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At least 415 records · Page 23

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Mingori, D. L.↗

Multi-Scale Modeling of Cross-Linked Nanotube Materials

The effect of cross-linking single-walled carbon nanotubes on the Young's modulus of a nanotube-reinforced composite is modeled with a multi-scale method. The Young's modulus is predicted as a function of nanotube volume fraction and cross-link density. In this method, the constitutive properties of molecular representative volume elements are determined using molecular dynamics simulation and equivalent-continuum modeling. The Young's modulus is subsequently calculated for cross-linked nanotubes in a matrix which consists of the unreacted cross-linking agent. Two different cross-linking agents are used in this study, one that is short and rigid (Molecule A), and one that is long and flexible (Molecule B). Direct comparisons between the predicted elastic constants are made for the models in which the nanotubes are either covalently bonded or not chemically bonded to the cross-linking agent. At a nanotube volume fraction of 10%, the Young's modulus of Material A is not affected by nanotube crosslinking, while the Young's modulus of Material B is reduced by 64% when the nanotubes are cross-linked relative to the non-cross-linked material with the same matrix.

Frankland, S. J. V.↗

Electron acceleration in solar flares

For the period Spetember 1978 to December 1982, 55 solar flare particle events for which the instruments on board the ISEE-3 spacecraft detected electrons above 10 MeV. Combining data with those from the ULEWAT spectrometer electron spectra in the range from 0.1 to 100 MeV were obtained. The observed spectral shapes can be divided into two classes. The spectra of the one class can be fit by a single power law in rigidity over the entire observed range. The spectra of the other class deviate from a power law, instead exhibiting a steepening at low rigidities and a flattening at high rigidities. Events with power-law spectra are associated with impulsive (less than 1 hr duration) soft X-ray emission, whereas events with hardening spectra are associated with long-duration (more than 1 hr) soft X-ray emission. The characteristics of long-duration events are consistent with diffusive shock acceleration taking place high in the corona. Electron spectra of short-duration flares are well reproduced by the distribution functions derived from a model assuming simultaneous second-order Fermi acceleration and Coulomb losses operating in closed flare loops.

Droge, Wolfgang↗

Solar-flare-induced Forbush decreases - Dependence on shock wave geometry

It is argued that the principal mechanism for the association of Forbush decreases with the passage of a solar flare shock wave is prolonged containment of cosmic ray particles behind the flare compression region, which acts as a semipermeable obstacle to particle motion along the field lines, leading to additional adiabatic cooling of the particles. Liouville's theorem is used to calculate the instantaneous distribution function at 1 AU for each particle arriving at the earth. By averaging over a large number of individual estimates, a representative estimate of the omnidirectional phase space density and the corresponding particle intensity is obtained. The energy change of individual particles at the shocks is found to be small in comparison to the energy lost by adiabatic cooling of the cosmic rays between the shock wave and the sun. The effects of particle rigidity, diffusion coefficient, and flare longitude on the magnitude of the Forbush decrease are quantitatively investigated.

Thomas, B. T.↗

"TPSX: Thermal Protection System Expert and Material Property Database"

The Thermal Protection Branch at NASA Ames Research Center has developed a computer program for storing, organizing, and accessing information about thermal protection materials. The program, called Thermal Protection Systems Expert and Material Property Database, or TPSX, is available for the Microsoft Windows operating system. An "on-line" version is also accessible on the World Wide Web. TPSX is designed to be a high-quality source for TPS material properties presented in a convenient, easily accessible form for use by engineers and researchers in the field of high-speed vehicle design. Data can be displayed and printed in several formats. An information window displays a brief description of the material with properties at standard pressure and temperature. A spread sheet window displays complete, detailed property information. Properties which are a function of temperature and/or pressure can be displayed as graphs. In any display the data can be converted from English to SI units with the click of a button. Two material databases included with TPSX are: 1) materials used and/or developed by the Thermal Protection Branch at NASA Ames Research Center, and 2) a database compiled by NASA Johnson Space Center 9JSC). The Ames database contains over 60 advanced TPS materials including flexible blankets, rigid ceramic tiles, and ultra-high temperature ceramics. The JSC database contains over 130 insulative and structural materials. The Ames database is periodically updated and expanded as required to include newly developed materials and material property refinements.

