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38649 results in Cambridge Textbooks

Page 1341 of 1933

  • 9 - What Help Can I Get?: Bibliography and Computer-Aided Design

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 144-164

  • Summary

    The previous chapters have shown the complexity of aircraft, and their constituent parts. Their design is a daunting, but potentially satisfying task. Designers need all the help that they can get to achieve successful results.

    The usual starting point is a sound aeronautical education. Design is learnt by a combination of theoretical education and design experience at university and/or in industry. It must be stressed that design is much more than analysis. It is a creative process involving the synthesis of knowledge from many disciplines, monitored by qualitative and quantitative checks. These should assess the value of the necessary design compromises and lead to optimum designs. Advice from, and work alongside, experienced designers is an invaluable part of the education process. People learn how to design by actually doing it! Less-experienced design organizations can be helped by specialist consultants. Such help is, however, not always available, but much design knowledge and experience has been encapsulated in the publications and programs described later in this chapter.

    Many individuals and organizations publish reports, papers and memoranda, many of which contain relevant data. Modern libraries use on-line computerized data bases that sort and codify these date sources on the basis of key words. A description of such reports is beyond the scope of this book. The most exciting new development has been the advent of the internet. There is a bewildering array of data, with much of interest to aircraft designers. Patience and good net-surfing skills are required.

    Any bibliography is a matter of personal choice. The books, magazines and programs listed below have been found by the author to be extremely useful and are reasonably easily available. Excluded data sources are not necessarily less valuable than those listed, but are not available to the author.

    The aircraft industry has seen a massive growth in the power and user-friendliness of computer aids. The latter part of this chapter gives an overview of a range of computerized design aids.

  • 4 - Why is it That Shape?: Other Types

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 40-64

  • Summary

    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. A very high thrust/weight ratio is implied by these requirements, particularly at altitude. Compatible with reasonable operational safety, everything must be placed second to climb and interception performance. Only one crew member can be carried and acquisition and life-cycle costs are reasonably low. Due to the relative simplicity of the equipment carried, reliability should be high. The Typhoon is in this category (see Fig. 4.2).

    The high thrust/weight ratio for combat manoeuvrability leads to the thought that only a little extra thrust might give vertical take-off and landing capability (VTOL). The BAE SYSTEMS Harrier has been developed into an extremely effective strike/bomber aircraft with the very significant operational advantage of lack of reliance on runways. The invention of the ski-jump runway improved payload/range by offering an extremely short take-off distance (STO). These innovations led to the extremely potent Sea Harrier interceptor aircraft flown from small aircraft carriers.

  • Preface

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp xiii-xiv

  • Summary

    This book acts as an introduction to the full breadth of both civil and military aircraft design. It is designed for use by senior undergraduate and post-graduate aeronautical students, aerospace professionals and technically inclined aviation enthusiasts.

    The book poses and answers pertinent questions about aircraft design, and in doing so gives information and advice about the whole aircraft design environment. It asks why we should design a new aircraft and gives examples of market surveys and aircraft specifications. It then answers the question, ‘Why is it that shape?’ and gives the rationale behind the configurations of a wide range of aircraft from micro-lights and helicopters to super-jumbos and V/STOL aircraft, with many others in between. Having looked at the shape, the book then examines and describes what is under the skin in terms of structure, propulsion, systems and weapons. Later chapters answer questions about aircraft costs and conceptual design and draw lessons from past projects, and then look into the future. A major part of the book answers the question, ‘What help can I get?’, with a combination of bibliography, lists of data sheets, computer tools and 100 pages of appendices of design data vital to aircraft conceptual designers (most of it previously unpublished).

    The book concentrates on fixed-wing civil and military aircraft, with some reference to light aircraft and rotorcraft, but does not address the design of sailplanes, airships, flying boats or spacecraft. While these are fascinating and important subjects it was decided that the current scope of the book is sufficiently wide and further extension would make it unwieldy, although information about references that address the design of aircraft in the excluded categories is provided.

