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NASA NTRS1988

Novel tether-connected two-dimensional structures for low earth orbits

This paper proposes novel tether-connected two-dimensional structures with a size of several hundred square kilometers for low earth orbits. The attitude of these structures is gravitationally stabilized with respect to an earth-oriented reference frame. A stable shape is obtained by utilizing environmental forces such as differential air drag or electrodynamic forces which stiffen the system. Configurations which differ in geometry and in the number of connecting tethers are presented in the paper. The static stability of each configuration is analyzed as a function of design and orbital parameters. A brief discussion of the applications of such tethered systems is provided at the end of the paper.

Lorenzini, Enrico C.↗

NASA NTRS1976

Computation of wave drag for transonic flow

The paper develops a method for calculating wave drag for two-dimensional transonic flow, with particular application to the prediction of the drag rise Mach number of a supercritical wing section. The method is based on a transonic similarity model which is defined by a normalized small perturbation equation and represents shock waves by the addition of an artificial viscosity term in the region of supersonic flow to the partial differential equation. The drag formula obtained allows the computer simulation of transonic wind tunnel data taking account of boundary layer and wall effects.

Garabedian, P. R.↗

NASA NTRS1990

A review of computational/experimental methodology developments in aeroacoustics

A number of studies in the area of propeller design and advanced configuration performance/acoustics are reviewed. Various designs are analyzed in the area of propeller efficiency, lift-to-drag ratio, and differential thrust and power coefficients. Predictions are compared to experiment and the numerical analyses are examined for restrictions and potential enhancements.

Eagleson, L. A.↗

NASA NTRS1993

Formation of planetesimals in the solar nebula

The evolution of solid particles in the solar nebula (or other circumstellar disk) is described. Motions of bodies less than about 1 km in size were dominated by gas drag rather than gravity. An original population of microscopic grains had to produce greater than km-sized planetesimals before gravitational accretion of planets could begin. Planetesimals probably formed by coagulation of grain aggregates that collided due to differential settling, turbulence, and drag-induced orbital decay. Growth of such aggregates depended on sticking mechanisms and their mechanical properties, which are poorly understood. Their growth was aided by concentration of larger bodies toward the central plane of the disk. The nebula could remain optically thick during this process. It is unlikely that a particle layer formed by settling would undergo gravitational instability, as a small amount of turbulence would keep the particle layer from reaching the critical density. This conclusion is independent of the particle size, as even large bodies do not effectively decouple from the gas. Even in a laminar disk, shear in the particle layer would generate enough turbulence to keep it stirred up.

Weidenschilling, S. J.↗

NASA NTRS1984

Comparison of various drag coefficient expansions using polynomials and splines

The longitudinal differential equation of motion has been used to investigate various aerodynamic expansion techniques. The total drag coefficient was expanded using conventional polynomials and splines with and without floating knot locations. This paper discusses the various techniques and approaches, compares results obtained from simultaneously fitting four separate flights (time vs distance measurements) and outlines the potential advantages and/or disadvantages of the various aerodynamic expansion techniques. It is believed that this is the first time splines have been used in the aerodynamic coefficient estimation process and that these results and techniques are germane to other applications.

Sabot, S. M.↗

NASA NTRS1979

Measurement in multiphase reacting flows

A survey is presented of diagnostic techniques and measurements made in multiphase reacting flows. The special problems encountered by the presence of liquid droplets, soot and solid particles in high temperature chemically reacting turbulent environments are outlined. The principal measurement techniques that have been tested in spray flames are spark photography, laser anemometry, thermocouples and suction probes. Spark photography provides measurement of drop size, drop size distribution, drop velocity, and angle of flight. Photographs are analysed automatically by image analysers. Photographic techniques are reliable, inexpensive and proved. Laser anemometers have been developed for simultaneous measurement of velocity and size of individual particles in sprays under conditions of vaporization and combustion. Particle/gas velocity differentials, particle Reynolds numbers, local drag coefficients and direct measurement of vaporization rates can be made by laser anemometry. Gas temperature in sprays is determined by direct in situ measurement of time constants immediately prior to measurement with compensation and signal analysis by micro-processors. Gas concentration is measured by suction probes and gas phase chromatography. Measurements of particle size, particle velocity, gas temperature, and gas concentration made in airblast and pressure atomised liquid spray flames are presented.

