In this thesis, near-optimum guidance schemes for abort landing trajectories in a windshear are investigated. These near-optimum guidance schemes are based on the properties of the optimum trajectories. The survival capability in a severe windshear is studied. The optimal trajectories are used as ideal benchmarks against which the goodness of any guidance scheme can be measured.

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. (Abstract shortened by UMI.)

The suitability of traditional fatigue design methods to deal with complex damage modes in composite materials is critically assessed. After a survey of the recent fatigue models, a new methodology is developed, based on both the Markovian discrete time discrete state stochastic processes and the Critical Element Model for damage in composite materials. In a practical application of the methodology, the fatigue behavior of cross ply Carbon Epoxy laminates is derived from a Monte-Carlo simulation.

This thesis considers windshear identification and detection problems by utilizing random process and statistical analysis techniques. A 3D windshear/turbulence model is developed, which covers a broad spectrum of windshear situations and can be utilized in the design of optimal and guidance trajectories. The existence of windshear patterns is justified from the analysis of simulated and real wind data. Random processes and their properties are discussed for the design of the correlation signal detectors. Numerical results demonstrate that the detection system is sensitive to the occurrence of a windshear encounter and is robust vis-a-vis noise effects. The results of this thesis make an early windshear detection possible, since computation can be performed onboard in real time. Application of the proposed detection system to the case of Flight Delta 191 leads to the conclusion that a windshear alert could have been issued 31 to 65 sec before impact, depending on the type of measurement employed in the crosscorrelation detector, specifically: 40 sec before impact for the longitudinal wind, 31 sec before impact for the vertical wind, and 65 sec before impact for the total wind. Therefore, if the Lockheed L-1011 aircraft of Flight Delta 191 had been hypothetically equipped with the present crosscorrelation detector, the pilot could have been warned 65 sec before impact, a time interval more than sufficient to avoid the crash by executing a safe abort landing maneuver.

The primary goal of this study is to develop a finite element method for the calculation of an attached, two-dimensional, laminar, compressible boundary layer about an air-foil in a subsonic free stream. An introduction to the subsequent viscous-inviscid interaction model is also given. The two-dimensional partial differential equations are reduced to integral equations that are independent of density and resemble the weak form of the two dimensional incompressible boundary layer equations. A Galerkin finite element method is applied to this Dorodnitsyn formulation and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of first order ordinary differential equations, solved by an implicit, non-iterative finite difference marching scheme in the stream-wise direction. Results presented include the coefficient of friction and displacement thickness about a circular cylinder in an incompressible freestream, the compressible boundary layer about a NACA 0012 airfoil, and a validation of the linear thermal equation.

Miele, Wang, and Deaton have demonstrated in Ref. 1 how optimal trajectories are produced by eliminating positive lift and fixing the lift coefficient at its lower, negative (downward) bound all throughout the atmospheric pass. Because of this fixed control, the problem is posed here as a highly nonlinear two-point boundary-value problem (TPBVP) which is solved by enlisting a multipoint version of the modified quasilinearization algorithm. This thesis supplements Ref. 1 by performing trade studies showing how all the performance indices improve with decreasing lift coefficient lower bound, that is, more negative lift. We also formulate a two-subarc TPBVP for the purpose of testing the effect of a short period of positive lift applied during the descent phase followed by a switch to negative lift. The result is that all performance indices worsen when any positive lift is applied compared to the constant negative lift coefficient case.

Dynamic analysis methods for computationally demanding systems are examined. Component Mode Synthesis methods are detailed and their limitations established. Decoupled analysis is offered as a solution for problems that traditional methods are incapable of addressing, such as systems with non-classical damping or geometric non-linearities. The methodology of decoupled analysis is detailed along with three modifications to the basic decoupled analysis method. This method is then applied to two large problems involving the International Space Station and the Space Shuttle.

This thesis deals with the optimization of the ascent trajectories for single-stage suborbital (SSSO), single-stage-to-orbit (SSTO), and two-stage-to-orbit (TSTO) rocket-powered spacecraft. The maximum payload weight problem has been solved using the sequential gradient-restoration algorithm. For the TSTO case, some modifications to the original version of the algorithm have been necessary in order to deal with discontinuities due to staging and the fact that the functional being minimized depends on interface conditions. The optimization problem is studied for different values of the initial thrust-to-weight ratio in the range 1.3 to 1.6, engine specific impulse in the range 400 to 500 sec, and spacecraft structural factor in the range 0.08 to 0.12. For the TSTO configuration, two subproblems are studied: uniform structural factor between stages and nonuniform structural factor between stages. Due to the regular behavior of the results obtained, engineering approximations have been developed which connect the maximum payload weight to the engine specific impulse and spacecraft structural factor; in turn, this leads to useful design considerations. Also, performance sensitivity to the scale of the aerodynamic drag is studied, and it is shown that its effect on payload weight is relatively small, even for drag changes approaching $\pm 50\%.$ The main conclusions are that: the design of a SSSO configuration appears to be feasible; the design of a SSTO configuration might be comfortably feasible, marginally feasible, or unfeasible, depending on the parameter values assumed; the design of a TSTO configuration is not only feasible, but its payload appears to be considerably larger than that of a SSTO configuration. Improvements in engine specific impulse and spacecraft structural factor are desirable and crucial for SSTO feasibility; indeed, it appears that aerodynamic improvements do not yield significant improvements in payload weight.

Spacecraft equipped with a Reaction Control System (RCS) for attitude control typically utilize a "bang-off-bang" control algorithm for rotational maneuvers. This type of algorithm, which commands two distinct control periods to initiate and terminate a maneuver, can be fuel-suboptimal for maneuvers in which neither the initial nor the final state is at rest. This work introduces a rotational control algorithm for inertially axisymmetric spacecraft that uses three distinct control periods in order to minimize propellant consumption for large-angle maneuvers with non-trivial initial and final angular rates.

This thesis research examines the fuel optimal trajectories for a spacecraft going to Mars and returning to Earth. Challenges encountered include the defining of equations of motion and optimality conditions, formulation of constraints, and overcoming difficulties deriving from large distances and times involved and the accuracy required. In addition to calculating an optimal trajectory, two different arrival orbits at Mars are compared: a clockwise and counterclockwise Martian orbit. The optimal trajectories are computed using a mathematical optimization algorithm SNOPT, developed at Stanford University and UC San Diego. A solution method is recommended where an initial guess is generated analytically via a patched conic approach. The problem is solved in two steps: first with relaxed constraints, then using that result to find the optimal solution. This approach is proven by separately solving two different trajectories: an Earth to Mars trajectory and a Mars to Earth trajectory. The results demonstrate that the two arrival conditions are very similar in most aspects, including planetary phase angles and total trajectory time. The trajectory using the counterclockwise Mars orbit has a slight advantage in propellant usage (DeltaV), but the difference is less than 1%. These transfers also have symmetries between the outbound and return portions of the trajectories. Both trajectories should be available for consideration for a mission to Mars depending on other mission requirements.