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NASA NTRS1992

Experimental and theoretical studies of the He(2+)-He system - Differential cross sections for direct, single-, and double-charge-transfer scattering at keV energies

Measurements and calculations of differential cross sections for direct scattering, single-charge transfer, and double-charge transfer in collisions of 1.5-, 2.0-, 6.0-, and 10.0-keV (He-3)2+ with an He-4 target are reported. The measurements cover laboratory scattering angles below 1.5 deg with an angular resolution of about 0.03 deg. A quantum-mechanical molecular-state representation is employed in the calculations; in the case of single-charge transfer a two-state close-coupling calculation is carried out taking into account electron-translation effects. The theoretical calculations agree well with the experimental results for direct scattering and double-charge transfer. The present calculation identifies the origins of oscillatory structures observed in the differential cross sections.

Gao, R. S.↗

NASA NTRS1991

Differential tracking data types for accurate and efficient Mars planetary navigation

Ways in which high-accuracy differential observations of two or more deep space vehicles can dramatically extend the power of earth-based tracking over conventional range and Doppler tracking are discussed. Two techniques - spacecraft-spacecraft differential very long baseline interferometry (S/C-S/C Delta(VLBI)) and same-beam interferometry (SBI) - are discussed. The tracking and navigation capabilities of conventional range, Doppler, and quasar-relative Delta(VLBI) are reviewed, and the S/C-S/C Delta (VLBI) and SBI types are introduced. For each data type, the formation of the observable is discussed, an error budget describing how physical error sources manifest themselves in the observable is presented, and potential applications of the technique for Space Exploration Initiative scenarios are examined. Requirements for spacecraft and ground systems needed to enable and optimize these types of observations are discussed.

Edwards, C. D., Jr.↗

NASA NTRS1992

Optimal moving grids for time-dependent partial differential equations

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Wathen, A. J.↗

NASA NTRS1992

The effect of temperature on attenuation-correction schemes in rain using polarization propagation differential phase shift

The study elucidates and quantifies differences in the response of the rate of change of polarization propagation differential phase shift Phi, the rate of attenuation for a horizontally/vertically polarized wave A(H,V), and the rate of polarization differential attenuation A(H-V) to temperature. It is shown that if the effects of temperature when estimating A(H) and A(H-V) from Phi are neglected, the average fractional standard error increases only slightly at 9 GHz but significantly at 5 and 3 GHz. Errors at 5 and 3 GHz are about two to three times those at 9 GHz. The performance of Phi-based schemes of attenuation correction at these lower frequencies is much more significantly degraded by temperature uncertainty than at 9 GHz. It is concluded that it is best to use Phi to correct for attenuation at the least-attenuating frequencies.

Jameson, A. R.↗

NASA NTRS1992

Inheritance of silicate differentiation during lunar origin by giant impact

It is pointed out that the implication of the popular giant impact model of lunar origin (e.g., Hartmann and Davis, 1975; Cameron and Ward, 1976; Stevenson, 1987) is that any depth-related silicate differentiation within the impactor (and/or the earth) at the time of the impact must be partly inherited by the preferentially peripheral matter that forms the moon. This paper presents calculations of the magnitude of the net differentiation of the protolunar matter for a variety of elements and scenarios, with different assumptions regarding the geometries of the 'sampled' peripheral zones, the relative proportions of the earth-derived to impactor-derived matter in the final moon, and the degree to which the impactor mantle had crystallized prior to the giant impact. It is shown that these differention effects constrain the overall plausibility of the giant impact hypothesis.

Warren, Paul H.↗

NASA NTRS1993

Differential Interferometry For Spacecraft Navigation

Report proposes use of differential very-long-baseline interferometry to measure accurately angular separation, viewed from Earth, of two spacecraft near another planet. One spacecraft would be in orbit around planet on trajectory already determined accurately, relative to planet, by conventional Doppler tracking. Other spacecraft would be approaching planet. Use of differential very-long-baseline interferometry "tie" between two spacecraft and previously determined "tie" between orbiter and planet increases accuracy of navigation of approaching spacecraft relative to planet.

Edwards, Charles D.↗

NASA NTRS1993

Fast Differential Adder

Differential adding circuit (or, equivalently, subtracting circuit) faster and consumes less power because it contains only one differential amplifier. Suitable for use in high-frequency-switching, high power-regulating circuit.

