Elastic displacements for various edge-cracked plate specimens
Elastic displacements for various edge-cracked plate specimens using boundary collocation computing procedures
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The bending of flat plate structures with rectangular symmetry.
Elastic bending moments and shear forces uniformly loaded flat plate structures with rectangular symmetry, using collocation technique and complex variable methods
Gupta, K. K.↗
Earth resources technology satellite. Volume 15 - Ground data handling system study Final report
OCC/NDPF collocation, facilities design, display system, and computer requirements for ERTS Ground Data Handling System
Source record↗
A numerical method for solving Fredholm integral equations of the first kind using singular values
First kind Fredholm integral equation approximation by numerical quadrature formulas plus collocation, using singular value decomposition for solution
Hanson, R. J.↗
Prediction of unsteady aerodynamic loadings caused by trailing edge control surface motions in subsonic compressible flow: Computer program description
A digital computer program has been developed to calculate unsteady loadings caused by motions of lifting surfaces with trailing edge control based on the subsonic kernal function approach. The pressure singularities at hinge line and side edges have been extracted analytically as a preliminary step to solving the integral by collocation. The program calculates generalized aerodynamic forces for user supplied deflection modes. Optional intermediate output includes pressure at an array of points, and sectional generalized forces. From one to four controls on the half span can be accommodated.
Redman, M. C.↗
Satellite altitude determination uncertainties
Satellite altitude determination uncertainties will be discussed from the standpoint of the GEOS-C satellite, from the longer range viewpoint afforded by the Geopause concept. Data are focused on methods for short-arc tracking which are essentially geometric in nature. One uses combinations of lasers and collocated cameras. The other method relies only on lasers, using three or more to obtain the position fix. Two typical locales are looked at, the Caribbean area, and a region associated with tracking sites at Goddard, Bermuda and Canada which encompasses a portion of the Gulf Stream in which meanders develop.
Siry, J. W.↗
Application of boundary integral method to elastic analysis of V-notched beams
A semidirect boundary integral method, using Airy's stress function and its derivatives in Green's boundary integral formula, is used to obtain an accurate numerical solution for elastic stress and strain fields in V-notched beams in pure bending. The proper choice of nodal spacing on the boundary is shown to be necessary to achieve an accurate stress field in the vicinity of the tip of the notch. Excellent agreement is obtained with the results of the collocation method of solution.
Rzasnicki, W.↗
A kernel function method for computing steady and oscillatory supersonic aerodynamics with interference.
The method presented uses a collocation technique with the nonplanar kernel function to solve supersonic lifting surface problems with and without interference. A set of pressure functions are developed based on conical flow theory solutions which account for discontinuities in the supersonic pressure distributions. These functions permit faster solution convergence than is possible with conventional supersonic pressure functions. An improper integral of a 3/2 power singularity along the Mach hyperbola of the nonplanar supersonic kernel function is described and treated. The method is compared with other theories and experiment for a variety of cases.
Cunningham, A. M., Jr.↗
Preliminary numerical analysis of improved gas chromatograph model
A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.
Woodrow, P. T.↗
Geometric adjustment of the South American satellite densification (PC-1000) network
Reduced normal equations were computed from observation data and combined with reduced normal equations of other satellite networks to provide station coordinates from a single least square adjustment. Terrestrial data, which include base-lines, heights, and survey coordinates, provide the necessary relative position constraints between collocated stations of two satellite networks. Survey information regarding the observation stations is summarized, and constraints used in the solution are given. Geoidal undulations are computed by using the formula and constants shown.
Mueller, I. I.↗
Free geometric adjustment of the SECOR Equatorial Network (Solution SECOR-27)
The basic purpose of this experiment is to compute reduced normal equations from the observational data of the SECOR Equatorial Network obtained from DMA/Topographic Center, D/Geodesy, Geosciences Div. Washington, D.C. These reduced normal equations are to be combined with reduced normal equations of other satellite networks of the National Geodetic Satellite Program to provide station coordinates from a single least square adjustment. An individual SECOR solution was also obtained and is presented in this report, using direction constraints computed from BC-4 optical data from stations collocated with SECOR stations. Due to the critical configuration present in the range observations, weighted height constraints were also applied in order to break the near coplanarity of the observing stations.
