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NASA NTRS2010

Analytic Development of a Reference Profile for the First Entry in a Skip Atmospheric Entry

This note shows that a feasible reference drag profile for the first entry portion of a skip entry can be generated as a polynomial expression of the velocity. The coefficients of that polynomial are found through the resolution of a system composed of m + 1 equations, where m is the degree of the drag polynomial. It has been shown that a minimum of five equations (m = 4) are required to establish the range and the initial and final conditions on velocity and flight path angle. It has been shown that at least one constraint on the trajectory can be imposed through the addition of one extra equation in the system, which must be accompanied by the increase in the degree of the drag polynomial. In order to simplify the resolution of the system of equations, the drag was considered as being a probability density function of the velocity, with the velocity as a distribution function of the drag. Combining this notion with the introduction of empirically derived constants, it has been shown that the system of equations required to generate the drag profile can be successfully reduced to a system of linear algebraic equations. For completeness, the resulting drag profiles have been flown using the feedback linearization method of differential geometric control as a guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. Satisfactory results were achieved when the gains in the error dynamics were changed at a certain point along the trajectory that is dependent on the velocity and the curvature of the drag as a function of the velocity. Future work should study the capacity to update the drag profile in flight when dispersions are introduced. Also, future studies should attempt to link the first entry, as presented and controlled in this note, with a more standard control concept for the second entry, such as the Apollo entry guidance, to try to assess the overall skip entry performance. A guidance law that includes an integral feedback term, as is the case in the actual Space Shuttle entry guidance and as is proposed in Ref 29, could be tried in future studies to assess whether its use results in an improvement of the tracking performance, and to evaluate the design needs when determining the control gains.

Garcia-Llama, Eduardo↗

NASA NTRS2013

Analysis of a Split-Plot Experimental Design Applied to a Low-Speed Wind Tunnel Investigation

A procedure to analyze a split-plot experimental design featuring two input factors, two levels of randomization, and two error structures in a low-speed wind tunnel investigation of a small-scale model of a fighter airplane configuration is described in this report. Standard commercially-available statistical software was used to analyze the test results obtained in a randomization-restricted environment often encountered in wind tunnel testing. The input factors were differential horizontal stabilizer incidence and the angle of attack. The response variables were the aerodynamic coefficients of lift, drag, and pitching moment. Using split-plot terminology, the whole plot, or difficult-to-change, factor was the differential horizontal stabilizer incidence, and the subplot, or easy-to-change, factor was the angle of attack. The whole plot and subplot factors were both tested at three levels. Degrees of freedom for the whole plot error were provided by replication in the form of three blocks, or replicates, which were intended to simulate three consecutive days of wind tunnel facility operation. The analysis was conducted in three stages, which yielded the estimated mean squares, multiple regression function coefficients, and corresponding tests of significance for all individual terms at the whole plot and subplot levels for the three aerodynamic response variables. The estimated regression functions included main effects and two-factor interaction for the lift coefficient, main effects, two-factor interaction, and quadratic effects for the drag coefficient, and only main effects for the pitching moment coefficient.

Erickson, Gary E.↗

NASA NTRS1986

Analytical determination of propeller performance degradation due to ice accretion

A computer code has been developed which is capable of computing propeller performance for clean, glaze, or rime iced propeller configurations, thereby providing a mechanism for determining the degree of performance degradation which results from a given icing encounter. The inviscid, incompressible flow field at each specified propeller radial location is first computed using the Theodorsen transformation method of conformal mapping. A droplet trajectory computation then calculates droplet impingement points and airfoil collection efficiency for each radial location, at which point several user-selectable empirical correlations are available for determining the aerodynamic penalities which arise due to the ice accretion. Propeller performance is finally computed using strip analysis for either the clean or iced propeller. In the iced mode, the differential thrust and torque coefficient equations are modified by the drag and lift coefficient increments due to ice to obtain the appropriate iced values. Comparison with available experimental propeller icing data shows good agreement in several cases. The code's capability to properly predict iced thrust coefficient, power coefficient, and propeller efficiency is shown to be dependent on the choice of empirical correlation employed as well as proper specification of radial icing extent.

