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At least 127 records · Page 7

Attitude stability of spinning flexible spacecraft

The stability of spinning flexible satellites in a force-free environment was analyzed. The satellite was modeled as a rigid core having attached to it a flexible appendage idealized as a collection of particles (point masses) interconnected by springs. Both Liapunov and Routh-Hurwitz stability procedures are used. In the former, the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, is used as a testing function. Equations of motion are written using the hybrid coordinate formulation, which readily accepts a modal coordinate transformation ultimately allowing truncation to a level amenable to literal stability analysis. Closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane containing the system center of mass and orthogonal to the spin axis. The effects of spin on flexible bodies are discussed by considering a very elementary particle model. Control of passively unstable spacecraft is briefly considered.

Likins, P. W.↗

The development of an earth resources information system using aerial photographs and digital computers

Analytical photogrammetry demonstrated that automatic three dimensional mapping of forest terrain was technically feasible. The examples were black and white photography at scales of 1:10,000 and 1:24,000. The major improvement in terrain modelling was the addition of the capability of joining small quadrangles together to form one large model about equal to the effective area of the pair of photographs. Improvements of somewhat lesser importance include: (1) the use of up to 16 grey levels; (2) the elimination of several coordinate transformations; and (3) the annotation of three-tone hysocline maps with elevations.

Amidon, E. L.↗

Numerical calculation of transonic flow about swept wings.

Description of a mixed elliptic-hyperbolic relaxation algorithm which calculates solutions to the three-dimensional, nonlinear transonic small disturbance potential equation for flows about thin swept lifting wings with free-stream Mach number less than 1. The algorithm is designed to treat supercritical flows, including cases with embedded shock waves. Nonrectangular planform shapes, including sweep and taper, are treated by a coordinate transformation which maps the wing planform into a rectangle. Computed results at angles of attack of 0 and 2 deg for a AR = 4, constant chord, 23.75 deg sweptback planform model with a Lockheed C141 airfoil section are compared with data obtained experimentally for both subcritical and supercritical flows. Subcritical results are also compared with those obtained by a subsonic 'panel' method.

Ballhaus, W. F.↗

Effects of circular geometry in simulation of convection in rotating spacecraft tanks

For computational simulation of the convection and mixing of stratified fluid in a rotating tank (such as used in Apollo flights) with time-dependent rotation, the Navier-Stokes convection problem was formulated for a circular tank configuration. The final equations results from a general approximate theory for combined forced and contained natural convection in a time-dependent rotating system. The equations are cast in terms of vorticity and stream function in a form convenient for computation, with a transformed coordinate system, and appropriate boundary conditions are derived. Accurate representations for the cryogenic supercritical oxygen thermodynamic properties are used in the computations, and an efficient numerical finite difference scheme and computational method are employed.

Martin, E. D.↗

Evaluation of usefulness of Skylab EREP S-190 and S-192 imagery in multistage forest surveys

The author has identified the following significant results. A set of digital interpretation programs have been developed which perform the following tasks: (1) extraction of images for a desired sample unit or combination of sample units by scanner channel and storage of these images on high speed storage devices; (2) extraction of tone and texture information of 8 x 8 pixel interpretation units by channel and storage of these features on a high speed storage device; (3) center of gravity cluster node seeking in higher dimensional space and subsequent nearest neighbor classification, and output of the classification results on a high speed storage device. In all instances the classification results can be related to the original place of subset extraction through the coordinate transformation work previously performed.

Langley, P. G.↗

Analysis of free turbulent shear flows by numerical methods

Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.

Korst, H. H.↗

Diurnal polar motion

An analytical theory is developed to describe diurnal polar motion in the earth which arises as a forced response due to lunisolar torques and tidal deformation. Doodson's expansion of the tide generating potential is used to represent the lunisolar torques. Both the magnitudes and the rates of change of perturbations in the earth's inertia tensor are included in the dynamical equations for the polar motion so as to account for rotational and tidal deformation. It is found that in a deformable earth with Love's number k = 0.29, the angular momentum vector departs by as much as 20 cm from the rotation axis rather than remaining within 1 or 2 cm as it would in a rigid earth. This 20 cm separation is significant in the interpretation of submeter polar motion observations because it necessitates an additional coordinate transformation in order to remove what would otherwise be a 20 cm error source in the conversion between inertial and terrestrial reference systems.

Mcclure, P.↗

STRAP IV - High accuracy, low drift attitude control system.

The STRAP IV attitude control system was designed, tested, and successfully launched to provide stable high accuracy pointing at nontrackable X-ray sources. On its initial flight (May 19, 1972), the STRAP IV control system updated its high accuracy, rate integrating gyros on two successive stellar targets and then maneuvered the rocket body to point the experimental payload at two separate X-ray sources and an X-ray-free background location. The third axis, which remained under the control of a coarse free gyro, was updated by a technique of successive star-target coordinate transformation to ensure the correct fine-axis azimuth alignment for the high accuracy inertial maneuvers. Pointing accuracies of 4 arc min with limit cycle stability of less than 20 arc sec peak to peak were obtained on all targets.

