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Showing papers on "Helicopter rotor published in 1988"



01 Jan 1988
TL;DR: In this article, structural optimization of a hingeless rotor is investigated to reduce oscillatory hub loads while maintaining aero-elastic stability in forward flight, and the sensitivity derivatives of blade response, hub loads, and eigenvalues with respect to the design variables are derived using a direct analytical approach.
Abstract: Structural optimization of a hingeless rotor is investigated to reduce oscillatory hub loads while maintaining aeroelastic stability in forward flight. Design variables include spanwise distribution of nonstructural mass, chordwise location of blade center of gravity and blade bending stiffnesses (flap, lag and torsion). A comprehensive aeroelastic analysis of rotors, based on a finite element method in space and time, is linked with optimization algorithms to perform optimization of rotor blades. Sensitivity derivatives of blade response, hub loads, and eigenvalues with respect to the design variables are derived using a direct analytical approach, and constitute an integral part of the basic blade response and stability analyses. This approach reduces the computation time substantially; an 80 percent reduction of CPU time to achieve an optimum solution, as compared to the widely adopted finite difference approach. Through stiffness and nonstructural mass distributions, a 60-90 percent reduction in all six 4/rev hub loads is achieved for a four-bladed soft-inplane rotor.

77 citations


Journal ArticleDOI
TL;DR: In this article, a method for converting steady state, potential panel methods into a time-dependent mode is derived and applied to several test cases, and an improved vortex wake model is constructed which is also suitable for simulating the leading edge separation of slender wings at high angles of attack.
Abstract: A method for converting steady state, potential panel methods into a time-dependent mode is derived and applied to several test cases. For this development, an improved vortex wake model was constructed which was also suitable for simulating the leading edge separation of slender wings at high angles of attack. Computed flow-field simulations are presented for various unsteady, and high-angle-of-attack conditions, involving geometries such as simple wings, rotors, and complete aircraft configurations.

76 citations


Patent
29 Feb 1988
TL;DR: In this paper, an angular moveable tail fin assembly and rudder are provided to improve the transition from hovering flight to horizontal airplane flight by differentially controlling aileron forces when the wings are aligned vertically with the vertically downward airflow from the helicopter rotor.
Abstract: This helicopter invention uniquely has no anti-torque tail rotor. The tail propeller is used only for forward thrust during the airplane mode of flight and during the transition from vertical helicopter flight to forward airplane mode of flight, when the helicopter rotor may be feathered in a no-lift attitude. The anti-torque balancing forces during the hovering mode are developed by the differentially controlled aileron forces when the wings are aligned vertically with the vertically downward airflow from the helicopter rotor. There is also a vertically moveable horizontal airfoil on the tail cone, or tail boom, with controllable means which can provide anti-torque reaction forces during the helicopter hovering mode from the lifting rotor down flow air. An angular moveable tail fin assembly and rudder are provided to improve transition from VTOL hovering flight to horizontal airplane flight. Means are provided to electronically schedule transition from the VTOL to horizontal cruise flight sensed by the wing attitude which can control the angular attitude of the fin and rudder in a completely computerized automatic transition to and from VTOL and airplane flight mode.

64 citations


Proceedings ArticleDOI
18 Apr 1988
TL;DR: In this article, a review of cross-sectional deformation analysis of composite helicopter rotor blades is presented, where the possible roles of both analytical and finite element methods are discussed as well as issues believed to be worthy of further investigation.
Abstract: Analyses applicable to composite helicopter rotor blades are reviewed. Important features of such analyses include transverse shear deformation, torsional warping, and nonlinearities associated with large displacement and rotation of the reference cross section. Additional consideration is given in some analyses to deformation of the reference cross section in its own plane. Published works are discussed in which cross sectional deformation, whether inor out-of-plane, is determined by both analytical and finite element methods. In evaluation of the various approaches, the possible roles of both analytical and finite element methods are discussed as well as issues believed to be worthy of further investigation.