Squire, Thomas H.↗

Turbulence Hazard Metric Based on Peak Accelerations for Jetliner Passengers

Calculations are made of the approximate hazard due to peak normal accelerations of an airplane flying through a simulated vertical wind field associated with a convective frontal system. The calculations are based on a hazard metric developed from a systematic application of a generic math model to 1-cosine discrete gusts of various amplitudes and gust lengths. The math model simulates the three degree-of- freedom longitudinal rigid body motion to vertical gusts and includes (1) fuselage flexibility, (2) the lag in the downwash from the wing to the tail, (3) gradual lift effects, (4) a simplified autopilot, and (5) motion of an unrestrained passenger in the rear cabin. Airplane and passenger response contours are calculated for a matrix of gust amplitudes and gust lengths. The airplane response contours are used to develop an approximate hazard metric of peak normal accelerations as a function of gust amplitude and gust length. The hazard metric is then applied to a two-dimensional simulated vertical wind field of a convective frontal system. The variations of the hazard metric with gust length and airplane heading are demonstrated.

Stewart, Eric C.↗

Acoustic propagation in rigid ducts with blockage

Acoustic levitation has been suggested for moving nonmagnetic material in furnaces for heat processing in space experiments. Basically, acoustic standing waves under resonant conditions are excited in the cavity of the furnace while the material blockage is located at a pressure node and thus at a maximum gradient. The position of the blockage is controlled by displacing the node as a result of frequency change. The present investigation is concerned with the effect of blockage on the longitudinal and transverse resonances of a cylindrical cavity, taking into account the results of a one-dimensional and three-dimensional (3-D) analysis. Based on a Green's function surface element method, 3-D analysis is tested experimentally and proved to be accurate over a wide range of geometric parameters and boundary shapes. The shift in resonance depends on the change in pressure gradient and duct shortening caused by the blockage.

El-Raheb, M.↗

Do Integrins Mediate the Skeletal Response to Altered Loading?

In vivo experiments were performed to examine the role of B1 integrin in skeletal adaptation to reduced and increased loading. Transgenic mice were generated with a dominant negative form of the B1 integrin cytoplasmic domain with expression driven by the osteocalcin promoter (pOCb1DN). This fragment consists of the transmembrane and intracellular domains and interferes with endogenous integrin signalling in vitro. This promoter targets expression of the transgene to mature bone cells. Expression of the transgene was confirmed by immunoprecipitation and western blotting. Reduced loading was generated by hindlimb suspension and increased loading the resumption of normal loading following hindlimb suspension. Two groups of female 35-day old mice were examined: poCb1DN transgenic mice (TG) and wild-type littermate controls (WT). Animals were hindlimb suspended for 1 week (HU, n = l0/gp) or 4 weeks (HU, n = 4 - 7/gp) or suspended for 4 weeks followed by reloading by normal ambulation for 4 weeks (RL, n = l0/gp). Age-matched controls (CT) were pairfed based on the HU food intake. The protocols were approved by the NASA Ames Research Center IACUC. Upon completion of the experimental protocol, body mass was recorded and tissues of interest removed and analyzed following standard procedures. Femoral whole bone structural behavior was measured in torsion to failure to obtain whole bone strength (failure torque) and torsional rigidity. Ash content (ash) and fraction (% ash) were determined for the tibia. Total ash is indicative of bone size whereas %ash is a material property. Tibial curvature was measured from microradiographs. For each experiment, the effects of genotype (TG, WT) and treatment (CT, HU/RL) were assessed by two-factor ANOVA followed by the Tukey-Kramer posthoc to identify significant differences at an alpha level of 0.05. Our goal was to understand differences resulting from altered integrin function in the adaptation to altered loading.

vanderMeulen, Marjolein C. H.↗

Instabilities of dynamic thermocapillary liquid layers. I Convective instabilities

A steady shear flow is set up in a planar liquid layer bounded below by a rigid plate, and above by an interface with a passive gas, by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. The thermal-convective instabilities to which this dynamic state is susceptible include stationary longitudinal rolls involving the classical Marangoni instability, and unsteady hydrothermal waves, whose new instability mechanism derives its energy from the horizontal temperature gradients. The thermal stability characteristics for liquid layers with and without return flow profiles are presently given as functions of the Prandtl number for the liquid and the Biot number for the interface, and comparisons are made with available experimental observations.

