Simulation of helicopter dynamics with external suspended loads

37

th

European Rotorcraft Forum

Paper n. 125

SIMULATION OF HELICOPTER DYNAMICS

WITH EXTERNAL SUSPENDED LOADS

Paolo Marguerettaz

Giorgio Guglieri

Politecnico di Torino - Dipartimento di Ingegneria Aeronautica e Spaziale

Corso Duca degli Abruzzi 24, 10129, Torino, Italy

paolo.marguerettaz@polito.it; giorgio.guglieri@polito.it

A

BSTRACT

The present work outlines a short review of available references and technical papers on the flight dynamics of a helicopter carrying a suspended load. A simplified but comprehensive model for helicopter and external suspended load, based on the linear superposition of effects, is defined. This model is then used to evaluate the impact of helicopter configuration (articulated rotors with different state-space representations) and slung load model (pendulum or 6-DOFs suspended body, both spherical and streamlined) on overall system dynamic stability. Impact of load parameters (drag area, mass, length and elastic properties of the suspension line) on the stability of helicopter modal response is also evaluated. Finally the effect of helicopter attitude/rate and suspended load force feedback on the stabilization of the in-flight release phase of the payload is verified.

N

OTATION

a Acceleration A Cable cross section

CD Drag coefficient

CL Lift coefficient

CM Pitching moment coefficient

CN Yawing moment coefficient

CS Sideforce coefficient

D Drag forces vector

E Young modulus of the cable

f Residual

F Force vector

g Gravity acceleration i, j, k Unit vectors along x, y, z axes Jx, Jy, Jz, Jxz Moments of inertia

KG Gravity forces vector

l Load length

L Nominal cable length M, N Moments w.r.t. y,z axes

m Mass

p, q, r Angular speed w.r.t. x,y,z axes

r Radius

R Position vector

S Reference area

u, v, w Velocity components along x, y, z axes

V Velocity vector

X, Y, Z Forces along x, y, z axes [A] State space helicopter matrix

[LBE] Rotation matrix from body to inertial axes

[X] States vector ΔL Elongation vector (cable) α Angle of attack

β Angle of sideslip

δ Command input

Ω Angular velocities vector φ, θ, ψ Euler angles

ρ Air density

ζ Damping ratio

Superscripts and Subscripts

˙ First derivative

¨ Second derivative

[ ]T _{Transposed vector/matrix operator}

[ ]-1 _{Inverse matrix operator}

A Aerodynamic

B Body frame

C Cable

crit Critical

CG Centre of mass

E Ground fixed inertial frame

el Elastic

eff Effective

F Fuselage

H Helicopter

L Load

LS Suspension point ( load) ref Reference

x, y, z x, y, z axes

2

I

NTRODUCTION

Carrying external suspended loads is a typical helicopter mission. Both military and commercial operators widely exploits the capabilities of helicopters to rapidly move heavy and bulky loads in impervious locations. Logging, construction, fire fighting, search and rescue, tactical transportation are only some of the possible missions in which a helicopter carries a suspended load. Unfortunately, suspend load adds its aerodynamics, rigid body dynamics and elastic suspension dynamics to that of the bare airframe helicopter. Less than satisfactory handling can result from the combined systems and flight envelope can be significantly degraded with great concern on safety of operations. In fact external suspended load operations account for more than 10% of helicopter accidents, often with severe consequences [1]. A careful study of helicopter dynamics and the assessment of flight and handling qualities is therefore vital for safe operations.

Helicopter dynamics with external suspended load has been widely investigated since the extensive helicopter use in the Vietnam war in the ’60s and ’70s. Early studies focused mainly on hover or low speed flight dealing with reduced order helicopter models, modelling the slung load as a pendulum and neglecting aerodynamics effects [2]. Results showed a stable pendulum mode, but, in some combination of load weight and cable length, helicopter instability could arise. Further works investigated the precision hover with slung load and verified that conventional stability augmentation systems were not up to the task, thus different possible stabilization techniques were studied. Better results were obtained by feeding back to the cyclic the relative motion of load and helicopter [3]. A theoretically good alternative stabilisation scheme required the active displacement of the suspension point, but practical implementation was not explored [4]. Beside electronic stabilisation, appropriate piloting techniques were, also, investigated for various manoeuvres [5]. More recent studies address stability with more complex models. Ref. [6] develops a stability analysis based on a state space helicopter model decoupled in longitudinal and lateral-directional planes. The load is modelled as a pendulum affected by isotropic drag and suspended by an inelastic cable. Results showed stability dependency on both cable length and load weight with the possibility of mildly unstable modes at the increasing of weight and cable length. In Ref. [7] full nonlinear rigid body equations for helicopter dynamics and rotor flap dynamics were derived and then linearised for stability study. Cable length, position of the suspension point with respect to the helicopter centre of mass and load weight all affected stability. Depending on the combination of parameters some modes could experience weak instability.