52 citations


Journal ArticleDOI
TL;DR: In this article, a new methodology for formulating the aeroelastic stability and response problem for helicopter rotor blades is described, combined with a finite-element model of the blade and a quasilinearization solution technique.
Abstract: This paper describes a new methodology for formulating the aeroelastic stability and response problem for helicopter rotor blades. The mathematical expressions for the aerodynamic loads heed not be explicit functions of the blade displacement quantities. The methodology is combined with a finite-element model of the blade and a quasilinearization solution technique. The resulting computer program is used to study the behavior of blades with noncoincident elastic axis, aerodynamic centers, and centers of mass.

49 citations


Journal ArticleDOI
TL;DR: In this article, a single-bladed model rotor in hover was tested with a laser Doppler velocimeter (LDV) to verify the stability of the tip vortex trajectory in the wake of a spinning rotor.
Abstract: Detailed measurements with a laser Doppler velocimeter (LDV) have been performed in the tip region and in the tip vortex core of a single-bladed model rotor in hover. The testing was conducted at a rotor tip speed of 32 m/s, a Reynolds number of 269,000, and at two values of the rotor thrust coefficient, 0.0022 and 0.0057. Strobed laser sheet flow visualization was used to verify the steadiness of the tip vortex trajectory in the near wake and quantify the vortex trajectory to guide LDV surveys of the vortex core. A remotely aligned off-axis receiving optics system enabled measurement of vortex core velocity profiles at large focal lengths. The core self-induced velocity components extracted from these data are presented. The data exhibit evidence of secondary structure even inside the rotational core of the vortex, the axial velocity profile along the core has been extracted and presented in the wake of a spinning rotor. It is seen that the tip vortex of a rotating blade differs considerably in structure from a fixed-wing vortex.

43 citations


01 Apr 1988
TL;DR: An experimental investigation was conducted in the 14- by 22-foot Subsonic Tunnel at NASA Langley to measure the inflow into a scale model helicopter rotor in forward flight (microinf = 0.15).
Abstract: An experimental investigation was conducted in the 14- by 22-Foot Subsonic Tunnel at NASA Langley to measure the inflow into a scale model helicopter rotor in forward flight (microinf = 0.15). The measurements were made with a two component Laser Velocimeter (LV) one chord above the plane formed by the path of the rotor tips (tip path plane). A conditional sampling technique was employed to determine the azimuthal position of the rotor at the time each velocity measurement was made so that the azimuthal fluctuations in velocity could be determined. Measurements were made at a total of 147 separate locations in order to clearly define the inflow character. This data is presented without analysis. In order to increase the availability of the resulting data, both the mean and azimuthally dependent values are included as part of this report on two 5.25 inch floppy disks in Microsoft Corporation MS-DOS format.

40 citations


Journal ArticleDOI
TL;DR: In this article, a study is made of midfield and far-field noise generated by transonic blade-vortex interactions (BVI), typical of helicopter main rotor noise, using the VTRAN2 small disturbance, two-dimensional, transonic-flow code that includes convected vorticity was used to compute near-field and midfield flowfield information.
Abstract: A study is made of midfield and far-field noise generated by transonic blade-vortex interactions (BVI), typical of helicopter main rotor noise. The VTRAN2 small disturbance, two-dimensional, transonic-flow code that includes convected vorticity was used to compute near-field and midfield flowfield information. Because of mesh size limitations, this information is restricted to the midfield and does not give the desired far-field and three-dimensional information. A method of extending the solutions to the far-field in three dimensions is developed based on Kirchhoff's solution to the linear flow outside a surface S enclosing the nonlinear near field. A spherical wave is first used as a test case for the method. The relation of unsteady-type "C" shock motion on the airfoil to far-field sound is shown. The far-field radiation is affected by Mach number, airfoil thickness, shape, and vortex miss distance.

33 citations


01 Nov 1988
TL;DR: In this paper, the second order lifting line theory was used to calculate blade-vortex interaction airloads on helicopter rotors, and a lifting surface theory correction was proposed to account for lifting-surface effects.
Abstract: Two alternative approaches are developed to calculate blade-vortex interaction airloads on helicopter rotors: second order lifting-line theory, and a lifting surface theory correction. The common approach of using a larger vortex core radius to account for lifting-surface effects is quantified. The second order lifting-line theory also improves the modeling of yawed flow and swept tips. Calculated results are compared with wind tunnel measurements of lateral flapping, and with flight test measurements of blade section lift on SA349/2 and H-34 helicopter rotors. The tip vortex core radius required for good correlation with the flight test data is about 20 percent chord, which is within the range of measured viscous core sizes for helicopter rotors.

