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Cycle life regression model, cycle life prediction model, and acceleration factors are discussed. A method was presented to: (1) select a mathematical model; (2) determine model coefficients using accelerated test data; (3) test model fit of the accelerated test data; and (4) predict normal packs.
A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.
A methodology of formulating the optimum design problem for structural systems with random parameters and subjected to random vibration as a mathematical programming problem is presented. The proposed method is applied to the optimum design of a cantilever beam with a tip mass and a truss structure supporting a water tank. The excitations are assumed to be Gaussian processes and the geometric and material properties are taken to be normally distributed random variables. The probabilistic constraints are specified for individual failure modes since it is easier to specify the reliability level for each failure mode keeping in view the consequences of failure in that particular mode. The time parameter appearing in the random vibration based constraints is eliminated by replacing the probabilities of failure by suitable upper bounds. The numerical results demonstrate the feasibility and effectiveness of applying the reliability-based design concepts to structures with random parameters and operating in random vibration environment.
Applications of Computational fluid dynamics (CFD) methods to determine the regimes of applicability of nonlinear models describing the unsteady aerodynamic responses to aircraft flight motions are described. The potential advantages of computational methods over experimental methods are discussed and the concepts underlying mathematical modeling are reviewed. The economic and conceptual advantages of the modeling procedure over coupled, simultaneous solutions of the gasdynamic equations and the vehicle's kinematic equations of motion are discussed. The modeling approach, when valid, eliminates the need for costly repetitive computation of flow field solutions. For the test cases considered, the aerodynamic modeling approach is shown to be valid.
With the objective to achieve the desired reduction in velocity by aerodynamic forces, an aeroassisted orbital transfer vehicle (AOTV) is expected to fly in the higher region of the atmosphere for a sustained period of time. This aeroassist maneuver will occur in the transitional regime, if the vehicle is designed for a low ballistic coefficient. In this case, a merged-layer (ML) is formed around the space vehicle. The flow characteristics of the vehicle can be studied by making use of the full Navier-Stokes (NS) equations, taking into account slip and temperature jump conditions. The present investigation has the objective to obtain a two-term series solution of the full Navier-Stokes equations with surface slip and temperature jump conditions for the ML flow on a sphere. Attention is given to the mathematical formulation of the problem, the numerical method of integration, and the results.
Mathematical models based on the finite element method of structural analysis as embodied in the NASTRAN computer code are widely used by the helicopter industry to calculate static internal loads and vibration of airframe structure. The internal loads are routinely used for sizing structural members. The vibration predictions are not yet relied on during design. NASA's Langley Research Center sponsored a program to conduct an application of the finite element method with emphasis on predicting structural vibration. The Army/Boeing CH-47D helicopter was used as the modeling subject. The objective was to engender the needed trust in vibration predictions using these models and establish a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process.
The underlying engineering and mathematical models as well as the computational methods used by the SOUP5 analysis programs, which are part of the R2BCSAT-83 Broadcast Satellite Computational System, are described. Included are the algorithms used to calculate the technical parameters and references to the relevant technical literature. The system provides the following capabilities: requirements file maintenance, data base maintenance, elliptical satellite beam fitting to service areas, plan synthesis from specified requirements, plan analysis, and report generation/query. Each of these functions are briefly described.
Applications of computational fluid dynamics (CFD) methods to determine the regimes of applicability of nonlinear models describing the unsteady aerodynamic responses to aircraft flight motions are described. The potential advantages of computational methods over experimental methods are discussed and the concepts underlying mathematical modeling are reviewed. The economic and conceptual advantages of the modeling procedure over coupled, simultaneous solutions of the gas dynamic equations and the vehicle's kinematic equations of motion are discussed. The modeling approach, when valid, eliminates the need for costly repetitive computation of flow field solutions. For the test cases considered, the aerodynamic modeling approach is shown to be valid.
The underlying engineering and mathematical models as well as the computational methods used by the Spectrum Orbit Utilization Program 5 (SOUP5) analysis programs are described. Included are the algorithms used to calculate the technical parameters, and references to the technical literature. The organization, capabilities, processing sequences, and processing and data options of the SOUP5 system are described. The details of the geometric calculations are given. Also discussed are the various antenna gain algorithms; rain attenuation and depolarization calculations; calculations of transmitter power and received power flux density; channelization options, interference categories, and protection ratio calculation; generation of aggregrate interference and margins; equivalent gain calculations; and how to enter a protection ratio template.
