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NASA NTRS2023

Split-Step Simulations to Assess the Effects of Atmospheric Boundary Layer Turbulence on the Dose Variability of N-Waves and Shaped Booms

The effects of atmospheric boundary layer turbulence on the loudness variability of a sonic boom N-wave and shaped boom are examined with split-step simulations. The shaped boom is representative of a design iteration of the NASA X-59 aircraft. Inhomogeneous atmospheric boundary layer turbulence is generated in the computational domain by a Fourier synthesis method. The N-wave and shaped boom are propagated through turbulent fields representing eight different convection levels measured at the NASA Kennedy Space Center and the NASA Armstrong Flight Research Center. Probability density functions of the formation of caustic regions along the propagation direction are computed from the N-wave results, and a parameter to collapse the caustic PDFs that accounts for both fluctuation intensities and length scales is proposed. Statistical results concerning loudness metric variability are presented, and the standard deviations of several metrics are shown to collapse across different convection levels of turbulence for small nondimensional propagation distances. The loudness metric distributions are observed to be well approximated by a normal distribution for a given range of propagation distances, and become increasingly skewed as distance increases. A model function for the dose variability is proposed, and the function parameters are found to be related to the convection level of the turbulence. The model for the dose variability distribution is compared to simulation data that were not used to find the regression parameters of the model. At several nondimensional propagation distances, agreement is observed between the model and the simulation data. These results indicate that the model may be suitable for providing quick estimates of noise dose variability in the primary carpet region across a wide range of atmospheric boundary layer conditions.

Sonic boom↗

NASA NTRS1997

Spectral Density of Laser Beam Scintillation in Wind Turbulence: Theory - Part 1

The temporal spectral density of the log-amplitude scintillation of a laser beam wave due to a spatially dependent vector-valued crosswind (deterministic as well as random) is evaluated. The path weighting functions for normalized spectral moments are derived, and offer a potential new technique for estimating the wind velocity profile. The Tatarskii-Klyatskin stochastic propagation equation for the Markov turbulence model is used with the solution approximated by the Rytov method. The Taylor 'frozen-in' hypothesis is assumed for the dependence of the refractive index on the wind velocity, and the Kolmogorov spectral density is used for the refractive index field.

Balakrishnan, A. V.↗

NASA NTRS1989

Probabilistic structural analysis methods for improving Space Shuttle engine reliability

Probabilistic structural analysis methods are particularly useful in the design and analysis of critical structural components and systems that operate in very severe and uncertain environments. These methods have recently found application in space propulsion systems to improve the structural reliability of Space Shuttle Main Engine (SSME) components. A computer program, NESSUS, based on a deterministic finite-element program and a method of probabilistic analysis (fast probability integration) provides probabilistic structural analysis for selected SSME components. While computationally efficient, it considers both correlated and nonnormal random variables as well as an implicit functional relationship between independent and dependent variables. The program is used to determine the response of a nickel-based superalloy SSME turbopump blade. Results include blade tip displacement statistics due to the variability in blade thickness, modulus of elasticity, Poisson's ratio or density. Modulus of elasticity significantly contributed to blade tip variability while Poisson's ratio did not. Thus, a rational method for choosing parameters to be modeled as random is provided.

Boyce, L.↗

NASA NTRS1974

On differentiating the probability of error in multipopular feature selection

A method of linear feature selection for n dimensional observation vectors which belong to one of m populations is presented. Each population has a known apriori probability and is described by a known multivariate normal density function. Specifically we consider the problem of finding a k x n matrix B of rank k (k n) for which the transformed probability of misclassification is minimized. Providing that the transformed a posterior probabilities are distinct theoretical results are obtained which, for the case k = l, give rise to a numerically tractable formula for the derivative of the probability of misclassification. It is shown that for the two population problem this condition is also necessary. The dependence of the minimum probability of error on the a priori probabilities is investigated. The minimum probability of error satisfies a uniform Lipschitz condition with respect to the a priori probabilities.

Peters, B. C.↗

NASA NTRS1975

Delta wing flutter based on doublet lattice method in NASTRAN

The subsonic doublet-lattice method (DLM) aeroelastic analysis in NASTRAN was successfully applied to produce subsonic flutter boundary data in parameter space for a large delta wing configuration. Computed flow velocity and flutter frequency values as functions of air density ratio, flow Mach number, and reduced frequency are tabulated. The relevance and the meaning of the calculated results are discussed. Several input-deck problems encountered and overcome are cited with the hope that they may be helpful to NASTRAN Rigid Format 45 users.