32 citations


Journal ArticleDOI
TL;DR: In this article, a qualitative analysis of a rotor system with a crack that grows at an angle of 45 degrees toward the axis of the shaft is presented, and it is shown by the solution that the steady-state response of a simple rotor system having a slant crack on its shaft induced by imbalance contains the frequencies represented by mΩ+ nωT/2 ; m=1, 2,..., and n=0, 1, 2,..., where Ω is the operating speed of the rotor, and ωT is the frequency of torsional vibration
Abstract: In this study, a qualitative analysis of a transverse vibration of a rotor system with a crack that grows at an angle of 45 degrees toward the axis of the shaft is presented. Based on the assumption that the bending stiffness of the shaft changes synchronously with the opening/closing behavior of the crack caused by the torsional vibration of the shaft, the equation of motion of a simple rotor system with a shaft having a slant crack is represented by a differential equation with parametric excitation in the coordinate system rotating at the operating speed of the rotor. It is shown by the solution that the steady-state response of the rotor system with a slant crack on its shaft induced by imbalance contains the frequencies represented by mΩ+ nωT/2 ; m=1, 2, ..., and n=0, 1, 2, ..., where Ω is the operating speed of the rotor, and ωT is the frequency of torsional vibration of the rotor system.

Patent
15 Dec 1988
TL;DR: In this paper, a hydraulic device for the individual control of the pitch of a helicopter rotor blade by a rotary hydraulic jack is described, the stator vanes of which are integral with a sleeve fitted on the hub.
Abstract: A hydraulic device for the individual control of the pitch of a helicopter rotor blade by a rotary hydraulic jack, the stator vanes of which are integral with a sleeve fitted on the hub. The jack rotor carries rotor vanes movable relative to the stator vanes and delimiting with these chambers of variable volume fed by a servo-distributor controlled as a function of pilot signals and signals from a detector of the angular position of the blade about its pitch axis. The jack is integrated in a pitch bearing and in an elastic ball joint integrated in a rotary hydroelastic shock absorber with vanes for lamination of a viscous fluid. The shock-absorber rotor is connected rigidly in terms of rotation about the pitch axis to the rotor of the jack and is connected to the blade by a rigid cuff.

Patent
30 Sep 1988
TL;DR: In this paper, a spherical bearing for a helicopter rotor connected a rotor blade to a rotor hub is described, and a coupon of elastomer, whose damping characteristics exceed those of the laminates, is fitted within each opening with suitable dimensions to minimize control loads and flapwise damping.
Abstract: A spherical bearing for a helicopter rotor connects a rotor blade to a rotor hub. The bearing includes an outer race supported on the hub and an inner race spaced axially from the outer race supported by a shackle attached to the blade root. Each race defines a concentric spherical surface. Multiple laminates of elastomer and shims of metal are arranged alternately between the races. The laminates and shims are bonded to each other to form an assembly that is bonded to the races at radially opposite ends. Each laminate has an opening formed at its center extending through its thickness. A coupon of elastomer, whose damping characteristics exceed those of the laminates, is fitted within each opening with suitable dimensions to minimize control loads and flapwise damping, yet the coupon increases lead-lag damping.

Journal ArticleDOI
TL;DR: In this paper, the prediction of transonic quadrupole rotor noise in hover using a frequency domain method is presented, which is applied to compute the high-speed noise of a model rotor.
Abstract: This paper presents a formulation of the prediction of transonic quadrupole rotor noise in hover using a frequency domain method. The technique is applied to compute the high-speed noise of a model rotor. Tests on the computational stability of the method are presented and theoretical results are compared with published experimental data. Noise predictions on rotors with swept-tip blades are discussed.

