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NASA NTRS1956

Stability derivatives of cones at supersonic speeds

The aerodynamic stability derivatives due to pitching velocity and vertical acceleration are derived for circular cones traveling at supersonic speeds. Both first-order and a combination of first and second order potential solutions are obtained, and in calculations for the forces, no approximations are made to the tangency condition or the isentropic pressure relation. In addition, expressions for the forces, moments, and stability derivatives of arbitrary bodies of revolution are derived from Newtonian impact theory.

Tobak, Murry↗

NASA NTRS1994

High-frequency techniques for RCS prediction of plate geometries and a physical optics/equivalent currents model for the RCS of trihedral corner reflectors, parts 1 and 2

Formulations for scattering from the coated plate and the coated dihedral corner reflector are included. A coated plate model based upon the Uniform Theory of Diffraction (UTD) for impedance wedges was presented in the last report. In order to resolve inaccuracies and discontinuities in the predicted patterns using the UTD-based model, an improved model that uses more accurate diffraction coefficients is presented. A Physical Optics (PO) model for the coated dihedral corner reflector is presented as an intermediary step in developing a high-frequency model for this structure. The PO model is based upon the reflection coefficients for a metal-backed lossy material. Preliminary PO results for the dihedral corner reflector suggest that, in addition to being much faster computationally, this model may be more accurate than existing moment method (MM) models. An improved Physical Optics (PO)/Equivalent Currents model for modeling the Radar Cross Section (RCS) of both square and triangular, perfectly conducting, trihedral corner reflectors is presented. The new model uses the PO approximation at each reflection for the first- and second-order reflection terms. For the third-order reflection terms, a Geometrical Optics (GO) approximation is used for the first reflection; and PO approximations are used for the remaining reflections. The previously reported model used GO for all reflections except the terminating reflection. Using PO for most of the reflections results in a computationally slower model because many integrations must be performed numerically, but the advantage is that the predicted RCS using the new model is much more accurate. Comparisons between the two PO models, Finite-Difference Time-Domain (FDTD) and experimental data are presented for validation of the new model.

Balanis, Constantine A.↗

NASA NTRS1977

An optimal Space Shuttle ascent trajectory for the first orbital flight test

An optimal solution of the ascent trajectory of the Space Shuttle for the first orbital flight test is presented; the optimization is a minimum propellant, four-control problem in yaw angle, roll angle, pitch angle and vacuum thrust of each Space Shuttle main engine. Piecewise linear segments with juncture points treated as parameters are employed to model the controls. Equations of motion for a three-dimensional flight with pitch plane moment balance about an oblate are integrated numerically with a fourth-order Runge-Kutta method; two- and one-dimensional cubic spline function curve fits of aerodynamic coefficients are used during the first and second stages, respectively. The constraint minimization problem is solved with the Davidon-Fletcher-Powell function method.

Johnson, I. L., Jr.↗

NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗

NASA NTRS1978

Extensions of guiding center motion to higher order

In a static magnetic field, some well-known guiding-center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding-center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, P-phi, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second-order motion is included, P-phi is no longer a constant. The above extensions of guiding-center theory help to resolve the different tokamak orbits obtained either by using the guiding-center equations of motion or by using conservation of P-phi.

Northrop, T. G.↗

NASA NTRS1975

A determination of the lunar moment of inertia

An estimate of the second zonal coefficient of the spherical-harmonic representation of the lunar gravitational field has been obtained from an analysis of particular orbital-element variations of the Explorer 35 and Explorer 49 spacecraft. Data from these spacecraft were used because the orbital configurations resulted in variations of the longitude of periapse and node which were, to first order, dependent only on the even zonal harmonics. The data time span for each satellite was extremely long: 2138 days for Explorer 35 and 230 days for Explorer 49. The value of the harmonic coefficient is determined and used to obtain a value of the lunar moment of inertia.

Gapcynski, J. P.↗

NASA NTRS2004

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗

NASA NTRS2003

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Taylor, Arthur C., III↗

NASA NTRS1989

Nonprincipal-plane scattering from flat plates: Second-order and corner diffraction and pattern control of horn antennas

Several high-frequency models for nonprincipal-plane scattering from a rectangular, perfectly conducting plate are examined. Two methods, the Method of Equivalent Currents and corner diffraction coefficients, are considered. Formulations for second-order Physical Theory of Diffraction equivalent currents and for corner diffracted fields are presented. Comparisons are made among plate models. Results away from grazing are accurate using only first-order terms. Near grazing, second-order and corner diffraction terms improve the results for many cases. The pattern control of horn antennas using lossy materials to coat the inner walls of the horn is also investigated. Integral Equation and Moment Method techniques are used to formulate the problem. It is clearly demonstrated that side lobe level reduction can be achieved using impedance surfaces on the inner walls of the horn.