Chigier, N. A.↗

NASA NTRS1993

Sensitivity derivatives for advanced CFD algorithm and viscous modelling parameters via automatic differentiation

The computational technique of automatic differentiation (AD) is applied to a three-dimensional thin-layer Navier-Stokes multigrid flow solver to assess the feasibility and computational impact of obtaining exact sensitivity derivatives typical of those needed for sensitivity analyses. Calculations are performed for an ONERA M6 wing in transonic flow with both the Baldwin-Lomax and Johnson-King turbulence models. The wing lift, drag, and pitching moment coefficients are differentiated with respect to two different groups of input parameters. The first group consists of the second- and fourth-order damping coefficients of the computational algorithm, whereas the second group consists of two parameters in the viscous turbulent flow physics modelling. Results obtained via AD are compared, for both accuracy and computational efficiency with the results obtained with divided differences (DD). The AD results are accurate, extremely simple to obtain, and show significant computational advantage over those obtained by DD for some cases.

Green, Lawrence L.↗

NASA NTRS1983

Integrals of motion for the classical two-body problem with drag

Integrals of motion for the two-body problem with drag are obtained by operating on the second-order vector differential equation describing the motion. The force field consists of an inverse-square gravitational attraction and a drag force proportional to the velocity vector and inversely proportional to the square of the distance to the attracting center. The developed integrals are the analogs of the Keplerian scalar energy, the vector angular momentum, and the Laplace vector.

Jezewski, D. J.↗

NASA NTRS1977

Effect of rotor wake on aerodynamic characteristics of a 1/6 scale model of the rotor systems research aircraft

Tests were conducted in the Langley V/STOL tunnel to determine the effect of the main-rotor wake on the aerodynamic characteristics of the rotor systems research aircraft. A 1/6-scale model with a 4-blade articulated rotor was used to determine the effect of the rotor wake for the compound configuration. Data were obtained over a range of angles of attack, angles of sideslip, auxiliary engine thrusts, rotor collective pitch angles, and rotor tip-path plane angles for several main-rotor advance ratios. Separate results are presented for the forces and moments on the airframe, the wing, and the tail. An analysis of the test data indicates significant changes in the aerodynamic characteristics. The rotor wake increases the longitudinal static stability, the effective dihedral, and the lateral static stability of the airframe. The rotor induces a downwash on the wing. This downwash decreases the wing lift and increases the drag. The asymmetrical rotor wake induces a differential lift across the wing and a subsequent rolling moment. These rotor induced effects on the wing become smaller with increasing forward speed.

Mineck, R. E.↗

NASA NTRS1981

An analytic solution to the classical two-body problem with drag

The two body problem was analyzed with a specific drag model. The model treats drag as a force proportional to the vector velocity and inversely proportional to the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time of flight is expressed as a quadrature in the true anomaly. The results are: (1) development of a vector differential equation which allows analysis of an infinite number of gravitational and drag models; and (2) obtaining the solution of a linear differential equation using the inverse method of laplace transforms.

Mittleman, D.↗

NASA NTRS1952

Landing-gear impact

Report deals with the impact forces in landing gears. Both the landing impact and the taxiing impact have been considered, but drag forces have so far been excluded. The differential equations are developed and their numerical integration is shown, considering the nonlinear properties of the oleo shock strut. A way is shown for determining the dimensions of the metering pin from a given load-time diagram. A review of German literature on landing-gear impact is also presented.

Flugge, W↗

NASA NTRS1979

Development of analytical orbit propagation technique with drag

Two orbit computation methods were used: (1) numerical method- The solution to the satellite differential equations were solved in a step-by-step manner, using a mathematical algorithm taken from numerical analysis; and (2) analytical method - The solution was expressed by explicit functions of the independent variable. Analytical drag modules, tesseral terms initialization module, second order and long period terms module, and verification testing of the ASOP program were also considered.