Patent
09 Nov 1988
TL;DR: In this paper, a set of lights are used to provide collimated beams intersecting at limit points located radially outwardly of the arc of the helicopter rotor blades so that light scattered from the intersecting beams at the limit points provides the helicopter pilot with visual references of the rotor arc.
Abstract: Visually observable safe limits for the proximity of an aircraft, such as a helicopter, to obstructions are provided by pairs of lights which provide collimated beams intersecting at limit points located radially outwardly of the arc of the helicopter rotor blades so that light scattered from the intersecting beams at the limit points provides the helicopter pilot with visual references of the rotor arc. Each light of each pair has a concave reflector and a lamp at the focal point of the reflector to provide the collimated beams and transparent plastic shields over the open ends of the reflectors have concavities in central portions to provide diverging beams that illuminate the obstructions.

01 Aug 1988
TL;DR: In this paper, a test of a 40 percent model MBB BO-105 helicopter main rotor was conducted in the anechoic open test section of the German-Dutch Windtunnel (DNW), where the measured data were in the form of acoustic pressure time histories and spectra from two out-of-flow microphones underneath and forward of the model.
Abstract: Acoustic data from a test of a 40 percent model MBB BO-105 helicopter main rotor are scaled to equivalent full-scale flyover cases. The test was conducted in the anechoic open test section of the German-Dutch Windtunnel (DNW). The measured data are in the form of acoustic pressure time histories and spectra from two out-of-flow microphones underneath and foward of the model. These are scaled to correspond to measurements made at locations 150 m below the flight path of a full-scale rotor. For the scaled data, a detailed analysis is given for the identification in the data of the noise contributions from different rotor noise sources. Key results include a component breakdown of the noise contributions, in terms of noise criteria calculations of a weighted sound pressure level (dBA) and perceived noise level (PNL), as functions of rotor advance ratio and descent angle. It is shown for the scaled rotor that, during descent, impulsive blade-vortex interaction (BVI) noise is the dominant contributor to the noise. In level flight and mild climb, broadband blade-turbulent wake interaction (BWI) noise is dominant due to the absence of BVI activity. At high climb angles, BWI is reduced and self-noise from blade boundary-layer turbulence becomes the most prominent.


Patent
31 Aug 1988
TL;DR: A rotor hub system for a helicopter is fabricated predominately of composite material as mentioned in this paper, and the pitch housing includes a pair of closed loop straps which define the lugs of the lead-lag hinge and a lug of the flap hinge.
Abstract: A rotor hub system for a helicopter is fabricated predominately of composite material. The flap hinge, pitch hinge and lead-lag hinge contain elastomeric bearings and one step blade folding in either the forward or aft direction using the same drive system is employed. The rotor hub includes closed loop straps which define generally opposed lugs of the flap hinge, and the pitch housing includes a pair of closed loop straps which define the lugs of the lead-lag hinge and a lug of the flap hinge. The use of composite materials as the predominant material of the rotor hub and the pitch housing results in a highly load redundant structure permitting a reduction in size and number of parts, a reduction in drag, and an increase in reliability and safety.

DOI
01 Jan 1988
TL;DR: In this paper, a finite-volume scheme based on the method of characteristic flux averaging solves the Euler equations formulated in the conservation form is presented for a non-lifting case and for a helicopter rotor in hover.
Abstract: A procedure for the computation of transonic steady and unsteady flow around helicopter rotors is presented. The algorithm is based on the Euler equations and allows the computation of anisotropic rotational flow and thus an implicitly accurate calculation of shocks. In addition the capturing of the rotor wake and the tip vortex is provided for arbitrary tip shapes. The code for the computation of steady, fully 3-D rotor flow is derived from the EUFLEX procedure originated by A. Eberle, that has successfully been applied to a lot of fixed wing configurations up to now. A finite-volume scheme based on the method of characteristic flux averaging solves the Euler equations formulated in the conservation form. The discretizatlon of the flow field is carried out in two different manners concerning the grid topology and the size of the physical domain. Calculations are presented for a non-lifting case and for a helicopter rotor in hover. The comparisons of the method in its present stage show good agreement with experimental data.

