AIAA 92-0487 A Multi-Body Approach To Modeling Tilt-Wing Rotorcraft Dynamics P.J. O’Heron Dynacs Engineering Company, Inc.

D. Kunz McDonnell Douglas Helicopter Company

P. Nikravesh and A. Arabyan University of Arizona

30th Aerospace Sciences Meeting & Exhibit

January 6-9,1992 / Reno, NV For permission to copy or republish, contact the American lnstiie of Aeronautics and Astronautics 370 LEnfant Promenade, S.W., Washington, D.C. 20024

AIM-92-0487

A Multibody Approach to Modeling Tilt-Wing Rotorcraft Dynamics

Patrick J. O’Heron Dynacs Engineering Co. *

Donald L. Kunz Engineering Specialist t

Parviz E. Nikravesh Professor of Aerospace & Mechanical Engineering $

Ara Arabyan Assistant Professor of Aerospace & Mechanical Engineering 5

October 30, 1991

Abstract A model is presented which can be used to compute the highly nonlinear transient dynamics which are associ- ated with advanced rotorcraft conversion processes. A minimal coordinate formulation is used to compute the dynamic response of a tilting rotor. An enhanced aero- dynamics model is used which accounts for unsteadi- ness and nonlinearity in the near-wake aerodynamics, a dynamic uniform inflow model is used to compute the far-wake aerodynamics, and a flight control system is employed to compute the blade pitch settings that are necessary to achieve a desired flight path. The model is subjected to a demanding simulation flight path which illustrates that it can effectively perform vertical take- off, hover, tilt-wing conversion, and high-speed forward flight maneuvers. Example results are presented which illustrate the fidelity of the simulations, and the na- ture of the results which can be obtained. It is con- cluded that multibody dynamical models can effectively be coupled to aerodynamics and flight control models, and that the result can be used under a surprisingly wide variety of flight conditions.

Nomenclature - M : Mass matrix. - (P: Constraint Jacobian. - A: Vector of Lagrange multipliers. 4: Vector of absolute coordinates. - F : Vector of applied and centrifugal forces. -

*former MDHC Fellow t McDonnell Douglas Helicopter Company Member AIAA iUniversity of Arizona §University of Arizona

1 Copyright 0 1992 American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

R: P:

1

Vector of nonlinear acceleration terms. Velocity transformation matrix. Vector of generalized coordinates. Generalized mass matrix. Generalized force vector. Vector of Lagrange multipliers associated with the driving constraints. Vector of nonlinear acceleration terms associated with the driving constraints. States associated with aerodynamics model. Angle of attack. Dimensionless pitch rate. Normal force coefficient. Moment coefficient. Thrust coefficient. Assumed separation point. Rotor azimuthal postion. Dimensionless uniform component of induced inflow. Rotor speed. Advance ratio.

Introduction

Many modern rotorcraft designs, for example tilt-wing and tilt-rotor configurations, will achieve high speed for- ward flight by the use of tilting rotors. Such configu- rations operate in two distinct modes, helicopter mode which facilitates VTOL type maneuvers, and fixed-wing mode, which allows high-speed forward flight. h nude! which captures the dynamics of the conversion Iwt~vcn these operating states: ib discussed in the cwrriiL ~LOSX.

As is pointed out in [l], most rotor analysis tools rely on a set of equations of motion which are derived under simplifying assumptions. These assumptions are appli- cable to analyses of conventional helicopter configura- tions, but are typically violated during the conversion process which is associated with tilt-wing and tilt-rotor aircraft. For example, the rotor rpm may not be con- stant during the conversion, the hub will, in general, un- dergo large accelerations, and the blade response may not be periodic. Moreover, advanced root geometries, which may be designed to allow the rotor to be folded, may not be supported by conventional analysis pack- ages.

The need to relax these simplifying assumptions in order to undertake analyses of advanced rotorcraft con- versions is well-known, and has been pointed out in previous studies [l], [a]. One of the issues facing the dynamics community involves developing rotor analysis tools which can efficiently generate and solve the dy- namical equations which govern the motion of advanced rotor systems during the conversion process. The prob- lem is augmented by the fact that dynamics model must be coupled with an aerodynamics model which captures both near and far-wake effects, flight control systems must be included in the analysis, and the simulation CPU requirements must be minimized.