Most of the previously described studies neglected the aerodynamics of the load because they were focused on hover or low speed flight. Slung loads usually are bluff

bodies and may experience instability due to unsteady flows. Studies conducted on containers and cylindrically shaped loads in forward flight showed that increasing cable length, load weight and speed improved stability [8]. These results were only partially confirmed by other works which pointed out that longer cables were destabilizing, but discrepancies can be an effect of the different aerodynamics of the load [9]. Despite most works try to address specific cases, it is generally possible to say that high drag proves to be destabilizing and lateral-directional motions are more affected by load dynamics than longitudinal ones. This is confirmed in Ref. [10] where extensive flight test and frequency response obtained by system identification show that increasing load weight reduces lateral bandwidth, while the longitudinal one is less affected. Ref. [11] analyses helicopter dynamics with suspended load in forward and turning flight. The proposed helicopter model is fully non linear, includes single blades flapping/lagging and rotor inflow and has been validated with flight test data [12]. The load is modelled as a pendulum affected by isotropic drag and suspended by an inelastic cable. Results show that pendulum modes can easily couple with helicopter Dutch roll leading to a degradation of flying qualities while effects on longitudinal motions are much less relevant. Unsteady aerodynamic behaviour of specific loads, in particular containers, has been widely investigated with simulation, wind tunnel testing and flight test [13][14]. It is known that external load instability can reduce safe flight envelope well below limits due to power loading. Ref. [15] provides means to passively stabilise a container, effectively restoring useful flight envelope up to power limits.

Many studies focused on external load modelling. In particular Ref. [16] describes in detail a formulation valid for arbitrary number of loads, suspensions lines and even helicopters. Ref. [17] proposes an interesting formulation to describe a generic slung load system taking into account different suspensions combination and cable collapse and tightening.

Helicopter handling qualities are widely addressed in Ref. [18]. Ref. [19] proposes qualitative and quantitative handling qualities criteria that specifically apply to suspended load operations. In particular, degraded visual environment operations with loads up to 1/3 of the helicopter mass are investigated, because, due to experience, they are considered the most demanding conditions. The quantitative criterion prescribes a lower limit in the available longitudinal and lateral-directional bandwidths. If the bandwidth is superior to the limit, and the helicopter without external load has Level 1 rating on the Cooper Harper scale in the performed manoeuvre, Level 1 rating is assured also with the external load. Below the bandwidth limit, Level 2 rating is still possible if the original helicopter has Level 1 rating. The authors recognise that it is not possible to ascribe a Level 3 rating due to the effects of the external load alone.

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M

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P

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M

ATHEMAT r models c approximatio al and heave y coupled as tors. Results p estricted to a possible to pe any case, whe a higher ord he transformat itioning of elicopter and e eakly coupled at higher orde s, has a mode cy modes o damping of th hange by mo amics are taken

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W

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M

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such as rotor he stability of ft and the utch roll, and t 5 % when r t). Hence a qu uselage states

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d the slung loa

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this study the h nine states mmed conditi

ed. In the sol efficients are tion, evaluatin gles in body ax

[ ]

XH = e system is de here X is theH trix. ree additional ss position in

[ ] [

VHE = x ere LBE is the ed frame. ternal load as o approaches both cases on nt on the helic load is mode pposed concen m a single po pendulum is delled as inex drag [11]. stem geometr cribed by ϕ_L

ween the cab pect to suspen

umber

1 – Helicopters

helicopter is m s. State spac ons for diffe lution process used to recon ng linear and xes. The state

[

u v wH, H, H,p fined as:

[

H X ⎡ ⎤ = ⎣ ⎦ e derived state equations ac an inertial fra

]

, , T HE HE HE x y z = rotation matri s a pendulum have been us ne suspension copter and on lled as a sphe ntrated in the oint. The only an isotropic xtensible, weig Fig. 1 – Syste ry is given , the azimuth le and the z nsion point is d 4 main character modelled as s ce matrices erent load an s helicopter st onstruct the n angular veloc vector is: , , , , H H H H p q r φ θ

[ ][ ]

A XH es vector and ccount for hel ame. These are

[

, BEH HB L u ⎡ ⎤ = ⎣ ⎦ ix from body m sed to model t line only is c ne on the load erical pendulu centre of mas y aerodynamic drag. The su ghtless and do em geometry in Fig. 1. L h angle, and b axis. Position defined as: 6 ristics state space mo are obtained nd forward fl tate space ma nine equations cities and attit

]

, T H H θ ψ A the state sp licopter centre e, in matrix fo

]

,vHB,wHB T axes to a gro the external lo connected to d. In the first c um with the m ss and suspen c force acting uspension lin oes not contrib

Load position by θ_L, the an n vector RG_Lw odel d in ight atrix s of tude (1) (2) pace e of orm: (3) und oad. one case mass nded g on e is bute n is ngle with