    Much of the material has been developed for use in Pre-Masters and Masters’ courses in aircraft design at Cranfield University. Many of the examples and illustrations have been produced as part of Cranfield's unique group design project programmes. With the Cranfield method, conceptual design is done by the staff, thus enabling the students to start much further down the design process. They thus have the opportunity to get to grips with preliminary and detail design problems, and become much more employable in the process. This method also allows students to use modern design tools such as CAD, finite elements, laminate analysis and aerodynamic modelling.

  • 5 - What's Under the Skin?: Structure and Propulsion

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 65-82

  • Summary

    GENERAL

    Having looked at the reasons for designing a new aircraft, its requirements and the reasons for its external shape, it is now the time to look at the interior. One might use the analogy of a human body to see that for successful operation it requires a skeleton, muscles, digestive system, sensors and a control system. These all work together efficiently even when they have different functions. The aircraft designer must produce a similar harmony within the aircraft interior. Each system is important, but each may have conflicting requirements. A good designer must weigh up the conflicts, use relevant analyses and synthesize the aircraft into an efficient whole. It is a truism that the outside of the aircraft has to be bigger than the space required inside the aircraft. It is often necessary to modify the external shape to accommodate the interior, with consequent aerodynamic changes.

    To return to the body analogy, this chapter will describe the aircraft's skeleton, muscles, sensors, etc. in terms of structure and propulsion. Fuel, flying controls, avionics, furnishing and weapon systems will be described in Chapters 6 and 7.

    THE STRUCTURE

    An aircraft structure should be designed to meet a number of conflicting requirements which include:

  • (i) Low weight.

  • (ii) Acceptable material and manufacturing costs.

  • (iii) Adequate strength to meet the maximum expected loads, with a suitable safety factor.

  • (iv) Adequate stiffness so that distortions are kept within acceptable limits.

  • (v) Good in-service properties, such as fatigue and corrosion resistance, together with tolerance of expected temperatures and other atmospheric conditions.

    • Materials

    Aircraft designers have a wide range of structural materials to choose from, including those described in the following subsections.

    Light Alloys

    Light alloys are essentially based on aluminium and are used on the majority of aircraft. Their advantages are the high strength and stiffness-to-weight ratios, relatively low cost, general ease of handling, except in special cases, availability, choice of many fabrication processes and, above-all, familiarity. Against this is the dependence upon relatively low-temperature heat-treatment processes to obtain the desired material properties, which implies poor strength and stiffness at elevated temperatures and relatively poor fatigue properties. The higher-strength alloys are poorer in fatigue and their use is restricted to predominantly compression-sensitive areas. Tensile loads produce more fatigue problems.

  • 8 - Why do Aircraft Cost so Much?

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 122-143

  • Summary

    GENERAL

    This chapter discusses the costs of buying and operating civil and military aircraft. The former costs are termed acquisition costs for both classes of aircraft, whilst the latter are termed operating costs for civil aircraft, and life-cycle costs (LCCs) for military aircraft. The acquisition costs are included as important elements of both operating costs and LCCs. The costs associated with aircraft reliability and maintenance are significant contributors to operating and LCCs, and design to reduce these costs is outlined at the end of this chapter.

    ACQUISITION COSTS (THE COSTS OF BUYING OR ACQUIRING THE AIRCRAFT)

    The Reasons for High Aircraft Acquisition Costs

    The main reasons are:

  • (i) High performance requirements – Civil and military aircraft operations are competitive, hence each new type is required to show improvements relative to existing aircraft. It is therefore necessary to undertake extensive research programmes and also to incorporate customer/operator refinements, which imply complexity.

  • (ii) Safety considerations – Civil and military aircraft have, rightly, very stringent safety requirements that must be proved before the aircraft enters service. Extensive proving and testing is required and there is a need for added complexity so that failure of individual components or systems can be tolerated. An aircraft has to continue functioning safely even after a failure has occurred. This applies to both hardware and software.

  • (iii) Quality control – The complexity and safety demands make it essential to have elaborate systems that record the complete history of not only each individual aircraft, but of each piece of material or part used in it. Inspection has to be complete, not sampled, and continuous throughout the life of the aircraft.

