Solution of second-order linear system by matched asymptotic expansions

Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed

In depth review of the 1979 AIAA Lighter-Than-Air Systems Technology Conference

The lighter than air (LTA) systems technology conference is reviewed. Highlights of the conference were: (1) the interest shown in patrol and surveillance airships, particularly for coastal patrol missions; (2) the session devoted to overviews of foreign activity; and (3) heavy lift and long range transport aircraft design considerations

Missions and Vehicle Concepts for Modern, Propelled, Lighter-Than-Air Vehicles

The results of studies conducted over the last 15 years to assess missions and vehicle concepts for modern, propelled, lighter-than-air vehicles (airships) were surveyed. Rigid and non-rigid airship concepts are considered. The use of airships for ocean patrol and surveillance is discussed along with vertical heavy lift airships. Military and civilian needs for high altitude platforms are addressed. Around 1970 a resurgence of interest about lighter-than-air vehicles (airships) occurred in both the public at large and in certain isolated elements of the aerospace industry. Such renewals of airship enthusiasm are not new and have, in fact, occurred regularly since the days of the Hindenburg and other large rigid airships. However, the interest that developed in the early 1970's has been particularly strong and self-sustaining for a number of good reasons. The first is the rapid increase in fuel prices over the last decade and the common belief (usually true) that airships are the most fuel efficient means of air transportation. Second, a number of new mission needs have arisen, particularly in surveillance and patrol and in vertical heavy-lift, which would seem to be well-suited to airship capabilities. The third reason is the recent proposal of many new and innovative airship concepts. Finally, there is the prospect of adapting to airships the tremendous amount of new aeronautical technology which has been developed in the past few decades thereby obtaining dramatic new airship capabilities. The primary purpose of this volume is to survey the results of studies, conducted over the last 15 years, to assess missions and vehicle concepts for modern propelled lighter-than-air vehicles

Solution of linear systems by a singular perturbation technique

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation

Structural weight analysis of hypersonic aircraft

The weights of major structural components of hypersonic, liquid hydrogen fueled aircraft are estimated and discussed. The major components are the body structure, body thermal protection system tankage and wing structure. The method of estimating body structure weight is presented in detail while the weights of the other components are estimated by methods given in referenced papers. Two nominal vehicle concepts are considered. The advanced concept employs a wing-body configuration and hot structure with a nonintegral tank, while the potential concept employs an all body configuration and cold, integral pillow tankage structure. Characteristics of these two concepts are discussed and parametric data relating their weight fractions to variations in vehicle shape and size design criteria and mission requirements, and structural arrangement are presented. Although the potential concept is shown to have a weight advantage over the advanced, it involves more design uncertainties since it is farther removed in design from existing aircraft

Barriers and dispersal surfaces in minimum-time interception

Minimum time interception of a target moving in a horizontal plane is analyzed as a one-player differential game. Dispersal points and points on the barrier are located for a class of pursuit evasion and interception problems. These points are determined by constructing cross sections of the isochrones and hence obtaining the barrier, dispersal, and control level surfaces. The game solution maps the controls as a function of the state within the capture region

Optimal feedback strategies for pursuit-evasion and interception in a plane

Variable-speed pursuit-evasion and interception for two aircraft moving in a horizontal plane are analyzed in terms of a coordinate frame fixed in the plane at termination. Each participant's optimal motion can be represented by extremal trajectory maps. These maps are used to discuss sub-optimal approximations that are independent of the other participant. A method of constructing sections of the barrier, dispersal, and control-level surfaces and thus determining feedback strategies is described. Some examples are shown for pursuit-evasion and the minimum-time interception of a straight-flying target

Preliminary estimates of operating costs for lighter than air transports

A preliminary set of operating cost relationships are presented for airship transports. The starting point for the development of the relationships is the direct operating cost formulae and the indirect operating cost categories commonly used for estimating costs of heavier than air commercial transports. Modifications are made to the relationships to account for the unique features of airships. To illustrate the cost estimating method, the operating costs of selected airship cargo transports are computed. Conventional fully buoyant and hybrid semi-buoyant systems are investigated for a variety of speeds, payloads, ranges, and altitudes. Comparisons are made with aircraft transports for a range of cargo densities

Parametric study of modern airship productivity

A method for estimating the specific productivity of both hybrid and fully buoyant airships is developed. Various methods of estimating structural weight of deltoid hybrids are discussed and a derived weight estimating relationship is presented. Specific productivity is used as a figure of merit in a parametric study of fully buoyant ellipsoidal and deltoid hybrid semi-buoyant vehicles. The sensitivity of results as a function of assumptions is also determined. No airship configurations were found to have superior specific productivity to transport airplanes

A formulation and analysis of combat games

Combat which is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives is outlined. A target set is associated with each opponent in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously, or in neither, a joint capture or a draw, respectively, occurs. Resolution of the encounter is formulated as a combat game; as a pair of competing event constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero sum differential game. Otherwise the optimal strategies are computed from a resulting nonzero sum game. Since optimal combat strategies may frequently not exist, approximate or delta combat games are also formulated leading to approximate or delta optimal strategies. The turret game is used to illustrate combat games. This game is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit evasion games