[l] and [a] present important first contributions to this issue. In these works a commercially available general-purpose multibody systems package is given sig- nificant enhancement, and the result is applied to a challenging conversion problem. The previous work fo- cused on the Trail Rotor Convertiplane, or TRC. In the TRC configuration main rotors are mounted to fixed- wing tips. During the conversion process, the rotors are tilted aft, the rotor rpm is decreased to zero, and the rotors are folded. The multibody dynamics model which was used for the simulation is cast in terms of a maximal set of absolute coordinates [3].

The current work differs in three main aspects. Firstly, the model is designed to simulate the conversion process which is employed in the tilt-wing configuration. In the tilt-wing configuration rotors are mounted to a wing which can tilt from a vertical to a horizontal ori- entation. The wing is locked in the vertical position for VTOL type maneuvers, and is tilted approximately 90' forward to enable conventional propeller-driven flight. The configuration is somewhat similar to a '1'-22 tilt- rotor, except that in the tilt-wing configuration the ro- tors are attached to a tilting wing.

The second difference between the previous work and the current study lies in the formulation that is used

to generate the equations of motion. The formulation is based on a minimal coordinate formulation that is commonly called the joint coordinate method [4]. Such reduced coordinate formulations can be expected to be more efficient than formulations which use a much larger set of absolute coordinates.

The third difference between the previous work and the current study is the nature of the aircraft model. In [l] and [2], only the tilting rotor system is modeled. In the current work a more complete aircraft model is used, which broadens the range of applicability of the model.

In the remainder of this work the multibody model of the aircraft is presented in some detail. The near and far-wake aerodynamics models are presented, and an autopilot-like flight control system is discussed. The entire model was originally presented in [5], and is ex- tensively validated therein.

2 Detailed Model Design

2.1 Multibody Rotor Model A multibody system typically consists of several rigid

and/or flexible bodies which are connected by a set of kinematic joints. Forces and constraints may be ap- plied to any of the bodies in the system. Well-defined methods exist by which the nonlinear equations of mo- tion which govern such systems can systematically con- structed and subsequently integrated numerically in the time domain. One approach, which uses a minimal set of relative joint coordinates, is the so-called joint coor- dinate method [4]. In this particular formulation, the system equations are constructed in a maximal coordi- nate space. A velocity-transformation matrix is then constructed, which is determined by the system topol- ogy, and is used to transform the equations of motion into a minimal coordinate space. The number of sys- tem equa.tions is reduced significantly by this transfor- mation. Thus, the computational effort that is required for their solution is also reduced. All of the constraints which are imposed on the system by kinematic joints are enforced by the velocity-transformation matrix. The approach has been used extensively in the past (see [6] for example), and is well documented [7].

Figure (1) depicts the multibody tilt-wing model that was used to generate the simulation results that are given below. In figure (1) the rotor assembly (A) is composed of four fully articulated blade assemblies (D and E) which are connected to a rigid hub (C). The ro- tor assembly rotates in the counter-clockwise direction (B) by the rotation of a mast (F) which is connected to

2

Figure

Figure 2: Schematic of the Model: Top View

(C). The rotation of (F) relative to the tilting wing (H) occurs about a revolute joint (G). The tilting wing (H) can rotate relative to the fuselage (L) about a revolute joint (J) in the direction which is given by (I). (L) pos- sess two translational degrees of freedom with respect to the inertial reference frame (M), and can, therefore, translate arbitrarily in the upper half-plane.

In figure (1) the tilting wing is in the vertical position, and the model is said to be in helicopter mode. Thus, as the rotor generates thrust the model can accomplish vertical flight and hover. As the wing is tilted about (J) the model is accelerated into forward flight.

Figure 3: Schematic of a Blade Assembly

and outboard of the pitch bearing is a lag hinge (R). The directions of positive flap, pitch, and lag are show by (0) (Q) and (S) respectively. A rigid blade (T) is connected to (S). The blade is fitted with several, 8 in the cases considered, Gaussian integration points (U) which are distributed appropriately about the center of mass (2). Each blade is fitted with a body fixed refer- ence frame (W) which is rigidly attached to (Z). The local body fixed axes s and y lie in the plane of (C) when the flap and pitch angles are zero. The blades are twisted about the body fixed y axis. The twist angle varies linearly as a function of the radial location. In order to model blade twist in subsequent calculations, the blade twist angle at each Gaussian integration point is evaluated, and a twisted reference frame (V) is at- tached to the appropriate integration point. So that vector quantities which are known in (W) can be eval- uated in (V) by a simple, temporally constant. matrix multiplication.