4

sin cos sin sin sin

L L L H L L H L H

RG = −L θ ϕ iG +L θ ϕ Gj +L θ kG (4) The position of the suspension point RH

G

with respect to the centre of gravity of the helicopter is:

H H H H H H H

RG =x iG +y jG +z kG (5) The absolute velocity VG_L of the load is:

L CG R R

VG =VG + + Ω × G G ₍₆₎

where R R= H +RL

G G G

is the position vector of the load with respect to the centre of mass of the helicopter and

B B B

pi qj rk

Ω =G G + G + G is its angular velocity. The absolute acceleration of the load is:

(

)

2

L CG R R R R

aG =aG + + Ω × + Ω × + Ω G G G  G× Ω×G G ₍₇₎

where aG_CG is the acceleration of the centre of mass of the helicopter. The weight vector is defined as:

(

sin sin cos cos cos

)

G F H F F H F F H

FG =mg − ϕ iG + ϕ θ Gj + ϕ ϕ kG (8) whereϕ_F andθ are the roll and pitch attitudes of the _F helicopter fuselage. The aerodynamic drag is given by:

1 2

L D

DG = ρV VC SG G (9)

where CD is the drag coefficient of a sphere (CD=0.5) and

Sis the sphere cross section.

By enforcing moment equilibrium about the suspension point a system of three second order differential equation in

L

θ and ϕ is obtained (here in matrix form): _L

(

)

0

L L G L

R × ma F D

−G − G + G + G = (10)

Any two of these equations is sufficient to compute the solution. The force and the moment applied by the load to the helicopter are:

H L G L H H H F ma F D M R F = − + + = × G _G G G G G G (11)

As a remark the differential equations for the pendulum type external load are singular when the cable is aligned to helicopter vertical. This slung load model is in some way limited considering that the elasticity of the cable is neglected. This last point prevents the investigation of the vertical bounce phenomenon particularly significant for light helicopters. This limitations are overcome by the following 6-DOFs rigid body model.

External load as a rigid body

The second approach treats the external load as a rigid body. Nine full non linear equations evaluates linear velocities, angular rates and attitude angles. Three additional equations account for the load centre of mass position in a reference

frame. Twelve first order non linear differential equations fully describe the load behaviour. The cable is modelled as elastic but without mass and no aerodynamic effects. A small damping is added.

The six non linear first order differential equations describing rigid body motion are the following:

sin( ) sin( ) cos( ) cos( ) cos( ) ( ) ( ) ( ) L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L u X m v r w q g v Y m w p u r g w Z m u q v p g p L Jx q r Jz Jy Jx q M Jy p r Jx Jz Jy r N Jz p q Jy Jx Jz θ φ θ φ θ = + − − ⎧ ⎪ = + − + ⎪ ⎪ = + − + ⎪ ⎨ _{= − −} ⎪ ⎪ = − − ⎪ = − − ⎪⎩       (12)

The system is derived for the case in which principal moments of inertia of the load are known. Three cinematic equations are added to account for the attitude angles:

sin( ) tan( ) cos( ) tan( ) cos( ) sin( )

sin( ) cos( ) cos( ) cos( )

L L L L L L L L L L L L L L L L L L L L p q r q r q r φ φ θ φ θ θ φ φ ψ φ θ φ θ ⎧ = + + ⎪⎪ _{= −} ⎨ ⎪ _{= +} ⎪⎩    (13)

Finally three further equations account for load centre of mass position in an inertial frame. These are, in matrix form:

[ ] [

, ,

]

T

[

, ,

]

T

LE LE LE LE BEL LB LB LB

V = x y z _{= ⎣}⎡L ⎤_⎦ u v w (14) In the previous system of equations, XL,YL,ZL are the total

forces and LL, ML, NL the total moments acting on the load.

Defined as vectors: L A C L A LS C X F F M M R F = + = + × G G G G G G G (15) Where FA G and FC G

are respectively the total aerodynamic forces and the cable forces along each axes,MG_Aare the aerodynamics moments andRG_LSis the position of the suspension point on the load with respect to the load centre of mass defined as:

LS LS L LS L LS L

RG =x iG +y jG +z kG (16) The elastic force along the cable FCel is obtained as follows:

Cel L F EA L Δ = − G G (17) where E is the elastic modulus of the material, A is the cross

section, L is the nominal length of the cable and LΔG is its elongation. Elongation is obtained by differencing the cable effective length Leff

G

and the nominal cable length LG:

eff

L L

L

5 where Leff

G

is the difference of the position vector of the suspension point XHE and the position vector of the load

centre of mass XLE expressed in an inertial frame:

eff HE LE

LG =XG −XG (19)

The force due to the cable damping is obtained in a similar way:

C

FG_ζ = Δζ LG (20)

where ΔLG is the difference of the velocity vector of the suspension point VHE

G

and the velocity vector of the load centre of mass VLE

G

expressed in an inertial frame:

HE LE

L V V

Δ =G G − G (21)

and ζ is the damping ratio of the cable defined as:

2 L crit m EA L ζ ζ ζ = (22)

where ζ ζcritis the ratio of the damping over the critical

damping (ζ ζcrit=0.02) and mL is the load mass.