Smith, M. K.↗

TPS Materials and Costs for Future Reusable Launch Vehicles

There is considerable interest in developing new reusable launch vehicles (RLVs) for reducing the cost of transporting payload to and from orbit. This work reviews thirteen candidate thermal protection system (TPS) options currently available for RLVs. It is useful to begin with the current Shuttle TPS layout as a reference. The nose cap and wing leading edge , which reach the highest temperatures, are made of reinforced carbon-carbon (RCC) that is protected from oxidation by an external coating (about 0.020" thick) of silicon-carbide. Most of the windward surface is 9 lb/cubic ft ceramic tiles (LI-900) with a thin (about 0.012") coating of Reaction Cured Glass (RCG). The leeward side of the vehicle is covered largely by AFRSI, a quilted ceramic blanket, and FRSI, a polyamide felt. These four materials can be considered first generation reusable TPS. Since the time of the Shuttle design, considerable progress has been made advancing TPS technologies in terms of thermal performance, robustness, and cost. For each of the major systems, a second generation ceramic TPS has been developed, tested, and characterized. Metallic-based systems have also been developed. For applications requiring RCC in the past, advanced carbon-carbon (ACC) is now available. This material has better mechanical properties, somewhat higher temperature capability to 2900F and greatly increased oxidation resistance. New carbon fiber reinforced silicon-carbide matrix composites (C/SiCs) have shown additional improvement in properties over ACC with use temperatures to 3000F and above. For rigid tiles, NASA Ames has made two significant advancements. The first is a tile substrate called Alumina Enhanced Thermal Barrier, or AETB, that incorporates alumina fibers for improved dimensional stability at high temperatures, to 2600F and above. This material can be made to densities as low as 8 lb/cubic ft. The second is a coating preparation called Toughened Uni-piece Fibrous Insulation, or TUFT, that penetrates about 0.1 in. into the tile substrate. The resulting composite, with a functionally gradient density near the surface, provides orders of magnitude increased damage resistance compared with RCG coated LI-900, with only a small weight increase. The TPS that combines these two developments is called AETB-8/TUFI and has been adopted for high damage areas on the Shuttles. Two notable developments have occur-red in flexible ceramic blanket technology. The first is aluminoborosilicate-based fibers with use temperatures of 2200F and above," in comparison to quartz and silica fiber used in AFRSI which have multi-use temperature limits of 1200 to 1400F. Blankets incorporating these new high temperature fibers are referred to as AFRSI-HT. The second is an integral weaving techniques that produces a fluted core blanket with a smoother surface and greater resistance to aero-acoustic noise, to levels as high as 170 dB. This Ames innovation is called Tailorable Advanced Blanket Insulation, or TABI. Finally, for felt-based TPS, Boeing is developing Polybenzimidazole Blanket Insulation, or PBI, with a multi-use temperature limit of 1000F and above, in contrast to Shuttle FRSI which has a multi-use temperature limit of about 700F. 1.6 NASA Langley and BF Goodrich (formerly Rohr Corp.) have led the development of metallic-based TPS. This activity uses essentially three approaches: metallic tiles which encase a fibrous ceramic batting in a box fabricated largely from metallic honeycombs, typically Nickel based alloys; metallic honeycomb sheets, made of Nickel-based alloys, incorporating a fibrous back-side insulation encapsulated in a metallic foil bag, providing reduced weight; and metallic multi-wall, which is comprised of dimpled Titanium metal sheets, which are stacked and then diffusion bonded at contact points to form the TPS. The Nickel-based systems can be used up to temperatures of about 1800F, and the Titanium system to about 100F. These thirteen TPS materials have pros and cons to their usage in terms of temperature capability, weight, initial cost, and maintenance. Carbon-carbon and C/SiC systems have the highest temperature capability but are relatively expensive and heavy, requiring significant time, expertise, and costly facilities and tools for design and fabrication. Second generation ceramic tiles are relatively light, durable, simple to fabricate and easy to install; however, waterproofing is a concern. Blankets and felts are light, simple, inexpensive, and easy to install over curved vehicle surfaces, but durability and waterproofing are concerns. Metallics are robust and appear to have eliminated waterproofing, but they tend to be heavy and relatively expensive, requiring costly facilities and tools. If thin metal sheets are used to reduce weights, then issues arise from possible metal fatigue and corrosion caused by thermal cycling, pressure oscillations, and environmental exposure. For application to future RLVs, system analyses show that a significant component of the vehicle life cycle cost is from the TPS; however, it is difficult to quantify and to compare the potential savings of advanced systems without performing full vehicle designs using each of the different options. Because this entails a considerable effort and also tends to submerge TPS cost impacts under unrelated vehicle design assumptions, there is a clear need for a simpler quantitative method to evaluate the cost impact of different TPS options. To this end, this work introduces a TPS life-cycle cost parameter which is easily computed and applicable to generic RLVs.