  • (iv) Tooling requirements – Complexity requires extensive and expensive tooling for production purposes, and the launch cost of a new type of aircraft is considerably influenced by this. Numerically controlled machine tools have considerable flexibility, and are very expensive. They can more than pay for themselves, however, on reasonable production runs, and their use is increasing. Automatic rivetting and bonding facilities also reduce labour content (see below). Another source of expense is that of assembly jigs.

  • (v) Labour-intensive production – In spite of the elaborate tooling, the complexity of an aircraft means that labour costs are by far the greatest part of the direct production costs (Fig. 8.1). Two approaches to reducing such costs are increasing automation or use of lower-cost labour.

  • 11 - What Can Go Wrong?: Some Lessons from Past Aircraft Projects, and a Glimpse into the Future

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 180-201

  • Summary

    INTRODUCTION

    The design, manufacture and operation of aircraft are very complex and potentially risky activities. There is a natural tendency towards trusting tried and tested configurations, and adopting an evolutionary approach. There are many cases, however, of revolutionary design changes, such as the advent of the jet engine, or the delta wing. Revolution involves more risk, but can be very rewarding. The history of aircraft design has had many examples of excitingly innovative, not to say weird designs. A minority of these are successful, some marginally successful, but many have been failures, some of them disastrously expensive failures! This chapter will describe a number of different projects and attempt to classify the reasons that led to their difficulties.

    On a more positive note, the chapter will conclude by describing a number of innovative designs that might have a great influence on the future of aeronautics – positively or negatively!

    AIRCRAFT THAT SUFFERED FROM REQUIREMENTS THAT WERE TOO RESTRICTIVE, TOO AMBITIOUS OR WERE CHANGED DURING DEVELOPMENT

    Ward [34] contains many examples of such projects from the depressing record of British aircraft developments since 1945, and several examples will be repeated here, both civil and military. Other sources were used for later aircraft.

    The Hawker Siddeley Trident

    This aircraft (Fig. 11.1) had many years of successful service in the UK and in China, and was a pioneer in the field of automatic landing, but sales were disappointing. British European Airways (BEA) were initially offered a short-haul jet transport, (the DH121) which would have carried 110 passengers over stage lengths of up to 1800 nmiles. The manufacturers’ projections in 1958 predicted sales of 550 aircraft. According to Ward [34] BEA had been examining market trends that showed a marked slip in 1958–9 and thus considered that the DH121 was too big. They required that the aircraft only have 97 seats over an 800 nmile range. The Trident was designed round this specification, as was the Spey turbo-fan engine. The aircraft satisfied the requirement, but it and the engine had limited development potential. The Boeing 727 design team developed a competing tri-jet to almost the same requirements as for the original DH121.

  • 2 - Why Should We Design a New Aircraft?

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 6-19

  • Summary

    The world has accepted that flying is an extremely efficient means of quickly transporting people, cargo or equipment, and performing a wide range of other activities. All operators need to increase efficiency, cost-effectiveness, environmental compatibility and safety. It is often possible to do this by modifying either the design or operation of existing aircraft. This is limited, however, by the inherent capabilities of the original design and the cost-effectiveness of modifications. Under these circumstances, it is necessary to consider the initiation of the design of a new aircraft. Aircraft manufacturers are usually in the business of making profit out of building aircraft. They may do this by means of building their own existing designs, modifying their designs or licence-building the designs of other companies. Another reason for the initiation of new designs is to retain or enhance their design capabilities.

    Safety is the most important aspect of aircraft design. This is the moral and legal responsibility of designers, manufacturers and operators of both civil and military aircraft. The regulations that have emerged aim to maximize safety, and must be complied with before an aircraft may receive a Type Certificate to allow it to be sold. A brief summary of such requirements is contained in Chapter 9.

    In recent years there has been a considerable increase in the importance of requirements associated with aircraft-related effects on the environment. These particularly concern noise, airport local air quality and global warming. Current environmental requirements are summarized in Chapter 9.

