Low-altitude windshear is a threat to the safety of aircraft in take-off and landing: over the past 20 years, some 30 aircraft accidents have been attributed to windshear. The Aero-Astronautics Group of Rice University under the direction of Dr. Angelo Miele has determined the optimal capability of an aircraft in take-off under windshear conditions and has developed near-optimal guidance strategies. In this thesis, using the above information, the values of the parameters for different guidance strategies are determined in order to provide the best approximation to the optimal capabilities. The calculation is treated as a mathematical programming problem, solved by the Nelder-Mead simplex algorithm. Then, the optimal parameters data are applied to guidance strategies. The resulting guidance trajectories are presented in graphical form along with the optimal trajectories for comparison.

This thesis deals with the optimization of four classes of combat maneuvers for a next-generation jet fighter aircraft: climb maneuvers, fly-to-point maneuvers, pop-up attack maneuvers, and dive recovery maneuvers. For the first three classes of maneuvers, the optimization criterion is the minimization of the flight time, resulting in a Mayer-Bolza problem of optimal control; for the fourth class, the optimization criterion is the minimization of the maximum altitude loss during dive recovery, resulting in a Chebyshev problem of optimal control. Each class of problems is solved using the sequential gradient-restoration algorithm for optimal control. Among the four classes of combat maneuvers studied, only dive recovery benefits from the ability of a next-generation fighter aircraft to maneuver at extremely high angles of attack. For the other three classes, relatively low angles of attack are required. The optimal climb trajectories are characterized by three distinct segments: a central segment often flown with a load factor of nearly 1 and two terminal segments (dive or zoom) to and from the central segment. The central and final segments are nearly independent of the initial conditions, instead being dominated by the final conditions. The optimal fly-to-point trajectories consist of three segments: turning, characterized by relatively high load factor; level acceleration at maximum thrust; and finally, resumption of steady-state cruising. The effects of the heading change magnitude and the load factor limit are discussed. The optimal pop-up trajectories consist of three segments flown at maximum power: pitch-up, zoom, and pitch-down. The effects of using the afterburner, heading change magnitude, and dive angle magnitude are discussed. The optimal dive recovery trajectories consist of one to three segments, depending on initial speed and flight path angle. All the optimal trajectories conclude with a pitch-up at the maximum available load factor. For very low initial speed, the pitch-up is preceded by a brief supermaneuver segment. For very low initial speed coupled with very high initial flight path angle, the supermaneuver segment is preceded by a dive initiation segment. The optimal trajectories reported here serve two purposes. First, they can benefit aircraft designers by highlighting those flight characteristics that are most beneficial in combat. Second, they can benefit aircraft pilots as the basis for guidance trajectories that approximate the optimal trajectories.

A method that combines experimental airfoil coefficient data with numerical data has been developed to construct airfoil performance tables given limited data sets. This work addresses the problem faced by engineers and aerodynamicists that currently rely on incomplete performance tables when researching airfoil characteristics. The method developed utilizes the Sequential Function Approximation (SFA) neural network tool and employs a simple regularization scheme to fuse multi-dimensional experimental and computational fluid dynamics (CFD) data efficiently. The method is considered an adaptive and robust tool requiring relatively little computational demand and minimal user dependence. An existing performance table for the NACA 0012 airfoil was used as a test case to verify the feasibility of the SFA-fused network. A second test case assesses the method's viability for a more realistic and challenging problem using highly sparse and scattered data sets for the SC1095 airfoil. Results from both studies realize the method's capability to make consistent approximations and smooth interpolations given only limited experimental data. Comparisons are made with other scattered data approximation techniques. The testing conditions, requirements, and limitations of this approach are discussed and future applications and recommendations are made.

