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NASA NTRS1991

Aerodynamic parametric studies and sensitivity analysis for rotor blades in axial flight

The analytical capability is offered for aerodynamic parametric studies and sensitivity analyses of rotary wings in axial flight by using a 3D undistorted wake model in curved lifting line theory. The governing equations are solved by both the Multhopp Interpolation technique and the Vortex Lattice method. The singularity from the bound vortices is eliminated through the Hadamard's finite part concept. Good numerical agreement between both analytical methods and finite differences methods are found. Parametric studies were made to assess the effects of several shape variables on aerodynamic loads. It is found, e.g., that a rotor blade with out-of-plane and inplane curvature can theoretically increase lift in the inboard and outboard regions respectively without introducing an additional induced drag.

Chiu, Y. D.↗

NASA NTRS1992

Deep-space navigation with differenced data types. Part 3: An expanded information content and sensitivity analysis

An approximate six-parameter analytic model for Earth-based differential range measurements is presented and is used to derive a representative analytic approximation for differenced Doppler measurements. The analytical models are tasked to investigate the ability of these data types to estimate spacecraft geocentric angular motion, Deep Space Network station oscillator (clock/frequency) offsets, and signal-path calibration errors over a period of a few days, in the presence of systematic station location and transmission media calibration errors. Quantitative results indicate that a few differenced Doppler plus ranging passes yield angular position estimates with a precision on the order of 0.1 to 0.4 micro-rad, and angular rate precision on the order of 10 to 25 x 10(exp -12) rad/sec, assuming no a priori information on the coordinate parameters. Sensitivity analyses suggest that troposphere zenith delay calibration error is the dominant systematic error source in most of the tracking scenarios investigated; as expected, the differenced Doppler data were found to be much more sensitive to troposphere calibration errors than differenced range. By comparison, results computed using wideband and narrowband (delta) VLBI under similar circumstances yielded angular precisions of 0.07 to 0.4 micro-rad, and angular rate precisions of 0.5 to 1.0 x 10(exp -12) rad/sec.

Estefan, J. A.↗

NASA NTRS2004

Multidisciplinary Analysis and Optimal Design: As Easy as it Sounds?

The viewgraph presentation examines optimal design for precision, large aperture structures. Discussion focuses on aspects of design optimization, code architecture and current capabilities, and planned activities and collaborative area suggestions. The discussion of design optimization examines design sensitivity analysis; practical considerations; and new analytical environments including finite element-based capability for high-fidelity multidisciplinary analysis, design sensitivity, and optimization. The discussion of code architecture and current capabilities includes basic thermal and structural elements, nonlinear heat transfer solutions and process, and optical modes generation.

design optimization↗

NASA NTRS1993

Nitrogen and noble gases in a glass sample from LEW88516

The Antarctic meteorite LEW88516 has been classified as a member of the SNC group of meteorites, specifically a shergottite. It is reported to be remarkably similar in mineralogy, petrogenesis and chemistry to the previously known ALH77005 shergottite, with both being compositionally distinct from other shergottites. LEW88516 shows pervasive shock features and has been found to contain glass veins attributable to a shock origin. In an effort to determine whether the glass in LEW88516 contains any of the isotopically-heavy trapped nitrogen component observed in EETA 79001 glass, as well as the related high-Ar-40/Ar-36 and high-Xe-129/Xe-132 components, we undertook an analysis of an 11.9 mg glass sample (LEW88516,4) provided to us by H. Y. McSween, Jr. as part of a consortium study of this meteorite. Nitrogen and noble gases were extracted from LEW88516,4 in a series of combustion steps at increasing temperatures followed by a final pyrolysis. Initial steps at 550 C were intended to remove any surface-sited nitrogen-containing contaminants, while the 700 C step was expected to show the onset of release of a trapped argon component, based on our previous data for EETA 79001. It was hoped that the bulk of any trapped gas release would be concentrated in one of two steps at 1100 C and approximately 1400 C, maximizing our analytical sensitivity. Results of the analysis are shown. Except for He and Ne, data obtained for the 550 C steps will be omitted from further consideration on the assumption that they represent terrestrial contamination.