    Operator requirements and aircraft specifications come from a number of different sources, but they must all consider the needs of the aircraft operators, whether they are airlines or air forces. A certain path to disaster is to produce an aircraft that no one will buy!

    Descriptions will be given of the two main means of deriving a requirement specification, namely the results of market surveys and individual aircraft operators’ specifications.

    MARKET SURVEYS

    The major aircraft manufacturers employ marketing departments that produce annual reports [2]. Historical data are analyzed and extrapolated in such areas as world economic indicators. Figure 2.1 shows gross domestic product (GDP) and highlights the recent recessions, and shows the close correlation between GDP and the world air travel growth in revenue passenger miles (RPM).

  • 7 - What's under the skin?: Avionics, Flight Control and Weapon Systems

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 101-121

  • Summary

    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 medium-range airliner of the future. 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.

    Communications

    Airborne communications systems vary considerably in size, weight, range, power requirements, quality of operation and cost, depending upon the desired operation.

    The most common communications system in use today is the very high frequency (VHF) system. In addition to VHF equipment, large aircraft are usually equipped with high frequency (HF) communications systems and some are fitted with ultra high frequency (UHF) systems.

    VHF airborne communication sets operate in the frequency range from 100 to 150 MHz. VHF receivers are manufactured that cover only the communications frequencies, or both communications and navigation frequencies. In general, the VHF radio waves follow approximately straight lines. Theoretically, the range of contact is the distance to the horizon and this distance is determined by the heights of the transmitting and receiving antennas. However, communication is sometimes possible many hundreds of miles beyond the assumed horizon range. Typical ranges are 200 miles at 20 000 ft. UHF systems are similar to VHF but operate in the 200–400 MHz band.

  • 6 - What's Under the Skin?: Airframe Systems

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 83-100

  • Summary

    SECONDARY POWER SYSTEMS

    We have looked at an aircraft's primary power system, its propulsion, and will now examine its secondary power systems (SPS). Secondary power is usually provided by an aircraft's main engines when they are operating, but can be supplied by other sources such as an auxiliary power unit (APU) in the aircraft or an external source on the ground.

    Almost all present aircraft SPS are of three types, shown in Fig. 6.1.

    Power is extracted from turbo-fan powerplants in two forms. Bleed air is tapped from one or more points along the engine compressor to provide pneumatic power. Drive shafts, from the engine's high-pressure shaft, drive an accessory gear box on which are mounted generators and hydraulic pumps, as well as the engine's own accessories. A typical large turbo-fan is shown in Fig. 5.13.

    Turbo-jet powerplants can also supply bleed air and shaft power for systems, but turboprop powerplants in general have difficulty in supplying sufficient bleed air for airframe requirements. In such a case, extraction of shaft power to drive separate compressors may be considered.

    SPSs are often linked with each other, but it is convenient to separate them into the types described below.

    Air-Conditioning and Pressurization

    On many civil transports the largest amounts of secondary power are extracted in the form of bleed air and the largest continual user of this power is the aircraft's air-conditioning and pressurization system.

    It is usual to maintain an aircraft cabin at a pressure equivalent to that at 8000 ft or less, and this requires a constant supply of pressurized air. In addition to this, oxygen used by the occupants must be replaced and the temperature and contaminant levels controlled, requiring a significant throughput of air, although some of it is recycled through the cabin, after filtering.

    It is the control of temperature that usually determines the rate at which air must be supplied and, with the type of air-conditioning system installed on most aircraft, this also requires the air be supplied at pressures significantly above those in the cabin.

    Figure 6.2 shows the major elements of an air-conditioning system. There are extremely remote events where the pressurization system fails. In this case, on-board emergency oxygen systems are used to preserve life. The combination of air-conditioning, pressurization and oxygen systems are usually termed the environmental control system (ECS).

  • 1 - Introduction

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 1-5

  • Summary

    WHY ANOTHER AIRCRAFT DESIGN BOOK?

    Aircraft design is a complex and fascinating business and many books have been written about it. The very complexity and dynamic nature of the subject means that no one book can do it justice.