In this work, we present a complete study of the Hohmann transfer maneuver between two circular coplanar orbits. After revisiting its known properties, we present a number of supplementary properties which are essential to the qualitative understanding of the maneuver. Specifically, along a Hohmann transfer trajectory, there exists a point where the path inclination is maximum: this point occurs at midradius and is such that the spacecraft velocity equals the local circular velocity. This implies that, in a Hohmann transfer, the spacecraft velocity is equal to the local circular velocity three times: before departure, at midradius, and after arrival. In turn, this allows the subdivision of the Hohmann transfer trajectory into a region where the velocity is subcircular and a region where the velocity is supercircular, with the transition from one region to another occurring at midradius. Also, we present a simple analytical proof of the optimality of the Hohmann transfer and complement it with a numerical study via the sequential gradient-restoration algorithm. Finally, as an application, we present a numerical study of the transfer of a spacecraft from the Earth orbit around the Sun to another planetary orbit around the Sun for both the case of an ascending transfer (orbits of Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto) and the case of a descending transfer (orbits of Mercury and Venus).

In recent years, there has been a growing demand for the autonomous rendezvous and docking capability of a spacecraft. Current guidance methods in existence are based on the human control of the chaser spacecraft and are not suitable nor sufficient for an autonomous vehicle. The optimal solution of the rendezvous problem investigated in this thesis consists of finding an allowable finite control distribution which minimizes some prescribed performance index (i.e. time, fuel, etc) and brings a chaser vehicle into coincidence with a target vehicle. This thesis first derives the well-known Clohessy-Wiltshire (CW) differential equations (Ref. 1) and focuses on the optimal solution of a linearized three-dimensional rendezvous with bounded thrust and limited fuel. To accomplish this, the sequential gradient-restoration algorithm is utilized to optimize several rendezvous trajectories for the case of a target spacecraft in a circular orbit at the International Space Station (ISS) altitude and a chaser spacecraft with typical initial conditions during the terminal phase of the rendezvous with bounded thrust and bounded DeltaV. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max thrust acceleration via the sequential gradient-restoration algorithm (SGRA). Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, two of which determine the thrust direction in space and one which determines the thrust magnitude. The main conclusion is that the optimal control distribution can result in two, three, or four subarcs depending on the performance index and the constraints. The time-optimal case results in a two-subarc solution with max thrust. The fuel-optimal case results in a four subarc solution consisting of an initial coasting period, followed by a maximum thrust phase, followed by another coasting period, followed by another maximum thrust phase. Regardless of the number of resulting subarcs, the optimal thrust distribution requires the thrust magnitude to be either at the maximum value or at zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust. Based on the above observations, the final potion of this thesis applies the multiple-subarc version of SGRA to solve the guidance problem based on the implementation of constant-control finite-thrust functions during each subarc. (Abstract shortened by UMI.)

This thesis considers both classical and minimax problems of optimal control arising in the study of noncoplanar, aeroassisted orbital transfer. The maneuver considered involves the transfer from a high planetary orbit to a low planetary orbit with a prescribed atmospheric plane change. With reference to the atmospheric part of the maneuver, trajectory control is achieved by modulating the lift coefficient and the angle of bank. The presence of upper and lower bounds on the lift coefficient is considered. Within the framework of classical optimal control, the performance indexes studied are the energy required for orbital transfer and the time integral of the square of the path inclination. Within the framework of minimax optimal control, the performance index studied is the peak heating rate. Numerical solutions are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Numerical examples are presented, and their engineering implications are discussed.

Sulfuric acid anodized aluminum coating systems possessing a low ratio of solar absorptance to infrared emittance are susceptible to vacuum-ultraviolet radiation. Vacuum-ultraviolet exposure can degrade the coating systems by increasing the solar absorptance without a commensurate increase in infrared emittance. Experimental findings from electron microprobe analysis, x-ray diffraction, exposure to vacuum, optical microscopy, and computer simulation have been used to propose the mechanisms for this degradation based on water loss from anodic coatings. It has been determined that water vaporization during vacuum-ultraviolet exposure can cause densification and cracking in a sealed anodic coating. Increased specific density and cracks reduce the reflectance in the short wavelength region and lead to an increase in absorptance.