Miller, T. L.↗

NASA NTRS2007

Analytic Guidance for the First Entry in a Skip Atmospheric Entry

This paper presents an analytic method to generate a reference drag trajectory for the first entry portion of a skip atmospheric entry. The drag reference, expressed as a polynomial function of the velocity, will meet the conditions necessary to fit the requirements of the complete entry phase. The generic method proposed to generate the drag reference profile is further simplified by thinking of the drag and the velocity as density and cumulative distribution functions respectively. With this notion it will be shown that the reference drag profile can be obtained by solving a linear algebraic system of equations. The resulting drag profile is flown using the feedback linearization method of differential geometric control as guidance law with the error dynamics of a second order homogeneous equation in the form of a damped oscillator. This approach was first proposed as a revisited version of the Space Shuttle Orbiter entry guidance. However, this paper will show that it can be used to fly the first entry in a skip entry trajectory. In doing so, the gains in the error dynamics will be changed at a certain point along the trajectory to improve the tracking performance.

Garcia-Llama, Eduardo↗

NASA NTRS1986

A three-dimensional dynamic analysis and libration study of a tethered satellites system

By a three-dimensional Lagrangian formulation, an exact set of ten coupled nonlinear second-order differential equations has been derived for a system with an extensible tether connecting two end satellites of distributed mass. The effects of tether mass, small orbital eccentricity, central body oblateness, aerodynamic drag force, and solar radiation pressure are also included in the formulation. By linearizing the exact differential equations, the in-plane (orbital plane) differential equations are found to be decoupled from the out-of-plane ones. The characteristic equation of the in-plane differential equations is derived and some associated stability constraints are shown.

Tang, C. C. H.↗

NASA NTRS1989

Ageostrophic effects on the stratospheric residual circulation and tracer distributions

The behaviors of idealized geostrophic and ageostrophic circulations forced by differential heating and parameterized eddy mixing in the absence of boundary drag are examined for a range of mixing values and boundary conditions, using a nonlinear version of Holton's (1986) channel model. It was found that geostrophic and ageostrophic flows can have fundamentally different behaviors. This may have important implications for the circulation and trace gas distributions in the stratosphere. It is shown that, as eddy forcing vanishes, an ageostrophic system is not constrained to approach radiative equilibrium and may tend to the limit of an inviscid diabatic circulation under a range of boundary conditions.

Hou, Arthur Y.↗

NASA NTRS2019

Real-Time Modeling of Thermal Interactions in Cryogenic Ball Bearings

Based on the integration of classical differential equations of motion of bearing elements, a real-time dynamic simulation of ball bearing performance is coupled with simultaneous modeling of thermal interactions between the bearing elements. The transient heat generations are time averaged over a significantly larger time step before they are used to compute the changes in bearing temperature fields. Such an averaging algorithm eliminates the numerical difficulties associated with simultaneous integration of mechanical thermal differential equations with vastly different time scales. Under stable operation, the step change in temperatures at each thermal time step converges to a steady-state solution. Following is a list of accomplishments in the present investigation: (1) A real-time dynamic performance of both 440C and hybrid ball bearings in a LOX environment is modeled in both transient and steady-state time domains, as the inner race accelerates to a prescribed operating speed. (2) The frictional interactions at the ball to race contacts are modeled by experimentally measured traction coefficients as a function of slide-to-roll ratios. (3) Bearing heat generation, as defined by the heat transferred to circulating LOX, is validated against experimental values determined by measured LOX temperatures under prescribed pressures and flow rates. The predicted heat generation is in good agreement with the experimental values. (4) The steady-state solutions are shown to be independent of initial conditions. This establishes convergence of the numerical integration of a differential equation of motion of the bearing elements. (5) Churning and drag losses in the circulating LOX constitutes the majority of bearing heat generation under the experimental test conditions. (6) The heat dissipated in frictional interactions in hybrid bearings is significantly lower in hybrid bearings in comparison to that simulated in all-steel bearings, while the churning and drag losses are relatively unchanged.