The multibody model contains 16 degrees of freedom. Two translation degrees of freedom are associated with the fuselage, one rotational degree of freedom is asso- ciated with the tilting wing, one with the azimuthal position of the hub. Each of the four blade assemblies possess three degrees of freedom: one degree of freedom required for flap. one for pitch, and one for lag.

The wing tilt angle, hub rpm, and blade pitch angles are constrained with time dependent ho~onomic con- straints. Thus, six algebraic equations of constraint are to be imposed upon the system. This is accomp~ishe~ by the use of Lagrange multipliers. A brief summary of the joint coordinate method is required to clarify this issue.

2.1.1 The Joint Coordinate Method

The equations of motion for a rigid multibody system consisting of .V bodies connected by a set ofjoincs ::an

The wing is tilted forward by driving constraint which governs the rotation Of the wing with respect to the fuselage. The rotor speed is regulated by use of a similar constraint which is applied to joint (G) in figure (1)- Figure (2) depicts a top view of the model.

The blade assemblies are shown schematically in fig- ures (1) & (Z), and blade assembly (D) is shown in detail in figure (3). Here the blade assembly is connected to the hub (C) by a revolute joint (called the flap hinge) (N). Outboard of the flap hinge is a pitch bearing (PI,

3

be expressed in terms of a maximal set of absolute co- ordinates [8] :

The matrix M is the mass matrix, 3 is the Jaco- bian matrix that is associated with the M holonomic equations of constraint. Such constraints may be im- posed on the system by kinematic joints, for example. The vector q consists of 6 x N absolute coordinates, and the vec& consists of a set of M Lagrange mul- tipliers which are associated with the generalized reac- tion forces. The 'vector y which appears in equation 1 contains the velocity dGpendent acceleration terms, and the vector E contains the applied generalized forces and generalized forces which are due to centrifugal ac- celeration terms. There exists a matrix l3, called the velocity-transformation matrix, which, maps the vector - q into the generalized velocity vector e:

were B is of dimension 6 N x IC, and the vector 1 is of dimension K, where K is the number of kinematic degrees of freedom associated with the system. It can be shown that:

Premultiplying equation 1 by BT, substituting the time derivative of equation equation 2, re-grouping the terms, and noting equation equation 3 gives:

(4) aT M B e = BT(F- M B 4)

or :

( 5 ) M $ = L

For the particular model that was presented above, the vector $ in equation 4 consists of the 16 degrees of freedom that were outlined above, and is commonly called the joint acceleration vector.

The joint accelerations that are associated with mo- tions (I) and (B) in figure ( l ) , and (P) in figure (3), are to be calculated by equations of constraint. The equations of constraint are given as functions of time:

which can be twice differentiated in the conventional manner:

Here @@ is the Jacobian matrix that is associated with equytion 6, and the contains the nonlinear ve- locity dependent acceleration terms. These constraints are imposed on the system by application of Lagrange multipliers which are to be appended to equation 4 to yield:

Note that Lagrange multipliers, A, do, in fact, ap- pear in this expression, but that they are not due to kinematic joints. Instead, they are forces and torques which drive the system. For the particular model given above equation 8 consists of 16 highly nonlinear sec- ond order differential equations, which are coupled to 6 algebraic equations of holonomic constraint. The re- mainder of the section describes the methods which are used to compute the vector of applied forces E, and the constraint forces A, which appear in equation 8.

2.2 Aerodynamics Model Some of the forces which must be included in the 2 vec- tor, which appears in equation 8, arise from the aero- dynamic environment to which the fuselage, the tilting wing, and the rotor blades are subjected. The aerody- namics associated with these bodies are modeled using differing levels of sophistication. The fuselage is mod- eled as a bluff body with a flat plate drag coefficient. The tilting wing is modeled as a NACA 0012 airfoil sec- tion with steady nonlinear table-lookup aerodynamics.

The aerodynamic environment to which helicopter blades are subjected is notoriously complex [9]. In the current work a model is used which captures the un- steady nature of the flow, and a first attempt is made at modeling stall effects. The blades are twisted linearly in the radial direction, and are of rectangular planform. Each of the blades is fitted with 8 Gaussian integration points which are distributed about the geometric cen- ter of the associated blade. A modified version of the Beddoes-Leishmann [lo], [ll], [12] unsteady linear aero- dynamics model is used, and a static stall correction is employed, This particular model was selected because it is extensively validated in the literature against both experimental, and numerical data and can be interfaced with the niultihody aircraft, model readily.