Balanis, Constantine A.↗

NASA NTRS2001

Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis

An efficient incremental-iterative approach for differentiating advanced flow codes is successfully demonstrated on a 2D inviscid model problem. The method employs the reverse-mode capability of the automatic- differentiation software tool ADIFOR 3.0, and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straight-forward, black-box reverse- mode application of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-order aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoint) procedures; then, a very efficient non-iterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hessian matrices) of lift, wave-drag, and pitching-moment coefficients are calculated with respect to geometric- shape, angle-of-attack, and freestream Mach number

Taylor, Arthur C., III↗

NASA NTRS1987

Positive ions of the first- and second-row transition metal hydrides

Theoretical dissociation energies for the first- and second-row transition metal hydride positive ions are critically compared against recent experimental values obtained from ion beam reactive scattering methods. Theoretical spectroscopic parameters and dipole moments are presented for the ground and several low-lying excited states. The calculations employ large Gaussian basis sets and account for electron correlation using the single-reference single- and double-excitation configuration interaction and coupled-pair-functional methods. The Darwin and mass-velocity contributions to the relativistic energy are included in the all-electron calculations on the first-row systems using first-order perturbation theory, and in the second-row systems using the Hay and Wadt relativistic effective core potentials. The theoretical D(0) values for the second-row transition metal hydride positive ions should provide a critical measure of the experimental values, which are not as refined as many of those in the first transition row.

Pettersson, Lars G. M.↗

NASA NTRS1983

On the joint bimodality of temperature and moisture near stratocumulus cloud tops

The observed distributions of the thermodynamic variables near stratocumulus top are highly bimodal. Two simple models of sub-grid fractional cloudiness motivated by this observed bimodality are examined. In both models, certain low order moments of two independent, moist-conservative thermodynamic variables are assumed to be known. The first model is based on the assumption of two discrete populations of parcels: a warm-day population and a cool-moist population. If only the first and second moments are assumed to be known, the number of unknowns exceeds the number of independent equations. If the third moments are assumed to be known as well, the number of independent equations exceeds the number of unknowns. The second model is based on the assumption of a continuous joint bimodal distribution of parcels, obtained as the weighted sum of two binormal distributions. For this model, the third moments are used to obtain 9 independent nonlinear algebraic equations in 11 unknowns. Two additional equations are needed to determine the covariance within the two subpopulations. In case these two internal covariance vanish, the system of equations can be solved analytically.

Randall, D. A.↗

NASA NTRS2021

What it Takes to Compute Highly Accurate Rovibrational Line Lists for Use in Astrochemistry

We review the Best Theory + Reliable High-resolution Experiment (BTRHE) strategy for obtaining highly accurate molecular rovibrational line lists with InfraRed (IR) intensities. The need for highly accurate molecular rovibrational line lists is two-fold: a) assignment of the many rovibrational lines for common stable molecules especially those that exhibit a large amplitude motion, such as NH3, or have a high density of states such as SO2; and b) characterization of the atmospheres of exoplanets which will be one of the main areas of research in astronomy in the coming decades. The first motivation arises due to the need to eliminate lines due to common molecules in an astronomical observation in order to identify lines from new molecules, while the second motivation arises due to the need to obtain accurate molecular opacities in order to characterize the atmosphere of an exoplanet. The BTRHE strategy first consists of using high quality ab initio quantum chemical methods to obtain a global potential energy surface (PES) and dipole moment surface (DMS) that contains the proper physics. The global PES is then refined using a subset of the reliable high-resolution experimental data. The refined PES then gives energy level predictions to an accuracy similar to the reproduction accuracy of the experimental data used in the refinement step in the interpolation region (i.e., within the range of the experimental data used in the refinement step). The accuracy of the energy levels will slowly degrade as they are extrapolated to spectral regions beyond the high-resolution experimental data used in the refinement step. However, because the degradation is slow, the predicted energy levels can be used to assign new high-resolution experiments, and the data from these can then be used in a subsequent refinement step. In this way, the global PES eventually can yield highly accurate energy levels for all desired spectral regions including to very high energies and high J values. We show that IR intensities computed with the BTRHE rovibrational wavefunctions and the DMS can be very accurate provided one has minimized the fitting error of the DMS and tested the completeness of the DMS. Some examples of our work on NH3, CO2, and SO2 are given to highlight the usefulness of the BTRHE strategy and to provide ideas on how to further improve its predictive power in the future. In particular, it is shown how successive refinement steps, once new high-resolution data is available, can lead to PESs that yield highly accurate transition energies to larger spectral regions. The importance of including non-adiabatic corrections to reduce the J-dependence of errors for H-containing molecules is shown with work on NH3. Another very important aspect of the BTRHE approach is the consistency across isotopologues, which allows for highly accurate line lists for any isotopologue once one is obtained for the main isotopologue (which has more high-resolution data available for refinement).