Gupta, P. K.↗

NASA NTRS1993

Skin friction measurement with partially exposed polymer dispersed liquid crystals

Partially exposed polymer dispersed liquid crystal thin film (10-25 microns) deposited on a flat glass substrate has been used for the first time to measure skin friction. Utilizing the shear-stress-induced director reorientation in the partially exposed liquid-crystal droplets, optical transmission under crossed polarization has been measured as a function of the air flow differential pressure. Direct measurement of the skin friction with a skin friction drag balance, under the same aerodynamic conditions, lets us correlate the skin friction with optical transmission. This provides a unique technique for the direct measurement of skin friction from the transmitted light intensity. The results are in excellent agreement with the model suggested in this paper.

Parmar, D. S.↗

NASA NTRSDate not supplied

Machine Learning Approach for Aircraft Performance Model Parameter Estimation for Trajectory Prediction Applications

Inaccurate prediction of aircraft trajectory by ground-based decision support tools (DST) is a major concern in air traffic management (ATM). Aircraft trajectory prediction tools rely on a simplified point-mass aircraft performance model (APM) to make their predictions. Even though the performance coefficients and weight of an aircraft are a vital part of the APM’s predictions and accuracy, these coefficients are proprietary in nature and therefore, unavailable to DSTs. Current ATM research focuses on improving the estimate of some APM parameters by freezing all other coefficients. This simplified approach introduces unwanted sources of bias and negatively impacts the accuracy of the performance model. In this paper, we apply machine learning (ML) techniques for the simultaneous prediction of three key APM parameters (two drag coefficients and the initial aircraft weight). To accomplish this, we employ an ordinary differential equation (ODE) fitting approach to generate optimized APM parameter labels customized to each individual flight record. Subsequently, we train ML models to capture the relationship between the historical data and the optimized APM parameters. Two different ML model solutions are applied and APM coefficients are predicted for unseen flights. The results indicate that the ML models are able to capture the relationship between APM parameters and flight-related features with good accuracy.

trajectory prediction, machine learning, aircraft ↗

NASA NTRS1974

The movement of small particulate matter in the early solar system and the formation of satellites

The motions of the abundant small particulate matter in the early solar system are discussed. The effects of gas drag and resonance effects of perturbing forces could have led to accretion and differentiation of the matter. The composition of the moon and the existence of the rings of Saturn can be explained on the basis of the assembly of small particulate matter in satellite orbits around the planets.

Gold, T.↗

DOE OSTI2023

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. We focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1972

Low speed aerodynamic characteristics of a large scale model with a thin, highly swept, 2.67 aspect ratio wing having a cranked leading edge

The low speed aerodynamic characteristics of a large-scale model intended to represent advanced fixed-wing fighters have been investigated in the Ames 40 by 80 foot wind tunnel. The model possessed positive static longitudinal stability to nearly 28 deg angle of attack, the maximum tested, both with and without leading-edge flaps deflected. Lateral control with differentially deflected ailerons and a right wing spoiler simultaneously deployed as combined controls was only slightly greater than that with the differentially deflected ailerons deployed as a separate control without the spoiler. Measured lift and drag were in close agreement with that predicted by theory to about 14 deg angle of attack, including the prediction of lift due to 30 deg of trailing edge flap deflection. Estimated takeoff performance of an aircraft 4/3 the scale of the test model showed takeoff distances of less than 2000 ft.

Giulianetti, D. J.↗

NASA NTRS1973

Primordial random motions and angular momenta of galaxies and galaxy clusters.

We study the decay of primordial random motions of galaxies and galaxy clusters in an expanding universe by solving a kinetic equation for the relaxation of differential energy spectra N(E, t). Systematic dissipative energy losses are included, involving gravitational drag by, and accretion of, intergalactic matter, as well as the effect of collisions with other systems. Formal and numerical solutions are described for two distinct modes of galaxy formation in a turbulent medium, corresponding to formation at a distinct epoch and to continuous formation of galaxies. We show that any primordial random motions of galaxies at the present epoch can amount to at most a few km/sec, and that collisions at early epochs can lead to the acquisition of significant amounts of primordial angular momentum.

