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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Reynolds number and cowl position effects for a generic sidewall compression scramjet inlet at Mach 10 - A computational and experimental investigation

Reynolds number and cowl position effects on the internal shock structure and the resulting performance of a generic three-dimensional sidewall compression scramjet inlet with a leading edge sweep of 45 degrees at Mach 10 have been examined both computationally and experimentally. Prior to the experiment, a three-dimensional Navier-Stokes code was adapted to perform preliminary parametric studies leading to the design of the present configuration. Following this design phase, the code was then utilized as an analysis tool to provide a better understanding of the flow field and the experimental static pressure data for the final experimental configuration. The wind tunnel model possessed 240 static pressure orifices distributed on the forebody plane, sidewalls, and cowl and was tested in the NASA Langley 31 Inch Mach 10 Tunnel.

Holland, Scott D.↗
NASA NTRS1994

Interlaminar shear test method development for long term durability testing of composites

The high speed civil transport is a commercial aircraft that is expected to carry 300 passengers at Mach 2.4 over a range of more than 6000 nautical miles. With the existing commercial structural material technology (i.e., aluminum) the performance characteristics of the high speed civil transport would not be realized. Therefore there has been a concerted effort in the development of light weight materials capable of withstanding elevated temperatures for long duration. Thermoplastic composite materials are such candidate materials and the understanding of how these materials perform over the long term under harsh environments is essential to safe and effective design. The matrix dominated properties of thermoplastic composites are most affected by both time and temperature. There is currently an effort to perform short term testing to predict long term behavior of in-plane mechanical properties E22 (transverse modulus of elasticity) and G12 (shear modulus). Out-of-plane properties such as E33, G13, and G23 are inherently more difficult to characterize. This is especially true for the out-of-plane shear modulus G23 and hence there is no existing acceptable standard test method. Since G23 is the most matrix dominated property, it is essential that a test method be developed. A shear test methodology is developed to do just that. The test method, called the double notched specimen, along with the previously developed shear gage was tested at room temperature. Mechanical testing confirmed the attributes of the methodology. A finite element parametric study was conducted for specimen optimization. Moire interferometry, a high sensitivity laser optical method, was used for full-field analysis of the specimen. From this work, material parameters will be determined and thus enable the prediction of long term material behavior of laminates subjected to general loading states.

Ifju, Peter G.↗
NASA NTRS1997

Results of Aerothermodynamic and Boundary-Layer Transition Testing of 0.0362-Scale X-38 (Rev. 3.1) Vehicle in NASA Langley 20-Inch Mach 6 Tunnel

The aeroheating characteristics of the X-38 Revision 3.1 lifting-body configuration have been experimentally examined in the Langley 20-inch Mach 6 Tunnel. Global surface heat transfer distributions, surface streamline patterns, and shock shapes were measured on a 0.0362-scale model of a proposed Space Station Crew Return Vehicle at Mach 6 in air. Parametric variations include angles-of-attack of 20 deg, 30 deg, and 40 deg; Reynolds numbers based on model length of 0.9 to 3.7 million; and body-flap deflections of O deg, 20 deg, 25 deg, and 30 deg. The effects of discrete roughness elements, which included trip height, location, size, and orientation, as well as multiple-trip parametrics, were investigated. This document is intended to serve as a quick release of preliminary data to the X-38 program; analysis is limited to observations of the experimental trends in order to expedite dissemination.

Berry, Scott A.↗
NASA NTRS1992

Reynolds Number and Cowl Position Effects for a Generic Sidewall Compression Scramjet Inlet at Mach 10: A Computational and Experimental Investigation

Reynolds number and cowl position effects on the internal shock structure and the resulting performance of a generic three-dimensional sidewall compression scramjet inlet with a leading edge sweep of 45 degrees at Mach 10 have been examined both computationally and experimentally. Prior to the experiment, a three-dimensional Navier-Stokes code was adapted to perform preliminary parametric studies leading to the design of the present configuration. Following this design phase, the code was then utilized as an analysis tool to provide a better understanding of the flow field and the experimental static pressure data for the final experimental configuration. The wind tunnel model possessed 240 static pressure orifices distributed on the forebody plane, sidewalls, and cowl and was tested in the NASA Langley 31 Inch Mach 10 Tunnel.

