Military aircraft types

Fighters

These aircraft have had several designations over the years, including pursuit and interceptor aircraft. There are many types, and definitions become blurred between fighters and bombers and ground-attack aircraft. True fighters may be divided into two major classes. The first class is that of relatively simple short-range interceptor aircraft (class 1), whilst the second used to be called ‘all-weather’ fighters which tend to have longer range and more avionic equipment (class 2). Figure 4.1 shows a plot of combat wing loading against thrust/weight ratio, which is a good indication of the manoeuvrability of combat aircraft (see Chapter 3 for the definition of thrust/weight and wing loading). Recent requirements for high agility have moved aircraft towards the top left-hand corner where high thrust/weight and low wing loading improve climb, sustained turn and attained turn performance. Most aircraft in this region are class 1 short-range fighters and class 2 are closer to the bottom-right quadrant, where the higher wing loading leads to better long-range cruise.

The class 1 short range, high performance interceptor carries the minimum of equipment and maximum speed is always important. However for such an aircraft the rate of climb and manoeuvrability may be even more important. This arises from the fact that due to the fighter's necessarily short range it cannot take off until a target is definitely located, but must then rapidly climb to interception.

Avionic systems

Avionics is one of the most rapidly developing fields of aircraft design. Its importance and range has increased over recent years and as much as 40% of the cost of a new aircraft can be attributed to avionics. There is a bewildering range of avionic systems, each of which usually requires the use of many acronyms.

Figure 7.1 shows an avionics fit for a small executive aircraft. This aircraft is intended for flight with a crew of one or two pilots. If this aircraft had been in operation during the early post-war years, three additional crew-members would have been required, namely navigator, wireless operator and flight engineer. Modern efficient, reliable avionics have dramatically simplified these operations and have eliminated to need for these crew members.

The growth in the capabilities of military avionics has been even more dramatic and make it possible for pilots of single-seat aircraft to navigate, communicate, detect and attack targets at heights of 100 ft and speeds approaching the speed of sound. Figure 7.2 shows a schematic of such an avionic system whilst Fig. 7.3 shows the installation of components on the instrument panel.

Having looked at typical aircraft installations the next stage is to examine the functions of various types of avionic systems in the following major groups: communications, navigation systems, radar systems and others.

There are many important systems that exhibit nonequilibrium or noncontinuum behavior. This final chapter examines some important examples of such systems. In doing so, we have two objectives. The first is to understand how, and under what conditions, the system behavior may deviate from the idealizations embodied in equilibrium theory or continuum theory. The second is to demonstrate theories and methods that are commonly used to model nonequilibrium and noncontinuum systems. Because they are commonly used to analyze such systems, kinetic theory and the Boltzmann transport equation are introduced. Nonequilibrium and noncontinuum phenomena associated with multiphase systems and electron transport in solids are examined in detail. The final section of Chapter 10 uses results from previous chapters to examine length scales and time scales at which classical and continuum theories become suspect. Doing so defines the range of conditions for which we expect classical and continuum theories to be accurate models of real physical systems. Although limited in its coverage, this chapter provides an introduction to microscale aspects of nonequilibrium and noncontinuum phenomena and serves to illustrate how they relate to the theoretical framework developed in the preceding chapters.

Basic Kinetic Theory

With increasing frequency engineers are dealing with microscale systems in which the applicability of classical macroscopic equilibrium thermodynamics becomes questionable. Generally, the applicability of classical equilibrium theory breaks down because the system is far from equilibrium and/or the system behavior deviates from a continuum model.

The statistical and classical thermodynamics framework developed in Chapters 1–8 of this text is based on analysis of systems at equilibrium. In Chapter 9 we explore the extension of this framework to systems that are not in equilibrium. This chapter focuses on systems that exhibit steady spatial variations of properties. Systems of this type are modeled as having local thermodynamic equilibrium and obeying a linear relation between fluxes and affinities. Analysis of microscale features of such linear systems is shown to link correlation moments and kinetic coefficients. The Onsager reciprocity relations are subsequently derived. Thermoelectric effects are examined as an example application of the nonequilibrium linear theory developed in this chapter.

Properties in Nonequilibrium Systems

The thermodynamic theoretical framework developed in previous chapters of this text is limited to analysis of equilibrium states. Often, however, it is the process that takes the system from one state to another that is of primary interest. Overall changes accomplished during the process can be determined by analyzing the initial and final states using equilibrium thermodynamics. If the process is very slow, it may be well approximated by a sequence of equilibrium states, and a quasistatic model may adequately predict the outcome of the process.

In many real processes, the departure from equilibrium is so severe that the quasistatic model is too inaccurate to be useful. The objective of this chapter is to develop thermodynamic tools that can be applied to irreversible processes in nonequilibrium systems.