The aerodynamics model is expressed in a canonical state space format:

- x = h + B { %> (7) 3 $ =

4

Here the matrices A, l3, C, Q are dependent upon Mach number, Prandtl-Glauert factor, freestream ve- locity, and other parameters. The reader is referred to the open literature for their derivation, physical inter- pretation and explicit form.

The vector E, which appears in equation 9, is a vector of internal states which are associated with the model. These states are coupled to the system equations of mo- tion. The full implementation of the B-L model requires 12 of these internal states. Four of the states are asso- ciated with the normal force coefficient, four with the pitching moment coefficient, and four are required to compute dynamic stall. In the current work only the four states that are associated with the normal force coefficient are retained.

The inputs into the aerodynamics model are simply the section angle of attack (Y and the dimensionless pitch rate I;. The output of the reduced model is the normal force coefficient CN at the blade section. In practice, 4 states are retained for each of the Gaussian integration stations, and the model must be re-computed at each station. The known velocity of the blade with respect to the air flow at a particular Gaussian integration sta- tion is rotated into a twisted reference frame which is associated with the Gaussian integration station. (Y and I; are then computed, as are the A, B, C, and D matri- ces. The aerodynamic state derivatives F and CN are then computed.

The flow at a particular blade station may be stalled. An algebraic correction for static stall is made a3 a first approximation. In the B-L literature a method is pre- sented to compute the nonlinear CN and CM coeffi- cients algebraically, and the results compare favorably with experimental airfoil data. Here the Chi for the at- tached flow is computed from equation 9. An assumed separation point is used, and the nonlinear CN and CM coefficients are calculated from the semi-empirical form:

Here the subscript nl is associated with a nonlin- ear quantity. The semi-empirical data which appear in these expressions are given in [lo]. The normal force and pitching moment are now known at each Gaussian integration station. In order to compute the integrated load, the results may be appropriately weighted, rotated from the twisted reference frame into the body fixed ref- erence frame, and replaced by equivalent force couple systems acting at the center of mass of the associated

blade. The resulting forces and moments can be added to the applied force vector which appears in 8.

This model is very straight forward to implement and the state derivatives are quite easy to compute. The model has been extensively validated in the literature against both experimental and CFD data. The specific implementation which couples the aerodynamics model and the multibody model was used to recover several of the test cases that were found in the literature with little trouble [5].

2.3 Induced Inflow Model The blade section angle of attack is required as input

into the B-L aerodynamics model. Here a uniform dy- namic inflow model is used as a first approximation to the far-wake aerodynamics that are associated with the rotor environment. Induced inflow modeling has been the subject of active research for quite some time and several review papers exist on the subject [13]. Based on the content,s of \13], t,he Pitt-Peters model was selected for use in the current model. The Pitt-Peters [14], [15] dynamic inflow model is designed to compute the uni- form and first sine and cosine components of the inflow field. In the current study only the uniform component is used, and the model reduces to:

The derivative here is with respect to rotor time. VT is a dimensionless measure of the total flow through the rotor disk, CT is the dimensionless rotor thrust, and A0

is the dimensionless collective component of the inflow field. The notation and terminology in this and the sub- sequent section are best defined in [9]. Note that the expression here is cast in terms of a first order differ- ential equation, and that inflow state, XO, is explicitly coupled to both the system equations, through VT, and to the aerodynamics model, through CT.

In practice, the inflow is assumed to be the velocity of the ambient air with respect to the inertial reference frame. The absolute velocity of the blade sections is known from integration of the dynaniical equations, so that the velocity of the blade sections with respect to the air flow, arid hence (I, can be readily determined. This is input into the B-L aerodynamics model, and the resulting rotor thrust is computed. The inflow deriva- t,ive, Xo, is then computed from the P-P model, and solut,ion is advanced to the next integration t h e step.

2.4 Flight Control Model The methods that are used l o ccxnpute the sy&m

dynainics have been csplained. 111 the emrent hectfosr

5

the flight control system is explained. The simulation is driven by constraint equations, which are used to en- forced commanded wing-tilt, hub, and collective pitch accelerations that were discussed above. The desired collective pitch accelerations must be determined dur- ing the simulation, as they are not known a priori. An autopilot flight control system is used to compute the blade pitch accelerations during the simulation.