Holland, Scott D.↗
NASA NTRS2009

Stress Analysis of Bolted, Segmented Cylindrical Shells Exhibiting Flange Mating-Surface Waviness

Bolted, segmented cylindrical shells are a common structural component in many engineering systems especially for aerospace launch vehicles. Segmented shells are often needed due to limitations of manufacturing capabilities or transportation issues related to very long, large-diameter cylindrical shells. These cylindrical shells typically have a flange or ring welded to opposite ends so that shell segments can be mated together and bolted to form a larger structural system. As the diameter of these shells increases, maintaining strict fabrication tolerances for the flanges to be flat and parallel on a welded structure is an extreme challenge. Local fit-up stresses develop in the structure due to flange mating-surface mismatch (flange waviness). These local stresses need to be considered when predicting a critical initial flaw size. Flange waviness is one contributor to the fit-up stress state. The present paper describes the modeling and analysis effort to simulate fit-up stresses due to flange waviness in a typical bolted, segmented cylindrical shell. Results from parametric studies are presented for various flange mating-surface waviness distributions and amplitudes.

Knight, Norman F., Jr.↗
NASA NTRS2010

N plus 2 Supersonic Concept Development and Systems Integration

Supersonic airplanes for two generations into the future (N+2, 2020-2025 EIS) were designed: the 100 passenger 765-072B, and the 30 passenger 765-076E. Both achieve a trans-Atlantic range of about 4000nm. The larger 765-072B meets fuel burn and emissions goals forecast for the 2025 time-frame, and the smaller 765-076E improves the boom and confidence in utilization that accompanies lower seat count. The boom level of both airplanes was reduced until balanced with performance. The final configuration product is two "realistic", non-proprietary future airplane designs, described in sufficient detail for subsequent multi-disciplinary design and optimization, with emphasis on the smaller 765-076E because of its lower boom characteristics. In addition IGES CAD files of the OML lofts of the two example configurations, a non-proprietary parametric engine model, and a first-cycle Finite Element Model are also provided for use in future multi-disciplinary analysis, optimization, and technology evaluation studies.

Wedge, Harry R.↗
NASA NTRS2014

Mars Sample Return Using Commercial Capabilities: Mission Architecture Overview

Mars Sample Return (MSR) is the highest priority science mission for the next decade as recommended by the recent Decadal Survey of Planetary Science. This paper presents an overview of a feasibility study for an MSR mission. The objective of the study was to determine whether emerging commercial capabilities can be used to reduce the number of mission systems and launches required to return the samples, with the goal of reducing mission cost. We report the feasibility of a complete and closed MSR mission design using the following scenario that covers three synodic launch opportunities, beginning with the 2022 opportunity: A Falcon Heavy injects a SpaceX Red Dragon capsule and trunk onto a Trans Mars Injection (TMI) trajectory. The capsule is modified to carry all the hardware needed to return samples collected on Mars including a Mars Ascent Vehicle (MAV), an Earth Return Vehicle (ERV), and hardware to transfer a sample collected in a previously landed rover mission to the ERV. The Red Dragon descends to land on the surface of Mars using Super Sonic Retro Propulsion (SSRP). After previously collected samples are transferred to the ERV, the single-stage MAV launches the ERV from the surface of Mars. The MAV uses a storable liquid bi-propellant propulsion system to deliver the ERV to a Mars phasing orbit. After a brief phasing period, the ERV, which also uses a storable bi-propellant system, performs a Trans Earth Injection (TEI) burn. Upon arrival at Earth, the ERV performs Earth and lunar swing-bys and is placed into a lunar trailing circular orbit - an Earth orbit, at lunar distance. A later mission, using Dragon and launched by a Falcon Heavy, performs a rendezvous with the ERV in the lunar trailing orbit, retrieves the sample container and breaks the chain of contact with Mars by transferring the sample into a sterile and secure container. With the sample contained, the retrieving spacecraft makes a controlled Earth re-entry preventing any unintended release of pristine martian materials into the Earth's biosphere. The analysis methods employed standard and specialized aerospace engineering tools. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships (MERs). The architecture was iterated until overall mission convergence was achieved on at least one path. Subsystems analyzed in this study include support structures, power system, nose fairing, thermal insulation, actuation devices, MAV exhaust venting, and GN&C. Best practice application of loads, mass growth contingencies, and resource margins were used. For Falcon Heavy capabilities and Dragon subsystems we utilized publically available data from SpaceX, published analyses from other sources, as well as our own engineering and aerodynamic estimates. Earth Launch mass is under 11 mt, which is within the estimated capability of a Falcon Heavy, with margin. Total entry masses between 7 and 10 mt were considered with closure occurring between 9 and 10 mt. Propellant mass fractions for each major phase of the EDL - Entry, Terminal Descent, and Hazard Avoidance - have been derived. An assessment of the effect of the entry conditions on the thermal protection system (TPS), currently in use for Dragon missions, shows no significant stressors. A useful payload mass of 2.0 mt is provided and includes mass growth allowances for the MAV, the ERV, and mission unique equipment. We also report options for the MAV and ERV, including propulsion systems, crewed versus robotic retrieval mission, as well as direct Earth entry. International planetary protection policies as well as verifiable means of compliance will have a large impact on any MSR mission design. We identify areas within our architecture where such impacts occur. We also describe preliminary compliance measures that will be the subject of future work. This work shows that emerging commercial capabilities as well as new methodologies can be used to efficiently support an important planetary science objective. The work also has applications for human exploration missions that use propulsive EDL techniques