Shrewsberry, D. J.↗

Calculation of unsteady transonic aerodynamics for oscillating wings with thickness.

An analytical approach is presented to account for some of the nonlinear characteristics of the transonic flow equation for finite thickness wings undergoing harmonic oscillation at sonic flight speed in an inviscid, shock-free fluid. The thickness effect is accounted for in the analysis through use of the steady local Mach number distribution over the wing at its mean position by employing the local linearization concept and a coordinate transformation. Computed results are compared with that of the linearized theory and experiments. Application to a flutter problem is shown.

Ruo, S. Y.↗

Numerical calculation of the three dimensional transonic flow over a yawed wing.

Results are presented of calculations of the three dimensional steady transonic flow over a finite yawed wing. The full potential flow equation is solved in a transformed coordinate system which permits the boundary conditions to be satisfied exactly. The correct differential properties are enforced by rotating the difference scheme to conform with the flow direction, and fast convergence is assured by simulating a time dependent equation designed to settle quickly to a steady state. Computed lift drag ratios are consistent with the results of wind tunnel tests of a yawed wing conducted by R. T. Jones (1972).-

Jameson, A.↗

Solutions of the Navier-Stokes equations for vortex breakdown

Steady solutions of the Navier-Stokes equations, in terms of velocity and pressure, for breakdown in an unconfined viscous vortex are obtained numerically using the artificial compressibility technique of Chorin combined with an ADI finite-difference scheme. Axisymmetry is assumed and boundary conditions are carefully applied at the boundaries of a large finite region in an axial plane while resolution near the axis is maintained by a coordinate transformation. The solutions, which are obtained for Reynolds numbers up to 200 based on the free-stream axial velocity and a characteristic core radius, show that breakdown results from the diffusion and convection of vorticity away from the vortex core which, because of the strong coupling between the circumferential and axial velocity fields in strongly swirling flows, can lead to stagnation and reversal of the axial flow near the axis.

Grabowski, W. J.↗

Conservation equations of gasdynamics in curvilinear coordinate systems

Description of a new method of writing the conservation equations of gasdynamics in curvilinear coordinates which eliminates undifferentiated terms. It is thus possible to readily apply difference schemes derived for Cartesian coordinates which conserve mass, momentum, and energy in the total flow field. The method is derived for orthogonal coordinates, and then extended to cover the most general class of coordinate transformations, using general tensor analysis. Several special features of the equations are discussed.

Vinokur, M.↗

Computation of transonic flow about lifting wing-cylinder combinations

Some results are described for a lifting rectangular wing centrally located on a circular-cylindrical body. This simple configuration has been utilized in order to assess the merits of a mapping technique for wing-body configurations. The procedure employed makes use of a coordinate transformation to simplify specification of the surface boundary condition in the computation of the flow about the wing. The method can be extended to incorporate wing sweep, finite length body of noncircular cross section, and arbitrary wing placement; however, these extensions involve a considerable increase in complexity of the problem.

Klunker, E. B.↗

Antenna performance and resolution

The performance of the antenna throughout SL-2, SL-3, and SL-4 was investigated along with the antenna resolution of brightness temperature during flight. The target area selected for the test flights was the Gulf of California, as it offered land/water interface. The coordinate transformations and antenna orientation, flight path simulation, and integration over the radiometric target are discussed.

Carney, J. J.↗

The effect of measurement errors and computational approximations on a perspective ILM radar image

The effect was examined of aircraft position and attitude, of measurement errors, and of computational approximations on the size, shape, and position of a perspective radar image of an airport runway as might be displayed by an independent landing monitor in transport aircraft. The effect on runway image geometry was examined for different aircraft attitudes and different aircraft positions relative to a standard three degree glide slope. Measurement errors investigated were errors in radar azimuth angle and range, and errors in those aircraft parameters supplied to the radar for use in converting the radar image into a perspective format (namely pitch, roll, and altitude). Also investigated were the effects of using certain mathematical approximations, such as small angle, in the coordinate transformation which converts the image to a perspective format.

Bundick, W. T.↗

Calculation of supersonic three-dimensional free-mixing flows using the parabolic-elliptic Navier-Stokes equations

A numerical method is presented which is valid for integration of the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to the three-dimensional supersonic flow of a jet issuing into a supersonic free stream. Difficulties associated with the imposition of free-stream boundary conditions are noted, and a coordinate transformation, which maps the point at infinity onto a finite value, is introduced to alleviate these difficulties. Results are presented for calculations of a square jet and varying-aspect-ratio rectangular jets. The solution behavior varies from axisymmetry for the square jet to nearly two-dimensional for the high-aspect-ratio rectangle, although the computation always calculates the flow as though it were truly three-dimensional.

Hirsh, R. S.↗

Three dimensional supersonic flows with subsonic axial Mach numbers

A numerical approach is presented for the computation of flows in which the component of velocity in the selected marching direction is subsonic although the total velocity is supersonic. A local coordinate rotation procedure is employed together with an implicit differencing scheme. Complex coordinate transformations and time-consuming iterations are avoided. The implementation of the described approach is illustrated with the aid of a two-dimensional problem. An application in the case of three-dimensional flows is also discussed.

Marconi, F.↗