Rasky, Dan J.↗

A wave envelope finite element scheme for acoustical radiation

The aeroacoustic problem associated with the radiation of fan noise from the inlet of a turbofan aircraft engine, the dimensions of which are generally many times larger than the acoustical wavelengths of the major energy-carrying frequencies, is considered. In the present approach, a conventional finite element solution in the inner region is compatibly matched to a 'wave envelope' finite element solution in a large but finite outer region. The inclusion of a wavelike variation with the correct asymptotic decay in the shape functions for the outer region preserves the correct behavior of the solution at large distances. The method is initially presented for a simple one-dimensional model based on the solution of Webster's horn equation. Results are presented for the specific case of a uniform cylindrical section joined to a conical expansion, and also for a simple axisymmetric test case of the calculation of acoustical pressure generated by a vibrating circular piston located at the center of an infinite rigid baffle.

Astley, R. J.↗

Structure and functions of water-membrane interfaces and their role in proto-biological evolution

Among the most important developments in proto-biological evolution was the emergence of membrane-like structures. These are formed by spontaneous association of relatively simple amphiphilic molecules that would have been readily available in the primordial environment. The resulting interfacial regions between water and nonpolar interior of the membrane have several properties which made them uniquely suitable for promoting subsequent evolution. They can (1) selectively attract organic material and mediate its transport, (2) serve as simple catalysts for chemical reactions, and (3) promote the formation of trans-membrane electrical and chemical gradients which could provide energy sources for proto-cells. Understanding the structure of interfaces, their interactions with organic molecules and molecular mechanisms of their functions is an essential step to understanding proto-biological evolution. In our computer simulation studies, we showed that the structure of water at interfaces with nonpolar media is significantly different from that in the bulk. In particular, the average surface dipole density points from the vapor to the liquid. As a result, negative ions can approach the interface more easily than positive ions. Amphiphilic molecules composed of hydrocarbon conjugated rings and polar substituents (e.g., phenol) assume at the interface rigid orientations in which polar groups are buried in water while hydrocarbon parts are located in the nonpolar environment. These orientational differences are of special interest in connection with the ability of some of these molecules to efficiently absorb photons. Flexible molecules with polar substituents often adopt at interfaces conformations different from those in the bulk aquaeous solution and in the gas phase. As a result, in many instances both specificity and kinetics of chemical reactions in which these molecules can participate is modified by the presence of surfaces. Of special interest is the mechanism by which polar molecules are transferred across interface between water and a nonpolar medium. Our recent study showed that simple ionophores bind ions by the same mechanisms as ion channels and carriers from modern cells.

Pohorille, A.↗

Concepts for Life Cycle Cost Control Required to Achieve Space Transportation Affordability and Sustainability

Cost control must be implemented through the establishment of requirements and controlled continually by managing to these requirements. Cost control of the non-recurring side of life cycle cost has traditionally been implemented in both commercial and government programs. The government uses the budget process to implement this control. The commercial approach is to use a similar process of allocating the non-recurring cost to major elements of the program. This type of control generally manages through a work breakdown structure (WBS) by defining the major elements of the program. If the cost control is to be applied across the entire program life cycle cost (LCC), the approach must be addressed very differently. A functional breakdown structure (FBS) is defined and recommended. Use of a FBS provides the visibifity to allow the choice of an integrated solution reducing the cost of providing many different elements of like function. The different functional solutions that drive the hardware logistics, quantity of documentation, operational labor, reliability and maintainability balance, and total integration of the entire system from DDT&E through the life of the program must be fully defined, compared, and final decisions made among these competing solutions. The major drivers of recurring cost have been identified and are presented and discussed. The LCC requirements must be established and flowed down to provide control of LCC. This LCC control will require a structured rigid process similar to the one traditionally used to control weight/performance for space transportation systems throughout the entire program. It has been demonstrated over the last 30 years that without a firm requirement and methodically structured cost control, it is unlikely that affordable and sustainable space transportation system LCC will be achieved.