Red Dragon↗
NASA NTRS2013

Mars Sample Return Using Commercial Capabilities: Mission Architecture Overview

Mars Sample Return (MSR) is the highest priority science mission for the next decade as recommended by the recent Decadal Survey of Planetary Science. This paper presents an overview of a feasibility study for a MSR mission. The objective of the study was to determine whether emerging commercial capabilities can be used to reduce the number of mission systems and launches required to return the samples, with the goal of reducing mission cost. The major element required for the MSR mission are described and include an integration of the emerging commercial capabilities with small spacecraft design techniques; new utilizations of traditional aerospace technologies; and recent technological developments. We report the feasibility of a complete and closed MSR mission design using the following scenario that covers three synodic launch opportunities, beginning with the 2022 opportunity: A Falcon Heavy injects a SpaceX Red Dragon capsule and trunk onto a Trans Mars Injection (TMI) trajectory. The capsule is modified to carry all the hardware needed to return samples collected on Mars including a Mars Ascent Vehicle (MAV); an Earth Return Vehicle (ERV); and hardware to transfer a sample collected in a previously landed rover mission to the ERV. The Red Dragon descends to land on the surface of Mars using Supersonic Retro Propulsion (SRP). After previously collected samples are transferred to the ERV, the single-stage MAV launches the ERV from the surface of Mars to a Mars phasing orbit. The MAV uses a storable liquid, pump fed bi-propellant propulsion system. After a brief phasing period, the ERV, which also uses a storable bi-propellant system, performs a Trans Earth Injection (TEI) burn. Once near Earth the ERV performs Earth and lunar swing-bys and is placed into a Lunar Trailing Orbit (LTO0 - an Earth orbit, at lunar distance. A later mission, using a Dragon and launched by a Falcon Heavy, performs a rendezvous with the ERV in the lunar trailing orbit, retrieves the sample container and breaks the chain of contact with Mars by transferring the sample into a sterile and secure container. With the sample contained, the retrieving spacecraft, makes a controlled Earth re-entry preventing any unintended release of pristine Martian materials into the Earth's biosphere. Other capsule type vehicles and associated launchers may be applicable. The analysis methods employed standard and specialized aerospace engineering tools. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships (MERs). The architecture was iterated until overall mission convergence was achieved on at least one path. Subsystems analyzed in this study include support structures, power system, nose fairing, thermal insulation, actuation devices, MAV exhaust venting, and GN&C. Best practice application of loads, mass growth contingencies, and resource margins were used. For Falcon Heavy capabilities and Dragon subsystems we utilized publically available data from SpaceX; published analyses from other sources; as well as our own engineering and aerodynamic estimates. Earth Launch mass is under 11 mt, which is within the estimated capability of a Falcon Heavy, with margin. Total entry masses between 7 and 10 mt were considered with closure occurring between 9 and 10 mt. Propellant mass fractions for each major phase of the EDL - Entry, Terminal Descent, and Hazard Avoidance - have been derived. An assessment of the entry conditions on the thermal protection system (TPS), currently in use for Dragon missions, has been made. And shows no significant stressors. A useful mass of 2.0 mt is provided and includes mass growth allowances for the MAV, the ERV, and mission unique equipment. We also report on alternate propellant options for the MAV and options for the ERV, including propulsion systems; crewed versus robotic retrieval mission; as well as direct Earth entry. International Planetary Protection Policies as well as verifiable means of compliance will have a large impact on any MSR mission design. We identify areas within our architecture where such impacts occur. This work shows that emerging commercial capabilities can be used to effectively integrated into a mission to achieve an important planetary science objective.