A cable applies a force only if stretched. If the instantaneous cable length is below the nominal length the cable doesn’t apply any force on the helicopter, thus the total forces and moments applied by the load to the helicopter are:

0 0 0 0 H Cel C H H H H H F F F L M R F F L M ζ ⎧ = + ⎪ Δ > → ⎨ = × ⎪⎩ ⎧ = ⎪ Δ ≤ → ⎨ = ⎪⎩ G G G G G G G G G G (23)

The great advantage of rigid body formulation is that it allows to take into account aerodynamic effects and inertial properties of the load. The main disadvantage is the increased dimension of the system of differential equations needed to describe the system.

Spherical load

For comparison purposes the first load studied is modelled as a sphere. As in the previous case only isotropic drag applies to the load. Inertial properties of the body are:

2 2 5

XL YL ZL L L

J =J =J = m r (24)

where rL is the radius of the sphere. As in the previous case

aerodynamic forces and moments reduce to: 1 2 0 A L D A F D V VC S M ρ = = = G G G G G (25) Finned body

The second type of load studied is a streamlined finned body with cruciform tail surfaces. To determine inertial properties

the body is considered an ellipsoid with principal semi-axes with the following properties:

L L r b c b c a l a = = = < = (26)

where a, b, c are respectively the principal semi-axes along x, y, z. Hence, considering uniform density, the inertial properties of the body are:

(

)

2 2 2 z 2 5 1 5 x L L y L L L J m r J J m l r = = = + (27)

where rL, lL and mL are respectively the maximum radius, the

length and the mass of the body.

Aerodynamic forces acting on the body are:

(

)

2 2 2 0 2 2 1 2 1 2 1 2 L D D D L S L L L L S L L S D V SC C C k C C L V SC C C C C S V SC α α ρ ρ α β ρ = = + + = = = = (28)

where due α is the angle of attack, β is the angle of sideslip

and 2

L

S=πr is the body cross section. Aerodynamic symmetry is assumed.

Aerodynamic moments are:

2 2 1 2 1 2 L M M L A N S A L N M V SC _{C C x} C C x N V SC ρ ρ = ₌ = = (29)

where xA is the distance between the centre of mass of the

body and its aerodynamic centre. Due to the axial symmetry no rolling moment is considered.

Stability Augmentation System (SAS)

Helicopters usually show a mildly unstable response, thus, SAS is often fitted to enhance stability and controllability. Two different implementations are applied to the present model in order to investigate their performance during the release phase of an external load (drop test).

SAS 1

The first system considered is a conventional SAS in which the longitudinal attitude angle θ and the relative angular rate q are used as a feedback to the longitudinal cyclic, while the roll angle φ and the roll angular rate p for the lateral cyclic. The controls are:

( ) ( ) ref q lon ref p lat K K q K K p θ φ δ θ θ δ φ φ = − + = − + (30) SAS 2

The second SAS is similar to the first one but a further loop is closed by feeding back the variation of the vertical force

6 (load cell measurement at the suspension point) to the collective pitch. Changing the collective pitch leads to a change in the torque applied by the rotor to the fuselage, with a consequent yawing motion. To avoid that, mixing with the pedal input is provided. The complete control vector is: 0 0 ( ) ( ) ( ) w ref w ref q lon ref p lat ped K w w K w K K q K K p θ φ δ δ θ θ δ φ φ δ δ = − + = − + = − + =   (31) where: 0 t H H H H Z w m Z w m Δ = Δ =

∫

 (32)

where w is the climb rate induced by the release of the external load, w is the vertical acceleration and ZH is the

vertical force applied by the load to the suspension point.

S

OLUTION

T

ECHNIQUE

To account for load effects, helicopter equations have to be modified. In particular the differences between the equilibrium forces and moments and the actual forces and moments applied to the helicopter by the suspended load must be added to the vehicle dynamics. The first six helicopter equation are modified as follows:

9 9 1, 4, 1 1 9 9 2, 5, 1 1 9 9 6, 3, 1 1 H i i H i i i i H H i i H i i i i H H i i i i H i i H X u A x p L A x m Y v A x q M A x m Z r N A x w A x m = = = = = = ⎧ ₌ Δ ₊ ⎧ _′ = + ⎪ ⎪ ⎪ ⎪ ⎪ _Δ ⎪ ⎪ _{= +} ⎪ _{= Δ +} ⎨ ⎨ ⎪ ⎪ ⎪ _Δ ⎪ ′ = + ⎪ = + ⎪ ⎪ ⎪ ⎩ ⎩