    This book, therefore, will primarily act as an introduction to the whole field of aircraft design leading towards the subjects summarized in Fig. 1.1. It will not attempt to duplicate material found in existing design books, but will give information about the whole aircraft design environment, together with descriptions of aircraft and component design. It also presents otherwise unpublished data and design methods that are suitable for aircraft conceptual, preliminary and detail design activities.

    TOPICS

    The following chapters are arranged as a series of questions about aircraft design, the answers to which give largely descriptive overviews of all aspects of aircraft design. This will provide an introduction to the conflicting requirements of aircraft design specialists in a design team, with a view to improving understanding and the integration of a sound overall design.

    The book is divided into chapters that answer a number of significant design questions.

    The question, ‘Why design a new aircraft?’ is answered in Chapter 2, which shows the derivation of aircraft requirements for civil and military aircraft from market surveys, and gives examples of operator-derived specifications.

    Chapters 3 and 4 answer the question, ‘Why is it that shape?’ with an initial discussion of aircraft wing and tail shapes, followed by descriptions of the configurations of a wide range of civil and military aircraft types.

    The question, ‘What's under the skin?’ is answered in Chapters 5, 6 and 7, which deal with structures and propulsion, airframe systems, avionics, flight controls and weapons, respectively. These chapters describe the interiors of aircraft, ranging from structures to weapons systems via airframe systems, avionic systems and landing gears.

    In Chapter 8 the crucial areas of acquisition and operating costs are discussed, some prediction methods are described and the importance of good reliability and maintainability are stressed in order to answer the question, ‘Why do aircraft cost so much?’

    The answer to the question, ‘What help can I get?’ is provided in Chapter 9, which contains a bibliography of the most important current aircraft design books.

  • 10 - The Shape of Things to Come: Should the Project Continue?

  • John P. Fielding, Cranfield University, UK
  • Book:
    Introduction to Aircraft Design
    Published online:
    28 May 2018
    Print publication:
    03 April 2017, pp 165-179

  • Summary

    INTRODUCTION

    This book has attempted to give an introduction to most aspects of aircraft design, with emphasis on giving the reasons for the shapes of aircraft, and descriptions of their constituent parts. The preface clearly stated that it was not intended to produce a book about aircraft conceptual design, as many good texts are currently available. Some of these are referred to in the previous chapter, and they should be used, with help, to produce aircraft conceptual designs. Conceptual designs, however, are not usually end-products, but merely important steps in the whole design–manufacture–operation cycle.

    Conceptual designs must be objectively assessed to see if they warrant the significantly increased expenditure that would be required to perform preliminary and detailed design. A vital precursor to this decision-making process is a clear definition of the characteristics of the conceptual design, and this is discussed in Section 10.2. Section 10.3 shows the options that are available following a conceptual design process and Section 10.4 describes simple decision-making techniques. The final section of this chapter gives an example of a conceptual-design definition, and describes the decisions that were made about its future.

    CONCEPTUAL DESIGN DEFINITION

    It is important to summarize clearly the results of the conceptual design process by providing the following types of information:

  • (i) Configuration description – This will be defined by means of conventional engineering drawings, tabular data, computer models, physical models or a combination of these methods, together with a brief description of the rationale of the design.

  • (ii) Mass estimates – These will include gross and empty masses, together with component mass estimates to be used as targets for subsequent work.

  • (iii) Performance estimates – Drag and lift predictions will be produced, together with powerplant data to give payload-range curves, field-performance, and direct operating cost targets for commercial aircraft. Military aircraft will also require predictions to be made of sortie performance, and point performance criteria such as attained turn rate, sustained turn rate and specific excess power.

  • (iv) Reliability and maintainability targets – The direct operating cost targets, mentioned above, imply estimates of acquisition costs as well as reliability and maintainability (R and M) characteristics. These may be used to set R and M targets for subsequent design stages (Appendix C).