Mars Sample Return↗
NASA NTRS2012

Design and Parametric Sizing of Deep Space Habitats Supporting NASA'S Human Space Flight Architecture Team

NASA's Human Space Flight Architecture Team (HAT) is a multi-disciplinary, cross-agency study team that conducts strategic analysis of integrated development approaches for human and robotic space exploration architectures. During each analysis cycle, HAT iterates and refines the definition of design reference missions (DRMs), which inform the definition of a set of integrated capabilities required to explore multiple destinations. An important capability identified in this capability-driven approach is habitation, which is necessary for crewmembers to live and work effectively during long duration transits to and operations at exploration destinations beyond Low Earth Orbit (LEO). This capability is captured by an element referred to as the Deep Space Habitat (DSH), which provides all equipment and resources for the functions required to support crew safety, health, and work including: life support, food preparation, waste management, sleep quarters, and housekeeping.The purpose of this paper is to describe the design of the DSH capable of supporting crew during exploration missions. First, the paper describes the functionality required in a DSH to support the HAT defined exploration missions, the parameters affecting its design, and the assumptions used in the sizing of the habitat. Then, the process used for arriving at parametric sizing estimates to support additional HAT analyses is detailed. Finally, results from the HAT Cycle C DSH sizing are presented followed by a brief description of the remaining design trades and technological advancements necessary to enable the exploration habitation capability.

Toups, Larry↗
NASA NTRSDate not supplied

Time-Frequency Analysis of Experimental and Analytical Hub Loads of a Rotor Undergoing a Rotor Speed Change

A two-part analytical study was conducted examining a small-scale, two-bladed rotor undergoing a change in rotor speed. First, a parametric study was conducted to understand how rotor transient response, determined using a time-marching solution, is affected by the choice of rotor wake model, blade elasticity, and inclusion of an elastic support structure model. The second part of the study compared results from an analytical model of the NASA Multirotor Test Bed (MTB) undergoing a rotor speed change to wind tunnel data. Since the analytical and experimental time histories were nonstationary signals, a Stockwell transform was employed to analyze the data in lieu of traditional Fourier transform-based methods. The analysis included extraction of time-varying frequency content of the rotor thrust and hub motion, damping ratios, instantaneous rotor speed, and instantaneous phase difference between thrust and hub motion. Use of a free wake model was found to be necessary to predict higher-harmonic thrust, however, it underpredicted the amplitude of the unsteady loads. Modeling the elasticity of the stiff rotor blades installed on the MTB resulted in minimal impact on the computed vibratory loads compared to a rigid blade model. The current analytical model of the MTB, including an elastic support structure, properly predicted the measured trends in the frequency content of the thrust.

Martin K Sekula↗
NASA NTRS1970

Hypersonic Research Facilities Study - Volume III, Part 2: Phase II Parametric Studies Flight Vehicle Synthesis

Airbreathing hypersonic aircraft employing liquid hydrogen fuel have the potential of satisfying a number of mission requirements in the 1980-2000 time period. However, major advances in the technological state of the art are necessary before such aircraft can be considered either feasible or practical. The objective was to assess the research and development requirements for hypersonic aircraft and based on these requirements, to provide the NASA with characteristics of a number of desirable hypersonic research facilities. The study is organized in three phases. Phase I was a preliminary analysis of a broad group of concepts which were reduced to seven flight research facilities and eleven ground research facilities for Phase II study. The purpose of Phase II was to perform parametric studies to refine the facility designs and obtain sensitivity information in the neighborhood of "near optimum" designs, and to select those facilities that appear most attractive in the sense of research potential vs cost for further refinement in Phase III. This part of Volume III presents the results of the synthesis of the flight research facilities.

