologieAerospaziali,Polite ni odi Milano

ViaLaMasa34,20156 MilanoItaly

e-mail: pierangelo.masaratipolimi.it

Abstra t

Thisworkpresentsa ompletebiome hani almodelofthepilot'supperpartofthebody,whi hin ludes

thetorso,theheadandbothupperlimbs. Themodelisusedtoinvestigatethebiodynami feedthrough,

namelytheinvoluntarymotionofthe ontrolin eptorsthatis ausedbythea elerationofthe o kpit.

Themodelis oupledwithadetailed multibodymodelofa heli opter.

1. INTRODUCTION

Tosu essfullya omplishaightmissiontaskitis

ne essaryforthepilotandthevehi leto ooperate

inajointenterprise. Infa t,thepilotandthe

vehi- le form a losedloopsystem, theso- alled

pilot-vehi lesystem. The losedloopstru tureensures

in generala good disturban e reje tion apability

to system. However, in some ases the feedba k

loopmayleadtoaninstability ondition,i.e. toan

unfavorable intera tion that resultin a divergent,

oftenos illatory, un ontrolled motion. These

phe-nomena are alled adverse Rotor raft Pilot

Cou-plings (RPC) and are often aused by a trigger

event that a tivates the transition to a divergent

motion. Classi alRPCeventsarethose ausedby

anerroneousper eptionofthepilotofthedynami

hara teristi softhevehi le. Thisleadstowhatis

betterknown as PilotIndu ed Os illations(PIO),

whi histheee tofavoluntary,out-of-phase,pilot

ontrol a tivity. However,piloted vehi les arealso

subje ted intera tionwith thepilot aused bythe

feedingofthevehi levibrationsintothe ontrol

in- eptorsthato ursthroughthebiodynami softhe

pilot. Inthis asethedivergentos illationisthe

re-sultofinvoluntary ontrol inputofthepilotinthe

loop,andthephenomenonisdenominatedPilot

As-sisted Os illation (PAO). A pra ti al onsequen e

of this intera tion is a modi ation of the losed

loop dynami s of the pilot-vehi le system, whi h

maybeper eivedasadegradation ofthehandling

qualitiesofthevehi le,andleadintheworst ases

tolimit y le os illations,ex essiveloads,and loss

of ontrol. Rotor raftarespe i allyproneto this

problembe ausetheymaysuerfromhigher

vibra-toryloadsthanxedwingair raft,andmaypresent

dynami sinthefrequen ybandofbiome hani s(2

Hzto8 Hz,[1 ℄). Areviewofthere entworkdone

onalltypesofRPC anbefoundinthesethree

pa-pers,Refs. [2, 3 ,4℄,where it isreported thework

done within the EU sponsored proje t

ARISTO-TEL.

The pilota tion on the air raftin eptors is

ex-ertedviathefor esgeneratedbythemus lesdriven

bythe neuromus ularsystem. Thepilotper eives

the air raft position and orientation through the

visualandvestibularsystem;additionally,the

pro-prio eption givestherelativepositionbetweenthe

pilot'sbodypartsandtheneighboringobje tswith

whom he/she is intera ting, i.e. the in eptors

andallotherhumanma hineinterfa eelement

in-sertedin the o kpit. Summing uptheme hani al

impedan eofthedierentpartsofthepilot'sbody

betweentheseatandthein eptorsthebiodynami

feedthrough (BDFT) is obtained, i.e. the

move-ment of the in eptors grabbed by the pilots due

to a elerations ofthe base. A largevariability of

andalsointra-subje t[5℄. Infa t,thebiodynami al

propertiesofthepilotmaybeinuen edbyseveral

parameters,whi hin lude theposture,the

mus u-lar a tivation,thetask andtheworkload. Most,if

notall,arehardlymeasurableobje tively.

Atypi alapproa hforthemodelingofthe

biome- hani softhepilotisbasedonexperimentally

mea-suredtransferfun tions. Typi ally,thepilot

biome- hani s is dominated by a pair of omplex

on-jugated poles that determine an equivalent

mass-spring-damper system. Well known voluntary

pi-lot models(e.g. Hess'sstru tural pilot model, [6 ℄)

in lude a pair of omplex onjugated biodynami

poles. Lumpedparametermodelshavebeen

devel-opedforxedwingair raft(forexample[7,8℄).