  • 7 - Legalist Philosophy

  • Karyn Lai, University of New South Wales, Sydney
  • Book:
    An Introduction to Chinese Philosophy
    Published online:
    28 May 2018
    Print publication:
    30 March 2017, pp 163-187

  • Summary

    The debates during the Warring States period challenged the beliefs and practices of the status quo. Confucian doctrine upheld many aspects of traditional life yet raised questions about possibilities for self-directed accomplishments, especially for those involved in government. Daoism rejected many more facets of conventional life and practices but retained a vision of the good life for the common people. Legalist thought is singular in its rejection of fundamental humanitarian values. It rejected the importance of relationships, the institutional fostering of ethical awareness and behaviour and, perhaps most of all, the idea of a compassionate government that looked after the interests of the people. Herrlee Creel, a historian of Chinese thought, argued that Legalist philosophy was, “in considerable degree, a philosophy of counterrevolution” (1953: 135). Creel maintained that the Legalists rejected the increasingly popular view that government exists for the people, focusing instead on the ruler's maintenance of power.

    The classification in the Shiji by Sima Tan, of Legalist philosophy as a “school” (fa jia: school of penal law), is misleading in a number of ways. First, there is no identifiable founder of Legalist thought, although Han Fei (c. 280–233 BCE) appears to be its most systematic proponent, on the basis of the text that bears his name. Yet the question of authorship of the Han Feizi is riddled with questions given the inconsistencies in the text. Second, not all thinkers who are considered Legalist actually discussed fa (penal law) as a fundamental theme. Third, it is not clear which ideas or themes best characterise the ideology of the Legalist thinkers. Those who articulated Legalist ideas or influenced Legalist philosophy in significant ways during the pre-Han period include Guan Zhong (d. 645 BCE), Shang Yang (d. 338 BCE), Shen Buhai (d. 337 BCE), Shen Dao (c. 350 BCE –275 BCE) and Han Fei.

    The impression we get from reading the Legalist texts is that there was lively debate and scrupulous consideration of the idea of fa, which could mean “standard,” on a broader reading, as well as penal law, in some of its uses.

  • 12 - Game Theory II: Nonzero-sum and Cooperative Games

  • Martin Peterson, Texas A & M University
  • Book:
    An Introduction to Decision Theory
    Published online:
    28 May 2018
    Print publication:
    30 March 2017, pp 263-286

  • Summary

    In the final sections of Chapter 11 we showed that all (two-person) zero-sum games can be solved by determining a set of equilibrium strategies. From a purely theoretical perspective, there is little more to say about zero-sum games. However, nonzero-sum games are more interesting, and require further attention by game theorists. This chapter gives a brief overview of what we currently know about nonzero-sum games. First, we will give a proper introduction to the equilibrium concept tacitly taken for granted in the previous chapter. We will then go on to analyze a couple of well-known nonzero-sum games. The chapter ends with a discussion of whether game theory has any implications for ethics, biology and other subjects, which some scholars believe is the case.

    The Nash Equilibrium

    The prisoner's dilemma is an example of a nonzero-sum game. This is because the loss or gain made by each player is not the exact opposite of that made by the other player. If we sum up the utilities in each box they do not always equal zero. In the prisoner's dilemma each prisoner will have to spend some time in prison no matter which strategy he chooses, so the total sum for both of them is always negative. To see this point more clearly, it is helpful to take a second look at the game matrix of the prisoner's dilemma (Table 12.1).

    Obviously, R2 is dominated by R1, whereas C2 is dominated by C1. Hence, rational players will select the pair of strategies (R1, C1). It follows that (R1, C1) is in equilibrium, because if Row knew that Col was going to confess (play C1), then he would not be better off by switching to another strategy; and if Col knew that Row was going to confess (play R1), then he would also be best off by not switching his strategy. The notion of equilibrium tacitly employed here was originally proposed by John Nash, a Princeton mathematician who was awarded the Nobel Prize in Economics for his contributions to game theory. Nash's basic idea was very simple: Rational players will do whatever they can to insure that they do not feel unnecessarily unhappy about their decision.

Page 1341 of 1933