Source record↗
NASA NTRS2007

Non-Parametric Collision Probability for Low-Velocity Encounters

An implicit, but not necessarily obvious, assumption in all of the current techniques for assessing satellite collision probability is that the relative position uncertainty is perfectly correlated in time. If there is any mis-modeling of the dynamics in the propagation of the relative position error covariance matrix, time-wise de-correlation of the uncertainty will increase the probability of collision over a given time interval. The paper gives some examples that illustrate this point. This paper argues that, for the present, Monte Carlo analysis is the best available tool for handling low-velocity encounters, and suggests some techniques for addressing the issues just described. One proposal is for the use of a non-parametric technique that is widely used in actuarial and medical studies. The other suggestion is that accurate process noise models be used in the Monte Carlo trials to which the non-parametric estimate is applied. A further contribution of this paper is a description of how the time-wise decorrelation of uncertainty increases the probability of collision.

Carpenter, J. Russell↗
NASA NTRS1990

Design and performance of an analysis-by-synthesis class of predictive speech coders

The performance of a broad class of analysis-by-synthesis linear predictive speech coders is quantified experimentally. The class of coders includes a number of well-known techniques as well as a very large number of speech coders which have not been named or studied. A general formulation for deriving the parametric representation used in all of the coders in the class is presented. A new coder, named the self-excited vocoder, is discussed because of its good performance with low complexity, and because of the insight this coder gives to analysis-by-synthesis coders in general. The results of a study comparing the performances of different members of this class are presented. The study takes the form of a series of formal subjective and objective speech quality tests performed on selected coders. The results of this study lead to some interesting and important observations concerning the controlling parameters for analysis-by-synthesis speech coders.

Rose, Richard C.↗
NASA NTRS2011

A Contemporary Analysis of the O'Neill-Glaser Model for Space-Based Solar Power and Habitat Construction

In 1975 Gerard O Neill published in the journal Science a model for the construction of solar power satellites. He found that the solar power satellites suggested by Peter Glaser would be too massive to launch economically from Earth, but could be financially viable if the workforce was permanently located in free space habitats and if lunar and asteroid materials were used for construction. All new worldwide electrical generating capacity could be then achieved by solar power satellites. The project would financially break even in about 20 years after which it would generate substantial income selling power below fossil fuel prices. Two NASA / Stanford University led studies at Ames Research center during the summers of 1974 and 1976 found the concept technically sound and developed a detailed financial parametric model. Although the project was not undertaken when suggested in the 1970s, several contemporary issues make pursuing the O Neill -- Glaser concept more compelling today. First, our analysis suggests that if in the first ten years of construction that small habitats (compared to the large vista habitats envisioned by O Neill) supporting approximately 300 people were utilized, development costs of the program and the time for financial break even could be substantially improved. Second, the contemporary consensus is developing that carbon free energy is required to mitigate global climate change. It is estimated that 300 GW of new carbon free energy would be necessary per year to stabilize global atmospheric carbon. This is about 4 times greater energy demand than was considered by the O Neill Glaser model. Our analysis suggests that after the initial investments in lunar mining and space manufacturing and transportation, that the profit margin for producing space solar power is very high (even when selling power below fossil fuel prices). We have investigated the financial scaling of ground launched versus space derived space solar power satellites. We find that for the carbon mitigation case even modernized ground launched space solar power satellites are not financially viable. For space derived solar power satellites, however, the increased demand makes them break even substantially sooner and yield much higher profit. Third, current awareness is increasing about the dangers of humanity remaining a single planet species. Our technological power has been increasing relative to the size of the planet Earth. Since the middle of the 20th century our technological power has grown large relative to our planet's size. This presents a very real potential for human self-extinction. We argue that the potential for human self-extinction is increasing with time in proportion to the exponential growth of our technological power making self-extinction likely within this century if humanity remains a single planet species. The O Neill model of multiple independent free space habitats, it is argued, can protect humanity from extinction in the same way that portfolio diversification protects ones assets from total loss. We show that about 1 million people for the electricity only case, and about 1 billion people for the carbon mitigation case, can be provided with permanent space habitats and transportation from Earth in 30 years and can be funded by the space derived solar power satellite program. 1.2 Scope of this Chapter The goal of this chapter is to illustrate the power and importance of the O'Neill-Glaser concept in the context of human survival and maintaining a healthy planet Earth. We argue that at this point in human history our technological power is too dangerous to our selves and our home planet for us not to expand into space. We show by the models presented in the chapter that the imminent dangers of global warming and human self-extinction mandate that humanity move aggressively into the solar system in this generation. We show that the production of solar power satellites using space resources and with a work foe living in space provides a viable financial model to mitigate CO2 preventing the worst global warming scenarios, and safeguards humanity against self-extinction by providing hundreds of habitats and a billion people living in space within about 35 years. To accomplish this goal we need only consider the classic O'Neill-Glaser model which was parameterized for 1970's technological projections. Only habitat size optimization for the first ten years of production is added. This is a conservative approach since the innovations of the last 30 years will make the financial projections more favorable. However, the classic O'Neill-Glaser model represented a broad technological consensus. The model is well documented in the references and our calculations can be easily reproduced In this chapter the economics of the O Neill - Glaser model is compared with models that rely exclusively on Earth launched materials. Although many studies of Earth launched Solar Power Satellites have been made, we found that the NASA "Fresh Look Study" was the most comprehensive and well documented. It also provided one of the most optimistic Earth launch financial projections. We thus chose it for comparison purposes.