Phase 1

2

3 4

5

The flight control system is a modified version of the collective pitch portion of the Peters, Chouchane, Ful- ton (P-C-F) approach [IS]. The P-C-F model is de- signed to compute the collective and cyclic pitch com- ponents which are required to achieve a desired trimmed flight condition. In the current application of the P-C- F approach the collective pitch accelerations that are required to achieve a desired unsteady flight condition are calculated. The original implementation computes the collective and cyclic components of pitch, but in the current implementation only the collective portion is used. The reduced P-C-F formulation is:

Start 1.0 s

6.0s

10.0s 12.0s

26.0s

The inputs into the controller are the actual rotor thrust coefficient CT, which is computed from the B-L model, and the commanded rotor thrust Cg, which is computed as is outlined below. The quantities p and R are the advance ratio and rotor hub speed respectively. The parameter T is a time constant and the parameter K

is a feedback gain. Suggested values for these quantities are given in [16].

End 5.0s

10.0s

12.0s 26.0s

The commanded rotor thrust is dependent upon the desired flight condition. For vertical flight, i.e. take- off and hover, the commanded thrust is found from the expression:

Description Rotor speed spinup from 0.0 rad/s to 40.0 rad/s Vertical climb from the ground to a commanded altitude of 200.0 ft. Hover at 200.0 ft 85.0° tilt-wing conversion during the first 75.0° of conversion use the controller to realize constant altitude. During the last 10.Oo of the conversion use the controller to accelerate the model to the

Here ye is simply a desired trajectory, altitude as a function of time, and g is the acceleration due to grav- ity, M is the total mass of the model, and FD is the aerodynamic drag acting on the model, ICv and ICp are position and velocity feedback gains. The difference ye - y is the error in betu-een the desired position, and the actual position of the model. y and y are computed from integration of the equations of motion.

The commanded rotor thrust is computed from eyua- tion 14, and the result is used to compute the desired collective pitch accelerations, i3$ from equation 13. The desired pitch accelerations are then enforced by the use of Lagrange multipliers 4 in equation 8.

During the simulation, the collective controller has three distinct applications, and a slightly different form of equation 13 is used for each. In the first application the controller is used to fly the model to some desired altitude along a previously specified curve ye. In the second application, the controller is used to maintain a desired altitude during the first 7 5 O of conversion. Fi- nally, during the last loo of conversion the controller is used to achieve, and maintain, the desired cruising speed. The simulation “flight path” is outlined in the next section.

3 A Typical Flight Path The maneuvers which are performed during the sim-

ulation are explained in this section. The flight path is designed to fully illustrate the capability of the model as it was outlined in the previous section. The following table is typical of a full length simu1ation“flight path”.

Table 1: The Simulation Flight Path.

I desired cruising speed. 30.0s I Maintain the desired cruising speed.

Note that the model is initially at rest, and that the constraints are “turned on” one at a time.

The simulation that is presented in the above table is presented graphically in figure (4). In the figure it can be seen that the model begins to climb at t = 6.0s, and reaches the desired altitude of 200.0 ft at t = 12.0s. The conversion begins at t = 12.0s. At position (A) in the figure the lift is fully transfered from the rotor to the tilting wing, as the flow on the wing attaches. At position’(B) the desired cruising speed of 200.0 knots is reached.

4 Example Results As Elliott 121 has pointed out, the amount of data that is generated by multi-body aircraft simulations is huge. For the sake of clari%y, only the computed thrust and

6

-7 - I.) ..I

I m i I

m i

a i

a 4

Figure 5: Required Thrust

1

I j

flap response for a typical simulation are presented here. More complete information may be found in [5].

Figure ( 5 ) shows the thrust that was required for the maneuver that is shown in figure (4). In the time pe- riod t = 6.0s to t = 15.0s there is a wide variation in the computed thrust. This is required to accelerate the model to the desired 200.0 ft altitude. Note that the lift is fully transfered from the rotor to the wing at postion (C). At postion (D) the desired speed is achieved and the controller commands the appropriate thrust level.