∑

∑

∑

∑

∑

∑

      (33) where: 2 2

1

1

xz_H xz_H H H H H xH zH H H xzH xzH x_H z_H x_H z_H

J

J

L

N

N

L

J

J

L

N

J

J

J J

J J

Δ +

Δ

Δ

+

Δ

′

=

′

=

−

−

(34)

WhereΔL_H,ΔM_HandΔN_H are already normalised with their respective moments of inertia Jx_H, Jy_Hand JzH. It is

now possible to linearise the full system of differential equations composed by 9+3 helicopter equations and, depending on the chosen model, the 4/9+3 suspended load equations. Linearization is performed through the residues method. Starting from a trimmed condition, the states, the controls and the derivative vector are iteratively perturbed. It is then possible to reconstruct a linear system of differential equations in the following form:

[ ]

E dx

{ }

 +

[ ]

A dx1

{ }

+

[ ]

B du1

{ }

=0 (35) where [E], [A1] and [B1] matrices are built as follows:

[ ]

11 01 1 01 1 1 0 0 n n n nn n f f f f x x A f f f f x x − − ⎡ ⎤ ⎢ _{Δ Δ} ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ _{− −} ⎥ ⎢ ⎥ Δ Δ ⎣ ⎦ " # % # " (36) where: ( , , ) f = f x x u (37)

is the residual of the single differential equation. The impact of the increment Δx in the range 10-4 _{÷ 10}-1 _{was found to be}

negligible in present model formulation. Hence, it is possible to derive a state space system:

{ }

[ ] [ ]

{ }

[ ] [ ]

{ }

{ }

[ ]

{ }

[ ]

{ }

1 1 1 1 dx E A dx E B du dx A dx B du − − = − − = +   (38)

The resulting formulation is used to assess the dynamic stability of the system by modal response analysis.

The non linearised equations are used to evaluate short term time response. In particular helicopter dynamics after impulsive load separation is assessed.

R

ESULTS

The nominal characteristics for the reference helicopters are given in Tab. 2. For the present analysis RG_H =RG_LS =0.

Helicopter 1 Helicopter 2 mTOT = mH + mL [kg] 6791 15876 mL [kg] 1360 3175 mL/mTOT [%] 20 20 L [m] 5 5 CDS [m2] 0.5 0.5

Tab. 2 – Helicopter reference conditions

Two types of analysis are performed: I) a preliminary assessment of dynamic stability of the coupled system in forward flight and II) an example of time domain response to perturbation for different levels of stability augmentation. All the stability plots (real and imaginary parts of the eigenvalues) assume that the total weight mTOT is constant

i.e. the weight of the slung load is subtracted to the bare airframe nominal weight (with the exception of Fig. 8). The stability matrix [A] and the control matrix [B] are multiplied by a scaling factor m_TOT/

(

m_TOT −m_L

)

in order to correct the sensitivity of the system as a consequence of helicopter mass reduction. The plots include the boundaries for pitch and roll oscillations as addressed by Ref. [18]. These requirements apply only to the helicopter poles, and not to the load poles.

Th in F F F Th pen veh the dam [11 pen osc e effect of slu Figs. 2÷4 for H Fig. 2 – Helicopt mL = 0; 1 Fig. 3 – Helicopte mL = 0; 1 Fig. 4 – Helicop mL = 0; 1 e poles of ndulum type m hicle (phugoid e suspended mped separat 1]) with its ndulum equa cillatory mod

ung load mode Helicopter 1 a ter 1, pendulum 1360 kg, L = 5 m er 1, 6 DOF mod 1360 kg, L = 5 m pter 1, 6 DOF mo 1360 kg, L = 5 m the coupled model in Fig. d and Dutch ro load, which te oscillatory natural frequ ation ωn = de (Dutch ro el on stability and Figs. 5÷7 model, mTOT = m m, CDS = 0.5 m2, μ

del, spherical loa m, CDS = 0.5 m2, μ

odel, finned load m, CDS = 0.5 m2, μ system are 2. The oscilla oll) exhibit a m is characteri response (a uency matchi g L . The oll) degrades plots is prese for Helicopte mL + mH = 6791 k μ = 0 ÷ 0.2 ad, mTOT = 6791 k μ = 0 ÷ 0.2 d, mTOT = 6791 kg μ = 0 ÷ 0.2 plotted for atory modes of marginal effec zed by a lig s shown in ing the class