Arditti, Mort A.↗

NASA NTRS1992

Diode injection - seeded, 940 nanometer (nm), titanium - sapphire laser for H2O DIAL (differential absorption lidar), measurements

Differential absorption of laser radiation by various molecular species represents both a selective and a sensitive method of measuring specific atmospheric constituents. DIAL measurements can be carried out via two different means. Both involve using two laser pulses with slightly different wavelengths (lambda), (one lambda at a strong absorption line of the molecule of interest, the other detuned into the wing of the line), and comparing the attenuation of the pulses. One approach relies on scattering of the radiation from some conveniently located topographical target. In the other technique elastic scattering from atmospheric aerosols and particulates is used to return the radiation to the lidar receiver system. This case is referred to as the differential absorption and scattering technique, and is the technique we are interested in to measure water vapor at 940 nm. The 940 nm wavelength is extremely desirable to atmospheric scientist interested in accurate DIAL measurements of H2O in the upper and lower troposphere. Simulated measurements using approximately 940 nm and 815 nm lasers at a range of altitudes and experimental conditions are shown. By offering access to larger absorption cross-sections, injected seeded, 940 nm DIAL laser transmitters would allow for more accurate water profile measurements at altitudes from 6 to 16 km than is currently possible with 730 nm and 815 nm DIAL laser transmitters. We have demonstrated the operation of an injected seeded titanium-sapphire (TS) laser operating at approximately 940 nm with an energy of more than 90 mJ per pulse. The TS laser is pumped by a commercial, 600 mJ, 532 nm, 10 Hz Nd:YAG laser. The slope efficiency of the laser using a flat 50 percent R output coupler and a 10 m end-mirror is shown. The laser was injected seeded with a CW, AlGaAs, semiconductor diode laser which had an output of 83 mW. The CW diode seed beam was introduced into the TS laser cavity through a HR end-mirror. When the diode beam is aligned to the TS resonator, it controls the TS laser output wavelength and its spectral line width with the required resolution for DIAL applications. This work supports the need for the development of 940 nm, titanium-sapphire DIAL transmitters.

Miller, George E.↗

NASA NTRS1992

COBE Differential Microwave Radiometer (DMR) data processing techniques

The purpose of the Differential Microwave Radiometer (DMR) experiment on the Cosmic Background Explorer (COBE) satellite is to make whole-sky maps, at frequencies of 31.5, 53, and 90 GHz, of any departures of the Cosmic Microwave Background (CMB) from its mean value of 2.735 K. An elaborate software system is necessary to calibrate and invert the differential measurements, so as to make sky maps free from large scale systematic errors to levels less than a millionth of the CMB.

Jackson, P. D.↗

NASA NTRS1992

Flight evaluation of differential GPS aided inertial navigation systems

Algorithms are described for integration of Differential Global Positioning System (DGPS) data with Inertial Navigation System (INS) data to provide an integrated DGPS/INS navigation system. The objective is to establish the benefits that can be achieved through various levels of integration of DGPS with INS for precision navigation. An eight state Kalman filter integration was implemented in real-time on a twin turbo-prop transport aircraft to evaluate system performance during terminal approach and landing operations. A fully integrated DGPS/INS system is also presented which models accelerometer and rate-gyro measurement errors plus position, velocity, and attitude errors. The fully integrated system was implemented off-line using range-domain (seventeen-state) and position domain (fifteen-state) Kalman filters. Both filter integration approaches were evaluated using data collected during the flight test. Flight-test data consisted of measurements from a 5 channel Precision Code GPS receiver, a strap-down Inertial Navigation Unit (INU), and GPS satellite differential range corrections from a ground reference station. The aircraft was laser tracked to determine its true position. Results indicate that there is no significant improvement in positioning accuracy with the higher levels of DGPS/INS integration. All three systems provided high-frequency (e.g., 20 Hz) estimates of position and velocity. The fully integrated system provided estimates of inertial sensor errors which may be used to improve INS navigation accuracy should GPS become unavailable, and improved estimates of acceleration, attitude, and body rates which can be used for guidance and control. Precision Code DGPS/INS positioning accuracy (root-mean-square) was 1.0 m cross-track and 3.0 m vertical. (This AGARDograph was sponsored by the Guidance and Control Panel.)