Mueller, I. I.↗
GEOS observation systems intercomparison investigation results
The results of an investigation designed to determine the relative accuracy and precision of the different types of geodetic observation systems used by NASA is presented. A collocation technique was used to minimize the effects of uncertainties in the relative station locations and in the earth's gravity field model by installing accurate reference tracking systems close to the systems to be compared, and by precisely determining their relative survey. The Goddard laser and camera systems were shipped to selected sites, where they tracked the GEOS satellite simultaneously with other systems for an intercomparison observation.
Berbert, J. H.↗
Description and flight performance of two systems for two-segment approach
This paper describes two different avionic systems which were designed and developed to provide guidance and control for two-segment noise abatement approaches. The concept of a low-cost retrofit avionic system evolved into a special-purpose two-segment computer which required a DME collocated with the ILS glide-slope transmitter. This system was evaluated in a Boeing 727-200 aircraft. The second system is an area navigation (RNAV) system modified to include the two-segment approach. This system is more sophisticated than the first system and does not restrict usage to any specific navigation ground aid. The modified RNAV system is a Collins ANS-70A and is currently being evaluated in a DC-8-61 aircraft.
Wehrend, W. R.↗
Delay time measurements of the propagation of radio waves in the atmosphere
The characteristics and operation of the Geodetic Secor System are described. The precision of the ionospheric radiation measurements was determined by a collocation experiment. The EGRS-13 satellite, which was used in the experiment, is discussed. The geodetic network is shown in a diagram form. Conclusions resulting from the experiments are reported.
Rohde, F.↗
Calibration and evaluation of Skylab altimetry for geodetic determination of the geoid
The author has identified the following significant results. The collocation technique to filter the remaining EREP passes no. 4, no. 6, and no. 9 was completed. The correlation studies of altimetry geoid profiles with the gravity data and ocean bottom topography were also completed.
Mourad, A. G.↗
Prediction of unsteady aerodynamic loadings caused by leading edge and trailing edge control surface motions in subsonic compressible flow: Computer program description
A digital computer program has been developed to calculate unsteady loadings caused by motions of lifting surfaces with leading edge or trailing edge controls based on the subsonic kernel function approach. The pressure singularities at hinge line and side edges have been extracted analytically as a preliminary step to solving the integral equation by collocation. The program calculates generalized aerodynamic forces for user supplied deflection modes. Optional intermediate output includes pressure at an array of points, and sectional generalized forces. From one to six controls on the half span can be accommodated.
Redman, M. C.↗
Calibration and evaluation of Skylab altimetry for geodetic determination of the geoid
The author has identified the following significant results. The Skylab altimeter experiment has proven the capability of the altimeter for measurement of sea surface topography. The geometric determination of the geoid/mean sea level from satellite altimetry is a new approach having significant applications in many disciplines including geodesy and oceanography. A generalized least squares collocation technique was developed for determination of the geoid from altimetry data. The technique solves for the altimetry geoid and determines one bias term for the combined effect of sea state, orbit, tides, geoid, and instrument error using sparse ground truth data. The influence of errors in orbit and a priori geoid values are discussed. Although the Skylab altimeter instrument accuracy is about plus or minus 1m, significant results were obtained in identification of large geoidal features such as over the Puerto Rico trench. Comparison of the results of several passes shows that good agreement exists between the general slopes of the altimeter geoid and the ground truth, and that the altimeter appears to be capable of providing more details than are now available with best known geoids.
Mourad, A. G.↗
Importance of helicopter dynamics to the mathematical model of the helicopter
A mathematical model of the helicopter requires appropriate representation of the constituent elements of rotor dynamics. General-purpose programs that model a variety of configurations for a broad range of operating conditions result in varying and incompatible levels of sophistication. Analysis of specific dynamic problems facilitates the identification of configuration parameters which determine system behavior. For the present analysis, the nonlinear equations of a torsionally rigid hingeless rotor are linearized about an equilibrium condition to determine flap-lag stability characteristics in hover. A collocation method was used to obtain the coupled natural frequencies and modes. These modes allow exact treatment of the effect of elastic coupling which more than compensates for the destabilizing inertial coupling. The sensitivity of damping to the number of modes was found to be small, and reasonable accuracy was obtained the first flapwise and edgewise coupled modes. The range of destabilizing precone was found to be small.
White, W. F., Jr.↗