lateral-directi its stability 7 ented er 2. kg, kg, g, the f the ct of ghtly Ref. sical ional for high for rigi for by Not aero (as with plan aero usu may stab con the is m the cha (eig the mai is m load deg (eig the Fig her advance r the equivalen id body mode phugoid and lightly dampe te that these odynamics of in Fig. 2). In h equivalent m nes. The pres odynamics, w ually character y induce non bility of the nsidered. The previous case mainly driven helicopter (v aracterized b genvector: wL, aerodynamic inly affecting missing i.e. de d). In all t gradation of i genvector: uH, suspended loa Fig. 5 – Heli mL = 0; 3 g. 6 – Helicopter mL = 0; 3 ratios when th nt spherical lo l (see Fig. 3) Dutch roll, w ed non oscillat last results f the load is s Fig. 4, the lo mass propertie sent analysis while in the rea rized by sepa n linearities a slung load. oscillatory re es, confirming by the force vector aligned by an oscil qL, θL) with m damping is st lateral-directi stabilizing the three cases, ts stability w θH) further d ad. icopter 2, pendul 175 kg, L = 5 m, r 2, 6 DOF mode 175 kg, L = 5 m, he load is pre oad obtained w reproduce ve while the load atory modes (r include cabl still modelled oad is replace es, stabilized b is performed al case the sus aration and w and changes

No aerodyna esponse of the g that the cou transmission d with the cab

llatory short marginal dyna till neglected ional respons e spiral mode the vehicle with increasin destabilized by ulum model, mTO , CDS = 0.5 m2, μ

el, spherical load , CDS = 0.5 m2, μ

esent. The res with the 6 DO ery similar tre d is characteri real eigenvalu e elasticity. T as a drag ve ed by an ellips by cruciform t assuming lin spended system wake patterns in the dyna amic damping e vehicle matc pling mechan from the load ble). The load t period m amic stability - and real mo e (dihedral ef of the suspen also shows ng forward sp y the presence OT = 15876 kg, μ = 0 ÷ 0.2 d, mTOT = 15876 k μ = 0 ÷ 0.2 sults OFs ends ized ues). The ctor soid tail-near m is that amic g is ches nism d to d is mode - as odes ffect nded s a peed e of kg,

Fig Th and dif mo fro der Re res lev the dyn Fi Th hov for eig the mo con use deg mo in beh ela mo . 7 – Helicopter mL = 0; 3 e results for H d Dutch roll s fferent behavio odal responses om Helicopter rive from par f. [21]) interp sults confirm t vel of comple e load while namic behavio ig. 8 – Helicopte load m mL = 0; 680 e effect of tot ver is outlined r either onboa genvalues for e external load odel. The data

ndensation of ed in Ref. [11] gradation in h odel. Quite pro hover alters haviour of t asticity of the odel. 2, 6 DOF model 3175 kg, L = 5 m Helicopter 2 d shows lower l

ours for increa s of the bare r 1. As a rem rametric mod polated for int that the model exity only affe the moderate our is substan

er 1, bare airfram models, mTOT = 67

0; 1360; 2040 kg,

tal mass mTOT

d in Fig. 8, in ard or external increasing ba d cases for bo a for the bare f the higher ]. The 6DOFs hover differe obably, the bo in a more the helicopter e cable, negl l, finned load, mT m, CDS = 0.5 m2, μ differ as the t levels of dyna asing advance airframe are mark, the data dels based on termediate for l for the suspe fect the rigid b

e coupling wi tially unchang me, pendulum an 791; 7470; 8149; , L = 5 m, CDS = T on phugoid n which the po l weight incre are airframe m oth pendulum airframe deri order model s type model p ently from th ouncing of the evident way r. This is e lected for the

TOT = 15876 kg, μ = 0 ÷ 0.2

trend for phug amic stability e ratios. The o stable, differe a for Helicopt n flight tests rward speeds. ended load an body respons ith the helico ged.

nd 6 DOF spheri 8828 kg, 0.5 m2_{, μ = 0}

and Dutch ro oles are comp ease. The tren mass differs f m and 6DOFs ive from dyna

for Helicopt predicts a stab e pendulum e suspended m y the oscilla enhanced by e pendulum 8 goid and other ently ter 2 (see The nd its se of opter ical oll in pared nd of from type amic ter 1 bility type mass atory the type Som mL, sph syst Fig Fig. In F The heli susp deg high dyn imp F me relevant p , cable length herical type su tem for both p

g. 9 – Helicopter 1360; 20 10 – Helicopter mL = 0; 680; 13 Figs. 9÷10 the e level of co icopter (phug pended mass gradation of s her advance namics seems pact of modell Fig. 11 – Helicop 1360kg, parametric eff h L, drag area spended load, pendulum and r 1, pendulum m 040 kg, L = 5 m, 1, 6 DOF model 360; 2040 kg, L = e effect of susp oupling with goid and Dutc

ses. Large s stability on la ratios, while to be quite in ling of the sus

pter 1, pendulum L = 3; 5; 10 m, C fects were in a CDS and cab , comparing th d 6DOFs type model, mTOT = 679 CDS = 0.5 m2, μ l, spherical load = 5 m, CDS = 0.5 pended mass m the oscillator tch roll) is la slung loads ateral-directio e low freque nsensitive to t spended load i m model, mTOT = CDS = 0.5 m2, μ nvestigated (m ble damping) he stability of models. 91 kg, mL = 0; 68 = 0 ÷ 0.2 , mTOT = 6791 kg 5 m2_{, μ = 0 ÷ 0.2} mL is conside ry modes of arger for heav also induce onal response ency longitud their effects. is not evident. 6791 kg, mL = 0 = 0 ÷ 0.2 mass for f the 80; g, red. the vier e a for dinal The . 0;