Source record↗

NASA NTRS2017

Assessment of a Conceptual Flap System Intended for Enhanced General Aviation Safety

A novel multielement trailing-edge flap system for light general aviation airplanes was conceived for enhanced safety during normal and emergency landings. The system is designed to significantly reduce stall speed, and thus approach speed, with the goal of reducing maneuveringflight accidents and enhancing pilot survivability in the event of an accident. The research objectives were to assess the aerodynamic performance characteristics of the system and to evaluate the extent to which it provided both increased lift and increased drag required for the low-speed landing goal. The flap system was applied to a model of a light general aviation, high-wing trainer and tested in the Langley 12- Foot Low-Speed Wind Tunnel. Data were obtained for several device deflection angles, and component combinations at a dynamic pressure of 4 pounds per square foot. The force and moment data supports the achievement of the desired increase in lift with substantially increased drag, all at relatively shallow angles of attack. The levels of lift and drag can be varied through device deflection angles and inboard/outboard differential deflections. As such, it appears that this flap system may provide an enabling technology to allow steep, controllable glide slopes for safe rapid descent to landing with reduced stall speed. However, a simple flat-plate lower surface spoiler (LSS) provided either similar or superior lift with little impact on pitch or drag as compared to the proposed system. Higher-fidelity studies are suggested prior to use of the proposed system.

Campbell, Bryan A.↗

NASA NTRS1975

Recent developments in density, temperature and momentum fluctuation measurement

Attention is drawn to recent advancements in the fluctuating line-reversal temperature measurement, the development of the two-dimensional drag-sensing probe into a three-dimensional drag-sensing probe, and the fluctuating density gradient cross beam Schlieren technique. An experimental apparatus is explained whereby the temperature fluctuation in a pulsating air-fuel ratio Bunsen burner is measured by means of sodium D-line reversal methods with a new photoelectric circuit to obtain both fluctuating and mean temperature data. The three-D drag probe is made possible by a newly invented differential and total magnetic sensing system that separates signals due to three orthogonal movements so that the vectorial momentum fluctuation can be measured. In the case of the Schlieren technique, the effect of anisotropic density gradients with respect to the angle between the polarization plane and the knife edge of a laser Schlieren system is studied.

Battle, T. M.↗

NASA NTRS1983

Time controlled descent guidance algorithm for simulation of advanced ATC systems

Concepts and computer algorithms for generating time controlled four dimensional descent trajectories are described. The algorithms were implemented in the air traffic control simulator and used by experienced controllers in studies of advanced air traffic flow management procedures. A time controlled descent trajectory comprises a vector function of time, including position, altitude, and heading, that starts at the initial position of the aircraft and ends at touchdown. The trajectory provides a four dimensional reference path which will cause an aircraft tracking it to touchdown at a predetermined time with a minimum of fuel consumption. The problem of constructing such trajectories is divided into three subproblems involving synthesis of horizontal, vertical, and speed profiles. The horizontal profile is constructed as a sequence of turns and straight lines passing through a specified set of waypoints. The vertical profile consists of a sequence of level flight and constant descent angle segments defined by altitude waypoints. The speed profile is synthesized as a sequence of constant Mach number, constant indicated airspeed, and acceleration/deceleration legs. It is generated by integrating point mass differential equations of motion, which include the thrust and drag models of the aircraft.

Lee, H. Q.↗

NASA NTRS1997

Wave Driven Exothermic Heating in the Mesopause Region

A full-wave propagation model was developed that describes the propagation of gravity waves from the Earth's surface to the upper boundary, which can be placed anywhere between 150 and 500 km altitude. The model includes a realistic background atmosphere, and includes the effects of mean horizontal winds and their vertical shears, mean vertical temperature gradients, the eddy and molecular diffusion of heat and momentum, and the effects of ion-drag. This model solves five coupled second-order differential equations (continuity, momentum, and energy) in the vertical coordinate to derive the perturbation variables u', v', w' (horizontal and vertical velocity components), T' (temperature) and p' (pressure). The upper boundary can be automatically selected based on tests using the radiation condition at the upper boundary, wherein the height is increased until the wave is experiencing severe dissipation at the upper boundary, ensuring that substantial absorption occurs for any waves reflected from the upper boundary. The determination of wave amplitude is a key requirement of wave energetics. Therefore, the fullwave model has been applied to airglow observations in order to determine wave amplitudes as a function of altitude. This was accomplished by using the full-wave model output to drive a chemistry perturbation module that describes minor species perturbations and the resulting airglow perturbations. The full-wave output was multiplied by an altitude-independent factor such that the modeled and observed relative airglow intensity perturbations were equal. The effects of mean winds were included in these studies, and found to be the most important model input affecting the calculations (being more important than the choice of eddy diffusion profiles and chemical kinetic coefficients). In one study (Hickey et al., 1997a) these winds could not be well estimated from the measurements, whereas in the second study (Hickey et al.,1997b) the mean were well defined with a sodium wind-temperature lidar.

Hickey, Michael P.↗

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.↗