Inre enttimes,adetailed,physi sbased

nonlin-earmultibodymodeloftheleftarmofaheli opter

pilothasbeendevelopedandinterfa edwitha

om-parablydetailedmultibodymodelofaheli opterto

investigate olle tiveboun e [9 , 10 ℄ (Fig. 1). The

radius

humerus

ulna

hand

Figure1: Multibodymodelofthearmholdingthe

olle tive ontrolin eptor.

samemodelwasusedtoidentifyalinearized,

para-metri modelofthepilot/ ontroldevi etobeused

fordesignpurposes[11 ,12℄.

The availability of a detailed, physi s based

model of the biome hani s of the pilot presents a

learadvan ewithrespe ttobla k-boxmodels: as

long as it is validated with experimental data, it

an be used to analyze and simulate novel

o k-pit ongurations withouttheneedto identifythe

parametersfrom dedi atedexperiments.

2. MODELDESCRIPTION

This work presentsan extension of thepreviously

mentioned biome hani al model of the pilot's left

the y li ontrolin eptoraremodeled,alongwith

the torso. The hara teristi properties of

losed-loop biodynami feedthrough and neuromus ular

admittan e of the right arm are evaluated. The

intera tionwiththetorsoisdis ussed.

2.1. Upperhuman body

The dynami s of the upper body has been

re og-nized as an important element to re onstru t the

BDFTof pilots sin ethe initial identi ation test

ampaignsperformedattheUniversityofLiverpool

during the GARTEUR HC AG-16and the

ARIS-TOTEL proje ts[2 ℄. InRef. [13 ℄ it is shown how

anon-negligible ampli ationfa toroftheverti al

a elerationtransmittedfromtheseatthroughthe

body was measured at pilot's shoulders. Kitazaki

andGrin[14 ℄showedthroughexperimentshowit

is possible to identify a prin ipal resonan e of the

humanbody lose to 5 Hz. The asso iated modal

form showsthe skeleton that movesverti ally due

to axial and shear deformation of butto ks tissue,

inphasewithaverti alvis eralmode,anda

bend-ingmode oftheupper thora i and ervi alspine.

Su h mode is expe ted to havea signi antee t

onthe BDFT; onsequently, a numeri almodel of

torsowasdeemedne essary.

Theupperbodyismodeledusingaphysi sbased

lumped parameters approa h, following the idea

proposed by Kitazaki and Grin [15 ℄ for a model

that only onsiders motion in the sagittal plane.

Themodelhasbeentransformedba kintoa

three-dimensional one exploiting the database provided

by Privitzer and Belyts hko [16 ℄, whose sagittal

plane data was also used by Ref. [15 ℄ (Fig. 2(a)).

Themodelislinear;it onsistsof34lumpedmasses

onne ted by lumped spring elements. The spine

is omposed by 24 elasti elements made of a

lin-earandarotationalspringpositionedbetweenea h

pairofvertebralbodiesrepresentingall

interverte-bral disks that onne t the head to the sa rum.

Theheadismodeledas asinglerigidbody. Inthe

originalmodelbyKitazakiandGrin,the

interver-tebralarti ulationweremodeledasbeamelements,

allowingadispla ementalongthesagittalaxis

be-tweenthevertebralbodieswhi hisnot ompatible

withthis typeofarti ulation. Themassesused to

representthetorso are rigidly atta hed to the

up-per vertebral bodies with an oset. Instead, the

masses of the vis era, below the diaphragm, are

representedusing8 on entratedmasses. Theyare

separatedfromthoseofthespineand onne tedto

thembylinearspringsalongthesagittaldire tion.

(a)Modelofhead,spine,pelvisandvis era.

(b)Modeloftorso oupledwithleftarm.

Figure 2: Multibody model of torso and left arm

holdingthe olle tive ontrolin eptor.

into a ountthe larger values asso iated with the

vis era internal organs and thefa t that they are

not onnedbytherib age. Finally,thepelviswas

modeled by a large mass rigidly onne ted to the

sa rum and groundedby two beam elements that

modelthebutto kstissue.

Thisdetailedmodelwas usedtoextra tlow

fre-quen yeigensolutions,whi hareusedtoprodu ea

redu edorder Component Mode Synthesis (CMS)

model. The resulting model orrelates well with

thoseobtainedinRef.[15 ℄andwiththe

experimen-taldatapresentedinRef.[14 ℄(Table1),atleastfor

the modes that dominate the response when the

body is subje ted to a verti al os illation in the

vi inityof5Hz.