Becker, R. H.↗

NASA NTRS1987

Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.

Cardoso, J. B.↗

NASA NTRS1988

Minimum weight design of rectangular and tapered helicopter rotor blades with frequency constraints

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.

Chattopadhyay, Aditi↗

NASA NTRS1988

Minimum weight design of rectangular and tapered helicopter rotor blades with frequency constraints

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 aurorotate 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.

Chattopadhyay, Aditi↗

NASA NTRS1989

Minimum weight design of helicopter rotor blades with frequency constraints

The minimum weight design of helicopter rotor blades subject to constraints on fundamental coupled flap-lag natural frequencies has been studied in this paper. A constraint has also been imposed on the minimum value of the blade autorotational inertia to ensure that the blade has sufficient inertia to autorotate in case of an engine failure. The program CAMRAD has been used for the blade modal analysis and the program CONMIN has been 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 blades in vacuum with both rectangular and tapered box beam structures. Design variables include taper ratio, nonstructural segment weights and box beam dimensions. The paper shows that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for blades with rectangular and tapered box beams.

Chattopadhyay, Aditi↗

NASA NTRS1988

Shape sensitivity analysis of wing static aeroelastic characteristics

A method is presented to calculate analytically the sensitivity derivatives of wing static aeroelastic characteristics with respect to wing shape parameters. The wing aerodynamic response under fixed total load is predicted with Weissinger's L-method; its structural response is obtained with Giles' equivalent plate method. The characteristics of interest include the spanwise distribution of lift, trim angle of attack, rolling and pitching moments, wind induced drag, as well as the divergence dynamic pressure. The shape parameters considered are the wing area, aspect ratio, taper ratio, sweep angle, and tip twist angle. Results of sensitivity studies indicate that: (1) approximations based on analytical sensitivity derivatives can be used over wide ranges of variations of the shape parameters considered, and (2) the analytical calculation of sensitivity derivatives is significantly less expensive than the conventional finite-difference alternative.

Barthelemy, Jean-Francois M.↗

NASA NTRS1988

Shape sensitivity analysis of wing static aeroelastic characteristics

A method is presented to calculate analytically the sensitivity derivatives of wing static aeroelastic characteristics with respect to wing shape parameters. The wing aerodynamic response under fixed total load is predicted using Weissinger's L-method; its structural response is obtained with Giles' equivalent plate method. The characteristics of interest in this study include the spanwise distribution of lift, trim angle of attack, rolling and pitching moments, wing induced drag as well as the divergence dynamic pressure. The shape parameters considered are the wing area, aspect ratio, taper ratio, sweep angle and tip twist angle. Results of sensitivity studies indicate that (1) approximations based on analytical sensitivity derivatives can be used for wide ranges of variations of the shape parameters considered and (2) the analytical calculation of sensitivity derivatives is significantly less expensive than the conventional finite difference alternative.

Barthelemy, Jean-Francois M.↗

NASA NTRS1988

Results of an integrated structure-control law design sensitivity analysis

Next generation air and space vehicle designs are driven by increased performance requirements, demanding a high level of design integration between traditionally separate design disciplines. Interdisciplinary analysis capabilities have been developed, for aeroservoelastic aircraft and large flexible spacecraft control for instance, but the requisite integrated design methods are only beginning to be developed. One integrated design method which has received attention is based on hierarchal problem decompositions, optimization, and design sensitivity analyses. This paper highlights a design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changess in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient that finite difference methods for the computation of the equivalent sensitivity information.

Gilbert, Michael G.↗

NASA NTRS1995

Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis

Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.

Livne, Eli↗

NASA NTRS1999

Sensitivity Analysis of ProSEDS (Propulsive Small Expendable Deployer System) Data Communication System

This paper discusses analytical approaches to evaluating performance of Spacecraft On-Board Computing systems, thereby ultimately achieving a reliable spacecraft data communications systems. The sensitivity analysis approach of memory system on the ProSEDS (Propulsive Small Expendable Deployer System) as a part of its data communication system will be investigated. Also, general issues and possible approaches to reliable Spacecraft On-Board Interconnection Network and Processor Array will be shown. The performance issues of a spacecraft on-board computing systems such as sensitivity, throughput, delay and reliability will be introduced and discussed.