Curreri, Peter A.↗
NASA NTRS1974

Relativistic stellar stability - Preferred-frame effects

In a previous paper, the PPN (parametrized post-Newtonian) formalism was used to analyze relativistic influences on stellar stability in nearly all metric theories of gravity. That analysis omitted all preferred-frame terms. In this paper, possible preferred-frame effects on stellar stability are examined and no new instabilities are found. Although terms linear in the preferred-frame velocity w (time-odd terms, analogous to viscosity and energy generation) change the shapes of the normal modes, their symmetry properties prevent them from changing the characteristic frequencies. Thus, no new vibrational or secular instabilities can occur. Terms quadratic in w do not change either the shapes of the normal modes or the characteristic frequencies for radial pulsations (except for the effects due to the renormalization of the gravitation constant which does not affect stability). Thus, they have no influence on radial stability. Terms quadratic in w do change both the normal modes and the characteristic frequencies of nonradial pulsations; but in the limit of a neutral mode these changes vanish.

Ni, W.-T.↗
NASA NTRS1985

Scaling studies of solar pumped lasers

A progress report of scaling studies of solar pumped lasers is presented. Conversion of blackbody radiation into laser light has been demonstrated in this study. Parametric studies of the variation of laser mixture composition and laser gas temperature were carried out for CO2 and N2O gases. Theoretical analysis and modeling of the system have been performed. Reasonable agreement between predictions in the parameter variation and the experimental results have been obtained. Almost 200 mW of laser output at 10.6 micron was achieved by placing a small sapphire laser tube inside an oven at 1500 K the tube was filled with CO2 laser gas mixture and cooled by longitudinal nitrogen gas flow.

Christiansen, W. H.↗
NASA NTRS1987

Structural analysis demonstration of constitutive and life models

The overall objective of this program is to demonstrate the applicability of NASA-developed advanced constitutive and life damage models for calculating cyclic structural response and crack initiation in selected components of reusable space propulsion systems. The computer model resulting from this program will enable the user to produce an accurate life prediction of hot gas path, life limiting components of propulsion systems such as the space shuttle main engine (SSME). Previously developed computer models addressing constitutive modeling and life damage will be combined in an advanced finite element analysis to generate a sophisticated baseline life prediction program. A material data base will be established for the constitutive and life models parametrically involving temperature, strain range, strain rate, mean strain/stress, and dwell time. The verified computer program will be used to accomplish the life predictions of three SSME critical components as evidence of the model functionality.

Bechtel, G.↗
NASA NTRS1988

Stability sensitivity analysis for the aeroelastic optimization of a helicopter rotor

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.

Lim, Joon W.↗