In order to onsider the full three-dimensional

motion, itwas ne essary to add thetwo moments

of inertia that were missing from ea h body, and

bodymodels. Mode [15℄ [14℄ Present [Hz℄ [Hz℄ [Hz℄ 1 0.28 1.10 0.27 2 1.59 2.20 1.78 3 2.81 3.40 3.14 4 5.06 4.90 5.09 5 5.77 5.60 5.99 6 7.51 8.10 7.45

Table2: Chara teristi frequen iesofthethree

di-mensionalupper bodymodels.

Mode Frequen y Plane

[Hz℄ 1 0.29 Sagittal 2 0.94 Coronal 3 1.88 Coronal 4 2.21 Sagittal 5 3.38 Coronal 6 3.89 Coronal 7 4.23 Coronal 8 5.27 Sagittal 9 5.65 Coronal 10 6.27 Sagittal

the torsional and oronal bending elasti

onne -tionsprings.

Thenewmodalformsobtainedwere learly

sep-arable into sagittal and oronal, with the

sagit-talmodesthatshowedalimitedmodi ationwith

respe t to those omputed with the original

two-dimensionalmodel(Table2).

Finally,themassesasso iatedwiththearmsthat

were equally distributed on thenodesof thetorso

were extra ted to prepare the model for

onne -tionwiththedetailedmultibodymodelofthearms'

skeletalandmus ularsystem.

2.2. UpperLimbs Biome hani al Model

A multibody model of the upper limbs has been

developed, as an extension of the left limb model

alreadypresentedinearlierworks[17 ,9,10 ℄,whi h

was derived from the one originally presented by

Pennestrì et al. [18℄. Ea h limb onsists of four

rigidbodiesthatrepresentthehumerus,theradius,

theulnaandthehand.Theyare onne tedbyideal

kinemati onstraints. Thetotalnumberofdegrees

offreedomisthus24. Thehandisrepresentedbya

singlerigidbody; a detailed hara terizationofits

simu-Currently,theshoulder omplexisalsonot

mod-eled in detail, disregarding the lavi le and the

s apula. Piloting tasks are typi ally performed

with very low elevation angles of the humerus for

boththelimbs;thereforetheexpe tedee tofthe

s apula and lavi le motionon the shoulder

kine-mati s is very limited. The glenohumeral joint

is represented by a spheri al joint lo ated at the

glenoid fossa, removing 3 degrees of freedom. A

revolutehingeapproximatesthehumeroulnarjoint

in orresponden e tothe enterofthetro hlea,

al-lowingtherotationoftheulnawith respe ttothe

humerus only about the lo al lateral axis. It

re-moves5degreesoffreedom. Thehumeroradialjoint

is represented bya spheri al hinge, lo atedat the

humeral apitulum,thatremoves3degreesof

free-dom. Theproximalanddistalradioulnarjointsare

modeled by asingleinlinejointbetweena pointP

andtheme hani alaxisoftheulna. Thepositionof

thepoint isosetfrom theradiusme hani al axis

inthelateraldire tion: theosetissu hastoleave

thetwobones'me hani alaxesparallelin therest

position(i.e. withthearmextendedanteriorly,the

palm fa ing upward). Theoriginal formulation of

thiskinemati representationoftheradioulnarjoint

isduetoPennestrìetal.,moredetails anbefound

in[18 ℄. Thejointremoves2degreesoffreedom. At

itsdistalend,theradius onne tswiththehandby

meansofa ardani joint,allowingthewrist

radio-ulnar deviationand exion-extensionrotations. It

removes 4 more degrees of freedom. As a

onse-quen e, the model had 7 degrees of freedom and

itskinemati s areunderdetermined evenwhenthe

motionofthehand is ompletelypres ribed.

Themus lesare modeled usingone-dimensional

vis oelasti elementswhose onstitutivelaws

repre-senta simplied Hillmodel,proposedin [18 ℄. The

for e exertedbya mus leisa fun tionof

x = l/l

0

and

v = ˙l/v

0

, non-dimensionallengthand normal-izedvelo ityofthemus lewithrespe ttoreferen e

parameters,andofthevoluntarya tivation

a

:

(1)

f = f

0

[f

1

(x)f

2

(v)a + f

3

(x)]

where

f

0

isthepeakisometri ontra tionfor e ex-erted by the mus le,

l

0

represents the length at whi h

f

0

is produ ed, while

v

0

is the maximum ontra tion velo ity of the mus le. Their values

aretakenfrom[19 ℄. Tendon omplian eisassumed

lowenoughtobedisregarded. Thetotalnumberof

mus lebundlesmodeledis25forea hlimb. Thus,

the upper limb multibody model is an

under on-strained,overa tuatedsystem,sin ethe25mus les

produ etorquesa tingonthe7degreesoffreedom

Themus ulara tivation isa-priori unknownfor

a given task, depending on the entral nervous

system ontrol strategy. It an be however

esti-mated by solving a non-linear optimization

prob-lem in whi h thetotalsquared a tivation

P

n

m

i=1

a

2

i

(

n

m

beingthe totalnumber of mus lebundles) is minimizedina given onguration,under the

on-straint that the torques produ ed by the mus les

must be equal to the ones required to guarantee

the dynami equilibrium of the limb and

ompli-an e with the bounds

0 ≤ a

i

≤

1

. More details ofthe ompletesolutionpro edure anbefoundin

[9 ℄. The al ulated a tivation values refer to the

passive, or involuntary hara teristi s of the pilot

body. Thea tive,orvoluntary(orbetterreexive)

part ofthe a tivation an beestimated by

onsid-eringa quasi-steadyapproximation

(2)

∆a = K

p

∆x + K

d

∆v

su h that thefor e perturbation an be expressed

as (3)

∆f =f

0



f

1

/x

a + f

1

K

p

f

2

+ f

3

/x

 ∆x

+ f

0

f

1

f

2

/v

a + f

2

K

_d

∆v

Thebaselineforthegeometryofthemodelis

repre-sented bythe rib age parametri model presented

in[20 ℄: theauthorsshareda ompletedataset

om-prisingthe oordinatesof464landmarksmeasured

ontherib ageof89subje tsbymeansofCTs ans,

along with the results of a PCA (Prin ipal

Com-ponent Analysis) with respe t to the parameters

age, sex, stature and Body Mass Index (BMI) of

thesubje t. Themostlikelyrib agegeometry ofa

subje t an bere onstru ted onthebasisof those

parameters. Thelandmarksrepresentingtheother

limbsegmentsandjointlo ationsaretheninferred

bytherib agedimensionsandanthropometri data

from[21 ,22 ℄,toyieldthe ompletegeometryofthe

limbsandtheirinertial properties.

For the presentwork, thegeometry ofthetorso

model has been onsidered as referen e. Optimal

age,sex,statureandBMIofthemostlikely

mat h-ingsubje thavebeenestimatedbyminimizingthe

squareddistan e oftheinsertionpointsoftheribs

from their lo ationwith respe t to thenodes

rep-resenting the vertebrae in the FEM model of the

torso. Theresultingpilotis a34 yearold male,of

1.78 m stature and a 26.5 BMI, orresponding to

anestimatedweightofapproximately 84kg.

The olle tive ontrol in eptor is modeled as a

purelykinemati onstraintfortheleft hand,that

leverandallowsitsrotationabouttheglobal

y

-axis about the lever hinge lo ation. The hoi e of not

assigning inertial properties to the olle tive (and

y li )leversis justiedby thewishto isolatethe

purelybiome hani altransfer fun tionofthepilot

bodywithrespe ttoalltheexternalinuen esand

toprodu eaparametri modelofthepilot/ ontrol

devi e.

2.3. Right Arm and Cy li Control

In ep-tor

Therightarmmodelrepresentsessentiallythe

spe -ular version of the left arm model about the

xz

-planewith regardto geometry. Theinertial

prop-ertiesofthebodysegmentsareagainseta ording

totheregressionanalysispublishedin[21 ,22 ℄. The

y li ontrol in eptor is modeled as an algebrai

onstraint, this time allowing the rotation of the

handwithrespe ttothe y li leverhingelo ation

abouttheglobal

x

-axisandabouttheglobal

y

-axis.

2.4. Heli opter Model

The omplete biome hani al model of the pilot's

upper part of the body is oupled with an

aeroe-lasti model of a medium weight heli opter, with

arti ulatedmainrotor.

Thenonlinearmodelofthevehi lehasbeen

pre-sented in [23 ℄, where it was also ompared to a

linearizedstate-spa e(LSS)modelofthesame

ve-hi le. It is based on the Aerospatiale (now

Air-busHeli opters)AS330Puma. Its analysiswithin

thebiome hani almodelofthepilot'sleftarmwas

originallypresentedanddis ussedin[9 ,24 ,10,25 ℄.

Adetailedand ompletemultibodymodelofthe

heli opter has been developed by oupling a

de-tailed aeroelasti model of the main rotor with a

stru tural model of theairframe, a ight

me han-i smodelanddynami modelsofthepit h ontrol

a tuators.