Park, Nohpill↗

NASA NTRS1977

Benefit-cost evaluation of an intra-regional air service in the Bay area

Utilization of an iterative statistical model is presented to evaluate combinations of commuter airport sites and surface transportation facilities in confunction with service by a given commuter aircraft type in light of Bay Area regional growth alternatives and peak and off-peak regional travel patterns. The model evaluates such transportation options with respect to criteria of airline profitability, public acceptance, and public and private nonuser costs. It incorporates information modal split, peak and off-peak use of the air commuter fleet, terminal and airport cost, development costs and uses of land in proximity to the airport sites, regional population shifts, and induced zonal shifts in travel demand. The model is multimodal in its analytical capability, and performs exhaustive sensitivity analysis.

Haefner, L. E.↗

NASA NTRS1978

Executive summary: Benefit-cost evaluation of an intra-regional air service in the Bay Area and a technology assessment of transportation system investments

The benefits and costs that would result from an intra-regional air service operation in the San Francisco Bay area were determined by utilizing an iterative statistical decision model to evaluate combinations of commuter airport sites and surface transportation facilities in conjunction with service by a given commuter aircraft type in light of area regional growth alternatives and peak and off-peak regional travel patterns. The model evaluates such transportation option with respect to criteria of airline profitability, public acceptance, and public and private non-user costs. In so doing, it incorporates information on modal split, peak and off-peak use of the air commuter fleet, terminal and airport costs, development costs and uses of land in proximity to the airport sites, regional population shifts, and induced zonal shifts in travel demand. The model is multimodal in its analytic capability, and performs exhaustive sensitivity analysis.

Haefner, L. E.↗

NASA NTRS1988

Metal with anomalously low Ni and Ge concentrations in the Allan Hills A77081 winonaite

The Ge content of metal in the Allan Hills A77081 winonaite was determined by high-sensitivity electron microprobe analysis. By optimizing analytical conditions for Ge determination, a detection limit of about 75 ppm could be achieved. In A77081 some small kamacite grains contain less Ni and Ge and more Co than coarse-grained metal. These small grains are always associated with sulfide, raising the possibility that anomalous metal is related to eutectic melting. However, when published partition coefficients for Ni and Ge in the Fe-Ni-S system are used to model fractionation of these elements during eutectic melting, one finds that secondary metal should be enriched in Ni and depleted in Ge. Thus, the positive Ni-Ge correlation found in this study is the opposite of the expected trend. No explanation for this discrepancy has yet been found. Nonetheless, the existence of anomalous metal is an indication that A77081, and probably other winonaites as well, have undergone some fractionation. This supports the notion that the high-temperature history of winonaites is related to the formation of IAB iron meteorites, whose silicate inclusions are very similar to winonaites.

Kracher, Alfred↗

NASA NTRS1989

Results of an integrated structure/control law design sensitivity analysis

A design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations is discussed. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changes in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient than finite difference methods for the computation of the equivalent sensitivity information.

Gilbert, Michael G.↗

NASA NTRS1975

Space shuttle SRM plume expansion sensitivity analysis

The exhaust plumes of the space shuttle solid rocket motors can have a significant effect on the base pressure and base drag of the shuttle vehicle. A parametric analysis was conducted to assess the sensitivity of the initial plume expansion angle of analytical solid rocket motor flow fields to various analytical input parameters and operating conditions. The results of the analysis are presented and conclusions reached regarding the sensitivity of the initial plume expansion angle to each parameter investigated. Operating conditions parametrically varied were chamber pressure, nozzle inlet angle, nozzle throat radius of curvature ratio and propellant particle loading. Empirical particle parameters investigated were mean size, local drag coefficient and local heat transfer coefficient. Sensitivity of the initial plume expansion angle to gas thermochemistry model and local drag coefficient model assumptions were determined.

Smith, S. D.↗