Journal ArticleDOI
TL;DR: From both the analysis and test data results, it is shown that the modified computer program could be a viable tool for future design of the advanced Servo flap controlled main rotor helicopter.
Abstract: The SH-2F helicopter flight test data correlation has been successfully performed using a modified version of the rotorcraft flight simulation computer program €81. This modified program has the capability for either the conventional rotor control option or the servo flap control option. The analytical model of the servo flap in the analysis is treated as a control system, not a degree of freedom. The airfoil data tables are modified to have the capability to simulate the appropriate servo flap aerodynamic coefficients Q, Q, and CM as a function of servo flap deflection. The blade index angle and servo flap control feedback coefficients are included to model the blade having various combinations of servo flap design variables. The existing SH-2F fuselage characteristics and the 101 Rotor system are utilized to perform the correlation with the flight test data to verify the analysis. Results obtained from the analysis, when compared with the flight test data, such as servo flap control position, fuselage attitude, main rotor torque, and bending moment distribution, correlate very well. From both the analysis and test data results, it is shown that the modified computer program could be a viable tool for future design of the advanced Servo flap controlled main rotor helicopter.

Journal ArticleDOI
TL;DR: In this article, a rotating blade finite element with coupled bending, torsion and axial stretching degrees-of-freedom is developed, which is used for symbolic manipulations required for the development of the element.

01 Feb 1988
TL;DR: In this paper, the minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied, and a constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to auto-otate in the case of engine failure.
Abstract: The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to autorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.

01 Oct 1988
TL;DR: In this article, a fully compressible method for determining helicopter rotor wake effects is described which computes the wake without requiring external specification of the wake, or separate computations for the wake and blade region.
Abstract: A fully compressible method for determining helicopter rotor wake effects is described which computes the wake without requiring external specification of the wake, or separate computations for the wake and blade region. The method is a modification of a compressible finite volume Potential Flow technique, and it has been implemented in a program, HELIX I, for computing compressible rotor flow fields in hover with free wakes. Wake positions in substantial agreement with experiment have been calculated for cases including subsonic and transonic flows, high and low aspect ratios, and two- and four-bladed rotors.

01 Sep 1988
TL;DR: In this paper, a computational method was developed to treat unsteady aerodynamic interactions between a helicopter rotor, wake, and fuselage and between the main and tail rotors.
Abstract: A computational method was developed to treat unsteady aerodynamic interactions between a helicopter rotor, wake, and fuselage and between the main and tail rotors. An existing lifting line prescribed wake rotor analysis and a source panel fuselage analysis were coupled and modified to predict unsteady fuselage surface pressures and airloads. A prescribed displacement technique is used to position the rotor wake about the fuselage. Either a rigid blade or an aeroelastic blade analysis may be used to establish rotor operating conditions. Sensitivity studies were performed to determine the influence of the wake fuselage geometry on the computation. Results are presented that describe the induced velocities, pressures, and airloads on the fuselage and on the rotor. The ability to treat arbitrary geometries is demonstrated using a simulated helicopter fuselage. The computational results are compared with fuselage surface pressure measurements at several locations. No experimental data was available to validate the primary product of the analysis: the vibratory airloads on the entire fuselage. A main rotor-tail rotor interaction analysis is also described, along with some hover and forward flight.

Journal ArticleDOI
TL;DR: In this article, a new computer program that uses Farassat's most advanced subsonic time domain formulation has been written to predict helicopter rotor discrete frequency noise, and a comparison of predicted and experimentally measured acoustic pressure and spectra for a V* scale UH-1 model rotor blade and a V? scale OLS (AH-1G) model rotor blades was made for different flight conditions and microphone locations with good results.
Abstract: A new computer program that uses Farassat's most advanced subsonic time domain formulation has been written to predict helicopter rotor discrete frequency noise. A brief description of the program (WOPWOP), is followed by a comparison of predicted and experimentally measured acoustic pressure and spectra for a V* scale UH-1 model rotor blade and a V? scale OLS (AH-1G) model rotor blade. The rotorcraft flight simulation computer program C81 was used to predict the spanwise loading on the rotor for aerodynamic input into the acoustic prediction. Comparisons are made for different flight conditions and microphone locations with good results. In general, the acoustic pressure is underpredicted. The acoustic predictions for a tapered rotor blade and predictions for microphones well below the tip path plane show less underprediction. Finally, in-plane motion of the rotor blade is shown to significantly affect the peak-to-peak amplitude of the acoustic pressure for high advancing tip Mach numbers.