Figure (6) shows the flap response during the simu- lation. The conversion process begins at t = 12.0s, but the model does not appreciably accelerate until position (B) in the figure. The acceleration of the model, and the associated increases in thrust, causes a l/rev vibration in the flap degree of freedom. This is observed in the figure. The amplitute of the vibration is increasing be- cause the model is accelerating. The dramatic increase in rotor thrust which occurs between postions (B) and (C) in figure 5 causes the increase in the mean flap angle which may be observed in figure 6. The final flapping

motion is a constant amplitude l/rev oscillation which is caused by the fact that the wing is only tilted forward by 85O. The flap angles are unusually high because the aircraft fuselage is modeled as a flat plate, hence the thrust requirements are unusually high.

5 Conclusions Several conclusions can be drawn from the results that were presented above:

1. The results presented here, and the results that were presented in [l] and [2], clearly indicate multibody simulations offer significant potential as highly flexible rotorcraft analysis tools.

2. Multibody formulation techniques can be coupled with aerodynamics, inflow, and flight control mod- els. The resulting model can be applied to a fairly wide range of flight scenarios.

Acknowledgement This work was funded by McDonnell Douglas Helicopter Company, under the MDHC Industrial Fellows Pro- gram.

References [l] Elliott, AS., J.B. McConville, “Application of a

General Purpose Mechanical Systems Code to Ro- torcraft Dynamics Problems”, Proceedings of the 1989 AHS National Specialists’ Meeting on Rotor- craft Dynamics, Nov. 1989.

[2] Elliott, AS. , “Dynamic Response of a Variable- Speed Rotor During Rapid Shaft Tilt’’“ Proceed- ings of the 47 th Annual Forum of the American Helicopter Society. Pheonis. AZ. May 1991.

[3] Ryan, R. R., “ADAMS-Multibody System Analy- sis Software”, in Multibody Systems Handbook, W. Schiehlen ed., Springer-verlag, Berlin, 1990.

[16] Peters, D. A., M. Chouchane, M. Fulton, “Heli- copter Trim with Flap-Lag-Torsion and Stall by an Optimized Controller”, J . of Guidance, Con- trol, and Dynamics, vol. 13, no. 5 , 1990.

[4] Kim, S. S., M. L. Vanderploeg, “A General and Ef- ficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations”, ASME J . Mechanisms, Transmissions, and Automation in Design, vol. 108, no 2, 1986.

[5] O’Heron, P. J., A Multibody Model Simulating Tilt- Wing Conversion, M.S. Thesis, University of Ari- zona, 1991. .

[6] Ambrosio, J. A. C., Elastic-Plastic Large Deforma- tion of Flexible Multibody Systems in Crash Anal- ysis, Ph.D. Dissertation, University of Arizona, 1991.

[7] Nikravesh, P. E., G. Gim, “Systematic Construc- tion of the Equations of Motion for Multibody Sys- tems Containing Closed Kinematic Loops”, Pro- ceedings A S M E Design Automation Conference, Montreal, Canada, 1989.

[8] Nikravesh, P. E., Computer Aided Analysis of Me- chanical Systems, Prentice Hall, Englewood Cliffs, NJ, 1988.

[9] Johnson, W., Helicopter Theory, Princeton Univer- sity Press, NJ, 1980.

[lo] Beddoes, T. S., “Representation of Airfoil Behav- ior”, Vertica, vol. 7 no. 2, 1983.

[ll] Leishmann, J. G., K. Q. Nguyen, “State-Space Representation of Unsteady Airfoil Behavior”, A I A A Journal, vol. 28, no. 5, 1990.

[12] Leishmann, J. G., G. L. Crouse Jr., “State Space Model for Unsteady Airfoil Behavior and Dynamic Stall”, paper 89-1319-CP AIAA/ASME/AHS/ASC 30 th Structures, Struc- tural Dynamics, and Material Conference, Mobile Alabama, 1989.

[13] Chen, R. T. N., “A Survey of Nonuniform Inflow Models for Rotorcraft Flight Dynamics and Con- trol Applications”, Vertica, vol. 14, no. 2, 1990.

[14] Gaonkar, G. H., D. A. Peters, “Effectiveness of Current Dynamic Inflow Models in Hover and For- ward Flight”, J. of the American Helicopter Soci- ety, vol. 31, no. 2 1986.

[15] Peters, D.A., N. HaQuang, “Dynamic Inflow for Practical Applications”, J. of the American Heli- copter Society, vol. 33, no 4, 1988.

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