Jew, H.↗

NASA NTRS1982

Surface fitting with biharmonic and harmonic models

The physical and geometric interpretation of a surface fitting technique, multiquadric equations (MQ), is discussed. The relation of this method and its reciprocal form to biharmonic and harmonic techniques respectively, is pointed out. In both forms the solutions may be viewed as being numerical approximations of an integral equation in which an unknown density function is the physical source for disturbing potential (reciprocal-MQ) or elastic displacement (MQ).

Hardy, R. L.↗

NASA NTRS1989

Monte Carlo calculation of dynamical properties of the two-dimensional Hubbard model

A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis. The method is based on a least-squares-fitting procedure with constraints of positivity and smoothness on the real-frequency quantities. Results are shown for the single-particle spectral-weight function and density of states for the half-filled, two-dimensional Hubbard model.

White, S. R.↗

NASA NTRS1991

Spectroscopic investigations of microwave generated plasmas

The study deals with the plasma behavior as applied to spacecraft propulsion from the perspective of obtaining better design and modeling capabilities. The general theory of spectroscopy is reviewed, and existing methods for converting emission-line intensities into such quantities as temperatures and densities are outlined. Attention is focused on the single-atomic-line and two-line radiance ratio methods, atomic Boltzmann plot, and species concentration. Electronic temperatures for a helium plasma are determined as a function of pressure and a gas-flow rate using these methods, and the concentrations of ions and electrons are predicted from the Saha-Eggert equations using the sets of temperatures obtained as a function of the gas-flow rate. It is observed that the atomic Boltzmann method produces more reliable results for the electronic temperature, while the results obtained from the single-line method reflect the electron temperatures accurately.

Hawley, Martin C.↗

NASA NTRS1994

Integral-moment analysis of the BATSE gamma-ray burst intensity distribution

We have applied the technique of integral-moment analysis to the intensity distribution of the first 260 gamma-ray bursts observed by the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory. This technique provides direct measurement of properties such as the mean, variance, and skewness of the convolved luminosity-number density distribution, as well as associated uncertainties. Using this method, one obtains insight into the nature of the source distributions unavailable through computation of traditional single parameters such as V/V(sub max)). If the luminosity function of the gamma-ray bursts is strongly peaked, giving bursts only a narrow range of luminosities, these results are then direct probes of the radial distribution of sources, regardless of whether the bursts are a local phenomenon, are distributed in a galactic halo, or are at cosmological distances. Accordingly, an integral-moment analysis of the intensity distribution of the gamma-ray bursts provides for the most complete analytic description of the source distribution available from the data, and offers the most comprehensive test of the compatibility of a given hypothesized distribution with observation.

Horack, John M.↗

NASA NTRS1996

Near-Optimal Operation of Dual-Fuel Launch Vehicles

A near-optimal guidance law for the ascent trajectory from earth surface to earth orbit of a fully reusable single-stage-to-orbit pure rocket launch vehicle is derived. Of interest are both the optimal operation of the propulsion system and the optimal flight path. A methodology is developed to investigate the optimal throttle switching of dual-fuel engines. The method is based on selecting propulsion system modes and parameters that maximize a certain performance function. This function is derived from consideration of the energy-state model of the aircraft equations of motion. Because the density of liquid hydrogen is relatively low, the sensitivity of perturbations in volume need to be taken into consideration as well as weight sensitivity. The cost functional is a weighted sum of fuel mass and volume; the weighting factor is chosen to minimize vehicle empty weight for a given payload mass and volume in orbit.

Ardema, M. D.↗

NASA NTRS1998

C2 Fragmentation Energy of C60 Revisited: Theory Disagrees with Most Experiments

Following our earlier work on the subject, we have carried out density functional theory (DFT) and second-order Moller-Plesset perturbation theory (MP2) calculations of the dissociation energy of the reaction C60 yields C58 + C2 using polarized basis sets and geometries optimized with DFT methods. The present theoretical results support an electronic fragmentation energy D(sub e) around 10-11 eV in disagreement with most experimental results that place the dissociation energy D(sub o) (including zero point energy) around 7-8 eV. The plausible errors remaining in the theoretical calculations are unlikely to account for this big difference (2-4 eV).