Silk, J.↗

NASA NTRS1961

A Comparison of Theory and Observation of the Echo I Satellite

Observations of the Echo I balloon satellite have been compared with a theory including the following perturbing effects: (1) solar radiation pressure; (2) lunar and solar gravitation; (3) second, third, and fourth harmonics of the earth's gravitational potential; and (4) atmospheric drag. With a set of orbital elements at the 26th day of the lifetime of the satellite, it was possible to match the observational data to 180 days with root mean square residuals as follows: Delta-a = 17.9 km, Delta-e = 0.0021, Delta-i = 0.0177 deg., Delta-omega = 1.1231 deg., Delta-Omega = 0.4821 deg., Delta-perigee height = 7.50 km. No differential correction has been applied as yet. Values of atmospheric density between 1500 and 930 km, assuming neutral drag effects only, have been inferred from the orbital data. The connection between solar activity and drag is also examined. As the Echo I perigee height continues to oscillate between 900 and 1500 km, more valuable orbital data will be obtained and atmospheric properties will be deduced. Further refinements in the mathematical model, especially in a time-dependent model atmosphere, should bring a substantial reduction in the residuals of the observations.

Bryant, R. W.↗

DOE OSTI2022

TEAMER: DAISY Flow-noise Testing (Abstract)

Evaluating impacts of marine energy devices is generally difficult given the dynamic environment where these devices need to be placed. The University of Washington’s (UW) DAISY (The Drifting Acoustic Instrumentation SYstem) is designed to measure radiated noise around marine energy converters operating in energetic waves and currents. In currents, a primary limitation for measurement fidelity at low frequencies (< 100 Hz) is the potential for non-propagating “flow-noise” to mask propagating sound and inflate estimates of the radiated noise from marine energy converters at frequencies that overlap with hearing sensitivities of fish and some marine mammals. While free-drifting measurements help to minimize the relative velocity that produces flow-noise, significant levels were still observed during initial DAISY tests. This motivated the development of a fabric “flow shield” around the hydrophone that disrupts both flow-noise generation mechanisms proposed by the initial tests. First, the flow shield is a source of substantial drag which keeps the hydrophone package moving with the approximate velocity of the surrounding water, compensating for differential wind or current forcing on the surface expression. By minimizing relative velocity around the hydrophone, turbulence shed by the hydrophone is also minimized. Second, the flow shield creates a largely quiescent pocket around the hydrophone, minimizing advection of free stream turbulence over the hydrophone element. Field data collected in these experiments will test effectiveness of these flow shields and provide quantitative data use and deployment.

16 TIDAL AND WAVE POWER↗

NASA NTRS1972

Earth zonal harmonics from rapid numerical analysis of long satellite arcs

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites including 2 of low inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 200 to 800 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, was accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation of the earth's pole, atmospheric drag, radiation pressure and luni-solar gravity are added at from 1- to 8-day intervals in the integrated orbits. The results agree well with recent solutions from other authors using different methods and different satellite sets.

Wagner, C. A.↗

NASA NTRS1973

Zonal gravity harmonics from long satellite arcs by a seminumeric method.

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites, including two of low (less than 20 deg) inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 50 to 660 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, is accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation, atmospheric drag, radiation pressure, and lunisolar gravity are added at 1- to 8-day intervals in the integrated orbits.

Wagner, C. A.↗

DOE OSTI2021

Analytic quasi-steady evolution of marginally unstable kinetic plasma instabilities in the presence of drag and scattering

The 1D bump-on-tail problem is studied in order to determine the influence of drag on quasi-steady solutions near marginal stability (1-γ d /γ L << 1) when effective collisions are much larger than the instability growth rate (ν>>γ). In this common tokamak regime, it is rigorously shown that the paradigmatic Berk–Breizman cubic equation for the nonlinear mode evolution reduces to a much simpler differential equation, dubbed the time-local cubic equation, which can be solved directly. It is found that in addition to increasing the saturation amplitude, drag introduces a shift in the apparent oscillation frequency by modulating the saturated wave envelope. Furthermore, excellent agreement is found between the analytic solution for the mode evolution and both the numerically integrated Berk–Breizman cubic equation and fully nonlinear 1D Vlasov simulations. Experimentally isolating the contribution of drag to the saturated mode amplitude for verification purposes is explored but complicated by the reality that the amount of drag cannot be varied independently of other key parameters in realistic scenarios. While the influence of drag is modest when the ratio of effective drag to effective scattering α/ν is very small, it can become substantial when α/ν ≳ 0.5, suggesting that drag should be accounted for in quantitative models of fast-ion-driven instabilities in fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