Using the basic features of microscale energy storage discussed in Chapter 1, in Chapter 2 we develop the foundations of statistical thermodynamics. In doing so, we introduce the concepts of microstates and macrostates and properly account for the fact that particles in fluid systems are generally indistinguishable. The development of the theoretical framework in this and subsequent chapters considers a binary mixture of two particle types. The statistical machinery is applied first to a microcanonical ensemble of systems, each having a specified volume, number of particles, and total internal energy. Definitions of entropy and temperature emerge from this development. Application of the results to a monatomic gas is discussed.

Microstates and Macrostates

In this chapter we will construct a general statistical mechanics foundation on which we will develop a full equilibrium thermodynamic theory for systems composed of a large number of particles. In doing so we will make use of the information about energy storage derived from quantum theory in the previous chapter.

In analyzing systems of particles, we can deal with the state of a system at two levels: the microstate of the system and the macrostate of the system. The system microstate is the detailed configuration of the system at a microscopic level. To specify the microstate we would have to specify the quantum state (including the position) of each particle in the system. If we observe a system at a macroscopic level, we can, at best, distinguish some of the gross characteristics of the system.

The structure of this book is designed to facilitate coherent development of classical and statistical thermodynamic principles. The book begins with coverage of microscale energy storage mechanisms from a modern quantum mechanics perspective. This information is then incorporated into a statistical thermodynamics analysis of many-particle systems with fixed internal energy, volume, and number of particles. From this analysis emerges the definitions of entropy and temperature, the extremum principle form of the second law, and the fundamental relation for the system properties. The third chapter takes the concepts derived from the statistical treatment and uses mathematical techniques to expand the macroscopic thermodynamics framework. By the end of the third chapter, the full framework of classical thermodynamics is established, including definitions of all commonly used thermodynamic properties, relations among properties, different forms of the second law, and the Maxwell relations.

In the fourth chapter, statistical ensemble theory is covered, building on the initial statistical treatment in Chapter 2 and the expanded macroscopic framework developed in Chapter 3. The canonical ensemble and grand canonical ensemble formalisms are developed, and the relations developed from these formalisms are used to explore the significance of fluctuations in thermodynamics systems. By the end of the fourth chapter all the fundamental elements of classical and statistical thermodynamics have been established. Chapters 5–7 deal with applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems.

The final three chapters of the text cover thermal phenomena that involve nonequilibrium and/or noncontinuum effects.

The basic elements of statistical thermodynamics were developed in Chapter 2. In this chapter, we digress briefly from development of the statistical theory to expand the theoretical framework using mathematical tools and macroscopic analysis. By doing so we more strongly link the statistical theory to classical thermodynamics and set the stage for alternative statistical viewpoints considered in Chapter 4.

Necessary Conditions for Thermodynamic Equilibrium

In the previous chapter, we have derived several important pieces of information about thermodynamic systems. The goal of this chapter is to expand the framework of macroscopic thermodynamic theory so that it can be applied effectively to a variety of system types. We will begin by summarizing the important ideas developed in the last chapter.

So far, we have taken the volume V, internal energy U, and particle numbers Na and Nb, to be intrinsic properties for any system we may consider. We subsequently defined the properties entropy S, temperature T, pressure P, and chemical potentials µa and µb. Our analysis of the statistical characteristics of thermodynamic systems has led to the conclusion that for a system with fixed U, V, Na, and Nb, equilibrium corresponds to a maximum value of the system entropy. This is referred to as the entropy maximum principle. The entropy of a composite system with an arbitrary number of subsystems is additive over the constituent subsystems. This is the additivity property of entropy.

Chapter 7 demonstrates the application of statistical thermodynamics theory to crystalline solids. Because of its relevance to electron transport in metallic crystalline solids, the electron gas theory for metals is also described in this chapter. This chapter provides only an introduction to the microscale thermophysics of solids. Readers interested in more comprehensive treatments of solid state thermophysics should consult the references cited at the end of this chapter.

Monatomic Crystals

Our objective here is to use statistical thermodynamics tools to evaluate thermodynamic properties of solid crystals. Our first goal is to derive a relation for the partition function Q. In doing so, we will specifically consider the structure of a monatomic crystal. One approach is to model the crystal as a system of regularly spaced masses and springs as indicated schematically in Figure 7.1. The springs represent the interatomic forces that each atom experiences. The mean locations of the masses are at regularly spaced lattice points.

Actually, each atom sits in a potential well whose minimum is at a lattice point. The potential well for each atom is usually very steep. Each atom vibrates about its equilibrium position with a small amplitude, which suggests that we can work with a Taylor series representation of the potential valid near the equilibrium point.

Rather than working with the potential for a single atom, we will consider the potential for the crystal as a whole, which we will designate as Φ.