Boese, A. Daniel↗

NASA NTRS2011

Musculoskeletal Modeling Component of the NASA Digital Astronaut Project

The NASA Digital Astronaut Project s (DAP) objective is to provide computational tools that support research of the physiological response to low gravity environments and analyses of how changes cause health and safety risks to the astronauts and to the success of the mission. The spaceflight risk associated with muscle atrophy is impaired performance due to reduced muscle mass, strength and endurance. Risks of early onset of osteoporosis and bone fracture are among the spaceflight risks associated with loss of bone mineral density. METHODS: Tools under development include a neuromuscular model, a biomechanical model and a bone remodeling model. The neuromuscular model will include models of neuromuscular drive, muscle atrophy, fiber morphology and metabolic processes as a function of time in space. Human movement will be modeled with the biomechanical model, using muscle and bone model parameters at various states. The bone remodeling model will allow analysis of bone turnover, loss and adaptation. A comprehensive trade study was completed to identify the current state of the art in musculoskeletal modeling. The DAP musculoskeletal models will be developed using a combination of existing commercial software and academic research codes identified in the study, which will be modified for use in human spaceflight research. These individual models are highly dependent upon each other and will be integrated together once they reach sufficient levels of maturity. ANALYSES: The analyses performed with these models will include comparison of different countermeasure exercises for optimizing effectiveness and comparison of task requirements and the state of strength and endurance of a crew member at a particular time in a mission. DISCUSSION: The DAP musculoskeletal model has the potential to complement research conducted on spaceflight induced changes to the musculoskeletal system. It can help with hypothesis formation, identification of causative mechanisms and supplementing small data samples.

Lewandowski, B. E.↗

NASA NTRSDate not supplied

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗

NASA NTRS2023

Analysis of VFR Traffic Uncertainty and its Impact on Uncrewed Aircraft Operational Capacity at Regional Airports

This paper proposes a method to characterize Visual Flight Rules traffic around a regional airport. The applicability of the method is discussed in the context of Uncrewed Aircraft operations at a regional airport. The relation between traffic interaction uncertainty and operational capacity at the runway is also investigated. The spatio-temporal distribution of traffic operating under Visual Flight Rules is analyzed from historical track data and visualized as heat maps generated at different altitudes. These are used to characterize the spatio-temporal uncertainty associated with traffic density, around a given airport, down to the runway. The traffic patterns at the runway are used to compute the runway capacity as a function of the probability of interaction with traffic operating under visual flight rules. Fort Worth Alliance is used as a representative regional airport for the study. Applications of the traffic characterization methods developed in this paper are also discussed.

VFR traffic, uncertainty, air mobility↗

NASA NTRS2023

Analysis of VFR Traffic Uncertainty and its Impact on Uncrewed Aircraft Operational Capacity at Regional Airports

VFR traffic↗

NASA NTRS1982

Mathematical analysis of the Photovoltage Decay (PVD) method for minority carrier lifetime measurements

When the diffusion length of minority carriers becomes comparable with or larger than the thickness of a p-n junction solar cell, the characteristic decay of the photon-generated voltage results from a mixture of contributions with different time constants. The minority carrier recombination lifetime tau and the time constant l(2)/D, where l is essentially the thickness of the cell and D the minority carrier diffusion length, determine the signal as a function of time. It is shown that for ordinary solar cells (n(+)-p junctions), particularly when the diffusion length L of the minority carriers is larger than the cell thickness l, the excess carrier density decays according to exp (-t/tau-pi(2)Dt/4l(2)), tau being the lifetime. Therefore, tau can be readily determined by the photovoltage decay method once D and L are known.

Vonroos, O. H.↗

NASA NTRS1973

Information preserving coding for multispectral data

A general formulation of the data compression system is presented. A method of instantaneous expansion of quantization levels by reserving two codewords in the codebook to perform a folding over in quantization is implemented for error free coding of data with incomplete knowledge of the probability density function. Results for simple DPCM with folding and an adaptive transform coding technique followed by a DPCM technique are compared using ERTS-1 data.

Duan, J. R.↗

NASA NTRS1993

A parameter identification method for the rotordynamic coefficients of a high Reynolds number hydrostatic bearing

In identifying the rotordynamic coefficients of a high-Reynolds-number hydrostatic bearing, fluid-flow induced forces present a unique problem, in that they provide an unmeasureable and uncontrollable excitation to the bearing. An analysis method is developed that effectively eliminates the effects of fluid-flow induced excitation on the estimation of the bearing rotordynamic coefficients, by using power spectral densities. In addition to the theoretical development, the method is verified experimentally by single-frequency testing, and repeatability tests. Results obtained for a bearing are the twelve rotordynamic coefficients (stiffness, damping, and inertia coefficients) as functions of eccentricity ratio, speed, and supply pressure.

Rouvas, C.↗