Xinchuan Huang↗

NASA NTRS1989

Study of the integration of wind tunnel and computational methods for aerodynamic configurations

A study was conducted to determine the effectiveness of using a low-order panel code to estimate wind tunnel wall corrections. The corrections were found by two computations. The first computation included the test model and the surrounding wind tunnel walls, while in the second computation the wind tunnel walls were removed. The difference between the force and moment coefficients obtained by comparing these two cases allowed the determination of the wall corrections. The technique was verified by matching the test-section, wall-pressure signature from a wind tunnel test with the signature predicted by the panel code. To prove the viability of the technique, two cases were considered. The first was a two-dimensional high-lift wing with a flap that was tested in the 7- by 10-foot wind tunnel at NASA Ames Research Center. The second was a 1/32-scale model of the F/A-18 aircraft which was tested in the low-speed wind tunnel at San Diego State University. The panel code used was PMARC (Panel Method Ames Research Center). Results of this study indicate that the proposed wind tunnel wall correction method is comparable to other methods and that it also inherently includes the corrections due to model blockage and wing lift.

Browne, Lindsey E.↗

NASA NTRS1974

Some improvements in DNA interaction calculations

Calculations are made on specific DNA-type complexes using refined expressions for electrostatic and polarization energies. Dispersion and repulsive terms are included in the evaluation of the total interaction energy. It is shown that the expansion of the electrostatic potential to include multipole moments up to octopole is necessary to achieve convergence of first-order energies. Polarization energies are not as sensitive to this expansion. The calculations also support the usefulness of the hard sphere model for DNA hydrogen bonds and indicate how stacking interactions are influenced by second-order energies.

Egan, J. T.↗

NASA NTRS2004

Lightweight Deployable Mirrors with Tensegrity Supports

The upper part of Figure 1 shows a small-scale prototype of a developmental class of lightweight, deployable structures that would support panels in precise alignments. In this case, the panel is hexagonal and supports disks that represent segments of a primary mirror of a large telescope. The lower part of Figure 1 shows a complete conceptual structure containing multiple hexagonal panels that hold mirror segments. The structures of this class are of the tensegrity type, which was invented five decades ago by artist Kenneth Snelson. A tensegrity structure consists of momentfree compression members (struts) and tension members (cables). The structures of this particular developmental class are intended primarily as means to erect large segmented primary mirrors of astronomical telescopes or large radio antennas in outer space. Other classes of tensegrity structures could also be designed for terrestrial use as towers, masts, and supports for general structural panels. An important product of the present development effort is the engineering practice of building a lightweight, deployable structure as an assembly of tensegrity modules like the one shown in Figure 2. This module comprises two octahedral tensegrity subunits that are mirror images of each other joined at their plane of mirror symmetry. In this case, the plane of mirror symmetry is both the upper plane of the lower subunit and the lower plane of the upper subunit, and is delineated by the midheight triangle in Figure 2. In the configuration assumed by the module to balance static forces under mild loading, the upper and lower planes of each sub-unit are rotated about 30 , relative to each other, about the long (vertical) axis of the structure. Larger structures can be assembled by joining multiple modules like this one at their sides or ends. When the module is compressed axially (vertically), the first-order effect is an increase in the rotation angle, but by virtue of the mirror arrangement, the net first-order rotation between the uppermost and lowermost planes is zero. The need to have zero net rotation between these planes under all loading conditions in a typical practical structure is what prompts the use of the mirror configuration. Force and moment loadings other than simple axial compression produce only second-order deformations through strains in the struts and cables.

Zeiders, Glenn W.↗

NASA NTRS1982

Linear force and moment equations for an annular smooth shaft seal perturbed both angularly and laterally

Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.

Fenwick, J.↗

NASA NTRS1977

Study of photon correlation techniques for processing of laser velocimeter signals

The objective was to provide the theory and a system design for a new type of photon counting processor for low level dual scatter laser velocimeter (LV) signals which would be capable of both the first order measurements of mean flow and turbulence intensity and also the second order time statistics: cross correlation auto correlation, and related spectra. A general Poisson process model for low level LV signals and noise which is valid from the photon-resolved regime all the way to the limiting case of nonstationary Gaussian noise was used. Computer simulation algorithms and higher order statistical moment analysis of Poisson processes were derived and applied to the analysis of photon correlation techniques. A system design using a unique dual correlate and subtract frequency discriminator technique is postulated and analyzed. Expectation analysis indicates that the objective measurements are feasible.

Mayo, W. T., Jr.↗