Patent
25 Apr 1988
TL;DR: An improved helicopter rotor flexbeam (20) comprises a pair of generally parallel outwardly open, cross-sectionally C-shaped beams of a geometry which defines therein a first inboard region (A) of enhanced out-of-plane flexibility and a second outboard region of enhanced in-plane and torsional flexibility as discussed by the authors.
Abstract: An improved helicopter rotor flexbeam (20) comprises a pair of generally parallel outwardly open, cross-sectionally C-shaped beams (25) of a geometry which defines therein a first inboard region (A) of enhanced out-of-plane flexibility and a second outboard region (B) of enhanced in-plane and torsional flexibility.

01 Jan 1988
TL;DR: In this article, a method is described for the analysis of the unsteady, incompressible potential flow associated with a helicopter in low advance ratio flight due to the contribution of the deformed wake to the airloads imposed on the fuselage.
Abstract: A method is described for the analysis of the unsteady, incompressible potential flow associated with a helicopter The fuselage, rotor, and rotor wake are considered together in forward flight This method is particularly useful in low advance ratio flight due to the contribution of the deformed wake to the airloads imposed on the fuselage The rotor geometry is prescribed and the unsteady wake geometry is computed from the local flow perturbation velocities The fuselage is modeled as a non-lifting body of source panels and the rotor and its wake are modeled as a full vortex lattice The rotor geometry is arbitrary and several rotor blades can be represented The unsteady airloads are computed in the presence of the deformed rotor wake by a time-stepping technique The wake is started impulsively from rest, allowing a natural convection of the wake with time

01 May 1988
TL;DR: In this article, a 40 percent scale model of the four-bladed BO-105 helicopter main rotor, tested in a large aerodynamic wind tunnel, was used to assess the acoustic far field of BVI noise, to map the directivity and temporal characteristics of the BVI impulsive noise, and to show the existence of retreating-side BVI signals.
Abstract: Acoustic data are presented from a 40 percent scale model of the four-bladed BO-105 helicopter main rotor, tested in a large aerodynamic wind tunnel. Rotor blade-vortex interaction (BVI) noise data in the low-speed flight range were acquired using a traversing in-flow microphone array. Acoustic results presented are used to assess the acoustic far field of BVI noise, to map the directivity and temporal characteristics of BVI impulsive noise, and to show the existence of retreating-side BVI signals. The characterics of the acoustic radiation patterns, which can often be strongly focused, are found to be very dependent on rotor operating condition. The acoustic signals exhibit multiple blade-vortex interactions per blade with broad impulsive content at lower speeds, while at higher speeds, they exhibit fewer interactions per blade, with much sharper, higher amplitude acoustic signals. Moderate-amplitude BVI acoustic signals measured under the aft retreating quadrant of the rotor are shown to originate from the retreating side of the rotor.

Patent
22 Apr 1988
TL;DR: In this paper, the fatigue properties of helicopter rotor blade flexbeam sections were determined using one motor driven eccentric for imparting combined bending, twisting and deflection loads to a flexbeam.
Abstract: Mechanism for determining the fatigue properties of helicopter rotor blade flexbeam sections using one motor driven eccentric for imparting combined bending, twisting and deflection loads to a flexbeam.

Proceedings ArticleDOI
01 Jan 1988
TL;DR: In this article, a sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method, which is based on a finite element method in space and time.
Abstract: A sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method. Structural design variables include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity, and blade bending stiffnesses (flap, lag and torsion). The formulation for blade steady response is based on a finite element method in space and time. The vehicle trim and blade steady response are calculated iteratively as one coupled solution using a modified Newton method. Eigenvalues corresponding to different blade modes are calculated using Floquet transition matrix theory. The formulation for derivatives of the eigenvalues with respect to design variables is implemented using a direct analytical approach (chain rule differentiation), and constitutes an integral part of the regular stability analysis. The stability sensitivity derivatives were obtained at a fraction of computation time compared to the frequently adopted finite difference method. A parametric study showed that nonstructural mass and chordwise cg offset of outboarad elements, and lag bending stiffness of inboard elements, have powerful influence on blade stability.