Fig In pen of eff of dir and per sus cha the pen by res pay rea Fig . 12 – Helicopter mL = 0; 136 Figs. 11÷12 th ndulum reacts the oscillatory fects, the most

the pendulum ectional mode d shorter cabl rformed with spension (Fig. ange of cable e cable as the ndulum type m the angular sult derives fro

yload for the alistic represen Fig. 13 – He mL = 0; 136 . 14 – Helicopter mL = 0; 136 r 1, 6 DOF mode 60kg, L = 3; 5; 10 the effect of c s as expected y modes of th t evident cons m is the higher es, mainly vis les. Different h the 6DOF . 12), the resp

length (i.e. by e section is u model the attit displacement om the indepe 6DOFs mod ntation of the elicopter 1, pend 60kg, L = 5 m, C r 1, 6 DOF mode 60kg, L = 5 m, C

el, spherical load 0 m, CDS = 0.5 m able length L changing the he load. As in equence of ch r level of coup sible for highe tly, when the Fs model w ponse is quite y the change unchanged). N tude of the pa of the cable endent attitude el, probably p suspended loa dulum model, mT CDS = 0.5; 1; 2 m

el, spherical load CDS = 0.5; 1; 2 m d, mTOT = 6791 kg m2_{, μ = 0 ÷ 0.2} is presented. natural freque n other parame hanging the len pling with late er forward spe same analysi with the ela unaffected by of the stiffnes Note that, for ayload is enfo . Hence, this e dynamics of providing a m ad. TOT = 6791 kg, m2_{, μ = 0 ÷ 0.2} d, mTOT = 6791 kg m2_{, μ = 0 ÷ 0.2} 9 kg, The ency metric ngth eral-eeds is is astic y the ss of r the orced last f the more kg, In F effe the eige mil stab 6DO Fig m The dam prev mod heli sug neg of t The repr the perf refe step leve com deta are Figs. 13÷14 t ect is apparent present para envalues for b

dly to the dra bilization of t OFs model (F g. 15 – Helicopte mL = 0; 1360kg, L e effect of c mping ratio o vious results del) does actu icopter (both ggests that mo glecting its elo the stability an e 6DOFs mod roduce the tim

release phase formed for μ erence config p integrator h els of stabi mpared with t ails on the sta given in the p

Fig. 16 – Load Helicopter 1, mL = 0;

the role of dr tly hardly obs ametric chang both the vehic ag increment.

the load mod ig. 14). er 1, 6 DOF mod L = 5 m, CDS = 0 μ = 0 able damping f the suspens presented fo ually stabilize phugoid and odelling the c ongation rate m nalysis of helic del for the sus me-domain re e of the suspe μ = 0.1 as uration presen has been used

lity augment the natural re ability augmen previous sectio release (3D traj , 6 DOF model, f ; 1360kg, L = 5 m rag area CDS servable as, w ges (CDS = 0

cle and the lo The only rele des (real eige

del, spherical loa 0.5 m2_{, ζ/ ζ} crit = 0; 0 ÷ 0.2 g is plotted sion system or the 6DOFs e the oscillato Dutch roll m cable as a rig may preclude copter suspen spended load esponse of He ended load. T a starting co ented in Tab. d (Δt = 10-2 _s tation of th esponse of the ntation system ons. ectory): no SAS finned load, , mT m, CDS = 0.5 m2, is outlined. T ithin the limit 0.5 ÷ 2 m2_), oad respond v evant effect is envalues) for ad, mTOT = 6791 k ; 0.01; 0.02; 0.03 in Fig. 15. (neglected in s suspended l ory modes of odes). This p gid suspension the completen nded loads.

was also used elicopter 1 dur This simulatio ondition for 2. A fixed t s). Two differ he airframe e helicopter. m implementat , SAS 1, SAS 2. TOT = 6791 kg, , μ = 0.1 This ts of the very the the kg, 3, The n all load f the oint n or ness d to ring n is the time rent are The tion