The rotor model features exa t kinemati s and

nonlinear nite element-like stru tural dynami s

thanks to an original nite volume beam

formu-lation[26℄. Rotorbladeaerodynami saremodeled

using the blade element theory, with stati

aero-dynami oe ientsfromlook-uptables,unsteady

aerodynami orre tionbasedona state-spa e

ap-proximationofTheodorsen'smodel[27 ℄,andglobal

dynami inow a ounted for using a momentum

theory-based model [28 ℄. A detailed view of the

mainrotor hubisshowninFig.3.

The airframe dynami s are modeled using the

CMS approa h, with eight stru tural modes,

ho-senamongthoseinthefrequen ybanduptoabout PSfragrepla ements

pit hbearing

pit hhorn

pit hlink

mast

laghingewithdamper

aphinge

bladeroot

swashplate

Figure3: Detailedviewofthemainrotor hub.

30 Hzthat show onsiderable modal parti ipation

of the main and tail rotor, and pilot and o-pilot

seatsatta hmentpoints.

The servoa tuators that ommand the pit h of

the main rotor blades are modeled using

se ond-order transfer fun tions, to provide the

appropri-ate ontrolbandwidthandphasedelaybetweenthe

ontroldevi emotionandthea tualbladepit h.

2.5. Coupled Pilot-Vehi le Model

The oupledmultibodypilot-vehi lemodel isused

to assess the integrability of the detailed

biome- hani al model within a nonlinearaeroservoelasti

simulationoftheheli opter.

TheCMSmodelofthepilot'storsois onne ted

to the CMS model of the airframe at a lo ation

orrespondingtothepilot'sseat. Thein eptorsare

also onne tedto theairframe's CMSmodel

rela-tive to the pilot's seat position. The rotation of

thein eptorsisfedintothemainrotor ontrol

sys-teminformofsignalsproportionaltotherequested

swashplate motions, and added to the values

re-quiredto trim theair raftandthose generatedby

theSCAS.

3. RESULTS

Inthefollowing,resultsobtainedwiththeproposed

detailedmultibodymodelofthepilotarepresented.

The o kpitgeometry islooselyinspiredto thatof

theHELIFLIGHT-R ightsimulatorin useat the

0.0001

0.001

0.01

0.1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(a)50%ref. oll.,fore/aftex itation

0.0001

0.001

0.01

0.1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(b)90%ref. oll.,fore/aftex itation

1e-05

0.0001

0.001

0.01

0.1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

( )50%ref. oll.,lateralex itation

1e-05

0.0001

0.001

0.01

0.1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(d)90%ref. oll.,lateralex itation

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(e)50%ref. oll.,verti alex itation

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(f)90% olle tive,verti alex itation

Figure4: Colle tive ontrolin eptormotionforlongitudinal,lateraland verti alex itationat50% and

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(a)Fore/aft y l.,fore/aftex itation

1e-05

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(b)Lateral y l.,fore/aftex itation

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

( )Fore/aft y l.,lateralex itation

1e-05

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(d)Lateral y l.,lateralex itation

0.0001

0.001

0.01

0.1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(e)Fore/aft y l.,verti alex itation

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

PT

RT

FT

(f)Lateral y l.,verti alex itation

Figure5: Fore/aft y li ontrolin eptormotionforlongitudinal,lateralandverti alex itationforarms

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

10%

50%

90%

(a)Fore/aft y l.,fore/aftex itation

1e-05

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

10%

50%

90%

(b)Lateral y l.,fore/aftex itation

1e-05

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

10%

50%

90%

( )Fore/aft y l.,lateralex itation

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

10%

50%

90%

(d)Lateral y l.,lateralex itation

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

10%

50%

90%

(e)Fore/aft y l.,verti alex itation

1e-05

0.0001

0.001

0.01

0.1

1

1

10

radian/(m/s^2)

-180

-135

-90

-45

0

1

10

deg

Hz

10%

50%

90%

(f)Lateral y l.,verti alex itation

Figure6: Fore/aft y li ontrolin eptormotionforlongitudinal,lateralandverti alex itationforarms

Control

Thisse tionpresentstheresultsoftheinvoluntary

(andreexive) a tionof thepilotonthe olle tive

ontrol in eptorthat is aused by vibration ofthe

o kpitalongthesurge,sway,andheavedire tions.