Rhodes, Russel E.↗

Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗

Computational methods for frictional contact with applications to the Space Shuttle orbiter nose-gear tire: Comparisons of experimental measurements and analytical predictions

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical-loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗

Inflatable Softgoods Testing Capability Development for Habitation

The Habitation Systems Development Office (HP40) at NASA Marshall Space Flight Center supports systems engineering, integration, and project management for next generation space habitats. The office is responsible for formulation activities for Lunar Surface Habitat and Mars Transit Habitat. HP40 also manages commercial partnerships for exploration habitat development. The Lunar Surface Habitat is intended to initially support a minimum of two crew on the lunar surface for an approximately 30-day mission, with the ability to accommodate four crew for short durations. The Mars Transit Habitat will transport four crew to and from Mars orbit on a potentially 1,200 day mission. Both concepts are envisioned to leverage inflatable softgoods as the primary structural material for the habitation portion of the architecture. Inflatable softgoods are a complex, multi-material system consisting of multiple layers which perform specific functions. A bladder layer (polymer) contains the habitat’s atmosphere. The bladder is indexed to a woven restraint layer, usually Kevlar or Vectran, which serves as the structural layer. The remaining outer layers are for micro-meteoroid orbital debris (MMOD) shielding, protection from atomic Oxygen (if the material system is to be deployed in low earth orbit), and thermal insulation. The primary advantage of inflatable softgoods is that they can offer a larger volume per unit mass relative to a rigid metal structure. Inflatable softgoods have a strong development heritage within NASA, beginning with work in the 1960s in partnership with Goodyear Aerospace and continuing with Johnson Space Center’s TransHab project in the 1990s . Some development efforts subsequently transitioned into the private sector to mature the material technology for flight applications, including human habitation. In August 2022, NASA published its guidelines for certification of crewed inflatable softgoods structures (JSC-67721). This document outlines a series of tests which will be needed to certify inflatable softgoods material systems for use in crewed mission applications. It includes burst testing at the subscale and full-scale to determine the ultimate burst pressure of the softgoods architecture. Creep (long term deformation of the material under stress) is a key failure mode which must be characterized. Creep testing at the component and module levels is also recommended to generate time to failure curves and verify that the inflatable system has a predicted operational life which exceeds mission parameters. ET (Test Engineering) at MSFC and HP40 have worked together to establish softgoods testing capabilities for the center. This includes the ability to conduct module level burst tests and creep tests. The poster will highlight these capabilities and provide examples of testing which has been performed to date by ET. NASA MSFC anticipates that these test capabilities will continue to offer critical support for companies pursuing inflatable softgoods for exploration applications (lunar surface habitation, Mars transit) as well as commercial low earth orbit platforms.

habitation↗

Maximum likelihood tuning of a vehicle motion filter

This paper describes the use of maximum likelihood parameter estimation unknown parameters appearing in a nonlinear vehicle motion filter. The filter uses the kinematic equations of motion of a rigid body in motion over a spherical earth. The nine states of the filter represent vehicle velocity, attitude, and position. The inputs to the filter are three components of translational acceleration and three components of angular rate. Measurements used to update states include air data, altitude, position, and attitude. Expressions are derived for the elements of filter matrices needed to use air data in a body-fixed frame with filter states expressed in a geographic frame. An expression for the likelihood functions of the data is given, along with accurate approximations for the function's gradient and Hessian with respect to unknown parameters. These are used by a numerical quasi-Newton algorithm for maximizing the likelihood function of the data in order to estimate the unknown parameters. The parameter estimation algorithm is useful for processing data from aircraft flight tests or for tuning inertial navigation systems.

Trankle, Thomas L.↗

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations. Phase 5B: Analysis of gust alleviation methods and rotor dynamic stability

The effects of various gust alleviation methods on the random blade response in flapping were studied analytically, assuming a rigid rotor support. The analytical model assumes rigid flapping blades with elastic root restraints. Linearized equations which are approximately valid at low lift conditions were used. Because of the interblade coupling from the feedback devices, the method of multiblade generalized coordinates was most convenient and was extended to include coning, differential coning, and warping of the rotor. The numerical examples cover the dynamic stability characteristics as affected by feedback gains of three- to six-bladed rotors. The number of blades had large effects on stability limits and modal time functions at these limits. The random flapping response of the blades to atmospheric turbulence was determined at 1.6 rotor advance ratio using feedback gains below the stability limit. The most effective reduction of the flapping response per unit gain was achieved with a rotor coning angle feedback.

Hohenemser, K. H.↗