Fi Fi Th div Fig the imp fro col atti init Fig

ig. 17 – Load rel Helicopter 1

mL = 0

ig. 18 – Load rel Helicopter 1

mL = 0

e short-term verge from equ gs. 16÷18). At e tendency to pulsive mass om the initial llective. Whe itude stabiliza tial flight para

g. 19 – Load rele 6 DOF model

lease (X-Z plane 1, 6 DOF model, 0; 1360kg, L = 5

lease (X-Y plane 1, 6 DOF model, 0; 1360kg, L = 5 response of uilibrium as s ttitude stabiliz abandon the i change but s level flight, a en collective ation (SAS2), ameters. ease (Helicopter l, finned load, m L = 5 m, CDS = trajectory): no , finned load, mT m, CDS = 0.5 m2 trajectory): no , finned load, mT m, CDS = 0.5 m2

the bare airfr soon as the loa zation (SAS1) initial trajecto still the altitud

as expected d feedback is the vehicle fo Euler angles): n mTOT = 6791 kg, m = 0.5 m2_{, μ = 0.1} SAS, SAS 1, SA TOT = 6791 kg, 2_{, μ = 0.1} SAS, SAS 1, SA TOT = 6791 kg, 2_{, μ = 0.1} frame is foun ad is dropped does compen ry induced by de response d due to untrim super-imposed ollows closely no SAS. Helicopt mL = 0; 1360kg, 10 AS 2. AS 2. nd to (see nsate y the drifts mmed d to y the ter 1, Fig Fig The is p stab stab any stra test this sim whi airf susp inte asse requ In t cou exte cha and sup Mo with forc attit g. 20 – Load rele 6 DOF model, g. 21 – Load rele 6 DOF model, e attitude resp presented in F bility augment bility of the t y general conc ategy propose t data is avail s time domain mulation mode ich the fidelity frame and th pended load ermediate mo essment of st uiring a very l

C

the present wo upled with a p ernal load m anging the type d the load pa perimposed in odal analysis o h the oscillato ce applied by tude dynamic ease (Helicopter E , finned load, mT L = 5 m, CDS = ease (Helicopter E , finned load, mT L = 5 m, CDS = ponse of the h igs. 19÷21, an tation is subst trajectory. Th clusion on the d, as no com lable for valid n analysis conf el of helicopt y of the simul he level of c is sufficien odels may be tability and c limited compu

C

ONCLUDIN ork a simple s endulum and model. The s e of helicopter arameters. Th the different c outlines that th ory dynamics y the cable i s of the suspe Euler angles): S TOT = 6791 kg, m = 0.5 m2_{, μ = 0.1} Euler angles): S TOT = 6791 kg, m = 0.5 m2_{, μ = 0.1} helicopter after nd it confirms tantially bene hese simulatio e validity of t mparison with dation purpos firms the avai ter and slung lation is prese complexity of ntly extended e helpful in control augme utational work NG

R

EMARK state space he then with a 6 system stabil er, the type of he impact of cases. he slung load s of the helico in the suspen ended load ha SAS 1. Helicopter mL = 0; 1360kg, SAS 2. Helicopter mL = 0; 1360kg,

r the load rele s that the leve eficial in term ons do not im the augmentat h reference fli es. Neverthel ilability of a li load system erved for the b

f model for d. This type the prelimin entation syste kload. KS elicopter mode 6DOFs suspen lity is evalua slung load mo advance ratio model is coup opter through nsion point. as a minor rol r 1, r 1, ease el of s of mply tion ight less, ight m, in bare the of nary ems, el is nded ated odel o is pled the The e in

11 the coupling of the two subsystems. Comparisons for different mass increases show that a direct increase of helicopter fuselage weight is not equivalent to suspending an additional mass underneath the vehicle.

Cable damping is apparently providing a source of additional dynamic stability to the coupled system. The comparison, between the pendulum type model and the 6DOFs type model for the slung load, points out the limitations of the first approach, in some way over simplifying the natural dynamics of the suspended rigid body.

Short term time domain responses, with different levels of helicopter stability augmentation, show that the proposed model, at least in its most complete formulation, is adequate to represent the impact of control design parameters on the response of the system. As a final comment, it is demonstrated that the 6DOFs type model for the suspended load may account for inertial and aerodynamics complexity of the slung load with very limited computational workload. Reported pilot experience validates, at least partially, the results obtained. In fact aerodynamic effects and cable length are known to have little effect on the dynamic behaviour of helicopter with suspended loads similar to those here considered (heavy weight, small CDS). On the

contrary helicopter dynamics in case of low density loads is much more influenced by aerodynamics and cable length. In particular short cables expose the load to the main rotor downwash. The implementation of the main rotor downwash in the present model would help to extend its validity to a wider range of external suspended loads. In any case validation with flight test data would be advisable for future developments of this research activity.

A

CKNOWLEDGMENT

This activity is part of a doctoral research program (Ph.D. in Aerospace Engineering at Politecnico di Torino) supported by AgustaWestland for which Riccardo Bianco Mengotti and Andrea Ragazzi are the industrial supervisors.

R

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