This thesis considers the numerical solution of minimax problems of optimal control (also called Chebyshev problems) arising in the reentry of a space glider. First, a transformation technique is employed in order to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations. The transformation requires the proper augmentation of the state vector x(t), the control vector u(t), and the parameter vector (pi), as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the vector parameter being optimized. The transformation technique is then applied to the following Chebyshev problems of interest in the reentry of a space glider: (Q1) minimization of the peak dynamic pressure; and (Q2) minimization of the peak heating rate. A new way of studying the problem of reentry is presented which decomposes the problem into two subproblems: Problem (R) and Problem (S). Problem (R) consists of optimizing the subsystem which defines the longitudinal motion and includes the relations due to the transformation of the Chebyshev problem. This problem, also called the primary problem, is solved as a Mayer-Bolza problem and yields the solution for the performance index and the controls determining the trajectory. Problem (S), also called the secondary problem, reduces to the determination of the switching times for the bank angle, so as to meet the remaining boundary conditions. Numerical results are obtained by means of the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. Reference is made to the hypervelocity regime, an exponential atmosphere, and a space glider whose trajectory is controlled by means of the angle of attack and the angle of bank.

This thesis considers both classical and minimax problems of optimal control arising in the study of coplanar aeroassisted orbital transfer. The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers via lift modulation in the sensible atmosphere. Within the framework of classical optimal control, the following problems are studied: (i) minimize the energy required for orbital transfer, Problem (P1); (ii) minimize the time integral of the heating rate, Problem (P2); (iii) minimize the time of flight during the atmospheric portion of the trajectory, Problem (P3); (iv) maximize the time of flight during the atmospheric portion of the trajectory, Problem (P4); (v) minimize the time integral of the square of the path inclination, Problem (P5); (vi) minimize the time integral of the square of the difference between the altitude and a reference altitude to be determined, Problem (P6); and (vii) minimize the sum of the squares of the initial and final path inclinations, Problem (P7). Within the framework of minimax optimal control, the following problems are studied: (i) minimize the peak heating rate, Problem (Q1); (ii) minimize the peak dynamic pressure, Problem (Q2); and (iii) minimize the peak altitude drop, Problem (Q3). If one disregards the bounds on the lift coefficient, one finds that the optimal solution from the energy viewpoint is the grazing trajectory, which is characterized by favorable values of the peak heating rate and peak dynamic pressure. While the grazing trajectory is not flyable, it represents a limiting solution that one should strive to approach in actual flight. For this reason, Problems (P5), (P6), (P7), (Q3) are introduced; their solutions, obtained by accounting for the bounds on the lift coefficient, are referred to as nearly-grazing trajectories. Numerical solutions are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Several numerical examples are presented, and their engineering implications are discussed. In particular, the merits of nearly-grazing trajectories are discussed.

This thesis presents a new approach based on a spline formulation for the analysis of thin aerofoils using the velocity singularity method. The method of velocity singularities was originally developed by Mateescu and Newman in conjunction with a polynomial representation of the normal perturbation velocities. The present method uses a cubic spline representation of the aerofoil contour, which led to improvements in the accuracy and stability of the solution, especially in the case of the jet-flapped aerofoils. / This method has been first validated for the cases of rigid and flexible aerofoils. The pressure distributions obtained with the spline formulation have proven to be in good agreement with the previous solutions based on conformal transformation, or obtained by Thwaites, Nielsen, and by Mateescu and Newman. / The spline-velocity singularity method has been used for the jet flapped aerofoils and then extended to analyze the aerofoils with multiple sections, such as aerofoils with a flap. The solutions for these problems have been found to be in good agreement with the results obtained theoretically or experimentally by Spence, and Dimmock, and by Seebohm and Newman, based on a surface vortex method. / The spline-velocity singularity method displayed a better accuracy and an enhanced stability of the solution, in comparison with the polynomial formulation, especially in the cases when the aerofoil contour is not known a priori, such as for the flexible or jet-flapped aerofoils.