Figure 4 shows the frequen y response of the left

armin termsof olle tive ontrolrotation. Figures

(a),( ),and(e),ontheleft,referto50% olle tive

referen e position, whereas Figures (b), (d), and

(f), on the right, referto 90% olle tive referen e

position. Figures (a) and (b) refer to ex itation

alongthesurgedire tion;Figures( )and (d)refer

to ex itation alongtheswaydire tion; Figures (e)

and(f)refertoex itationalongtheheavedire tion.

Thelatter asewasalreadypresentedanddis ussed

in previous works. Figures (a) to (d) show that

olle tiveisalsoae tedbymotionintheplaneof

thevehi le,although the amplitudeof themotion

isnearlyoneorder ofmagnitudesmallerthanthat

ausedbyex itationalongtheheavedire tion.

3.2. Involuntary Pilot A tion on Cy li

Control

This se tion presents the results of the

involun-tary(andreexive)a tionofthepilotonthe y li

ontrol in eptorthat is aused by vibration ofthe

o kpitalongthesurge,sway,andheavedire tions.

Figure5 showsthefrequen yresponseoftheright

arm in terms of y li ontrol fore/aftand lateral

rotation. Figures (a), ( ), and (e), on theleft,

re-fer to fore/aft rotation, whereas Figures (b), (d),

and(f),ontheright,refertolateralrotation.

Fig-ures(a)and(b)refertoex itationalongthesurge

dire tion; Figures ( ) and (d) refer to ex itation

along thesway dire tion; Figures (e) and(f)refer

toex itationalongtheheavedire tion. Thegures

show that the magnitude of both omponents of

y li ontrol rotation are similarly inuen ed by

both omponents of horizontal ex itation;

ex ita-tionalongthe heavedire tion provideslower

ex i-tation. Analogous resultsin Figure 6 alsoin lude

themodelofthetorso.

3.3. Coupled Pilot-Vehi le Model

Figure7showsthemotionofthemainrotorduring

Colle tive Boun e, an instability hara terized by

theintera tionbetweenthemainrotor oning

mo-tion,theheavemotionofthevehi le,andthe

bio-dynami feedthroughofthepilot'sleftarmholding

the olle tive ontrolin eptor. Colle tiveboun eis

en ountered after in reasing the gearing ratio

be-0deg 72deg 144deg 216deg 288deg 360deg 432deg

Figure 7: Frames of main rotor motion taken at

azimuthin rementsof72degduringa y leof

ol-le tiveboun eos illationaftertheinstability

devel-opedintoa limit y leos illation.

tween the motion of the ontrol in eptor and the

swashplate motion to less than twi e the nominal

value.

Figure8presentspreliminaryresultsofthesame

oupled heli opter-pilot model related to motion

about the roll axis. The system is perturbed by

for ing a lateral y li doublet. The `baseline'

re-sponse isobtained by notfeeding the in eptor

ro-tationintothe ontrolsystem;the`G=*'responses

are obtained by feeding the thein eptor rotation.

`G=1' onsidersthenominalgearingratio,whereas

`G=1.6' refers to a gearing ratio 60% larger than

nominal. For this problem, no instability is

ex-pe ted.

4. CONCLUSIONS

A biome hani al model of a heli opter pilot's

up-per portion of the body is presented. The model

in ludesthetorso,thehead,andbothupperlimbs.

Thepilotmodelisusedto hara terizebiodynami

-0.04

-0.02

0

0.02

0.04

0.06

0.08

8

10

12

14

16

18

20

Roll rate, rad/s

Time, s

baseline

G=1

G=1.6

(a) Rollrate

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

8

10

12

14

16

18

20

Roll accel., rad/s

2

Time, s

baseline

G=1

G=1.6

(b)Rolla eleration

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

8

10

12

14

16

18

20

Lateral, deg

Time, s

baseline

G=1

G=1.6

( )Lateral y li rotation

Figure 8: Response to perturbation abouttheroll

axis.

ofthe o kpit. Thepilotmodelisalso oupledwith

adetailedmultibodymodelofamediumweight

he-li opter. Coupledsimulationsare ondu tedto

as-sess the feasibility of using a detailed pilotmodel

within a urate time mar hing simulations of

de-tailedheli optermodels.

ACKNOWLEDGMENTS

The authors a knowledge the ontribution of

Mr. Filippo Tunesi to the implementation of the

model of the torso. The resear h leading to

these results has re eived funding from the

Euro-peanCommunity'sSeventhFrameworkProgramme

(FP7/2007-2013)undergrantagreementN.266073.

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