Mathematical models based on the finite element method of structural analysis as embodied in the NASTRAN computer code are widely used by the helicopter industry to calculate static internal loads and vibration of airframe structure. The internal loads are routinely used for sizing structural members. The vibration predictions are not yet relied on during design. NASA's Langley Research Center sponsored a program to conduct an application of the finite element method with emphasis on predicting structural vibration. The Army/Boeing CH-47D helicopter was used as the modeling subject. The objective was used to engender the needed trust in vibration predictions using these models and establish a body of modeling guides which would enable confident future prediction of airframe vibration as part of the regular design process.
Some of the recent work at NASA Langley on transition, turbulence, and reacting flows is summarized. Much of this effort has been motivated by outstanding technological problems in high-speed flow. A class of numerical algorithms for these problems has been developed and a variety of physical problems have been simulated. Descriptions are provided of the basic mathematical models, the nature of the numerical methods, and some of the recent simulations.
A numerical technique is developed to reduce the size of models describing the nonlinear dynamic response of quasi-symmetric structures (i.e., structures with unsymmetric geometry). The response vectors of the structure are approximated by a linear combination of the symmetric and antisymmetric vectors at each time step. The mathematical formulation and numerical implementation of the method are described in detail, and results for a shallow laminated anisotropic panel of quadrilateral planform are presented in graphs and normalized contour plots.
A laser based method was employed to measure and numerically describe the architecture of a corn canopy. Use of the method provides an interception coefficient for classes of vegetation in layers of the canopy viewed in various directions. Architectural data obtained for similar corn canopies but measured by differing methods are comparable to the results obtained using the laser based method. These results provide input data to mathematical models employed in remote sensing for describing the radiation environment in a plant canopy and predicting its reflectance.
The fabrication and testing of a pair of robot fingers designed to grasp two types of Orbital Replacement Unit (ORU) interfaces, the H Handle type and the Micro Square type are discussed. A closed-form solution is given for the force inverse kinematics. A numerical solution using the Newton-Raphson Method for force forward kinematics is given. Mathematical expressions are derived to compute forces/torques applied to the finger. Suggestions are given for improving finger fabrication. The results of numerous experiments conducted to study the characteristics and feasibility of the fingers are given. The first part of the study was devoted to obtaining data on the forces applied by the finger to the interfaces under various translational and rotational misalignments; the second part was devoted to determining the maximum allowed capture angles that would insure successful mating; and the third part was devoted to the processing and interpretation of the forces/torque data.
Upper bounds on rates of single-event upsets (SEU's) in digital integrated circuits and other electronic devices exposed to anisotropic fluxes of energetic ionizing particles computed by use of improved method. Derived from simplified, worst-case mathematical models of charge-collecting volumes and physical phenomena in electronic devices.
Methods are proposed that exploit a microgravity environment to obtain highly accurate measurement of contact angle. These methods, which are based on our earlier mathematical results, do not require detailed measurement of a liquid free-surface, as they incorporate discontinuous or nearly-discontinuous behavior of the liquid bulk in certain container geometries. Physical testing is planned in the forthcoming IML-2 space flight and in related preparatory ground-based experiments.
A method is presented which allows the use of nonlinear section lift data in the calculation of the spanwise lift distribution of unswept wings with flaps or ailerons. This method is based upon lifting line theory and is an extension to the method described in NACA rep. 865. The mathematical treatment of the discontinuity in absolute angle of attack at the end of the flap or aileron involves the use of a correction factor which accounts for the inability of a limited trigonometric series to represent adequately the spanwise lift distribution. A treatment of the apparent discontinuity in maximum section lift coefficient is also described. Simplified computing forms containing detailed examples are given for both symmetrical and asymmetrical lift distributions. A few comparisons of calculated characteristics with those obtained experimentally are also presented.
The merits and limitations of the optimality criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement, and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the Optimality Criteria Design Code that was developed for this purpose at NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. Salient features of the code include multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analyzers, and analytical and numerical sensitivities. The performance of the OC method, on the basis of the examples solved, was found to be satisfactory for problems with few active constraints or with small numbers of design variables. For problems with large numbers of behavior constraints and design variables, the OC method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.