Mcnally, B. David↗

NASA NTRS1992

Automatic Differentiation as a tool in engineering design

Automatic Differentiation (AD) is a tool that systematically implements the chain rule of differentiation to obtain the derivatives of functions calculated by computer programs. In this paper, it is assessed as a tool for engineering design. The paper discusses the forward and reverse modes of AD, their computing requirements, and approaches to implementing AD. It continues with application to two different tools to two medium-size structural analysis problems to generate sensitivity information typically necessary in an optimization or design situation. The paper concludes with the observation that AD is to be preferred to finite differencing in most cases, as long as sufficient computer storage is available.

Barthelemy, Jean-Francois M.↗

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 NTRS1992

Mapping the sky with the COBE differential microwave radiometers

The Differential Microwave Radiometers (DMR) instrument on COBE is designed to determine the anisotropy of the Cosmic Microwave Background by providing all-sky maps of the diffuse sky brightness at microwave frequencies. The principal intent of this lecture is to show how these maps are generated from differential measurements.

Janssen, M. A.↗

NASA NTRS1938

A flight investigation of the reduction of aileron operating force by means of fixed tabs and differential linkage, with notes on linkage design

Flight tests were made to demonstrate the particularity of employing fixed tabs in conjunction with a suitably designed differential linkage to reduce the force required to operate ailerons. The tests showed the system to be practicable with tabs of the inset type. The relative ineffectiveness of attached tabs for changing the aileron floating angle rendered them unsuitable. Experience gained in the investigation has indicated that the use of the system is limited to maximum deflections of one aileron relative to the other of less than 30 degrees and that the differential linkage should always be designed on the basis of the highest probable floating angle.

Soule, H A↗

NASA NTRS1928

Differential Pressures on a Pitot-venturi and a Pitot-static Nozzle over 360 Degrees Pitch and Yaw

Measurements of the differential pressures on two navy air-speed nozzles, consisting of a Zahm type Pitot-Venturi tube and a SQ-16 two-pronged Pitot-static tube, in a tunnel air stream of fixed speed at various angles of pitch and yaw between 0 degrees and plus or minus 180 degrees. This shows for a range over -20 degrees to +20 degrees pitch and yaw, indicated air speeds varying very slightly over 2 per cent for the Zahm type and a maximum of about 5 per cent for the SQ-16 type from the calibrated speed at 0 degree. For both types of air-speed nozzle the indicated air speed increases slightly as the tubes are pitched or yawed several degrees from their normal 0 degrees altitude, attains a maximum around plus or minus 15 degrees to 25 degrees, declines rapidly therefrom as plus or minus 40 degrees is passed, to zero in the vicinity of plus or minus 70 degrees to 100 degrees, and thence fluctuates irregular from thereabouts to plus or minus 180 degrees. The complete variation in indicated air speed for the two tubes over 360 degree pitch and yaw is graphically portrayed in figures 9 and 10. For the same air speed and 0 degree pitch and yaw the differential pressure of the Zahm type Pitot-Venturi nozzle is about seven times that of the SQ-16 type two-prolonged Pitot-static nozzle.

Bear, R M↗

NASA NTRS1933

Measurement of the Differential and Total Thrust and Torque of Six Full-Scale Adjustable-Pitch Propellers

Force measurements giving total thrust and torque, and propeller slip stream surveys giving differential thrust and torque were simultaneously made on each of six full-scale propellers in the 20-foot propeller-research tunnel of the National Advisory Committee for Aeronautics. They were adjustable-pitch metal propellers 9.5 feet in diameter; three had modified Clark Y blade sections and three had modified RAF-6 blade sections. This report gives the differential thrust and torque and the variation caused by changing the propeller tip speed and the pitch setting. The total thrust and torque obtained from integration of the thrust and torque distribution curves are compared with those obtained by direct force measurements.

Stickle, George W↗

NASA NTRS1994

Algorithms For Integrating Nonlinear Differential Equations

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Freed, A. D.↗

NASA NTRS1993

A hybrid Pade-Galerkin technique for differential equations

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Geer, James F.↗